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A NMR study of solid methane: The low temperature phase transition
Volume
47, number
CHEMICAL
1
PHYSICS LETTERS
A NMR STUDY OF SOLID METHANE: THE LOW TEMPERATURE
1 April 1977
PHASE TRANSITION
A.J. NIJMAN and N.J. TRAPPENIERS Van der Waaklaboratorium, Universueit van Amsterdam. Amsterdam, The Nethertands (235th publication of the Van der Waals Fund)
Received
7 January
1977
Proton magnetic resonance measurements have been carried out between 5 and 80 K and up to pressures of 3 kbar in order to investigate two phase transitions in solid methane. The P versus T plot of the low temperature (P-7) phase transition is strongIy curved and, consequently, this transition can only be found at pressures above 200 atm. The effects of the tunnel splïttings between the ground states of the three spin ïsomers on the curvature of thïs transition line are discussed.
1. Introduction Nuclear magnetic-resonance constitutes an elegant method for investigating the characteristic changes in the molecular dynamïcs associated with phase transitions in molecular crystals. It is wel1 known that a fìrst order phase transition leads to a discontinuity in the spin-lattice reIaxation time, Tl [ 1] , often accompanied by a discontinuity in the NMRseconä moment, whiIe in genera1 , a higher order phase transition is accompanied by more subtle typesLof anomalies in the spin-lattice relaxation. Usinga low temperature, high pressure, NMR spectrometer we have determined second moments, M2, and spinlattice relaxation times, Tl, of solid methane from 5 to 80 K and at pressures up to 3 kbar. From the discontinuities in the T, curves it has been posslble to construct the P versus T plot of the various transition lines in the phase diagram of solid CH,, as shown in fig. 1. The high temperature phase, called (Y,has a fee structure with disordered molecules. The structure of the intermediate temperature phase, called 0, was predicted by James and Keenan [2] on the basis of a classica1 mean field theory, assuming electrostatic octupole-octupole interactions between molecules located on a fee lattice. This structure consists of eight sublattices as shown in fig. 2. The molecules on six of these sublattices are ordered in such a way that their octupole interactions with molecules on the other two sublattices add to zero and, thus, the molecules on 188
these two sublattices rotate freely. For many years the applicability of the James and Keenan model to methane appeared rather doubtful. However, in 1972 Press [3] established by neutron scattering that the P phase of CD, and by inference also the p phase of CH4 did in fact correspond to the James and Keenan structure. Later Press and KoIImar [4], among others, determined the energy levels of the nearly free rotator molecules as wel1 as the tunnel splittings of the oriented molecules. The resulting leve1 scheme shown in fig. 3 fits very well in the theoretical scheme [5] ob tained from an extended James-Keenan model, whïch also includes van der Waals interactions. One of the most puzzling phenomena occurring in the solid methanes is that al1 deuterated methanes exhïbit hvo phase transitions at zero pressure while CH4 shows just one phase transition at zero pressure. However, for many years there has been serious disagreement about the question whether or not there is evïdence for a second phase transition in solid methane around 8 K. Thus, Colwell et al. [6] found a thermal inertia in the temperature region about 8 K and they described this phenomenon as a sluggish transition from a low temperature phase called 7 to the fl phase. At present this thermal ïnertia is easily explained by interconversion of the spin species of the freely rotating nïolecules which are present in the p phase. Code and Higgenbotham [7]
CHEMICAL PHYSICS LETTERS
Volume 47, number 1
1 April f077
CH‘
3cloc atm
2ooc
II
I
11
II
11
10
IIII
I
15
11
20
25
30K
Fig. 1. Tbe phase diagram of solid CH4.
Sublattlce
1 and 2 .“Free
Sublattice
3 - 8
Rotors”
:“Ordered
Molecules”
UI K
I= lil51
Tz E
30
I=O WJI
Energy
I f T2-1=1
[91
A-1
1=2 IS)
IFree Rotor” Molecules
Fi.
Fig. 2. The structure of phase P.
