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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 T h e s i s submitted f o r the Degree of M A ST E E  OF  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.  Historical.  II.  Current T h e o r i e s . 1.Raman's Theory. 2.Stewart's  Theory.  3. Delay©'s Theory, 4. Zernike and P r i n s  Theory.  I I I . Experimental. 1. Transformer, 2. X-ray tube. 3,Spectrograph and C e l l . 4. Experimental Procedure. 5. D i s c u s s i o n o f R e s u l t s . IV.  Conclusion, Bibliography.  1. X-ray D i f f r a c t i o n In L i q u i d s  *r  I.  HISTORICAL Debye and S c h e r r e r showed i n 1916 t h a t  passage  of a p e n c i l of x-rays through a t h i n unenclosed  stream o f l i q u i d produced a broad halo surrounding the c e n t r a l undeviated beam*  They e s t a b l i s h e d the  phenomenon as i n t e r f e r e n c e by comparing  the diameter of  the r i n g when u s i n g d i f 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 h a l v e s f o r oxygen, argon, and n i t r o g e n , i n the l i q u i d s t a t e s .  In  the same year Hewlett examined benzene, octene, and m e s i t y l e n e , c o n t a i n e d i n t h i n o e l l u l o i d c a p s u l e s , by the spectrometer i o n i z a t i o n method*  He showed that  the s c a t t e r i n g a t s m a l l angles i s s m a l l .  Since that  time c o n s i d e r a b l e work has been done on t h i s  phenomenon,  e s p e c i a l l y by Raman, Stewart, P r i n s , 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  e f f e c t s i n d i c a t e s p a t i a l o r d e r l y arrangement o f molecules. II.  CURRENT THEORIES. 1. Raman's Theory. The f i r s t s e r i o u s attempt t o e x p l a i n the  d i f f r a c t i o n o f x-rays by l i q u i d s was made by Raman and R  2. Ramanathan i n 1923.  The approach i s s i m i l a r t o t h a t o f  Smoluohowski and E i n s t e i n i n the s c a t t e r i n g o f 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 s u b j e c t to l o c a l f l u c t u a t i o n s i n d e n s i t y , The assumption o f c o n t i n u i t y i s v a l i d i n the case of v i s i b l e l i g h t because o f the l a r g e d i f f e r e n c e between the wave-length o f l i g h t and the s i z e o f a molecule:  but t h i s  i s not the case w i t h x - r a y s . The s t a t i s t i o a l - t h e r m o d y n a m i c a l c o n s i d e r a t i o n s van be a p p l i e d d i r e c t l y when the angle o f s c a t t e r i n g i s small.  F o r l a r g e r a n g l e s , i t i s necessary to f i n d an  expression f o r the l o c a l v a r i a t i o n s o f d e n s i t y .  For  the i n t e n s i t y , Raman gets  where 1  0  i s the mean d i s t a n c e between neighboring  and given by B r a g g s equation,  i s the  5  i s o t h e r m a l c o m p r e s s i b i l i t y o f the f l u i d ,  0  0  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 h a l o , and scattering  molecules  i s the h a l f &,  f o r any  angle. I f I i s p l o t t e d a g a i n s t -sf-the sharpness  of the maximum depends upon  •  The curves f o r  water and g l y c e r i n e correspond f a i r l y w e l l w i t h  those  obtained e x p e r i m e n t a l l y , but the agreement i s not so good f o r ether.  In the l a t t e r case the l a r g e value o f 1  0  makes the t h e o r e t i c a l curve sharp whereas the experimental curve i s broad.  The theory has been w i d e l y a p p l i e d  by Raman's a s s o c i a t e s to e x p l a i n the e f f e c t of change of temperature and c o n c e n t r a t i o n o f s o l u t i o n on the r i n g s . 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 t o the t r u t h . 2, Stewart's t h e o r y . A crude i d e a of the l i q u i d as a mass of fragmentary c r y s t a l s had been suggested soon a f t e r the phenomenon a t t r a c t e d a t t e n t i o n .  Keeson and de Smedt  and Hewlett made t h i s hypothesis more l o g i c a l by a k i n d o f temporary c r y s t a l l i z a t i o n .  assuming  The atoms  or molecules would i m i t a t e , over s h o r t elements of space and time, the arrangement This may  o f the c r y s t a l l i n e  state.  