J . Phys. Chem. 1987, 91. 1674-1681
1674
The enthalpy differences in the three solvents follow a wellestablished trend: the enthalpy in cyclohexane is more negative than that in CC1, which is, in turn, more negative than that in benzene. The origin of these enthalpy differences is now fairly well understood. They arise from dipolar and specific interactions by the free acid and base with the solvent. For example the phenol-benzene specific interaction is the formation of a phenol-n cloud hydrogen bond with an accompanying enthalpy of 1.1 kcal mol-' of phen01.~ Pyridine interactions with CCl, and benzene relative to cyclohexane can be analyzed from solvatochromic parameters. Fuchs and Stephensons have shown that the difference in enthalpy of vaporization of pyridine and benzene from a solvent correlates well with ?r*, the solvatochromic parameter which reflects dipolar-polarizability interaction.
AAW = -0.580 - 1.485iP Any deviation from the straight line described by the above equation is due to interactions other than dipolar interactions. The pyridine-CC1, point falls 0.3 kcal mol-' above the line and thus gives the value of the well-known pyridine-CC1, specific interaction. A similar treatment can be applied to cyclohexane and benzene solvents with the following results. Relative to cyclohexane, the pyridine-CC1, interaction is 0.7 kcal mol-', 0.3 kcal mol-' being due to a specific interaction and 0.4 kcal mol-' to dipolar interactions; the pyridine-benzene interaction is 0.9 kcal (7) Spencer, J. N.; Holmboe, E. S.; Firth, D. W.; Kirshenbaum, M. R. J . Solution Chem. 1981, 10, 745. (8) Fuchs, R.; Stephenson, W. K. J. Am. Chem. 1983, 105, 5159.
mol-' which is almost entirely due to dipolar interactions. The phenol-benzene specific interaction as previously mentioned is 1.1 kcal mol-' of phenol due to hydrogen bond formation, and the phenol-CC1, hydroxyl interaction is 0.2 kcal mol-' due to dipolar interactions. Thus the enthalpy differences relative to cyclohexane for the phenol-pyridine complex should be
AHcc14 = AHcy+ 0.9 kcal mol-]
+
AH,, = AHcy 2.0 kcal mol-' The equation relating AHcc, with AHcywas first established by Drago et aL9v1Ofrom experimental data. We had, through other methods,'*" arrived at the same relationship. We have also reported the benzene-cyclohexane enthalpy relation" obtained from experimental data. Thus the enthalpy relationships for the phenol-pyridine complex in cyclohexane, CCl,, and benzene are well-established from several sources and this gives considerable confidence in the values reported here for those enthalpies. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to Franklin and Marshall College for support of this research. Registry No. PhOH, 108-95-2; CSHsN, 110-86-1
(9) Drago, R. S.; Parr, L. B.; Chamberlain, C. S. J . Am. Chem. Soc. 1977, 99, 3203. (10) Nozari, M. S.; Drago, R. S. J . Am. Chem. Sac. 1972, 94, 6877. (11) Spencer, J. N.; Campanella, C. L.; Harris, E. M.; Wolbach, W. L. J . Phys. Chem. 1985,89, 1888.
Computer Simulation Methods for the Calculation of Solubility in Supercritical Extraction Systems K. S. Shing* and S. T.Chung Department of Chemical Engineering, University of Southern California, Los Angeles, California 90089- I21 1 (Received: September 8, 1986)
In this work, we developed two simulation techniques for the calculation of solubilities in supercritical extraction systems. The first is the test-particle method based on the potential distribution theorem implemented in the isothermal-isobaric ensemble. This technique is useful for low to moderate densities where the solute is not too large compared to the solvent. The second method is an extension of the Kirkwood chemical potential equation, also implemented in the isothermal-isobaric ensemble. This method is useful at high densities and/or when the solute is considerably larger than the solvent in size. These methods were then applied to a prototype supercritical extraction system, naphtha1ene-CO2. Solubilitieswere calculated as a function of pressure for several supercritical isotherms and compared to experimentally measured values in the literature. The qualitative trends were all well represented. Quantitative agreement can be improved by using more realistic potential models with optimized potential parameters.
