Manual 13252549

Manual 13252549
•
X-RAI AIJALYSIS OF THE CIS FOBIi
OF 2.5 DE-fflTIIYLTHIilCYCIjOPECTAIlE
by
GECRGE RAY QALIAGIMt
A* B., Kansas State Teachers College, Engporia., 1953
A THESIS
siibmitted in partial
fill
f i 1 Itiient of the
requirenients for the degree
MASTER OF SCIENCE
Department of Physics
KAI^AS STATE COTJEGF,
OF AGRICULTURE AID APPf.im SCIENCE
1955
4\ BRARY \
k
l-w
I...J
Is
\
1
LD
1^^^
G3:r
,_
'
.
^^
^
Co y
,
n.
'
<>_.7.
QoturM>e*-+-5-
II«BCinjCTION
PROCEDURE
REDUCTION OF DATA
TABI£ OF CONTENTS
1
2
31
CONCLUSION
36
FUTURE STUDIES
39
ACKIJC7A'LSDGJ-iENT
lA
REFERENCES
U2
DURODUCTION
[The
cis ard trans forms of 2,5 Dimethylthiacyclopentane are riercuric
These derivatives are prepared
chloride coEplexes of the cyclic sulfides.
by adding 0,02^ mole of the cyclic sulfide to 0,125 mole issrcuric ciaoride
dissolved in 100 nilli liters of ethanol.
The solution is agitated for
30 udnutes then cooled and filtered.
solid derivatives are then
Tiie
crystallized to a constant laelting point froan etlianol (iJliitehead, et al, 8),
The cis
fom
contains two mercuric chloride groups both pi^suned to
be positicffied on the same side of the ring, vhereas the trans isomer
includes only one riercuric chloride group.
The cis and trans forms differ
in space relationships within the molecule, and can occur in ring cocipounds
^&ere rigidity of
rin^^-
structure prevents rotation.
The study presented here atteirpts to acquire knowledge of the ciystal
structure and the positions occupied by the mercury atoms in
tJie
cis form
The x-ray diffraction method
of the 2,5 D:Linetliylthiacyclopentane molecule.
was the iseans chosen to attack the problem,
TIae
x-ray unit used
a copper target tube,
vjas
a General Electric
}[PJ}-1
power supply utilizing
A nickel filter produced nearly monochramatic
CuKp^
radiation of average %ravelength of 1,51^-78 A°»
A Weisseriberg camera \hich operates on the moving film principle -ma
used to obtain all photographs (Buerger, 2),
Tiie
constants of the camera
includes a cala.brated diameter of 57,23 - 0,C4i millimeters
afid
a synclironized
film translation and crystal rotation of 90 millixieters and lOO degrees,
respectively.
Since direct physical laeasiiroKents of the photographs were rwcessary to
carry out the analysis, as nany individual measuronents as possible were
taken of each paracieter in order to obtain a good statistical average
FROCEDUEE
Duo to the crystal's high vapor pressure, it was necessary to coat it
with collodion.
The coating served the two fold purpose of supporting the
fragnent on the carbon taount
aixi
preventing it fron vaporizing.
The crystal was aligned so tiiat one of its axes was parallel to the
rotation axis of the caiiera, and thereby perpendicular to the x-ray beam,
by using the method outlined by Dragcdorf
(!;).
It was found, however, that
an exposure tine of 20 niinutes gave clearer patterns than the suggested tine
of
frcBJi
one to five minutes.
After the proper alignment of the crystal was
attained, a rotation photograph was made by allowing the crystal to rotate
at a uniforn angular velocity about the axis set perpendicular to the incident
x-ray beam.
When x-rays strike a single plane of atons at any glancing angle, &
,
they
are diffracted in such a way as to obey the standard laws of optical re-
flections.
The condition that the reflections from each of
tlie
planes of
atoms do not apjml one another is that their individual reflected \javes be
in pliase.
This condition is satisfied when reflection occurs at the Bragg angle
given by Eragg's law,
Bin
©
n » a positive integer
=
^^,
wl;ore
)\
» Timvelengtlx
d = the distance between crystal
planes.
If the rotation axis of tho crystal is desi^natGd as the a^ axis, then
by Laue's equation (Bunn, 3)>
(S - Sq)
'a.^
vhere S » the unit vector giving
=j^^
the direction of the
diffracted beam
So » the unit vector civing
tlae
direction of the
incident beam
X.
This becomes S^a^ - So*a3 ;?^> but S^'ao "
to a3.
Therefore,
)S|a3
a3
cos {90-^
sin^
)
"Ih
= an integer.
since Sq is perpendicular
(See Plate I)
»^^
sinfl=
iZ:.
For a particular value o£ J, ^ is constant, therefore, the diffracted
rays appear to form two cones, one on each side of the incident bean, vdiose
axis is parallel to the rotation axis.
a narrower cone than
tlie
second, etc. (Plate II).
Tlie
second order diffractions form
firct order, the third order narrower than the
By using a cylindrical film, \*iose axis is the
axis of rotation of the crystal, to record the x-ray pattern, the conical
surface containing the diffracted beams will intercept
tlie
film in a series
of parallel layer lines, Plate II.
The rotation pattern yields the necessary infonaation for the setting
of the l^yer line screen.
This screen allows only reflections from the
desired layer line to reach the f ilmj all other reflections being absorbed
by the screen.
Proper setting of the screen made it possible to obtain
Weissenberg photograplis of the zero, one, and two layer lines.
