/smash/get/diva2:160605/FULLTEXT01.pdf

/smash/get/diva2:160605/FULLTEXT01.pdf
Comprehensive Summaries of Uppsala Dissertations
from the Faculty of Science and Technology 556
_____________________________
_____________________________
Characterization of
Selective Solar Absorbers
Experimental and Theoretical Modeling
BY
TUQUABO TESFAMICHAEL
ACTA UNIVERSITATIS UPSALIENSIS
UPPSALA 2000
Dissertation for the Degree of Doctor of Philosophy in Solid State Physics presented at Uppsala
University in 2000
Abstract
Tesfamichael, T. 2000. Characterization of Selective Solar Absorbers. Experimental and Theoretical
Modeling. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertation from the
Faculty of Science and Technology 556.79 pp. Uppasla. ISBN 91-554-4772-4.
This thesis deals with the preparation, optical characterization and analyses of experimental work and
theoretical modeling on selective solar absorbers used in solar thermal collectors. The overall goal has
been to obtain efficient absorbers by optimizing the optical properties, and to improve their durability
using cost-effective techniques.
A Ni-Al2O3 absorber was pyrolytically coated with SnO2 to improve its coating quality.
Undesirable increase of solar reflectance obtained as a result of the SnO2 was reduced by applying a
silica antireflection layer produced by a dipping technique from colloidal silica sol. Annealing of Ni
particles in an Al2O3 matrix was also carried out and compared to particles heated without the matrix.
Due to the Al2O3 matrix, a much slower oxidation rate was found for the embedded particles. In
addition, the optical performance of commercial Ni-Al2O3 and Ni-NiOx absorbers were experimentally
compared at oblique incidence. A better solar-absorptance of the Ni-Al2O3 at higher angles of incidence
was found. This is due to enhanced optical interference in the double-layer structure of Ni-Al2O3, which
could not be achieved in the graded index film of Ni-NiOx.
The optical properties of Si-Al2O3 films of different thicknesses have been investigated by
preparing the films using an integral coloration method. The solar-absorptance and thermal-emittance
were found to increase with increasing film thickness. Due to high thermal-emittance, the Si-Al2O3
coating shows non-selective absorbing properties. Its feasibility for a selective solar absorber was
studied by modeling the coating as a function of coating thickness for different particle size and volume
fraction using four-flux theory. The results indicated that the Si-Al2O3 coating is not a suitable
candidate for selective solar absorbers.
Scattering and absorption cross-sections of FeMnCuOx and black carbon pigments have been
obtained from reflectance and transmittance measurements in the solar wavelength range. The crosssections were determined by using pellets consisting of low pigment volume fractions dispersed in KBr
matrix. The cross-sections exhibit linear dependence of the volume fraction, indicating that single
scattering dominates. The cross-sections were used to model the optical properties of solar selective
paints using four-flux model resulting in good agreement between calculations and experiments.
Tuquabo Tesfamichael, Department of Materials Science, The Ångström Laboratory, Uppsala
University, Box 534, SE-751 21 Uppsala, Sweden
 Tuquabo Tesfamichael 2000
ISSN 1104-232X
ISBN 91-554-4772-4
Printed in Sweden by University Printers, Uppsala 2000
For Her Devotion, To My Sister Alem
and
my Family
4
Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
LIST OF PUBLICATIONS
I.
T. Tesfamichael, W. E. Vargas, E. Wäckelgård and G.A. Niklasson, Optical Properties of Silicon
Pigmented Alumina Films, J. Appl. Phys. 82, (1997) 3508-3513.
II.
T. Tesfamichael, W. E. Vargas, E. Wäckelgård and G.A. Niklasson, A Feasibility Study of
Integrally Colored Al-Si as Solar Selective Absorber, Solar Energy Mater. Solar cells, 55, (1998)
251-265.
III.
T. Tesfamichael and A. Roos, Treatment of Antireflection on Tin Oxide Coated Anodized
Aluminum Selective Absorber Surface, Solar Energy Mater. Solar cells, 54, (1998) 213-221.
IV.
T. Tesfamichael, S. Andersson, T. Chibuye and E. Wäckelgård, Study of Oxidation Kinetics for
Metal-Dielectric Films Using IR Optical Measurements, SPIE, 3138 (1997) 146-153.
V.
R. Karmhag, T. Tesfamichael, E. Wäckelgård, G.A. Niklasson and M. Nygren, Oxidation
Kinetics of Nickel Particle. Comparison between free particles and particles in an oxide matrix.
Solar Energy, 68 (2000) 329-333.
VI.
R. Karmhag, T. Tesfamichael, E. Wäckelgård, G.A. Niklasson and M. Nygren, Oxidation
Kinetics of Nickel Solar Absorber Nanoparticles, J. Phys.: Condens. Matter (submitted,
2000).
VII.
T. Tesfamichael and E. Wäckelgård, Angular Dependence of Solar Absorptance for Selective
Absorber Surfaces, Appl. Opt., 38 (1999) 4189-4197.
VIII. T. Tesfamichael and E. Wäckelgård, Angular Solar Absorptance and Incident Angle Modifier of
Selective Absorbers for Solar Thermal Collectors, Solar Energy, 68 (2000) 335-341.
IX.
T. Tesfamichael, A. Hoel, G.A. Niklasson, E. Wäckelgård, K. M. Gunde and Z. C. Orel, Optical
Characterization of Black Pigments for Solar Selective Absorbing Paints. Appl. Opt.
(Submitted, 2000)
X.
T. Tesfamichael, A. Hoel, G.A. Niklasson, E. Wäckelgård, K. M. Gunde and Z. C. Orel, Optical
Characterization and Modeling of Black Pigments Used in Thickness Sensitive Solar Selective
Absorbing Paints. Solar Energy. (Submitted, 2000)
My contribution in the above papers:
I and II
III
IV
V and VI
VII and VIII
IX and X
Experiments and part of calculations
Experiments and calculations
Calculations and part of experiments
Part of experiments
Experiments and calculations
Calculations and part of experiments
Paper not included in this thesis:
Anna Helgesson, Tuquabo Tesfamichael, Ewa Wäckelgård, Impact of Angular Solar Absorptance on
Collector Performance Investigated by Dynamic Collector Testing and Optical Angular Characterization of
Solar Absorbers, Proc. NorthSun 99, Edmonton, Canada, (1999).
Tuquabo Tesfamichael
5
TABLE OF CONTENTS
GLOSSARY AND CONSTANTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2
THEORETICAL BACKGROUND . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 11
2.1
2.2
2.3
Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
2.1.1
Thermal Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
2.1.2
Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Optical Properties of Inhomogeneous Media . . . . . . . . . . . . . . . . . . . . . . . .13
2.2.1
Lorenz-Mie Scattering Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.2.2
Effective Medium Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3
Two and Four Flux Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4
Cross-Sections from Reflection-Transmission Measurements. . . . . . . . . . . . . .22
Selective Solar Absorbing Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Understanding Selective Solar Absorbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
2.3.2
2.4
Solar Collectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .29
2.4.1
3
Selective Solar Absorber Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Flat Plate Solar Collectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
EXPERIMENTAL METHODS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1
3.2
3.3
Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .31
3.1.1
Chemical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
3.1.2
Spray Pyrolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
3.1.3
Dip-Coating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.4
Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.5
Production of Black Pigment Pellets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
High Temperature Accelerated Aging Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1
Oxidation of Nickel Particles in Alumina Matrix (Ni-Al2O3). . . . . . . . . . . . . . . 35
3.2.2
Oxidation of Nickel Particles in Air Matrix (Ni-air). . . . . . . . . . . . . . . . . . . . . . 36
Optical and Non-Optical Characterization .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . 36
3.3.1
Spectrophotometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
3.3.2
Optical Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
3.3.3
Non-Optical Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6
Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
3.4
4
Dynamic Testing of Solar Collectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
RESULTS AND DISCUSSION .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
4.1
Nickel Pigmented Aluminum Oxide (Ni-Al2O3) . . . . . . . . . . . . . . . . . . . . . . .41
4.2
Anodized Al-Si Alloy (Si-Al2O3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
4.3
Angular Performance of Selective Solar Absorbers. . . . . . . . . . . . . . . . . . . . . 53
4.4
4.3.1
Angular Solar Absorptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
4.3.2
Angular Optical Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Selective Solar Absorbing Paints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
4.4.1
FeMnCuOx Black Pigment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
4.4.2
Black Carbon Pigment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.3
Thickness Sensitive Solar Selective (TSSS) Paints . . . . . . . . . . . . . . . . . . . . . . . 65
5
CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
6
ABSTRACTS OF APPENDED PAPERS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
Tuquabo Tesfamichael
GLOSSARY AND CONSTANTS
Symbol
Quantity
Abs
AM
Ac
B(λ,T)
Cabs
Cext
Csca
Ext
Ea
EMT
F
FR
F'
G(λ)
GT
G sc
I
J
K
Kτα
L
N
NIR
Q or q
R
RUC
T (italic)
T
P
S
S(0)
UL
UV
Vis
a
d
f
k
k (italic)
(mC)eff
Absorptance
Air mass
Area of a collector
Blackbody spectrum
Absorption cross-section
Extinction cross-section
Scattering cross-section
Extinction
Activation energy
Effective Medium Theory
Weight fraction
Collector heat removal factor
Collector efficiency factor
Solar spectral irradiance
Total solar energy flux
Solar constant
Flux in the forward direction
Flux in the backward direction
Effective absorption coefficient per unit length
Incident angle modifier
Depolarization factor
Complex refractive index
Near-infrared wavelength range
Collector energy output
Reflectance
Random unit cell
Temperature
Transmittance
Pressure
Effective scattering coefficient per unit length
Forward Scattering amplitude
Collector heat coefficient
Ultraviolet wavelength range
Visible wavelength range
Particle radius
Film thickness
Particle volume fraction
Wavenumber
Intrinsic absorption coefficient per unit length
Effective thermal capacitance
7
8
Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
n
r
r0
rs
s
t
x
αsol
εtherm
ε
ε
θ
θD
Refractive index
Reflection coefficient
Sun-earth distance
Mean radius of the solar disk
Intrinsic scattering coefficient per unit length
Time
Scattering size parameter
Solar absorptance
Thermal emittance
Dielectric function
Average dielectric function
Angle of incidence
Diffraction angle
Extinction coefficient
Wavelength
Mass density
Collector efficiency
Angular transmittance of glass
Relaxation time
Frequency
κ
λ
ρ
η
τ
τ'
ω
Symbol
Constants
Value
kB
σ
h
c1
c2
G sc
Boltzmann constant
Steffan-Boltzmann constant
Planck’s constant
first Planck’s radiation constant
second Planck’s radiation constant
Solar constant
(8.61739⋅10-5) eV/K
(5.6697 x 10-8) Wm-2K-4
(1.0545 x 10-34) Js
(3.7405⋅108) W µm4 m-2
(1.43879⋅104) µm K
(1367±1%) W/m2
Tuquabo Tesfamichael
1
9
INTRODUCTION
The amount of clean air varies with geographical locations, elevation and seasons. These variations are
a function of industrial and agricultural activities of the place and its surroundings, the use of fossil fuels
for energy and transport, and the general dynamic nature of the atmosphere. This means that, due to
human activities the composition of our atmosphere is changing rapidly. Gases such as carbon
monoxide, carbon dioxide and ozone are created as a consequence of the above activities. The
enhancement of the environmental problems on the one hand and the increasing need of energy from
time to time on the other alarm people to look for alternative energy resources. This has stimulated the
utilization of solar, wind, geothermal, biomass and other renewable energy technologies. Despite the
encouraging signs in developing such alternative energy resources and technologies on a large scale,
slowness of effective policy has contributed to a gradual progress. 1 In order to see the prospects of
clean energy systems using cost competitive and efficient technologies that satisfy demands, an
intensive research on renewable energy must be encouraged.
Solar energy, which is abundantly available in many parts of the world, can play a major role as
an alternative energy resource. Using the sun's energy one can produce heat or electricity by capturing
the radiation of the sun. Photo-voltaic devices use semiconducting materials to convert sunlight directly
into electricity (quantum conversion), while solar thermal devices convert solar radiation into heat
(thermal conversion). Solar thermal devices are used to heat water and air inside buildings at lower
temperatures (T<300°C) and to create steam for electricity generation at high temperatures. Photothermal devices used for heating water and air conditioning are mainly flat plate collectors which are
simple and inexpensive. The most important and critical part of the flat plate solar collectors is the
absorber surface. In order to maximize the output from the solar collectors, the absorber should be
spectrally selective; exhibit high solar absorptance and low thermal emittance. Thermal losses from
heated absorbers are due to conduction, convection and radiation. Selective surface coatings play an
important role, especially when temperatures are required in the vicinity of boiling temperature of
water or when the temperature difference between absorber and ambient is high. High quality of the
absorber surfaces is important in order to achieve collector durability. What is needed are coatings
which will not optically degrade significantly during the life time of the collector and also withstand
stagnation temperature and humidity. Coating life time of the absorber and hence the collector
performance can also be influenced by the tribological properties of the absorbing surface.
The possibility of practical selective absorbing surfaces was first shown by Tabor (Israel) and
by Gier-Dunkle (USA) at the first international solar energy conference in Tucson, AZ in 1955. 2-4
Their work was based on coatings of some oxides and sulfides deposited on a metal substrate. A
thorough investigation of selective surfaces was, however, not started until the time of the oil crisis in
the mid 1970s. A review of several varieties of commercial and research selective absorbers, and an
annotated bibliography for such work, can now be found elsewhere. 5-9 The most common type of
selective absorber is the absorber-reflector tandem which is obtained by combining two surfaces, one
surface which is highly absorbing in the solar region and another highly reflecting in the infrared. Several
techniques can be used to produce this surface, generally divided into wet-chemical, paint and vacuum
deposition techniques. 10 In general, the wet chemical approaches have been the most widely used
techniques for low temperature solar absorber applications. Some of the well known commercial
absorbers developed by wet chemical technique are black chrome (USA), nickel pigmented aluminum
10 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
oxide (Sweden and Japan) and MAXORB (UK). Paints have the potential of being a less expensive
coating that can be produced by simpler methods. Various potential pigments that could be developed
for selective paint coatings are described elsewhere. 5,11,12 There are at least two commercialized
selective paints on the market under the trademarks Solarect-Z (Slovenia) and SolkoteHI/SORB-II™
(USA). Vacuum deposition techniques are nowadays also gaining advantages which allow roll coating
processes for large scale production at a relatively low cost. Commercial absorbers such as Sunstrip
(Sweden) and Interpane (Germany) produced by reactive dc magnetron sputtering and TiNOX GmbH
(Germany) made by activated reactive evaporation are products obtained using the vacuum deposition
processes. This thesis discusses results of selective solar absorber surfaces which are of the absorberreflector tandem types obtained by some several of the above mentioned methods.
Section 2 gives a general theoretical background on thermal and solar electromagnetic radiation.
It also discusses the optical properties of inhomogeneous media treated using Lorenz-Mie theory,
effective medium theories, two-flux and four-flux radiative transfer theories. A novel approach of
determining optical properties of absorbing-scattering medium using reflection-transmission
measurements are also explained. Optical characterization of an energy-efficient selective absorbing
surface and the most commonly used selective surface designs with emphasis on non homogeneous
composite absorbers are also describes in this section. In addition, a commonly used flat plate solar
thermal collector is discussed here briefly. Section 3 deals with experimental techniques including
sample preparation, optical measurements and characterization of different absorbing surfaces. The
absorbers are inhomogeneous, consisted of particles such as metal, semiconductor, or black-pigment
embedded in dielectric matrices. Methods used for high temperature accelerating aging to test durability
of solar absorbers is also mentioned. Covering absorber surfaces by a transparent coating to protect it
from degradation and the use of an antireflection layer to reduce front-surface reflection of the
transparent coating is presented in this section. The experimental results are summarized in section 4.
Finally, concluding remarks and abstracts of the appended papers are given in sections 5 and 6,
respectively.
11
Tuquabo Tesfamichael
2
THEORETICAL BACKGROUND
2.1
Electromagnetic Radiation
Electromagnetic phenomena have been recognized as originating from a distribution of electric charge
and current which gives rise to the electromagnetic field. J. C. Maxwell was the first who concisely
formalized the known results of electricity and magnetism in a theory of classical electromagnetism in
1865. A spectacular immediate result of Maxwell’s electromagnetic theory was the prediction that
light itself was a form of electromagnetic radiation. Electromagnetic radiation can be divided into ranges
of wavelengths according to the different criteria. Certain wavelength ranges of the electromagnetic
spectrum, namely the solar which covers the UV/Vis/NIR (λ=0.3-2.5 µm) and thermal (λ=2.5-50 µm),
are the most important for the application of solar energy (see section 2.3 for the spectral distribution).
2.1.1
Thermal Radiation
All heated objects emit thermal electromagnetic radiation whose wavelength and intensity are
dependent on the temperature of the body and its optical characteristics. A blackbody is one that
absorbs all wavelengths of the incident radiation and emits the maximum amount of energy for a given
body temperature, T. It is an ideal surface whose emissive power, given by Planck’s law 13, is used as a
reference to compare with the properties of real surfaces. The spectral blackbody radiation is given by:
B(λ , T ) =
[
λ5 e
c
1
( c 2 / λT )
]
−1
,
(2.1)
where c1=3.7405⋅108 W µm4 m-2 and c2=1.43879⋅104 µm K are the first and second Planck’s radiation
constants, respectively. The wavelength λ is given in µm and B(λ,T) in W m-2 µm-1. The total emitted
energy can be obtained by integrating the Planck’s spectrum over the whole wavelength range. StephanBoltzmann law gives the hemispherical total emitted energy for an ideal blackbody as :
B(T ) = σT 4 ,
(2.2)
where σ=5.6696⋅10-8 W m-2 K-4 is the theoretical Stephan-Boltzmann constant which differs from the
experimentally determined value by 0.3% (σexp=5.729⋅10-8 W m-2 K-4). 14
2.1.2
Solar Radiation
The sun which is the center of the solar system is about 1.496⋅1011 m from the earth. With an estimated
diameter of 1.39196⋅109 m, it has a total radiated energy of about 3.84451⋅1023 kW. The spectrum of
the radiated energy varies from long infrared wavelengths to very short wavelengths of gamma radiation.
But most of the radiation is absorbed or scattered far up in the ionosphere, the ozone layer or the
atmosphere by nitrogen, oxygen, ozone, water vapor, carbon-dioxide and other atmospheric
components. The extraterrestrial solar radiation prior to the atmospheric absorption just above the
earth’s atmosphere is almost a constant with the numerical value Gsc=1367±1% W/m2 throughout the
year. 15 Gsc is called as the solar constant. About 8.03% of the radiation in the range UV, 46.41% is
visible and the rest 46.40% falls into the NIR. The effective blackbody temperature of the sun can
easily be obtained from the solar constant, Gsc as 16:
12 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
1/ 4
G  r  2 
T =  sc ⋅  0  
 σ  rs  
,
(2.3)
where, r0 and rs are the sun-earth distance and the mean radius of the solar disk, respectively. Equation
(2.3) gives a temperature of 5777 K. However, the blackbody spectrum of the sun doesn’t strictly
follow the extraterrestrial spectrum 16 and hence can not be used for characterizing solar energy
coatings such as solar absorbers.
Absorption and scattering are the major phenomena that occur when incident electromagnetic
radiation strikes a particle depending on the size, shape and optical properties of the particle. Scattering
can be produced by small or large particles as well as by multiply reflected radiation and is favored at
shorter wavelength as confirmed by scattering theory. 16 For any sufficiently small particle as compared
to the incoming wavelength, regardless of its shape, a strong Rayleigh scattering that is symmetric in the
forward and backward directions dominates. 17 One example of Rayleigh scattering is the scattering of
solar radiation by atmospheric molecules which gives the sky its blue color. The terrestrial solar
spectral distribution and intensity can vary with the change of the atmospheric scattering and
absorbing components and also the path of the rays that traverse the atmosphere (air mass). 16 The
irradiation of the solar flux that reaches the surface of the earth, therefore, varies considerably.
Theoretical as well as measured spectral distribution of solar irradiance at the surface of the earth for
typical atmospheric conditions can be found elsewhere. 15,16,18-20 Unlike the direct and diffuse spectral
irradiance, the change of the total intensity with change of the atmospheric components is not large
except with the variation of air mass at shorter wavelengths. For a given geographical location of
pressure P, air mass is defined as the ratio of optical mass at an oblique path to that of the vertical path
and can be approximated mathematically by 21:
AM =
P
−1
[cosθ + 0.15(93.885 − θ )−1.253 ] ,
P0
(2.4)
where P0 is the atmospheric pressure at sea level and θ angle of incidence of light with respect to the
zenith. For angles of incidence less than 60° equation (2.4) can be replaced by:
AM =
P
−1
[cosθ ] .
