The Pennsylvania State College The Graduate School Department of Chemistry AN X-RAY STUDY OF THE STRUCTURE OF BENZENE, CYCLOHEXANE AND THEIR MIXTURES A Thesis by Paul H. Bell Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy June, 1940 Approved £2 JHead of Department Major Professor l-q./fpo______Date of Approval ACKNOWLEDGMENT The author wishes to express his gratitude to Dr. Wheeler P. Davey for his direction during the course of the experimental work and assistance in preparation of this manuscript. 220147 TABLE OF CONTENTS Page 1 Introduction......................... A p p a r a t u s ........ ................. ............. 2 ..................... 2 A. X-Ray Radiation . B. Spectrometer and Slit S y s t e m ...... 0. Sample-holder and Temperature Control . . . 3 D. Counting C i r c u i t ........... 5 2 ....................................... 6 Experimental Procedure ........................... 7 Experimental Results . . . .............. . . . . . 9 Materials Interpretation ofExperimental Results ............ 14 S u m m a r y ........................................... 29 Bibliography....................................... 30 Appendix I. Apparatus....................... 32 A. X-Ray Tube Circuit and Arrangement .... B. Counter Circuit..................... 33 32 (1) Geiger-Mueller Counter T u b e ...........33 (2) High Voltage Rectifier.............. 33 (3) Power Supply for AmplifierCircuit . . 35 (4) Amplifier Oircuit 38 .................. Appendix II. Filter Transmission C u r v e ............ 40 Appendix III. Additional D a t a ............... 42 A. Shape of Entire Diffraction Curves B. Experimental and Theoretical Curves .... for Other M i x t u r e s ..................... 42 42 TABLE OF CONTENTS Introduction..................................... A p p a r a t u s ........... Page 1 2 A. X-Ray Radiation ......................... 3 B. Spectrometer and Slit System . . . . . . . 3 0. Sample-holder and Temperature Control . . . 3 D. Counting C i r c u i t ................... 5 ....................................... Materials 6 Experimental Procedure........... 7 Experimental Results ............................. 9 Interpretation of Experimental Results . . . . . . . 14 Summary ................................... 29 Bibliography.................................... 30 Appendix I. 32 Apparatus ........................... A. X-Ray Tube Circuit and Arrangement B. Counter Circuit .... ......................... 33 (1) Gelger-Mueller Counter Tube . . . . . (2) High Voltage Rectifier (4) Amplifier Oircuit . . 35 .................. Appendix II. Filter Transmission Curve 33 .............. 33 (3) Power Supply for AmplifierCircuit Appendix III. 32 .......... 38 40 Additional D a t a .................. 42 A. Shape of Entire Diffraction Curves .... B. Experimental and Theoretical Curves for Other M i x t u r e s ........................ 42 42 TABLES I. Page Peak Positions..................................18 II. Relative Peak Intensities...................... 23 FIGURES I. Sample-holder ............................... Page 4 II. X-Ray Diffraction Curves; 100$ Benzene.......... 10 III. X-Ray Diffraction Curves; 100$ Cyclohexane . . . 11 IV. X-Ray Diffraction Curves; 51.4$ Benzene Solution 12 V. Diffraction Curves; 74.5$ Benzene, 74.6$ X-Ray Cyclohexane S o l u t i o n s ......... 13 VI. Theoretical Curve due to Addition ofCurves for Benzene and Cyclohexane ..... ........... 20 VII. Theoretical Curves; 51.4$ Benzene Solution . . . 25 VIII.Theoretical Curves; 74.5$ Benzene, 74.6$ Cyclohexane Solutions ....................... 26 IX. High Voltage Rectifier.............. ......... 34 X. Power Supply.................................... 36 ........................... 37 XII. Balanced Filter Transmission Curve............ 39 XIII.Entire Diffraction Curves ................... 41 XIV. X-Ray Diffraction Curves ..................... 43 XI. Amplifier Circuit XV. Theoretical Curves; 62.4$ Benzene,62.8$ Cyclohexane Solutions ....................... XVI. Temperature versus Angle Graphs ........ . . . XVII.Temperature versus Intensity Graphs .......... 44 45 46 0. Page Peak Shift with Temperature............... 42 D. Decrease in Peak Intensity with Temperature . 47 Bibliography for A p p e n d i c e s ....................... 48 Introduction The structure of liquids has been studied by many methods, including that of x-ray diffraction^ *^ their structure is not yet well understood. , but It is the purpose of this paper to give the results of an x-ray study of the mutual solutions of benzene and cyclohexane. These results, differing from those so far reported in the literature^ * (4)»(5)» (6),(7),(8)^ ie£Uj a better understanding of the physical state of liquid structure. All authors, with the exception of H. K. Ward, seem to have obtained only one peak in their diffraction curves from liquid solutions. (8) Ward' , working with benzene - cyclohexane solutions, obtained two peaks corresponding to those given by pure /g\ benzene and pure cyclohexane. Murray and Warren' ' repeated Ward1s work and were unable to obtain two peaks. Since the experimental results conflicted with each other and with the thermodynamic data of Scatchard, Wood and Mochel^, new x-ray investigation was made on the same system with an entirely different type of x-ray diffraction apparatus. The new data showed not one or two peaks, but