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A neutron diffraction study on solid methane CD4 in I
Volume 31A, number 5
A NEUTRON
PHYSICS LETTERS
DIFFRACTION
STUDY
ON
SOLID
9 March 1970
METHANE
CD 4 IN P H A S E
I
W. PRESS and B. DORNER
Institut f a r Festk~rper- und Neutronenphysik der Kernforschungsanlage diilich GrnbH, Germany and G. WILL
Abteilung f a r Kristallstrukturlehre und Neutronenbeugung, Mineralogisch-Petrologisches lnstitut der Universiti~t Bonn, Germany Received 21 January 1970
The crystal structure of solid CD4 in phase I is found to be face-centered cubic, within the space group Fra3~n. The molecules are distributed into 12 equivalent orientations of lower symmetry (point group C2V) and have large librational and translational amplitudes.
Solid d e u t e r a t e d methane, CD4, exhibits two p h a s e t r a n s i t i o n s at 27.0 OK and 22.1 OK [1]. F r o m X - r a y d i f f r a c t i o n d i a g r a m s it i s concluded that the c e n t r a l c a r b o n a t o m s of the m e t h a n e t e t r a h e d r o n s occupy fcc l a t t i c i e s i t e s in a l l t h r e e p h a s e s of CD 4 [2] as well a s of CH 4 [3] One may " a s s u m e , t h e r e f o r e , that the t r a n s i t i o n s a r e c a u s e d by a change in the o r i e n t a t i o n a l o r d e r of the m o l e c u l e s [4] In this p a p e r we r e p o r t the • r e s u l t s of n e u t r o n d i f f r a c t i o n e x p e r i m e n t s on the o r i e n t a t i o n a l o r d e r of CD 4 in the high t e m p e r a t u r e pha se at 77 ° K . In an e a r l i e r n e u t r o n d i f f r a c t i o n e x p e r i m e n t [5] on p o w d e r e d CD 4 the i n t e r p r e t a t i o n s turned out to be difficult due to p r e f e r r e d o r i e n t a t i o n s in the powder and a r a p i d d e c r e a s e of the m e a s u r e d i n t e n s i t i e s . We have taken up the p r o b l e m again, us ing a CD 4 s i n g l e c r y s t a l of approxi m a t e l y 20 c m 3 (99.6 % D, 0.4 ~ H; i m p u r i t i e s 1%); the g r o w i n g p r o c e d u r e will be d e s c r i b e d in a s e p a r a t e p a p e r [6]. The m o s a i c s p r e a d of the c r y s t a l w a s a p p r o x i m a t e l y 3' a s d e t e r m i n e d f r o m a r o c k ing c u r v e . The n e u t r o n w a v e l e n g t h w a s 1 . 2 2 6 ~ . Due to the a c c i d e n t a l growth o r i e n t a t i o n of the c r y s t a l only the [110] zone could be studied and 17 r e f l e c t i o n s of i n d i c e s hhl w e r e m e a s u r e d by a 0 - 2 0 scan, (sin 0/~<0.7). The c e l l constant was c a l c u l a t e d to 5.96 ± 0.01 A at 77 OK. S t r u c t u r e a m p l i t u d e s [Fhhl] o -Q have been d e r i v e d f r o m the i n t e g r a t e d intensl~ies and a r e l i s t e d in table 1. Th e o b s e r v e d s y s t e m a t i c a b s e n c e s conf i r m the f a c e - c e n t e r e d t r a n s l a t i o n a l s y m m e t r y , at l e a s t in the o b s e r v e d zone. In addition, h o w e v e r , the r e f l e c t i o n s 222 and 331 w e r e m e a s u r e d z e r o .
