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X-ray diffraction in liquids Danielson, Gordon Charles 1935

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X-RAY DIFFRACTIOH IS LIQUIDS by Gordon Oharles Danielson A Thesis submitted f o r the Degree of M A S T E E O F A R I, S In the Department of PHYSICS, THE UNIVERSITY OF BRITISH COLUMBIA APRIL 9 1935 G 0 N T B S T S I. H i s t o r i c a l . I I . Current Theories. 1.Raman's Theory. 2.Stewart's Theory. 3. Delay©'s Theory, 4. Zernike and Prins Theory. I I I . Experimental. 1. Transformer, 2. X-ray tube. 3,Spectrograph and C e l l . 4. Experimental Procedure. 5. Discussion of Results. IV. Conclusion, Bibliography. 1. X-ray D i f f r a c t i o n In Liquids *r I. HISTORICAL Debye and Scherrer showed i n 1916 that passage of a pencil of x-rays through a thin unenclosed stream of l i q u i d produced a broad halo surrounding the central undeviated beam* They established the phenomenon as interference by comparing the diameter of the ring when using dif f e r e n t wave-lengths. In 1922, Keesoni and de Smedt i d e n t i f i e d weak secondary halves f o r oxygen, argon, and nitrogen, i n the l i q u i d states. In the same year Hewlett examined benzene, octene, and mesitylene, contained in thin o e l l u l o i d capsules, by the spectrometer io n i z a t i o n method* He showed that the scattering at small angles i s small. Since that time considerable work has been done on t h i s phenomenon, especially by Raman, Stewart, Prins, Debye and t h e i r associates. By a l l , i t i s agreed that the d i f f r a c t i o n effects indicate s p a t i a l orderly arrangement of molecules. I I . CURRENT THEORIES. 1. Raman's Theory. The f i r s t serious attempt to explain the d i f f r a c t i o n of x-rays by li q u i d s was made by Raman and R 2. Ramanathan i n 1923. The approach i s similar to that of Smoluohowski and Einstein i n the scattering of v i s i b l e l i g h t by l i q u i d s . The l i q u i d i s considered continuous as a whole but subject to l o c a l fluctuations i n density, The assumption of continuity i s v a l i d in the case of v i s i b l e l i g h t because of the large difference between the wave-length of l i g h t and the size of a molecule: but this i s not the case with x-rays. The statistioal-thermodynamical considerations van be applied d i r e c t l y when the angle of scattering is small. For larger angles, i t i s necessary to f i n d an expression f o r the l o c a l variations of density. For the i n t e n s i t y , Raman gets where 1 0 i s the mean distance between neighboring molecules and given by Bragg 5s equation, i s the isothermal compressibility of the f l u i d , 00 i s the half d i f f r a c t i o n angle f o r the p r i n c i p a l halo, and &, f o r any scattering angle. If I i s plotted against -sf-the sharpness of the maximum depends upon • The curves f o r water and glycerine correspond f a i r l y well with those obtained experimentally, but the agreement i s not so good f o r ether. In the l a t t e r case the large value of 1 0 makes the theoretical curve sharp whereas the experimental curve i s broad. The theory has been widely applied by Raman's associates to explain the effect of change of temperature and concentration of solution on the rings. No account i s given f o r the two or three d i f f r a c t i o n bands of some l i q u i d s , however, so the theory can be no more than an approximation to the truth. 2, Stewart's theory. A crude idea of the l i q u i d as a mass of fragmentary crystals had been suggested soon after the phenomenon attracted attention. Keeson and de Smedt and Hewlett made thi s hypothesis more l o g i c a l by assuming a kind of temporary c r y s t a l l i z a t i o n . The atoms or molecules would imitate, over short elements of space and time, the arrangement of the c r y s t a l l i n e state. This may have been the beginning of Stewart's theory, Stewart explains the d i f f r a c t i o n pattern on the basis of molecular grouping which he c a l l s oybotaxis* At any p a r t i c u l a r instant small orderly groups of molecules exist at various points in the l i q u i d . The volume occupied by grouped molecules w i l l depend upon the substance under consideration. The molecules do not remain permanent members of any one well defined group but are continually moving from one to another. 