EXPLAJIATION OF
A secticm of ciylindrical f ilia,
PUTE I
viiose axis is
parallel to the
rotation axis of the crystal, showing the coordinates necessary to
define a diffraction spot
cai
a Weissenberg photograj^.
5
PLATE
•
Spot
J
^^v
""^
><^J-^^'^^B^^
Ky^^^^^^""^
^^^,^1^9
i:
c 5
^
f
EZPIAMTION OF PIATE II
Canes of diffraction intersecting a coaxial cylindrical film.
PLATE
Entranet port
u
^
II
9*
,
Exit port
6
Each spot on
y, ^diercas
tloo
Weisceriberg
tlie
photc^mph has two film coordinates, x and
rotation photograph
lias
on3^ one coordinate, x*
The layer
line of a rotation photograph is thus the collapsGd equivalent of a v^eisseriberg
photo^/raph in idiich the
y coordinate has been eliminated.
eaqjressing this is that
a Weisseriberg photqpraph is the resolved equivalanfc
Anotlier
way of
of a layer line on a rotation pattern, viiere the resolved eleroent is the
y
coordinate of each diffraction spot (Plate III)«
Eadi of the various layer lines \TQTe exposed for 60 hours
BBudiiTum
tile
daitening of
tlie
A double film
strongest spots.
tHaldb.
assured
used so that
-uas
relative intensities of the stronger spots could bo differentiated.
The
inforaiation necessary for the construction of the reciprocal lattice may be
obtained hy direct neasurerient of the layer line photograph.
Theoretically,
the reciprocal lattice points are the tips of tte
Hie H vectors
define specific planes of the real lattice.
II
vectors.
These vectors are constructed
perpendicular to the planes and are of magnitude equal to the reciprocal of
tlie
d spacing of the particula r defined plane.
Drawing all
tlie
H vectors
for a given crystal lattice froaa an arbitrary origin and denoting only the
tijxs
of the vectors produces the reciprocal lattice.
The filxi to be interpreted vas taped on an illuiainated -dLewing stand,
and a steel role adjusted to its center.
A celluloid triangle
-was
then placed
on the steel rule and shifted naking each reflection successively coincid©
with the hypotenuse (Plate r/).
vertical scale and
tlie
triangle, (Table 1).
The>H value for
^/2 coordinate
the spot
froci the index
-was
read froo the
on the baes of the
Plotting the angle ^ and the corresponding >H values
on polar coordinate pcper gave the reciprocal lattice plot (Plate V).
The slope of the rieasuring triangle and its vortical calibration mis
deteinined frcaa the following derivation.
EXPLANATION OF
PUTE
III
Fig. 1.
A Weisseriberg photograph showing a diffraction spot and its x
Fig. 2.
A rotation photograph of the sane spot recorded in Fig.
and y coriponents.
having only one coordinate.
1,
but
EXPLANATION OF
PUTE
17
The calibrated triangle used for risasuririG the AH value and the
^/2 coordinate for each diffraction spot on a IJeisseribcrg photograph
of the zero layer line.
12
PLATE V
Ah
0.5
1
-
^
mm
Scale
EXPUII/LTIOIJ OF PIATE
A reproduction of the
Z"
V
reciprocal lattice.
li;
PLATE V
)
)
15
Table 1.
Data obtained from the £ «
calibration strip, and the
Weissenberc photograph, the intensity
d
vs. L.P, graph.
Krel.
Idne No.
AH
hkl
e
L.P.
F^Crel.
1
0.37
020
250
11.2
U.8
52
2
0.56
030
9
17.1
3.0
3
0.5U
1:30
250
16.0
3.2
3
78
U
0.89
^0
50
26.9
1.6
31
$
0.35
hhQ
10.U
5.2
86
6
0.71
X20
lUo
15
21.3
2.25
7
1.25
U70
10
39.3
1.0
7
10
6
0.69
:j5o
10
26.9
1.6
6
9
0.53
?30
60
15.7
3.3
18
10
0.72
3^0
30
21.5
2.21
11*
11
0.36
720
371;
11.0
h^9
76
12
0.75
HUo
10
22.6
2.1
33
i.m
1560
5
35.3
1.13
5
k
1
2h
0.60
330
k
18.0
2.78
15
0.99
1550
10
30.0
1.1;
7
16
0.61
1*30
25
18.3
2,8
9
17
0.80
5*0
U
2U.0
1.92
2
18
1.05
750
30
32.2
1.25
21;
19
O.I;3
320
70
12.8
li.l2
17
20
l.lli
B50
20
35.0
1.18
17
21
0.69
530
20.5
2.U
23
22
1.23
^
^$
8
38.7
1.03
8
23
0,52
1120
20
I5.1i
3.1;
6
2U
0.78
530
123
23.5
2.0
62
25
0.25
?10
7
7.8
7.17
1
26
1.32
T05O
h
lil.7
1.0
U
27
0.89
730
1|2
26.9
1.61
28
0.63
6
IG.8
2.65
2
29
0.99
520
^30
9
3^.1
1.U
6
26
30
0,36
?°
55
11.0
U.so
31
0.71*
620
22.0
2.19
2
32
0.86
720
5
6
26.0
1.72
3
33
1.35
II30
$
U3.0
1.01
5
11
)
1
1
16
Table 1. Cont.
Line
IvO.
•
m
!
•
hkl
'
Krel.
:
:
•
•
L.P.
:
t,
'
/^(rel.)
>
15
3U
0.ii9
TTio
$$
1];.6
3.6
35
i.U?
