- Email: [email protected]
Phase relationships in mercury telluride under high temperature and pressure
Pergamon
0022~3697(94)0023210
J. Pfiys. Chem. Solids Vol. 56, No. 314, pp. 525-530, 1995 Copyright @ 1995 Elsevin Science Ltd Printed in Great Britain. All rights nserved 0022.3697195 $9.50 + 0.00
PHASE RELATIONSHIPS IN MERCURY TELLURIDE UNDER HIGH TEMPERATURE AND PRESSURE P. GRIMA,?
G. WEILL,?
A. POLIAN,? M. GAUTHIER,? J. P. IT&,? M. MEZOUAR,? J. M. BESSON,? D. HA~SERMAN~ and H. HANFLAND~
tPhysique des Miileux Condenses, Universite P. et M. Curie, T. 13, E. 4, B. 77, 4 place Jussieu. F-75252 Paris Cedex 05, France IEuropean Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, France Abstract-The p,T phase diagram od mercury telluride has been investigated up to 5.4 GPa and 1200K for the first time, by the energy dispersive powder X-ray diffraction method. Our results and analysis
reconcile the apparent contradictions which appear in previous reports using differential thermal analysis. The proposed p,T diagram shows a liquid-liquid phase transition and a negative slope for the cinnabar-liquid
melting curve.
Keynaords: A. semiconductors,
C. high pressure, C. X-ray diffraction, D. phase transitions.
1. INTRODUCTlON
of-flight neutron scattering experiments and can be used for X-ray diffraction [7]. The tungsten carbide anvils, t9.6mm in diameter, are supported by steel binding rings. The experimental space is a spheroid -250mm’ in volume. The powder sample (Fig. 1) is 2.5 mm in height and 0.3 mm in diameter. It is surrounded by amorphous graphite and h-BN, inside a high resistivity graphite heater. The sample is a mixture of NaCl and HgTe (9: 1 by volume). The pressure reading [S] from the NaCl calibrant has been corrected for uniaxial stress components [9]. Temperature is measured from the electrical power in the heater, which has been calibrated in a number of separate experiments against thermocouples located in the sample space. The relative un~rtainty on pressure is lOOMPa and 20 K on temperature. Incident and scattered beams are in the equatorial plane of the anvils and go through the LiF-cpoxy gaskets between the anvils. Figure 2ta-c) shows a series of diffraction spectra taken on beamline 3 at ESRF, with a 6 GeV current of 45 mA. Slits of 30 x 30 micrometers were used to collect spectra in about 5 min. The diffraction angle was 20 = 9’, giving a diffraction parallelogram less than 0.5 mm in length. Over 20 lines are identified in the spectrum of the cinnabar phase. When temperature is increased under quasi isobaric conditions, they disappear upon melting between 778 and 798 K at 3.6 GPa (Fig. 2(c) and hollow symbols in Fig. 3). No modification is observed upon further heating, except for the temperature shift of the NaCl lines. Upon decrease of temperature alone, or of
Mercury telluride, HgTe, has a zinc-blende structure at ambient pressure. It transforms to a cinnabar structure at about ISGPa, at 300 K, and then to a NaCl lattice at 8 GPa. Its phase diagram in the pressure-temperature (p, T) plane has been investigated [l] over thirty years ago. Nevertheless a number of features in this diagram have remained controversial to this day. The slope of the cinnabarliquid melting curve drjdp has been reported to be positive [ 11, negative f2] or even zero [3]. The relative volume variation A V/ V = 10.6% at the zinc-blendecinnabar (Z-C) phase transition has only recently been correctly [4] measured. In the present paper we report the first X-ray diffraction measurements on the melting curve of HgTe up to 5.4 GPa and 1200 K. Our results and analysis reconcile the contradictions which exist in previous reports. When thermodynamic constraints are applied to the observed phase lines, it is shown that two phase transitions possibly exist in the liquid region in the p, T plane.