4. The cause of t h i s molecular grouping i s attributed to the shape of the molecules. I f the molecules were cigar-shaped, p a r a l l e l grouping would "be more probable than another owing to the nature of the molecular forces. The k i n e t i c energy of the molecules w i l l not necessarily disturb the cybotactic state f o r i t has been shown that the r e l a t i v e v e l o c i t i e s of any two adjacent molecules may be small.in comparison with the actual v e l o c i t y of either. As the temperature of ether i s increased i t has been shown that the maximum scattering intensity i s shi f t e d toward smaller angles and the peak heights decrease. The s h i f t i s attributed to thermal expansion which would produce an increase i n spacing and hence make the maximum occur at a smaller angle, T he decrease in peak height i s caused by an increase i n thermal agitation which would make conditions less favorable for the existence of cybotactic groups. The scattering at small angles i s proportional to the numbereof random molecules.and hence increases with r i s e in temperature. At the c r i t i c a l temperature the l i q u i d and vapor phases merge and the cybotactic group formation ceases to exi s t . Ordinarily a l i q u i d mixture w i l l give a d i f f r a c t i o n pattern on which the patterns of the two components are superimposed. If the two l i q u i d s are completely miscible, however, the d i f f r a c t i o n pattern i s di f f e r e n t from either constituent, The main peak has as angular position between the peaks of the constituents and s h i f t s d i r e c t l y * i t h the concentration. This indicates a single type of cybotactie group formed by melecules of both groups. The x-jbay pattern may thus be used to distinguish between dif f e r e n t types of l i q u i d mixtures. The va r i a t i o n of gas v i s c o s i t y i s fundament-a l l y d i f f e r e n t from that of l i q u i d s . The former increases with r i s e i n temperature, the l a t t e r decreases, Andrade develops a theory f o r l i q u i d s on the basis of mementum transfer taking place during a temporary union of melecules. The conception i s thus s i m i l a r to that of Stewart's. Stewart and Edwards have found an unmistakable correlation between the c o e f f i c i e n t of v i s c o s i t y and the perfection of grouping f o r chain molecules?, as shown by x-ray d i f f r a c t i o n . The cybotactie condition may therefore be a satisfactory basis f o r explanation of l i q u i d v i s c o s i t y . 3* Debye»s Theory, Debye assumes that the d i f f r a c t i o n i s caused by neighboring molecules. He derives a d i s t r i b u t i o n function f o r the arrangement of the molecules i n a l i q u i d . The maximum scattering angle i s defined by the quotient of the wave-length of the radiation and the diameter of 6. the sphere occupied by the molecule. The curves are only approximate but the scattering angle i s of the right order or magnitude f o r simple molecules, 4. Zanike and Prins Theory. This theory i s also l a r g e l y mathematical. A d i s t r i b u t i o n function i s assumed and evaluated in an empirical way. To apply the theory* the l i q u i d i s assumed to consist of spherical atoms cl o s e l y packed together so that the free space i s n e g l i g i b l e . A reasonably good agr^ment with the experimental intensity curve f o r mercury Is obtained. The approximate" nature of t h i s assumption l i m i t s the application to monatomic l i q u i d s . The p o s s i b i l i t y of a comprehensive theory for l i q u i d s , as exists for gases, seems to be in further study of x-ray d i f f r a c t i o n patterns. What i s needed most, perhaps, i s information on the d i f f r a c t i o n of some simple substance i n a l l three states and at different temperatures, I I I . EXPERIMENTAL. 1, Transformer. The transformer consists of two 30,000 ohm secondary c o i l s wound on a 0,85 ohm primary and the whole immersed i n . o i l . The primary i s tapped i n two places so three connections are possible. 0 - 1 Resistance • 0.231 ohms. 0 - 2 " 0.242 " 0 - 3 " 0.255 1 7. A rheostat of 12 ohms i s placed, in series with the primary whennstarting since the instantaneous current in the x-ray tube may be large* The secondary c o i l s are connected to the primary (terminal 3) t© prevent sparking between the inside layers of the former and the outside layers of the l a t t e r . This allows an e f f i c i e n t and compact transformer but i s rather unfortunate in this case. Since the target end of the x-ray tube must be grounded and one side of the 110 v o l t a.c. supply i s also grounded only half of the transformer can be used. Thus the voltage available was only 35,000 when the f u l l 70,000 volts would have been much better. An ammeter, reading up