P0
(2.5)
At large air mass number, the UV and blue end of the Vis spectrum undergoes much stronger depletion
(by absorption and scattering) than the red end Vis spectrum and hence at sun set, most of the shortwavelengths are scattered back which gives a red color to the sun. To characterize the optical properties
of solar selective absorbing surfaces, as discussed in the following sections, an air mass of 1.5 (AM1.5)
is employed. AM1.5 is commonly used particularly at higher latitudes and a smaller number should be
applied for lower latitudes. On the other hand, air mass variation have shown only small differences on
the solar weighted optical properties of selective solar absorbers. 22
13
Tuquabo Tesfamichael
2.2
Optical Properties of Inhomogeneous Media
Light traversing a medium is scattered only when the medium has inhomogeneties. Many materials used
in applications are inhomogeneous or disordered. Their optical properties are derived from optical
measurements combined with modeling of the experimental results using appropriate theoretical
considerations. In this section, as it gives basis to the main work of this thesis, we present the optical
properties of particles embedded in a non-absorbing medium. For particles which have a size much
smaller than the wavelength of the incident light effective medium theories can be applied. 23-25 If the
particles are of the order or larger than the incident wavelength, scattering become important in addition
to absorption and Lorenz-Mie theory provides a solution to the single scattering problem. 25-30 In case
of multiple scattering radiative transfer models are used to handle such effects. 31-34
2.2.1
Lorenz-Mie Scattering Theory
Electromagnetic radiation scattered into a particular direction by an isotropic, homogeneous sphere is
described by Lorenz-Mie theory. 29 For a particle smaller or larger than the incoming wavelength, the
Lorenz-Mie scattering theory can generally be applied for solving the scattering and absorption
phenomena. When a single particle is illuminated by an incident electromagnetic radiation, part of the
incident energy is absorbed and the rest is scattered out. Mie26 explicitly solved Maxwell’s
electromagnetic equations 35 and investigated scattering by a single particle in a non-absorbing matrix
for a wide size range. Due to the proceeding work of Lorenz the complete solution is called Lorenz-Mie
theory.28,29 The theory is extremely complex and involves the index of refraction and size of the
particle, the wavelength of light and the index of refraction of the host medium as parameters in
combinations of spherical Bessel functions. Scattering by small and large particles were extensively
summarized by Kerker 29, van de Hulst 27 and Bohren-Huffman 28. The scattering conditions have been
characterized by the application of boundary conditions and the series expansion of the electric and
magnetic fields of a scattering amplitude in the forward direction, S(0):
S( 0 ) =
∞
1
2
∑ (2n + 1)(b
n
+ cn ) ,
(2.6)
n =1
where bn and cn denote scattering coefficients containing Bessel functions and their derivatives. 29 The
Lorenz-Mie theory is applicable for a single spherical particle and hence is treated as single scattering
event. For particles with complex shapes, an approximate expressions can be obtained elsewhere. 3 6
The scattering size parameter, x for spherical particle of radius, a, complex refractive index, N1,
surrounded by a non-absorbing medium of refractive index, N2, is given by:
x= k⋅a ,
(2.7a)
where k is wavenumber in the medium:
k=
2π 2πN2
,
=
λ
λ0
(2.7b)
and λ, λo are the wavelengths in the medium and vacuo, respectively. 29 Note that the symbol k (nonitalic) used for wavenumber and k (italic) will be used later for absorption coefficient. Using Eq. (2.7)
and the forward scattering amplitude, S(0) evaluated from Lorenz-Mie 28, scattering parameters such
14 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
as, cross-sections of scattering and absorption 29, the forward scattering ratio, ζ, the single-particle
scattering diagram (phase function) 27,28 and other parameters 37 can be obtained.
The forward scattering ratio under collimated illumination, ζc, gives the fraction of the total
energy scattered into the forward hemisphere and is used in the four flux calculations discussed later. Its
value varies considerably with a change of particle size parameter that are easily viewed from the
scattering diagram or phase function. The phase function can be evaluated by considering a particle to
scatter independently, when observed at a distance large compared to the individual particle size. 3 8
Figure 2.1 shows polar diagrams of the single-particle phase function for non absorbing particles with
different size parameters. The phase function represents the amount of scattered energy and has no
relation to the phase of the electromagnetic radiation. 39 From Fig. 2.1 it can be seen that for small
spherical particles as much as equal energy is scattered to the backward hemispheres as is scattered
forward (Rayleigh scattering) whereas for larger particles the forward scattering from the sphere
increases and the backward scattering gets smaller.
Fig. 2.1 Polar diagram of single-particle phase function for non-absorbing particle of refractive index 2.0
calculated at wavelength, λ0= 0.55 µm and different size parameters, x. The forward scattering ratio under
collimated illumination, ζc is also shown in the figure. 37
The optical theorem which is a useful quantity yields a relation between extinction cross-section
(Cext) and the real, Re, part of the forward scattering amplitude, S(0). 28,40 The relation is
mathematically given by:
Cext = 4 ⋅ π ⋅ Re{S(0) k 2 } .
More explicit expressions for the extinction (Cext),
sections follow from the series expansions 28:
(2.8)
scattering (Csca) and absorption (Cabs) cross-
15
Tuquabo Tesfamichael
Cext =
Csca =
2π
x2
∑ (2n + 1) ⋅ Re{(b
2π
x2
∑ (2n + 1) ⋅ { b
∞
n
n =1
∞
n
2
+ cn )} ,
+ cn
n =1
Cabs = Cext − Csca .
2
},
(2.9)
(2.10)
(2.11)
These cross-sections which are proportional to the particle geometric cross-section are the basis for
scattering and/or absorbing particles in a medium. If the size of the particle is much smaller than the
wavelength, Cabs is inversely proportional to the wavelength, λ and directly proportional to the particle
volume39, whereas the scattering cross-section is proportional to the square of the volume but inversely
proportional to the fourth power of the wavelength (Rayleigh scattering). On the other hand, if the size
of the particle is much greater than the incident wavelength, both Cabs and Csca approach the geometric
cross-section. 39
2.2.2
Effective Medium Theory
For inhomogeneous composite media consisting of small particles hosted in a dielectric matrix, the
optical constants can be derived from the optical constants of the homogeneous constituents. If the size
of the inhomogeneties is much less than the wavelength of the incident light, the electric and magnetic
fields are almost constant over this characteristic length, which is the quasistatic approximation. We
then describe the response of a material to an electromagnetic field by the dielectric function and
magnetic permeability. In the solar and infrared wavelength regions, the magnetic permeability
approaches unity and the optical properties can be treated with an effective dielectric function of the
medium on the basis of effective medium theory (EMT). The most commonly used effective medium
theories are the Maxwell-Garnett 23 and Bruggeman 24 as well as the Ping Sheng 41 models. They can be
used to model the effective dielectric function of the composite coating for spherical inclusions and the
effective quantity depends only on the dielectric functions of the components and their volume
fractions. The Maxwell-Garnett theory, in its simplest form, assumes that the medium has a separatedgrain structure (Fig. 2.2a). The Bruggeman and Ping Sheng theories , on the other hand, apply to a two
component mixture having aggregate microstructure (Fig. 2.2b). The Ping Sheng model derives for the
more general case of coated spheroid particles in an effective medium. The difference in microstructures
between the mentioned theories have indeed an effect on the modeled optical properties of the
composite. 42
To derive the effective dielectric function, each particle in the composite is considered to be
embedded in an effective medium and the composite can be of two or higher component systems. 2325,41,43-45 Here we deal with two components of dielectric constants ε and ε on the work of
A
B
Niklasson et al. 44 using the microstructures of Fig. 2a and Fig. 2b. The calculation has been simplified
by using the random unit cell (RUC) of Fig. 2c and Fig. 2d that properly accounts for the essential
features of the separate and aggregate microstructures, respectively. 25,44 Using the Lorenz-Mie theory
and the basic definition of EMT, the RUC can be expressed as a function of the scattering amplitude in
the forward direction. 27,28
16 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
(b)
(a)
εMG
εBr
εΒ εΑ
(c)
εΑ, εΒ
(d)
Fig. 2.2 Microstructures of (a) separated-grain, (b) aggregate structures for a two component medium, (c)
and (d) are random unit cells (RUC) to derive the effective dielectric function of the separated-grain
(Maxwell-Garnett model) and aggregate (Bruggeman model) structures, respectively. The arrow indicates
the direction of the polarized light.
According to the definition of EMT, the RUC should not be detectable by the field in the given
electromagnetic wavelength range of the experiment 25 and this is an important condition for the optical
theorem of Eq. (2.8) to be equal to zero (Cext=0):
S(0) = 0 .
(2.12)
According to the meaning of the EMT the particles should satisfy a certain size range (smallest and
largest size limits). The magnitude of the large-size limits are determined by the onset of the higher
order terms in the series expansion whereas the small-size limit is governed in the transition of the bulklike band structure towards molecular-cluster state. 44 Eq. (2.12) can also be applied for non-spherical
shapes by neglecting the higher order series expansion. 25 This is advantageous since particles in
practical coatings are found in different shapes. The Bruggeman and Maxwell-Garnett EMT extended to
non-spherical particles are discussed below.
The Bruggeman model, which considered aggregate structure (Fig. 2.2b), in its general form has
been derived by expanding Eq. (2.12) in terms of the size parameter, ka. 27,28 By considering only the
first order expansion (i.e. for small sphere limit) the forward scattering amplitude for an ellipsoid of
semi-axes aj (j=1,2,3) is examined. The RUC in Fig. 2.2d for an ellipsoid aligned with the applied
electric field polarized along one of the principal axes is applied. The small sphere limit expansion of
Eq. (2.12) gives: 27,28
17
Tuquabo Tesfamichael
S j (0) = ik 3
a1a2 a3
3


ε −ε
⋅
 = 0,
 ε + L j (ε − ε ) 
(2.13)
where ε is the dielectric function of either of the constituents A or B, ε is the average dielectric function
of the effective medium and Lj is the depolarization factor along the field which satisfies:
0 ≤ Lj ≤ 1 ,
(2.14a)
L1+L2+L3=1 .
(2.14b)
and
Both constituents are treated symmetrically and each ellipsoid is taken to be embedded in the effective
medium (Fig. 2.2d). From Eqs. (2.13-14), an implicit equation for Bruggeman effective dielectric
function, ε BR for an ellipsoid are obtained given by the expression 25:
ε A − ε BR
ε B − ε BR
+ (1 − fA ) BR
fA BR
= 0,
ε + Lj (ε A − ε BR )
ε + Lj (ε B − ε BR )
(2.15a)
where fA is the filling factor for component A and (1-fA) that for component B. In a collection of
particles randomly oriented it is reasonable to assume an average value. 46-48 The effective dielectric
function for the three principal axes stated above becomes:
3
1
3
⋅ ∑ fA
j =1
ε A − ε BR
ε B − ε BR
(
)
+
1
−
f
= 0,
A
ε BR + Lj (ε A − ε BR )
ε BR + Lj (ε B − ε BR )
(2.15b)
The Bruggeman model does not strictly apply to a particulate medium since there is no way to decide
which component is the particles and which the surrounding medium. Since it is derived from an
aggregate structure it is useful for a higher particle filling factor which is often used for solar energy
applications. For spheres, all the depolarization factors in Eq. (2.14) are the same and for spheroids
two of them are equal. The Bruggeman effective medium approximation for spherical particles ( L j = 1 3)
follows from Eq. (2.15):
ε A − ε BR
ε B − ε BR
+ (1 − fA )
= 0.
fA
ε A + 2ε BR
ε B + 2ε BR
(2.16)
Similarly, the generalized Maxwell-Garnett model can be obtained from an expansion of
Eq.(2.12) for a separate grain structure (Fig. 2.2a ) by considering a coated ellipsoid 27,28 in the RUC
(Fig. 2.2c). The effective Maxwell-Garnett dielectric function, ε MG has been given by: 25
ε
MG
= εB
ε B + (ε A − ε B ) LAj + f A (ε A − ε B )(1 − LBj )
ε B + (ε A − ε B ) LAj − f A (ε A − ε B ) LBj
,
(2.17)
where LAj and LBj are the depolarization factors along the field for the inner and outer ellipsoid,
respectively. Since particle interactions are not taken into account in an explicit manner, Eq. (2.17) is
then valid for a low filling factor of particles. For the inverted structure, in which one replaces A→B and
18 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
B→A, one gets a similar relation. The Maxwell-Garnett expression in its simplest form ( LAj = LBj =
reduces to:
ε
MG
= εB
ε A + 2 ε B + 2 f A (ε A − ε B )
.
ε A + 2 ε B − f A (ε A − ε B )
1
3
)
(2.18)
There is a basic difference between Maxwell-Garnett and Bruggeman theories. Bruggeman
assumes the composite to consist of randomly intermixed particles of dielectric and metal, whereas
Maxwell-Garnett considers the metal to be dispersed as particles through the dielectric or vice versa.
Their dielectric functions are, however, similar at low filling factors. 49 Both theories have in common
that the effective dielectric function does not depend explicitly on the size of the inhomogeneties and
this is because the electric dipole term, which is proportional to particle volume, is retained in the series
expansion of the amplitude of the electric field scattered by a single particle. 50 The EMT has been
applied extensively in optical characterization of spectrally selective absorber composite coatings.
25,51-55
2.2.3
Two and Four Flux Theories
If the inhomogeneties in a composite medium are large enough to give rise to magnetic dipole and higher
order multipole radiation, then the effective magnetic permeability of the composite medium cannot be
taken to be that of free space even if the particles are non magnetic. Effective medium theories are not
valid and instead radiative transfer theories such as two-flux and four-flux models are used. 50 The two
flux model proposed by Kubelka and Munk was based on a model of two light fluxes traveling in the
forward and backward directions relative to the normal incident radiation. 32 Isotropic directional
intensity and isotropic scattering are necessary conditions for the derivation of the two flux
expressions.
Consider a composite medium of thickness d along the z-axis illuminated by diffuse light as
shown in Fig. 2.3a. The fluxes have been formulated by a pair of linear differential equations 39:
dId
= −( K + S ) Id + SJd ,
dz
(2.19a)
dJd
= ( K + S ) Jd − SId ,
dz
(2.19b)
where K, S are the absorption and scattering coefficients per unit length of the medium, respectively.
The differential flux Id, decreases due to absorption within dz and scattering in the backward direction
but also increases due to the backward scattering contribution from Jd. Similar conditions also apply for
the flux Jd of Eq. (2.19b).
19
Tuquabo Tesfamichael
medium
Incident light
medium
Incident light
Id
Id
Ic
Jc
Jd
z=0
Jd
z=d
(a)
z=0
z=d
(b)
Fig. 2.3 Incident light striking a medium of thickness, d, perpendicularly. (a) Two diffuse fluxes obtained
from a medium illumined by diffuse light (two flux theory) and (b) two collimated and two diffuse fluxes
obtained from a collimated incident beam (four flux theory).
Neglecting surface reflections, the diffuse reflectance, Rd and transmittance, Td as a function of the
thickness of the medium, d are then given by: 32
Rd =
sinh(qSd )
,
p ⋅ sinh(qSd ) + q ⋅ cosh(qSd )
(2.20)
Td =
q
,
p ⋅ sinh(qSd ) + q ⋅ cosh(qSd )
(2.21)
where p = 1 + ( K / S ) and q = p 2 − 1 . The coefficients, K and S, can then easily be extracted from
optical measurements of Rd and Td and a fitting to Eqs. (2.20-21). The diffuse reflectance of the
Kubelka-Munk theory when applied on a substrate of reflectance, Rg can easily be modified: 56
Rd =
1 − Rg ⋅ [ p − (q ⋅ coth(qSd ))]
p + (q ⋅ coth(qSd )) − Rg
.
(2.22)
If the substrate is highly reflecting, Rg can be replaced by unity and if the medium is not supported by
a substrate Rg=0 and Eq. (2.22) is reduces to Eq. (2.20). The Kubelka-Munk two flux theory which
assumes diffuse illumination is a good approximation to calculate the transmittance and reflectance of
highly scattering and weakly absorbing coatings. It has, however, limited applicability for partially
scattering and absorbing samples. 57 The equations were formulated with the assumption of diffuse
illumination of the incident light on a diffusely scattering medium which is not applicable to the case of
a collimated beam and weakly scattering medium. Instead the four flux theory which includes both
diffuse and collimated fluxes should be used. 33,39,58,59 Here we present analytical solutions of
collimated as well as diffuse components of reflectance of a four flux model developed by Maheu and
his co-authors. 33,60
20 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
As shown in Fig. 2.3b, the medium is now illuminated perpendicularly by a collimated beam
along the z-coordinate. In addition to the directly transmitted (Ic) and specularly reflected (Jc) light,
diffusely transmitted (Id) and reflected (Jd) light can be considered. The intensities of the collimated
beams decay due to scattering and absorption by the particles. The intensity of the diffuse flux Id is
decreased by absorption and scattering into the backward hemisphere, and it is increased by scattering
from the Ic, Jc and Jd fluxes into the forward hemisphere. A similar analysis corresponds to the flux Jd.
A set of differential equations for the four flux components is given by:
dIc
= − ( k + s ) Ic ,
dz
(2.23a)
dJc
= ( k + s ) Jc ,
dz
(2.23b)
dId
= −ξkId − ξ (1 − ζ c )sId + ξ (1 − ζ c )sJd + ζ c sIc + (1 − ζ c )sJc ,
dz
(2.23c)
dJd
= ξkJd + ξ (1 − ζ c )sJd − ξ (1 − ζ c )sId − ζ c sJc − (1 − ζ c )sIc ,
dz
(2.23d)
where the intrinsic absorption, k and scattering, s coefficients per unit length, with their sum called
extinction coefficient per unit length, can be obtained from the cross-section per unit volume as:
k Cabs
=
,
f
v
(2.24a)
s Csca
=
,
f
v
(2.24b)
where v and f are particle volume and particle volume fraction, respectively. (Note the symbol k (italic )
for absorption coefficient). If k and s are expressed in µm-1, then the corresponding volumetric crosssections (cross-section per unit volume) have also units of µm-1. Solutions of the volumetric absorption
(Cabs/v) and scattering (Csca/v) cross-sections, are found in Eq. (2.10-11) for single scattering calculation
for spherical particles by Lorenz-Mie theory. 28,61 An alternative way for determining the volumetric
cross-sections from optical measurements is described in section 2.2.4. In Eq. (2.23), ξ is the average
path length parameter which is introduced to take into account the different path length of the diffuse
radiation, as compared to the path length of the collimated component (ξ =1 for collimated beam and
ξ=2 for semi-isotropic diffuse beam). The quantity ζ c defined in section 2.2.1 is the forward scattering
ratio obtained using the Lorenz-Mie theory (see also Fig. 2.1). The differential equations, Eqs. (2.23ad), have been solved previously, and explicit relations for collimated and diffuse components of the
reflectance and transmittance have been obtained. 33,60 They can easily be modified for the case of a
metallic substrate. The collimated, Rc and diffuse, Rd reflectances respectively are given by the
following equations:
(1 − rc )2 Fe −2 ( k + s ) d
,
Rc = rc +
1 − rc Fe −2 ( k + s ) d
(2.25)
21
Tuquabo Tesfamichael
[(1 − r )(1 − r )e ][C + C e + C e ]
,
− ( k + s) )(1 − r Fe
)]{[ A (r G − 1)] cosh( A d ) + [ A (G + r ) − A (1 + r G)]sinh( A d )}
−(k + s)d
Rd =
[( A
1
c
d
2
(k + s)d
0
−(k + s)d
1
2
−2 ( k + s ) d
2
c
1
d
1
5
d
4
1
d
(2.26)
The sum of the collimated and diffuse components of reflectance is defined as the total reflectance, Rt:
Rt=Rc+Rd
(2.27)
In the above equations rc and rd (rc´ and rd´), are the reflection coefficients for collimated and diffuse
radiation at the medium-air (medium-substrate) interface, respectively. The Fresnel formulae are used to
evaluate these coefficients, in terms of which the metallic substrate effects are taken into account by
means of F≅ rc´ and G≅ rd´. Moreover:
C0 = A1[( A3 + FA2 ) − G( A2 + FA3 )] ,
(2.28a)
C1 = {[ A1 (GA2 − A3 )] cosh( A1d ) + [ A2 ( A5 − GA4 ) + A3 (GA5 − A4 )]sinh( A1d )} ,
(2.28b)
{
}
C2 = F [ A1 (GA3 − A2 )] cosh( A1d ) + [ A3 ( A5 − GA4 ) + A2 (GA5 − A4 )]sinh( A1d ) ,
(2.28c)
A1 = ξ k[k + 2 s(1 − ζ c )] ,
(2.29a)
A2 = s[ξkζ c + ξs(1 − ζ c ) + ( k + s)ζ c ],
(2.29b)
A3 = s{ξ[s(1 − ζ c ) + k (1 − ζ c )] − ( k + s)(1 − ζ c )} ,
(2.29c)
A4 = ξ[k + s(1 − ζ c )],
(2.29d)
A5 = A4 − ξk .