I. Introduction Supercritical extraction is a separation process where instead of a liquid solvent, a highly compressed gas solvent is used for extraction. A gas solvent offers several advantages over a liquid solvent.' First of all, solvent recovery can be easily achieved by decompression or temperature change. Secondly, due to the high volatility of the gaseous solvent, there is very little solvent iontamination of the extraction product. This is of importance in food and pharmaceutical industries, as well as in the purification (1) Schneider, G. M.; Stahl, E.; Wilke, G. Extraction with Supercritical Gases; Verlag Chemie: Weinheim, 1980. Paulaitis, M. E.; Penninger, J. M. L.; Gray, R. D., Jr.; Davidson, P. Chemical Engineering at Supercritical Conditions; Ann Arbor Science: Ann Arbor, MI, 1983. McHugh, M. A,; Krukonis, V. J. Supercritical Fluid Extraction, Principle and Practice; Butterworth: London, 1986.
0022-3654/87/2091-1674$01.50/0
of fine chemicals. Finally, since one can manipulate the chemical composition as well as the density of the solvent, it is possible to optimize the solvent system to achieve enhanced selectivity. Two major difficulties exist in the theoretical study of supercritical extraction systems. First of all, the processes usually operate close to the critical point of the mixture where the mixture is highly compressible. Therefore, the theoretical treatment should be able to represent the thermodynamic behavior (chemical potential, solubility) over a wide range of pressure (and density). Perturbation theories which rely on the rapid convergence of a series expansion at high densities would not be reliable near the critical density. The second difficulty is that the mixtures encountered in supercritical extraction are all highly nonideal. The solute is usually a heavy hydrocarbon, the solvent is normally a smaller molecule, usually a simple gas. There are no satisfactory mixing rules for such highly nonideal mixture^.^ Consequently, 0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 1675
Solubility in Supercritical Extraction Systems computer simulation is the ideal tool for the theoretical study of these systems, since it assumes neither the form of an equation of state nor the form of the mixing rules. The only assumptions are the form of the intermolecular potentials and the validity of classical statistical mechanics. In this paper, we present some simulation techniques for the calculation of chemical potentials (and hence the solubilities). Emphasis will be placed on systems relevant to supercritical extraction processes, although the expressions derived are applicable to other systems of interest. These methods are based on extensions of two well-known equations: the potential distribution theorem2 and the Kirkwood chemical potential e q ~ a t i o n . ~We applied these techniques to the simulation of the C02/naphthalene system, which has been extensively examined in experimental supercritical extraction studies. 11. Theory The physical system being examined is one in which a pure solid phase (e.g., naphthalene) is in equilibrium with the supercritical solvent (e.g., C 0 2 ) saturated with the solid solute. The main objective in this work is to express the solubility of the heavy solute in the supercritical solvent. The thermodynamic constraint is given by NulS =
where wls is the chemical potential of solid solute (component 1 here) and p l G is the chemical potential of solute in the supercritical gas. If we make the usual assumption that the gas solvent 2 is insoluble in the solid solute 1, then pls(T,P) is given by
+ J,UI
k T In
dp
(2)
(g i) AI3
(3)
where A, is the thermal de Broglie wavelength of 1 and q 1 the molecular partition function of 1 accounting for internal contribution such as vibration and rotation. We note that p I Sdepends only on T and P, whereas p I G depends on T, P, and y l , where y l is the solubility. The problem reduces to finding y , so that eq 1 is valid. We calculate wlGusing computer simulation and use experimental vapor pressures and molar volumes to calculate pis. A variety of techniques can be used to obtain llGfrom simulation. We consider the two most popular methods, namely the potential distribution theorem of Widom2 and the Kirkwood chemical potential e q ~ a t i o n . ~ 2.1. The Potential Distribution Theorem. The potential distribution theorem originally derived by Widom2 in the canonical ensemble can be written for a binary mixture (consisting of N, particles of solute and N 2 particles of solvent in a volume V at temperature 7') as p,r
=
- plidea18as
where
P
where P* is the vapor pressure of solute at temperature T and u, is the volume occupied by one solute particle and is equal to Vl/NAvo, VI being the molar volume of solute and NAvoAvogadro's number. pis( T,P*) = plidra'gas( T,P*) since the pure solid a t T,P* is in equilibrium with a vapor (assumed ideal) of pure 1. The ideal gas chemical potential is given by4 pIideal gas (T,P*) =
+
(1)
PIG
ILI~(TJ')= KI'(T,P*)
Vis the system volume, @ = l / k T , k is Boltzmann constant, T is the temperature, and $, is the potential energy experienced by a solute test particle (arbitrarily designated as the ( N 1)th particle) placed at random in a system consisting of N , solute particles and N 2 solvent particles. ( )NI,N2,V,Tis a canonical ensemble average of the (N,, N2, V, 7') system in which the test particle is invisible to the other (N, + N 2 ) real particles. If we were able to simulate a macroscopic system, then we can choose any convenient ensemble to use. However, in practice, we are limited to working with a small number of molecules, and as a result, different ensembles will give different results. In simulating supercritical extraction systems, we need to study states with high compressibility (or significant local density fluctuations). Canonical ensemble simulation of small system size artificially suppresses these density fluctuations, and will in general have a stronger system size dependence than the isothermal-isobaric (NPT) ensemble, since the latter permits density fluctuations. A further advantage of using the NPT ensemble is that pressure can be specified at the beginning of simulation. In the NPT ensemble, the potential distribution theorem takes the following form (for details of the derivation, see Appendix A)
= -k T In (exp(-P$l)
where p l r is the residual chemical potential and ideal gas chemical potential given by4
)NI,N~,V,T plideaigas is
(4)
the
(2) Widom, B. J . Chem. Phys. 1963, 39, 2808. (3) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1973; Chapter 13. (4) Reed, T. M.; Gubbins, K. E. Applied Statistical Mechanics; McGraw-Hill: New York, 1973; Chapter 3.
