JOURNAL DE PHYSIQUE. Colloque Cl, suppl6ment au no 3, Tome 48, mars 1987. HIGH-RESOLUTION NEUTRON POWDER DIFFRACTION STUDY OF ICE Ic.
JOURNAL DE PHYSIQUE Colloque Cl, suppl6ment a u no 3, Tome 48, mars 1987
HIGH-RESOLUTION NEUTRON POWDER DIFFRACTION STUDY OF ICE Ic
W.F. KUHS, D.V. BLISS* and J.L. FINNEY* Institut Laue-Langevin, 156 X , F-38042 Grenoble Cedex, France i irk beck College, Department of Crystallography, Malet Street, GB-London WClE 7HX, Great-Britain
-
R6sum6 La glace cubique 1, deut6r6e a 6t6 6tudi6e par diffraction de neutrons haute r6solution. La structure fine du groupe dlespace Fd3m a 6t6 examin6e. Les atomes dPhydrog8ne sont totalement d6sordonn6s et les distances interatomiques sont identiques & celles de la glace Ih. Bien que l'apparence g6n6rale du diagramme de poudre soit cubique, plusieurs anomalies ont 6t6 observ6es. Les effets de taille des particules sont importants et 2 partir de 1'6largissement du pic, une taille moyenne des particules de 160 (30) 2 a 6t6 calcul6e. Quelques pics de Bragg montrent un Blargissement suppl6mentaire ou une dissym6trie du c6t6 des faibles angles indiquant l'existence de fautes dlempilement. La presence enfin dlun pic de Bragg non cubique qui a 6tB index6 100 dans le r6seau de la glace Ih est expliqu6 en terme de sequence hexagonale dans l'empilement. Abstract - High-resolution neutron powder diffraction data on deuterated cubic ice (ice 1,) prepared by transforming recovered ice I1 have been obtained. Structure refinements in the cubic spacegroup Fd3m were performed. The hydrogen atoms are fully disordered and the interatomic distances are found to be identical with those inice Ib. Although the general appearance of the powder pattern is cubic, several anomalies have been observed. Paticle size effects are important and from the peak broadening a mean particle size of 160(30) 8 was calculated. Some Bragg peaks show additional broadening or distinct skewness on the high- or low-angle side indicating the existence of deformation faults in the stacking sequence. The presence of at least one non-cubic Bragg peak, which can be indexed as 100 in the lattice of ice Ih, is explained in terms of hexagonal sequences in the stacking.
The existence of a second crystalline ambient pressure modification of the water substance besides hexagonal ice (ice Ih) is well established. O n crystalloKonigg, although it had b y n graphic evidence it was named cubic ice (ice Ic) observed5as a new phase earlier on by Barendrecht , Dewar , *on and Oliver and McParlan A great deal of work has been done since K6nig*ssuelectron diffraction study on cubic ice, but one is still far from a full understanding of its structure and properties and even its stability range. There are several ways of preparing ice Icr it can be formed by 1temperature deposition of water vapour in a range between 130 and 150 XZeSg' 1,s, by transformation on heating of vapour-deposited amorphous iceebg' transformation on heating of various rec~~~f~ high-pressure icese 'by' 8,9,lO or by rapid cooling of aqueous solutionse'g' once formed, it is stable from O°K to approximately 200 K, where it begins to transform into ice Ih. This transfor-
p
.