(2.29e)
with
Two and four flux theories have been used extensively in the past for optically related applications
such as; oxygen content in blood 62, minerals 63, paint or paper industry 64,65 , thickness sensitive
spectral selective paints 66,67 and spectrally selective composite absorbers 68.
22 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
2.2.4
Cross-Sections from Reflection-Transmission Measurements
As mentioned earlier exact values of the absorption and scattering cross-sections for single particle can
be obtained using the Lorenz-Mie theory if a great deal of computing time is applied and the optical
constants of the medium are known. But optical constants of some complex materials cannot be found
in the literature and are not easily measurable. A method is devised to obtain the single particle
absorption and scattering cross-sections of a slab from reflectance and transmittance measurements. In
order to apply the concept of single scattering, the incident light traversing the slab that reaches the
detector must encounter very few particles. This method is then applicable for sufficiently transparent
media i.e. for low volume fractions of the absorbing particles.
The total reflectance (Rt) as defined in Eq. (2.27) is given by the sum of collimated (Rc) and
diffuse (Rd) components of reflectance. Similarly, the total transmittance (Tt) is defined by:
T t=T c+T d ,
(2.30)
where, Tc is the collimated transmittance and Td diffuse transmittance. Light incident on a medium can
either be reflected, transmitted or absorbed. Thus, the absorbed light is represented by the absorptance
(Abs) and is defined as:
Abs=1- Rt - Tt
(2.31)
Scattered light can be defined as the sum of the diffuse components of the total reflectance and
transmittance the sum of the scattered light (Rd, Td) and absorptance (Abs) gives the extinction (Ext):
Ext= Rd +Td + Abs
(2.32)
Inserting Eqs. (2.27), (2.30) and (2.31) into Eq. (2.32), the extinction of light in the scattering-absorbing
medium becomes:
Ext=1- Rc - Tc
(2.33)
From Eqs. (2.31) and (2.33) we see that the absorptance is determined from measurements of the total
while the extinction from the collimated reflectance and transmittance. In order to understand scattering
by a particle, we take the analogy of reflection-transmission by a slab. 28,69
Consider collimated light passing through a composite slab of thickness d (see Fig. 2.3b)
undergoing attenuation by extinction i.e. absorption and scattering. This extinction is due to randomly
distributed particles in the medium. A fraction R0 of the incident light is reflected at each interface. The
light traversing the medium undergoes attenuation by a factor exp(-(K+S)d), where K and S are effective
absorption and scattering coefficients coefficient per unit length as defined before and K+S effective
extinction coefficient per unit length. The collimated transmittance and reflectance of the slab are easily
found by addition of the intensities of the multiply reflected beams. The extinction coefficient, can be
approximately determined from the ratio:
23
Tuquabo Tesfamichael
-(K + S)d
T
c ≈ (1 − R 0 )e
.
1− R
1 − R 0 e -2(K + S)d
c
(2.34)
For weakly absorbing medium, exp(-2(K+S)d) ≈1 and hence for slab materials with refractive indices of
1.5 to 1.6 (like glass, KBr and most polymers), Eq. (2.34) can, within an accuracy better than 5%, be
simplified further to 28,69:
T
c ≈ exp(-(K + S)d ).
1− R
c
(2.35)
The approximation is especially good when (K+S) is small i.e. when the particle density is small and
single scattering prevails.
The effective absorption coefficient, K can analogously be obtained from the total transmittance
and reflectance:
T
t ≈ exp(-Kd ) ,
1− R
t
(2.36)
since the scattered light contributes to either Tt or Rt . This expression presumes single scattering of
light by the particles. The approximation is within 5% when absorption dominates totally over
scattering. 28,69 In our materials, absorption is larger than scattering, as shown below, hence we are
close to this limit. The effective scattering coefficient, S is then obtained from the difference of the
extinction and absorption coefficients.
As mentioned earlier, the concentration of the particles in the medium should be very small, and
hence multiple scattering can been ignored. A simple test for the absence of multiple scattering is to
check the concentration dependence of S and K. If a linear dependence as a function of the
concentration is obtained, then only single scattering is important. 27 By assuming all the particles
embedded in the matrix to be identical, the volumetric absorption and scattering cross-sections of Eq.
(2.24a-b) are expressed: 28
Cabs K
=
f
v
(2.37a)
Csca S
=
v
f
(2.37b)
Equations (2.24a-b) obtained from Lorenz-Mie theory are analogous to Eqs. (2.37a-b), respectively.
The Lorenz-Mie theory considers single scattering for spherical particles but in this work we have
used the cross-sections without regard to particle geometry.
In all the theories for inhomogeneous materials discussed earlier, the particle concentration was
given in terms of volume fraction, f. In practice we can find particle concentration in weight fraction, F.
Thus it is important to relate these two factors provided the density of the constituents is known as:
24 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
f =
1
ρ 1− F
1+ p 
ρm  F 
(2.38)
where ρp and ρm are the mass density of the particle and the medium or matrix, respectively.
2.3
Selectively Solar Absorbing Surfaces
2.3.1
Understanding Selective Solar Absorbers
The blackbody spectrum at a given temperature and the spectral distribution of the sun needed to be
known in order to evaluate absorbing surface behavior. The standard spectral solar flux incident at the
surface of the earth, after atmospheric absorption, is limited to the range between 0.3 and 2.5 µm i.e.
UV/Vis/NIR wavelength ranges. Our eye is sensitive only to the visible part of the solar spectrum.
Figure 2.4 shows the hemispherical solar irradiance that reaches the surface of the earth after passing
the atmosphere during clear sky conditions. This is adapted from the International Organization for
Standardization (ISO) 20 for air mass 1.5 (AM1.5) i.e. when the sun is about 42° above the horizon.
The spectrum consists of direct and diffuse radiation and both fluxes contribute to heat-up flat plate
solar collectors.
The solar absorptance is one parameter that characterizes the performance of the absorber. It is
defined as the fraction of incident radiation at a given wavelength that is absorbed. For an opaque
material the spectral absorptance can be expressed in terms of the total reflectance, R(λ,θ), as:
α sol (λ ,θ ) = 1 − R(λ ,θ ) ,
(2.39)
where λ is the wavelength and θ angle of incidence of light measured from the surface normal of the
absorber. The solar absorptance is obtained by weighting the spectral absorptance with the spectral
solar irradiance and for a given angle of incidence θ, it can be obtained by integrating over the
wavelength dependent solar spectrum, G(λ):
λ
2
∫ [1 − R(λ ,θ )]G(λ )dλ
λ
,
α sol (θ ) = 1
λ
2
∫ G ( λ ) dλ
λ
1
(2.40)
where λ1, λ2 denote the lower and upper solar wavelengths, respectively. Since the blackbody spectrum
of the sun and the solar irradiance at the surface of the earth are not the same, we cannot use the sun’s
blackbody spectrum for weighting solar absorber coatings.
25
Tuquabo Tesfamichael
1.2
Solar AM1.5
Power Density (kW/m 2 µm)
1
300 °C
0.8
0.6
Blackbody
0.4
200 °C
0.2
100 °C
0
0.3
1
10
50
Wavelength (µm)
Fig. 2.4 Solar hemispherical spectral irradiance for AM1.5 in the wavelength range 0.3 to 4.045 µ m (note
the irradiance λ > 2.5 µ m is negligible). This measurement was done at ground albedo 0.2, thickness of
perceptible water vapor 1.42 cm, ozone layer 0.34 cm and turbidity 0.27. 20 A blackbody radiation
spectrum calculated from Planck’s law for three different temperatures is also shown in the infrared
wavelength range.
Solar reflectance measurements are usually performed in the wavelength range 0.3-2.5 µm at
near normal (θ≈0) angle of incidence using standard spectrophotometers. This means the solar
absorptance is characterized at near normal incidence for which the sun is at the zenith angle relative to
the absorber. For oblique incidence where the sun is at other elevations than the zenith, the near normal
solar absorptance must be modified when characterizing solar thermal collector systems. This is usually
done by using the angle of incidence modifier (optical efficiency), Kτα (θ) which is a function of θ given
by 15:
K
τα
(θ )
=
(τα )
1
= 1 − b0 ⋅ 
− 1 ,

(τα )0
cosθ 
(2.41)
where α is the solar absorptance defined in Eq. (2.40) and τ is the transmittance of the collector cover.
The subscript “o” represents values at normal (zero) angle of incidence. The constant bo is called an
incidence angle modifier coefficient and its value can be different for different collectors. The collector
system and application of the incident angle modifier will be discussed later in section 2.4.
The optical properties of a real body in the infrared wavelength range can be characterized by its
thermal emittance compared to the ideal blackbody. Figure 2.4 shows blackbody spectra at three
different temperatures calculated from Planck’s law. As the temperature rises, the total amount of
radiation increases and the peak wavelength shifts towards shorter wavelength, which can be
determined by Wien’s displacement law. The emittance is then defined as the fraction of radiant energy
emitted by the heated surface as compared with the radiation energy emitted by a blackbody at a the
26 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
same temperature and wavelength. Since the radiation is emitted in all directions, then the thermal
emittance is characterized by the hemispherical thermal emittance, εtherm(λ,T). Using Kirchhoff’s law
stating that the absorptance is equal to the emittance and Eq. (2.39) for an opaque object, we get:
ε therm (λ , T ) = 1 − R(λ , T ) ,
(2.42)
and the total hemispherical emittance at a given temperature, T can be evaluated by:
λ2 π / 2
∫ ∫ [1− R(λ,θ ,T )](2cosθ sin θdθ )B(λ,T )dλ ,
λ 0
ε therm (T ) = 1
λ2
∫ B(λ,T )dλ
λ1
(2.43)
where B(λ,T) is the blackbody spectrum given in Eq. (2.1). The absorbers for flat plate solar collectors
are normally used at low temperatures and their thermal emittances are usually characterized at
temperatures between 50° to 100°C. The emitted radiation from a body at these temperatures are found
in the infrared region, and λ1, λ2 are then 2.5 µm and 50 µm, respectively. The denominator of Eq.
(2.43) is the so called Stephan-Boltzmann law (Eq. 2.2). For a blackbody, εtherm(T) is unity and for a
real body it varies between 0 and 1.
The blackbody spectrum for temperatures between 50° to 100°C and the solar spectrum do not
overlap in any wavelength range, as was shown in Fig. 2.4. It is, therefore, possible to design a surface
which absorbs the maximum possible of the incident solar radiation, but does not re-emit the absorbed
energy. A material having high absorptance (low reflectance) in the solar spectrum and low emittance
(high reflectance) in the thermal infrared is called a selective solar absorber. An ideal spectrally selective
surface should have a reflectance of zero in the solar wavelength range and unity in the thermal infrared.
For temperatures below 100°C the on-set wavelength for the low to high reflectance is about 3 µm and
for higher temperatures (≈300°C) the critical wavelength is around 2 µm (see Fig. 2.4).
2.3.2
Selective Solar Absorber Designs
In principle there are several ways of achieving selective solar absorbing surfaces. Descriptions of
various selective absorbers produced by different techniques can be found elsewhere. 5-7,70-72 The
coatings are based on different optical absorption mechanisms including light trapping, particulate
coatings, semiconductor-metallic layers, multilayer films, quantum size effects and intrinsic absorption.
The simplest type of design would be to use materials having intrinsic solar selective properties, but
there are no materials in nature that have such ideal solar selective properties. There are, however,
reports on some transition metal compounds and semiconductors that indicate the existence of intrinsic
selective materials. 5,73,74 The most common absorber type is the absorber-reflector tandem and some
of the widely applied designs are discussed below.
An absorber-reflector tandem is obtained by combining two surfaces, one surface which is
highly absorbing in the solar region and another highly reflecting in the infrared. 75,76 . One way to do
this is to cover a base metal of high infrared reflectance by a thin highly solar absorbing coating. This
Tuquabo Tesfamichael
27
configuration is called a dark mirror. Most of the commercially available selective absorbers are of this
type. An alternative way to achieve the absorber-reflector tandem is to cover a thick absorbing surface
by a solar transparent infrared reflecting coating which is normally called a heat mirror. Some of the
absorber-reflector tandem designs of the first type are discussed below.
Semiconductor Coatings
Spectrally selective semiconductor coatings can be obtained by depositing a semiconductor, which has
low band gap so that it absorbs the solar radiation, on a highly infrared reflecting metal substrate. The
semiconductor coating absorbs photons having energies greater than the band gap as a result of raising
the material’s valence electrons into the conduction band. Photons with energies less than the band gap
energy are transmitted through the coating unaffected. To obtain high solar absorptance, the refractive
index of the semiconductor should be as low as possible. Unfortunately, semiconductor coatings have
high refractive index, which gives high reflectance at the air-coating interface. The reflectance can be
reduced through proper thickness control to obtain a destructive interference effect or by applying
antireflection coatings. Chemical vapor deposition of silicon in a stack of SiO2/Si3N4/Si/Cr2O3/Ag/Cr2O3
on stainless steel was developed for high temperature solar collectors with an antireflection coating on
top of the multilayer stack . 77 From this coating, a solar absorptance of 0.85 and a thermal emittance of
0.07 at 500°C was achieved. Ge, PbS and Si produced by gas and vacuum evaporation, chemical vapor
deposition and spray pyrolysis are examples of semiconductor materials that have been utilized for
solar absorber applications. 77-79
Textured Surface Coatings
Solar selective absorbing surfaces may be produced by creating texture of a suitable scale on a highly
reflecting metal substrate. The rough surface absorbs solar energy by trapping the light through
geometric effects of multiple reflection and absorption. For long wavelength radiation, the surface looks
fairly smooth, thereby acting like a poor radiator of energy (low εtherm). A dendrite structure of rhenium,
tungsten and nickel made by chemical vapor deposition and textured copper, nickel, and stainless steel
made by sputter etching are examples of textured metal surfaces. 80-84 Al-Si alloy (20 vol.% Si)
produced by simultaneous evaporation of the constituents from two electron-beam sources on a glass
substrate and chemically etched in a NaOH solution form an irregular textured surface. 85 The textured
surface is due to the preferential etching of the aluminum phase, which gives a dark appearance for an
appropriate etch time. The microstructure of the above textured absorbers could be interpreted as a top
absorbing layer of air filled metal (rough surface) backed by a highly reflecting substrate. The optical
properties of such coatings can be obtained using effective medium theories. 23,24
Composite Coatings
Composite coatings are surfaces consisting of small particles embedded in a dielectric matrix (also called
cermet) deposited on a highly infrared reflecting metal substrate. The particles are usually transition
metals embedded in an oxide matrix. The particles could either be uniformly distributed in the matrix or
gradient index with decreasing content of the particles towards the front surface of the coating. These
types of coatings have optical properties appropriate for selective solar absorbers. 8,10 The coatings
absorb solar radiation strongly and are almost transparent in the infrared region and hence the base
metal gives the desired infrared properties. Depending on the volume fraction, shape of the particles
28 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
and optical constants of the constituents, the wavelength of the transmittance-absorption transition can
be controlled by the thickness of the composite coatings. This offers a high degree of flexibility to solar
selectivity. The composite coatings have typical values of the order of 0.5 to 1.0 µm in thickness, 0.3
to 0.4 metal volume fraction. 8,10,86,87 Such coatings have a solar absorptance between 0.94 to 0.97 and
a thermal emittance of about 0.10 to 0.20. Thicker films with lower particle content is also possible but
the thermal emittance is also higher. The optical properties of composite coatings could be understood
from effective medium or radiative transfer theory discussed in section 2.2. 23,24,28,33 An advantage of
using radiative transfer theory over the EMT is the possibility of predicting size dependent selectivity
of composite coating. Recently, it has been reported that solar selectivity of coatings with metallic
inclusions in an alumina matrix is not possible for particles with a diameter greater than 0.2 µm. 68
Figure 2.5 is a schematic cross-sectional diagram of two selective composite coatings one with
particles uniformly distributed in the matrix, (nickel pigmented anodic aluminum oxide) and the other
with graded index microstructure (sputtered nickel/nickel oxide). 52,87,88 In both cases a top layer that
reduces the refractive index mismatch (antireflection) between air and the absorbing layer is used. It is
convenient to produce the antireflection layer from the same oxide layer as is the case of Fig. 2.5a.
These two types of coatings will be discussed in detail in the following sections. There are
commercially available metal-dielectric absorbers used for flat plate solar collectors, such as
molybdenum/aluminum oxide (Mo-Al2O3), nickel/nickel oxide (Ni-NiOx), both produced by sputtering,
electroplated black chrome (Cr-Cr2O3) and nickel pigmented anodic aluminum oxide (Ni-Al2O3). 8
(a)
(b)
Fig. 2.5 Schematic cross-sectional diagram of two selective composite coatings (a) nickel pigmented
anodic aluminum oxide (Ni-Al2O 3), and (b) sputtered nickel/nickel oxide (Ni-NiOx) absorbers.
Painted Coatings
Selective solar absorbing paints have the potential of being a less expensive alternative to the selectively
solar-absorbing coatings described above. They can also be classified as the tandem type of absorbing
particles uniformly distributed in a matrix deposited on a metal substrate. Their optical performance is
governed by intrinsic optical constants as well as particle size-dependent scattering and absorption. The
combined effect gives the effective scattering and absorption coefficients of the pigment particles.
Polymers such as silicone, siloxane resin or phenoxy resin are usually used as binders. Unfortunately,
binders in general absorb infrared radiation and thereby the thermal emittance is higher. The particles
usually agglomerate and their size becomes comparable to or larger than the incident wavelength of light.
In order to reduce the agglomeration, fumed silica can be added during the preparation of the paints.
29
Tuquabo Tesfamichael
Laboratory studies of a range of pigments (mostly metal oxides) on aluminum substrates have been
reported and the best obtained result was for an iron-manganese-copper oxide (FeMnCuOx) pigment
with a silicone binder, giving a solar absorptance of 0.92 and a thermal emittance of 0.13. 12 Thickness
sensitive spectrally selective (TSSS) paints obtained from FeMnCuOx in a siloxane resin matrix have
good optical properties (αsol=0.90-0.92 and εtherm=0.20-0.25). 89 In addition to the particle volume
fraction and thickness, the solar selectivity of such coatings also depend on the dispersion of the
particle (size) in the matrix. Paints are thicker (d≈2-3 µm) and have a smaller volume fraction (f≈0.2)
than the metal-composite absorbers (d≈0.2-1.0 µm and f>0.3). Their optical properties can be studied
using radiative transfer theories. 28,32,33,39 Selectively solar-absorbing paints have also reached
commercialization recently, and there are at least two such products on the market, namely, the
Solarect-Z, and the SolkoteHI/SORB-II™.
2.4.
Solar Collectors
2.4.1
Flat Plate Solar Collectors
Figure (2.6) shows a cross sectional view of a commonly used flat plate solar collector design. The
major components of the collector as shown in the figure are , transparent cover, absorber, fluid conduit
and an insulation.
incident
radiation
cover glass
θ
absorber
conduit fluid
insulation
Fig. 2.6 Simplified cross-sectional view of a simple flat plate solar collector design used for domestic hot
water application.
The function of the collector system is to heat a fluid passing through the conduit by converting
incident solar radiation into thermal energy with minimum heat losses. The heat losses can be due to
conduction, convection and radiation and these losses are expressed in terms of the collector over all
heat coefficient, UL. The relation between thermal losses UL and the above parameters has been given in
detail by Duffie-Beckman. 15 Glass is usually used as cover for the absorber since it is transparent for
the solar spectrum but opaque for the infrared wavelength and thereby suppresses thermal radiation
emitted from the absorber. Glass reflects some of the incident solar radiation, however, and an
antireflection coating can be applied in order to decrease the reflection. The cover also suppresses
convection, and for minimum losses the spacing between the cover and absorber should be between 1015 cm. 15 Convection losses can be further reduced by using an additional transparent insulation
material such as a thin transparent foil or honeycomb between the cover and the absorber. Conduction
heat losses are avoided by using insulation at the back side of the collector box, as shown in Fig. (2.6).