and (V) is the average volume of the (N,, N2, P, 7') ensemble. Previous work on the constant pressure simulation using the potential distribution theorem5 simply used eq 4 for the canonical ensemble rather than the more appropriate eq 5. We see that if neither Vnor exp(-p$,) fluctuate significantly (when the ensemble is macroscopic in size, for example) then both eq 4 and 5 will give the same result. However, when either V or exp(-@$,) show significant fluctuation, then the two ensembles will in general give different results. Physically, we would expect the difference to be more pronounced near the critical region (where Vfluctuates significantly) or when the density is relatively high and the solute particle interacts strongly with the solvent through either a large energy of interaction or large size resulting in significant fluctuations in exp(-@$,). As mentioned above, such situations are frequently encountered in supercritical extraction processes. Therefore, it is important to use the more appropriate eq 5 in constant pressure simulations. The simulation method based on the potential distribution theorem is usually known as test-particle method or particle insertion method. In this method, at regular intervals during the simulation, a specified number of test particles are brought into the simulation cell and placed at random locations within the cell. The potential energies experienced by these test particles ($) are calculated and the quantity exp(-@$) averaged to obtain the chemical potential using eq 5. If the test particles are solute particles, then $ = $, and the average of exp(-p$) gives wlr whereas if the test particles are solvent particles, then $ = $2 and the average of exp(-@$,) gives p;. 2.2. The Kirkwood Chemical Potential Equation. This equation was originally derived by Kirkwood for an one component system in the canonical e n ~ e m b l e .Consider ~ a binary mixture consisting of ( N , 1) particles of component 1 (solute) and N2 particles of component 2 (solvent) in a volume Vat temperature T, N1 of the ( N , + 1) type 1 (solute) particles interact with each other and with the N2 (solvent) particles through the potentials rfJI1 and rfJ12, respectively (see Figure 1 ) . The ( N , + 1)th solute particle interacts with the other N , solute and N 2 solvent particles through charged (or coupled) potentials and respectively.
+
(5) Heyes, D. M. Chem. Phys. 1983, 8 2 , 285.
1676 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Shing and Chung N A P H T H A L E N E . C A R B O N DIOXIDE TEMPERATURE 320 O K
lo-’
Figure 1. Intermolecular interactions for simulating fill according to eq 8. 0 is component 1, 0 is component 2, and @ is the coupled particle.
E
is the Kirkwood coupling parameter and varies from 0 to 1. When $, = 0, the coupled particle is an ideal gas molecule; when = 1.0, it is a regular solute molecule. Then, the Kirkwood chemical potential equation can be written as PI = k T l n
[ (-44 + Nl
1
ill
+
REDUCED PRESSURE Figure 2. A typical supercritical extraction isotherm.
