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Phase transitions of solid CH4 at pressures up to 9 kbar determined by NMR
Physica 114B (1982) 281-286 North-Holland Publishing Company
281
P H A S E T R A N S I T I O N S O F S O L I D CH4 A T P R E S S U R E S UP TO 9 kbar D E T E R M I N E D BY N M R D. V A N D E R P U T I ' E N , K . O . P R I N S a n d N.J. T R A P P E N I E R S Van der Waals-Laboratorium,
Universiteit van Amsterdam, Amsterdam, The Netherlands
(282nd publication of the Van der Waals Fund) Received 8 April 1982 Conclusive evidence for a new phase transformation in solid CI4~, with a hysteresis of 20 K, is presented. At pressures above 5 kbar this new phase IV is definitely stable while at lower pressures, even down to P = 0 bar, phase IV is stable for at least several days. Previous high-pressure results which were not completely understood are re-examined and re-interpreted in terms of this new phase transition. The spin-lattice relaxation time Tx has been measured in the phases I, II, III and IV up to 9 kbar and from 2.5 to 90 K. In addition, the triple point of the I-II and II-III phase lines is established at 3.9 kbar and 32.1 K.
1. Introduction A t 20.4 K a n d n o r m a l p r e s s u r e CH4 t r a n s f o r m s f r o m an o r i e n t a t i o n a l l y d i s o r d e r e d p h a s e I to a p a r t i a l l y o r d e r e d p h a s e II. T h e p e c u l i a r s t r u c t u r e of this p h a s e was first d e r i v e d t h e o r e t i c a l l y by J a m e s a n d K e e n a n [1] for CD4, w h o a s s u m e d t h e e l e c t r o s t a t i c o c t u p o l e - o c t u p o l e c o u p l i n g as t h e dominant interaction, the structure being later c o n f i r m e d in a n e u t r o n diffraction e x p e r i m e n t b y P r e s s [2]. Six o u t of e i g h t m o l e c u l e s in this s t r u c t u r e a r e o r d e r e d o n t h e sites of an fcc lattice. T h e o c t u p o l e - o c t u p o l e i n t e r a c t i o n s with t h e n e i g h b o u r i n g m o l e c u l e s cancel out, l e a v i n g the remaining two molecules orientationally d i s o r d e r e d . W h e r e a s t h e d e u t e r a t e d s p e c i e s of m e t h a n e s h o w a f u r t h e r p h a s e t r a n s f o r m a t i o n to a t o t a l l y o r d e r e d p h a s e I I I at l o w e r t e m p e r a t u r e , CH4 d o e s not. P r e s s u r i z i n g a s a m p l e of solid CI-I4 has o f t e n l e d to puzzling p h e n o m e n a . A p i s t o n d i s p l a c e m e n t m e t h o d was u s e d b y S t e v e n s o n [3] t o r e v e a l f o u r p h a s e s , t w o of w h i c h o n l y e x i s t e d at e l e v a t e d p r e s s u r e s . A l s o a t r i p l e p o i n t was f o u n d 0378-4363/82/0000-0000/$02.75 O 1982 N o r t h - H o l l a n d
at 2.5 k b a r , w h e r e p h a s e I I c e a s e d to exist. T h e low t e m p e r a t u r e - h i g h p r e s s u r e p h a s e I V c o u l d n o t b e f o u n d b y S t e w a r t [4], w h o u s e d t h e s a m e p i s t o n - d i s p l a c e m e n t m e t h o d . A r e m a r k a b l e feat u r e in S t e w a r t ' s r e s u l t i n g p h a s e d i a g r a m was t h e fact t h a t t h e e r r o r b a r s at p r e s s u r e s h i g h e r t h a n 2.5 k b a r i n c r e a s e d s u d d e n l y b y m o r e t h a n a fact o r 5. A n u n e x p e c t e d a n o m a l o u s b e h a v i o u r of t h e d i e l e c t r i c c o n s t a n t e0 at p r e s s u r e s a b o v e 5 k b a r was f o u n d by C o s t a n t i n o et al. [5]. O n cooling they found the expected I-III transition, while e0 r e m a i n e d t e m p e r a t u r e i n d e p e n d e n t below the transition temperature. After repeated runs, h o w e v e r , t h e I - I I I t r a n s i t i o n d i s a p p e a r e d a n d e0 i n c r e a s e d with d e c r e a s i n g t e m p e r a t u r e . L a t e r a t t e m p t s to o b t a i n t h e R a m a n s p e c t r u m w e r e n o t c o n c l u s i v e [6]. A h i g h - p r e s s u r e N M R s t u d y b y N i j m a n a n d T r a p p e n i e r s [7] a c c u r a t e l y e s t a b l i s h e d t h e p h a s e d i a g r a m u p to 3 k b a r , a n d showed that the II-III transformation only takes p l a c e at p r e s s u r e s h i g h e r t h a n 400 bar. F u r t h e r m o r e , a m i n i m u m of t h e I I - I I I p h a s e line occurr e d at a b o u t 7 K. T w o q u a n t u m effects a r e resp o n s i b l e for this b e h a v i o u r . First, t h e a b s e n c e of
282
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