four. Since the data were definitely reproducible, they seemed to warrant further study. In the present work a Geiger-Mueller counter method was used with compensating filters. This method appears to be much more sensitive than the photographic method and less cumbersome than the ionization chamber method. Apparatus A. X-Ray Radiation A (G. E. X-ray Oorp.) molybdenum anode, Ooolidge type tube was operated at 42 kilovolts (r.m.s.) and a tube current of 30 milliamperes. The voltage and tube current were maintained to within ± 1 , 5 percent by use of voltage regulators on the transformer primary circuits (Raytheon Mfg. Go.). To obtain a monochromatic beam of high intensity, the method of balanced filters was u s e d ^ ^ * ^ ^ . A filter of filter paper saturated with Sr( 1103)2 was made such that its x-ray transmission was equal to a Zr03 filter (Patterson Screen Co.) for all wavelengths except the K«( the tube. doublet of This was carefully balanced and ohecked over the entire x-ray speotrum using the (100) plane of NaCl. B. Spectrometer and Slit System A Spencer spectrometer (No. 818), on which angles could be read to one minute of arc, was mounted in a rigid frame in such a way that the moveable arm moved in a vertical plane. Soller slits^*^ were substituted for the slits and telescope. The slits for the collimator and Geiger-Mueller counter consisted of 6 parallel slits 20 erne, long, 0.075 cm. wide, by 1.0 cm. high. The lead foil between slits was 0.0075 cm. in thickness, the spreaders 0.075 cm. The geometry of the incident beam was such that only three of the six collimating slits could be used. The thickness of liquid used in the specimen holder was such that all six of the slits could be used on the swinging spectrometer arm. 0. Sample-holder and Temperature Oontrol To eliminate the possibility of any contamination the sample-holder was constructed entirely of glass. (See Fig. I). Fig. I The cell windows were of Pyrex glass approximately 0.007 cm. in thickness. 1.7 cm. The thickness of the liquid in the cell was This was large enough to insure a high intensity of diffracted beam. It was slightly less than the optimum thickness given by * = ? where t is the thickness and j-A is the linear coefficient of absorption. The liquid under investigation was brought up to temperature, (io.5°C), in a glass coil immersed in a thermostat. The liquid was circulated through the coil and the cell, by means of a pyrex paddle, at a linear speed of approximately 3 cm. per second. The temperature difference between the cell and the thermostat was therefore negligible. Temperatures between 5°0 and 10°C were obtained by circulating ice water through a cooling coil immersed in the thermostat. For a temperature of -21°0 a dry ice - acetone mixture was X-RAYS THERMOSTAT LI QUI D GO Figure I LEVEL syphoned through the cooling coil, and a eutectic mixture of NaCl and water was used in the bath. D. Oounting Circuit The Geiger-Mueller counter was argon - oxygen filled. The cathode had a sufficiently large opening to allow all x-rays coming from the slits to enter the counter. The voltage supply was maintained at 850 volts by a voltage regulator of the Street and Johnson t y p e ^ ^ . The amplifier circuit consisted of three stages of voltage amplification, using a 57 and finally two 56 tubes. The amplified pulse was fed into a modified Pickering^4^ recording circuit, using a single 885 thyratron tube. The final counts were recorded by a Cenco counter in the plate circuit of the thryatron tube. With this oircuit it was found necessary to shield the first stage of amplification. The time constants for the circuit were sufficiently small to allow the 60 cycle of the incident beam to be recorded. A small loudspeaker was also built in the circuit, powered by a 45 tube, so that the quality of sound from the speaker gave an indication of the proper operation of the G.-M. counter and of its circuit. Materials The benzene was Baker* s "O.P. Thiophene Free" with the following physical constants: B.P. 80°0; M.P. + 5.5°C; Index of refraction 1.5009 at 20°C. The cyolohexane was obtained from Rohm and Haas Co. It was purified by a method somewhat similar to that used by other workers^®^ . The material as received was shaken for 12 hrs. with fuming H3S04 (25$ S03), washed with water, shaken with alkaline KMn04 and finally shaken with water again. It was then dried over metallic sodium and finally distilled at a high reflux ratio in a 15 plate column. Further purifications were carried out by fractional recrystallizations. The physioal constants of the final material were: B.P. 80.5°C; M.P.f-6.4°C; and index of refraction of 1.4263 at 20°0. The solutions, to be examined by diffraction methods, were prepared on a weight basis. They had weight-compositions of (l) 74.5 percent benzene - 25.5 percent cyclohexane; (2) 51.4 percent benzene - 48.6 percent cyclohexane; (3) 25.4 percent benzene - 74.6 percent cyclohexane. These corresponded to mol fraction compositions of (l) 0.76 benzene - 0.24 cyclohexane; (2) 0.53 benzene 0.47 cyclohexane; (3) 0.27 benzene - 0.73 cyclohexane. The exact percentages had no special significance, but were those obtained after measuring the approximate amounts by volume* The index of refraction was measured before and after each run and was found to be the same within 0*0001. This indicated that the composition did not change during the course of the experiments* Experimental Procedure To be certain that the apparatus was in a condition to operate uniformly over a long period, it was in every case allowed to warm up for one hour before making any measurements. The temperature of the G.