• 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

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