phase I I I at normal pressure is due to the large zero-point energy of the ordered molecules in Phase III, as is explained by Y a m a m o t o and co-workers [8], who developed a quantummechanical version of the classical James and Keenan model, and o n more general thermodynamic grounds by Sprik, Nijman and Trappeniers [9]. The rapid conversion (in about two hours) from the T ( I = l, J = l) to the A ( I = 2, J = 0) spin species of the free rotor molecules [10, 11] is responsible for the minimum in the I I - I I I phase boundary. When spin conversion is completed the five-fold degeneracy of the A level leads to a value of k In 5 per molecule for the entropy of the disordered molecules. The ordered ones still have k In 16 as a result of the sixteen close-spaced tunnel levels of the three spin isomers in their librational ground state. In the hight e m p e r a t u r e limit, the entropy of a freely rotating molecule is larger than that of an ordered molecule. Thus, the entropy change As associated with the I I - I I I transition is negative at high temperatures and positive at low temperatures. Recently, R a m a n spectra of solid CH4 under pressure at 4 . 2 K [12] have produced evidence for the existence of two phase transitions at 1.7 and 5 kbar. Wieldraaijer, Schouten and Trappeniers used the volume jumps at the I - I I I transformation to establish the transition temperatures and pressures in a pressure range from 20 to 60 kbar with a diamond anvil cell [13]. T h e phase line showed a hysteresis of approximately 20 K; furthermore, the connection with phase diagrams of previous authors [4, 14], obtained at lower pressures, suggested a point of inflexion or, what is m o r e likely, the existence of a fourth phase, or another triple point. The purpose of carrying out a high-pressure N M R experiment in a t e m p e r a t u r e range of 2.590 K at up to 10 kbar, was to establish the triple point of the I - I I and I I - I I I phase lines, the pressure dependence of the proton spin-lattice relaxation time T1 in phase III, and possibly to
solve the disagreement about the existence of a fourth phase.
2. Experimental
T h e experiments were p e r f o r m e d in a N M R spectrometer equipped with a high-pressure, low-temperature facility. The pulse spectrometer is of a conventional design, and has a working frequency of 24 MHz. A 10 x 90°-~--1 x 90 ° pulse sequence was employed to obtain the spin-lattice relaxation time T1. The discontinuities in T1 were used to detect the phase transitions [15]. The high-pressure part of the system consists of a pressure generating system (Harwood Engineering Co., Inc.) and a 1 4 k b a r beryllium-copper pressure vessel. Helium is used as the pressurizing medium, and the pressure is read from a manganin gauge which is calibrated against a H a r w o o d deadweight pressure balance with an accuracy within 5 bar. In order to determine the pressure in the region where the helium solidifies, use was made of a method employing the equation of state of helium [16]. At the helium melting point the t e m p e r a t u r e is slowly decreased, taking care that the helium solidifies first at the b o t t o m of the pressure vessel, by applying a t e m p e r a t u r e gradient along the vessel. During the solidification of helium, the pressure is kept constant. In this way the pressure just below the transition is the same as in the liquid helium just above the transition. In addition, strain gauges were attached to the outside of the pressure vessel in order to obtain a separate reading. Below the helium melting line, the T1 data in fig. 4 are taken along isochores. A variable t e m p e r a t u r e cryostat was developed to control the t e m p e r a t u r e of the pressure vessel from 2.5 to 90 K within 0.01 K. T e m p e r a t u r e s below 5 K were reached by pumping off the liquid helium. For the m e a s u r e m e n t of the temperature, a magnetic field independent c a r b o n glass t h e r m o m e t e r was used, which was checked
283
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
at regular intervals against a g e r m a n i u m thermometer. The accuracy in t e m p e r a t u r e was better than 0.1 K.
~o 1o
~,,~,~ ~, '~ (~
v~ ~
0.~
~ ~
0
~' e
~o~
oe
I
5[
3. Experimental results
T h e experimental results show a triple point of the I - I I and I I - I I I phase lines at 3.9 k b a r and 32.1 K, and a new phase transformation to a phase I V with a very large hysteresis of about 20 K (figs. 1, 2, 3). This hysteresis was also observed by Wieldraaijer et al. [13], and the connection with their phase line, obtained at pressures above 20 k b a r with a diamond anvil cell, is very good. It can therefore be concluded that the influence of the dissolving helium is of no importance as to the position of the phase line.
10
G fv_ I transilion ~. I - / ~ transition E3 I -][~ transition (metostoble} Nijmon ond Trappeniers this experiment _ _ P Hel . . . . .
I 70
I 75
I 80
I 85 K
Fig. 2. The hysteresis of the I-IV phase transition at P = 9053bar. O: Increasing temperature; ~7: decreasing temperature.