Indices hk/
Fob s
Table 1. Fcalculated
Fspherical symmetry
111 002 220
(2.62) 6.78* (2.18) 4.80* (1.65) 1.88'
6.38 5.19 1.67
6.40 5.12 1.71
113 222 004
0.97 n.o 0.80
0.75 0.16 0.72
0.67 0.51 0.29
331 224 333
n. o 0.39 0.83
0.24 0.50 0.37
0.39 0.67 0.81
115 440 442
0.94 0.75 0.72
1.00 1.07 0.80
0.81 0.94 0.95
006 335 226 444 551 117 553 oo8
0.95 0.78 0.95 0.53 0.53 0.63 0.39 n. o
1.04 0.70 0.78 0.54 0.67 0.52 0.36 0.18
0.95 0.84 0.81 0.67 0.57 0.57 0.37 0.25
*these values have been corrected for extinction
It is not p o s s i b l e to d e t e r m i n e the point group uniquely f r o m the t w o - d i m e n s i o n a l data set. We have, t h e r e f o r e , c a l c u l a t e d s t r u c t u r e f a c t o r s for s e v e r a l o r d e r e d s t r u c t u r e s [7] with the o b s e r v e d t r a n s l a t i o n a l s y m m e t r y , e s p e c i a l l y F43m, but a l s o in t e t r a g o n a l , o r t h o r h o m b i c and t r i g o n a l 253
Volume 31A, number 5
PHYSICS LETTERS
sp a c e groups. None of t h e s e m o d e l s could explain the e x p e r i m e n t a l data. One is thus lead to e x a m i n e l e s s o r d e r e d s t r u c t u r e s . C o m p l e t e o r i e n t a t i o n a l d i s o r d e r can be d e s c r i b e d by a u n i f o r m d i s t r i b u t i o n of the D - a t o m s on a s p h e r e with the C - D d i s t a n c e s as r a d i u s (R = = 1.09/~). The f o r m f a c t o r of this s p h e r i c a l l y s y m m e t r i c density d i s t r i b u t i o n is F = b C +4b D (sinKR),/(KR); b c , bD= n e u tr o n s c a t t e r i n g length of C and D; K = 4~ sina,/;~ = = m o m e n t u m t r a n s f e r . The o b s e r v e d s t r u c t u r e f a c t o r v a l u e s s c a t t e r around this mean c u r v e and e s p e c i a l l y the r e f l e c t i o n s of h i g h e r o r d e r a r e fitted r a t h e r well. It f ai l s to explain, h o w e v e r , both the z e r o - o b s e r v e d r e f l e c t i o n s 222 and 331 and the r e l a t i v e l y s t r o n g 0 0 4 - r e f l e c t i o n . The p r o b l e m was, t h e r e f o r e , c a r r i e d f u r t h e r to the a s s u m p t i o n of p a r t l y o r d e r e d s t r u c t u r e s , i.e. of r a n d o m d i s t r i b u t i o n s of the m o l e c u l e s onto a n u m b e r of d i s c r e t e o r i e n t a t i o n s , as p r o po se d for p l a s t i c c r y s t a l s [8]. E n e r g e t i c a l l y fav o u r e d o r i e n t a t i o n s will be those, for which a s u b - g r o u p of the t e t r a h e d r a l group c o i n c i d e s with a s u b - g r o u p of the cubic l a t t i c e s y m m e t r y . P o s s i b l e point g r o u p s a r e Td,D2d,C3v and C2v , the s y m m e t r y conditions of which a r e fulf i l l e d by 2, 6, 8 and 12 e q u i v a l e n t o r i e n t a t i o n s , r