'
.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987187
JOURNAL DE PHYSIQUE
mation is slow and apparently depends t o some e x t e n t on t h e sappple h i s t o r y . Transformation tt3mperatUIXS as low as 153 K have been observed , which i n d i c a t e s that ice Ic is probably a l w a y s metastable w i t h respect t o ice Ih. For a more d e t a i l e d discussipg o f i c e Ic preparation and its transformation behaviour we refer t o the l i t e r a t u r e The hef&,fg,$gansformation f o r t h e i c e Ic ice Ih t r a n s i t i o n has been me ured repeatedly The heat evolved was found t o be very small ( < 20 J 1 . This is not r e a l l y s u r p r i s i n g since the hexagonal arrangement o f t h e oxygen atoms i n ice Ih is e n e r g e t i c a l l y very s i m i l a r t o t h e presumed cubic arrangement i n ice Ic. Indeed t h e nearest neighbour s i t u a t i o n as w e l l as t h e number o f next-nearest neighbours are i d e n t i c a l i n both forms ae, fqnsequently, are t h e averaged dipolfomoments and t h e Coulombic i n t e r a c t i o n eygrgies Moreover t h e and t h e nuclear calculated densitylg, the l i b r a t i o n a l and v i b r a t i o n a l bands magnetic resonance are found t o be the same wi m the experimental e r r o r . Only ?illt h e t r a n s l a t i o n a l bands show a slight difference , which is expected from the d i f f e r e n t number o f acoustic branches according t o t h e change i n symmetry. However, the two forms are d i s t i n c t i n terms of their three-dimensional s t r u c t u r e and d i f f r a c t i o n seema t o be t h e appropriate t o o l t o quantify s i m i l a r i t i e s and d i f f e r e n c e s i n t h e i r s t r u c t u r e s , which u l t i m a t e l y may lead t o a better understanding o f their r e l a t i v e stabilities. 1 A s e r i e s o f s t r u c t u r a l i n v e s t i g a t i o n s has been p e r f o m 2 s i n c e a n a l y s i s . Ice Ic h~ been studied by e l e c t r o n d i f f r a c t i o n , X-ray neutron d i f f r a c t i o n It has been repeatedly ObSerped that t h e paweler p a t t e r n was not a cle one b u t contained some extra l i n e s , which were mainly attributed sq'f"' t o t h e conggant presence o f ice Ih f o r a l l t h e preparation procedures. B e r t i e 6. Jacobs hawever suggested that the extra f e a t u r e s may not be due t o ice I h impurity, but the q u a l i t y o f t h e i r d a t a d i d not allow them t o pursue t h i s point. P a r t i c l e s i g e broadening has been found i n s e v e r a l s t u d i e s with mean g r a i n s i z e s between 130 A lo A f u l l s t r u c t u r e refinement has not been d' t h a t i c e Ic has a disordered hydrogen reported, but there is some evldence arrangement very s i m i l a r t o i c e Ih. The spacegroup f o r t h e idealized cubic s t r u c t u r e is Pd3m and a hypothetical ordered form could c r y s t a l l i z e i n the spacegroups 141md o r P2 2 2 A partial o r f u l l y ordered hydrogen arrangement f o r ice I c has been sugges$e&,lbased on a d i f f e r e n c e i n the h e a t capacities o f cubic and hexagonal ice. C o n t r 3 g i n g with the generally accepted c l o s e resemblance o f cubic and hexagonal iceeeg' t h i s finding still awaits f u r t h e r c l a r i f i c a t i o n . W e present here the r e s u l t s o f a high-resolution neutron powder d i f f r a c t i o n study on the deuterated i c e Ic and a preliminary a n a l y s i s o f the powder p a t t e r n obtained w i l l be given, whereby special a t t e n t i o n w i l l be paid t o t h e anomalies i n the pattern.
.
.
+
.
l(f!~&a;$~
.
rmlkz'
.
C u b i c ice Ih ( D 0 ) has been obtained by warming ice I1 recovered at ambient pressure and 77 K. d e heating process was not contsglled and occurred when the sample was t r a n s f e r r e d from t h e helium-pressure cell t o the c r y o s t a t , which was held at a temperature o f 7 8 ( l ) K. Neutron powder d i f f r a c t i o n p a t t e r n s were recorded on t h e high-resolution powder diffractometer V I A at the I g s t i t u t Laue-Langevin, Gregoble, at wavelengths o f 1.390, 1.909 and 2.988 A . The p a t t e r n obtained a t 1.909 A is shown i n Fig. 1. A l l peaks i n the d i f f r a c t i o n p a t t e r n were analysed i n t h e usual way by f i t t i n g t h e position, the full-width a t half-height (PWHtl) and t h e h e i g h t o f a Gaussian d i s t r i b u t i o n t o the observed peak-shape. Integrated i n t e n s i t i e s were c a l c u l a t e d from the obtained peak parameters and corrected f o r Lorentz e f f e c t s . A f i r s t inspection of t h e p a t t e r n s indicated a broadening o f the Bragg peaks a t higher angles. The broadening s p e c i f i c t o the i c e Ic sample was obtained by comparing it w i t h the instrumental broadening as established with an ice I&sample o f comparable s i z e . S t r u c t u r e refinements were performed with the 1.390 A d a t a using t h e PROMWHEWS~~s u i t e of programs modified f o r the use o f integrated powder i n t e n s i t i e s ; due t o the i r r e g u l a r broadening o f some Bragg pea- t h e usual p r o f i l e refinement technique could not be applied.
300C
.
. . . , . . . . , . . . . , . . . . , . . . . , . . 11 1
+
I d
0
2000
1000 33 1
&
0
-
35
10
.