extent the experimentally observed qualitative behavior of supercritical extraction systems are represented in these equations. It is more illustrative to consider the Kirkwood equation (6). If we combined eq 1, 2 , and 6, we obtain where +ij(r,w)is the pair potential of an i-j pair, r is the distance between the pair, w is the normalized relative orientation of the pair, and g,(r,w,t;)is the pair correlation function for an i-j’ pair coupled to the extent 6. Equation 6 can also be written as
where $, is the potential energy the coupled particle would experience if the particle were fully coupled (.$= 1.O) and ( )[ is a canonical ensemble average for a system coupled to the extent .$. Equation 7 was derived in the canonical ensemble. If the canonical ensemble were macroscopic in size, then it would give the same result as any other ensemble. However, since in simulation studies we are constrained to work with a relatively small number of particles, it is apparent that the canonical (constant volume) ensemble is inferior to the constant pressure N P T ensemble. This is because as we increase the coupling strength of the coupled particle we are changing it from an invisible ideal gas molecu!s (.$= 0) to a full-fledged solute molecule (.$= 1). If this process takes place in the canonical (constant volume) ensemble, we are changing the pressure rather significantly, especially when the coupled particle is large in size and the fluid is rather dense, and we are limited to a small sample size. In the isothermalisobaric (NPT) ensemble, the volume is increased (or decreased) as the coupling process p r d s (the pressure being kept constant). As a result, we would expect the N P T result to be closer to the macroscopic limit where we expect the coupling process to have negligible effect on the pressure. We can derive the Kirkwood chemical potential equation for the NPT ensemble (see Appendix B for details). The result is
which is exactly the same as eq 7 for the canonical ensemble, except that, in this case, ( V ) is the N P T ensemble averaged volume, and ( is taken over a constant pressure rather than a constant volume ensemble. Before we proceed to use eq 5 and 8 in simulation studies of supercritical extraction, it might be worthwhile to examine to what
In
(5)+ l S p u , kT
P*
d P = In p
+ In y , +
where y , is the mole fraction of solute in the supercritical solvent, y 2 (= 1 - y , ) is the mole fraction of solvent, and p is the number density of the supercritical phase. Equation 9 represents the variation of the solubility (yl) with temperature and pressure. We consider a supercritical isotherm not far above the critical temperature of the solvent. At constant T, the vapor pressure contribution In ( P * / k T ) is a constant. For P not too high, the Poynting correction l / k T S u l d P is small. The left-hand side (LHS) of eq 9 (which is the chemical potential of the solid solute kIs) is approximately constant. Consider P > p and In p varies more rapidly than p. Consequently, for P 0.5 where y , exceeds lo%, the solution is certainly not infinitely dilute and the term ylgl1411 on the RHS of eq 9 can no longer be ignored. Therefore, the true solubility for P* > 0.5 is probably higher than shown here. To calculate the exact solubility, we need to perform simulations for a series of compositions and equate the chemical potential to that of the solid to obtain y,. This is quite time consuming, but poses no new simulation difficulties. 4.2. Comparison with Experimental Data for the C02Naphthalene System. The calculated solubilities y l are plotted against P* = Pa22/e22and p* = p~~~~ in Figure 5 and 6 together with experimental results. Agreement between experimental and calculated results depends primarily on the adequacy of the chosen model potentials. On the whole, the qualitative trends are well represented. For example, the increase in y1 with temperature at moderately high pressure, the crossing over of the isotherms near the critical pressure, and the approximate linear dependence of In y , on p* a t moderate to high pressure are all adequately represented. The temperature dependence of the calculated solubilities is too weak and can be improved by adjusting the C02/naphthalene pair potential d12. To achieve better qualitative and quantitative agreement, all potential parameters, especially those involved in 412and 422r should be adjusted. Since it is known that density of the supercritical phase has a strong effect on the solubility, the C02-C02 potential 422used must accurately represent the experimental P-V-T behavior of C 0 2 in the region of interest, in this case, the critical region. The C 0 2 potential we used here is a crude one developed on the basis of a perturbation theory fit to saturated vapor and liquid densities without optimizing agreements in the critical region. Therefore, we probably do not have adequate representation of the P-V-T behavior in the critical region. From Table 111, we see that at low pressure (P* = 0.15) the densities at the three different temperatures are relatively low and rather similar in magnitude, corresponding presumably to a gaslike density. At moderately high pressure (P* = OS), the densities at the three temperatures are again rather similar, though higher,
1
1
100-
1
1
1
1
1
~
To= L5634(320*K)
0 0
z
c0 a a
1
Test Porllcle Method K i r k w o o d Method Experiment
-
,,d
,Y'
REDUCED DENSITY
Figure 6. Naphthalene solubility in supercritical C 0 2at various p* and T* = 1.5634.