2. EXPERIMENTAL
X-ray measurements were performed by energy dispersive powder diffraction methods at the synchrotron facilities of LURE (Orsay) and ESRF (Grenoble). The high pressure high temperature device was a large volume [5,6] Paris-Edinburgh press which had originally been designed for time525
P. GRIMA PI al.
526
Stainless steel electrical leads
A1203 ceramic
Zirconium oxide
1
NaCl(95%)
+ HgTe (5%) sample
1 mm
Fig. I. Sample environment for high pressure high temperature measurements.
tem~rature and pressure down to ambient, the zincblende HgTe (Z-HgTe) spectrum is observed, showing the melting-recrystallization process to be reversible. No decomposition of HgTe, or chemical reaction with the components of the cell has been observed. Our results for the cinnabar-liquid phase transition are shown in Fig. 3. When compared with previous [l-3] results, they clearly show this line to have a negative slope of about -25 KGPa-‘.
3. ANALYSIS
AND DISCUSSION
At 2.5 GPa, HgTe is observed to melt at 820 K. By contrast, a previous report [l] had located a transition at this pressure around 1000 K from the observation of a DTA signal, and it has been proposed in this paper that line (a) in Fig. 3 represented the cinnabar melting line. In fact, line (a) wholly lies in the liquid domain of the p, T plane and therefore must be assigned to a liquid-liquid phase transition, a point which had been proposed [2] before from DTA experiments, but not proven, since DTA will not distjngujsh between solid-liquid and liquid-liquid phase transformations [IO]. The liquidus of Z-HgTe has a change of slope [2,3] when line (a) crosses it, although Refs [2+31 are at variance (Fig. 3) as regards the precise shape of the melting line. We shall now proceed to analyse the results shown in Fig. 3 by relating the various phase lines between the low-density and high-density (L, and L,), the zinc-blende (Z) solid, and the cinnabar (C) phase.
At least two triple points must exist: TP, between Z, L, and L,, and TPZ between Lz, Z and C. For this we shall assume all phase boundaries to be straight lines with dT/dp constant all along the phase line. This is the case, experimentally, within experimental accuracy. Even the results of Ref. [3] which were interpreted with a quadratic p(T) shape for the melting curve of HgTe, can be fitted with two straight lines well within their experimental uncertainty (20-30 K). Since dT/dp is constant, we can also take the reiatit~e volume variation to be constant along the various phase lines and use the Clapeyron equation (eqn I) together with the thermodynamic constraints (eqn 2) around triple points dT
_-
TAV
&iZAV=O
1,
(1)
(2)
with L the enthalpy variation and AS the entropy variation, at the transition. These thermodyn~~mic constraints around triple points will be applied both to solid-solid-liquid and to solid--liquid-liquid points. First-order liquid-liquid phase transitions arise from a sudden change in the local order in the melt and have been shown [I I] thcoreticaliy to be expected close to the melting line of solids cxperiencing a change in coordination number. Experimentally they are indeed accompanied by a change in enthalpy
521
Phase rekitionships in mercury telluride (latent heat) which is observable by DTA, and a volume discontinuity, as shown by thermobaric measurements f lo]. Thus, around the first triple point we shall use the following relations between Z, L, and L,:
and:
+AV,?,
0 10
30
20
40
50
60
70
80
Energy [KeV]
9 g
t i
T= 778K P= 3.57 GPa
I
I
3OooO-
$ 9
2 “1 2OOOos
10000 ti 2 2.N M.-O 0 10
20
J
30
I
t
I
I
I
40
50
60
IO
80
=o * ( dT > L,Z
(5)
528
P. GRIMA et al.
T= 79% P= 3.60 GPa
0 10
20
30
40
JO
60
IO
a0
Energy [KeV]
Fig. 2(c). Fig. 2. Energy dispersive diffraction spectra at different temperatures and pressures. In (a) HgTe is a solid. In (b) the solid and liquid probably coexist. In (c) HgTe is in its liquid phase. BL #3 at ESRF-26 = 9”-30 x 30 pm sIits--E = 6 GeV-I = 45 mA--collection time = 30 s.