3.1. T h e p h a s e d i a g r a m
kbor
I 65
60
Iting line
THE PHASEDIAGRAM OF SOLID CH&
TV~
T ~ /
I
T h e procedure for obtaining phase I V needs some clarification. Starting for instance at 6 . 5 k b a r and 8 0 K , which is the t e m p e r a t u r e where the sample is normally held before a m e a s u r e m e n t takes place, and cooling slowly, we find the expected I - I I I transition at 38 K. During cooling to 5 K in about 5 h, 7"1 in phase I I I is measured at regular intervals. The same procedure is followed with increasing t e m p e r a t u r e and the I I I - I transition appears again. At 80 K the pressure is raised to 9 k b a r , and the procedure is repeated. The I - I I I transformation appears at 45 K. However, when the t e m p e r a t u r e is fixed for 3 h in the neighbourhood of the transition t e m p e r a t u r e in phase I, 7'1 decreases slowly from 20 s to a value of about 5 s, and on cooling, the I - I I I transition is lost. Instead, with increasing t e m p e r a t u r e 7'1 shows a discontinuity at 84 K from 14 to 25 s (fig. 2), the regular value in phase I. This value is reached within a few minutes. When the sample is cooled, still in phase I, a discontinuity appears at 64 K (fig. 2). On cooling, T1 shows no discontinuity at the former I - I I I transition, but behaves quite differently from 7"1 in phase III (fig. 4). Once
600bar P
~7
/ //'/~/f "--J
0/
' I/ 20
~ I 40
I 60
Fig. 1. The phase diagram.
z.O
r I 80 K
~
I ~5
i 50
1 55
----~T I 60
I 65 K
Fig. 3. The hysteresis of the I-IV phase transition at P = 6004bar. O: Increasing temperature; V: decreasing temperature.
284
D. van der Putten et al. I Phase transitions of solid CH4 at high pressures
T ISOBARS IN SOLID CH4
20
T,
s
, 'Z.~,~ -
5
/
0.2
I
, ~-~'
10
~
J f l 20
~
,.:39o
_~"_~J~"
I 0
I
I
PHASE 17 I 30
I 40
• •
p=2300 p=6370
•
p=9050 I 50
.. ., ..
" >
T
I 60 K
Fig. 4. TI in solid CI-h at various pressures. O p e n symbols: phases I, II and III; closed symbols: phase IV.
phase IV is obtained the discontinuities in T1 at the 1-IV and IV-I transformations are reproduced almost instantaneously at various pressures down to 5 k b a r , provided that the sample is not w a r m e d up far into phase I. When the t e m p e r a t u r e of the pressure vessel is increased to about 20 K above the I V - I transformation in phase I, and is held there for a few days, the 1-IV transition is lost on cooling. Phase I V can again be obtained by waiting for three hours at 9 k b a r or by waiting for three days at 38 K and 6 kbar. Below 5 kbar no I - I V transition could be observed, because the sample would first transform to phase III. However, the I V - I and I V - I I transformations could be followed down to zero pressure. Thus, phase IV even exists down to zero pressure (fig. 5) and is stable for at least two days. To maintain phase IV at pressures below 5 kbar, the following procedure was followed: Phase IV is produced at 9 k b a r . Then the pressure and t e m p e r a t u r e are lowered on a path in the P - T diagram along the helium melting line, taking care that at no point the helium solidifies in the capillary. At the desired pressure the sample is cooled slowly to 5 K, still in phase IV, Then, with increasing temperature, T1 is measured in phase IV and the I V - I and
I V - I I (fig. 6) transition temperatures are established. The reason for not obtaining the I l l - I V transformation below 5 kbar is not clear. Waiting for several days in phase I I I would not change T1. In another attempt, a mixture of phases I I I and IV was made at 4.5 kbar. This was achieved by not letting the I V - I transformation complete itself at the transition temperature. The sample was cooled quickly after T1 had reached a value in between the values for the phases IV and I, 14 s and 25 s respectively. At the I - I I I transition T1 decreased, but its value was still in P = 2 bar" 5.0 s
2.0
1.0
/ d
0.5
> T 0.2
I
I
5
10
Fig. 5. T1 in phase IV at P = 2 bar.
I 15 K
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
10.0 P = 390 bor
s 5.0
--
T
1
t
®
/x
®
z%
2.0
1.0
® ®
0.5 ®
A A
0.2
A A
0.1
A
A
:~T
t 10
I 15
I 2O
K
Fig. 6. T1 in phases IV and II at P = 390 bar. O: T1 in phases IV and II with increasing temperature; A: T1 in phase II with decreasing temperature. between the values of either phase III or phase IV. Again, waiting for several days did not change T~. This procedure was repeated at 3 kbar and at zero pressure were mixtures of IV and III, and IV and II, respectively, were present. No change in T~ was observed.