corresponding to a more liquidlike density. At intermediate pressures, the densities change rather abruptly with temperature as well as with pressure. (See, for examples, the densities at P* = 0.15 and 0.2 at 320 K and at 342 K). Such abrupt changes are usually associated with the presence of the critical point. We conclude that the critical temperature of COzcorresponding to our potential model is actually higher than the real C 0 2critical temperature. Therefore, the two lower isotherms are probably subcritical, and the critical temperature corresponding to our model C 0 2 potential is probably closer to 342 K rather than the assumed value of 304 K, the actual T,of C 0 2 . This is further confirmed by the fact that a simulation performed at P* = 0.2 and T = 332 K showed very large density fluctuations, indicating that the fluid is probably in the two-phase region. The critical temperature may be easily brought down to 304 K by adjusting the magnitude of ez2, the C 0 2 - C 0 2 Lennard-Jones energy parameter. The calculated solubilities are in general higher than the experimental values and can be reduced simply by reducing 4,2,the C02-naphthalene pair potential. This can be most conveniently accomplished by reducing e12, the Lennard-jones energy parameter. We have not make these adjustments to the potential parameters used here since our primary objective in this paper is to develop and test simulation methods rather than to optimize potential models in order to reproduce experimental results. Work is in progress to develop better models, including site-site potential models, and to study dilute but finite concentration systems.
V. Conclusion In this work, we developed some Monte Carlo simulation methods in the N P T ensemble to calculate solubilities in supercritical extraction systems. We found that the test-particle method can be used in supercritical extraction studies provided the solute is not too large compared to the solvent and the pressure (or density) is not too high; otherwise, the more time consuming Kirkwood coupling method would have to be used. We have applied these methods to a prototype supercritical extraction system, namely the CO,/naphthalene system. The qualitative behavior of naphthalene solubility in supercritical C 0 2 is well represented in simulation. A better C 0 2potential in the critical region and a better C0,-naphthalene potential are needed to reproduce quantitative agreement and accurate temperature dependence. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Financial support by the National Science Foundation under Grant CBT845200 is also acknowledged.
1680 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Shing and Chung
Appendix A The Potential Distribution Theorem in the Isothermal-Isobaric Ensemble. Consider, for convenience, a binary mixture with N1 particles of component 1 and N2 particles of component 2. The chemical potential of component 1 in the mixture, p,,is given by
where A is the isothermal-isobaric ensemble partition function, in this case, given by
+
where N = NI N2; = l / k T , Ai is the thermal de Broglie wavelength of component i; qiis the molecular partition function of i accounting for internal contributions such as vibration, nuclear spin, electronic, etc.; U , F )is the potential energy of configuration f i P“ are the positions and orientations of the N particles in the system; and Vis the volume occupied by the N particles. From eq A.l and A.2, we obtain
( V ) is the average volume of the (Nl, N,, P, T ) system. plr
- p,idealgas = -k T l n
[
A’(NI+ l,N,,P,T,(=l) A’(NI+ 1,N2,P, T,(=O)
From this point on, we write A’(Nl+l,N2,P,T,(=1) as A’((=l) for simplicity. Following the procedure Kirkwood used,3we have In
-= I d In A’(() = A’((=O)
1(
d In A’(() dE
)
d(
(B.4)
= -@($I)[ Therefore Here ( )N,,N2,P,Tindicate an ensemble average over the (Nl, N2, P, T ) system. is the potential energy of a particle of component 1 added at a random location to the (Nl, N2,P, T ) system. p I = (N, l ) / ( V ) is the number density of component 1. The chemical potential of an ideal gas of N, particles of component 1 in the volume ( V ) ,at temperature T is4
+
pIideal gas
= kTln
[ G]
Here Ot is an ensemble average over the (N, + 1, N2, P, T ) system. Equation B.6 is exactly the same as that derived originally by Kirkwood for a one-component system in the canonical ensemble.
Appendix C (plr - p;) from the Kirkwood Method. According to the potential distribution theorem2
Therefore, plr,the residual chemical potential of 1 in the mixture is given by
plr(N1+l,N2,P,T) = -kT X
Appendix B Kirkwood Chemical Potential Equation in the IsothermalIsobaric Ensemble. We can write eq A.3 as
Similarly
where A’(N,+1,N2,P,T) is given by
/ . L ~ ~ ( N ~ , N ~ + ~=, -kT P , T )X
J. Phys. Chem. 1987, 91, 1681-1684
1681
+
where N = N , N2;$I($2) is the potential energy experienced by a solute (solvent) molecule randomly placed in the system; and U N ( f l )is the potential energy of the N , solute and N2 solvent particle configuration fl Awl'
= -kT
1.11'
- 11.2'
X
Awl' = -kT In A*((=l) = -kT A*(f=O)
1
I(
ln:*('))
d(
where ( is the Kirkwood coupling parameter. Using similar manipulations as in Appendix B for wl1, we have
where A$
$,
- q2; Awl1 can also be written as9
where ( ) E is a N P T ensemble average over a system with N , normal solute particles, N2 normal solvent particle, and a coupled particle, which when completely coupled (( = 1) acts as a solute particle, but acts as a solvent particle when uncoupled (( = 0).