with similar equations between C, 2 and L2 around the second triple point. In the following calculation, two sets of experimental data will be used for the slope of the L-Z line. Those of Ref. [2] will be designated as I and those of Ref. [3] as II. Large differences exist between those
two sets and we have no reason to choose between them. We shall show that despite this, unambiguous and quantitative conclusions can be drawn on the coherence of the proposed phase diagram. The values for the slopes and volume variations will be quoted here as the average results from I and II and the
Pressure [GPa] Fig. 3. Summary of experimental results in the melting curve of HgTe. Full diamonds and full line b: Ref. [2]-Hollow diamonds (full line a): Ref. [II-Asterisks: Ref. [3]-Full circles, squares and triangles: our results in the cinnnabar phase-Hollow symbols: liquid phase-Dashed line: melting curve of the cinnabar phase-Circles, squares and inverted triangles: results obtained at ESRF-Other triangles: results obtained at LURE.
529
Phase relationships in mercury telluride limits quoted as + are the upper and lower values obtained from I and II, not real error bars, which understandably are not known. The meltmg enthalpy IS: Lz-L, = 3.65 x IO4Jmol-‘, at ambient pressure from Ref. [12]. From this, the melting temperature (248 K) (Ref. [13]) and (dT/dp)z_,, from Refs [2,3], one obtains the values of (Av/V)r,_z (columns 1 and 3 of Table 1). Using the equations quoted above, we now use the values [2,3] of (dT/dp),_,, (column 2 of Table 1) and (dT/dp),, rl= I 1.5K GPa- r from Ref. [l] to obtain the volume variations around TP, (columns 4 and 5). We are now in a position to predict the behavior of the C-L, phase line close to the TP, point (1.5 GPa, 830 K). The slope of the Z-C line [2] is -4500 K GPa--’ and the volume variation 119 is 10.6%. From this and the parameters of the Z-L, transition which have been determined above, we obtain the C-L, melting line (columns 6 and 7 of Table 1). The calculated value of fdT/dp),_,, is positive, and thus, completely different from the observation. Using our own data (Fig. 3), we find a negative slope: (dT/dp),_, 2 - 25 K GPa-‘. Values of Refs [2,3] are somewhat different but rather imprecise, because of the very small pressure domain (< 500 MPa) which was explored above the triple point in these references. In any case, the slope of the cinnabar melting line which is reported to be either negative [2] or zero [3] does not fit the large positive value calculated in column 7. Thus, at high pressure the cinnabar structure must melt to a denser L, liquid. The phase boundary with Lz remains to be determined. The location of the C-L,-L, triple point also remains to be identified. It is not impossible that it might be located only 70 MPa and 5 K above TP, where an angular point [3] on the melting curve has been reported but this small difference is within the experiment error of Ref. (31. The negative slope of the C-HgTe melting curve, corresponding to a denser fluid phase, is to be noted. Tetrahedrally bonded phases consistently exhibit such negative slopes, but solids with six-fold coordination as a rule show a melting curve with a positive
slope. Notable exceptions are HgS which has positive melting curve slopes for both blende and cinnabar structures [3] and zinc-biende HgSe which has a change in slope from positive up to 1 GPa to negative above. In the case of HgTe, an explanation