3.2. The proton spin-lattice relaxation time T1 In many molecular crystals such as C2H4, CF4 etc., the dipolar coupling, modulated by thermal fluctuations, phonons or librons are responsible for the interaction between the orientational degrees of freedom of the molecules and the zeeman system of the spins. Below 10 K, T~, corrected for the influence of spin conversion, in CI-LII proved to be nearly temperature independent down to 100 mK [17, 18]. This implies that another relaxation mechanism is responsible for the relaxation in CFLII. Bloom [19] proposed the so-called adiabatic molecular reorientation model, in which the anisotropic interactions between the molecules are responsible for the relaxation. Recently, a model for the dynamics of the coupling between the orientations of the ordered CI--L molecules in phase II
285
was proposed by Sprik and Trappeniers [20], in which no reorientation occurs. The four-proton exchange interaction is responsible for both the observed tunnel splittings and for the broadening of the degenerate T states of the molecules. This broadening appears as an interaction between the T molecules in the molecular field, and is observed as a modulation of the intra-molecular dipolar coupling. In phase III the details of the structure are still not known. Therefore, an analysis of the relaxation data would be quite speculative. However, some remarks can be made. Tunnelling, as recently proved to exist in phase III [21], tends to lower the relaxation rate. This could be an explanation for the fact that the minimum values of T1 are too long to be accounted for by a classical reorientational process. The T manifold, which only contributes to the relaxation, is split because of the low site symmetry, the splitting becoming smaller at increasing pressure. Thus, a large pressure dependence of the T1 minimum can be expected [22] as is confirmed from the minimum values of T1 in fig. 4, i.e. 160 and 95 ms at P = 0.5 and 6.5 kbar, respectively. The T~ minima in phase IV are shifted towards lower temperatures as compared to phase III (4.5 K at normal pressure in phase IV, fig. 5). This indicates that the reorientational motion, probably accompanied by tunnelling, is faster than in phase III.
4. S u m m a r y
In this section we shall summarize our results on the I - I V phase transition, and compare them with related observations in the literature. We have presented conclusive evidence for the existence of a phase IV in solid CFL. The I - I V phase transition shows a very large hysteresis of about 20 K, which explains the sudden increase in error bars in the phase diagram of Stewart [4] at pressures above 2.5 kbar. Inherent to the pistondisplacement method used by Stewart is the hys-
286
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
teresis of the apparatus. Therefore, the volume jumps of the transitions were measured isothermally, with increasing and decreasing pressure, the transition pressure being the average of the two. At lower pressures the I-II and II-III phase lines were determined rather accurately, but at higher pressures the hysteresis of the I - I V transformation causes a sudden increase in pressure difference of the volume jumps at increasing and decreasing pressure. Thus, the I-III transition of Stewart at higher pressure is in fact the I - I V transformation. A striking p h e n o m e n o n is the importance of the thermal history of the sample in phase I with respect to the time needed for obtaining phase IV. When the sample is cooled from higher temperatures in phase I, it takes 3 days at 6 kbar and only 3 h at 9 k b a r to complete the transformation to phase IV. If phase IV had already been obtained the I V - I and I - I V transitions would occur almost instantaneously. This explains the different behaviour of the dielectric constant and the disappearance of the I-III transition after several runs in the experiment of Costantino et al. [5]. The I I I - I V transformation observed by Thi6ry et al. [12] at 1.7 kbar and 4.2 K fits very well with the extrapolation of our I-IV transition. However, the I V - V transition at 5 k b a r and 4 . 2 K could not be reproduced in our experiment.
Acknowledgements The authors wish to thank Dr. M. Sprik for many helpful discussions and Mr. P. Kortbeek for assisting with the measurements. This in-
vestigation is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)", supported by the "Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.)".
References ]1] H.M. James and T.A. Keenan, J. Chem. Phys. 31 (1959) 12. [2] W. Press, J. Chem. Phys. 56 (1972) 2597. [3] R. Stevenson, J. Chem. Phys. 27 (1957) 656. [4] J.W. Stewart, J. Phys. Chem. Solids 12 (1959) 122. [5] M.S. Costantino, W.B. Dani61s and R.K. Crawford, Phys. Rev. Lett. 29 (1972) 1098. [6] F.D. Medina and W.B. Dani61s, J. Chem. Phys. 70 (1979) 2688. [7] A.J. Nijman and N.J. Trappeniers, Chem. Phys. Lett. 47 (1977) 188. [8] T. Yamamoto, Y. Kataoka and K. Okada, J. Chem. Phys. 66 (1977) 2701. [9] M. Sprik, A.J. Nijman and N.J. Trappeniers, Physica 98A (1979) 231. [10] J. Higinbotham, B.M. Wood and R.F. Code, Phys. Lett. 66A (1978) 237. [11] A.J. Nijman and A.J. Berlinsky, Can. J. Phys. 58 (1980) 1049. [12] M.M. Thi6ry, K. Kobashi and D. Fabre, VIIth Int. Conf. of Raman Spectroscopy, 1980, Ottawa. [13] H. Wieldraaijer, J.A. Schouten and N.J. Trappeniers, to be published. [14] M.S. Costantino and W.B. Dani~ls, J. Chem. Phys. 62 (1975) 764. [15] N.J. Trappeniers and F.A.S. Ligthart, Chem. Phys. Lett. 19 (1973) 465. [16] I.L. Spain and S. Segall, Cryogenics 2 (1971) 26. [17] (3. Briganti, P. Calvani, F. DeLuca and B. Maraviglia, Can J. Phys. 56 (1978) 1182. [18] B. Bouchet and H. Gl~ittli, J. Physique Lettres 42 (1981) 159. [19] M. Bloom, Colloque Ampere 14 (1967) 65. [20] M. Sprik and N.J. Trappeniers, Physica 103A (1980)411. [21] J. Eckert, C.R. Fincher, J.A. Goldstone and W. Press, J. Chem. Phys. 75 (1981) 3012. [22] A. HOller and J. Raieh, J. Chem. Phys. 71 (1979) 3851.