3. The
E-. T:_-.I=
I=O 12)
Al
i.zr51
1 (91
Ordered Molecules leve1 scheme.
were able to interpret a number of NMR results obtained in pure (oxygen free) methane in terms of a mode1 in which the freely rotating molecules convert rapidly (7 = 1 h), while no conversion occurs on the ordered sublattices. The slow spin conversion of the ordered molecules also follows from the specifïc heat measure189
Volume 47, numbcr 1
CHEMICAL PHYSICS LElTERS
ments of Vogt and Pitzer [4]. The same conclusions using our second moment [S] measurements. As shown by Nijman and Berlinsky [9], the interconversion of thc spin species of the freely rotating molecules is caused by a process in which spin states are mixed by intermolecular dipole-dipole coupling and transitions between orientational states are caused by thc intermolecular octupole-octupole coupling being modulated by phonon emission At low temperatures the conversion process of the freely rotating molecules is fast (r =5 2 h) while the one of the ordered molecules is slow (7- 5 1 year). The principal result of thc present study is that it fies the position of the low temperature 0-7 transition in the phase diagram. The remarkable fact thereby is that the transition curve is strongly curved so that a minimum occurs and the y-phase can be observed at pressures above 200 atm. The physical reasons for the absente of the P-7 phase transition at zero pressure can be found in the theory which was bricfly outlined above. can be obtained
2. Experimental
results
The proton spin-lattice relaxation time T, in methane was mcasured with a NMR pulse spectrometer at a working frequency of 28.8 MHz. This spectrometer IS on line with a CDC 1700 computer which regulates the timing of the pulse sequences and performs “real time” calculation of T, or Q. Because of lts better signal stability we employed
the 10 X 90”-1
The pressure generated by a combination of a hydraulic oil compressor and a mercury piston gas compressor is measured with calibrated manometers with an accuracy better than 0.5%. Both isothermal and isobaric measurements of the spin-lattice relaxation time were performed in the region from 5 to 80 K and at pressures up to 3000 atm. Helium was used for applying hydrostatic pressure to the methane sample. Consequently, at a given pressurc it is not possible to perform measurements at temperatures below the melting temperature of helium. The experimental values of Tr , at four different pressures, are shown in fig. 4: the two phase transitions show up rcspectively as a sizeable and a smal1 discontinuity. These measurements, together with the isothermal experiments used at temperatures below 15 K [8,10], lead to the phase diagram which is shown in fig. 1_ The P-7 transition has several very unusual and remark able properties. First of ah, as already pointed out, the P versus T plot of the transition line, as measured with decrcasmg pressure, is strongly curved and the transition pressure shows a minimum as a function of temperature. Secondly, the hysteresis of the transition pressure at low temperatures is much larger than at high temperatures. In thc third place, there is also a discontinuity in the proton magnetic susceptibility xo and the second moment M2. These discontinuities disappear at high temperatures.
X 90°
pulse sequence. However, it has to bc noted that the spin-lattice relaxation timc did not depend on the pulse sequence used. NO deviation from exponential recovery of the proton spin magnetization was detected. The measurements on solid CH4 were performed on a very pure polycrystalline sample contained in a high pressure vessel of beryllium copper. A glass (later Ai,03) specimen holdcr restricts the actual sample volume to the region inside the rf coil. The variable temperature cryostat in which the pressure vessel is contained ensures a temperature constant to within 0.0 1 K. The temperature is measured with a platinum or a germanium resistance thermometer mounted in the bottom of the pressure vessel. Magnetic field effects on the resistance of the germanium or platinum thermometer were taken into account, resulting in a temperature accuracy better than 0.1 K. Special provisions are made to eliminate temperature gradients along the pressure vessel. 150
1 April 1977
3. Discussion 3.1. l’7re curvature of the 0-7
transition
Ene
From the Afz and Tl data interesting conclusions can be reached concerning the molecular reorientation [8,1 l] and the spin conversion [8,9] but we shall restrict ourselves in thrs letter to a discussion of the !ow temperature (í3-7) phase transition. The curvature of the 5-7 transition line is a natura1 consequente of the James-Keenan structure (fig. 2) for the a phase and of the fast spin conversion process of the freely rotating molecules. A!though the prediction by James and Keenan as regards the structure of the 7 phase is not correct, we may use the reasonable assumption that the moleculcs which rotate freely in the p phase are ordered in the 7 phase. The slope of a fïrst order transiaion line is given by the relation of Clausius-Clapeyron: dP/dT = k?/AV-
Volume 47, number 1
CHEMICAL PHYSICS LETTERS
[Apri[ t977
80 $
60 L.O
..... ~
7 C
3O
'~
O
;3
%
O% !!