of its behavior may be found in the fact that the cinnabar high pressure phase has not really six-fold coordination but rather has (2 + 2) + 2 coordination, that is intermediate [4. 141between zinc-blende (4) and NaCl (6). The ful1 &fold coordination is expected to occur above 8 GPa, when the transition to the NaCl structure occurs, accompanied by a further -2.5% decrease in volume 1151,at which point one expects the melting curve to resume a positive slope. A very approximate evaluation of the variation of the effective coordination number of the liquid phases can be done by assuming that it is proportional to the relative volume variation, both in the liquid and in the solid phases. In the solid, the transition from the Cfold coordinated zinc-blende to the 6-fold coordinated NaCI, through the intermediate cinnabar structure is accompanied by a volume variation of roughly 10.6 + 2.5 z 13% for an increase of 2 units in the coordination. Using the above proportionality we could assign a coordination of 4.6 to L,, 5 to L, and >5.6 to LX. This approach admittedly is an oversimplified view and only shows general trends in the structure of the liquid. It nevertheless stresses the large differences which may exist in the so-called ‘liquid phase’. 4. CONCLUSIONS Phase lines in the liquid domain on the p, T plane have been found in a number of elements and compounds. This seems to be the case here, and a systematic study of liquid HgTe by DTA or thermobaric methods is certainly needed. Solids with tetrahedral coordination, the structure of which is derived from the diamond structure, have long been favorites for experimental investigations under high pressure and temperature, since they usually are good
Table I. Slopes of the phase lines in the p, T plane, and volume differences between the various phases of HgTe around the two triple points. Set I from Ref. [2]. Set 11 from Ref. [3]. The L,-L, line is from Ref. [I]. The average value (3rd line) is between lines 1 and 2 and the + sign does not represent the experimental uncertainty. Values quoted in columns I and 2 are taken directly from the experimental values published in Refs [2,3]. They do not necessarily exactly coincide with the values quoted in the text by the authors of the above references
I
set I Set 11 Average
2
Exp. Refs 2 and 3 (dTldp),-,, (d Tldp )L-,.~ KGPa-’ KGPa -’ -35 -91 -55 -76 -45 +- IO -84&X
3
4
5
6
(A VI I’),,-, % 3.3 5.2 4.2 & I.0
(A VI I’),,_,, % 2.9 1.2 2.1 io.9
(A V/t’),,, % 6.2 6.4 6.3 & 0.1
(.L\UU(..,.I % 4.4 4.2 4.3 Jr 0.1
7 (dT/dp)c+ KGPa 62 48 55 5 7
530
P. GRIMA et al
models for calculation. Their structural properties were thought to be reasonably well understood two decades ago. With the advent of new techniques, for pressure generation, for data acquisition, together with the availability of large facilities, new aspects of their properties under high temperature and high pressure now appear and show how little is actually known about their behavior under such thermodynamic conditions. Acknowledgements-We acknowledge financial support for this work from the French Ministere de la Recherche et de
la Technologie, and from the European Union. One of us (P.G.) thanks the Fundayacucho, the CONICIT and Universidad de 10s Andes (Venezuela) for a maintenance grant for his stay in France. REFERENCES I. Jayaraman A., Klement Jr, W. and Kennedy G. C., Phys. Rev. 130, 2227 (1963). 2. Omel’chenko A. V. and Soshnikov V. I., Izv. Akad. Nauk. SSSR, Neorg. Mater. 18, 685 (1982).