281
P H A S E T R A N S I T I O N S O F S O L I D CH4 A T P R E S S U R E S UP TO 9 kbar D E T E R M I N E D BY N M R D. V A N D E R P U T I ' E N , K . O . P R I N S a n d N.J. T R A P P E N I E R S Van der Waals-Laboratorium,
Universiteit van Amsterdam, Amsterdam, The Netherlands
(282nd publication of the Van der Waals Fund) Received 8 April 1982 Conclusive evidence for a new phase transformation in solid CI4~, with a hysteresis of 20 K, is presented. At pressures above 5 kbar this new phase IV is definitely stable while at lower pressures, even down to P = 0 bar, phase IV is stable for at least several days. Previous high-pressure results which were not completely understood are re-examined and re-interpreted in terms of this new phase transition. The spin-lattice relaxation time Tx has been measured in the phases I, II, III and IV up to 9 kbar and from 2.5 to 90 K. In addition, the triple point of the I-II and II-III phase lines is established at 3.9 kbar and 32.1 K.
1. Introduction A t 20.4 K a n d n o r m a l p r e s s u r e CH4 t r a n s f o r m s f r o m an o r i e n t a t i o n a l l y d i s o r d e r e d p h a s e I to a p a r t i a l l y o r d e r e d p h a s e II. T h e p e c u l i a r s t r u c t u r e of this p h a s e was first d e r i v e d t h e o r e t i c a l l y by J a m e s a n d K e e n a n [1] for CD4, w h o a s s u m e d t h e e l e c t r o s t a t i c o c t u p o l e - o c t u p o l e c o u p l i n g as t h e dominant interaction, the structure being later c o n f i r m e d in a n e u t r o n diffraction e x p e r i m e n t b y P r e s s [2]. Six o u t of e i g h t m o l e c u l e s in this s t r u c t u r e a r e o r d e r e d o n t h e sites of an fcc lattice. T h e o c t u p o l e - o c t u p o l e i n t e r a c t i o n s with t h e n e i g h b o u r i n g m o l e c u l e s cancel out, l e a v i n g the remaining two molecules orientationally d i s o r d e r e d . W h e r e a s t h e d e u t e r a t e d s p e c i e s of m e t h a n e s h o w a f u r t h e r p h a s e t r a n s f o r m a t i o n to a t o t a l l y o r d e r e d p h a s e I I I at l o w e r t e m p e r a t u r e , CH4 d o e s not. P r e s s u r i z i n g a s a m p l e of solid CI-I4 has o f t e n l e d to puzzling p h e n o m e n a . A p i s t o n d i s p l a c e m e n t m e t h o d was u s e d b y S t e v e n s o n [3] t o r e v e a l f o u r p h a s e s , t w o of w h i c h o n l y e x i s t e d at e l e v a t e d p r e s s u r e s . A l s o a t r i p l e p o i n t was f o u n d 0378-4363/82/0000-0000/$02.75 O 1982 N o r t h - H o l l a n d
at 2.5 k b a r , w h e r e p h a s e I I c e a s e d to exist. T h e low t e m p e r a t u r e - h i g h p r e s s u r e p h a s e I V c o u l d n o t b e f o u n d b y S t e w a r t [4], w h o u s e d t h e s a m e p i s t o n - d i s p l a c e m e n t m e t h o d . A r e m a r k a b l e feat u r e in S t e w a r t ' s r e s u l t i n g p h a s e d i a g r a m was t h e fact t h a t t h e e r r o r b a r s at p r e s s u r e s h i g h e r t h a n 2.5 k b a r i n c r e a s e d s u d d e n l y b y m o r e t h a n a fact o r 5. A n u n e x p e c t e d a n o m a l o u s b e h a v i o u r of t h e d i e l e c t r i c c o n s t a n t e0 at p r e s s u r e s a b o v e 5 k b a r was f o u n d by C o s t a n t i n o et al. [5]. O n cooling they found the expected I-III transition, while e0 r e m a i n e d t e m p e r a t u r e i n d e p e n d e n t below the transition temperature. After repeated runs, h o w e v e r , t h e I - I I I t r a n s i t i o n d i s a p p e a r e d a n d e0 i n c r e a s e d with d e c r e a s i n g t e m p e r a t u r e . L a t e r a t t e m p t s to o b t a i n t h e R a m a n s p e c t r u m w e r e n o t c o n c l u s i v e [6]. A h i g h - p r e s s u r e N M R s t u d y b y N i j m a n a n d T r a p p e n i e r s [7] a c c u r a t e l y e s t a b l i s h e d t h e p h a s e d i a g r a m u p to 3 k b a r , a n d showed that the II-III transformation only takes p l a c e at p r e s s u r e s h i g h e r t h a n 400 bar. F u r t h e r m o r e , a m i n i m u m of t h e I I - I I I p h a s e line occurr e d at a b o u t 7 K. T w o q u a n t u m effects a r e resp o n s i b l e for this b e h a v i o u r . First, t h e a b s e n c e of
282
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