30 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
The most important and critical part of the collector is the absorber surface. Spectral selective
solar absorbers increase the useful energy output, Qu, of the collector system as compared with nonselective absorbers. In addition to the intrinsic properties of the selective absorber surface (i.e. αsol and
εtherm) another useful performance criterion, is the collection efficiency. It involves temperature of
operation (Ti -Ta), where Ti is the inlet fluid temperature of the collector and Ta is the ambient
temperature. For flat plate collectors the collector efficiency,η , is the fraction of the available solar
energy retained in the collector and is in its simplest form given by 15:
η=

Qu
U (T − Ta ) 
= FR (τα ) − L i
,
Ac GT
GT


(2.44)
where (τα) from Eq. (2.41) is the optical efficiency that includes the angular dependence of the
collector, Ac is the collector (absorber) area and GT the total solar energy flux. FR is the collector heat
removal factor, a quantity that relates the actual useful energy gain of a collector to the useful gain if the
whole collector surface were at the fluid inlet temperature. 15 If most of the radiation is beam radiation
that is near normal to the collector, and FR and UL do not vary greatly in the range of operation of the
collector, then FR(τα) indicates the amount of energy absorbed and FRUL is the dissipation of energy in
Wm-2K-1. The collection efficiency decreases with increasing operating temperature and at higher
temperatures radiation losses are dominant as compared with conduction and convention losses. It is
important, however, to stress that an increase in the solar absorptance, αsol is more important than an
equal decrease in the thermal emittance, εtherm for better collector performance. 10,90
To characterize the solar collector during a relatively short testing period with no requirement
for steady state climatic conditions, systematic studies of the collector performance are needed.
Dynamic testing can be used to predict the energy output of the collector by identifying collector
parameters using a multiple linear regression method. The energy output, qu (Wm-2) is determined using
the following mathematical model 91:
qu = F ' (τα )n Kταb (θ )GTb + F ' (τα )n Kταd (θ )GTd − F ' U0 ∆T − F ' U1 ( ∆T )2 − ( mC )eff
dTf
dt
,
(2.45)
where, F ' (τα )n Kταb (θ ) and F ' (τα )n Kταd (θ ) are the optical efficiency for beam radiation (GTb) and the
diffuse radiation (GTd) respectively, F ' U0 is the heat loss coefficient in units of Wm-2K-1, F ' U1 the
temperature dependence of the heat loss coefficient, W(mK)-2, dTf/dt, the mean time derivative for the
fluid temperature (°Cs-l) and (mC)eff the collector effective thermal capacitance, Jm-2K-1. ∆T is the
temperature difference between the mean fluid temperature in the collector and ambient air temperature
(°C). The relation between F ' and FR is well described in the book of Duffie-Beckman. 15
31
Tuquabo Tesfamichael
3
EXPERIMENTAL METHODS
The experimental methods for preparation of samples will be described in section 3.1. Each sample
analyzed in this thesis was a thin film coating obtained from one or more of the following techniques:
electrochemical deposition, spray pyrolysis, dip coating or sputtering. Preparation of pellets from
black pigments in a non absorbing matrix for studying their optical properties is also given in this
section. Oxidation of a solar absorber (metal particles) using accelerating aging technique at high
temperature which is important for estimating the durability or life time of an absorber is described in
section 3.2 followed by optical and non-optical characterization of the solar absorbers in section 3.3. A
dynamic testing of two solar collectors which we have planned to do in the future are briefly described
in section 3.4.
3.1 Sample Preparation
3.1.1
Chemical Methods
Anodizing aluminum samples
Aluminum sheet is cheap, has good thermal conductance and high infrared reflectance. By anodizing the
aluminum, porous alumina of considerable interests for many practical uses including solar energy
applications can be obtained. The formation of anodic oxide is very complex and the coating
composition is largely controversial. 92 Without going into details of the theories, we present here the
experimental procedure of anodization of aluminum. A 0.5 mm thick rolled electroplated aluminum
sheet (99.99% pure) was cut into samples of a size of 5.5 cm x 3.5 cm. These samples were anodized in
2.0 M phosphoric acid (H2PO4) at room temperature using a dc voltage of 15 V (current density about
4 mA/cm2). The time of anodization was set to 12 minutes to produce a film thickness of about 0.5 µm.
An aluminum plate was used as counter electrode. The experimental set-up of the anodizing process is
shown in Fig. 3.1.
V
+
A
Counter
Electrode
Anode
(Sample)
Electrolyte
Fig. 3.1 Experimental set-up for anodizing aluminum sheet in phosphoric acid electrolyte.
32 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
The anodizing bath was continuously stirred (not shown in the set-up) to minimize local heating of the
substrate which would result in uneven oxide coatings. The oxide thickness was measured using an
Alpha step 200 mechanical stylus profilometer.
Pores are formed within preferred cells of the aluminum due to field assisted dissolution and an
additional mechanism involved direct loss of Al+3 ions to the solution. 93,94 These conditions produce
a transparent porous amorphous aluminum oxide film with a pore fraction as large as 30 to 40 percent
by volume. 95,96 The pores are columnar of regular morphology and extend through the oxide from the
metal-oxide interface to the surface (see also Fig. 2.5a for schematic diagram). The porosity and the
thickness of the coating depend on the operating conditions (such as voltage, temperature, time of
anodization) as well as on the concentration of the electrolyte. 92 A very thin, about 1.4 nm/V, nonporous barrier alumina layer buffers the aluminum substrate.
Electrochemical Deposition (Coloration) of Anodized Samples
Due to aesthetic reasons, processes have been developed for coloration of anodized aluminum products.
Coloration can be made either directly (integral coloration) during anodization or as a post treatment 92 .
Post treatment coloring of porous aluminum oxide can be made by organic dyes or by chemical or
electrochemical deposition of inorganic compounds inside the pores 92,97-99 . By adding inorganic
compounds of metal sulfates to the bath of Fig. 3.1 and applying ac electrolysis the alumina film can be
colored. In this work coloration of the anodic aluminum oxide was done by using a nickel sulfate salt
using a nickel counter electrode.
The composition of the chemical bath was 20 g nickel sulfate, NiSO4, 20 g magnesium sulfate,
MgSO4, 20 g ammonium sulfate, (NH4)2SO4 and 20 g boric acid, H3BO3 in one liter distilled water. The
ammonium sulfate improves the conductivity of the solution, and magnesium sulfate improves the
coloring condition. 100 Boric acid maintains the solution at a pH value of about 7. An ac voltage of 15 V
(current density about 20 mA/cm2) was applied for 4 minutes at room temperature. Metallic nickel
particles of about 300 nm long with a rod shape were grown within the pores of the alumina, one in
each pore, starting to grow from the pore base. 101-103 In addition to the laboratory produced samples,
some commercial nickel pigmented aluminum oxide absorbers obtained from Sunstrip (Sweden) were
analyzed in this thesis. The commercial absorber has a total thickness of about 700 nm with a nickel
pigmented base layer of 300 nm and an unpigmented alumina top layer of about 400 nm. Rolled
aluminum was used as substrate.
Integral Coloration of Samples
Although the two step anodization-coloration has been an inexpensive and successful technique for
production of solar absorbers, further reduction of cost could be achieved by reducing the coating
formation to one step. Direct, or integral coloration of anodized aluminum (99.99 % pure) from a
mixture of organic and inorganic electrolyte acids forms metallic aluminum particles embedded in
alumina matrix (Al-Al2O3). 104-106 Since the particle volume fraction was very low (< 1%), the alumina
had to be thick enough (>10 µm) to change the appearance of the coatings from transparent to a grayish
(brownish) color. A darker alumina film ( about 50 µm thick and with a 0.002 particle volume fraction)
has been reported by anodizing aluminum (99.99 % pure) in a sulfuric acid solution at high current
Tuquabo Tesfamichael
33
density (>100 mA/cm2). 107 The integrally colored anodized aluminum, however, has high thermal
emittance due to the large thickness of the coating and is not feasible for solar absorber applications.
Anodization of aluminum alloys allows the incorporation of alloying elements in the oxide 108
and this has been observed from anodizing commercially available silicon rich Al-Si alloy. This coating
has been proposed 109 for use as a solar absorber but its performance as a solar selective coating was
not investigated. In this report we have investigated the optical properties of integrally colored Al-Si
alloy as a function of oxide thickness. Samples of Al-Si of size 5.5 cm x 3.5 cm and 0.1 mm thick were
cut out from a rolled sheet of the Al-Si alloy. The type of the alloy was AA4047, and contains 11.6
wt. % of silicon, which was the highest content of Si commercially found.
The solution in the bath of Fig. 3.1 was replaced by 1.8 M sulfuric acid, H2SO4 solution and the
samples were anodized at room temperature using a constant anodizing voltage of 15 V dc. An
aluminum plate was used as counter electrode and the anodizing bath was continuously stirred to
minimize local heating. The time of anodization was between 5 and 120 minutes and this produced 1.0
to 17 µm thick films. The aluminum oxide is integrally colored by the silicon particles when forming the
silicon-alumina coating (Si-Al2O3) during the anodization process. The appearance of the coatings
changes from gray to dark with increasing the Si-Al2O3 film thickness. The results are discussed in
section 4.
3.1.2
Spray Pyrolysis
The pyrolytic spray technique which is inexpensive and well suited for large-scale applications is one
of the most suitable techniques for depositing high visible transmission and high infrared reflection (low
thermal emittance) coatings. 110 The basic principle of this technique is to transport and disperse a
solution in the form of an aerosol through nozzles by means of a carrier gas controlled by a flow rate
meter and deposit it onto a heated sample situated in a chamber (See Fig. 3.2). The chamber has an
opening channel to let the byproducts out of the chamber. The temperature of the heater is controlled
by a temperature controller and a thermocouple can be used to measure the temperature at the sample
surface.
The solutions prepared in this work were 2.3 M tin chloride, SnCl4 in alcohol and 2 M
ammonium fluoride, NH4F in water. Each solution was put in separate nozzles and pyrolytically
sprayed simultaneously to a sample held at temperatures between 400 and 500°C. For simplification
only one spray nozzle is shown in the figure. The air flow rates of the SnCl4 and NH4F solutions were
65 l/min and 22 l/min, respectively. The aerosols evaporate and a solid fluorine doped tin oxide
(SnO2:F) film is grown on the substrate. The samples coated were nickel pigmented aluminum oxide
solar absorber (Ni-Al2O3) and the deposition rate was about 60 nm/min at 450°C. The reason for
covering the Ni-Al2O3 absorber is to protect its surface from abrasion and corrosion since it is sensitive
to such degradation mechanisms. However, tin oxide has large refractive index (n ≥ 2) resulting in
significant reflectance in the visible spectrum and thereby reducing the solar absorptance of the
absorber. Thus, a complimentary mechanism such as antireflection is needed to reduce the reflectance of
the surface. This has been performed using dip-coating process as explained below.
34 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
Gas product
Spray solution
Deposition
Chamber
Flow meter
x
Thermocouple
Substrate
Air compressed
Temp.
Control
Heater
Fig. 3.2 Schematic diagram of the experimental set-up for pyrolytic spraying.
3.1.3
Dip-Coating
A solution of silica was prepared in a bath by first mixing water (25 ml), ethanol (90 ml), methanol (80
ml) and a small amount of sulfuric acid (0.4 ml). 111 Then 50 ml of sol and 250 ml of ethanol were
added and used after curing for a few days (appx. 4 days of preparation). The acid stabilizes the sol,
(sol is stable at only high or low pH) and prevents it from aggregation to a thick gel. The aging of the
sol is important in order to give rise to a larger porosity of the antireflection layer. 112 The samples in
section 3.1.2 were immersed into the bath and withdrawn at different rates to produce a silica layer on
the surface of the samples for antireflection. The thickness of the layer was controlled by the
withdrawal speed ranging from 5 to 10 mm/s. A silica (SiO2) layer appropriate for antireflection was
produced from this process. 112 It is to be noticed that antireflection films prepared from a
commercially available colloidal silica sol allows a simple preparation and low cost coatings.
3.1.4
Sputtering
Sputtering is one of the most widely used thin film deposition techniques and is clean compared to
chemical processing methods, where large quantities of chemical waste products have to be handled.
The basic principle of sputtering is to knock out atoms from a source (target) and deposit them on a
substrate. A vacuum chamber containing a low pressure inert gas such as argon can set-up a glow
discharge by applying a sufficiently large voltage between the target (raw material for coating) and the
substrate inside the chamber. Energetic ions can bombard the surface of the target and knock out atoms
or particles which are then transported and deposited on the substrate. Sputtering gives the flexibility
of selecting different substrates and materials to deposit, uses various kinds of reactive gases, and can
also be controlled accurately to make coatings with micro- and multilayer structures. The working
principle and description of sputtering can be found in detail elsewhere. 113,114
Currently, sputtering technologies are also employed for depositing thin film absorber coatings
in large-scale production. Here we mention a roll coating dc magnetron sputtering technique used for
Tuquabo Tesfamichael
35
production of a nickel/nickel oxide absorber (Ni-NiOx) on a rolled aluminum substrate. A Ni target is
sputtered as the substrate loaded with a 1000 m long coil sheet is moving in the vacuum chamber.
Oxygen inlet during the sputtering is designed to give a gradual decrease of nickel content and an
increasing amount of nickel oxide from the substrate to the front surface. This produces a grading in the
optical refractive index through the coating and a graded nickel/nickel oxide composite absorber is
obtained. Meanwhile, an antireflection layer is deposited on top of the graded absorber layer using a
second target in a row. The coating is described in detail by Wäckelgård and Hultmark. 88 The
schematic microstructure of nickel/nickel oxide coating has been shown in Fig. 2.5b. The total thickness
is about 200 nm including the antireflection layer of about 50 nm thickness. This type of absorber was
obtained from Sunstrip (Sweden) and its optical properties were compared with nickel pigmented
aluminum oxide absorber (Ni-Al2O3) obtained from the same industry.
3.1.5
Production of Black Pigment Pellets
Characterization of black pigments used for selective solar-absorbing paints have been performed. Two
types of pigments, namely, FeMnCuOx (Ferro Crop., F-6331) and organic black carbon (Fw2,
Degussa) initially in powder form were obtained. Each of them was mixed with potassium bromide
(KBr) powder, ground in a pearl mill for about five minutes to disperse the pigment and finally pressed
using a load of about 8-tons. Potassium bromide was chosen as matrix for the pigment because of its
low absorptance in the solar wavelength range. The light scattering should also be very low due to the
hard pressure exerted on the KBr powder during the pellet pressing.
The use of 0.1 grams of the ground material in the press produced pellets with a diameter of 13
mm and a thickness of 0.4 mm. The range of pigment concentration was between 0.1 to 2.0 wt. % for
the FeMnCuOx and 0.05 to 1.0 wt. % for the black carbon. These ranges correspond to a volume
fraction of 0.053-1.07 % and 0.076-1.52 %, respectively. The volume fractions were obtained from Eq.
(2.38) using the density of KBr, 2.75 g/cm-3 115, FeMnCuOx, 5.2 g/cm-3 and black carbon , 1.8 g/cm-3.
To get high transmittance, the pigment to binder volume fraction was very low. For comparison a KBr
pellet without pigment was also produced. Since KBr is hygroscopic, precaution was taken to prevent
the samples from being exposed to the environment for longer periods to avoid water absorption that
may affect the results. The samples were then kept in a container with a silica-gel from the start of the
production to the optical measurements.
3.2
High Temperature Accelerated Aging Test
This section is focused on accelerated aging of the nickel pigmented aluminum oxide solar absorber. The
work was divided into two parts: one is oxidation of the nickel particles embedded in the aluminum
oxide matrix (Ni-Al2O3) and the second oxidation of “free” nickel particles (Ni-air) i.e. when the
particles are not surrounded by the alumina matrix.
3.2.1
Oxidation of Nickel Particles in Alumina Matrix (Ni-Al2O3)
Samples of Ni-Al2O3 were placed in a pre-heated oven in air at temperatures of 300, 400 and 500°C.
Each sample was taken out of the oven at different times from 1 to 500 hours. After the oxidation
process the alumina coating was etched for 5 minutes in a bath containing 35 g chromic VI oxide and 20
g H2PO4 at 80°C. The etching does not have a noticeable effect on the nickel and nickel oxide but 5
36 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
minutes was enough to remove all of the porous alumina film surrounding the particles. The nickel rods
are not washed away by this treatment. They remain as free standing rods perpendicular to the surface
loosely attached to the barrier alumina layer. They lean against each other in some areas but they still
adhere to the substrate during the experiment (see Fig. 4.1 in section 4). Great care was taken in
handling the samples otherwise the particles could easily be wiped off.
3.2.2
Oxidation of Nickel Particles in Air Matrix (Ni-air)
The alumina of the Ni-Al2O3 samples was first etched away before starting the oxidation process. The
chemicals used and the process applied for etching were the same as for the Ni-Al2O3 in the previous
section. A Heareus RO furnace connected to a Heareus RE 1.1 temperature control unit was used in the
oxidation experiment (Fig. 3.3).
Thermocouple
Sample
Gas
outlet
end-piece
Glass
tube
Shirnk SS
tube
tube
O 2 inlet
Fig. 3.3 Experimental set-up for oxidation of nickel particles in air matrix (Ni-air). The end piece is
disconnected in this figure.
The furnace consisted of a glass tube of 7 cm diameter and length 50 cm with an air tight end-piece on
both ends. Each sample together with a thermocouple was then mounted at the end of the tube furnace
and connected to a 1 m stainless steel (SS) tube, free to move in and out of the center of the furnace.
After inserting the sample, a high rate flow of oxygen gas (99.99 % pure) was admitted into the furnace
for five minutes to establish a pure oxygen atmosphere after which the flow was lowered to 0.04 l/min.
The sample was then pushed slowly, below 10 °C/min to avoid ignition of the particles, into the center
of the oven for oxidation. Different samples were heated at furnace temperatures 260, 280, 300, 320
and 350°C for oxidation times between 5 minutes to 20 hours. After oxidation the samples were pulled
out slowly (<10 °C/min ) for optical measurements as described in section 3.3.
3.3
Optical and Non-Optical Characterization
3.3.1
Spectrophotometers
Spectrophotometers are frequently used for the investigation of the optical properties of solar
absorbers. Two kinds of equipment are of interest: UV/Vis/NIR spectrophotometers which measure in
the wavelength range of the solar spectrum and the IR spectrophotometers that cover the infrared
37
Tuquabo Tesfamichael
wavelength range. Total and diffuse reflectance and transmittance can be measured using
spectrophotometers equipped with an integrating sphere. Figure 3.4a-b illustrates the position of a
sample for total reflectance (reflectance mode) and transmittance (transmittance mode) measurements
using an integrating sphere. For diffuse reflectance measurements, plate-1 in the reflectance mode is
removed to let the specular reflectance, Rs out of the sphere and Rd is contained in the sphere. The
diffuse transmittance, Td is measured by trapping the specular component of the transmittance, Ts.
This is achieved by replacing plate-2 in the transmittance mode with a black cone to damp the
specularly transmitted light and thus measuring the remaining diffuse quantity. The specular
component is then obtained from the difference of the total and diffuse measurements as in Eq. 2.27
and Eq. 2.30. The interior wall of integrating spheres are coated with almost perfectly diffusing
(Lambertian) and highly reflecting materials. In the solar wavelength range barium-sulfate (BaSO4)
powder and in the IR gold coated walls are usually used. The theory and design of integrating spheres,
spectral measurements and analyses of different kinds of samples, the cause of errors in the
measurements and correction algorithms have been extensively reported in the literature. 116-121
plate-1
plate-1
Sample
Rs
Td
Ts
Rd
Sample
plate-2
(a)
(b)
Fig. 3.4 Optical measurements of a sample using an integrating sphere. (a) For total and diffuse
reflectance (reflectance mode) and (b) total and diffuse transmittance (transmittance mode) measurements.
3.3.2
Optical Characterization
Measurements of total and diffuse reflectance and transmittance for absorbers in the solar and infrared
wavelength ranges were performed. Depending on the type of measurements to be done, different kinds
of spectrophotometers have been used. In the solar spectrum (0.3-2.5 µm), a Beckman UV 5240 and a
Perkin Elmer Lambda 9 UV/Vis/NIR double-beam spectrophotometers with a photomultiplier (0.3-0.8
µm) and PbS (0.8-2.5 µm) detectors have been used. The Beckman instrument was equipped with a
150 mm diameter integrating sphere while the Perkin Elmer had a 60 mm diameter sphere. Both
instruments were used for measurements at near normal angle of incidence. For oblique angle of
incidence a single-beam spectrophotometer built at the Division of Solid State Physics, equipped with
an integrating sphere of size 150 mm and a sample holder in the central of the sphere have been used.
The instrument has a two color detector; a Si detector that measures in the wavelength 0.3-1.1 µm but
is transparent above 1.1 µm is combined with a PbS detector which detects signals between 1.1-2.5 µm.
38 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
The sample holder in the central of the sphere can be rotated so non-normal reflectance is measured
between 5° and 80° angles of incidence using p- or s- polarized light. The measuring routines and
description of the spectrophotometer is found in detail elsewhere. 121 The inner walls of all the above
spheres were painted with BaSO4 and a BaSO4 painted plate was used as a reference.