-M* tube was always kept within one or two degrees of 25°0 since these tubes have a marked decrease in efficiency with rising temperature. The data reported are for the K aC doublet lines of Molybdenum, 0.710 $. This was obtained by subtracting the ”strontium filter” reading from the "zirconium filter” reading, the difference being the K * diffracted beam intensity. contribution to the The background correction due to cosmic rays need not be subtracted because its average intensity was eliminated by the two filter readings. A blank run with the empty sample holder gave a very small diffraction scattering with no peaks in the region used in this work. The counting rates were never higher than 300 per min., so that it was possible to detect failure of the mechanical counter by an audible method. The loudspeaker volume was adjusted so that it was not audible to the operator when the counter was operating. Any skipping of the counter made it possible to hear the loudspeaker pulse and thus to detect the failure of the counter. The ZrOg and Sr(N0g)2 filters were changed after each minute interval, and all readings were thrown out for which any counter failure was detected. Statistics of Geiger-Mueller counters have been developed by several authors^15^' (16)* Hughes^17) points out that where n is the number of counts in a given time interval and x the average number arriving in that time interval. The mean deviation is therefore equal to the square root of the counts recorded. Sufficient counts were taken to insure a valid graph over the range studied. In the region between 8°00* and 8o40' enough counts were made so that the differences between counts of the peaks and of the adjacent minima between the peaks were, in the most extreme cases, greater than twice the mean deviation. The shapes of the curves and peak positions were determined for eaoh liquid sample at 40°C, 25°G, and in the case of pure benzene, pure cyclohexane and the 51.4 percent benzene mixture, additional curves were taken at 60°C, 10°0 and as close as possible to the melting points. The melting points are 5.5°0; 6.4°0; and -22°C^18^; respectively. The shapes of the curves were reproducible but the relative intensities varied from week to week. This was probably due to long time changes in the characteristics of the counter circuit. In order to put all curves on a oommon intensity scale, the following method was used: (1) Data on all the peaks of all the liquid samples studied were taken at each Of the constant temperatures mentioned above, using a separate day for each temperature. (2) Measurements of the peaks of the 51.4 percent benzene mixture (M.P. -23°C) at -21°C, 10°0, 25°0, 40°0 and 60°0, were made on the same day. (3) The data from (2) were used to correct the measurements of (1) so that the final results shown in Figures II, III, IV and V, were what might have been expected if all the data could have been obtained on a single day. Figures II, III, IV, V Experimental Results Diffraction curves for the pure liquids and mixtures at various temperatures are shown in Figures II, III, IV and V. One unit on the intensity scale represents one hundred counts per five minutes. 2 -O' is the angle of deviation from the incident beam made by the diffracted x-rays. INTENSITY Q Oo Figure Oo II $ m Oo INTENSITY f0» .>• Oo Figure ro III 4> 51.4 r?o b N ZEN E CD)0 COO (A) I (B)Q Figure IV 13. 74.5 7. BE 74.6 % cyclohexane: (C.D)0 (B)0 CA)0 2 ■©■ Figure V The range of 3 -©-studied, was from 2°00' to 11°00'. This is not entirely reproduced in the curves shown, because of the size of graphs necessary. In all oases a small intensity peak was observed at a low angle of diffraction. The exact position of this peak was oarefully checked in several cases. In the case of pure benzene and cyclohexane it was found, within the accuracy of measurement, to be at one-half the angle of the high intensity peak (for small angles sin©- =•©-). For the mixtures no sharp peak was obtainable but a diffuse peak was found between 2 © - = 4o00' - 4°30'• The intensities of these peaks were approximately one eighth of the high intensity peaks. The lowest temperature curves in the cases of Figures II, III and IV were taken to determine whether the liquid structure might change at a temperature just above the melting point. Interpretation of Experimental Results Several theories have been proposed to explain x-ray diffraction in liquids. are those due to: The more important of these (19) Raman and Ramanathan , Zernike and Prins^20) > ( 22), Debye^23) and Stewart^2). The approach of the first three is definitely mathematical in oharacter, while that of Stewart is a non—mathematical picture of the state of the liquid. Raman and Ramanathan's function was able to predict only one peak in the diffraction curve and its exact position had to be obtained experimentally. Zernike and Prins used a distribution function evaluated in an empirical way. Debye used the experimental data to determine the distribution function. These methods were applicable in the case of