to 20 amperes, i s placed i n the primary c i r c u i t and a milliammeter, with a maximum of 12 milliamperes* i s in the secondary c i r c u i t , 2, X-ray Tube, The x-ray tube i s of the Shearer type, which is the most suitable f o r the study of d i f f r a c t i o n e f f e c t s . The three most important advantages are: (1) replaceable targets, (2) water cooling, (3) aluminium window. The f i r s t enables one to change the wave-length of the x-rays, the second allows continuous operation, and the t h i r d increases the intensity of the rays by giving l e s s absorption and by permitting the 8. spectrometer to be placed nearer the target. The tube has considerable r e c t i f y i n g properties so the transformer •r can be connected to i t d i r e c t l y . The cathode end i s cooled by convection in a long, insulated brass vessel f i l l e d with water. The x-ray tube i s evacuated by means of 4 i mercury pump and an o i l back pump. Since the operation of the tube depends upon the ionization of the a i r by fast electrons,too low pressure i s possible. The a r t i f i c i a l leak used consisted of a variable needle valve connected by rubber tubing to a jar evacuated by the o i l uump alone. The right order of leak was obtained by making a number of small needle holes i n the rubber tubing; fine adjustment of the pressure could then be made with the needle valve. Heavy stop cock grease i s needed f o r the threads of the valve. This arrangement keeps the pressure constant at the right value for s i x hours or more as shown by the reading of the millianplter, 3, Spectrograph and C e l l . The Dr. Muller x-ray spectrograph i s suitable f o r the study of x-ray d i f f r a c t i o n by l i q u i d s as well as by c r y s t a l s . The arrangement i s nearly the same as that fo r the LaWe spot method of investigating c r y s t a l structure. The x-ray beam i s li m i t e d by a narrow c y l i n d r i c a l channel 9, in a brass rod,, which has one end about 4 mm from the aluminium window and the other 2 to 3 cm from the l i q u i d , The plate holder i s 5 cm on the other side of the l i q u i d . Black paper covers the face of the plate holder so plates may be taken i n daylight, A small c i r c u l a r piece of lead prevents fogging of the plate owing to the direct beam. The c e l l used f o r containing the l i q u i d seems to be a d i s t i n c t improvement over others that have been used. The l i q u i d i s contained between two mica windows 1,5 mm apart. The mica i s held in position by a ring of brass on each side of the centre piece. The three rings are clamped to-gether with s i x screws. The l i q u i d to be examined Is pouted into a brass c y l i n d r i c a l vessel above the c e l l and the l i q u i d enters the c e l l by small metal tubing 1 mm i n diameter. The whole i s supported by an iron rod 7 cm. long which f i t s into the centre of the spectrograph table. The advantage of using mica windows i s that no ring i s given by this substance, as is the case with glass and metals, but only spots which do not interfere 10. with the ring given by the l i q u i d , The method of clamp-ing enables one to clean the c e l l e a s i l y and th change .,the windows. A s p e c i a l cutter was constructed f o r cutting out mica windows 10 mm in diameter and 0,01 mm thick. The vessel on top i s convenient when f i l l i n g the c e l l and also makes i t easier to examine l i q u i d s with high vapor pressure at room temperature. By placing a n l i t t l e stop cock grease around the cover on top l i q u i d s such as cyclohexane and ether may be contained in the c e l l for several hours. The supporting iron rod screws into the c e l l so that the height may be adjusted u n t i l the beam of x-rays passes through the centre of the c e l l . 4. Experimental Procedure. Having chosen the target desired (copper was used throughout th i s experiment) and having properly put i t in place with a l i t t l e stop cock grease, the tube i s evacuated. An e l e c t r i c heater for the mercury pump i s most convenient but i t takes about 20 minutes to heat the mercury s u f f i c i e n t l y . The pressure in the tube can be estimated by the color and the ammeter reading. The current i s s l i g h t l y positive as the purple glow gradually extends along the cathode. As the glow f i l l s the tube and s t r i a t i o n s appear the current s h i f t s to the negative. The glow recedes and f i n a l l y disappears 11, almost completely. The Current s h i f t s abruptly from a strong negative to a strong positive reading (about 12 m a) and