The solar absorptance, αsol of an absorber is obtained by measuring the total reflectance in the
solar wavelength range and weighting by the solar irradiation using Eq. (2.40). The Beckman instrument
was used for measuring reflectance to determine αsol of Si-Al2O3 and Ni-Al2O3 coatings as reported in
papers I, II and III. The Perkin-Elmer Lambda 9 was used for measuring transmittance and reflectance
to determine scattering and absorption cross-sections for the FeMnCuOx and black carbon pigments
(paper IX) as well as total reflectance of the TSSS paints (paper X). The solar absorptance of the two
commercial absorbers obtained from Sunstrip (Ni-Al2O3 and Ni-NiOx) was measured as a function of
angle of incidence, using the single beam spectrophotometer. Papers VII and VIII contain results
obtained from this instrument.
In the infrared wavelength range a single-beam FT-IR Bomem-Michelson 110
spectrophotometer and a double-beam Perkin Elmer 983 spectrophotometer were used. The FT-IR was
equipped with a Labsphere of 4/5-inch inner/outer diameters, infragold-coated integrating sphere and
could measure total and diffuse reflectance as well as transmittance at near normal angle of incidence.
The instrument had a liquid nitrogen cooled mercury cadmium telluride detector. The Perkin Elmer 983
spectrophotometer had no integrating sphere and could be used to measure only specular reflectance
and transmittance. However, it is equipped with accessories for oblique angle of incidence
measurements. The instrument has a thermocouple detector and dry air can be circulated in the sample
compartment to reduce water and carbon-dioxide absorption during measurements. For both the
instruments gold or aluminum mirrors were used as reference.
The FT-IR instrument was used to measure the total reflectance between 2.0 to 20 µm and
from the measurements, the thermal emittance was obtained by applying Eq. (2.43). Papers I, II and III
contain results obtained from this instrument. The Perkin Elmer 983 spectrophotometer was used for
quantifying the amount of nickel oxide in the annealed Ni-Al2O3 and Ni-air samples (papers IV, V and
VI). This was obtained by measuring the reflectance of p-polarized light at higher angles of incidence
(60°). The measurements were performed between 1500 to 300 cm-1 (6.6-33µm) covering the position
of the longitudinal optical (LO) phonon mode of nickel oxide. Before these measurements, the porous
aluminum oxide matrix for the Ni-Al2O3 samples had been etched away. This was done because
aluminum oxide has strong absorption in the 1000 to 900 cm-1 range due to absorption by the alumina
LO phonon mode 122 which masks the absorption band of the thermally created nickel oxide.
3.3.3
Non-Optical Characterization
X-Ray Diffraction (XRD)
XRD is a well known analysis tool which yields crystallographic information from studying the
interaction of monochromatic X-rays with a periodic crystal lattice. 123 X-ray diffraction measurements
are made by causing a beam of X-radiation to fall onto a suitably prepared specimen and measuring the
angles at which the specific characteristic X-ray wavelength is diffracted. The diffraction angle, θD can
be related to the atomic spacing (or crystallographic information) by Bragg law. 123 For thicker films
Tuquabo Tesfamichael
39
the diffraction peak is recorded at 2θD degrees. There are various XRD configurations and in this work a
conventional Siemens D-5000 powder diffractometer which scans between θD-2θD (degrees) have been
used. Samples of Si-Al2O3 and annealed Ni-Al2O3 coatings were analyzed by rotating the source and
detector at a constant angular speed for angles between 20 and 100 degrees.
Scanning Electron Microscopy (SEM)
When a well-focused electron beam (e-beam) is scanned over a surface of a sample, the interaction
between the electrons and the matter gives the emission of X-rays, Auger electrons, backscattered as
well as secondary electrons. In SEM the signals of greatest interest are, the secondary electrons which
have fairly low energy and the reflected (backscattered) electrons, both give information about sample
topography. Using appropriate detectors, the signals from the surface of the sample can be detected
and then focused on a screen using cathode ray tube (CRT) to reproduce the image. A schematic
diagram of a Scanning Electron Microscope is shown in Fig. 3.5. In general, SEM requires a conducting
sample in a low vacuum chamber but for non-conducting samples a very thin gold-palladium film is
applied to reduce charging effects. SEMs often have a microprobe for energy dispersive analysis by
studying the characteristic X-ray lines for rapid evaluation of elemental constituents. High Resolution
Leo 1550 SEM with field emission gun and Zeiss DSM 960 SEM have been used for surface and
cross-sectional morphologies, particle size and elemental analyses of different absorbing samples. The
samples analyzed were Si-Al2O3 coatings, FeMnCuOx and black carbon pigments and nickel pigmented
aluminum oxide coatings.
Fig. 3.5 Schematic diagram of Scanning Electron Microscopy (SEM), showing the electron column, the
deflection system, and the electron detectors. 124
40 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
3.4
Dynamic Testing of Solar Collectors
In order to evaluate and compare the performance of the two commercial solar absorbers (Ni-Al2O3 and
Ni-NiOx), they have been mounted in two similar collector boxes at Vattenfall’s laboratory at
Älvkarleby (Sweden). The evaluation is according to the principle of dynamic testing, with day by day
variation of the operating temperature 91. The actual output can be determined by measuring the water
flow and the temperature increase over the collector. These measurements together with Multiple
Linear Regression can be used to obtain the collector parameters in the model (see Eq. (2.45)). Angular
dependent performances and possible yearly energy output of each of the two collectors, are planned
to be carried out in the future using MINSUN simulation program. 125
Tuquabo Tesfamichael
4
41
RESULTS AND DISCUSSION
In this section results of the experiment from section 3 and theoretical modeling for the experiments are
discussed. Most of the theoretical models have been introduced in section 2.
4.1
Nickel Pigmented Aluminum Oxide (Ni-Al2O3)
Scanning Electron Microscopy (SEM) pictures of a nickel pigmented aluminum oxide absorber is
shown in Fig. 4.1. The aluminum oxide has been dissolved and nickel particles are freely standing on the
aluminum substrate (Fig. 4.1a). Figure 4.1b shows a few nickel rods that has fallen on the substrate.
The average length of the rods were about 300 nm and from TEM it has been determined that the
particles are approximately 30 to 50 nm in diameter.
(a)
(b)
Fig. 4.1. SEM picture of nickel pigmented aluminum oxide absorber. (a) top view of standing nickel
rods and (b) a few fallen rods. The alumina matrix is etched away for the SEM micrographs. The length
scales, the electron high tension, EHT and microscope working distance, WD are shown in the inset.
The nickel pigmented aluminum oxide solar absorber, was first documented by Andersson et al.
in 1979. 52,126 It has a good optical performance (αsol=0.95 and εtherm=0.12-0.20) but its service life
time can be shortened by too high temperature, humidity or atmospheric pollution such as sulfur
dioxide. 127 The absorber is also sensitive to abrasion. Thus covering the surface with a chemically and
mechanically stable transparent coating can reduce degradation mechanisms. We have applied a
pyrolytically deposited fluorine doped tin oxide coating (SnO2:F), on the surface of the absorber. A
similar coating was previously applied on a black-enameled/steel absorber and has given a good spectral
selective surface for solar collectors. 128 By suitable doping and appropriate substrate temperature one
can increase both the solar transmittance and infrared reflectance of the SnO2 coating. The presence of
oxygen deficiency in the SnO2 coating also gives high infrared reflection. However, due to the large index
of refraction of the transparent oxide, a large amount of the incident light can be reflected. In our work, a
significant increase of reflectance (reduction of αsol ≈4%) occurs as shown by the dotted curve in Fig.
42 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
4.2a. The increase of reflectance in the solar region has been reduced by applying an antireflection
coating of silica (SiO2) which has little or no noticeable effect in the infrared (Fig. 4.2a). The best values
obtained for this experiment after antireflection was αsol=0.94 and εtherm=0.15. This is shown in Fig.
4.2b and compared with a commercially produced Ni-Al2O3 absorber (αsol=0.95 and εtherm=0.14).
1
1
Ni-Al2O 3
Ni-Al O (Commercial)
2 3
SnO2/Ni-Al2 O3
SnO2 /Ni-Al2O 3
SiO /SnO /Ni-Al O
2
2
2
SiO 2 /SnO2 /Ni-Al2 O 3
0.8
3
Reflectance
Reflectance
0.8
0.6
0.4
0.2
0.6
0.4
0.2
0
0.3
1
Wavelength (µm)
10
20
0
0.3
1
10
Wavelength (µm)
(a)
(b)
Fig. 4.2 (a) Reflectance versus wavelength of Ni-Al2O3, SnO2/Ni-Al2O 3 and SiO2/SnO2/Ni-Al2O 3 coatings.
(b) Best values obtained for coatings in (a) as compared with a commercially produced Ni-Al2O 3 absorber.
To be of practical use, an antireflection film for solar collectors must show adequate durability
and should not deteriorate the optical properties significantly with time. Preliminary test results
indicate that SiO2/SnO2/Ni-Al2O3 samples are resistant to high temperatures as well as to corrosion.
Figure 4.3a shows reflectance spectra of one sample after heating at 300, 400 and 500°C, each
temperature being kept for 24 hours. The optical properties of the sample before and after aging at
300°C are found to be the same. With increasing annealing temperature, the reflectance in the solar
region tends to increase and the onset of reflectance shifts toward longer wavelengths. This was also
observed previously for SnO2/Ni-Al2O3 samples.129 An antireflection treated sample was also tested
by immersing it in water containing 8% sulfuric acid for three hours, and the result was compared with
that of an identically treated Ni-Al2O3 sample. In Fig. 4.3b, it is shown that the Ni-Al2O3 surface is
dissolved by the acid and degrades quite severely. The sample with SiO2/SnO2 layer, however,
withstands the acid and the reflectance spectra before and after the acid test are found to be practically
the same. In summary, the silica (SiO2) antireflection layer is found thermally and chemically stable.
43
Tuquabo Tesfamichael
0.6
0.6
High temperature test
0.5
0.5
Ni-Al O
0.4
SiO 2/SnO 2 /Ni-Al2O 3
300 o C, 24 hours
400 o C, 24 hours
0.3
500 o C, 24 hours
Not-heated
0.2
0
2
Wavelength (µm)
2.5
2
3
before
after
0.2
0
1.5
2
Acid test
0.1
1
2
0.3
0.1
0.5
SiO /SnO /Ni-Al O
3
before
after
0.4
Reflectance
Reflectance
2
0.5
1
1.5
2
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.3 Spectral reflectance data taken under accelerated aging tests of SiO2/SnO2/Ni-Al2O 3 samples. (a)
A sample annealed at 300, 400 and 500°C, each temperature kept for 24 hours. (b) Testing in 8% sulfuric
acid solution for 3 hours compared with identically treated Ni-Al2O3 coating. The untreated samples are
also shown for comparison.
Another degradation mechanism of the nickel pigmented aluminum oxide solar absorber is
oxidation of the nickel particles. 130 In order to get information about the durability properties, studies
under conditions of accelerated aging are necessary for an estimation of the service life time of the
absorber. The International Energy Agency (IEA) has outlined a program for accelerated life testing of
commercial solar absorber materials prior to their market introduction. 131 High temperature
degradation is one method used in this program in order to develop models from which the service life
time of the absorber can be estimated. The rate of oxidation of the nickel particles was previously
determined indirectly from the relative decrease of solar absorptance at high temperature accelerated
aging test. 130 In this work we report results on thermal oxidation of laboratory prepared nickel
pigmented aluminum oxide samples and present a method from which the rate of oxidation can be
determined directly from infrared measurements (see section 3 for preparation, oxidation processes and
infrared measurements). The growth rate of the oxide has been analyzed by measuring p-polarized
reflectance at 60° angle of incidence in the wavelength range around the longitudinal optical (LO)
phonon mode frequency of nickel oxide which is around 550 cm-1 (18 µm). 132,133
Figure 4.4 shows reflectance spectra of NiO obtained from annealing of the Ni particles in Al2O3
matrix at a temperature of 500°C. There is no absorption band from the porous Al2O3 (LO-phonon
between 1000-900 cm-1 122) since it has been etched away before the optical measurements. The
reflectance minimum at about 540 cm-1 originates from absorption of NiO in the wavelength range
around its LO-phonon mode. The depth of the minimum increases with increasing time of exposure i.e.
an increasing amount of NiO in the coatings. A similar behavior is seen also for the samples annealed at
300°C and 400°C but with more shallow minima. The absorptance peak height was then determined
and used as a measure of the degree of oxidation.
44 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
1
Reflectance
0.95
time (hours):
0
2
50
200
500
0.9
500 oC
0.85
0.8
1000
900
800
700
600
500
400
300
-1
Wavenumber (cm )
Fig. 4.4 Reflectance spectra (p-polarized light) at 60° incidence angle for NiO obtained by oxidation of Ni
particles in alumina matrix as a function of wavenumber (cm -1). The measured spectra are shown before
and after annealing at 500°C for different times as shown in the inset.
Reflectance spectra of Ni particles oxidized without the Al2O3 matrix, (Ni-air samples) annealed
at 280°C is shown in Fig 4.5a. The oxidation time (hour:min) is shown in the inset and is much shorter
than for Ni particles embedded in Al2O3 (see Fig. 4.4). A similar behavior as in Fig. 4.5a is seen also for
Ni-air samples annealed at 260, 300, 325 and 350°C but with more shallow minima for the lower
temperature and deeper ones for temperatures higher than 280°C at the corresponding oxidation time.
1
1
0.9
0.9
0.85
Ni-Al2 O3 :60 min
time (hour:min):
0:0
0:16
0:39
3:52
10:53
21:12
Reflectance
Reflectance
0.95
280 °C
0.8
Ni-air:10 min
0.7
500°C
0.6
0.75
1000
0.8
900
800
700
600
500
-1
Wavenumber (cm )
400
300
0.5
1000
900
800
700
600
500
400
300
-1
Wavenumber (cm )
(a)
(b)
Fig. 4.5. Reflectance spectra (p-polarized light) at 60° angle of incidence as a function of wavenumber
(cm-1). (a) Nickel particles oxidized without Al2O 3 matrix at 280°C for annealing time (hour:min) is drawn
together with unoxidized Ni particles (solid line). (b) Comparison between free nickel particles (Ni-air) and
particles embedded in alumina matrix (Ni-Al2O 3) heated at 500 °C for 10 min and 60 min, respectively.
45
Tuquabo Tesfamichael
Figure 4.5b shows spectra of two samples heated at 500°C for oxidation times as shown in the inset
when the Ni particles are free and when they are kept intact in the Al2O3 matrix. Comparing the
oxidation of the particles, it is clear that the alumina acts as a barrier for rapid oxidation. Moreover, the
reflectance minimum obtained from the two oxidation processes is found to be different i.e. at 540 cm-1
for the Ni-Al2O3 and 580 cm-1 for the Ni-air.
In order to determine the degree of oxidation, modeling for the NiO absorptance peak has been
performed using the Berreman relation 134 and the Bruggeman EMT 24. From the SEM and TEM
analyses, oxidation takes place at the end of the nickel rods facing the pore opening. If oxidation takes
place also around the other surfaces of the rods, the amount of oxide must be too small to be detected
by TEM. The surface of the treated samples can then be considered as a thin NiO film on top of the
metallic Ni particles as shown by the schematic diagram in Fig. 4.6a. Since it is the top NiO which gives
rise to the LO-phonon mode absorption, an equivalent system regarding this absorption is found by
omitting the unoxidized part of the nickel rods and just treating the film as a single inhomogeneous NiO
layer on a metallic substrate (Fig. 4.6b). This consideration helps in the modeling, using the Berreman
relation for a thin dielectric film, for which the p-polarized reflectance loss is proportional to the film
thickness, d in the wavelength range of the LO-phonon mode. Bruggeman model (Eq. 2.15) was used to
calculate the effective dielectric function of the inhomogeneous NiO film. The inhomogeneties are
considered to be NiO particles in an air matrix (NiO-air). The optical constants of NiO and Al have
been taken from the literature 132,135.
NiO
Ni
NiO
b
a
Al
Al
Fig. 4.6 (a) A cross-sectional view illustrating front surface oxidation of nickel rods and (b) a simplified
diagram to describe the effect of the phonon mode by considering a single layer of the oxidized part of the
nickel rods on aluminum that was used in the modeling.
Figure 4.7 shows calculated reflectance as a function of wavenumber (cm-1) for different film
thicknesses. The shape of the NiO is taken to be similar to that of the Ni rods and hence an appropriate
depolarizing factor Lj as defined in Eq. (2.14) is used. A sharp reflectance minimum around 510 cm-1
was obtained for a cylindrical nickel oxide geometry. By varying the depolarization factor the width and
depth of the reflectance minimum can be changed to some extent. In this calculation, the particle volume
fraction of NiO was taken to be the same as for the nickel rods, which is f=0.3, but the volume
expansion upon oxidation of Ni to NiO is about 1.67 and this increases the volume fraction of NiO. It
has been observed from the calculation that with an increase of the filling factor of NiO the position of
the reflectance minimum is shifted towards a higher wavenumber. Experimentally, the minimum
appears at a higher wavenumber (540 cm-1, Ni-Al2O3 oxidation) and is also broader, which may be
explained by additional surface mode absorption produced by particle shape effects 136, than the
calculated ones. For comparison, a calculated reflectance spectrum of a 30 nm solid nickel oxide film on
aluminum substrate is also shown in Fig. 4.7. A sharp and much deeper reflectance minimum at a higher
46 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
wavenumber than the corresponding one of the porous film is obtained. The important results of the
calculations are that the reflectance in the minimum decreases with increasing NiO film thickness just as
we found experimentally and the oxide thickness, d of the absorber has been validated by the modeling
using the Berreman relation.
1
Reflectance
0.95
0.9
d (nm):
0
30
50
70
30 (sf)
0.85
0.8
f = 0.3,
L = 0.1, 0.45, 0.45
j
0.75
0.7
700
650
600
550
500
450
400
350
-1
Wavenumber (cm )
Fig. 4.7 Calculated spectral reflectance for p-polarized light at 60° angle of incidence for given filling (f)
and depolarization (Lj) factors and varying film thicknesses, d. For comparison the reflectance spectra of a
30 nm isotropic solid film (sf) is also displayed.
If the oxide thickness d has a general time dependence and an Arrhenius temperature dependence
then it can be written as:
d = exp( − Ea / k BT ) ⋅ f (t ) ,
(4.1)
where kB is the Boltzmann constant and Ea is the activation energy. The thickness, d can then be
approximated from measurements of the p-polarized reflectance, Rp by considering the Berreman
relation 134:
1 − Rp ∝ d .
(4.2)
The best resolution for the determination of the film thickness, is expected at the LO-phonon frequency
with, the largest reflectance losses. The unity in Eq. (4.2) has been modified by the p-polarized
reflectance value of the reference of the unoxidized nickel particles, Rpref , since the metal particles also
contribute with a background level of absorptance. 133 The thickness is then proportional to the
absorptance peak height:
Rpref − Rp ∝ d .
(4.3)
The relation between the measured reflectance and oxide thickness now makes it possible to quantify
the thickness of the thermally created nickel oxide.
47
Tuquabo Tesfamichael
From Eq. (4.1) the logarithm of the oxidation time at a specific thickness value, between two
different temperatures T1 and T is given by:
 1 1
ln f (t ) − ln f (t1 ) ∝ −( Ea / k B ) −  ,
 T1 T 
(4.4a)
and for the function f(t)=t the above equation can be written as:
 1 1
ln(t ) − ln(t1 ) ∝ ( Ea / k B ) −  .
 T T1 
(4.4b)
From Eq. (4.4), we can see that the logarithm of the time dependence of the oxide thickness, ln(t) is a
constant translation from ln(t1) for any given thickness d at temperature T. Similarly, the absorptance
peak height of Eq. 4.3 can be expressed by 133 :
ln( Rpref − Rp ) ∝
Ea 1
( ).
kB T
(4.5)
The oxidation rate of nickel can, therefore, be determined from Eq. (4.5), by extracting the measured
reflectance at the wavelength of its minimum value for each temperature and plotted against the
oxidation time along a time axis. The isotherms in Eq. (4.4) or Eq. (4.5), should therefore fall onto a
single curve in a double logarithmic plot by translating the temperature along the time axis since the
translation depends on the temperatures only. This is the master plot technique that have been applied
to the measured reflectance data.
From the power-law approximation in the master plot, it is seen that there were fairly large
deviations from a single curve for both the Ni-Al2O3 and Ni-air oxidation processes. In the case of NiAl2O3 the exponential range (kinetic exponent) was between 0.08 to 0.19 for the temperatures 300 to
500°C and this is much lower than for the Ni-air oxidation process which was between 0.52 to 0.63 for
the temperature range 260 to 350°C. Kinetic exponents smaller than the value 0.5 for parabolic law
behavior are usually found and have been explained as due to a decreasing number of available grain
boundaries 137,138 because of grain growth observed during oxidation 137,139,140 . It then appears that
diffusion in the matrix surrounding the metal particles is of prime importance for the durability of the
solar absorber coatings. The low observed kinetic exponents of the oxidation of Ni particles situated in
the alumina matrix (Ni-Al2O3) are found to be consistent with the previous reports. 130,141 It should be
noted that the nickel particles in the porous alumina are not totally surrounded by the matrix. An even
more improved stability is expected for metal-insulator coatings, where the particles are completely
surrounded by a dielectric matrix such as the very stable Mo-Al2O3 based coating that was previously
investigated in detail. 142 In order to evaluate the life time of the nickel pigmented aluminum oxide, an
evaluation mechanism has been presented 131 and hence the activation energy of the particles should
first be determined.