.
.
.
422
zii
.
.
.
I
60
A
85
440 531 442 I
.
l I0
2THETA
I
Figure 1
.
.
I
135
I N DEGREES
Neutron p o 4 e r d i f f r a c t i o n p a t t e r n o f heavy ice Ic recorded a t 78 K with 1.909 A neutrons. Note t h e shoulders on the 111 and 222 r e f l e c t i o n s (arrows).
The powder p a t t e r n o f i c e Ic shows t h r e e unusual features: the l i n e s are broadened i n a complicated way, same l i n e s have d i s t i n c t shoulders and at least one r e f l e c t i o n cannot be indexed i n the presumed cubic l a t t i c e . S t i l l , the general appearance o f the p a t t e r n is c l e a r l y cubic as confinned by the s t r u c t u r e refinement. The integrated i n t e n s i t i e s used i t i t h e refinement include a l l anomalies (shoulders, broadening), which w e r e described - i f necessary by a d d i t i o n a l Gaussian components overlapping with the main peak. The refinement was done i n the spacegoup Fd3m and converged with a weighted R-factor of 0.058. There w a s - apart from t h e cubic 111 r e f l e c t i o n no indication o f t h e presence of hexagonal r e f l e c t i o n s superimposing on t h e cubic l i n e s . S t r u c t u r e f a c t o r c a l c u l a t i o n s i n t h e hypothetical f e r r o e l e c t r i c a l l y and a n t i f e r r o e l e c t r i c a l l y ordered spacegroups I 4 md and P2 2 2 respectively gave strong disagreement. Table 1 111 1 gives the refined s t r u c t u r a l parameters.
-
-
Table 1; The idealized s t r u c t u r e * of ice Ic at 78 K Atom
Position
0
3 22
D
xxx w i t h x = 0.%70( 19)
8 8
**
Isotropic B 1.56(59)
8
*
2.02(64)**
Origin a t c e n t r e of inversion Equivalent i s o t r o p i c B; t h e r o o t mean-square d i s placements o f the anisotropic,thermal motions are 0.093 A alpng t h e OH bond and 0.184 A perpendicular t o the bond d i r e c t i o n .
The l a t t i c e constan$ obtained from a %east-squares refinement based on f i v e strong peaks o f t h e 1.909 A run is 6.358(3) A . With t h i s value and t h e p o s i t i o n a l parameters given,in Table 1 t h e f o l l q i n g interactomic distan%es are found: 1.013(14) A , ro.., 2.735(2) A and r D . , .D 2.287(4) A . Within the l i m i t 0 ke-r they agree n t h the corresponding duitances i n ice 13.It should be
-
-
-
JOURNAL DE PHYSIQUE
mentioned that the a c t u a l interatomic d i s t a n c e s a r e l i k e l y t o d i f f e r from t h e quoted values due t o unresolved molecular disordeg similar t o the s i t q t i o n i n i c e Ih28, 29 , where equilibrium d i s t a n c e s r& 0.974 A and roe, 2.76 A have been found. The limited accuracy o f the powder d a t a prevents a more d e t a i l e d a n a l y s i s of t h e atomic p r o b a b i l i t y d i s t r i b u t i o n s i n i c e Ic. The a n a l y s i s o f particle s i z e broadening e f f e c t s was not e n t i r e l y s t r a i g h t forward. Some r e f l e c t i o n s seemed t o be more a f f e c t e d than others, i n p a r t i c u l a r t h e 331 and 533 peaks were much broader than expected Eor i s o t r o p i c p a r t i c l e s . The hypothesis o f a n i s o t r o p i c particle s i z e broadening was considered, but a model c o n s i s t e n t with the obsemed broadening could not be found. Indeed t h e anomalous broadening of the 331 and 533 peaks can be explained otherwise, as discussed below. The p a r t i c l e s i z e L was calculated according t o t h e Scherrer formula Q
The Scherrer constant f o r s p h e r i c a l p a r t i c l e s (K = 1.209) was used1 A is t h e wavelength and 9 t h e s c a t t e r i n g aggle. The p a r t i c l e s i z e obtained from the 111, 220, 222 and 440 peaks is 160(30) A . The b e s t i n t e r n a l consistency between the values obtained for d i f f e r e n t wavelengths w a s achieved by c a l c u l a t i n g the halfiv th W' 48 o r i g i n a t i n g i n the small p a r t i c l e s i z e according t o t h e empirical formula
t h e observed full-width at half-height, and W the width c a l c u l a t e d from t h e measured instrumental resolution. The distributionOof particle sizes 2 t h e r e f o r e seems t o be n e i t h e r o f a Gaussian (W' = (wZbs - w2 ) nor o f a Cauchy type ( W e Webs - W ), but it is located somewhere between theo*. Line broadenigg and skewness have a v a r i e t y of o r i g i n s . The c h a r a c t e r i s t i c s of the ice Ic p a t t e r n however i n d i c a t e s t r o n g l y the existence of deformation f a u l t s , i.e. stacking f a u l t s o f t h e type
with WobS
-
which means that the r e g u l a r packing sequence o f a cubic s t r u c t u r e is perturbed only a t t h e indicated position. This c o n t r a s t s with so-called grawth-faults, where
t h e whole sequence is mirrored from t h e f a u l t y plane onwards
The two stacking f a u l t s may be distinguished by their powder p a t t e r n
Figure 2 :
. I n Pig. .