1530
7
1+8.6
1.0
7
36
0.61
•^10
50
18,3
2.8
18
37
0.7U
^10
35
22.0
2.0
16
38
1.25
1010
5
39.3
1.01
39
i.Uo
mo
5
1*5.0
1.0
Uo
0.25
200
lU*
7.8
7.17
20
15
5
5
hx
0.38
300
67
11.5
U.62
1|2
0.51
Uoo
13
15.1*
3.39
1*
1*3
0.65
500
52
19.3
2.59
20
kk
0.79
Zoo
50
23.6
1.98
25.3
h$
0.92
700
19
26.0
1.57
12
It6
1.05
800
16
32.2
1.27
8
U7
1.19
900
1*
37.0
1.09
u
U8
1.U6
T5oo
1*
1*7.8
1.0
u
1*9
1.15
Wo
6
35.5
1.15
5
50
1.00
710
1*
30.1
l.U
3
51
1.13
7?o
7
3U.9
1.2
6
52
1.00
^0
11
30.1
l.U
11
53
0.87
"520
27
26.3
1.68
16
51*
0.75
Ji?o
U2
22.6
2.09
20
55
56
0.6u
3?o
29
19.0
2.61
11
0.93
1*30
6
29.9
l.lil
1*
57
0.25
110
28
7.8
7.18
1*
58
Ho
Tfo
3
1.08
»
2U.0
3.25
1.93
60
5
5
5
15.9
59
0.53
0.50
33.3
1.21
61
0.93
3IIo
17
29.9
l.Jil
2
U
12
62
0.70
"550
26
21
2.30
11
63
6U
0.90
1.30
mo
15
27.2
10
350
5
U.o
1.60
1.01
65
0.63
130
1^3
18.7
2.70
16
66
0.82
mo
11
2U.8
1.83
6
5
8
17
Table 1. Concl.
line
JJo,
«
hkl
»
Krel.
)
5
9
»
'
L.P,
F^Crel.)
«
t
,
:
67
1.01
1^0
5
3U.0
1,20
68
0.37
020
295
11.0
li.88
h
61
69
0.57
030
Uoo
17.2
2.95
136
70
0.9$
0?0
Ih
29.0
l.li8
9
71
0.92
1^0
hx
27.
1.59
26
72
1.27
270
8
39.9
1.02
8
73
0.51i
130
500
16.0
3.23
155
Ik
0.90
250
50
27.2
1.62
31
IS
1.26
370
13
39.7
1.02
13
13
76
0.71
2!Io
29
21.2
2.26
77
1.25
1*70
6
39.3
1.03
6
78
1.51
880
h
li9.8
1.01
h
Plate VI shows a reciprocal lattice and its sphere of reflection (2, 7).
The sphere was arbitrarily- drawn through the origin 0, with its center on
the incident ray AG at a distance (So|
!aie
,
which is the radius of the sphere.
sphere is called "sphere of reflection" because reciprocal lattice points
such as P will diffract
(2,6,7).
tl;e primarj'-
bean only when they lie on its sio'face
If the crystal is rotated, the sphere of reflection will sweep
about the origin generating a torus in reciprocal lattice space.
P.ef lections
will occur whenever a lattice point touches the surface of the sphere.
general equation states i S-Sq
»>H,
Laue»s
H - voctor ^lich specifies crystal
wiiere
planes
H --g~ -
hb^ + kb2
lb,
d " distance between crystal planes.
Ifit
the crystal rotate through an angle
(Plate VI).
if
until a reflection point P, is reached,
Thus:
^f=&^^
(1)
EXPU1IA.TI0N OF
The
^
of reflections.
PUTE VI
rociprocal lattice showins two positions of the sphere
20
In the Weissehberg canera
lafes90
ran.
crystal rotates 180° while
tlie
tlie
film trans-
This gives the ratios
ICO^
90 mm.
(2)
" 2
^
y (mm)
y is the distance in nilllineters fron an
idiere
arbitral^''
point to the dif-
fraction spot shown in Plate III.
Substituting equation (2) into eqxiation (1)
2
y
(ran)
-6)°
+<|>°
(3)
From Plate VII, Fig. 2,
eR
2
ci
®"
(ran)
T^iere
x(m)
™
^
^
X
»
x(rar:)
© is
in radians
2R(r,m)
180
(ra-.)
^
" x(inn)
Substituting this value back into equation (3) gives,
2
7 (nrO
x
(ran)
+p°.
Taking the derivative to find the slope,
4iL
- 1/2
Therefore, for the equatorial layer line
tlie
triangle will have a slope of
1/2, corresponding to an angle of 63° 26' with the horizontal.
it is seen that the
x coordinate
at the botton of the triangle.
Frori
Plate IV
is always zero since neasurerients are taken
Substituting this value of x in equation 3,
gives the relation between y and ^.
21
o
2
y
=
2
y
(nan)
+(f
ik)
-^^
The y cocsrdinate can be read directly frcoa the film
doubled fco*^
•
its value
aixi
Fran Laue's coneral equation:
(s-sJ-|>hI
IS-Soi = 2 sinfl=»|/i:/
but ©^ = X
(nsa),
therefore, 2 sin x
X (mm)
/>H/
(ram)
- sin'-^
(-^
(5)
Since the sine cannot exceed the value unity,
froci
>H
is restricted to values of
zero to two.
By letting Ml assune values from zero to two in steps of
5
vri.ll
give corresponding values of x*
triangle to be calibrated directly in terms of
The
Z"
n (n
*i
.05, equation
This allows the hypotenuse of the
All,
o) layer lin^s presents a scneyhat different approach
since they are situated in layers above the
a«
lattice.