molecules having spherical symmetry, and many liquids have been worked out on the basis of the theories of Prins and Debye, The application of these theories to unsyrametrical molecules such as benzene or cyclohexane has not been so successful. Several distribution functions have been used ^ for b e n z e n e > ( 25)>(26) »(S7). these functions gave fair checks at high diffraction angles, but not at angles less than the principle peak. It seems that one must resort to the method of Stewart to explain the experimental facts in the cases of solutions. It is well accepted, that a liquid approximates a crystalline powder in the sense that.the diffraction peak positions must be close to those given by Bragg's formula n A - 3 d sin-o- (l) Applying this formula (l) to the data of Figures II, III we obtain, for the x-ray radiation used ( A = 0.710 $), the following values of d at 25°C: for 100 percent cyclohexane, 2 0 = 8°00' and d = 5.09 ±.01 A; for 100 percent benzene, 2 0 s 8°40' and d >= 4.70 ±.01 $. Such values of d have been interpreted b y several authors as the effective thickness of the molecules in the liquid (28) It remains to explain, if possible, the low peaks at 2 ® = 4°00' - 4°20', and the three peaks shown by all the mixtures at 2 ■©• = 8°00', 8°20« and 8°40’. Let us consider the solution to be made.up partly of randomly distributed molecules of benzene and cyclohexane, and partly of small groups, each existing temporarily, whose molecules have an almost orderly arrangement. This is consistant with Stewart's explanation^^ of x-ray diffraction in pure liquids. It is inherent in the theory of x-ray diffraction that sharp diffraction peaks require the diffract ing material to have a periodic structure, with enough repetition of the fundamental structure to give a noticeable contribution to the diffraction pattern. For convenience of reference we shall use the symbol (-B-B-B-) to represent some definite grouping, composed entirely of pure benzene, the symbol (-C-C-C-) to represent a similar grouping of pure cyclohexane, and the symbols (-B-C-B-C-), (-B-0-C-B-C-C-) (-B-C-B-C-C-B-), etc., to represent groups composed of both benzene and cyclohexane. Obviously the groupings (-B-B-B-) and (-C-0-C-) show a repetitive structure with the single molecule as the fundamental unit. We should therefore expect definite diffraction peaks corresponding to the grating spaces given by adjacent molecules. Such peaks were observed experimentally in the present work. Since we are dealing with non-rigid liquids, instead of solid crystals, we must expect the pure liquid to show an equilibrium state between (“ ■®k” ^l Bm“ Sn") anc* (“ ®k— ®r*®m— ®ri“) or between (-0k-0i— Om-On-) and (-C^— C-^-Cra— Cn-). This should give a diffraction peak corresponding to the distance, B^-B^ (or 0]£“0ra)• This spacing is obviously not far from twice the mean spacing between adjacent molecules. Such peaks have been observed experimentally in every case. They are not shown in Figures II to 7 for lack of space. The groupings (-Bd-Ge-B.f-0g-) show a slightly more complicated periodic structure. Such a grouping should show a diffraction peak corresponding to the fundamental spacing -B^-Bf- or -Cg-Gj?-, but since the diffracting power of B and 0 are similar, this peak should be weak due to inter ference between B and 0. Such peaks have been observed in the case of all the mixtures studied. The spacing -Bd-Ce- obviously should be intermediate between the spacings -B-B- and -0-0- appearing in the (-B-B-B-) and (-0-0-0-) groupings, and this is found to be the actual case. Because of the similarity in diffracting power of B and 0, a definite diffraction peak should be found for all mixtures of B and C at a distance corresponding to -Bd-Ce-, (i.e. half the spacing Bd-Bf). Experimentally such peaks were found for all our mixtures. They are shown in Figures IV and V, and in detail in Table I; within experimental error, these peaks fall half-way between the peaks of (-B-B-B-) and (-C-0-C-). Table I Peak Positions. Composition Temperature 100# 0 6 % 3 it i! 6.7°C Peak Positions -0-C3-C2 d 10 °C 8°02« 5.07 ii 25 °C 8°00‘ 5.09 II ii 40 °0 7°58' 5.11 II ii 60 °0 7°55‘ 5.14 ii 10 °0 8°41» 4.69 II ii 25 °C 8°40» 4.70 II ii 40 °C 8 q 38« 4.72 II ii 60 °C 8°35' 4.74 -31°0 8°04» 5.05? 8°43» 4.67 » ii ii ■B-0d 8°43' 4.682 5.7°C II 51. 4# CgHg 3 -&• 8°03« 5.062 II 100# c 6h 6 -B-B-B3«d i ? 01 Table I 8°24» 4.852 10°0 8°02» 5.07 8°42« 4.68 8°22» 4.87 it 25°C 8°00» 5.09 8°40» 4.70 8°20' 4.88 n n 40 °0 7°58' 5.11 8°38' 4.72 8°18' 4.90 ii ii 60 °C 7°56‘ 5.13 8°36' 4.73 8°15* 4.93 25°C 8°00* 5.09 8°40' 4.70 8°20« 4.88 40 °C 7°58‘ 5.11 8°39' 4.71 8°19» 4.89 25°C 8°00‘ 5.09 8°40' 4.70 8°20' 4.98 40 °0 7° 59' 5.10 8°38» 4.72 8°18» 4.90 62 .4$ CgHg 25°C 8°00» 5.09 8°40' 4.70 8°21' 4.88 63 .Sj, OgH12 25°C 8°00' 5.09 8°40' 4.70 8°19« 4.89 74 •5$ CgHg it II 74 .6% CgH^g ii H The next most complicated grouping can be repre sented by (-Bg-Of-Cg-Bk-Cj-Cj-). The basic repetitive distance for this grouping is Be-Bh . This distance would have to be repeated several times to give a definite diffraction peak. The probability of many successive units of (-B-0-C-) occurring in a single group is so small that any diffraction peak would necessarily be weak. Even if such a definite peak were strong enough to be detected, it would lie at too small a diffracting angle to be observed on our apparatus with Mo Kflf rays. A similar argument could be used for still more complicated molecular groups. It might be argued that the shapes of the experi mental curves are due to addition of two complete curves for (-C-0-0-) and (-B-B-B-). Fig. VI shows, by dotted lines, the curves for (-B-B-B-) and for (-C-C-C-) obtained by multiplying the experimental curves (at 25°C) of Figures II and III by the mol fractions 0.534 and 0.466 respectively. This composi tion corresponds to the weight-fractions 0.514 and 0.486 shown in Fig. IV. Fig. VI shows that the sum of the two dotted-line curves does not even approximate the experimental curve. ■ I ■ — M | ...... — ... ■■ — I .... ■— ... . I . 