31
t h e r e c i p r o c a l lattice o f a deformation f a u l t e d cubic l a t t i c e is given
2
Section o f r e c i p r o c a l lattice o f an ice Ic s i n g l e c r y s t a l with deformation f a u l t s . The arrows i n d i c a t e the s h i f t d i r e c t i o n o f t h e broadened i n t e n s i t y maxima. Note t h a t along [ i l l ] t h e r e is no s h i f t and no broadening. Powder p a t t e r n s correspond t o a superposition of a l l reciprocal l a t t i c e p o i n t s at a given d i s t a n c e from the o r i g i n .
It shows t h a t t h e shoulder on t h e 111 r e f l e c t i o n is on t h e high-angle s i d e , while it is on t h e low-angle Bide o f t h e 222 r e f l e c t i o n . Some o t h e r r e f l e c t i o n s exhibit
both a high- and a low-angle component. Most r e f l e c t i o n s have sharp c e n t r a l f e a t u r e s ( a s seen i n t h e f i g u r e f o r t h e 111 d i r e c t i o n ) . Indeed, a l l r e f l e c t i o n s with indices h+k+Q = 3n are not broadened, which on the o t h e r hand means t h a t a l l equivalent r e f l e c t i o n s o f h k Q 1 swith two indices equal t o 3n and one index unequal t o 3n have no sharp component at a l l ( e . g . 400, 800, 331, 533). Thus the anomalous broadening o f t h e 331 and 533 can be understood (the 400 and 800 are very weak A quantitative analysis r e f l e c t i o n s and cannot be analysysedf o r t h e i r broa$:dfng$. are s t r i c t l y v a l i d only has not been performed; the a v a i l a b l e forooalitrms f o r i n f i n i t e crystals and random d i s t r i b u t i o n o f f a u l t s ; it is established t h a t t h e c r y s t a l l i t e s a r e very small and it is probable t h a t some c l u s t e r i n g of f a u l t s occurs as discussed below. The magnitude of t h e skew co;mponents and t h e i r p o s i t i o n however, i n d i c a t e s t h a t the p r o b a b i l i t y o f a deformation f a u l t occurring is o f t h e order of a few percent. Finally. the f i r s t d i f f r a c t i o n peak needs some consideration. Its c e n t r e is very c l o s e t o t h e calculated p o s i t i o n of t h e 100 r e f l e c t i o n o f ice Ih. A high d e n s i t y o f growth f a u l t s would r e s u l t i n the appearance of broadened hexagonal peaks. Indeed the 100 peak probably h a s a shoulder on its high angle s i d e ( a s indicated by f i t t i n g the complex first d i f f r a c t i o n peak with overlapping Gaussians), but t h e r e is no s i g n o f any r e f l e c t i o n of hexagonal i c e with L + 9; t h u s t h e p r o b a b i l i t y o f t h e occurrence o f growth f a u l t s must be small. Eexagonal r e f l e c t i o n s o t h e r than t h e 100 are not observed (with t h e possible exception o f t h e 101 peak, which coincides with the high-angle shoulder of t h e cubic 111 peak). The presence o f a strong hexagonal lo0 peak may be explained by t h e occurrence of regular stacking sequences. M o s t of t h e o t h e r hexagonal r e f l e c t i o n s of such a polytype are Wc2ak o r coincide with cubic r e f l e c t i o n s . Another possible explanation is t h e existence o f sequences ABABAB... which are t o o t h i n t o show w e l l defined r e f l e c t i o n s from planes oblique t o t h e hexagonal base plane. These sequences may be l a t e r a l l y disordered, which would explain the sawtooth p r o f i l e of the hexagonal 100 peak. I n t h i s case t h e higher order hexagonal r e f l e c t i o n s would be weak ( i n agreement with the observation from t h e s t r u c t u r e refinement of ice I c , which i n d i c a t e s t h e absence o f strong hexagonal peaks under t h e cubic l i n e s ) . A clear d i s t i n c t i o n between t h e s e two options cannot be made a t present, although t h e formation o f complicated polytypes i n a solid-solid r e c r y s t a l l i z a t i o n seems s d a t unlikely.