The activation energy can be found by plotting either the shifts of the logarithms of the different
isotherms (ln(t)-ln(t1)) or ln( Rpref − Rp ) versus inverse temperature, 1/T using Eq. (4.4) or Eq. (4.5),
respectively. The slope of the curve then gives the activation energy, Ea. Figure 4.8 shows ln(t)-ln(t1)
versus 1/T for the Ni-air oxidation process and an approximated apparent activation energy of 1.73 eV
48 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
was found from the linear fit. For the Ni-Al2O3 the activation energy was estimated to be about 1.4 eV
but the result could be uncertain since the value of the activation energy below and above the Curie
temperature is reported to be different. 130,143
6
5
ln(t)-ln(t1 )
4
Ea= 1.73 eV
3
2
1
0
16
17
18
19
Inverse temperature, 10 4/T (K-1)
Fig. 4.8. Plot of ln(t)-ln(t1) against inverse temperature for annealing temperatures between 260-350°C
and time, t=16 min. The activation energy is found from the slope of the linear fit to the data.
After determining the activation energy using the above methods, then the actual service life time of
solar absorber, tservice, under a given operating condition, can be estimated using: 127
E  1
1 
tservice = ttest ⋅ exp  a 
−
 ,
 k B  Top Ttest  
(4.6)
where, Top is average operating temperature of the absorber (collector), Ttest is the testing temperature,
and ttest is the time needed to reach a certain extent of degradation for the optical performance of the
absorber during the temperature Ttest. From the IEA criteria, the service life time of a collector is defined
as the time when the optical performance of the absorber is reduced by 5 % of its original value. The
effect of high temperature on the degradation of the nickel pigmented aluminum oxide absorber was
found to be small since the presence of the alumina around the nickel particle decreases the oxidation
rate. If degradation was caused by temperature only, then about 25 years service life has been estimated
for this type of coating at stagnation temperature, Top=290°C. 127 It is important to mention here that,
the Ni-Al2O3 absorber is severely degraded in condensation test 127,144 and hence covering the absorber
by the transparent oxide mentioned before can minimize this effect. Condensation, on the other hand,
may not be a major problem if the absorber is placed in a well ventilated and rain tight collector box.
4.2 Anodized Al-Si Alloy (Si-Al2O3)
Composite coatings of Si have been produced by co-sputtering of CaF2 with silicon on an aluminum
mirror. Also a paint consisting of silicon particles dispersed in thick silicone binder deposited on
Tuquabo Tesfamichael
49
stainless steel has been reported. 145,146 The optical behavior can be considered as being similar to that
of the parent semiconductor with the same energy gap. But the refractive index is dependent on the
concentration of the Si particles in the coating and is controlled by the volume fraction of particles. 7
Silicon-alumina composite coatings can be produced by anodizing silicon rich aluminum alloys.
We have investigated the optical properties of anodized Al-Si alloy (11.6 wt% Si) (see section 3 for
sample preparation). The anodization of the sample provides a Si-Al2O3 composite coating growing at a
rate of 0.14 µm per minute. From the θD-2θD, X-ray diffraction analysis, sharp diffraction patterns for
silicon and aluminum (substrate) were detected but not for aluminum oxide. Hence, the alumina (Al2O3)
is found to be amorphous and is integrally colored by the crystalline Si particles during the anodization
process. The shape of the Si particles is irregular and their sizes vary between 1 and 10 µm with an
average size of about 2 µm as is shown from the Scanning Electron Microscope (SEM) in Fig. 4. 9.
Fig. 4.9 Scanning Electron Microscopy (SEM) picture of Si-Al2O 3 coating produced by anodizing Al-Si
alloy for two hours.
Figure 4.10a shows the measured reflectance of the Si-Al2O3 coatings for different thicknesses
between 1.0 to 10 µm in the wavelength range 0.3 to 20 µm. Thick porous plain aluminum oxide has a
broad and deep absorption band in the region of its lattice vibration modes between 10 to 20 µm as seen
in Fig. 4.10a. The anodization also produces compounds involving hydrogen, such as aluminum
hydroxide, oxyhydroxide, crystal water and sulfate anions causing absorption in the infrared wavelength
range. From the figure the characteristic absorption bands of O-H-groups at 3.6 µm and 6.2 µm 147, and
sulfate anions in the wavelength range 9 to 13 µm, 148 can be observed. These features of the
absorption bands are found from anodized plane alumina (Al2O3) but the bands are deeper and the
reflectance between band regions, 3 to 8 µm, is higher than the Si-Al2O3 coating.
The intrinsic bandgap of crystalline silicon is 1.12 eV which implies that its optical absorption
covers the solar spectrum up to 1.11 µm. Impurities, dislocations and non-crystallinity create electron
states within the bandgap. The Si particles contain defects and impurities introduced during the
manufacturing of the Al-Si, causing the absorption to extend to wavelengths longer than the bandgap
edge (Fig. 4.10a). It has been found in earlier work that defects can be removed by annealing, thereby
50 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
lowering the infrared absorption 149. For that reason one sample was annealed at 500°C for 24 hours
and the absorptance in the near infrared decreased by 0.03 and the thermal emittance by 0.05.
1
Anodizing time:
0 minutes
5 min. (1.0 µm)
30 min. (5.0 µm)
60 min. (10 µm)
Total Reflectance
0.8
0.6
0.4
0.2
0
0.3
1
Wavelength (µm)
10
Solar absorptance, Thermal emittance
1
0.8
Solar absorptance
0.6
Thermal emittance
0.4
0.2
0
0
5
10
15
20
Coating Thickness (µm)
(a)
(b)
Fig. 4.10 (a) Total reflectance of anodized Al-Si alloy as a function of wavelength between 0.3 and 20 µm
for different anodizing times (film thickness) and (b) solar absorptance and thermal emittance, calculated
from the measured reflectance, as a function of coating thickness.
The optical measurements showed a continuous decrease of the reflectance, i.e. an increase of
absorptance, with increasing film thickness. The Si-Al2O3 coatings are opaque-grey and become darker
for a larger thickness, a higher silicon content and smaller particle size 150. A maximum solar absorption
of 0.85 was achieved for 13 µm or thicker Si-Al2O3 coatings (Fig. 4.10b). The deep absorption band of
alumina above the wavelength of 10 µm (Fig. 4.10a) is the main cause of the very high thermal
emittance as apparent in Fig. 4.10b. This result can be compared with that of the previous work of the
composite coatings obtained from co-sputtering or paint with Si pigment. 145,146 A solar absorptance
of 0.70 and a thermal emittance of 0.10 at 300°C was obtained from a 5 µm thick Si-CaF2 coating. For
the paint coating a solar absorptance of 0.83 and a thermal emittance over 0.70 have been reported. The
high thermal emittance of the paint was mainly due to the large thickness of the paint. In our
experiments, we have used a low concentration of silicon (f=0.138) because that was the highest one
commercially found. It was believed that such a low concentration of Si would be far from the optimal
one for a selective absorber coatings. Therefore we used a theoretical model to calculate the optical
properties as a function of silicon content, particle size and oxide thickness searching for a feasible SiAl2O3 coating for solar selective absorbers.
The optical properties of the Si-Al2O3 coatings have been modeled using the four flux model,
since the particles are of the order of or larger than the wavelength of the incoming light. The
expressions for the total reflectance given in Eq. (2.27) was used to model the optical properties of the
Si-Al2O3 films and the calculated results are compared to spectroscopic measurements. There is poor
agreement between measurements and calculated reflectance when optical constants of pure Si is used.
51
Tuquabo Tesfamichael
The predicted reflectance is high in the near infrared wavelength, as shown in Fig. 4.11a. It is known
that dielectric functions depend on the type of scattering mechanisms which influence the mean free
path of the electron in semiconductors. Contributions to scattering can be originated from defects such
as grain boundaries, dislocations, inhomogeneties and impurities. Hence the optical constants of Si has
to be modified to account for the contribution from these effects. Our model is simplified and assumed
to take into account only Al-doping of silicon introduced during the production of the Al-Si alloy. The
simplest approach to describe the contribution of the impurities to the optical properties are by using
the Drude model with a plasma frequency, ωp as a fitting parameter. The frequency dependent real, εr
and imaginary, εi dielectric functions of this additional contribution to the dielectric function of the pure
Si are given by:
ω p2 (τ ′)2
ε r (ω ) = 1 −
,
1 + ω 2 (τ ′)2
(4.7a)
ω p2τ ′
,
ε i (ω ) =
ω [1 + ω 2 (τ ′)2 ]
(4.7b)
where τ' is the relaxation time of silicon.
1
1
-15
hω p = 0.37 eV,γ =2.9, d=17 µm τ 0' =10 s
No Drude
correction
0.8
0.5
-13
R
0.6
1/0
Total Reflectance
Total Reflectance
τ'=1.6x10 s
exp
τ ' =τ' (ω)
r
x
0.4
h ω =0.45 eV, γ =3.7, d=13 µm
p
0.5
1/0
h ωp =0.49 eV, γ =2.5, d=10 µm
0.5
1/0
h ωp =1.04 eV, γ =7.1, d=5 µm
0.2
0.5
0
0.3
0.4
0.6
0.8
1
Wavelength (µm)
3
0
0.5
1
1.5
2
2.5
3
Wavelength (µm)
(a)
(b)
Fig. 4.11 Total calculated (lines) and experimental (circle) reflectance spectra of Si-Al2O 3 film on
aluminum substrate as a function of wavelength. (a) For 17 µ m thick film. (b) For different film
thicknesses, d with optimal fitting parameter values of each film as shown in the inset. For all the films, τ0'
converges to 10-15 s.
The modified optical constants of Si improve the calculated results by lowering the reflectance in the
near infrared wavelength range, as shown by the dashed curve in Fig. 4.11a. There is a discrepancy
between calculation and experiment and hence further calculation was performed. Theories for
frequency dependent ionized impurity scattering suggested that, the impurities act as scattering centers
thus decreasing the relaxation time, τ'. 151,152 It is, therefore, reasonable to consider a frequency
52 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
dependent relaxation time, τ'=τ'(ω) considering the incorporation of ionized Al impurities in the Si
during the manufacturing of the alloy. Our calculation is based on the expression outlined by Gerlach
151,152 since it gives a simplified approach. It can be shown that for most scattering mechanisms in
semiconductors the influence on the optical properties can be described by a simple frequency
dependent power law as shown in Eq. (4.8). For frequencies between the plasma frequency and the
energy gap, the relaxation time due to the presence of charged impurities is proportional to ω3/2 152 and
we write it as Aω3/2. Here A is a proportionality constant which decreases with the ionized impurity
concentration, and the atomic number of the impurities. The expression for the total relaxation time is
then given by:
τ ′(ω ) =
τ 0′
,
1 + γ (ωτ 0′ ) −3 / 2
(4.8)
where,
γ =
(τ 0′ )5 / 2
.
A
(4.9)
Using τ'0 and γ as fitting parameters in addition to ωp, a very good agreement is obtained as displayed
by the circles in Fig. 4.11a-b. The values of the fitting parameters are displayed in the inset. The model
fits well for films of the order of or larger than 5 µm. As expected, there is no good agreement for films
thinner than 5 µm since the film thickness is comparable to the particle size and the four flux model is
not applicable.
The model leads to an understanding of the absorptance of the Si particles with variation of
particle size and concentration as well as film thickness. It is well known that the degree of absorption
by a particle which is small compared to the measured wavelength is proportional to its volume. As the
particle size increases, however, the absorption becomes proportional to the particle surface. It means
that there is an optimal particle size which leads to the highest absorption for a given film thickness and
particle concentration, as shown in Fig. 4.12a.
1
1
Solar Absorptance
0.8
0.6
Optimum Solar Absorptance
Particle volume fraction
0.01
0.10
0.20
0.25
0.30
0.4
0.2
Film thickness: 5.0 µm
0
0.001
0.01
0.1
1
Particle Radius (µm)
10
0.9
0.8
0.7
0.6
Film thickness (µm):
0.5
1.0
5.0
10.0
0.4
0.3
0.2
0
0.04 0.08 0.12 0.16
0.2 0.24 0.28 0.32
Particle Volume Fraction
(a)
(b)
Fig. 4.12 Calculated solar absorptance of Si-Al2O 3 films as a function of (a) particle radius for different
particle volume fractions of a 5.0 µm thick film and (b) particle volume fraction at different film thicknesses
using optimum particle radii of each film.
Tuquabo Tesfamichael
53
As the particle concentration increases, the optimal particle size increases and for higher particle
volume fractions it approaches a constant value. The resulting optimum solar absorptance as a function
of particle volume fraction and film thickness using the optimal particle size is shown in Fig. 4.12b. For
a high concentration of silicon of sub-micron particle size, a solar absorptance around 0.90 can be
achieved from a thick film (~10 µm) but as discussed before the thermal emittance is high. For a thinner
film of 1 µm thickness, the infrared emittance is reduced to about 0.27 in the ideal case of smooth
surfaces but the solar absorptance is lower, only 0.70. In short, for Si-Al2O3 coatings there is no
thickness range with high solar absorptance and at the same time low thermal emittance, which indicates
that the coating is not a candidate for selective solar absorbers.
4.3
Angular Performance of Selective Solar Absorbers
4.3.1
Angular Solar Absorptance
The optical characterization of solar absorbers for thermal solar collectors is usually performed by
measuring spectral reflectance at near normal angle of incidence and calculating the solar absorptance
from the measured reflectance. The solar absorptance is, however, a function of the angle of incidence of
the light impinging on the absorber. In this section angular solar absorptance of two types of
commercial selective solar absorbers; nickel-pigmented aluminum oxide (Ni-Al2O3) and sputtered
nickel/nickel oxide (Ni-NiOx) coatings are discussed. Both coatings contain particles of nickel but they
differ in microstructure (particle shape and distribution) as well as coating thickness, d. In section 4.1,
SEM pictures of a Ni-Al2O3 absorber have been shown (Fig. 4.1) and its microstructure has been
discussed. For the Ni-NiOx absorber, top and cross sectional views of the coating using Transmission
Electron Microscopy (TEM) were investigated. It was observed that the coating consists of nano-sized
grains compactly packed in the absorbing base layer and less densely as columns in the antireflection
layer. It was beyond the resolution of the instrument to analyze the grain composition in order to
determine the nickel and nickel oxide content in a depth profile. Schematic diagrams of both types of
absorbers have been shown previously in section 2, Fig. 2.5.
In order to determine the angular solar absorptance of the two absorbers, reflectance
measurements at different angles of incidence have been performed (see section 3 for optical
measurements). Figure 4.13 presents p- and s polarized spectral reflectance (Rp and Rs) of the Ni-Al2O3
coating as a function of wavelength between 0.3 to 2.5 µm for different angles of incidence from 5 to
80°. For clarity we have shown some selected angles of incidence. Due to the coating thickness, optical
thin film interference within the measured wavelength range is inevitable. 87 The interference maxima
and minima become very pronounced at high angles of incidence. A small shift of the maxima and
minima to shorter wavelengths can be noticed for the reflectance curves from 50 to 80°. This is because
the layer at higher angles of incidence corresponds to a coating with thinner effective thickness, which is
a very characteristic behavior of optical interference coatings. 153 Another feature of thin film
interference is that reflectance minima and maxima do not occur at the same wavelengths for p- as for s
polarized light. 153 This effect is also clearly seen in the curves of high-angle spectral reflectance in Fig.
4.13.
54 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
0.7
0.7
80°
0.6
Ni-Al2 O3
Ni-Al2 O3
0.6
Total Reflectance
Total Reflectance
75°
0.5
80°
Rp
0.4
75°
0.3
70°
0.2
0.5
Rs
70°
0.4
0.3
50°
0.2
5°
5°
0.1
0.1
50°
0
0
0.5
1
1.5
2
0.5
2.5
1
Wavelength (µm)
1.5
2
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.13 Total reflectance (a) Rp and (b) R s for Ni-Al2O3 coating as a function of wavelength in the solar
spectrum recorded at different angles of incidence from near normal to 80°.
The p- and s-polarized spectral reflectance of the Ni-NiOx coating between the wavelengths 0.3
to 2.5 µm for different angles of incidence are shown in Fig. 4.14. Here the interference pattern is
suppressed by having a graded-index layer with an antireflection coating on top. The antireflection layer
is necessary in order to reduce front surface reflection. 88
0.8
0.7
0.8
Ni-NiOx
0.7
80°
Rs
75°
0.6
0.5
R
Total Reflectance
0.6
Total Reflectance
Ni-NiOx
p
0.4
80°
0.3
75°
0.2
70°
70°
0.4
50°
0.3
0.2
5°
50°
0.1
0.5
0.1
5°
0
0
0.5
1
1.5
2
Wavelength (µm)
2.5
0.5
1
1.5
2
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.14 Reflectance (a) R p and (b) R s for Ni-NiOx coating as a function of wavelength in the solar
spectrum measured at different angles of incidence from near normal to 80°.
55
Tuquabo Tesfamichael
When comparing the spectral angular reflectance of the two types of absorbers it is found that
thin film interference patterns dominate the spectral behavior of the two-layer structured Ni-Al2O3
absorber while the graded Ni-NiOx absorber has smoother reflectance curves. It is known that p- and s
polarized reflectance at near normal are the same and this, as expected, has been observed for both the
Ni-Al2O3 and Ni-NiOx coatings. As the angle of incidence increases the p- and s- curves split. At higher
angels of incidence, Rs was found to be higher than Rp but due to the enhanced interference effects, in
the case of the Ni-Al2O3 coating only, the p- polarized reflectance was also higher than the s- ones in
certain wavelengths intervals.
The average reflectance of the p- and s- polarized reflectance given by
R(λ ,θ ) =
[
]
1
⋅ Rp (λ ,θ ) + Rs (λ ,θ ) ,
2
(4.10)
over the measured wavelength range is observed to be larger for the Ni-NiOx than for the Ni-Al2O3
coating at higher angles. Using the measured results of the two coatings, the angular solar absorptance
was determined from Eq. (2.40), where R(λ,θ) is replaced by Eq. (4.10). The solar absorptance of the
Ni-Al2O3 absorber is constant over a wide range of angles of incidence. It absorbs about 0.95 of the
solar radiation from near normal up to 50° but the absorptance decreases steeply to about 0.70 when
approaching 80° as shown in Fig. 4.15. The solar absorptance of the Ni-NiOx absorber decreases
gradually from near normal up to 40° and beyond this angle it drops steeply (Fig. 4.15). The solar
absorptance of the Ni-NiOx absorber begins to decrease at lower angles as compared with the Ni-Al2O3
absorber. The angular solar absorptance at higher angles of incidence is significantly different for the
two types of coatings.
1
0.95
Experiment
Solar Absorptance
0.9
0.85
0.8
Ni-Al O
0.75
Ni-NiOx
2
3
0.7
0.65
0.6
0
20
40
60
80
Angle of Incidence (degree)
Fig. 4.15 Solar absorptance of Ni-Al2O 3 and Ni-NiOx absorber coatings against angle of incidence from 5
to 80° obtained from the results of Figs. 4.13 and Fig. 4.14 using Eq. (2.40).
We have already shown that the solar absorptance decreases with increasing angle of incidence.
A significant amount of solar absorptance can be gained at higher angles of incidence due to surface
roughness of the coatings. As mentioned in section 3 rolled aluminum substrates were used for the two
56 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
absorbers. The rolling creates parallel grooves in the aluminum surface, which scatter the reflected light
in directions perpendicular to the direction of the rolling grooves. 120 This one-dimensional texture
introduces orientation dependent reflectance, i.e. orientation dependent solar absorptance. A noticeable
difference in solar absorptance at higher angles was obtained when the groove orientation was
perpendicular to the plane of the incident light as compared with parallel oriented grooves for both
types of absorbers (see also paper VII). It is therefore advantageous to install a solar collector with
grooves of the absorber in the north-south direction in order to gain more solar energy in the mornings
and afternoons.
We have also performed theoretical modeling of the solar absorptance as a function of angle of
incidence for the two absorbers. The reflectance calculations were based on 2 x 2 matrix technique using
a surface impedance and admittance approach 154 and the Fresnel amplitude coefficients were calculated
for each interface in a multi-layer stack of thin films for different angles of incidence between 5 to 80° in
the wavelength interval 0.3 to 2.5 µm. The modeling included the calculation of effective optical
constants for two component inhomogeneous materials for a given particle shape of appropriate Lj (Eq.