1! ■■■ ■■■ 1.1 * I ■■■ — ■ Fig. VI Considering the diffraction effects of such groups as (-Bg-Cf-Cg-Bh-Ci-C-j-) mentioned above, we see that scattering over an angular range ought, however, to occur due to spacings, Be-Cf, Cf-Cg, Cg-Bfc, etc., because of the .11 \ > g o o Figure ro VI A IN T E N S I T Y — ro u> 4^ c/i o> similarity of diffracting power of B and C, and the close similarity of the distances, Be-Cf, 0f-0g, 0^-Bh, etc. The same argument applies also to more disordered groups, such as (-B-C-B-C-C-B-), and to molecules which may be in such a chaotic configuration as not to show even a definite molecular orientation. The contribution to the diffraction curve due to all such groupings should be a diffuse peak, with its maximum between 2-©-= 8°00' and 8°40'. To summarize the above, we may consider that the total x-ray diffraction curve is made up of the following:(1) sharp peaks due to the order states (-B-B-B-), (-0-C-0-) and (-B-G-B-B-) and (2) a diffuse peak, due to more compli cated groupings and randomly distributed molecules. It remains to determine the relative magnitude of the order and disorder contributions to the diffraction curve, both in the case of the pure liquids and in the case of the solutions. This may be done as follows:- (1) A smooth curve was drawn on the curves of Figures II, III, IV, V connecting the points on both sides of the main peak, where the slope seemed to change most rapidly. This was 4 entirely arbitrary but is apparently justified by the end results. It is similar to the method of Stewart in obtaining half-peak width^28^. The area under this curve was considered to represent the contribution due to all the disorder states. (2) The area above the smooth curve of (1) was considered to be due to the x-ray diffraction of the order states (-B-B-B-), (-C-0-C-) for pure benzene and pure cyclohexane respectively, and of the order states (-B-B-B-), (-0-0-0-) and (— B-G—B-G— ) of the mixtures. If we assume that the (-B-B-B-) and (-C-C-C-) groupings in the mixtures are in every way the same as in the pure liquids, then the amounts of (-B-B-B-) and (-C-C-G-) present in a given mixture should be proportional to the mol fraction of each in that mixture. In other words, the intensity of (-C-C-C-) in the pure cyclohexane times the mol fraction of 0 in the solution should equal the intensity of (-0-C-C-) in the solution. A similar argument should hold for benzene. Using the (-B-B-B-) and (-0-C-C-) values of Figures II and III placed on an arbitrary base line, as shown, the theoretical curves of Figures VII and VIII were obtained. The (-B-0-B-C-) peak intensity was made such that the addition of all curves would give the experimental peaks of Figures IV and V. Using the method of (1) and (2) the peak intensi ties were determined and tabulated in Table II. Table II The Relative Peak Intensities intensities are expressed in terms of counts per 5 minutes, as before. Those given in parenthesis are the theoretical values from Figures VII and VIII. Figures II, III, IV and V. The others are from The half-peak widths are for the order state curves for the pure liquids, and over the entire three-order peaks for the solutions. Table II Relative Peak Intensities Composition Tempera ture 100# OsH 12 6.7°C 290 30* Relative Peak Intensity Half Peak -0-0-C—B-B-B- -C-B-C-BWidth II II 10 °0 240 35' II II 35°0 200 35' II II 40 °C 170 35* II II 60 °0 150 25* 100# 06H6 5.7°0 340 20* tl II 10 °0 200 30* II II 25°0 150 30* II II 40 °C 130 30* II II 60 °C 110 30* 51.4# 06H 6 -21 °C 160 (135) 150 (130) (140) 55' (no) 1°05* ii ii 10 °0 120 (110) 110 (110) it ii 35°0 110 (100) ii ii 40 °C 85 ii ii 60°C 74.5# 06H6 ii ii 74.6# 06H12 ii ii 90 (85) (90) 1°00» (80) 80 (70) (80) 1°05* 80 (70) 70 (60) (60) 1°05* 25°0 60 (50) 110 (110) (100 ) 55* 40 °0 80 (40) 90 (100) (90) 1°05* 25°C 140 (145) 100 (40) (130) 1°00* 40 °C 110 (130) 40 (35) (100 ) 1°00* (70) 130 (90) (130) 55* 90 (60) (no) 1°00' 62.4# C6H6 25°C 62.8# C6H12 25°0 70 180 (120) The complete theoretical curves are shown in Figures VII and VIII, The top dotted line is the addition Figures VII and VIII of all the curves contributing to the x-ray diffraction. Curves of Figures VII and VIII and those of Figures IV and V are in good agreement. The data for absolute intensities in the case of the 51.4 percent benzene mixture was better than the other mixtures since they were very carefully checked. The other mixtures were studied more to prove whether all the peaks could be detected than to ascertain their absolute heights. The theory did not give very good agreement in the case of the -21°C curve of the 51.4 percent