I
I
20
I
lO 8 6
3--
2--
3O
35
z,O
/-S
50
55
60 K "I
Fig. 4. The spin-lattice relaxation time. The main contribution to the entropy difference between the f3phase and the 7 phase resuRs from the change in the orientational state o f those molecules which rotate freely in the 13phase. The entropy o f a rotating molecule being considerably larger than that o f an ordered molecule, it is to be expected that the transition from phase q¢ to phase /3 is accompanied by an increase o f entropy. This argument will be true at h i ~ temperatures where classical statistical mechanics are applicable but at low temperatures the situation is completely different. In this region the level scheme o f ordered molecules with one steric position is now characterized by sixteen levels close together [12,8] which describe the ground states o f the spin isomers (fig. 3). ~'ilae first excited states o f the ordered molecules are found at much higher energies (e.g. ~ 70 K.) The entropy associated with these ordered molecules is thus about k In16 per molecule. In contrast, freely rotating molecules have a five fold degenerate ground state leading to the "zeropoint" entropy k In5 per molecule. O f course, this
value for the entropy is only correct if, due to spin version, transitions to this ground state are possible Consequently, the change in odentational state o f t molecules on sublattices 1 and 2, when going from /3 phase at low temperatures, results in an entropy c with opposite sign to that expected at higher tempe tures. The slope o f the transition line wil[ therefore change sign at an intermediate temperature. Indeed (as can be seen from fig. 1), this behaviour o f the phase transition is found in our experimertt. This qualitative description o f the/~-)' phase t r tion also explains some additional phenomena [8,~ like the discontinuities in X0 and M 2 while the inc o f the hysteresis with decreasing temperature fits 1 the present model as well. 3.2. The 13--~1phase transition at hig[t pressure Besides the dominant electrostatic o c t u p o [ e - o pole coupling, van der Waals type interactions also tribute to the anisotropic inte[molecular potential
[9[
CHEMICAL PHYSICS LETTERS
Volume 47, number 1
these, the (330) interaction 1131 is probably the most important one. Tb& interaction has the property of des?abi~i~ng structures with parallel ordering of the methane tetrahedra. The destabilization may be the reason for the incorrect prediction by James and Keenan of the structure of the 7 phase. The decrease with pressure of the temperature region in which the ,8 phase is the thermodynamicatfy stable ene is in contradiction with the prediction of the James-Keenan theory that at high pressure the two phase lines CY-@and @--7 are parallel. The oz--@transítion temperat ure [8 1 depcnds on density in almost exactly the same marmer as predicted by the quantum -mechanica1 version of the James-Keenan theory 1141 for equilibrium mixtures ofspin isomers. In contrast, as is shown in fig. 5, thc 8-7 phase transition depends on density in a way (T = P~-~) essentially different from the one predicted by the James-Keenan theory (Tap 2.33). In constructing this diagram use was made of densities obtained from second moment measurements at 34 K. The density dependence of the interactions stabilizing the(stil1 unknown) structure of the 7 phase wil1 in genera1 be different from the one due to the octupoieoctupole interaction Cp7j3). Taking into account this rather weak density dependence, it seems reasonabfe to assume that, especially at high pressures where fhe “hardcore” of the intermolecuIar interactions is important, this density dependence is weaker than the one of the interactions stabihzing the 7 phase. This line of reasoning would explain the slape of the transition Ene at high pressure (T* Paap). os.
os3 3.L F’
T_ p3__ _-
r32L
_ _---
- -
. il InT L f
1
30',
/T-psf,--
c experimentaf
i 20
I i
/’
5”’ ,-
r’ , -0.62
-Yikö-
--+tnp t -0 58
Fig. 5. The r 4 p transition temperature.
192 -
tions. This will lead to a (Y,/3, y triplepoint at high pressure f)3 kbar) which, however, couId not be observed
with t@ presect apparatus. Due to the unknown nature of the 7 phase 131, the analysis cannot be pursued any further at this point and it is not possible to_ïdentify the interaction(s) governing the &--7 phase transition. However, the present resdts wil1 be usefut for checkîng out any future mode1 which is proposed for this phase transition.