Pressure-Induced Phase Transltion in K,Co( CN)6 Studied by Raman Scattering A. Saito, Y. Morioka, and I. Nakagawa* Department of Chemistry, Faculty of Science, Tohoku University, Aoba, Aramaki, Sendai 980, Japan (Received: August 4, 1986; In Final Form: October 10, 1986)
High-pressure Raman spectra of monoclinic and orthorhombic polytypes of K,Co(CN), have been measured up to 70 kbar, using a diamond anvil cell. In the orthorhombic crystal, a pressure-induced phase transition takes place at -30 kbar. An optical mode at 17 cm-' (at 1 bar) shows soft-mode behavior as in the case of the temperature-induced phase transition studied previously. The 29-cm-' band at 42 kbar is assigned to the corresponding soft mode in the high-pressure phase due to its behavior with pressure variation. In the monoclinic crystal, a phase transition takes place in the pressure range 30-40 kbar. A soft mode is not found for this transition. A similarity of the pressure-induced phase transition to the temperature-induced phase transition does not seem to hold in the monoclinic crystal.
Introduction K3Co(CN), is known to crystallize in various polytypes. Kohn and Townes have established four polytypes, such as 1 M (onelayer monoclinic), 20r (two-layer orthorhombic), 3M (three-layer monoclinic), and 7M (seven-layer monoclinic),' and Reynhardt and Boeyens added 40r (four-layer orthorhombic).2 The 1M structure is monoclinic with two formula units in a Bravais unit cell and is considered to be the basic structure for all polytype~.~ The other structures are derived from 1M by the periodic stacking fault. By examining a X-ray photograph of ( h l l ) plane, a distinction between the monoclinic and orthorhombic forms is possible.' We prepared both the monoclinic (1M) and orthorhombic (20r) polytypes, and in the Raman spectra at room temperature characteristic spectral features of both polytypes have been clarified. Spectroscopic evidence for the second-order displacive phase transition has been obtained on the basis of the soft-mode behavior for both forms of crystake The transition temperatures have been determined, 63 K for the monoclinic form and 81 K for the orthorhombic form, which are in good agreement with those (1) Kohn, J. A.; Townes, W. D. Acta Crystallogr. 1961, 14, 617. (2) Reynhardt, E. C.; Boeyens, J. C. A. Acta Crystallogr., Sect. B 1972, B28, 524. (3) Curry, N. A.; Runciman, W. A. Acta Crystallogr. 1959, 12, 674. (4) Morioka, Y.; Nakagawa, I. J . Phys. SOC.Jpn. 1982, 51, 2241. ( 5 ) Morioka, Y.; Nakagawa, I. J . Phys. Soc. Jpn. 1983, 52, 23. (6) Saito, A.; Morioka, Y.; Nakagawa, I. J. Phys. Chem. 1984,88, 480.
0022-3654/87/2091-1681$01.50/0
determined from a recent N Q R study.' With this background we have undertaken a Raman spectroscopic study on the pressure-induced phase transition and investigated the spectral behavior under high pressure at ambient temperature. As fully discussed in our previous papers, a striking difference in the mechanism of the phase transition between the two polytypes is seen, though the nature is of second order for both; for the orthorhombic crystal the instability of the roomtemperature lattice is ascribed to the Brillouin zone center nonpolar phonon, while for the monoclinic crystal it is ascribed to the zone-boundary phonon.e6 Such a difference is closely related to the polymorphism of this crystal. The aim of the present investigation is to get further information on the nature and mechanism of the phase transition for both types of crystals by taking into account pressure as an environmental factor.
Experimental Section Single crystals of K3Co(CN), were grown by slow cooling of saturated aqueous solution. The 1M and 20r polytypes were distinguished by Raman spectra based on the criteria described ~~
(7) Fukada, S.;Horiuchi, K.; Asaji, T.; Nakamura, D. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 22. ( 8 ) Piermarini, G . J.; Block, S.;Barnett, J. D.; Forman, F. A. J. Appl. Phys. 1975. 46, 2774. (9) Mao, H. K.; Bell, P. M.; Shaner, J. W.; Steinberg, D. J. J . Appl. Phys. 1978, 49, 3276.
0 1987 American Chemical Society