benzene mixture, since it was necessary to use the data for the pure liquids, approximately 15 degrees higher. A few possible objections to this present work must be met and, if possible, satisfied. The matter of peak (29) resolution, which was first considered by Meyer , and later by Murray and Warren^ seems to be adequately answered, if the interpretation given in Figures VII and VIII is correct. It is true that these separate peaks have not been observed by other workers, but most of them except Wara^®^, used a photographic method. It seems questionable that a photographic method would ever resolve peaks of such intensities as those obtained, because of the high background density of the film, and the small distance on the film between peaks. The experimental peaks, it is true, as 51.4 7o benzene - T H E O R E T CAL oO z 3 / -/ : \/ V v \ / \ ' \/ t)s_ A -7 \ 7 ' (E)0 (D)0 COO (B)0 CA) I Figure VII \ V \ 26. 5 7* i i E N Z E N I . O H i X AN E EOF! CAL i \.lLA Figure VIII pointed out by Murray and Warren, should not be sharp but slightly rounded. The data of the present work, taken at small angular intervals show a definite rounding, although the scale of Figures II, III, IV and V does not bring this out clearly. Also one might ask whether the (-B-B-B-) and (-C-G-C-) groupings found in the mixtures were due to insufficient mixing of the components. Experimentally, the x-ray diffraction results were independent of the amount of stirring. The effects observed could not have been caused by a streaming effect in the liquid, for curves run at room temperature, with and without stirring, were identical. The results reported here may be discussed with relation to other data from the literature. The data for the unit diffraoting distance in a given group, (d = nV2sin^), read off a graph of d versus T, over a temperature range from 10°G to 60°0, (see Table I) show that the increase in d is more than 6 percent and less than 18 percent, with a probable value of 12 percent. results now in the literature diffraction of liquids. This is consistant with the ' (30), (31), (32) Qn 3C_ray The faot that the I.O.T. tables show, for both benzene and cyclohexane, a volume expansion of only 6 percent, indicates strongly that only a small fraction of the liquid can be in an order state at any one time. This conclusion is consistant with thermodynamic data on liquids in general^*^ * hexane systen/^. , and on the benzene - cyclo The positions of the (-B-B-B-) and (.0-0-0-) peaks at the freezing points of the pure liquids strongly indicate that the order state is nearly that of the solid, in one dimension at least. The two strong lines of the solid benzene arising from the (ill) and (020) planes give an average d of 4.65 X^35), the experimental value from the liquid peak at 5.7°0 gives d = 4.68 X. Two very strong lines for solid cyclohexane gave an average d of 5.04 X compared to a value at 6.7°0 of 5.06 X for the liquid cyclohexane. The positive deviation of the benzene - cyclohexane system from Raoult' s L a w ^ on mixing^®) * and the increase in molal volume would lead to the conclusion that the intermolecular forces between benzene and cyclohexane molecules were less than those between benzenejbenzene or cyclohexane-^cyclohexane molecules. Therefore the probability of the (-B-0-B-C-) array appearing in the liquid should be less than that predicted on the basis of mol fractions. If the forces had been all equal, the (-B-C-B-C-) peak intensity should have been between the (-B-B-B-) and (-C-0-0-) inten sities. In the case of the carefully studied 51.4 percent benzene mixture, Table II shows that not only is the (-B-C-B-C-) peak intensity lower than the average intensity of the benzene and cyclohexane peaks, but also that it is almost always lower than the benzene peak itself. This is consistant with the above prediction based on Raoult* s Law. Summary (1) A low intensity peak at half the diffraction angle of the main peaks has been detected and a plausable explana tion has been given for its existance. (2) The main peak from x-ray diffraction measurements of benzene - cyclohexane solutions has been resolved experi mentally into three peaks. (3) The observed diffraction peaks in the liquid mixtures are explained on an order - disorder basis, which is consistant with existing thermodynamic data. (4) Theoretical curves are shown to give intensities comparable to measured values, for the most probable order states in the solutions. (5) The usefulness of Geiger-Mueller counters for liquid x-ray diffraction studies has been demonstrated. Bibliogranhv (1) G. W. Stewart, Ohem. Rev. 6, 483 (1929). (2) 3 G. W. Stewart, Rev. Mod. Phys. 2, 116 (1930). For reviews of papers and theories see: (a) The Diffraction of X-rays and Electrons by Amorphous Solids, Liquids and Gases. J. T. Randall, John Wiley & Sons, Inc. New York (1934) (b) 0. Drucker, Phys. Zeits. 29, 273 (1928). (3 P. Krishnamurti, (1929). Ind. J. Phys. 3, 331 (1929); 3, 507 “ “ (4 A. W. Meyer, Phys. Rev. 38, 1083 (1931). (5 R. W. 0. Wyokoff, Am. J. Sci. 5, 455 (1923). (6 G. E. Murray and B. E. Warren, J. of Ohem. Physics 7, 141 (1939). (7 S. Parthasarathy, Phil. Mag.' 18, 90-7 (1934). (8 H. K. Ward, J. Ohem. Physics 2, 153 (1934). (9 G. Scatchard, S. E. Wood and Chem. 43, 1119-130 (1939). 10 P. A. Ross, Phys. Rev. 28. 425A (1926). 11 W. C. Pierce, ibid. 38, 1409 (1931). 