3. (a) Record M. C., Thesis, unpublished, Montpellier (1992). (b) Tedenac J. C., Record M. C., Ayral R. M., Brun G., Jun J., Grzegory I. and Bockowski M., Jpn. J. Appl. Phys. 32( Ii 26 (1993). 4. San Mieuel A.. Thesis. unoublished. Paris (1993)
5. Besson j. M., Nelmes ‘R. j., Hamel’G., Loieda; J. S. and Weill G., Physica B 180-181, 907 (1992). 6. Besson J. M., Pruzan Ph., Klotz S., Hamel G., Silvi B., Nelmes R. J., Loveday J. S. and Wilson R. M., Phys. Rev. B 49, 12540 (1994). 7. Besson J. M., Hamel G., Grima P., Nelmes R. J. and Loveday J. S., High Press. Res. 8, 625 (1992). 8. Decker D. L., J. Appl. Phys. 42, 3239 (1971). 9. Singh A. K., J. Appl. Phys. 73, 4278 (1993). 10. Brazhkin V. V., Voloshin R. N. and Popova S. V., High Press. Res. 4, 348 (1990). 1I. Mitus A. C. and Patashinskii A. Z., Acra Phys. Pal. A 74, 779 (1988). 12. Hua C. H., Liao P. K., Tung T. and Brebrick R. F.. High Temp. Sci. 14, 181 (1981). 13. Harman T. C. and Strauss A. J., J. Appl. Phys. 32,
2265 (1961). 14. San Miguel A., Polian A. and Itit J. P., J. Phys. C’hem. Solids 56, 555 (1995). 15. Werner A., Hocheimer H. D. and Phys. Rev. B 28, 3330 (1983).
Striissner
K.,
0022~3697(94)0023210
J. Pfiys. Chem. Solids Vol. 56, No. 314, pp. 525-530, 1995 Copyright @ 1995 Elsevin Science Ltd Printed in Great Britain. All rights nserved 0022.3697195 $9.50 + 0.00
PHASE RELATIONSHIPS IN MERCURY TELLURIDE UNDER HIGH TEMPERATURE AND PRESSURE P. GRIMA,?
G. WEILL,?
A. POLIAN,? M. GAUTHIER,? J. P. IT&,? M. MEZOUAR,? J. M. BESSON,? D. HA~SERMAN~ and H. HANFLAND~
tPhysique des Miileux Condenses, Universite P. et M. Curie, T. 13, E. 4, B. 77, 4 place Jussieu. F-75252 Paris Cedex 05, France IEuropean Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, France Abstract-The p,T phase diagram od mercury telluride has been investigated up to 5.4 GPa and 1200K for the first time, by the energy dispersive powder X-ray diffraction method. Our results and analysis
reconcile the apparent contradictions which appear in previous reports using differential thermal analysis. The proposed p,T diagram shows a liquid-liquid phase transition and a negative slope for the cinnabar-liquid
melting curve.
Keynaords: A. semiconductors,
C. high pressure, C. X-ray diffraction, D. phase transitions.
1. INTRODUCTlON
of-flight neutron scattering experiments and can be used for X-ray diffraction [7]. The tungsten carbide anvils, t9.6mm in diameter, are supported by steel binding rings. The experimental space is a spheroid -250mm’ in volume. The powder sample (Fig. 1) is 2.5 mm in height and 0.3 mm in diameter. It is surrounded by amorphous graphite and h-BN, inside a high resistivity graphite heater. The sample is a mixture of NaCl and HgTe (9: 1 by volume). The pressure reading [S] from the NaCl calibrant has been corrected for uniaxial stress components [9]. Temperature is measured from the electrical power in the heater, which has been calibrated in a number of separate experiments against thermocouples located in the sample space. The relative un~rtainty on pressure is lOOMPa and 20 K on temperature. Incident and scattered beams are in the equatorial plane of the anvils and go through the LiF-cpoxy gaskets between the anvils. Figure 2ta-c) shows a series of diffraction spectra taken on beamline 3 at ESRF, with a 6 GeV current of 45 mA. Slits of 30 x 30 micrometers were used to collect spectra in about 5 min. The diffraction angle was 20 = 9’, giving a diffraction parallelogram less than 0.5 mm in length. Over 20 lines are identified in the spectrum of the cinnabar phase. When temperature is increased under quasi isobaric conditions, they disappear upon melting between 778 and 798 K at 3.6 GPa (Fig. 2(c) and hollow symbols in Fig. 3). No modification is observed upon further heating, except for the temperature shift of the NaCl lines. Upon decrease of temperature alone, or of
Mercury telluride, HgTe, has a zinc-blende structure at ambient pressure. It transforms to a cinnabar structure at about ISGPa, at 300 K, and then to a NaCl lattice at 8 GPa. Its phase diagram in the pressure-temperature (p, T) plane has been investigated [l] over thirty years ago. Nevertheless a number of features in this diagram have remained controversial to this day. The slope of the cinnabarliquid melting curve drjdp has been reported to be positive [ 11, negative f2] or even zero [3]. The relative volume variation A V/ V = 10.6% at the zinc-blendecinnabar (Z-C) phase transition has only recently been correctly [4] measured. In the present paper we report the first X-ray diffraction measurements on the melting curve of HgTe up to 5.4 GPa and 1200 K. Our results and analysis reconcile the contradictions which exist in previous reports. When thermodynamic constraints are applied to the observed phase lines, it is shown that two phase transitions possibly exist in the liquid region in the p, T plane.