x-rays may then be observed with a phosphorescent screen. The current i s kept from decreasing beyond 6 or 8 m. a. by means of the a r t i f i c i a l leak. The spectrograph i s adjusted, by looking through the small c i r c u l a r hole 9 u n t i l the c e l l and lead s h i e l d on the plate holder are in proper alignment. The spectrograph can be put into the correct position to allow maximum inte n s i t y of x-rays through the c i r c u l a r hole by Hsing a zinc sulphide phosphorescent screen. The l i q u i d i s put into the c e l l and a plate exposed f o r s i x hours, A shade was ms3#? for the windo* so the plates could be developed i n the same room. I t i s desirable to have "the room dark„ a l s o 9 when using the phosphorescent screen. Fogging of the plates was prevented to some extent by surrounding the entire spectrograph with lead, 5, Discussion of Results. Eighteen l i q u i d s have been examined and a l l show marked differences i n the d i f f r a c t i o n patterns. Many 0f the patterns are very f a i n t but a sample of eight is shown. An explanation of the observed effects w i l l be attempted in terms of Stewart's theory. This theory i s chosen because 12, i t gives the most complete picture and beoause the math-ematioal theories are s t i l l very l i m i t e d in application. •i 1. Benzene and Qyclohexane. These two d i f f r a c t i o n patterns are very s i m i l a r in both size and sharpness of the r i n g . The two l i q u i d s have s i m i l a r s t r u c t u r a l formulae; hence i t would seem that the shape of the molecule i s involved in the formation of cybotactie groups. The distance between groupi and the number of groups per unit volume i s then determined by the shape of the molecule. In both cases, the number of molecules i n groups as compared to the numeer not in groups must be great; for the scattering at small angles given by random molecules i s very weak. Why this benzene ring should give such an orderly arrangement of molecules i s d i f f i c u l t to see. There i s a s t r i k i n g difference in intensity, however. When the double bonds between the carbons in o benzene are replaced by a single bond and an additional hydrogen i n oyclohexane we get a great increase in intensity, -& H Thus the arrangement seems to be much more effective • H i n scattering x-rays than "^0 2 C, ?be change in i n t e n s i t y might be due to the addition of more hydrogen (Cg H l 2 as compared to C g H g) but i t i s doubtful i f the explanation i s as simple as t h i s . 13. 2, Ethyl Alcohol and Ether, These two l i q u i d s d i f f e r in that ethyl alcohol has one ethyl group per molecule while ether has two. Two explanations seem possible for the ether ring being smaller and more d i f f u s e . The ether cybotactic groups are fewer and farther apart because the shape of the molecule i s dif f e r e n t or because the ether was nearer i t s b o i l i n g point. It i s to be noted that the b o i l i n g point of benzene and cyclohexane are about the same (80° C) so no difference in size or diffuseness of the ring would result in that case. Ether, however, b o i l s at 35° C while alcohol b o i l s at 78° C at atmospheric pressure. The l a t t e r explanation seems most probable but further investigation on this point i s necessary. The d i f f r a c t i o n by .ether i s more intense than that by alcohol. It would seem that, i f replacing a carbon bond of hydrogen i s effe c t i v e i n increasing the intensity, replacing the hydrogen by an ethyl group i s even more so. This hypothesis i s borne out I n the next two plates in which hydrogen in acetic acid i s replaced by an ethyl group in ethyl acetate and the intensity thereby increased, 3. Acetic Acid, Ethyl Acetate, and Ethyl Malonate, When acetic acid and ethyl alcohol combine to form ethyl acetate we get an x-ray d i f f r a c t i o n pattern 14, quite d i f f e r e n t from either of the o r i g i n a l materials. The aew ring i s not a combination of the other two since the ethyl acetate ring i s the smallest. The distance between cybotactic groups has been increased while the number of groups, as shown by the broadening of the band, has been decreased. Ethyl malonate i s different from a l l the other patterns shown i n there being two rings d i s t i n c t l y v i s i b l e . The outer ring i s s i m i l a r in size and appearance to ethyl alcohol. It would be interesting to see i f the inner ring i s s i m i l a r to malonie acid. In any case, the combination of ethyl alcohol and malonie acid has resulted i n a compound which has a dual cybotactic