have been the beginning o f Stewart's theory, Stewart e x p l a i n s the d i f f r a c t i o n  pattern  on the b a s i s o f molecular grouping which he c a l l s oybotaxis* At any p a r t i c u l a r i n s t a n t s m a l l o r d e r l y groups o f molecules e x i s t at v a r i o u s p o i n t s i n the l i q u i d .  The volume  occupied by grouped molecules w i l l depend upon the substance under c o n s i d e r a t i o n .  The molecules do not remain  permanent members o f any one w e l l d e f i n e d group but are c o n t i n u a l l y moving from one to another.  4. The cause o f t h i s molecular grouping i s a t t r i b u t e d to the shape o f the molecules.  I f the  molecules were c i g a r - s h a p e d , p a r a l l e l grouping would "be more probable than a n o t h e r molecular f o r c e s .  owing to the nature of the  The k i n e t i c energy of the molecules  w i l l not n e c e s s a r i l y d i s t u r b the c y b o t a c t i c s t a t e 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 s m a l l . i n comparison w i t h the actual v e l o c i t y of either. As the temperature  of ether i s i n c r e a s e d i t  has been shown that the maximum s c a t t e r i n g i n t e n s i t y i s s h i f t e d toward s m a l l e r angles and the peak h e i g h t s decrease. The s h i f t i s a t t r i b u t e d to thermal expansion which would produce an i n c r e a s e i n spacing and hence make the maximum occur at a s m a l l e r angle,  T he decrease i n  peak h e i g h t i s caused by an i n c r e a s e i n thermal a g i t a t i o n which would make c o n d i t i o n s l e s s f a v o r a b l e f o r the e x i s t e n c e o f c y b o t a c t i c groups.  The s c a t t e r i n g at  s m a l l angles i s p r o p o r t i o n a l to the numbereof random molecules.and hence i n c r e a s e s with r i s e i n 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 c y b o t a c t i c group formation ceases t o e x i s t . O r d i n a r i l y a l i q u i d mixture w i l l g i v e a d i f f r a c t i o n p a t t e r n on which the p a t t e r n s o f the two components are superimposed.  I f the two l i q u i d s are completely m i s c i b l e ,  however, the d i f f r a c t i o n p a t t e r n i s d i f f e r e n t from e i t h e r constituent,  The main peak has as angular p o s i t i o n  between the peaks o f the c o n s t i t u e n t s and s h i f t s * i t h the c o n c e n t r a t i o n .  directly  T h i s i n d i c a t e s a s i n g l e type  o f c y b o t a c t i e group formed by melecules of both groups. The x-jbay p a t t e r n may thus be used to d i s t i n g u i s h between d i f f e r e n t types o f l i q u i d m i x t u r e s . The v a r i a t i o n o f gas v i s c o s i t y i s fundamenta l l y d i f f e r e n t from that o f l i q u i d s .  The former i n c r e a s e s  w i t h 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 b a s i s of mementum t r a n s f e r t a k i n g p l a c e d u r i n g a temporary union o f melecules. The conception i s thus s i m i l a r t o t h a t o f Stewart's. Stewart and Edwards have found an unmistakable  correlation  between the c o e f f i c i e n t o f v i s c o s i t y and the p e r f e c t i o n of grouping f o r c h a i n molecules?, as shown by x-ray d i f f r a c t i o n . The c y b o t a c t i e c o n d i t i o n may t h e r e f o r e be a s a t i s f a c t o r y 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 d e r i v e s a d i s t r i b u t i o n  f u n c t i o n f o r the arrangement of the molecules i n a l i q u i d . The maximum s c a t t e r i n g angle i s d e f i n e d by the quotient of the wave-length  o f the r a d i a t i o n and the diameter of  6. the sphere occupied by the molecule. only approximate  The curves are  but the s c a t t e r i n g angle i s o f the r i g h t  order or magnitude f o r simple molecules, 4. Zanike and P r i n s  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 f u n c t i o n i s assumed and evaluated i n an e m p i r i c a l way.  To apply the theory* the l i q u i d i s assumed  to c o n s i s t of s p h e r i c a l atoms c l o s e l y packed t o g e t h e r so that the f r e e space i s n e g l i g i b l e .  