e s p e c t i v e l y . A v e r a g i n g o v e r a l l p o s s i b l e e q u iv a l e n t o r i e n t a t i o n s of one point group always l e a d s to the cubic point s y m m e t r y m 3 m and thus to the s p a c e g ro u p Fm3m. The best a g r e e m e n t between o b s e r v e d and c a l c u l a t e d data is obtained by a combination of a v e r a g e d C2v s y m m e t r y (for C3v: only the c a l c u l a t e d Fhhh a r e slightly d i f f e r ent) with the s p h e r i c a l d i s t r i b u t i o n in a r a t i o 1 : 2 ;
254
9March 1970
this combinationtakes into account the librational amplitudes of the molecules. By plotting In (Fobs/Fcalc) versus K2 information on the D e b y e - W a l l e r f a c t o r exp(-I u 2 K 2) f o r the t r a n s l a t i o n a l motion can be obtained. The m e a n soquared a m p l i t u d e s w e r e found to be u 2 = = 0.20A 2. A s s u m i n g an i d eal D e b y e - s o l i d this v al u e c o r r e s p o n d s to a D e b y e - t e m p e r a t u r e ~ 90 OK. F u r t h e r work is in p r o g r e s s with single c r y s t a l s and a l s o with p o l y c r y s t a l l i n e s a m p l e s in al l t h r e e p h a s e s of CD 4. The question, w h et h er the equivalent o r i e n t a t i o n s in the high t e m p e r a t u r e p h ase have to be c o n s i d e r e d a s s t a t i c o r as dyn a m i c will be i n v e s t i g a t e d by i n e l a s t i c n eu t r o n scattering. The a u t h o r s would like to thank Dr. H. S t i l l er and Mr. H. G r i m m f o r many valuable d i s c u s s i o n s and Mr. F. F r e d e l f o r r e l i a b l e help.
ReferFRces 1. J . H . Colwell, E . K . Gill and J. A. Morrison J. Chem. Phys. 39 (1963) 635. 2. S . C . G r e e r a n d L . M e y e r , J . C h e m . Phys., to be
published. 3. S.C. Greer and L. Meyer, Z. Angew. Phys. 27(1969) 198; Schallamaeh, Proc.Roy. Soe. A 171 (1939) 569. 4. L.Pauling, Phys.Rev. 36 (1930)430. 5. W.Gissler and H.Stiller, Naturwiss. 18 (1965) 512. 6. W.Press, H.Egger, to be published. 7. G. Savitsky and D. Hornig, J. Chem. Phys. 36 (1962) 2634. 8. G. B. Guthrie and J. P. McCullough, J. Phys. Chem. Solids 18 (1961) 53.
A NEUTRON
PHYSICS LETTERS
DIFFRACTION
STUDY
ON
SOLID
9 March 1970
METHANE
CD 4 IN P H A S E
I
W. PRESS and B. DORNER
Institut f a r Festk~rper- und Neutronenphysik der Kernforschungsanlage diilich GrnbH, Germany and G. WILL
Abteilung f a r Kristallstrukturlehre und Neutronenbeugung, Mineralogisch-Petrologisches lnstitut der Universiti~t Bonn, Germany Received 21 January 1970
The crystal structure of solid CD4 in phase I is found to be face-centered cubic, within the space group Fra3~n. The molecules are distributed into 12 equivalent orientations of lower symmetry (point group C2V) and have large librational and translational amplitudes.