The strong curvature of the &-7 phase transition is explained by the remarkable structure of the p phase as predicted by James and Keenan and by the recently understood e~u~ib~urn [9] between the pop~at~ons of the spin species of the freely rotating moiecules. The densîty dependence of the transition temperature cIearIy shows that the octupole-octupole coupling used in the James-Keenan theory does not explain the high pressure behaviour of this phase transition. An extensive theoretical treatment is to bc found in the thesis by Nijman [8f.
Acknowfedgement This investigation 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.)“. The authors are much indebted to Dr. K.O. Prins and Mr. M. Sprik for many hetpful discussions and to Mr. M. v.d. Werf, Mr. J. Veldhuis and Mrs. F.M. Been-tiayo with the measurements.
T
2
1s -056
References [ l] N.J. Trappeniers and F.A.S. LiSthart, Chem. Phys Letters
J
-0 6L
me temperature region of the /3phase decreases with pressure as a result of the differente between the interactions which are responsibie for the two pbase transi-
for their assistance
1
1 ApriI 1977
19 (1973) 465. [2] H.M. James and T.A. Kcenan, 3. Chem. Phys. 3 1 (1959) [3] k!Press, J. Chem. Phys. 56 (1972) 2597. [4] H. GIattti, A. Sen& and M. Eíscnkremer, Phys. Rev.
Letters 28 (1972) 871;
Volume 47, numbcr 1
CHEMICAL PHYSICS LETTERS
R. Kahn, Phys. Letters A54 (1975) 285; W. Press and A. KoBmar, Sohd State Commun. 17 (1975) 405; C.J. Vogt and K.S. Pitzer, J. Chem. Phys. 63 (1975) 3667. IS] Y. Kataoka, K. Okada and T. Yamamoto, Chem. Phys. Letters 19 (1973) 365. f6] J.H. ColaeB, E.K. GiB and J.A. Morrison, J. Chem. Phys. 39 (1973) 653. (71 R.F. Code and J. Higginbotham, Can. J. Phys. 54 (1976) 1248.
1 April 1977
[S] A.J. Nijman, Thesis, to be pu5iïshed. A.I. Nijman and N.J. Trappeniers, to be pubhshed, [9] A.J. Nijman and N.J. Berìinsky, Phys. Rev. Letters, submitted for publication. [ 101 A.J. Nijman and N.J. Trappeniers, Proceedings of the 18th Ampère Congress, Nottingham (1974) p_ 2.53. [ 11 f A.J. Nijman end N.J. Trappeniers, Proceedings of the 19th Ampère Congress, Heidelberg (1976). [ 121 T. Nagamiya, Progr. Theoret. Phys. 6 (1951) 702. (131 H. Yasuda, Progr. Theoret. Phys. 45 (1971) 136L ] 141 Y. Kataoka and T. Yamamoto, Progr. Theorct. Phys SuppL (1968) 436.
133
47, number
CHEMICAL
1
PHYSICS LETTERS
A NMR STUDY OF SOLID METHANE: THE LOW TEMPERATURE
1 April 1977
PHASE TRANSITION
A.J. NIJMAN and N.J. TRAPPENIERS Van der Waaklaboratorium, Universueit van Amsterdam. Amsterdam, The Nethertands (235th publication of the Van der Waals Fund)
Received
7 January
1977
Proton magnetic resonance measurements have been carried out between 5 and 80 K and up to pressures of 3 kbar in order to investigate two phase transitions in solid methane. The P versus T plot of the low temperature (P-7) phase transition is strongIy curved and, consequently, this transition can only be found at pressures above 200 atm. The effects of the tunnel splïttings between the ground states of the three spin ïsomers on the curvature of thïs transition line are discussed.