A reasonably good  agr^ment w i t h the experimental i n t e n s i t y curve f o r mercury Is o b t a i n e d .  The approximate" nature of t h i s  assumption  l i m i t s the a p p l i c a t i o n 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 f o r l i q u i d s , as e x i s t s f o r gases, seems to be i n f u r t h e r study of x-ray d i f f r a c t i o n p a t t e r n s .  What i s needed most,  perhaps, i s i n f o r m a t i o n on the d i f f r a c t i o n of some simple substance i n a l l three s t a t e s and at d i f f e r e n t  temperatures,  I I I . EXPERIMENTAL. 1,  Transformer. The transformer c o n s i s t s of two 30,000  secondary c o i l s wound on a 0,85 immersed i n . o i l .  ohm  primary and the whole  The primary i s tapped i n two p l a c e s  so three connections are p o s s i b l e . 0-1 0 - 2 0 - 3  ohm  Resistance " "  •  0.231 ohms. 0.242 " 0.255 1  7. A r h e o s t a t of 12 ohms i s placed, i n s e r i e s w i t h the whennstarting tube may  be  s i n c e the instantaneous c u r r e n t i n the x-ray  large* The secondary  primary  primary  c o i l s are connected to the  ( t e r m i n a l 3) t© prevent sparking between the i n s i d e  l a y e r s of the former and the o u t s i d e l a y e r s o f 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 r a t h e r u n f o r t u n a t e i n t h i s case. of  Since the t a r g e t end  the x-ray tube must be grounded and one s i d e of the  110 v o l t a.c. supply i s also grounded only h a l f of the transformer can be used. was  Thus the v o l t a g e a v a i l a b l e  o n l y 35,000 when the f u l l 70,000 v o l t s would have been  much b e t t e r .  An ammeter, reading up to 20 amperes, i s  p l a c e d i n the primary c i r c u i t and a milliammeter, with a maximum of 12 m i l l i a m p e r e s * i s i n the secondary  circuit,  2, X-ray Tube, The x-ray tube i s of the Shearer type, which i s the most s u i t a b l e f o r the study of d i f f r a c t i o n effects.  The three most important advantages are:  (1) r e p l a c e a b l e t a r g e t s , (2) water c o o l i n g , (3) aluminium window.  The f i r s t  enables one to change the wave-  l e n g t h of the x - r a y s , the second allows  continuous  o p e r a t i o n , and the t h i r d i n c r e a s e s the i n t e n s i t y of the rays by g i v i n g l e s s a b s o r p t i o n and by p e r m i t t i n g the  8. spectrometer t o be p l a c e d nearer the t a r g e t .  The tube  has c o n s i d e r a b l e r e c t i f y i n g p r o p e r t i e s so the transformer •r  can be connected to i t d i r e c t l y .  The cathode end i s  c o o l e d by c o n v e c t i o n i n a l o n g , i n s u l a t e d brass v e s s e l 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.  of  Since the operation  the tube depends upon the i o n i z a t i o n of the a i r by f a s t  e l e c t r o n s , t o o low pressure i s p o s s i b l e .  The a r t i f i c i a l  leak used c o n s i s t e d of a v a r i a b l e needle v a l v e connected by rubber t u b i n g t o a j a r evacuated by the o i l uump alone. The r i g h t order of leak was obtained by making a number o f s m a l l needle h o l e s i n the rubber tubing; f i n e of  adjustment  the pressure c o u l d then be made w i t h the needle v a l v e .  Heavy stop cock grease i s needed f o r the threads of the valve. at  This arrangement keeps the pressure constant  the r i g h t v a l u e f o r s i x hours or more as shown by the  reading o f the m i l l i a n p l t e r , 3, Spectrograph and C e l l . The Dr. M u l l e r x-ray spectrograph i s s u i t a b l e for  the study o f x-ray d i f f r a c t i o n by l i q u i d s as w e l l as  by c r y s t a l s . for  The arrangement i s n e a r l y the same as that  the LaWe spot method of i n v e s t i g a t i n g c r y s t a l s t r u c t u r e .  