This makes it
necessary to use the horizontal corponents of some of the vectors in the
calibration derivation.
The result is that the measuring triangle will not
have a constant slope.
The heavy lines in Plate VIII represents the
and the dotted lines the
^"
distance above the £.-
lattice.
If
\p
n
(nH
j2
«
is the angle of rotation of the crystal, tlien
are the respective angles between
after rotation.
reciprocal lattice
o) lattice, which is postioned soia©
tlie
»f
• ^l
<.
y[_
and ^
b^ axis and the H vector before and
J
22
Jjf
_X.(nn)
90 (im)
=.
100°
</'•=
From the rotation photograph, Plate
y (m)
2
I,
tan p - y/R
p - tan"^ (y/R)
SA
»
Plate VII, Fig. 1 gives S'/>
cosp
.
By the cosine law,
H'2 - (So
But
2'/;i
so H'
-
« s cosp
1
arxi
+_£osJ
>H' » (1
+ cos^p
)^
«
ISqI
f
+ (S»
- 2 cosfl
COSfl^.
-I
|S/
- 2 cosfl
2^^
-
coscc
cosoc
(6)
)
From Plato II,
OCR
»
(irj.)
cC -
X (mn)
2
.
^(f).
^^
2
X (m)
180
2
X
«
is in
j
LrBd^sns
180
TT
(mi.
IT
«d
r^iiere
X (nO
2R(im:0
R(ra.O
(mri)
This relation substituted into equation (6) Gives,
/K« "jll * cos^^ -2 cos^ cos
cos 2 X
(im^i)
» 1
*•
2
X (mm J '
cos^g ~ <^%i»2
2 cosfi
2
X
(im) • cos"
/ 1
[
» cos^~>2iii2
2 cos
A
\
/
P is a constant for a particular layer line so by alla-ring AH* to assune
values from zero to two in steps of ,05, corresponding values of x are
(7)
EXPIAiaTIOH OF PIATE VII
of the base of the spiierical triangle of Plate
Fig. !•
Enlarged
Pig, 2«
A cross sectional view of the cylindrical film looking along
tiie
vie^/T
axis of the canera.
I.
EXPIAMTION OF ?1ATE VIII
The
the
/=
>£
1# dotted lines, reciprocal lattice superiit^oced upon
Oj solid lines, reciprocal lattice.
27
Plate VII, Fig. 1 is a reproduction of the base of the spherical
obtained,
triangle Illustrated in Plate I.
sponds to the
hj_
AB is perpendicular to Sq
A
and corre-
axis of the reciprocal lattice.
By the law of sines:
s^
Sin (90-T\) = cos
-v^
and
(90-^)
since
.
= S/> cosp
S»/;»
cos >i
S COB^
,
therefore:
cincC
^
"
XlV
and
COS
r[
" sinoc cos B
TUT
1=*
COS
"
cos'
>l
since
But
>:i'
Ij/*-
/
'^
sin< cos^ )
Asin2 X cosfl
^(1 cos^p -2cos^ cos 2
.2.
» (1 + cos^j^
-2 cosp
cosocp
^i]
x)y
and
^»
2
x (m).
7l*+ ^*
therefore
O/*- 2y » cos"^
/sin
2
\Jl +
cos^-2cospcos2xly
x cosg
,^
Substituting in the values of x found from equation
of y were calculated.
7
+
(p
corresponding values
Plotting x vs y on milliineter graph paper gave the
desired shape of the neasuring device.
VJhen measuring the filn,
x
^°
= o.
«•
Therefore,
2y-
cos'^ (0)
2y - 90° +
+^°
(|>°
Since y is measured froia an arbitraiy point, the correction terra nay be
neglected and 2y(nn)
«=
(^°.
The relative intensities of the diffraction spots raist be known in
order to corpute the relative
crj-'stal
structure factors, F(hkl). The intensity
)
28
of a diffracted x-ray beam at a point p ic,
L
/
JiiJ-^- \
= Iq e*^
1 + cos^ 26
2 Sin 29
)
I
F(likl)^ (2), ^aere,
= Intensity of bean at point P
I
I
= intensity of incident
e
» charge of an electron
la
= Eiass of electron
c
= velocity of light
R
= distance
(1 + 008^2^
—s—rj^r-og"
*»
/^
\^
is a constant.
from diffraction center to point P
Lor I'sniE polarization term, (L.P.
« Crystal stracttire factor
P(hkl)
^
This ray be vjritten as I„ = K
T^
beam
1 + cos 2g \
sin2©
F(likl)2 vdiere K = Iq e^
/
and
^c£r2
Since only the relative intensities are desired, the equation
nay be written asj
IpOC(L.P.) F(hkl)2.
The crystal was rotated tintil a strong diffraction plane was in a
reflecting position.
tiiose
Exposures were raade of this diffraction spot for
ranging ftcaa two and one-half to zero ninutes dropping in steps of
one-half of one second for each exposure.
Tlie
film was translated after
each esposiire, thus giving a strip containing 300 spots ranging in intensity
frcm zero to naximoa blackening.
"Hie
calibrated strip was then used to
deteitndne the relative intensity of each diffraction spot of the equatorial
layer line.
A graph of d versus the Lorailz-Polarization factor was plotted
& ranging from
for values of
-oo to-^oo
,
The angle ©
^
zero to 90
and Loraitz-Polarization terms fJPOB
= x(r.i.)/for each diffraction spot was measured
29
and from the graph its Loraitz- Polarization factor determined.
Using the
relation I0C(L.P.) F(likl)^, the relative F(hkl)2 value for each diffraction
spot was calculated.