1. Introduction Nuclear magnetic-resonance constitutes an elegant method for investigating the characteristic changes in the molecular dynamïcs associated with phase transitions in molecular crystals. It is wel1 known that a fìrst order phase transition leads to a discontinuity in the spin-lattice reIaxation time, Tl [ 1] , often accompanied by a discontinuity in the NMRseconä moment, whiIe in genera1 , a higher order phase transition is accompanied by more subtle typesLof anomalies in the spin-lattice relaxation. Usinga low temperature, high pressure, NMR spectrometer we have determined second moments, M2, and spinlattice relaxation times, Tl, of solid methane from 5 to 80 K and at pressures up to 3 kbar. From the discontinuities in the T, curves it has been posslble to construct the P versus T plot of the various transition lines in the phase diagram of solid CH,, as shown in fig. 1. The high temperature phase, called (Y,has a fee structure with disordered molecules. The structure of the intermediate temperature phase, called 0, was predicted by James and Keenan [2] on the basis of a classica1 mean field theory, assuming electrostatic octupole-octupole interactions between molecules located on a fee lattice. This structure consists of eight sublattices as shown in fig. 2. The molecules on six of these sublattices are ordered in such a way that their octupole interactions with molecules on the other two sublattices add to zero and, thus, the molecules on 188
these two sublattices rotate freely. For many years the applicability of the James and Keenan model to methane appeared rather doubtful. However, in 1972 Press [3] established by neutron scattering that the P phase of CD, and by inference also the p phase of CH4 did in fact correspond to the James and Keenan structure. Later Press and KoIImar [4], among others, determined the energy levels of the nearly free rotator molecules as wel1 as the tunnel splittings of the oriented molecules. The resulting leve1 scheme shown in fig. 3 fits very well in the theoretical scheme [5] ob tained from an extended James-Keenan model, whïch also includes van der Waals interactions. One of the most puzzling phenomena occurring in the solid methanes is that al1 deuterated methanes exhïbit hvo phase transitions at zero pressure while CH4 shows just one phase transition at zero pressure. However, for many years there has been serious disagreement about the question whether or not there is evïdence for a second phase transition in solid methane around 8 K. Thus, Colwell et al. [6] found a thermal inertia in the temperature region about 8 K and they described this phenomenon as a sluggish transition from a low temperature phase called 7 to the fl phase. At present this thermal ïnertia is easily explained by interconversion of the spin species of the freely rotating nïolecules which are present in the p phase. Code and Higgenbotham [7]
CHEMICAL PHYSICS LETTERS
Volume 47, number 1
1 April f077
CH‘
3cloc atm
2ooc
II
I
11
II
11
10
IIII
I
15
11
20
25
30K
Fig. 1. Tbe phase diagram of solid CH4.
Sublattlce
1 and 2 .“Free
Sublattice
3 - 8
Rotors”
:“Ordered
Molecules”
UI K
I= lil51
Tz E
30
I=O WJI
Energy
I f T2-1=1
[91
A-1
1=2 IS)
IFree Rotor” Molecules
Fi.
Fig. 2. The structure of phase P.
3. The
E-. T:_-.I=
I=O 12)
Al
i.zr51
1 (91
Ordered Molecules leve1 scheme.
were able to interpret a number of NMR results obtained in pure (oxygen free) methane in terms of a mode1 in which the freely rotating molecules convert rapidly (7 = 1 h), while no conversion occurs on the ordered sublattices. The slow spin conversion of the ordered molecules also follows from the specifïc heat measure189
Volume 47, numbcr 1
CHEMICAL PHYSICS LElTERS
ments of Vogt and Pitzer [4]. The same conclusions using our second moment [S] measurements. As shown by Nijman and Berlinsky [9], the interconversion of thc spin species of the freely rotating molecules is caused by a process in which spin states are mixed by intermolecular dipole-dipole coupling and transitions between orientational states are caused by thc intermolecular octupole-octupole coupling being modulated by phonon emission At low temperatures the conversion process of the freely rotating molecules is fast (r =5 2 h) while the one of the ordered molecules is slow (7- 5 1 year). The principal result of thc present study is that it fies the position of the low temperature 0-7 transition in the phase diagram. The remarkable fact thereby is that the transition curve is strongly curved so that a minimum occurs and the y-phase can be observed at pressures above 200 atm. The physical reasons for the absente of the P-7 phase transition at zero pressure can be found in the theory which was bricfly outlined above. can be obtained