The x-ray beam i s l i m i t e d by a narrow c y l i n d r i c a l channel  9, i n 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 p l a t e holder i s 5 cm on the other s i d e of the l i q u i d . Black paper covers the f a c e o f the p l a t e h o l d e r so p l a t e s may be taken i n d a y l i g h t , l e a d prevents  A small c i r c u l a r piece of  f o g g i n g o f the p l a t e owing to the d i r e c t  beam. The c e l l used f o r c o n t a i n i n g 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 h e l d i n  p o s i t i o n by a r i n g o f brass on each s i d e o f the centre p i e c e . The  three r i n g s are clamped t o -  gether w i t h s i x screws.  The  l i q u i d to be examined Is pouted i n t o a brass c y l i n d r i c a l v e s s e l above the c e l l and the l i q u i d enters the c e l l by s m a l l metal tubing 1 mm i n diameter. The whole i s supported  by an i r o n r o d 7 cm. long which  f i t s i n t o the centre o f the spectrograph t a b l e . The advantage of u s i n g mica windows i s t h a t no r i n g i s given by t h i s substance,  as i s the case  w i t h g l a s s and metals, but only spots which do not i n t e r f e r e  10. w i t h the r i n g given by the l i q u i d , ing .,the out  The method of clamp-  enables one to c l e a n the c e l l e a s i l y and t h change windows.  A s p e c i a l c u t t e r was  mica windows 10 mm  constructed f o r cutting  i n diameter and 0,01  The v e s s e l on top i s convenient when f i l l i n g  mm  thick.  the c e l l  and  a l s o makes i t e a s i e r to examine l i q u i d s w i t h high vapor p r e s s u r e at room temperature.  By p l a c i n g  anlittle  stop cock grease around the cover on top l i q u i d s such as cyclohexane and ether may s e v e r a l hours.  be c o n t a i n e d i n the c e l l f o r  The s u p p o r t i n g i r o n rod screws i n t o the  c e l l so that the h e i g h t may  be a d j u s t e d u n t i l the beam  of x-rays passes through the centre of the c e l l . 4. E x p e r i m e n t a l Procedure. Having chosen the t a r g e t d e s i r e d (copper was used throughout t h i s experiment) and having p r o p e r l y put i t i n p l a c e w i t h 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 f o r the mercury pump  i s most convenient but i t takes about 20 minutes t o heat the mercury  sufficiently.  The pressure i n the tube  can be estimated by the c o l o r and the ammeter r e a d i n g . The c u r r e n t i s s l i g h t l y p o s i t i v e as the purple glow g r a d u a l l y extends along the cathode. the  As the glow  fills  tube and s t r i a t i o n s appear the c u r r e n t s h i f t s t o 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 a b r u p t l y from a  strong negative to a s t r o n g p o s i t i v e r e a d i n g (about 12 m a) and x-rays may then be observed w i t h a screen.  phosphorescent  The c u r r e n t 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 l e a k . The spectrograph i s a d j u s t e d , by l o o k i n g through the s m a l l c i r c u l a r h o l e  9  u n t i l the c e l l and l e a d  s h i e l d on the p l a t e h o l d e r are i n proper alignment.  The  spectrograph can be put i n t o the c o r r e c t p o s i t i o n t o allow maximum i n t e n s i t y o f x-rays through the c i r c u l a r hole by Hsing a z i n c s u l p h i d e phosphorescent  screen.  The l i q u i d i s put i n t o the c e l l and a p l a t e exposed f o r s i x hours,  A shade was ms3#? f o r the windo* so  the p l a t e s c o u l d be developed  i n the same room.  d e s i r a b l e to have "the room dark„ a l s o phosphorescent to  screen.  Fogging  9  It is  when using the  o f the p l a t e s was prevented  some extent by surrounding the e n t i r e spectrograph with  lead, 5,  Discussion of Results. Eighteen l i q u i d s have been examined and a l l  show marked d i f f e r e n c e s i n the d i f f r a c t i o n p a t t e r n s . the p a t t e r n s are v e r y f a i n t  Many 0 f  but a sample of e i g h t i s shown.  An e x p l a n a t i o n of the observed e f f e c t s w i l l be attempted i n terms o f Stewart's  theory.  This theory i s chosen because  12, i t g i v e s the most complete p i c t u r e and beoause the mathematioal  t h e o r i e s are s t i l l very l i m i t e d i n a p p l i c a t i o n .  •i  1. Benzene and  Qyclohexane.  