2. EXPERIMENTAL
X-ray measurements were performed by energy dispersive powder diffraction methods at the synchrotron facilities of LURE (Orsay) and ESRF (Grenoble). The high pressure high temperature device was a large volume [5,6] Paris-Edinburgh press which had originally been designed for time525
P. GRIMA PI al.
526
Stainless steel electrical leads
A1203 ceramic
Zirconium oxide
1
NaCl(95%)
+ HgTe (5%) sample
1 mm
Fig. I. Sample environment for high pressure high temperature measurements.
tem~rature and pressure down to ambient, the zincblende HgTe (Z-HgTe) spectrum is observed, showing the melting-recrystallization process to be reversible. No decomposition of HgTe, or chemical reaction with the components of the cell has been observed. Our results for the cinnabar-liquid phase transition are shown in Fig. 3. When compared with previous [l-3] results, they clearly show this line to have a negative slope of about -25 KGPa-‘.
3. ANALYSIS
AND DISCUSSION
At 2.5 GPa, HgTe is observed to melt at 820 K. By contrast, a previous report [l] had located a transition at this pressure around 1000 K from the observation of a DTA signal, and it has been proposed in this paper that line (a) in Fig. 3 represented the cinnabar melting line. In fact, line (a) wholly lies in the liquid domain of the p, T plane and therefore must be assigned to a liquid-liquid phase transition, a point which had been proposed [2] before from DTA experiments, but not proven, since DTA will not distjngujsh between solid-liquid and liquid-liquid phase transformations [IO]. The liquidus of Z-HgTe has a change of slope [2,3] when line (a) crosses it, although Refs [2+31 are at variance (Fig. 3) as regards the precise shape of the melting line. We shall now proceed to analyse the results shown in Fig. 3 by relating the various phase lines between the low-density and high-density (L, and L,), the zinc-blende (Z) solid, and the cinnabar (C) phase.
At least two triple points must exist: TP, between Z, L, and L,, and TPZ between Lz, Z and C. For this we shall assume all phase boundaries to be straight lines with dT/dp constant all along the phase line. This is the case, experimentally, within experimental accuracy. Even the results of Ref. [3] which were interpreted with a quadratic p(T) shape for the melting curve of HgTe, can be fitted with two straight lines well within their experimental uncertainty (20-30 K). Since dT/dp is constant, we can also take the reiatit~e volume variation to be constant along the various phase lines and use the Clapeyron equation (eqn I) together with the thermodynamic constraints (eqn 2) around triple points dT
_-
TAV
&iZAV=O
1,
(1)
(2)
with L the enthalpy variation and AS the entropy variation, at the transition. These thermodyn~~mic constraints around triple points will be applied both to solid-solid-liquid and to solid--liquid-liquid points. First-order liquid-liquid phase transitions arise from a sudden change in the local order in the melt and have been shown [I I] thcoreticaliy to be expected close to the melting line of solids cxperiencing a change in coordination number. Experimentally they are indeed accompanied by a change in enthalpy
521
Phase rekitionships in mercury telluride (latent heat) which is observable by DTA, and a volume discontinuity, as shown by thermobaric measurements f lo]. Thus, around the first triple point we shall use the following relations between Z, L, and L,:
and:
+AV,?,
0 10
30
20
40
50
60
70
80
Energy [KeV]
9 g
t i
T= 778K P= 3.57 GPa
I
I
3OooO-
$ 9
2 “1 2OOOos
10000 ti 2 2.N M.-O 0 10
20
J
30
I
t
I
I
I
40
50
60
IO
80
=o * ( dT > L,Z
(5)