The Patterson analysis gives a method of obtaining information about
interatomic distances in crystals by using a Fofurier series, the coefficients
of
-sdiich
are the values of F(hkl)
instead of those of F(hkl).
procedure is very useful due to the fact that it does not
taice
This
account of
the relative phases of the reflections and requires no assuraptions based
on tentative ideas of the structxire of the
crj'-stal.
crystal structure factor, F(hkl) is given by:
Tiie
F(hkl) « £fji exp
'.iiere,
f^
x,y,z
=•
atcanic scattering
factor of the
27H.(hx+ky+/r.)
n*'^
atcm
= fractional increments along ai, a2, ao, respectively, for the
position of the
n'^^
atom.
This may be written more generally for an electron distribution as,
F(hkl) - /p(x,y,z)dV e2;^(bx+LT+/z)
F(hkl) -y7?p(x,y,z) V e^^i
(^*^M^)^
dydz
and finally
F(hkl) . V /yT(x,y,z) e2^(^*^/^^)dxdydz
Tne Fourier series representation of the electron density at a point (x,y,z)
in a crystal is,
.^
p(x,y,z)--f|
Consider the function p(x+u, y+v, z-m),
constant while x, y, z vary.
£ £
-vdiere
F(h>k.l.;e-^^(^'^^^'^'*«'^^
u, v, and
w are parameters kept
The function j3(x+u, y+v, z+w) represents an
30
electron density exactly similar to that corresponding to P(x,y,z), but
displaced ^dth reference to it.
The product of the
tvro
integrated over all
of the cell is the Patterson function, P.
P (u,v,w) =
/P(x,y,z)
y/// /f(x,y,z)
p(x+u,
P(x+u, y+v, z+w) dx dy dz
Substituting in the density representations c^ves:
P(u,v,w) -
^J J 1^ f//
F(hkl) exp. £-2»'i(hx+ky+iz)/F(h'k'4« )exp.
^^ ^^
+l'(z+wjj
[^2;ri{li'(x+u)+k' (y+v)
The integral vanishes unless h "-h', k "-k', /=-;£'.
P*(h'k»l'), and
P(u,v,w) --ij f ^ZF{hia)2
h k 1
''
P(u,v,w)
"-^
i ZZ7{hklf
^
e:q>.
In this case F(likl) »
r-2/n(hu+kv+i;;)7
"^
*-
cos 2T7(hu+kv+Aw)
(6)
h k 1
For the equatorial layer line,
>^
= 0, and referring to the origin of the
cell, equation 6 inay be written,
P(x,y) ' -i^
i
£
F(hkO)2 cos 2;y(hx+ky).
h k
-•0
The Patterson series ^-ields a type of density distribution which is periodic
with the periodicity of the crystal, has maxima at the origin, and subsidiary
riaxina at vector distances fron the origin equal to the vector distaiices
between every pair of atoms in the crystal.
The s\U!Tmation of even a double series involves a considerable amount
of nur.erical work, so it is desirable to reduce this as isuch as possible
by utilizing one of the available shortened methods.
Lipson and Becvers
eased the work of summinc these series by devising sets of cardboard strips
upon
^^ch
values of A sin
of h cover the range of
nli3°
£rcea.
and A cos nh3° are printed.
-30 to +30 in steps of unity.
The index values
The amplit'jdes
A ran^e from -9? to +99 in steps of unity and from - 100 to - 900 in steps
,
31
of 100.
n assumes values from
to 30 in steps of 1/30.
In using these
strips to perform the surration of the Patterson function, the cos2n5xx
term of the Patterson scries irast be equivalent in value to cos nh3° of
the strips for everj- value of n.
in the sane way as n.
X will vary from
In order for this to be true x nust vaiy
For eicarple, if n assumes values of from
to 30/30,
to 1, and the summation will have been conducted over
one side of the unit cell.
In order to facilitate the handling of the
strips, n was divider' hy two and h doubled.
This did not change the value
of the strips, but made it necessary to sum over onljr the even integer
values of h.
In this case, however, n assumed values of from
to 15/30,
and consequently, the summation occurred over l/2 the cell edge.
The same
strips and tecliniques were used to carry out summations with respect to k.
The results of the sumnation are ;jiven in Table 2.
REDUCTION OF DATA
The crystal was found to be monoclinic by analysis of the Jt " 0,1,2
reciprocal lattices.
The origins of the first and second layer reciprocal
lattices were not displaced thus indicating that the
b->
axis was perpen-
dicular to the bi, and b2 axis and also parallel to the a^ axis.
b2 axes were unequal in length and contained an acute angle,
/3
The
.
b-,
VJhen
referred to real space this gives the ai, a2 axes containing an obtuse
angle ,0^22'
^^^ conditions for the monoclinic system are thus satisfied
in that there are tliree xinequal axes, one perpendicular to the plane of
the other two, and the two coplanar axes containing an obtuse angle.