These two  d i f f r a c t i o n p a t t e r n s are very  s i m i l a r i n both s i z e 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 i n v o l v e d i n the formation  of c y b o t a c t i e groups.  The  d i s t a n c e between groupi  and the number of groups p e r u n i t 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 i n groups must be great; f o r the s c a t t e r i n g at small given by random molecules i s very weak.  Why  angles  t h i s benzene  r i n g should g i v e such an o r d e r l y arrangement of molecules is difficult  to  see. There i s a s t r i k i n g d i f f e r e n c e i n i n t e n s i t y ,  however.  When the double bonds between the carbons i n o  benzene are r e p l a c e d by a s i n g l e bond and an a d d i t i o n a l hydrogen i n oyclohexane we get a great increase i n i n t e n s i t y , -& H Thus the arrangement seems to be much more e f f e c t i v e • H i n s c a t t e r i n g x-rays  i n t e n s i t y might be due (Cg H  l 2  ^"0 2 C,  than  ?be change i n  t o the a d d i t i o n of more hydrogen  as compared to C  e x p l a n a t i o n i s as simple  g  H) g  as  but i t i s d o u b t f u l i f the this.  13. 2, E t h y l A l c o h o l  and E t h e r ,  These two l i q u i d s d i f f e r i n that e t h y l has  alcohol  one e t h y l group per molecule while ether has two.  e x p l a n a t i o n s seem p o s s i b l e f o r the ether r i n g being and  more d i f f u s e .  and  f a r t h e r apart  The ether c y b o t a c t i c  Two  smaller  groups are fewer  because the shape o f the molecule i s  d i f f e r e n t or because the ether was nearer i t s b o i l i n g p o i n t . I t i s to be noted that the b o i l i n g p o i n t  o f benzene and  cyclohexane are about the same (80° C) so no d i f f e r e n c e i n s i z e or d i f f u s e n e s s  of the r i n g would r e s u l t i n that  case.  E t h e r , however, b o i l s at 35° C w h i l e a l c o h o l b o i l s at 78° C at atmospheric p r e s s u r e .  The l a t t e r explanation  seems  most probable but f u r t h e r i n v e s t i g a t i o n on t h i s p o i n t i s necessary. The that by a l c o h o l .  d i f f r a c t i o n by .ether i s more intense  than  I t would seem t h a t , i f r e p l a c i n g a carbon  bond of hydrogen i s e f f e c t i v e i n i n c r e a s i n g the i n t e n s i t y , replacing  the hydrogen by an e t h y l group i s even more so.  This hypothesis i s borne out I n the next two p l a t e s i n which hydrogen i n a c e t i c a c i d i s r e p l a c e d  by an e t h y l group i n  e t h y l a c e t a t e and the i n t e n s i t y thereby  increased,  3. A c e t i c A c i d , E t h y l A c e t a t e , and E t h y l Malonate, When a c e t i c a c i d and e t h y l a l c o h o l combine to form e t h y l acetate we get an x-ray d i f f r a c t i o n p a t t e r n  14,  q u i t e d i f f e r e n t from e i t h e r of the aew  r i n g i s not  a combination of the  e t h y l acetate r i n g i s the cybotactic  o r i g i n a l materials.  groups has  other two  smallest.  The  since  The  the  d i s t a n c e between  been i n c r e a s e d while the number of  groups, as shown by the  broadening of the band, has  been  decreased. E t h y l malonate i s d i f f e r e n t from a l l the p a t t e r n s shown i n there being two The  rings  outer r i n g i s s i m i l a r i n s i z e and  alcohol.  I t would be  which has  and  malonie a c i d has  a dual cybotactic  group combination must be 4.  In any  is interesting.  inner r i n g  case, the  combination  resulted  i n a compound  arrangement.  Two  types of  occurring,  v e r y d i s t i n c t r i n g given by p i l c h a r d o i l F i s h o i l i s a mixture of unsaturated  ( i . e . double or t r i / p l e bonds between the  carbons) g l y c e r o l  Since complicated long chain molecules e x i s t  i n t h i s substance, the i n the  i f the  ethyl  Pilchard O i l , The  esters.  visible.  appearance to  i n t e r e s t i n g to see  i s s i m i l a r to malonie a c i d . of e t h y l a l c o h o l  distinctly  other  d i f f r a c t i o n may  arrangement of the  be caused by  regularity  atoms i n the molecule r a t h e r than  by r e g u l a r i t y of the molecules i n the molecule would act as a small c r y s t a l .  