...
Ice Ic is found t o be the cubic counterpart of i c e Ih. Undoubtedly it is f u l l y ( o r almost f u l l y ) disordered i n its hydrogen arrangement with interatomic distances i d e n t i c a l within the l i m i t of e r r o r t o ice Ih. The only s i g n i f i c a n t s t r u c t u r a l difference is i n the averaged O...O...O angles, which are p e r f e c t l y t e t r a h e d r a l (by symmetry) i n i c e Ic, while they are s l i g h t l y d i f f e r e n t i n i c e Ih (according to t h e deviation from the i d e a l c/a r a t i o ) . The small p a r t i c l e s i z e of i c e Ic, t h e existence o f deformation f a u l t s and some hexagonal component i n t h e p a t t e r n obviously are inherent f e a t u r e s o f the material. Quantitati~f~differences e x i s t , e.g. f o r cubic i c e s prepared from d i f f e r e n t high pressure i c e s , and can be r e a d i l y explained by d i f f e r e n t amounts o f hexagonal colnponents e x h i b i t i n g d i f f e r e n t degrees o f disorder and/or d i f f e r e n t d e n s i t i e s of deformation f a u l t s . I t should be pointed o u t t h a t t h e hexagonal components do not o r i g i n a t e i n ice Ih impurities, b u t should be understood as a component i n t h e stacking sequence. Ice Ic is generally assumed 39 be a metastable phase, although its n a t u r a l occurrence seems to be established A transformation from'ice Ih i n t o ice Ic on cooling h a s never been observed; it e i t h e r forms d i r e c t l y from the vapour o r from some o t h e r s o l i d i c e phase. It has been observed repeatedly t h a t very smal& crystallites of ice have a cubic habit33834 usually with dimensions < 1000 A . Moreover sggw polycrystals very o f t e n show a misorientation of 70.5-70.6O between the c-axes , which i $ 5 q a l t o t h e angle between t h e 111 d i r e c t i o n s i n cubic i c e . It h a s been suggested ' t h a t ice nucleates p r e f e r e n t i a l l y w i t h 3 p i c symmetry, may occur t h u s forming mall c r y e t a l l i t e s o f cubic h a b i t . Multi-nucleation producing b u f i cubic a t m c t u r e s and hexagonal c r y s t a l s ( a s t h e more stable phase)
.
JOURNAL DE PHYSIQUE
w i l l u l t i m a t e l y grow on t h e 111 f a c e s of such a cubic (multi)nucleus, e v e n t u a l l y forming hexagonal l a y e r s o r twin crystals w i t h t h e c h a r a c t e r i s t i c a n g l e o f 70.5S0. It is conceivable t h a t t h e change from a c u b i c t o a hexagonal s t a c k i n g is n o t Indeed, abrupt, b u t happens over some d i s t a n c e , t h u s c r e a t i n g t h e s t a c k i n g f a u l t s . t h e a n a l y s i s of t h e ice Ic powder p a t t e r n i n d i c a t e s t h e presence o f both s t a c k i n g f a u l t s and hexagonal sequences, t h e latter probably with some lateral d i s o r d e r displacemm~ts. Apparently t h e i n i t i a l s t a g e o f forming ice Ih is j u s t reached when t h e r e c r y s t a l l i z a t i o n frcun amorphous o r recovered high p r e s s u r e ices ceases. The reorganization o f t h e i r three-dimensionally hydrogen-bonded network o f water molecules does n o t allow f o r t h e gmwth of t h e described twin crystals without This s i t u a t i o n is d i f f e r e n t h e a v i l y d i s t o r t i n g t h e network at t h e twin boundary. f o r crystal growth from t h e vapour, where t h e two twin domains could grow a? columns w i t h o ~ gg6twin boundary from t h e cubic nucleus aa observed f r e q u e n t l y i n Branching o f t h e c r y s t a l leaves u n f i l l e d space between t h e snow c r y s t a l s ' twin d o w i n s , which is h a r d l y p o s s i b l e when a r e o r i e n t a t i o n n and r e o r g a n i z a t i o n o f Thus t h e gruwth of ice Ih i n t o t h e t h e hydrogen bonding t a k e s p l a c e i n t h e bulk.