relation between components of a real and reciprocal space are (2):
The
32
O
•
•
•
•
•
CM
VO
•
•
CM
CO
•
UN UA
•
o
•
•
CO
VO
vO
•
I'N
•
«
•
CM
O
CO
•
o
On
CM
<3
• • ••
Lr\
a
•
o
UN UN UN
o
>H
•
CO
C-J
CM
H
O
•
VO
UN
•
•
•
CM
CN
VO
UA XA
•
•
C
H
C\ CM
XfN
•
H
•
CM
•
i
H
NO O
CM
H
O
•
H
o
•
g
H
O
r\
§
•• «•
•
\
•
CO
•
i
•
vO
CO CO
1A UA
•
•
lA
o
o
•
•
\A
O
o
•
•
vO
CN
o•
•
*
•
C>-
CO
•
o
•
•
r-
•
U'N
CO
XA
•
•
•
o
»
O
•
•
•
•
•
H
i
VO
•
•
•
•
«
«
•
CM
*
•
•
•
•
CO
vO
•
•
fA
o
•
•
•
•
XA o
xK xK
»
I—
CO UN
CN
CM CO
Ov
\A vO vO vO VO XA xK UN
•
•
H
o VO
UN
•
•
•
•
•
CM
•
•
C- rA vO
CM
•
CO
•
•
vO
CM
Os
•
Q
O
•
H
H
•
•
•
vO
CM
c—
vO
55
fA 7^
vO
XT,
fA
CVI
•
•
•
•
«
CM vO
CJ
«
«
•
CO CO
O
COvO
•
c~-
•
•
liN
•
QvOCM
iH O
•
i>-
3
CO
CM
CM
9
CN
•
^
H
fA
fA r—
cj
•
eg
*
•
f
CN
•
•
•
CM
CM
CM
O
CM
•
C?nv0
.:\
«
•
XA
6
•
•
<X>
•
*
o
•
•
CO CO
CN
XA vO
On
•
*
_;t3-=t
cnxa
fA
fA
i
XA i
CO
•
CO
UN vO c2
•
N
UN
CN
CO
C>.
}9
fA
•
•
CM
3
»
vO
XA UN
vO
_3-
«
o
CA
0\
r-CNXAf-r^tM
^
XA C— CO
^
CO
r-t
•
*
XA
•
XA
.::fXAC>-C»-C>-NO
XA
CO
fA
•
*^
vO
UN
•
CJ\
•
1r-
vO
CA CO vO l>- CO
vO UN XA XA U'N
'^
eg eg vO vO
•
•
O
i
CM
-A
XA
CM
»
H
UN
•
•
vO
VO
-4-
vO
•
VO
CM
UN
•
«
i i
fA vO UN
•
•
U-N
»
•
•
CX CD
•
CM
CD
•
CO XA
XA XA
cn
VO
IfN
CA
•
*
•
CO
*
9
CN f~
fA
OA XA CO
CO CM
CU CO XA
•
o o
UN H vO
en CM
UN \A UN vO
XA r- C?v CM -o
OA fA <A
r>- XA
fA
•
r-
_:3-
•
•
iH
C—
CN
fA
fA
CN CO
o
_::J
•
CM
CO
_:t
vO
0\
o
CM
CO
CN
UN
O _3^
vO
O
H
C— vO
cs
^
ra
•
«*N
UN
•
XA
On
O. rH
vO r~
_Ct
O
o•
CM
o
H
Cs o 3
o vO
o
CO
•
•
H
CM
UN
p
•
C\
1A u^
5^
•H
O
•
CM
CO
••
•
•
UN
vO
CO
0)
CTv
•
o
CM
vO vO VO
u^ UN UN VO
CN
CM
CA
-p
a.
9
vO
(A
•H
-P
q
•
•
o
•
CM
O
<^
«
CO CD
vO eg eg vO
•
Cv)
H
•
vO
i
t
•
O
to <A r-N
t— CM CA
fA XA eg XA CO CO
CM
'^
•
3
•
•
CO
vO
•
•
•
o CO
o
XA
O
CJ
fA
fA
•
1H
t~-CO OvCMCOCr--^ „^04fAH^_3-H OvQ
CO^H
fAO
H r~0 CACOfACNXAvOvOcO
r~-X-\OXACJCMCM
fAXAvOCOCNCNI^-XA-=t
•
•
•
r-i
r-i
r-i
•
fA
•
•
•
•
•
•
•
•
•
<M
G)
H
^O
1-4
O O
O O O o o o o o o o o o
fA fA f^ .fA fA fA fA fA fA fA CA
fA
CO CN O
CJ r^ ^ XA vO
H
n
H rM
H
-fA
r-\
t~-
r~i
7=]
r-i
33
":}
^a
bibjj sin ^12
" ^^'^^
^1* ^2' ^3
^^^'•^ ^"^^^
"^
real space
3.^
1
"
b2 X ^3
^12' ^13'
^b
^2 "
b^x
h
b-i>
^2
^12*^23' ^13
Vb
'^-
b^x
^3»
'^
^®^ angles in
roai space
bpj b^ " unit cell axes in
reciprocal space
" ^^^'^ an<;les in
reciprocal space
^b
V
"^3
=
The value of
a
90°
v^ » reciprocal unit cell voluwe
o<^= 180°-
Graph.
a.^
Pl2
was corputed from neasurenent of the rotation photo-
For an aligned crystal a^
=«
^£A
^
,
sin |9
Fron Plate VII:
« "
tan p
x
or
^^^
sin
Substituting in the proper value of
X.
a>
y/R
- tan*"' y/R
|3
a^ •
Therefore
Magnitude of a^.
unit cell volume
v„
and
(tan"-"-
y/R)
^ and the
neasiired y/R gives the
The equatorial reciprocal lattice was ineasured with a
calibrated steel rule to obtain the values of /b^ and/h.2»
protractor was used to measure
tlae
" F2*ecision
angle 0i2*
Substituting the neasm-ed quantities
(b-j^,
b2, a^ and ^^2^
^^°
*^®
above relationships gives the unit coll dimensions and the unit cell volume.
ai = 12.617 i .012A°
ag - 8.71+8 i
.OlM°
a^ - 7.169 - .007A°
C
3h
oC^^ = 111° 11' ± 5.5«
Va
A knowledge of the
nxuriber
= 737.8 i li.U
Ao3
of molecules per unit cell is an important aid
in detemininG to wiaich one of the 13 possible nonoclinic space groups
The nuriber of molecules per unit coll is
the crystal belongs.