12 W. Soller, ibid. 24, 159 (1924). 13 J. C. Street and T. H. Johnson, J. of Franklin Institute, 214. 155 (1932). 14 W. H. Pickering, Rev. Sci. Inst. .9, 180 (1938). 15 Ruark and Brammer, Phys. Rev. 52. 322 (1937). 16 Alaoglu and Smith, ibid. 53. 832 (1938). 17 A. L. Hughes, Am. Phys. Teacher _7, 271-292 (1939). 18 International Critical Tables IV p. 133. J. M. Mochel, J. of Ph. 0. V. Raman and K. R. Ramanathan, Proc. Indian Assn. for Cultr. Sc. p. 127 (1923). Zernike and J. A. Prins, Z. ftlr Phys. 41, 184 (1927). J. A. Prins, ibid. 56, 617 (1929). J. A. Prins, Naturwiss. 19. 435 (1931). P. Debye, Phys. Zeits. 31, 348 (1930). S. Katzoff, J. Ohem. Phys. 12, 841 (1934). von L. Bewilogua, Ph. Zeits. 33, 688-92 (1932). von Gustav Thomer, ibid. 38, 48-58 (1937). 0. M. Sogani, Indian J. Phys. 1, 357 (1927). G. W. Stewart, Phys. Rev. 33, 889 (1929). A. W. Meyer, ibid. 38, 1083-93 (1931). E. W. Skinner, ibid. 36, 1625-30 (1930). S. S. Ramasubramanyan, Indian J. Phys. 3, 137-4-9 (1928). V. I. Vaidynathan, ibid. 5, 501-24 (1930). J. G. Kirkwood, J. Ph. Ohem. 43,97 (1939). G. Scatchard and W. J. Hamer, J. Am. Ohem. Soc. 57, „ 1805 (1935). E. G. Cox, Proc. Roy. Soc. A. 135, 491 (1932). K. Lonsdale and H. Smith, Phil. Mag. 28, 614 (1939). H. Poltz, Z. fur Ph. Chemie B32 243-73 (1936). appendix I Apparatus A. X-Ray Tube Circuit and. Arrangement The wiring of the x-ray tube was very similar to that used previously in this laboratory^38). To insure steady x-ray tube currents, a Raytheon voltage regulator was used to supply the 110 v. A.O. used for the filament transformer. Voltage regulator data: Raytheon Manufacturing Oo., Waltham, Mass. Type VR-3 Model 1 Watts 120 A.O. voltage 95-130, 60 cycle Output 115 ll The x-ray tube was mounted in a vertical position with the high-potential anode projecting through the table top to the transformer. The table was tall enough to allow for 10 inches of clearance between the transformer high potential and the table-top. The transformer was completely protected with wire netting fastened to the table legs. The x-ray tube shield, consisting of an iron pipe with flange, was fastened to the table-top at an angle of 4° from the vertical. Inside the iron pipe a lead oxide packed glass shield protected the iron shield from high potential. One- quarter of an inch of lead gave x-ray protection around the iron shield. The x-ray tube was supported by an adjustable damp on the cathode, fastened securely to the iron shield. The transformer cage, x-ray tube cathode and metal shielding were all grounded to a water pipe. This arrangement allowed the most intense beam produced by the x-ray tube, to be collimated by slits parallel to the table-top, and passed through the spectrometer and counter system previously described. B. Counter Circuit (1) Qeiger-Mueller Counter Tube The counter tube used was constructed by Mr. A. G. Nestor of Bartol Research Foundation, Swarthmore, Pennsylvania, and was very similar to those used previously in this (39) laboratory' ', the essential difference being in the size of the slit in the cathode. The cathode had the following dimensions:- 3.0 cm. long; 1.3 om. in diameter and a slit 3.0 cm. by 0.9 cm. through which the x-rays entered. Geiger-Mueller tube characteristics: Starting Potential 830 volts Tested to 950 volts Operating Potential 840-860 volts Resistance 500 meg. ohms. (2) High Voltage Rectifier The constant D.C. voltage for the G.-M. tube was supplied by the circuit shown in Fig. IX. This circuit is essentially that of Street and Johnson^^, except that a 57 R.C.A. tube was used rather than the 24A which they HIGH V O LT A G E RECTIFIER j | IIOV.A.G. mnmm fttrvn KI 5 I 2 c a> ;o I^ I^ 4 5V K2538 X CM IIOV.A.C. F IG U R E M IX reoommended. The rectified D. C. high voltage was supplied through a 866 half-wave mercury vapor rectifier tube. voltage delivered was measured by the ammeter the current through the bleeder resistances. positive or negative side may be grounded. The measuring Either the In this case the positive was connected to the chassis and grounded. All part numbers as given in Fig. IX refer tojWholesale Radio Co. catalog numbers, Catalog No. 69 (1938). (3) Power Supply for Amplifier Circuit Use was made of two 83 full-wave mercury vapor rectifier tubes to supply D.C. voltages for the plate circuits of the amplifier (See Figure X). Voltages for the grid biases were supplied by potentiometers connected in parallel between the center tap and ground on one of the transformers. The voltages given by these potentiometers could be varied from 0 to -37 volts. Condensers were connected between the grid bias leads and ground to smooth out the voltages (not shown in Fig. X). R 5 and R 6 were 5000 ohms. These resistors should be 100,000 ohms to reduce continuous drain on the transfor mers. Difficulty was experienced with the fine wire of these high resistances burning out, hence the smaller resistances were used. These power supplies were each capable of producing 235 milliamperes at a maximum of 400 volts. POWER SUPPLY K42S r\ ^IwOtwuiK «4*-<■> nrmn (Tsvnr 8&S" • • fil.Supply GRID BIAS Rr 2SOOJX All p^Kt Numbers Rx R ^ R ^ - S O O O H Wholesale Radio C ata lo g No.'s No. G9 (1938) R s R fc- SOOOSi C, Ca C3 C4 - .dufF IG U R E X jUUtUMlUiU/ 83 ivnvrnrsi 83 R,~-— >v. COUNTER CIRCUIT 45V +220 V 4 57 56 865 56 r\ r\ 050V 4SV— Rx- / o v i o ‘ i i R2> ^ By —SoooIL stHrlxidfl (3)- M A GNETIC SPEAKER @ F IG U R E V! - CENCO COUNTER 37. Rll-5'06fl0il ^ C„- .25C^oCB )C^jC/0 (4) Amplifier Circuit The circuit finally adopted is shown in Fig. XI. One advantage of this circuit is that it is only necessary to shield the first amplifier tube (57 tube), condenser 0^ and the resistances Rg and Rg. The quality of the pulse could be checked in each stage of the amplification by use of phones in the jacks in the plate circuits. The volume of the speaker could be varied by R^g, without changing the tube current in the 45 power tube. The filament for the 885 thryatron must be supplied by a separate filament transformer which is not grounded. This is essential for operation of this circuit, since the cathode potential goes from+*20 v to+-230 v when a pulse causes the tube to lose control and discharge condenser Cg. The amplifier, power and high voltage supplier were all mounted in a cabinet so that adjustments might be made from the bottom of each chassis without removing. If necessary each chassis could be removed independently. The bias voltages used for most efficient operation were approximately: No. 1 57 tube bias - 3v. No. 3 56 tube bias -lOv. No. 3 56 -4.5v. tube bias 885 thryatron bias -llv. 885 thryatron cathode potential + 20v above ground. 40 BALANCED 38 F IL T E R T R A N S M IS S IO 1V0. 30 Sr 34 32 30 ,30 .40 .5 0 X -K A Y .60 WAVELENGTH Figure XII 80 IN A 90 APPENDIX II Filter Transmission Qurve The transmission of the ZrOg and Sr(NC>3)3 filters measured for the x-ray spectrum of molybdenum is shown in Fig# XII# The wavelengths were determined using a NaCl crystal, aligned so that the (100) plane was diffracting. Using the value of d],qq = 2.8135 2 and measured on the spectrometer, the wavelengths were determined by Bragg's law# The x-ray tube was operated at 42 kilovolts (r.m.s.), the value used in all the experimental measurements, with a tube current of 10 railliamperes to reduce the counting rate. The cross hatohed area, of Fig. XII, represents the wavelengths transmitted by the Zr02 filter and not by the Sr(N03)2* It was therefore these wavelengths which contri buted to the diffraction curves. The intensity of the doublet was very much greater than indicated, since the counter would only record 3600 pulses per minute (60 cycle of the x-ray tube). IN TEN SITY FIGURE XIII 'If' APPENDIX III Additional Data A. Shape of Entire Diffraction Curves Since it was not possible to reproduce the entire range of angle of diffraction studied in Figs. II - V, three representative curves are shown in Fig. XIII. All of the curves taken exhibited the small peak at angles between 3^-= 4°00' to 4o20' depending on the mixture taken. B. Experimental and Theoretical Curves for Other Mixtures Curves were obtained for mixtures other than those given in the main body of this thesis. The shape of the curves and peak intensities were in agreement with the others taken. These are reproduced in Figures XIV and XV. As pointed out previously, these curves were not checked so carefully for absolute peak intensities as for existance of peaks, hence the check between theory and experiment was not as good as the 51.4 percent benzene C. case. Peak.Shift with Temperature The values of d corresponding to each peak increases with rising temperature, as can be seen from Table I. This increase in d is given by a decrease in the angle of diffrac tion for the peaks. In Fig. XVI the peak positions (2-©*) are plotted against temperature, for each peak of the 51.4 percent benzene mixture and the two pure liquids. 43. CA) - 3 7 . 2 7. B\iN Z fIN E CB) -B 2 .4 7. B H N Z I1 N E (B)0 Figure XIV 44. ( A ) - 3 7 . 2 7, B E N Z E N E <B) 4 - 6 2 . 4 7 . BE N Z E N - THEORETICAL oG (B)0 CA) 0 Figure X V 45 • ----- — -----i---- - CB) — 8°2 0' 11 CO — 8°4 o' ri (D) — e?oo'p EA K CE) &°o4► \ U 8°0 y p EA K — 8°4 0' \ *• ----- ii 5 14 7. io !** CVI CA) 1 p ° Vo o 1 ® * ! <t> ---- j----- 100 7. Hb JIV c * H* / ' . * vL / i. r \ \ w / &N f) trfc.7 fC.\ - /n\ ) VI37 r 8 4 0J \\-»7 CA') WV/ •>— 4i * / r»\ ) "VO/ t i % (C) 8 0 0) rAv 9 >Tttr |--- .10 0 10 20 TEMPERATURE 30 C° C) r> r*\ o c?rn V / WS-S TEM PER C°C) &VII. ATURE Figure m D. Decrease in Intensity with Temperature The intensity data tabulated in Table II may be found reproduced graphically in Figure XVII for the liquids studied over the range of temperatures. If the diffraotion peaks are due to the so called "cybotactic1* order groups existing in the liquid, then the - intensity of the peak should be proportional to the number of such groups present at any given instant. Then the intensity I should be some function of the form of a Maxwell-Boltzman distribution. where is some function of the energy. - In I = 4> T°K + constant If this was true then a plot of In I against l/T°K should give a straight line. These plots were made for the pure benzene and cyclohexane and the peaks of the 51.4 percent benzene solution. Nearly straight lines were obtained except in the region near the freezing points. The data however do- , not seem accurate enough to justify saying anything further about the distribution function. 48. Appendices Bibliography (38) 0. W. Mclenathen, M.S. Thesis (1939). (39) H. M. Sullivan, Ph. D. Thesis (1938). (40) Duffendack, Lifschutz, and Slawsky, Ph. Rev. 51. 1331 (1937).