arrangement. Two types of group combination must be occurring, 4. Pilchard O i l , The very d i s t i n c t ring given by pilchard o i l i s i n t e r e s t i n g . Fish o i l i s a mixture of unsaturated ( i . e . double or t r i / p l e bonds between the carbons) glycerol esters. Since complicated long chain molecules exist i n this substance, the d i f f r a c t i o n may be caused by regularity in the arrangement of the atoms in the molecule rather than by r e g u l a r i t y of the molecules in the l i q u i d . Thus each molecule would act as a small c r y s t a l . This -^should be 15. possible when the molecules are several times the wave-length of the l i g h t used. If thi s i s the cause of the 'ring we should expect i t to be sharp since the number of regular arrangements would be greater. The difference i n i n t e n s i t y of two sides of some plates, p a r t i c u l a r l y that of pilchard o i l , i s due to improper screening. The black spot, which overlaps the central spot made by the lead on the front of the plate holder, i s caused by some experimental error which has not yet been found. IV. 0OHCLUSI0H The study of x-ray d i f f r a c t i o n patterns has not progressed as rapidly as desired because of the long time necessary f o r exposure. Intensifying screens that have been used have not been satis f a c t o r y , A higher potential i s the only other method of increasing the int e n s i t y . Tentative arrangements have been made for the design of a c e l l which w i l l allow substances to be examined over a temperature range - 100° 0 to 400° G or higher. By studying the intensity of the d i f f r a c t i o n patterns with a microphotometer, interesting results should be obtained. The temperatures at which the s o l i d changes to l i q u i d and the l i q u i d to gas would be p a r t i c u l a r l y important. X-RAY DIFFRACTION PATTERNS 16. Benzene (Cg E&) I I j Ethyl Alcohol (CgH50 H) Ether ( CgHgO-02H5) Pilchard O i l B I B It 1 0 G R A P H Y "The d i f f r a c t i o n of x-rays and electrons by amorphous s o l i d s , l i q u i d s , and gases." - J .T.Randall. 2, "2-ray d i f f r a c t i o n in l i q u i d s . " - C.M.Sogani, Indian Journal of Physics, vol.1, page 357, (1987) 3. "Further studies i n x-ray l i q u i d d i f f r a c t i o n " -C.M.Sogani, Ind. Jo*r. Phy., 2, 99 (1927) 4. "Relation between chemical constitution and x-ray d i f f r a c t i o n i n l i q u i d s " - P.Krishnamurti, Ind.Jour.Phy. 2, 355 (1928) 5. "X-ray d i f f r a c t i o n in carbon tetrachloride" -C.M.Sogani, Ind.Jour.Phy. 2,377 (1928) 6. "X-ray d i f f r a c t i o n and molecular complexity in the l i q u i d state" - P.Krishnamurti, Ind.Jour,Phy.2,491 (1928) 7. "Thermal degeneration of the x-ray haloes in li q u i d s and amorphous s o l i d s " - S,S.Ramasubramanyam, Ind, Jour. Phy. 3,137 (1928) 8. "Nature of solutions as revealed by x-ray d i f f r a c t i o n " - P. Krishnamurti, Ind.Jour.Phy. 3,307 (1928) 9. "X-ray d i f f r a c t i o n i n l i q u i d mixtures" -P. Krishnamurti, Ind.Jour.Phy. 3,331 (1928) 10. "X-ray d i f f r a c t i o n in li q u i d s of the terpene series" - V,I.Yaidyanathan. Ind.Jour.Phy. 3,372 (1929) 11. "Influence of temperature on the x-ray l i q u i d haloes" - V.I.Vaidyanathan, Ind. Jour. Phy. 3,391 (1929) 12. "X-ray d i f f r a c t i o n in li q u i d s and solutions" P.Krishnamurti. Ind.Jour.Phy. 2,507 (1929) 13. "X-ray d i f f r a c t i o n in primary normal alcohols" G. W. Stewart and R. M. Morrow. Phy.Rev.30,232 (1927) 14. "Comparison of primary normal alcohols and the i r isomers" - G.W.Stewart and E.W.Skinner. Phy.Rev. 31,1 (1928) 15* "X-ray d i f f r a c t i o n i n l i q u i d normal paraffins" -G.W.Stewart, Phy.Rev. 31, 174 (1928) 16. " D i f f r a c t i o n of x-rays in l i q u i d s " - G.W.Stewart. Phy.Rev* 33, 889 (1929) 17. " D i f f r a c t i o n of x-rays in organic mixtures" A. W.Meyer. Phy.Rev, 38,1083 (1931) 18. "Viscosity and molecular arrangement in 22 liquids; o c t y l alcohols" - G.W.Stewart and R.L.Edwards. Phy.Rev, 38, 1575 (1931) 19. "X-ray d i f f r a c t i o n in ethyl ether near the c r i t i c a l point" ~ W, N o l l . Phy.Rev. 42, 336 (1932) 20. "X-ray d i f f r a c t i o n in long chain l i q u i d s " -B, I.Warren, Phy.Rev. 44 ,969 (1933) 21. "X-ray d i f f r a c t i o n in l i q u i d s " - G.W.Stewart. Rev. of Mod. Phy. 2, 116 (1930) 22. "Gyhotactic condition in l i q u i d s " - G.W.Stewart. Phy.Ref• 35, 726 (1930) 23. "Theory of the Viscosi t y of Liquids" - E.N.DaC.Andrade, Phil.Mag, 17, 497 (1934) 


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