phase I I I at normal pressure is due to the large zero-point energy of the ordered molecules in Phase III, as is explained by Y a m a m o t o and co-workers [8], who developed a quantummechanical version of the classical James and Keenan model, and o n more general thermodynamic grounds by Sprik, Nijman and Trappeniers [9]. The rapid conversion (in about two hours) from the T ( I = l, J = l) to the A ( I = 2, J = 0) spin species of the free rotor molecules [10, 11] is responsible for the minimum in the I I - I I I phase boundary. When spin conversion is completed the five-fold degeneracy of the A level leads to a value of k In 5 per molecule for the entropy of the disordered molecules. The ordered ones still have k In 16 as a result of the sixteen close-spaced tunnel levels of the three spin isomers in their librational ground state. In the hight e m p e r a t u r e limit, the entropy of a freely rotating molecule is larger than that of an ordered molecule. Thus, the entropy change As associated with the I I - I I I transition is negative at high temperatures and positive at low temperatures. Recently, R a m a n spectra of solid CH4 under pressure at 4 . 2 K [12] have produced evidence for the existence of two phase transitions at 1.7 and 5 kbar. Wieldraaijer, Schouten and Trappeniers used the volume jumps at the I - I I I transformation to establish the transition temperatures and pressures in a pressure range from 20 to 60 kbar with a diamond anvil cell [13]. T h e phase line showed a hysteresis of approximately 20 K; furthermore, the connection with phase diagrams of previous authors [4, 14], obtained at lower pressures, suggested a point of inflexion or, what is m o r e likely, the existence of a fourth phase, or another triple point. The purpose of carrying out a high-pressure N M R experiment in a t e m p e r a t u r e range of 2.590 K at up to 10 kbar, was to establish the triple point of the I - I I and I I - I I I phase lines, the pressure dependence of the proton spin-lattice relaxation time T1 in phase III, and possibly to
solve the disagreement about the existence of a fourth phase.
2. Experimental
T h e experiments were p e r f o r m e d in a N M R spectrometer equipped with a high-pressure, low-temperature facility. The pulse spectrometer is of a conventional design, and has a working frequency of 24 MHz. A 10 x 90°-~--1 x 90 ° pulse sequence was employed to obtain the spin-lattice relaxation time T1. The discontinuities in T1 were used to detect the phase transitions [15]. The high-pressure part of the system consists of a pressure generating system (Harwood Engineering Co., Inc.) and a 1 4 k b a r beryllium-copper pressure vessel. Helium is used as the pressurizing medium, and the pressure is read from a manganin gauge which is calibrated against a H a r w o o d deadweight pressure balance with an accuracy within 5 bar. In order to determine the pressure in the region where the helium solidifies, use was made of a method employing the equation of state of helium [16]. At the helium melting point the t e m p e r a t u r e is slowly decreased, taking care that the helium solidifies first at the b o t t o m of the pressure vessel, by applying a t e m p e r a t u r e gradient along the vessel. During the solidification of helium, the pressure is kept constant. In this way the pressure just below the transition is the same as in the liquid helium just above the transition. In addition, strain gauges were attached to the outside of the pressure vessel in order to obtain a separate reading. Below the helium melting line, the T1 data in fig. 4 are taken along isochores. A variable t e m p e r a t u r e cryostat was developed to control the t e m p e r a t u r e of the pressure vessel from 2.5 to 90 K within 0.01 K. T e m p e r a t u r e s below 5 K were reached by pumping off the liquid helium. For the m e a s u r e m e n t of the temperature, a magnetic field independent c a r b o n glass t h e r m o m e t e r was used, which was checked
283
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
at regular intervals against a g e r m a n i u m thermometer. The accuracy in t e m p e r a t u r e was better than 0.1 K.
~o 1o
~,,~,~ ~, '~ (~
v~ ~
0.~
~ ~
0
~' e
~o~
oe
I
5[
3. Experimental results
T h e experimental results show a triple point of the I - I I and I I - I I I phase lines at 3.9 k b a r and 32.1 K, and a new phase transformation to a phase I V with a very large hysteresis of about 20 K (figs. 1, 2, 3). This hysteresis was also observed by Wieldraaijer et al. [13], and the connection with their phase line, obtained at pressures above 20 k b a r with a diamond anvil cell, is very good. It can therefore be concluded that the influence of the dissolving helium is of no importance as to the position of the phase line.
10
G fv_ I transilion ~. I - / ~ transition E3 I -][~ transition (metostoble} Nijmon ond Trappeniers this experiment _ _ P Hel . . . . .
I 70
I 75
I 80
I 85 K
Fig. 2. The hysteresis of the I-IV phase transition at P = 9053bar. O: Increasing temperature; ~7: decreasing temperature.