Solid d e u t e r a t e d methane, CD4, exhibits two p h a s e t r a n s i t i o n s at 27.0 OK and 22.1 OK [1]. F r o m X - r a y d i f f r a c t i o n d i a g r a m s it i s concluded that the c e n t r a l c a r b o n a t o m s of the m e t h a n e t e t r a h e d r o n s occupy fcc l a t t i c i e s i t e s in a l l t h r e e p h a s e s of CD 4 [2] as well a s of CH 4 [3] One may " a s s u m e , t h e r e f o r e , that the t r a n s i t i o n s a r e c a u s e d by a change in the o r i e n t a t i o n a l o r d e r of the m o l e c u l e s [4] In this p a p e r we r e p o r t the • r e s u l t s of n e u t r o n d i f f r a c t i o n e x p e r i m e n t s on the o r i e n t a t i o n a l o r d e r of CD 4 in the high t e m p e r a t u r e pha se at 77 ° K . In an e a r l i e r n e u t r o n d i f f r a c t i o n e x p e r i m e n t [5] on p o w d e r e d CD 4 the i n t e r p r e t a t i o n s turned out to be difficult due to p r e f e r r e d o r i e n t a t i o n s in the powder and a r a p i d d e c r e a s e of the m e a s u r e d i n t e n s i t i e s . We have taken up the p r o b l e m again, us ing a CD 4 s i n g l e c r y s t a l of approxi m a t e l y 20 c m 3 (99.6 % D, 0.4 ~ H; i m p u r i t i e s 1%); the g r o w i n g p r o c e d u r e will be d e s c r i b e d in a s e p a r a t e p a p e r [6]. The m o s a i c s p r e a d of the c r y s t a l w a s a p p r o x i m a t e l y 3' a s d e t e r m i n e d f r o m a r o c k ing c u r v e . The n e u t r o n w a v e l e n g t h w a s 1 . 2 2 6 ~ . Due to the a c c i d e n t a l growth o r i e n t a t i o n of the c r y s t a l only the [110] zone could be studied and 17 r e f l e c t i o n s of i n d i c e s hhl w e r e m e a s u r e d by a 0 - 2 0 scan, (sin 0/~<0.7). The c e l l constant was c a l c u l a t e d to 5.96 ± 0.01 A at 77 OK. S t r u c t u r e a m p l i t u d e s [Fhhl] o -Q have been d e r i v e d f r o m the i n t e g r a t e d intensl~ies and a r e l i s t e d in table 1. Th e o b s e r v e d s y s t e m a t i c a b s e n c e s conf i r m the f a c e - c e n t e r e d t r a n s l a t i o n a l s y m m e t r y , at l e a s t in the o b s e r v e d zone. In addition, h o w e v e r , the r e f l e c t i o n s 222 and 331 w e r e m e a s u r e d z e r o .
Indices hk/
Fob s
Table 1. Fcalculated
Fspherical symmetry
111 002 220
(2.62) 6.78* (2.18) 4.80* (1.65) 1.88'
6.38 5.19 1.67
6.40 5.12 1.71
113 222 004
0.97 n.o 0.80
0.75 0.16 0.72
0.67 0.51 0.29
331 224 333
n. o 0.39 0.83
0.24 0.50 0.37
0.39 0.67 0.81
115 440 442
0.94 0.75 0.72
1.00 1.07 0.80
0.81 0.94 0.95
006 335 226 444 551 117 553 oo8
0.95 0.78 0.95 0.53 0.53 0.63 0.39 n. o
1.04 0.70 0.78 0.54 0.67 0.52 0.36 0.18
0.95 0.84 0.81 0.67 0.57 0.57 0.37 0.25
*these values have been corrected for extinction
It is not p o s s i b l e to d e t e r m i n e the point group uniquely f r o m the t w o - d i m e n s i o n a l data set. We have, t h e r e f o r e , c a l c u l a t e d s t r u c t u r e f a c t o r s for s e v e r a l o r d e r e d s t r u c t u r e s [7] with the o b s e r v e d t r a n s l a t i o n a l s y m m e t r y , e s p e c i a l l y F43m, but a l s o in t e t r a g o n a l , o r t h o r h o m b i c and t r i g o n a l 253
Volume 31A, number 5
PHYSICS LETTERS