2.14) by use of Bruggeman effective medium model (Eq. 2.15). The surfaces were assumed to be
smooth and the effect of surface roughness on absorptance, polarization or coating interference was not
considered. The optical constants of nickel, nickel oxide, alumina and the aluminum substrate were
taken from the literature.132,135,155,156
When the Ni-Al2O3 was modeled, we considered two layers of inhomogeneous media: a base
layer of thickness d2=300 nm with nickel rods in alumina and a top unpigmented porous alumina layer
of thickness d1=200 nm. The nickel rods and the air filled pores are idealized in the model to be
cylinders with the long axis perpendicular to the sample surface. The volume fraction, f of the air-pore
in the top layer of the coating was assumed to be the same as that of the nickel particles in the base
layer, f=0.3. From the calculated reflectance we obtained the solar absorptance for each angle of
incidence. The calculated solar absorptance decreases with increasing angle of incidence similar to the
measured results. Since the absolute values of the calculated angular solar absorptance are lower than
the measured ones, we have chosen to present the angular solar absorptance normalized to its nearnormal value. As shown in Fig. 4.16, the calculated normalized solar absorptance models the
experimental result quite well. The calculated solar absorptance remains almost constant over a wide
range of angles of incidence with maximum solar absorptance around 40° and drops steeply beyond
60°, similar to the experimental data. The existence of this maximum is due to the more pronounced
interference effects of the ideal model coating.
Tuquabo Tesfamichael
57
Normalized Absorptance
1
0.9
Ni-Al 2O3 :
Calculated
Experiment
0.8
Ni-NiO :
0.7
x
Calculated
Experiment
0.6
0.5
0
20
40
60
80
Angle of Incidence (degree)
Fig. 4.16 Calculated and experimental normalized solar absorptance of Ni-Al2O3 and Ni-NiOx coatings as
a function of angle of incidence from 5° to 80°.
The Ni-NiOx coating was modeled by considering a single graded-index structure of spherical
nickel particles in a nickel oxide matrix. The total thickness which was taken to be about 240 nm was
divided into eight equally thick sub-layers. The content of nickel in the sub-layers was assumed to
increase when going from the front surface to the substrate. For best fit to the experimental reflectance,
the filling factor was found to be greater than 0.6 at the substrate-film interface and zero at the film
surface. The composition of the coating at the front surface is considered to consist of homogeneous
nickel oxide and hence the porosity was not modeled as it did not improve the fitting. There is no
significant difference in the results when the numbers of stratified layers exceed eight. From the
reflectance we calculated the solar absorptance for each angle of incidence. The solar absorptance is
normalized to the value at near normal and the calculated results model the experiment well, as shown in
Fig. 4.16.
In order to sort out the key features that govern the angular behavior of solar absorptance of the
selective absorbers, we have also made a thorough theoretical investigation for different types of
microstructures. The various microstructures were determined by varying, the shape, Lj and volume
fraction, f of the particles inside the matrix as well as the thickness, d and layer structure of the
composite coating. From this study, it was found that the difference in particle shape (cylindrical or
spherical) has no significant effect on the angular solar absorptance. The main effect was observed from
the type of layer structure (double-layer or graded-index layer) of the composite coatings as presented
in paper VII. As seen from the experimental and theoretical results, the solar absorptance of the two
types of absorbers at higher angles of incidence is significantly different. A higher high-angle solar
absorptance is obtained for the nickel-pigmented aluminum oxide coating than for the sputtered
nickel/nickel oxide coating and this is found to be due to thin film interference effects which cannot be
achieved from a graded-index thin film coating since the interference patterns is suppressed by the
graded index layer and the antireflection film on top.
58 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
4.3.2
Angular Optical Efficiency
Another way of characterizing absorbers in a system of solar collectors is the use of a model that
considers the effect of the angle of incidence of the radiation reaching the absorber. For flat plate solar
collectors, the angular optical performance is often modeled with an incident angle modifier, Kτα(θ) (Eq.
(2.41)). For an absorber without cover Eq. (2.41) can be modified as: 157
c
1
Kτα (θ ) = 1 − b0 
− 1 ,
 cosθ 
(4.11)
where c is an additional parameter specific for each type of absorber and bo (incidence angle modifier
coefficient) as was defined in Eq. (2.41). Equation 4.11 has been used to model the experimental angular
solar absorptance of the two types of commercial absorbers. As shown in Fig. 4.17, the experimental
results are fitted quite well. Since the two absorbers have different absorptance at higher angles, the
fitting coefficients differ considerably. The nickel pigmented aluminum oxide has b0= 0.017 and c =1.8,
while the sputtered nickel/nickel oxide absorber has b0= 0.057 and c =1.2. Both b0 and c are found to
be important parameters in order to fit to the angular solar absorptance of unglazed absorbers.
1
0.9
Ni-Al2O 3:
Incident Angle Modifier
Normalized Absorptance
1
Experiment
Fit:
b 0=0.017, c=1.8
0.9
0.8
Ni-NiO x:
Experiment
Fit:
b 0=0.057, c=1.2
0.7
Ni-Al2O 3:
0.8
(τα)/(τα)5°
0.7
Fitted:
b0 =0.11, c=1.12
0.6
Ni-NiO x :
0.5
(τα)/(τα)5°
Fitted:
b0 =0.13, c=1.05
0.4
0.3
0.6
0
20
40
60
Angle of Incidence (degree)
80
0
20
40
60
80
Angle of Incidence (degree)
(a)
(b)
Fig. 4.17 (a) Experimental normalized solar absorptance for Ni-Al2O 3 and Ni-NiOx absorbers as a function
of angle of incidence as fitted using Eq. (4.11). (b) Optical performance of the absorbers in (a) when they
considered to have a glass cover. In both of the figures the fitting parameters are displayed in the inset.
Most solar collectors have some kind of cover glazing and the absorbed radiation is the result of
the combined effect of the absorber and the cover. Figure 4.17b shows the transmittance-absorptance
product, (τα)θ/(τα)5°, for the two types of absorbers at different angles of incidence normalized to the
near normal angle of incidence (θ=5°). In the calculations the transmittance of a 4 mm thick low-iron
glass taken from reference 15 was used. The experimental results were fitted using the incident angle
modifier expression given in Eq. (4.11) and the fitting parameters are shown in the inset of Fig. 4.17b.
From the figure we observe that the exponent, c for both absorbers approaches unity and hence the
59
Tuquabo Tesfamichael
original Eq. (2.41) can be applied. This shows that the glass cover has a large impact on the optical
performance of the collector at higher angles of incidence. Using the optical measurements obtained in
this work, an investigation of collector output for glazed and unglazed systems using dynamic collector
testing (Eq. (2.45)) 91 is planned for the future.
4.4
Selective Solar Absorbing Paints
The characterization of the optical properties of two types of pigments, namely, FeMnCuOx and black
carbon (section 4.4.1 and 4.4.2, respectively) and thickness sensitive solar selective paints (section
4.4.3) produced from these pigments are discussed. The effective volumetric cross-sections defined in
section 2 (Eq. 2.37) have been determined from spectral reflectance and transmittance measurements in
the wavelength range 0.3 to 2.5 µm. Data were obtained using pellets consisting of low volume
concentrations of the FeMnCuOx (f=0.053-0.53 %) and black carbon (f=0.076-0.31 %) dispersed in
KBr matrix. The sample preparation and optical measurements were described in section 3.
Cross-sectional SEM views of FeMnCuOx (f=0.21%) and black carbon (f=0.21%) as well as
KBr pellets are shown in Fig. 4.18. The KBr matrix have large grains as shown in Fig. 4.18a. The small
grain clusters appearing in Fig. 4.18b-c were identified from Energy Dispersion Spectrometer (EDS)
analyses to be the agglomeration of the primary particles of the FeMnCuOx (Fig. 4.18b) and black
carbon (Fig. 4.18b) pigments.
(a)
(b)
Fig. 4.18 Cross-sectional SEM pictures of
(a) KBr, (b) FeMnCuOx and (c) black
carbon pellets. The length scales are shown
in the inset of the pictures together with the
Electron
High
Tension
EHT
and
microscope Working Distance WD.
(c)
60 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
It can be interpreted from these micrographs that the pigments are mainly located in the KBr grain
boundaries or at defects. The cluster sizes vary considerably from about 0.05-0.5 µm for the
FeMnCuOx and 0.02-2.5 µm for the black carbon and are much smaller than the grain size of the KBr.
The primary average particle size as observed from the powders were found to be about 0.06 µm for
the FeMnCuOx and about 0.02 µm for the black carbon. The size of the black carbon was comparable
to what has been reported previously 66,67 , but the primary particle size of the FeMnCuOx (≈ 0.06
µm) was much smaller than given by the manufacturer which reported an average size of about 0.4
µm 66,67.
4.4.1
FeMnCuOx Black Pigment
The measured total transmittance, Tt and reflectance, Rt of FeMnCuOx in KBr matrix as a function of
wavelength for different concentrations of the pigment are shown in Fig. 4.19. The total transmittance
decreases with increasing pigment volume fraction, f and is mainly collimated. The transmittance (Fig.
4.19a) decreases as the wavelength of the incident radiation is decreased. The total reflectance (Fig.
4.19b) increases at the shortest and longest wavelengths with a minimum value around 0.5 µm. The
change of reflectance is insignificant with increasing pigment volume fraction in the 0.053-0.53 % range
but significantly increases at the highest volume fraction of 1.07 %. This increase of reflectance at larger
f is probably due to the change of refractive index of the pellet material since the reflectance from the
back surface of the pellet can be negligible.
0.8
0.14
FeMnCuO
0.7
FeMnCuO
x
0.053
0.11
0.16
0.27
0.53
1.07
0.5
0.4
0.3
Total Reflectance
Total Transmittance
f (%)
0.6
x
0.12
0.2
0.1
0.1
0.08
f(%)
0.06
0.053
0.11
0.16
0.27
0.53
1.07
0.04
0.02
0
0
0.5
1.0
1.5
2.0
Wavelength (µm)
2.5
0.5
1.0
1.5
2.0
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.19 Total (a) transmittance and (b) reflectance of FeMnCuOx pigment in KBr matrix as a function
of wavelength for different volume fractions of the pigment (f=0.053-1.07 percent).
No significant difference was observed when comparing the ratio of diffuse to total reflectance between
the different pellets in the volume fraction range 0.053-0.53 %. The ratio of the transmittances,
however, increases slowly with increasing pigment concentration. Therefore, a change in the volume
fraction of the pigment causes a change in transmittance but not in the reflectance. As a result the
Tuquabo Tesfamichael
61
absorptance (Eq. 2.31) and extinction (Eq. 2.33) increase with increasing amount of pigment in the
range f=0.053-0.53 % .
From the total reflectance and transmittance measurements and the thickness of the pellet
(d=0.4 mm), the effective absorption coefficient per unit length, K, of FeMnCuOx was calculated using
Eq. (2.36). The absorption coefficient increases with increasing pigment volume fraction and
decreasing wavelength. The effect of the KBr matrix on the absorption especially at short wavelengths
was not negligible. Thus a net absorption coefficient of the pigments has been obtained by subtracting
the absorption coefficient of the KBr pellet. A linear relation of the absorption coefficient as a function
of the pigment volume fraction was observed. The total and collimated transmittance were very low at
short wavelengths (see also Fig. 4.19). In order to apply Eq. (2.36) successfully, the transmittance at a
given wavelength should not be too low. Thus for transmittance lower than 0.02 no reasonable values of
the coefficients were observed and have been excluded.
Using Eq. (2.35), the effective extinction coefficient per unit length for the FeMnCuOx pigments
as a function of wavelength for the sufficiently transparent samples has been determined. The
contribution of KBr to the extinction of the pigment has been subtracted as was done for the absorption
coefficient above. The effective scattering coefficient per unit length, S is then numerically obtained by
subtracting absorption from extinction. The scattering coefficient increases linearly with increasing
pigment concentration but the correlation fails for the higher volume fractions. It can be assumed that
the linear region is where single scattering occurs. This can be supported from different scattering
experiments. Single scattering by small latex particles, mean size about 0.03 µm, has been reported to
occur for volume fractions lower than 0.64 %. 34 Varadan et al has suggested that multiple scattering
effects must be considered for volume concentrations larger than 1% especially for scattering size
parameter, πa/λ ≤ 10. 158 These results are then comparable to the upper pigment volume fraction limit
presented in this work.
The scattering and absorption coefficients obtained in this work are for very low concentration
(f=0.053-0.53 %) of the pigments, as compared with solar absorbing paints. Absorber paints made from
FeMnCuOx or black carbon have volume concentration of f≈20%. 66,67 To compare the results of the
low and high volume concentrations, the volumetric cross-sections defined in Eq. (2.37) can easily be
used. Figure 4.20 shows volumetric absorption and scattering cross-sections of the FeMnCuOx pigment
in the wavelength range 0.3 to 2.5 µm. The absorption cross-section of the FeMnCuOx decreases with
increasing wavelength with absorption maximum and minimum obtained at 0.64 µm and 0.46 µm,
respectively. The scattering cross-section of the pellets (Fig. 4.20) remains almost constant as a
function of wavelength but decreases at short wavelengths.
62 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
FeMnCuOx
-1
Volumetric Cross-sections (µm )
10
8
K/f
6
4
2
S/f
0
0.5
1.0
1.5
2.5
2.0
Wavelength (µm)
Fig. 4.20 Volumetric absorption, K/f and scattering, S/f cross-sections as a function of wavelength for
FeMnCuO x (f=0.053-0.53 %) pigment.
4.4.2
Black Carbon Pigment
The total transmittance, Tt and reflectance, Rt of carbon pigment in KBr matrix as a function of
wavelength for volume fractions ranging between 0.076 and 1.52 percent are shown in Fig. 4.21.
0.14
0.6
f (%)
Black carbon
Black carbon
0.12
0.076
0.15
0.21
0.31
0.46
1.52
0.4
0.3
Total Reflectance
Total Transmittance
0.5
0.2
0.1
0.08
0.06
f(%)
0.076
0.15
0.21
0.31
0.46
1.52
0.04
0.1
0.02
0
0
0.5
1.0
1.5
2.0
Wavelength (µm)
2.5
0.5
1.0
1.5
2.0
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.21 Total (a) transmittance and (b) reflectance of black carbon pigment in KBr matrix as a function
of wavelength for different volume fraction of the pigment (f=0.076-1.52 percent).
The transmittance increases with increasing wavelength but also with decreasing amount of carbon. The
total transmitted intensity is dominated by the collimated beam as was also the case for the FeMnCuOx
Tuquabo Tesfamichael
63
pellet. The total reflectance which remained almost the same for low fractions increases when the
amount of pigment is greater than f=0.46 %. The increased reflectance at larger f=1.52% is probably due
to the change of refractive index of the pellet as the reflectance from the back surface of the pellet can be
negligible.The collimated component of reflectance increases with increasing pigment filling factor
particularly at longer wavelengths. Comparing the ratio of diffuse to total reflectance for different
volume fractions results in a very small difference. But the ratio of diffuse to total transmittance
increases slowly with increasing carbon concentration. The absorptance (Eq. 2.31) and extinction (Eq.
2.33) of the black carbon, extracted from the reflectance and transmittance measurements, increase with
increasing pigment volume concentration.
The effective extinction, absorption and scattering coefficients for the black carbon were
obtained using the same method as for the FeMnCuOx pigment. The coefficients increase linearly with
increasing pigment concentration between f=0.076-0.31% but the correlation fails for higher volume
fractions. This linear region is where single scattering prevails. The volumetric cross-section for the
black carbon pigments were calculated using the relation in Eq. (2.37). The absorption cross-section
decreases with increasing wavelength and no absorption peak has been observed (Fig. 4.22). The
scattering cross-section on the other hand remains fairly constant over the wavelength range 0.6-2.5 µm
and below 0.6 µm it starts to decrease.
-1
Volumetric Cross-sections (µm )
10
Black carbon
8
6
K/f
4
2
S/f
0
0.5
1.0
1.5
2.0
2.5
Wavelength (µm)
Fig. 4.22 Volumetric absorption, K/f and scattering, S/f cross-sections as a function of wavelength for black
carbon (f=0.076-0.31 %) pigment.
From Fig. 4.20 and Fig. 4.22 we observe that most of the extinction in the pellets comes from
absorption rather than scattering. The scattering cross-section of FeMnCuOx (0.12-0.8 µm-1) is larger
than the corresponding values for the black carbon (0.004-0.47 µm-1). The absorption cross-section for
FeMnCuOx (0.61-9.3 µm-1), on the other hand, drops faster than black carbon (1.72-7.01 µm-1) with
increasing wavelength and this may indicate a better selectivity of FeMnCuOx. The absorption to
scattering ratio for both types of pigments decreases sharply with increasing wavelength from 0.3-0.75
µm. Beyond this wavelength both ratios decrease less rapidly with the rate of FeMnCuOx being faster
than that of the black carbon. In short, the absorption and scattering cross-sections of the black
pigments exhibited a linear function of the volume fraction at low concentrations. The pigment volume
64 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
concentrations for the linear region were between 0.053-0.53 % for FeMnCuOx and 0.076-0.31 % for
the black carbon.
The volumetric cross-sections obtained above were compared to a previous two-flux
calculations applied for paints 66,67 . The absorption maximum and minimum of the FeMnCuOx
obtained in this work at 0.64 µm and 0.46 µm (Fig. 4.20) were found to be at 0.60 µm and 0.48 µm for
the two-flux calculation on paint 67. The scattering cross-section of the pellets (Fig. 4.20) and the twoflux calculation on paint 67 remains almost constant as a function of wavelength. But it decreases at
short wavelengths for the pellets in this work whereas the corresponding values of the paint at short
wavelengths increases with decreasing wavelength. The magnitude of the absorption and scattering
cross-sections of the FeMnCuOx pellet are, however, found to be higher than for the paint. The
absorption cross-section for the black carbon determined from pellet (Fig. 4.22) is found to be similar to
that of the two-flux calculation for black carbon paint 66. The scattering cross-section for the pellet and
paint remains fairly constant for longer wavelengths. For shorter wavelengths the scattering crosssection for the pellet starts to decrease whereas for the paint 66 it increases slightly. The absorption and
scattering cross-sections of the pellet are higher compared to the corresponding values of the black
carbon paint. The scattering cross-sections of the black pigments determined in this work were found to
be different as compared to the two-flux calculation for the corresponding paints especially at the short
wavelengths. On the other hand, the absorption cross-sections obtained in this work looked very
similar to the corresponding values of the two-flux calculation for paints except that the values obtained
here were found to be higher. The reason could be that we have determined the volumetric cross-section
for single particle scattering. This condition is satisfied for the small pigment volume fractions used in
this work f=0.053-0.53% (FeMnCuOx) and f=0.076-0.31% (black carbon) but the paints have larger
concentration (f≈20 %) and are out of this region.
In addition to the above cross-sections, we have determined the real and imaginary part of the
refractive index (n and κ respectively) of the phenoxy resin and the silicone film used as binders for the
FeMnCuOx and black carbon paints, respectively. The optical constants were determined by measuring
the reflectance and transmittance of the film and calculating n and κ using a known method from
reflectance and transmittance measurements 159. The method employs a direct inversion of the Fresnel
relations by numerical calculations. A correct solution can be obtained by minimizing the calculated and
measured quantities, |Rcal-Rmeas| and |Tcal-Tmeas|, using a Newton-Raphson iteration algorithm. The
technique of calculation has been described in detail elsewhere. 160 In the calculations, optical constants
of the glass substrate were taken from the literature 161. Figure 4.23 shows calculated n and κ as a
function of wavelength of phenoxy resin and silicone films. The resin film has κ values that vary
between 1x10-4 at lower wavelengths up to about 2.5x10-3 at longer wavelengths and the silicone film
has only slightly lower κ values. The refractive index of both films is in the range of n=1.6±0.05. For
comparison the refractive index, n of KBr obtained from Palik 162 is shown in the figure and it has been
found very similar to the n value of the films.
65
Tuquabo Tesfamichael
2
0.02
Optical Constants
1.5
0.015
n
n (silicone)
k (silicone)
n (resin)
k (resin)
n (KBr)
1
0.5
0.01
0.005
k
0
0
0.5
1
1.5
2
2.5
Wavelength (µm)
Fig. 4.23 Optical constants, n and κ of phenoxy resin and silicone films calculated from reflectance and
transmittance measurements as a function of wavelength in the solar spectrum. For comparison the n value
of KBr is also shown 162.
From Eqs. (2.9-2.11) we can see that particle cross-sections are functions of the refractive index of the
embedding medium. Therefore, the single particle cross-sections of the black pigments in KBr matrix
obtained in this paper can used for pigments dispersed in a binder which have similar n value to that of
the KBr.