liquid.  Thus each  This -^should be  15. p o s s i b l e when the molecules are s e v e r a l times the wavel e n g t h o f the l i g h t used.  I f t h i s i s the cause of the  'ring we s h o u l d expect i t to be sharp s i n c e the number of r e g u l a r arrangements  would be g r e a t e r .  The d i f f e r e n c e i n i n t e n s i t y of two s i d e s of some p l a t e s , p a r t i c u l a r l y that of p i l c h a r d o i l , improper s c r e e n i n g .  i s due to  The b l a c k s p o t , which o v e r l a p s  the c e n t r a l spot made by the l e a d on the f r o n t o f the p l a t e h o l d e r , i s caused by some experimental e r r o r which has not y e t been found. IV.  0OHCLUSI0H The study o f x-ray d i f f r a c t i o n p a t t e r n s has  not p r o g r e s s e d as r a p i d l y as d e s i r e d because of the long time necessary f o r exposure.  I n t e n s i f y i n g screens that  have been used have not been s a t i s f a c t o r y ,  A higher  p o t e n t i a l i s the only other method of i n c r e a s i n g the intensity. T e n t a t i v e arrangements  have been made f o r  the design o f 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 s t u d y i n g the i n t e n s i t y of the d i f f r a c t i o n  p a t t e r n s with a microphotometer, s h o u l d be o b t a i n e d .  interesting  results  The temperatures at which the s o l i d  changes t o l i q u i d and the l i q u i d t o gas would be p a r t i c u l a r l y important.  16.  X-RAY DIFFRACTION PATTERNS  Benzene  (Cg  E&)  I I  j  Ethyl Alcohol  Ether  (CgH 0 H) 5  ( CgHgO-0 H ) 2  5  Pilchard  Oil  B I B It 1 0  G R A  PHY  "The d i f f r a c t i o n of x-rays and e l e c t r o n s 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 i n l i q u i d s . " - C.M.Sogani, Indian J o u r n a l of P h y s i c s , v o l . 1 , page 357, (1987)  3.  " F u r t h e r s t u d i e s 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. J o * r . Phy., 2, 99 (1927)  4.  " R e l a t i o n between chemical c o n s t i t u t i o n and x-ray diffraction in liquids" - P.Krishnamurti, Ind.Jour.Phy. 2, 355 (1928)  5.  "X-ray d i f f r a c t i o n i n carbon t e t r a c h l o r i d e " 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 i n the l i q u i d state" - P.Krishnamurti, Ind.Jour,Phy.2,491 (1928)  7.  "Thermal degeneration o f the x-ray haloes i n l i q u i d s and amorphous s o l i d s " - S,S.Ramasubramanyam, Ind, Jour. Phy. 3,137 (1928)  8.  "Nature o f s o l u t i o n s as r e v e a l e d by x-ray d i f f r a c t i o n " - P. K r i s h n a m u r t i , 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. K r i s h n a m u r t i , Ind.Jour.Phy. 3,331 (1928)  10.  "X-ray d i f f r a c t i o n i n l i q u i d s of the terpene s e r i e s " - V,I.Yaidyanathan. Ind.Jour.Phy. 3,372 (1929)  11.  " I n f l u e n c e of temperature on the x-ray l i q u i d h a l o e s " - V.I.Vaidyanathan, Ind. Jour. Phy. 3,391 (1929)  12.  "X-ray d i f f r a c t i o n i n l i q u i d s and s o l u t i o n s " P.Krishnamurti. Ind.Jour.Phy. 2,507 (1929)  13.  "X-ray d i f f r a c t i o n i n primary normal a l c o h o l s " G. W. Stewart and R. M. Morrow. Phy.Rev.30,232  14.  (1927)  "Comparison of primary normal a l c o h o l s and t h e 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 p a r a f f i n s " G.W.Stewart, Phy.Rev. 31, 174 (1928)  -  16.  " D i f f r a c t i o n o f x-rays i n 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 i n organic mixtures" A. W.Meyer. Phy.Rev, 38,1083 (1931)  18.  " V i s c o s i t y and molecular arrangement i n 22 liquids; octyl 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 i n e t h y l ether near the c r i t i c a l p o i n t " ~ W, N o l l . Phy.Rev. 42, 336 (1932)  20.  "X-ray d i f f r a c t i o n i n 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 i n l i q u i d s " Rev. o f Mod. Phy. 2, 116 (1930)  22.  "Gyhotactic c o n d i t i o n i n l i q u i d s " - G.W.Stewart. Phy.Ref• 35, 726 (1930)  23.  "Theory of the V i s c o s i t y of L i q u i d s " - E.N.DaC.Andrade, Phil.Mag, 17, 497 (1934)  G.W.Stewart.  

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