3.1. T h e p h a s e d i a g r a m
kbor
I 65
60
Iting line
THE PHASEDIAGRAM OF SOLID CH&
TV~
T ~ /
I
T h e procedure for obtaining phase I V needs some clarification. Starting for instance at 6 . 5 k b a r and 8 0 K , which is the t e m p e r a t u r e where the sample is normally held before a m e a s u r e m e n t takes place, and cooling slowly, we find the expected I - I I I transition at 38 K. During cooling to 5 K in about 5 h, 7"1 in phase I I I is measured at regular intervals. The same procedure is followed with increasing t e m p e r a t u r e and the I I I - I transition appears again. At 80 K the pressure is raised to 9 k b a r , and the procedure is repeated. The I - I I I transformation appears at 45 K. However, when the t e m p e r a t u r e is fixed for 3 h in the neighbourhood of the transition t e m p e r a t u r e in phase I, 7'1 decreases slowly from 20 s to a value of about 5 s, and on cooling, the I - I I I transition is lost. Instead, with increasing t e m p e r a t u r e 7'1 shows a discontinuity at 84 K from 14 to 25 s (fig. 2), the regular value in phase I. This value is reached within a few minutes. When the sample is cooled, still in phase I, a discontinuity appears at 64 K (fig. 2). On cooling, T1 shows no discontinuity at the former I - I I I transition, but behaves quite differently from 7"1 in phase III (fig. 4). Once
600bar P
~7
/ //'/~/f "--J
0/
' I/ 20
~ I 40
I 60
Fig. 1. The phase diagram.
z.O
r I 80 K
~
I ~5
i 50
1 55
----~T I 60
I 65 K
Fig. 3. The hysteresis of the I-IV phase transition at P = 6004bar. O: Increasing temperature; V: decreasing temperature.
284
D. van der Putten et al. I Phase transitions of solid CH4 at high pressures
T ISOBARS IN SOLID CH4
20
T,
s
, 'Z.~,~ -
5
/
0.2
I
, ~-~'
10
~
J f l 20
~
,.:39o
_~"_~J~"
I 0
I
I
PHASE 17 I 30
I 40
• •
p=2300 p=6370
•
p=9050 I 50
.. ., ..
" >
T
I 60 K
Fig. 4. TI in solid CI-h at various pressures. O p e n symbols: phases I, II and III; closed symbols: phase IV.
phase IV is obtained the discontinuities in T1 at the 1-IV and IV-I transformations are reproduced almost instantaneously at various pressures down to 5 k b a r , provided that the sample is not w a r m e d up far into phase I. When the t e m p e r a t u r e of the pressure vessel is increased to about 20 K above the I V - I transformation in phase I, and is held there for a few days, the 1-IV transition is lost on cooling. Phase I V can again be obtained by waiting for three hours at 9 k b a r or by waiting for three days at 38 K and 6 kbar. Below 5 kbar no I - I V transition could be observed, because the sample would first transform to phase III. However, the I V - I and I V - I I transformations could be followed down to zero pressure. Thus, phase IV even exists down to zero pressure (fig. 5) and is stable for at least two days. To maintain phase IV at pressures below 5 kbar, the following procedure was followed: Phase IV is produced at 9 k b a r . Then the pressure and t e m p e r a t u r e are lowered on a path in the P - T diagram along the helium melting line, taking care that at no point the helium solidifies in the capillary. At the desired pressure the sample is cooled slowly to 5 K, still in phase IV, Then, with increasing temperature, T1 is measured in phase IV and the I V - I and
I V - I I (fig. 6) transition temperatures are established. The reason for not obtaining the I l l - I V transformation below 5 kbar is not clear. Waiting for several days in phase I I I would not change T1. In another attempt, a mixture of phases I I I and IV was made at 4.5 kbar. This was achieved by not letting the I V - I transformation complete itself at the transition temperature. The sample was cooled quickly after T1 had reached a value in between the values for the phases IV and I, 14 s and 25 s respectively. At the I - I I I transition T1 decreased, but its value was still in P = 2 bar" 5.0 s
2.0
1.0
/ d
0.5
> T 0.2
I
I
5
10
Fig. 5. T1 in phase IV at P = 2 bar.
I 15 K
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
10.0 P = 390 bor
s 5.0
--
T
1
t
®
/x
®
z%
2.0
1.0
® ®
0.5 ®
A A
0.2
A A
0.1
A
A
:~T
t 10
I 15
I 2O
K
Fig. 6. T1 in phases IV and II at P = 390 bar. O: T1 in phases IV and II with increasing temperature; A: T1 in phase II with decreasing temperature. between the values of either phase III or phase IV. Again, waiting for several days did not change T~. This procedure was repeated at 3 kbar and at zero pressure were mixtures of IV and III, and IV and II, respectively, were present. No change in T~ was observed.