'L
=»
—
_±-
-y^
B number of molecules per unit cell
P " density in grans per cc
N
=
number of molecules per nole
V
volume in cc per unit cell
A «
nuiiiber
of grama per mole
Solving for the ratio P/n and substituting in the values for A,
II,
and v gives
f/n - 1.U83 ± .009
(9)
The density vas determined by placing a known amount of the material
into a calibrated pipette containing water and observing the change in
height of the water column,
Tlie
increase in column height caused by
addition of one ml water to the pipette was noted, and the volume of cis
material determined from the relation
volume of cis
1 cc waters
chanj;;e
in water column heipht by cis
change in water column height by 1 ml water
This procedure alorig with the mass of the crj-^stals used gives an experimental
density of
i 0.026 gms/cc
f- 2.78
Since the solubility of the cis in water was not known, and since some of the
material surely went into solution, the measured value of the density is
probably some^^t lower than the true density.
Substituting
tlie
value of
35
Into equation 9 and solving for n gives a value of
The value n
cell.
= 2 was
tifjo
molecules per unit
then substituted into equation (9) and the x-ray
determined density value found was equal to 2.966 - 0.018
gr.is/cc.
The cis derivative, since it is monoclinic, may belong to any one of
13 possible space groups.
The systematic absence of spectra provides the
data for the deduction of the space group.
spectra vas not present the jt" 1 and
X
=•
were plotted and each reflection indexed.
In order to determine vAiich
2 layer line reciprocal lattices
Tables listing the space groups
and conditions for their existaiice were consulted and by the process of
elimination it was found that the cis belongs to either one of two groups (5)»
The two groups as given by their Schoenflies symbols are:
1.
Cg with the center of each molecule at x, y, z and x, y,
2.
(T*
Tlie
Patterson functions exhibits pealcs at vector distances from the
with the center at ^, y, ^ and ^, y,
3A
t'
* z.
or o, y, ^ and o, y,
3A«
2
origin equal to vector distances between pairs of maxima in the electron
density.
The height of each peak is proportional to
scattering powers of
tlie
two atoms concerned (3).
used gives a large peak at the origin,
wl:iich
tlie
product of the
Ihe F(hkl)
sjTithcsia
expresses the fact that any
atom is at zero distance from itself.
The interpretation of the Patterson series for coi;fAex structures is
difficult.
This is due to the fact that for unit cells containing many
atoms, some of the vectors are very lil:ely to lie close together so that
the individual peaks are not resolved.
are great.
Also, the chances of overlapping
Therefore, in order to completely fix the atomic distribution
in space, it laay be necessary to obtain a density map projected along one of
36
tlae
other two coordinate axis.
The correctness of the positions can then
be checked from the projection along the third axis.
A reproduction of the electron density contour map produced by the
synthesis of all the hkO values is shown in Plate IX.
The x and y coordinate
and the ragnitudes of the eight resolved peaks are given in Table 3.
Attenpts
to determine the actual positions of the nercury atoms have not been suc-
cessful at this time.
Table 3.
No.
III
Indices and ragnitudes of the peaks on the Patterson plot.
Maximm
'
1
X
cooixiinates
*
•
1
:
y coordinates
:
1787
1
1032
2
878
63/375
O1/2UO
3
735
10/30
29/96
31/80
h
6U0
13/30
2C9A80
$
650
15/30
87/2liO
6
725
l/2itO
7
m
15/30
10/30
8
906
10V750
CONCLUSION
The crystal was found to belong to the nonoclinic system and be in
r,
,2
either the Cg or
j
Cgj^
space group.
The unit cell dijaensions were caiputed to
bei
a^
» 12.617 i .012A°
a2
- G.7I18 i
a3
- 7.169 - .007A°
.01M°
38
X
Ld
<
CL
39
c(^
- 111° ll'l 5.5'
Va
- 737.8 - ii.i;Ao3
The cis derivative contains two molecules per imit cell, and has an x-ray
determined density of 2,966 i .018 gms/cc.
infonaation obtained iron
tlic
The contour
raap
plotted rrora
Patterson analysis cave vector relations
between points of high electron density.
The interpretation of the map
to give the actvial atomic distribution has not been acconplished at this
tine.
PJTUEE STUDIES
The information that can be obtained from a two dimensional Patterson
synthesis usually depends upon
In the
FvjIco
tlie
coaqilexity of the molecule being studied.
projection, the vector corresponding to a given interatcaTdc
distance is always drawn from the origin, no matter
Bay lie in the time projection.
^ere
the two atoms
If there are several equal and parallel
interatomic distances in the true projection, all give the same peak on
the contour map.
Tiie
and unresolved maydma.
plot may also be further complicated by overlapping
One method of overcoming this deficiency is to obtain
a density map projected along one of the other two coordinate aais.
should give sufficient information to fix the position of
This procedure could not be followed ixnless there were
tiie
sostie
This
heavy atoms.
means of
rotating the crystal on its mount so that proper alignment could be obtained.
The r^axina in the F^^^q^ distribution are rather diffuse because the
coefficients
Fjiijo
oi" "tlie
way to systematically
series diminish rapidly,
Patterson devised a
decrease the rate at which the coefficient
thus sharpenintT the maxima in the distribution given by the serie
_
i;0
suggests using F(hk; /f in the coerficients instead of F(hk) where;
f
"^ ^/v^nn^
^m
"
scattering factor of
the sunraation being over all atoms in the tinit cell.
m
atom.