528
P. GRIMA et al.
T= 79% P= 3.60 GPa
0 10
20
30
40
JO
60
IO
a0
Energy [KeV]
Fig. 2(c). Fig. 2. Energy dispersive diffraction spectra at different temperatures and pressures. In (a) HgTe is a solid. In (b) the solid and liquid probably coexist. In (c) HgTe is in its liquid phase. BL #3 at ESRF-26 = 9”-30 x 30 pm sIits--E = 6 GeV-I = 45 mA--collection time = 30 s.
with similar equations between C, 2 and L2 around the second triple point. In the following calculation, two sets of experimental data will be used for the slope of the L-Z line. Those of Ref. [2] will be designated as I and those of Ref. [3] as II. Large differences exist between those
two sets and we have no reason to choose between them. We shall show that despite this, unambiguous and quantitative conclusions can be drawn on the coherence of the proposed phase diagram. The values for the slopes and volume variations will be quoted here as the average results from I and II and the
Pressure [GPa] Fig. 3. Summary of experimental results in the melting curve of HgTe. Full diamonds and full line b: Ref. [2]-Hollow diamonds (full line a): Ref. [II-Asterisks: Ref. [3]-Full circles, squares and triangles: our results in the cinnnabar phase-Hollow symbols: liquid phase-Dashed line: melting curve of the cinnabar phase-Circles, squares and inverted triangles: results obtained at ESRF-Other triangles: results obtained at LURE.
529
Phase relationships in mercury telluride limits quoted as + are the upper and lower values obtained from I and II, not real error bars, which understandably are not known. The meltmg enthalpy IS: Lz-L, = 3.65 x IO4Jmol-‘, at ambient pressure from Ref. [12]. From this, the melting temperature (248 K) (Ref. [13]) and (dT/dp)z_,, from Refs [2,3], one obtains the values of (Av/V)r,_z (columns 1 and 3 of Table 1). Using the equations quoted above, we now use the values [2,3] of (dT/dp),_,, (column 2 of Table 1) and (dT/dp),, rl= I 1.5K GPa- r from Ref. [l] to obtain the volume variations around TP, (columns 4 and 5). We are now in a position to predict the behavior of the C-L, phase line close to the TP, point (1.5 GPa, 830 K). The slope of the Z-C line [2] is -4500 K GPa--’ and the volume variation 119 is 10.6%. From this and the parameters of the Z-L, transition which have been determined above, we obtain the C-L, melting line (columns 6 and 7 of Table 1). The calculated value of fdT/dp),_,, is positive, and thus, completely different from the observation. Using our own data (Fig. 3), we find a negative slope: (dT/dp),_, 2 - 25 K GPa-‘. Values of Refs [2,3] are somewhat different but rather imprecise, because of the very small pressure domain (< 500 MPa) which was explored above the triple point in these references. In any case, the slope of the cinnabar melting line which is reported to be either negative [2] or zero [3] does not fit the large positive value calculated in column 7. Thus, at high pressure the cinnabar structure must melt to a denser L, liquid. The phase boundary with Lz remains to be determined. The location of the C-L,-L, triple point also remains to be identified. It is not impossible that it might be located only 70 MPa and 5 K above TP, where an angular point [3] on the melting curve has been reported but this small difference is within the experiment error of Ref. (31. The negative slope of the C-HgTe melting curve, corresponding to a denser fluid phase, is to be noted. Tetrahedrally bonded phases consistently exhibit such negative slopes, but solids with six-fold coordination as a rule show a melting curve with a positive