3.2. The proton spin-lattice relaxation time T1 In many molecular crystals such as C2H4, CF4 etc., the dipolar coupling, modulated by thermal fluctuations, phonons or librons are responsible for the interaction between the orientational degrees of freedom of the molecules and the zeeman system of the spins. Below 10 K, T~, corrected for the influence of spin conversion, in CI-LII proved to be nearly temperature independent down to 100 mK [17, 18]. This implies that another relaxation mechanism is responsible for the relaxation in CFLII. Bloom [19] proposed the so-called adiabatic molecular reorientation model, in which the anisotropic interactions between the molecules are responsible for the relaxation. Recently, a model for the dynamics of the coupling between the orientations of the ordered CI--L molecules in phase II
285
was proposed by Sprik and Trappeniers [20], in which no reorientation occurs. The four-proton exchange interaction is responsible for both the observed tunnel splittings and for the broadening of the degenerate T states of the molecules. This broadening appears as an interaction between the T molecules in the molecular field, and is observed as a modulation of the intra-molecular dipolar coupling. In phase III the details of the structure are still not known. Therefore, an analysis of the relaxation data would be quite speculative. However, some remarks can be made. Tunnelling, as recently proved to exist in phase III [21], tends to lower the relaxation rate. This could be an explanation for the fact that the minimum values of T1 are too long to be accounted for by a classical reorientational process. The T manifold, which only contributes to the relaxation, is split because of the low site symmetry, the splitting becoming smaller at increasing pressure. Thus, a large pressure dependence of the T1 minimum can be expected [22] as is confirmed from the minimum values of T1 in fig. 4, i.e. 160 and 95 ms at P = 0.5 and 6.5 kbar, respectively. The T~ minima in phase IV are shifted towards lower temperatures as compared to phase III (4.5 K at normal pressure in phase IV, fig. 5). This indicates that the reorientational motion, probably accompanied by tunnelling, is faster than in phase III.
4. S u m m a r y
In this section we shall summarize our results on the I - I V phase transition, and compare them with related observations in the literature. We have presented conclusive evidence for the existence of a phase IV in solid CFL. The I - I V phase transition shows a very large hysteresis of about 20 K, which explains the sudden increase in error bars in the phase diagram of Stewart [4] at pressures above 2.5 kbar. Inherent to the pistondisplacement method used by Stewart is the hys-
286
D. van der Putten et al. / Phase transitions of solid CH4 at high pressures
teresis of the apparatus. Therefore, the volume jumps of the transitions were measured isothermally, with increasing and decreasing pressure, the transition pressure being the average of the two. At lower pressures the I-II and II-III phase lines were determined rather accurately, but at higher pressures the hysteresis of the I - I V transformation causes a sudden increase in pressure difference of the volume jumps at increasing and decreasing pressure. Thus, the I-III transition of Stewart at higher pressure is in fact the I - I V transformation. A striking p h e n o m e n o n is the importance of the thermal history of the sample in phase I with respect to the time needed for obtaining phase IV. When the sample is cooled from higher temperatures in phase I, it takes 3 days at 6 kbar and only 3 h at 9 k b a r to complete the transformation to phase IV. If phase IV had already been obtained the I V - I and I - I V transitions would occur almost instantaneously. This explains the different behaviour of the dielectric constant and the disappearance of the I-III transition after several runs in the experiment of Costantino et al. [5]. The I I I - I V transformation observed by Thi6ry et al. [12] at 1.7 kbar and 4.2 K fits very well with the extrapolation of our I-IV transition. However, the I V - V transition at 5 k b a r and 4 . 2 K could not be reproduced in our experiment.
Acknowledgements The authors wish to thank Dr. M. Sprik for many helpful discussions and Mr. P. Kortbeek for assisting with the measurements. This in-
vestigation is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)", supported by the "Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.)".
References ]1] H.M. James and T.A. Keenan, J. Chem. Phys. 31 (1959) 12. [2] W. Press, J. Chem. Phys. 56 (1972) 2597. [3] R. Stevenson, J. Chem. Phys. 27 (1957) 656. [4] J.W. Stewart, J. Phys. Chem. Solids 12 (1959) 122. [5] M.S. Costantino, W.B. Dani61s and R.K. Crawford, Phys. Rev. Lett. 29 (1972) 1098. [6] F.D. Medina and W.B. Dani61s, J. Chem. Phys. 70 (1979) 2688. [7] A.J. Nijman and N.J. Trappeniers, Chem. Phys. Lett. 47 (1977) 188. [8] T. Yamamoto, Y. Kataoka and K. Okada, J. Chem. Phys. 66 (1977) 2701. [9] M. Sprik, A.J. Nijman and N.J. Trappeniers, Physica 98A (1979) 231. [10] J. Higinbotham, B.M. Wood and R.F. Code, Phys. Lett. 66A (1978) 237. [11] A.J. Nijman and A.J. Berlinsky, Can. J. Phys. 58 (1980) 1049. [12] M.M. Thi6ry, K. Kobashi and D. Fabre, VIIth Int. Conf. of Raman Spectroscopy, 1980, Ottawa. [13] H. Wieldraaijer, J.A. Schouten and N.J. Trappeniers, to be published. [14] M.S. Costantino and W.B. Dani~ls, J. Chem. Phys. 62 (1975) 764. [15] N.J. Trappeniers and F.A.S. Ligthart, Chem. Phys. Lett. 19 (1973) 465. [16] I.L. Spain and S. Segall, Cryogenics 2 (1971) 26. [17] (3. Briganti, P. Calvani, F. DeLuca and B. Maraviglia, Can J. Phys. 56 (1978) 1182. [18] B. Bouchet and H. Gl~ittli, J. Physique Lettres 42 (1981) 159. [19] M. Bloom, Colloque Ampere 14 (1967) 65. [20] M. Sprik and N.J. Trappeniers, Physica 103A (1980)411. [21] J. Eckert, C.R. Fincher, J.A. Goldstone and W. Press, J. Chem. Phys. 75 (1981) 3012. [22] A. HOller and J. Raieh, J. Chem. Phys. 71 (1979) 3851.