2. Experimental
results
The proton spin-lattice relaxation time T, in methane was mcasured with a NMR pulse spectrometer at a working frequency of 28.8 MHz. This spectrometer IS on line with a CDC 1700 computer which regulates the timing of the pulse sequences and performs “real time” calculation of T, or Q. Because of lts better signal stability we employed
the 10 X 90”-1
The pressure generated by a combination of a hydraulic oil compressor and a mercury piston gas compressor is measured with calibrated manometers with an accuracy better than 0.5%. Both isothermal and isobaric measurements of the spin-lattice relaxation time were performed in the region from 5 to 80 K and at pressures up to 3000 atm. Helium was used for applying hydrostatic pressure to the methane sample. Consequently, at a given pressurc it is not possible to perform measurements at temperatures below the melting temperature of helium. The experimental values of Tr , at four different pressures, are shown in fig. 4: the two phase transitions show up rcspectively as a sizeable and a smal1 discontinuity. These measurements, together with the isothermal experiments used at temperatures below 15 K [8,10], lead to the phase diagram which is shown in fig. 1_ The P-7 transition has several very unusual and remark able properties. First of ah, as already pointed out, the P versus T plot of the transition line, as measured with decrcasmg pressure, is strongly curved and the transition pressure shows a minimum as a function of temperature. Secondly, the hysteresis of the transition pressure at low temperatures is much larger than at high temperatures. In thc third place, there is also a discontinuity in the proton magnetic susceptibility xo and the second moment M2. These discontinuities disappear at high temperatures.
X 90°
pulse sequence. However, it has to bc noted that the spin-lattice relaxation timc did not depend on the pulse sequence used. NO deviation from exponential recovery of the proton spin magnetization was detected. The measurements on solid CH4 were performed on a very pure polycrystalline sample contained in a high pressure vessel of beryllium copper. A glass (later Ai,03) specimen holdcr restricts the actual sample volume to the region inside the rf coil. The variable temperature cryostat in which the pressure vessel is contained ensures a temperature constant to within 0.0 1 K. The temperature is measured with a platinum or a germanium resistance thermometer mounted in the bottom of the pressure vessel. Magnetic field effects on the resistance of the germanium or platinum thermometer were taken into account, resulting in a temperature accuracy better than 0.1 K. Special provisions are made to eliminate temperature gradients along the pressure vessel. 150
1 April 1977
3. Discussion 3.1. l’7re curvature of the 0-7
transition
Ene
From the Afz and Tl data interesting conclusions can be reached concerning the molecular reorientation [8,1 l] and the spin conversion [8,9] but we shall restrict ourselves in thrs letter to a discussion of the !ow temperature (í3-7) phase transition. The curvature of the 5-7 transition line is a natura1 consequente of the James-Keenan structure (fig. 2) for the a phase and of the fast spin conversion process of the freely rotating molecules. A!though the prediction by James and Keenan as regards the structure of the 7 phase is not correct, we may use the reasonable assumption that the moleculcs which rotate freely in the p phase are ordered in the 7 phase. The slope of a fïrst order transiaion line is given by the relation of Clausius-Clapeyron: dP/dT = k?/AV-
Volume 47, number 1
CHEMICAL PHYSICS LETTERS
[Apri[ t977
80 $
60 L.O
..... ~
7 C
3O
'~
O
;3
%
O% !!