.
bulk may be i n h i b i t e d by competing hexagonal l a y e r s on t h e cubic nucleus, which e x p l a i n s t h e absence o f bulk ice ?3i n t h e d i f f r a c t i o n p a t t e r n as w e l l as t h e lateral d i s o r d e r w i t h i n t h e hexagonal s t a c k i n g sequences. ~1Eerences
1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11. 12.
13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.
H. Konig, 2. K r i s t . 105 (1983) 279. 20 (1896) 234. H.P. Barendrecht, 2. Phm. Ch-. J. Dewar, C h a . N e w s 91 (1905) 216. E.P. Burton & W.P. Oliver, Proc. Roy. Soc. London A l l (1936) 166. R.L.McParlan,Phys.ReV.S(1936)644. G , ffonijo, N. Kitamura, K. Shimaoka 6 K. Mihama, J. Phys. Soc. Japan 11 ( 1956) 527. L.G. Dowel1 & A.P. R i n f r e t , Nature 188 (1960) 1144. J.E. B e r t i e , L.D. Calvert 6 E. Whalley, J. Chem. Phys. 38 (1963) 840. J.E. B e r t i e , L.D. Calvert 6 E. Whalley, Can J. Chem. 42 (1964) 1373. G.P. Arnold, E.D. Pinch, S.W. Rabideau & R.G. Wenzel, J. Chem. Phys. 49 (1968 ) 4365. A.J. N 0 Z i k & M. Kaplan, J. Ch-. Phys. 47 (1967) 2960. A. Elarby, J.P. Jal, J. Dupuy, P. Chieux, A. Wright 6 R. P a r r i e n s , J. Phys, L e t t . 43 (1982) L355. P.V. H a s , Ice Physics, Clarendon Press, Oxford, 1974. R.H. Beaumont, H. Chihara & J . A . Morrison, J. Chem. Phys. 2 (1961) 1456. J.A. MCMillan & S.C. LOB, Nature 206 (1965) 806. J.A. Q l o I U l l ~ , J. Ch-. Phys. 48 ( 1968) 503. C.A. Coulson 9 D. Eisenberg, Proc. Roy. Soc. London A 3 2 (1966) 445. W. Hagen, A.G.G.M. T i e l e n s & J.M. Greenberg, Chem. Phys. 6 (1981) 367. E.D. Finch, S.W. Rabidean & A.B. Denison, J. Chem. Phys. r)9 (1968) 4660. J.E. Berie 6 S.M. Jacobs, J. Chem. Phys. 67 (1977) 2445. M. Blackman & N.D. Lisgarten, Proc. Roy. Soc. London A Z s (1957) 93. G. Honjo 6 K. Shimaoka, Acta Cxyst. 10 (1957) 710. P.V. Shallcross & G.B. Carpenter, J. Chem. Phys. 26 (1957) 782. D.D. Klug 6. E. Whalley, J. G l a c i o l . 21 (1978) 782. H. G r h i c h e r , 2. Krist. 110 (1958) 432. J. Paureau & C. V e t t i e r , Rev. S c i . Instrum. 46 (1975) 1484. U.H. Zucker, E. Perenthaler, W.P. Kuhs, R. B~Chmann6 H. Schulx, J. Appl. Cryst. 16 (1983) 358. w.P. ~ u h s6 M.S. Lehmann, water Science Reviews 2 (Ed. P. Pranks) i n p r e s s . W.P. Kuhs 6 M.S. Lehmann, this conference. T.R. Anantharaman & J . W . C h r i s t i a n , Acta Cryst. 9 (1956) 479. M.S. Paterson, J. Appl. Phys. 23 (1952) 805. E. Whalley, J. Phys. Chem. 87 (1983) 4174. a. Pernandez-Moran, Ann. N.Y. Acad. S c i . 85 (1960) 689. V.N. Vertsner & G.S. Zhdanov, Sgv. Phys. Cryst. (1966) 597. T. Kobayashi, Y . Furukawa, T. Takahashi & H. Uyeda, J. Cryst. Growth J5 (1976) 262. T. Takahashi & T. Kobayashi, J. Cryst. Grcmth 64 (1983) 593.