slope. Notable exceptions are HgS which has positive melting curve slopes for both blende and cinnabar structures [3] and zinc-biende HgSe which has a change in slope from positive up to 1 GPa to negative above. In the case of HgTe, an explanation
of its behavior may be found in the fact that the cinnabar high pressure phase has not really six-fold coordination but rather has (2 + 2) + 2 coordination, that is intermediate [4. 141between zinc-blende (4) and NaCl (6). The ful1 &fold coordination is expected to occur above 8 GPa, when the transition to the NaCl structure occurs, accompanied by a further -2.5% decrease in volume 1151,at which point one expects the melting curve to resume a positive slope. A very approximate evaluation of the variation of the effective coordination number of the liquid phases can be done by assuming that it is proportional to the relative volume variation, both in the liquid and in the solid phases. In the solid, the transition from the Cfold coordinated zinc-blende to the 6-fold coordinated NaCI, through the intermediate cinnabar structure is accompanied by a volume variation of roughly 10.6 + 2.5 z 13% for an increase of 2 units in the coordination. Using the above proportionality we could assign a coordination of 4.6 to L,, 5 to L, and >5.6 to LX. This approach admittedly is an oversimplified view and only shows general trends in the structure of the liquid. It nevertheless stresses the large differences which may exist in the so-called ‘liquid phase’. 4. CONCLUSIONS Phase lines in the liquid domain on the p, T plane have been found in a number of elements and compounds. This seems to be the case here, and a systematic study of liquid HgTe by DTA or thermobaric methods is certainly needed. Solids with tetrahedral coordination, the structure of which is derived from the diamond structure, have long been favorites for experimental investigations under high pressure and temperature, since they usually are good
Table I. Slopes of the phase lines in the p, T plane, and volume differences between the various phases of HgTe around the two triple points. Set I from Ref. [2]. Set 11 from Ref. [3]. The L,-L, line is from Ref. [I]. The average value (3rd line) is between lines 1 and 2 and the + sign does not represent the experimental uncertainty. Values quoted in columns I and 2 are taken directly from the experimental values published in Refs [2,3]. They do not necessarily exactly coincide with the values quoted in the text by the authors of the above references
I
set I Set 11 Average
2
Exp. Refs 2 and 3 (dTldp),-,, (d Tldp )L-,.~ KGPa-’ KGPa -’ -35 -91 -55 -76 -45 +- IO -84&X
3
4
5
6
(A VI I’),,-, % 3.3 5.2 4.2 & I.0
(A VI I’),,_,, % 2.9 1.2 2.1 io.9
(A V/t’),,, % 6.2 6.4 6.3 & 0.1
(.L\UU(..,.I % 4.4 4.2 4.3 Jr 0.1
7 (dT/dp)c+ KGPa 62 48 55 5 7
530
P. GRIMA et al
models for calculation. Their structural properties were thought to be reasonably well understood two decades ago. With the advent of new techniques, for pressure generation, for data acquisition, together with the availability of large facilities, new aspects of their properties under high temperature and high pressure now appear and show how little is actually known about their behavior under such thermodynamic conditions. Acknowledgements-We acknowledge financial support for this work from the French Ministere de la Recherche et de
la Technologie, and from the European Union. One of us (P.G.) thanks the Fundayacucho, the CONICIT and Universidad de 10s Andes (Venezuela) for a maintenance grant for his stay in France. REFERENCES I. Jayaraman A., Klement Jr, W. and Kennedy G. C., Phys. Rev. 130, 2227 (1963). 2. Omel’chenko A. V. and Soshnikov V. I., Izv. Akad. Nauk. SSSR, Neorg. Mater. 18, 685 (1982).
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Striissner
K.,