I
I
20
I
lO 8 6
3--
2--
3O
35
z,O
/-S
50
55
60 K "I
Fig. 4. The spin-lattice relaxation time. The main contribution to the entropy difference between the f3phase and the 7 phase resuRs from the change in the orientational state o f those molecules which rotate freely in the 13phase. The entropy o f a rotating molecule being considerably larger than that o f an ordered molecule, it is to be expected that the transition from phase q¢ to phase /3 is accompanied by an increase o f entropy. This argument will be true at h i ~ temperatures where classical statistical mechanics are applicable but at low temperatures the situation is completely different. In this region the level scheme o f ordered molecules with one steric position is now characterized by sixteen levels close together [12,8] which describe the ground states o f the spin isomers (fig. 3). ~'ilae first excited states o f the ordered molecules are found at much higher energies (e.g. ~ 70 K.) The entropy associated with these ordered molecules is thus about k In16 per molecule. In contrast, freely rotating molecules have a five fold degenerate ground state leading to the "zeropoint" entropy k In5 per molecule. O f course, this
value for the entropy is only correct if, due to spin version, transitions to this ground state are possible Consequently, the change in odentational state o f t molecules on sublattices 1 and 2, when going from /3 phase at low temperatures, results in an entropy c with opposite sign to that expected at higher tempe tures. The slope o f the transition line wil[ therefore change sign at an intermediate temperature. Indeed (as can be seen from fig. 1), this behaviour o f the phase transition is found in our experimertt. This qualitative description o f the/~-)' phase t r tion also explains some additional phenomena [8,~ like the discontinuities in X0 and M 2 while the inc o f the hysteresis with decreasing temperature fits 1 the present model as well. 3.2. The 13--~1phase transition at hig[t pressure Besides the dominant electrostatic o c t u p o [ e - o pole coupling, van der Waals type interactions also tribute to the anisotropic inte[molecular potential
[9[
CHEMICAL PHYSICS LETTERS
Volume 47, number 1
these, the (330) interaction 1131 is probably the most important one. Tb& interaction has the property of des?abi~i~ng structures with parallel ordering of the methane tetrahedra. The destabilization may be the reason for the incorrect prediction by James and Keenan of the structure of the 7 phase. The decrease with pressure of the temperature region in which the ,8 phase is the thermodynamicatfy stable ene is in contradiction with the prediction of the James-Keenan theory that at high pressure the two phase lines CY-@and @--7 are parallel. The oz--@transítion temperat ure [8 1 depcnds on density in almost exactly the same marmer as predicted by the quantum -mechanica1 version of the James-Keenan theory 1141 for equilibrium mixtures ofspin isomers. In contrast, as is shown in fig. 5, thc 8-7 phase transition depends on density in a way (T = P~-~) essentially different from the one predicted by the James-Keenan theory (Tap 2.33). In constructing this diagram use was made of densities obtained from second moment measurements at 34 K. The density dependence of the interactions stabilizing the(stil1 unknown) structure of the 7 phase wil1 in genera1 be different from the one due to the octupoieoctupole interaction Cp7j3). Taking into account this rather weak density dependence, it seems reasonabfe to assume that, especially at high pressures where fhe “hardcore” of the intermolecuIar interactions is important, this density dependence is weaker than the one of the interactions stabihzing the 7 phase. This line of reasoning would explain the slape of the transition Ene at high pressure (T* Paap). os.
os3 3.L F’
T_ p3__ _-
r32L
_ _---
- -
. il InT L f
1
30',
/T-psf,--
c experimentaf
i 20
I i
/’
5”’ ,-
r’ , -0.62
-Yikö-
--+tnp t -0 58
Fig. 5. The r 4 p transition temperature.
192 -
tions. This will lead to a (Y,/3, y triplepoint at high pressure f)3 kbar) which, however, couId not be observed
with t@ presect apparatus. Due to the unknown nature of the 7 phase 131, the analysis cannot be pursued any further at this point and it is not possible to_ïdentify the interaction(s) governing the &--7 phase transition. However, the present resdts wil1 be usefut for checkîng out any future mode1 which is proposed for this phase transition.
The strong curvature of the &-7 phase transition is explained by the remarkable structure of the p phase as predicted by James and Keenan and by the recently understood e~u~ib~urn [9] between the pop~at~ons of the spin species of the freely rotating moiecules. The densîty dependence of the transition temperature cIearIy shows that the octupole-octupole coupling used in the James-Keenan theory does not explain the high pressure behaviour of this phase transition. An extensive theoretical treatment is to bc found in the thesis by Nijman [8f.
Acknowfedgement This investigation 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.)“. The authors are much indebted to Dr. K.O. Prins and Mr. M. Sprik for many hetpful discussions and to Mr. M. v.d. Werf, Mr. J. Veldhuis and Mrs. F.M. Been-tiayo with the measurements.
T
2
1s -056
References [ l] N.J. Trappeniers and F.A.S. LiSthart, Chem. Phys Letters
J
-0 6L
me temperature region of the /3phase decreases with pressure as a result of the differente between the interactions which are responsibie for the two pbase transi-
for their assistance
1
1 ApriI 1977
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