sp a c e groups. None of t h e s e m o d e l s could explain the e x p e r i m e n t a l data. One is thus lead to e x a m i n e l e s s o r d e r e d s t r u c t u r e s . C o m p l e t e o r i e n t a t i o n a l d i s o r d e r can be d e s c r i b e d by a u n i f o r m d i s t r i b u t i o n of the D - a t o m s on a s p h e r e with the C - D d i s t a n c e s as r a d i u s (R = = 1.09/~). The f o r m f a c t o r of this s p h e r i c a l l y s y m m e t r i c density d i s t r i b u t i o n is F = b C +4b D (sinKR),/(KR); b c , bD= n e u tr o n s c a t t e r i n g length of C and D; K = 4~ sina,/;~ = = m o m e n t u m t r a n s f e r . The o b s e r v e d s t r u c t u r e f a c t o r v a l u e s s c a t t e r around this mean c u r v e and e s p e c i a l l y the r e f l e c t i o n s of h i g h e r o r d e r a r e fitted r a t h e r well. It f ai l s to explain, h o w e v e r , both the z e r o - o b s e r v e d r e f l e c t i o n s 222 and 331 and the r e l a t i v e l y s t r o n g 0 0 4 - r e f l e c t i o n . The p r o b l e m was, t h e r e f o r e , c a r r i e d f u r t h e r to the a s s u m p t i o n of p a r t l y o r d e r e d s t r u c t u r e s , i.e. of r a n d o m d i s t r i b u t i o n s of the m o l e c u l e s onto a n u m b e r of d i s c r e t e o r i e n t a t i o n s , as p r o po se d for p l a s t i c c r y s t a l s [8]. E n e r g e t i c a l l y fav o u r e d o r i e n t a t i o n s will be those, for which a s u b - g r o u p of the t e t r a h e d r a l group c o i n c i d e s with a s u b - g r o u p of the cubic l a t t i c e s y m m e t r y . P o s s i b l e point g r o u p s a r e Td,D2d,C3v and C2v , the s y m m e t r y conditions of which a r e fulf i l l e d by 2, 6, 8 and 12 e q u i v a l e n t o r i e n t a t i o n s , r e s p e c t i v e l y . A v e r a g i n g o v e r a l l p o s s i b l e e q u iv a l e n t o r i e n t a t i o n s of one point group always l e a d s to the cubic point s y m m e t r y m 3 m and thus to the s p a c e g ro u p Fm3m. The best a g r e e m e n t between o b s e r v e d and c a l c u l a t e d data is obtained by a combination of a v e r a g e d C2v s y m m e t r y (for C3v: only the c a l c u l a t e d Fhhh a r e slightly d i f f e r ent) with the s p h e r i c a l d i s t r i b u t i o n in a r a t i o 1 : 2 ;
254
9March 1970
this combinationtakes into account the librational amplitudes of the molecules. By plotting In (Fobs/Fcalc) versus K2 information on the D e b y e - W a l l e r f a c t o r exp(-I u 2 K 2) f o r the t r a n s l a t i o n a l motion can be obtained. The m e a n soquared a m p l i t u d e s w e r e found to be u 2 = = 0.20A 2. A s s u m i n g an i d eal D e b y e - s o l i d this v al u e c o r r e s p o n d s to a D e b y e - t e m p e r a t u r e ~ 90 OK. F u r t h e r work is in p r o g r e s s with single c r y s t a l s and a l s o with p o l y c r y s t a l l i n e s a m p l e s in al l t h r e e p h a s e s of CD 4. The question, w h et h er the equivalent o r i e n t a t i o n s in the high t e m p e r a t u r e p h ase have to be c o n s i d e r e d a s s t a t i c o r as dyn a m i c will be i n v e s t i g a t e d by i n e l a s t i c n eu t r o n scattering. The a u t h o r s would like to thank Dr. H. S t i l l er and Mr. H. G r i m m f o r many valuable d i s c u s s i o n s and Mr. F. F r e d e l f o r r e l i a b l e help.
ReferFRces 1. J . H . Colwell, E . K . Gill and J. A. Morrison J. Chem. Phys. 39 (1963) 635. 2. S . C . G r e e r a n d L . M e y e r , J . C h e m . Phys., to be
published. 3. S.C. Greer and L. Meyer, Z. Angew. Phys. 27(1969) 198; Schallamaeh, Proc.Roy. Soe. A 171 (1939) 569. 4. L.Pauling, Phys.Rev. 36 (1930)430. 5. W.Gissler and H.Stiller, Naturwiss. 18 (1965) 512. 6. W.Press, H.Egger, to be published. 7. G. Savitsky and D. Hornig, J. Chem. Phys. 36 (1962) 2634. 8. G. B. Guthrie and J. P. McCullough, J. Phys. Chem. Solids 18 (1961) 53.