4.4.3
Thickness Sensitive Solar Selective (TSSS) Paints
We have calculated the reflectance of thickness sensitive solar selective paints (TSSS) for
FeMnCuOx in silicone and black carbon in phenoxy resin using four-flux model. The calculated
reflectances were compared with measurements for different thicknesses and volume fractions of the
paints. In the calculations, the cross-sections of the pigments in Fig. 4.20 and Fig. 4.22 and optical
constants for the matrix in Fig. 4.23, were used as input parameters. Additional input factors that have
been used in the four flux model were: particle volume fraction, f, and coating thickness, d, as well as the
forward scattering ratio, ζc, and average path-length parameter, ξ. The thickness, d of the paint coating
was taken as a free parameter since the thickness of the paints were given in g/m2. Both ζc and ξ depend
on the particle size parameter, x given in Eq. (2.7). Figure 4.24 shows top and cross-sectional SEM
pictures of FeMnCuOx TSSS paint consisting of 2.04 g/m2 coating thickness and 0.20 pigment volume
fraction. From the depth profile of the coating, we can observe that the particles are uniformly
distributed in the silicone matrix. The pigments in the paint, could be seen as particles with a size
distribution similar to the previous investigation on the powder pigments. Using the single scattering
albedo, S/(K+S) and the primary size of the pigments (a=0.06 µm, FeMnCuOx and a=0.02 µm, black
carbon), a ζc value of about 0.5 and ξ=1.0 have been chosen for both of the paints 163. However, the
value of ζc and ξ were not crucial to the calculated reflectance of the absorbing paints. It is worth to
mention here that a backward average path-length parameter, which is not incorporated in the four flux
model, differs from ξ and exceeds 2.0 for absorbing particles. 163
66 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
(a)
(b)
Fig. 4.24 Scanning Electron Micrograph of 2.04 g/m 2 thick and f=0.20 FeMnCuOx TSSS paint. (a) top
view and, (b) cross-sectional view.
The calculated reflectances of FeMnCuOx and black carbon TSSS paints on aluminum substrate
for different thicknesses and f=0.20 are shown in Fig. 4.25a-b together with the experimental results,
respectively.
1
1
FeMnCuO
Calculated
Experiment
f=0.20
0.6
0.4
thin film
0.2
f=0.20
Experiment
0.8
Reflectance
Reflectance
0.8
Black carbon
Calculated
x
0.6
0.4
increasing thickness
0.2
thick film
0
0
0.5
1
1.5
Wavelength (µm)
2
2.5
0.5
1
1.5
2
2.5
Wavelength (µm)
(a)
(b)
Fig. 4.25 Calculated and experimental total reflectance of (a) FeMnCuOx and (b) black carbon TSSS
paints as a function of wavelength for different coating thicknesses and f=0.20.
The calculated reflectance spectra fit the experimental ones well especially for the thicker films. Similar
results were also obtained for the FeMnCuOx paint with f=0.16, 0.18, 0.24 and 0.28. For the black
carbon we had only one particle volume fraction, f=0.20. A discrepancy is obtained for thinner films of
the black carbon paint at long wavelengths in which the interference patterns seen from the
measurements were not reproduced in the calculations. The aluminum substrate has grooves and this
67
Tuquabo Tesfamichael
substrate surface roughness could affect the optical properties for the thinner films of the TSSS coating.
In the four flux calculations, the surfaces were assumed to be smooth and the effect of surface roughness
on absorptance or coating interference was not considered.
In the four flux calculation, the thickness, d in microns was taken as free parameter since the
thickness of the paint coatings were given in mass per unit area (g/m2). The relation between these
quantities is linearly fitted as is shown in Fig. 4.26.
Fitting Thickness, d (µm)
4.5
FeMnCuO
4
x
f=0.16
f=0.18
f=0.20
f=0.24
f=0.28
3.5
3
2.5
2
1.5
1
0.5
1
2
3
4
5
6
7
8
2
Weight of Paint (g/m )
Fig. 4.26 Relation between thickness, d of the paint in (µm) and weight of the paint per unit surface area
(g/m2) of the FeMnCuOx TSSS paint. The thickness is determined from the fitting of the calculations to the
experiments.
Using SEM, the average thickness for the 2.04 g/m2 thick FeMnCuOx paint shown in Fig. 4.24 was
analyzed and has been estimated to be of about d=1.1 ± 0.1 µm. Comparing this thickness with the fit
in Fig. 4.26 for 2.04 g/m2 weight of the paint which corresponds to d=1.2 µm, the results were found to
be similar within the estimated error of the measured result. The above results conclude that the single
scattering and absorption cross-sections obtained from reflectance and transmittance measurements can
be used to predict the optical properties of the TSSS paints.
68 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
5
CONCLUDING REMARKS
This thesis covers preparation, optical and non-optical investigations and durability tests of the
absorbing surfaces used in solar thermal collectors. It also deals with coatings that can improve the
quality of the absorbers.
Accelerated aging tests of Ni-Al2O3 absorbers at high temperatures were performed, and the
level of oxidation of the Ni particles was quantified using IR spectroscopy. The Ni particles were also
annealed without the supporting Al2O3 matrix, free standing on the substrate. A comparison between
the free particles and particles embedded in the Al2O3 matrix showed that the matrix reduces the
oxidation rate and hence provides long life time of the absorber. However, the Ni-Al2O3 surface
degraded when it was exposed to humid air containing sulpher-dioxide or when water condensed on the
surface. To protect the coating from degradation, the surface was coated with mechanically and
chemically stable SnO2 using the spray pyrolysis technique. The front surface reflection due to the
SnO2 coating was reduced by applying a silica antireflection layer using a dipping method in a colloidal
silica sol. The silica layer was found to be thermally and chemically stable.
The solar absorptance of commercial Ni-Al2O3 and Ni-NiOx absorbers as a function of angle of
incidence has been determined by measuring the angular spectral reflectance in the solar wavelength
range. An enhanced interference pattern was observed in the measured reflectance of the Ni-Al2O3 but
not for the Ni-NiOx. This gives a higher solar absorptance for the Ni-Al2O3 at higher angles of
incidence. From theoretical modeling, it was found that the double-layer structure of the Ni-Al2O3
causes strong interference and this could not be achieved from the graded index layer structure of the
Ni-NiOx coating. The optical efficiency of the two absorbers with and without glazing has also been
determined using an incident angle modifier expression. It was found that the optical efficiency at higher
angles is dominated by the transmittance of the cover, irrespective of the type of absorber. The
performance of the absorbers in solar collectors as a function of angle of incidence for glazed and
unglazed systems is to be evaluated in a future project.
When the Ni-Al2O3 coating is produced, large quantities of chemicals are used in the two-step
processes, i.e. anodization and pigmentation. An alternative method, which reduces the use of chemicals
and the number of steps, is the integral coloration method. A Si-Al2O3 coating is obtained by anodizing
a Si rich Al-Si alloy in a sulfuric acid solution. In order to get high solar absorptance, a thick coating
(~10 µm) was required, but this gives high thermal emittance and does not fulfill the requirement of
selective absorption. Theoretical calculations were performed searching for a feasible Si-Al2O3 solar
selective coating as a function of film thickness, particle size and volume fraction. A solar absorptance
of 0.70 and thermal emittance of about 0.27 can be achieved for a 1.0 µm thick film with a high volume
fraction and optimum particle size. This indicate that a thickness range with high solar-absorptance and
at the same time low thermal-emittance does not exist.
In order to study the performance of selective solar absorbing paints systematically, their
optical properties must be known. From optical measurements, scattering and absorption crosssections of FeMnCuOx and black carbon pigments were obtained. This was achieved by dispersing the
pigments in KBr matrix and measuring the reflectance and transmittance of the pigmented samples in
the solar wavelength range. The pigment volume fraction, was low, 0.053-0.53% for the FeMnCuOx
and 0.076-0.31% for the black carbon. The cross-sections exhibit a linear relation to the volume fraction
which shows that single scattering dominates. In addition, optical constants of resin and silicone films,
used as binders for the selective paints, have been determined from optical measurements. From the
cross-sections of the pigments and optical constants of the binders, the reflectance of FeMnCuOx and
black carbon TSSS paints as a function of thickness and/or volume fraction have been calculated using a
four-flux model. The calculations were compared with experiments and a good match was found,
especially for the thicker layers.
Tuquabo Tesfamichael
6
69
ABSTRACTS OF APPENDED PAPERS
Paper I: Optical Properties of Silicon Pigmented Alumina Films
Plates of Al-Si alloy were anodized in a sulfuric acid solution. This treatment provides a Si-Al2O3
coating growing at a rate of 0.14 µm/min. The Si particles had sizes between 1 and 10 µm, as seen by
scanning electron microscopy. Optical measurements showed a continuous decrease of reflectance with
increasing film thickness. The reflectance of the Si-Al2O3 coated aluminum could be understood from a
four flux radiative transfer theory. In order to explain our measurements it was found necessary to
include a free carrier term in the dielectric permittivity of Si. The free carriers are probably due to
doping with Al. Hence the relaxation time of the free carriers is determined by scattering from the
charged Al impurities.
Paper II: A Feasibility Study of Integrally Colored Al-Si as Solar Selective Absorber
The solar selective properties of integrally colored Al-Si alloy (11.6 wt% Si) have been investigated.
Optical measurements showed a continuous decrease of reflectance, i.e. an increase of absorptance, with
increasing film thickness. A maximum solar absorption of 0.85 was achieved for Si-Al2O3 coatings
thicker than 13 µm but such thick aluminum oxide coatings have very high thermal emittance.
The reflectance of the Si-Al2O3 coated aluminum could be understood from a four flux radiative
transfer theory. Using this theory the optical performance of the coating as a solar absorber was
modeled for different size and volume fractions of silicon particles and coating thicknesses. A solar
absorptance of barely 0.90 can be achieved from a 10 µm thick coating of about 0.3 volume fraction of
silicon. For thinner coatings (1 µm) the solar absorptance was only 0.70 for the same volume fraction
and the thermal emittance can only reduced to about 0.27.
Paper III: Antireflection Treatment on Tin Oxide Coated Anodized Aluminum Selective Absorber
Surface
Nickel-pigmented anodic aluminum oxide, Ni-Al2O3 was pyrolytically coated with tin oxide (SnO2).
The undesirable increase of reflectance in the solar spectrum due to the high refractive index of the SnO2
film was compensated by an antireflection layer. The layer was applied by a simple dipping technique
in a bath containing a commercial colloidal silica sol which forms a silica (SiO2) layer. The infrared
reflectance is nearly unaffected by the silica sol treatment process. Preliminary test results indicate that
treated samples are resistant to temperatures as high as 300°C as well as to corrosion when immersed in
an 8% sulfuric acid aqueous solution. In addition, the optical properties were unaffected by outdoor
exposure for two months.
Paper IV: Study of oxidation kinetics for metal-dielectric films using IR optical measurements
The thermal oxidation of small metallic particles was studied using infrared spectroscopy. The
oxidation was quantified by measuring the absorption of p-polarized light at 60° angle of incidence at
the wavelengths around the longitudinal optical (LO) phonon mode of the thermally created oxide. The
case presented in this report is nickel rods embedded in alumina (Ni-Al2O3) exposed to temperatures in
the range between 300 and 500°C from 1 to 500 hours. The rate of oxidation was found to be of the
same order of magnitude as previously reported for large particles and bulk nickel.
70 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
Paper V: Oxidation Kinetics of Nickel Particles. Comparison between Free Particles and
Particles in an Oxide Matrix.
The degradation of selective solar absorbers through oxidation has been studied. We compare the
oxidation kinetics of nickel particles of various sizes. Both free particles and particles embedded in an
oxide matrix were studied. The oxidation kinetics of polycrystalline nickel nano-rods was determined
by IR spectroscopy in the temperature range 300-500°C. The particles were oxidized when situated in
the porous alumina matrix of an electrochemically deposited solar absorber coating. The oxidation
kinetics was compared to that of free nano-particles at the same temperature and to µm-sized
polycrystalline nickel particles, which were studied by thermogravimetry in a wider temperature range.
It was found that the oxidation rate of nickel oxide was markedly lower for the particles in the matrix.
Implications for the durability of selectively solar absorbing coatings are discussed.
Paper VI: Oxidation Kinetics of Nickel Solar Absorber Nano-particles
The alumina matrix of an electrolytically deposited solar absorber coating was etched away leaving
nickel nano-rods standing on the aluminum surface The oxidation kinetics of the nickel nano-rods, with
an approximate diameter of 30 nm and a height of approximately 300 nm, was determined by IR
spectroscopy. The infrared absorption by the LO-phonon mode of nickel oxide was measured before
and after exposure to pure oxygen at 260, 280, 300, 320 and 350°C for different times. The absorptance
peak height was determined and used as a measure of the amount of the thermally created oxide. The
five different isotherms showed a power law behavior with an exponent varying between 0.52 and 0.69.
A fit to the homogeneous linear diffusion equation, derived for spherical geometry, gave parabolic rate
constants, which are in agreement with data for larger nickel particles and bulk nickel. The deviations in
the exponent from that of the parabolic law are discussed in terms of particle geometry and particle
agglomeration. The apparent activation energy was determined by the use of a master plot technique to
be 1.73 eV.
Paper VII: Angular Solar Absorptance of Absorbers Used in Solar Thermal Collectors
The optical characterization of solar absorbers for thermal solar collectors is usually performed by
measuring spectral reflectance at near normal angle of incidence and calculating the solar absorptance
from the measured reflectance. The solar absorptance is, however, a function of the angle of incidence of
the light impinging on the absorber. In this report the total reflectance of two types of commercial solar
selective absorbers; nickel-pigmented anodized aluminum and sputtered nickel/nickel-oxide coated
aluminum are measured at angles of incidence from 5 to 80° in the wavelength range 300 to 2500 nm
using an integrating sphere. From these measurements the angular integrated solar absorptance is
determined. Experimental data are compared with theoretical calculations and it is found that optical
thin film interference effects can explain the significant difference in solar absorptance at higher angles
for the two types of absorbers.
Paper VIII: Angular Solar Absorptance and Incident Angle Modifier of Selective Absorbers for
Solar Thermal Collectors
The solar absorptance of absorbers for thermal solar collectors is usually characterized at near normal
angle of incidence. The solar absorptance is however a function of the angle of the incident light on the
absorbers. In this paper the angular solar absorptance of commercial nickel pigmented aluminum oxide
Tuquabo Tesfamichael
71
and sputtered nickel/nickel oxide solar selective absorbers are reported. The solar absorptance was
calculated from experimental total reflectance spectra in the wavelength range 300 to 2500 nm for angles
of incidence between 5 and 80°. It was found that the solar absorptance at higher angles of incidence is
lower for the sputtered nickel/nickel oxide than for the nickel pigmented aluminum oxide coating. This
could be understood from theoretical calculations based on microstructure models of the two types of
coatings. The nickel pigmented aluminum oxide with a double-layer structure of its coating has an
enhanced higher angle solar absorptance due to thin film interference which cannot be achieved from a
graded-index thin film coating as the case for the sputtered nickel/nickel oxide absorber. When the
absorbers were covered by glass, as is common for most solar collectors, a negligible difference in
optical performance at the higher angles of incidence have been obtained. These results were consistent
with a theoretical calculations by use of an incident angle modifier model.
Paper IX: Optical Characterization of Black Pigments for Solar Selective Absorbing Paints
The aim of this work is the characterization of the optical properties of two types of pigments,
namely, FeMnCuOx and black carbon. The effective scattering and absorption coefficients per unit
length of these pigments have been determined from spectral reflectance and transmittance
measurements in the wavelength range 300 to 2500 nm. The data were obtained using pellets consisting
of low concentrations of FeMnCuOx or black carbon pigments dispersed in KBr matrix. The pigment
volume concentrations used for evaluating the coefficients were between 0.053-0.53 % for FeMnCuOx
and 0.076-0.31 % for the black carbon . These ranges were found to exhibit the linear dependence of the
coefficients as a function of volume fraction, given by single scattering theory.
Paper X: Optical Characterization and Modeling of Black Pigments Used in Thickness Sensitive
Solar Selective Absorbing Paints.
The performance of black pigments used in thickness sensitive solar selective absorbing paints for
solar thermal collectors depend on the optical properties of the pigments. Knowledge of the
intrinsic optical properties of most paint pigments is very limited. Pellets made from either
FeMnCuOx or black carbon dispersed in KBr matrix have been used to determine the effective
optical coefficients of the pigments. Scattering and absorption cross-sections were derived from
reflectance and transmittance measurements at near normal angle of incidence in the wavelength
range 0.3 to 2.5 µm. Volume concentrations of the pigments that gave linear dependencies for the
coefficients were found to be between 0.053 to 0.53% (FeMnCuOx) and 0.076 to 0.31% (black
carbon). Subsequently, a four flux model has been used for calculation of reflectance for thickness
sensitive spectrally selective paints. The paints were obtained from the FeMnCuOx and black
carbon pigments embedded in silicone and phenoxy resin, respectively. We have used the
experimentally determined scattering and absorption cross-sections of the pigments as input to the
four flux theory and the calculations have been performed for different thicknesses and/or pigment
volume fraction of the paints. The calculated reflectance spectra were compared with experiments
and the results for thick films fit well.
72 Characterization of Selective Solar Absorbers. Experimental and Theoretical Modeling.
ACKNOWLEDGMENTS
I thank God for all the guide in which I have now opened a chapter to express my deep heart feeling in
the following acknowledgments. This thesis would not have been written without incentive and
cooperation of many people, their good will, thoughtful and faith.
First, I would like to thank my supervisor Dr. Ewa Wäckelgård for the limitless effort she
exerted in the outcome of this thesis and makes it possible. Without her my dream would not have
shoot its goal as it is real now. My appreciation goes further for her close and careful supervision. I am
also indebted to Prof. Gunnar Niklasson for co-authoring in most of the papers I have published. His
tremendous help and contributions led my way forward and also broadened the area of my interests.
Many thanks to Dr. Arne Roos for the simulating discussions, the sharing of his deep knowledge on
optical measurements and for his English remarks on most of the papers. I have got proof-read, fruitful
suggestions, recommendations and comments of my thesis from Ewa, Gunnar, Prof. Claes-Göran
Granqvist, Arne and Boby Roos. Thank you, I am grateful to all of you.
There are other people from this department who deserve credit and need special thanks. I
thank, William Vargas for being a good co-worker who also provided help after his dissertation. Per
Nostell and Tomas Lindstöm are acknowledged for their cooperation who always remained positive to
give any assistance. It is both educational and enjoyable to work with Richard Karmhag as well as
Anders Hoel. I would like to thank Bengt Götesson, Esbjörn Bilius, Enrique C. and Shuxi Zhao, for all
the technical assistance. I am also grateful to Lisen Kullman for all the information she provided me in
the beginning of my arrival and above all for her social personality. Annette Hultåker has been a good
office-telephone companion. I appreciate, Assoc. Prof. Carl-Gustaf Ribbing and his co-workers for the
well organized Tuesday-morning seminar which I have greatly benefited, and Monika A. and Monica V.
for the nice parties. I would like to transmit my big thank to all of the Division of Solid State Physics
members for the friendly and comfortable atmosphere within the group. They made my stay beautiful
and pleasant including the honor I got in each ones house which undoubtedly inculcated in my memory.
I wish them success in their daily life.
It is worth to thank Sida/SAREC for financing my study and the Intentional Science Program,
ISP for facilitating administrative works. The warm welcome offer of the ISP members, their help and
indefatigable co-operation are facts that I have experienced. I am also indebted to Dr. Lennart
Hasselgren for his valuable advice and encouragement, and the effort he made for my study at Uppsala
University, Prof. Bengt Gustafsson for his determination to support my home University including his
great role on staff development program. I also thank the Asmara University staff development
committee for handling the program. I am grateful to Dr. Wolde-ab Yisak and my home department
(Physics Dept.) for providing this golden opportunity of my study which otherwise I would not have
got the chance all the ways upto here. I am also indebted to Dr. Ghebrebrhan Ogubazghi and Mehreteab
Tsegai. I would like to say good luck to all my friends and SAUAs members in their study and daily
activities without them life would have been boring. I, particularly, regard Frezghi H., Stefan A., Juan
R., Habte T., Somsak D., Monica G., Mwamburi M., Roland M., Woldai G., Tewelde A., Michael Z.,
Ralph & Tanja, Tom O., Yordanos B., Paulos T., Samson M., Berhane G., Pravina G., my Swedish
host family Inga & Tore Furberg, my corridor mates, and others who couldn’t be mentioned here. I
sincerely love my sister Alem and the rest of my family who always give me unlimited affection and
moral that makes my life colorful. Finally, I would like to wish all the best for everyone who shared
both my joy and sorrow and one who prayed to bring peace, without it, what so ever is useless.
This work is carried out at the Division of Solid State Physics, Department of Materials Science,
Uppsala University, Uppsala, Sweden. It is financially supported by Sida and is administrated by ISP.
Uppsala, 2000
Tuquabo Tesfamichael
Tuquabo Tesfamichael
73
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