The general effect of
this is to produce a scattering factor corresponding more closely to one due
to point atons, and to sharpen the inaxima in the resvilting distribution.
Probably
the most comraon procedure for fixing the positions of the
atoms in a unit cell is to carrj^ out at least a two-dimensional F^kO
synthesis
to see if it yields any clear information on the positions of some of the
atons or the general form or orientation of the molecule.
If it does yield
sudi information, this may be sufficient to settle the signs of
FjjJjq's, vdiich
scoae
of the
are then used for a regular Fourier electron density analysis.
This first electron density map should indicate approximate positions for the
lighter atoms thus giving information for the recalculating of the doubtful
signs.
A second, third, etc, F-^q synthesis can be performed until
desired refinement is reached.
tlie
lil
ACKNOWLEDGMENT
The excellent advice, encourasenent, and help civen by Dr. R. D.Dragsdorf
throughout this research are gratefully ackncnrledged.
Appreciation is also
expressed to Dr. S, E. Whitcorib for his much appreciated moral support, and
to the meribers of the faculty for their undorstandinc of the personal
problems encountered.
U2
REFERENCES
1.
Bijvoet, J. K.
New York: Interscience Publishers Inc.
X-ra^' Analysis of Crystals,
Chapt. V, VI; Appendix I, V, VI,
19^1.
2»
Bucri;;er, H.
J.
X-ray Crystallography. New York: John \Jiley and Sons.
Chapt. V, VI, VIII, XI, XII, XIII, XJCII.
3,
W.
Chemical Crj'stallography.
19^3»
Eirnn, C.
London: Oxford University I'ress.
19^6.
Chapt. IX.
k»
Dragsdorf, R. D.
Crystal Alignment on the Weisseriberc Gonioneter.
Acta Qryst. 6:220
(193'3).
^.
Henry, Norman F. K. and K. Lonsdale.
International Tables for X-ray Crystallography,
Press. 1952.
BinninghaEi: Kynoch
6,
James, P.. W.
London: G, Bell
The Optical Principles of the Diffraction of X-rays.
and Sons Ltd. 19U&. Chapt. II, III, VII. Appendix II.
7»
Sproull, W. T.
X-rays in Practice.
Chapt. XV, XVII.
8.
Ilew
York: licGraw-Hill Book Co. Inc.
19li6*
\^itehead, E. V., R. A. Dean, and F. A. Fidler.
Tlae Preparation and Physical Properties of Sulfur Conpounds Related
to ^ctroleun. Jour, An, Chen. Soc. 730632. 1951.
TliE CIS FOKI
OF 2.5 DE-£TIIYLTIiIACyCLO.'EIITAJJE
X-RAY MIALISIS OF
by
GEORGE RAY GALUGHER
A. B., Kansas State Teachers College, Emporia, 1953
Ah'
ABSTRACT OP A THESIS
Bubmitted in partial folfilliiient of the
requirements for the degree
MASTER OF SCIENCE
Department of Physics
KANSAS STATE COLLEGE
OF AGRICULTURE kW APPLIED SCIEJ^CE
1955
The 2,5 Dteethylthiacyclopentane molecule occurs in the cis and trans
The cis
forns.
fom
of the nercuric cliloride conplex contains two mercuric
chlortde groups both presumed to be positioned on the same side of the
The trans isomer has only one mercuric chloride group.
ring.
The object of this study was to determine the crystal structure and,
if possible, the relationships of the Kiercury atoms in the cis form of
the mercuric chloride complex of the 2,$ Dimetliylthiacyclopontane molecule.
The
x-ra;/-
diffraction method using moving film techniques was the means
chosen to study the problem.
The \'.'eissenberg camera was used to obtain a rotation photograph and
also normal beam Weissenberg photographs of the jC= 0, 1 and 2 layer lines.
The
a-j
axial length was determined for the layer separation on the rotation
pattern.
Then, using data taken from the
Ji
"0 layer line, the reciprocal
lattice was constructed, measurement of which yielded the lengths of the
reciprocal space parameters b^,
angle, fii2*
i>2
and the magnitude of their included
^ calibration intensity strip was
iriade
the relative intensity, I, of each diffraction spot.
in order to obtain
The relative crystal
structure factors squared, F(hkl)2, for each reflection was calculated,
using the relative intensity and the Lorenz-Polarization term, from the
expression, loC(L,P.
)
F(hkl)
?
.
A knowledge of the F(hkl)
2
values made
it possible to use the Patterson analysis to obtain information about inter-
atomic distances.
Tlic
Patterson series vfoen surmued by Fourier methods
yields a type of density distribution wiiich is periodic with the periodicity
of the crystal.
The summation provided data for the construction of a
contour map which showed peaks at vector distances from the origin equal
to vector distances between pairs of maxima in the electron density.
Analysis of the ji= 0, 1, 2 reciprocal lattices placed the crj-^tal in
the nonoclinic system.
a-,,
ar>
space.
andoC-|2*
Tlac
'•'sre
The unit cell axes
arai
included angle in real space,
computed using equations relating reciprocal to real
cis form was found to contain two molecules per unit cell, and
have a density of 2.966 * O.OlG
j-^ns/cc.
Tae 13 possible nonoclinic space
groups to idiich the crystal could belong were reduced to two.
as given by tlieir Schoenflies symbols are C
2
and
These groups
h
C^,
.
II
I
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement