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Assessment of the thermodynamic properties of vanadium silicides utilizing ternary phase equilibria
185
Journal of the Less-Common Metals, 60 (1978) 185 - 193 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
ASSESSMENT OF THE THERMODYNAMIC VANADIUM SILICIDES UTILIZING TERNARY
PROPERTIES OF PHASE EQUILIBRIA
PETER F. FREUND and KARL E. SPEAR Materials Research Laboratory, 16802 (U.S.A.)
The Pennsylvania
State
University,
University
Park, Pa.
(Received February 14,1978)
Summary
The ternary V-Si-0 phase equilibria and auxiliary oxide data are used to set relative limits on the free energies of formation of the condensed vanadium silicide phases VsSi, Vr,Si3, and VSiz. The assessed free energies of formation are then used with entropies derived from heat capacity data to calculate a set of enthalpies of formation for these silicide phases which is also consistent with the ternary phase equilibria constraints. The thermodynamic values reported in the literature are compared with the consistent set of values derived in the present study.
1. Introduction
Considerable interest has been shown in the vanadium silicides since Hardy and Hulm [l] found a superconducting transition temperature of 17.1 K for VsSi in 1954. A sample-dependent martensitic transformation from cubic to tetragonal occurring at about 21 K and anomalous temperature dependences of the Knight shift, magnetic susceptibility and elastic behaviour [ 21 have made this Al5 compound of special interest. The cubic VsSi is one of three intermediate solid phases that were identified in the V-Si system in the early work of Kieffer et al. [3] and Rostoker et al. [ 41. The other phases are a tetragonal V&Z& phase and a hexagonal VSis phase. An impurity-stabilized hexagonal form of VaSis has been characterized by Nowotny et al. [ 51. More recent phase equilibria studies by Bruning [ 61, Efimov [ 71 and Kocherzhinskii et al. [ 81 have confirmed the existence of the three binary solid phases. A study by Hallais [9] reports the formation of an orthorhombic VsS&, compound as well, but others have not confirmed its existence as a stable binary phase. The present study is part of a research program on the crystal growth and chemical vapor deposition of niobium and vanadium superconducting compounds with the Al5 structure type. A computerized thermodynamic analysis of the chemical vapor deposition (CVD) of VsSi(s) from a mixture of
186
gaseous chlorides and hydrogen has been undertaken following the work of Besmann and Spear [lo] on the CVD of titanium borides and of Wan and Spear [ 111 on the CVD of niobium germanides. The analysis of the high temperature equilibrium behavior of the V-Si-H-Cl system requires accurate knowledge of the thermodynamic properties of the reacting species. Relatively small changes in thermodynamic values of species in this fourcomponent system can cause the equilibrium to shift from favoring the deposition of VsSi to not favoring its deposition. The binary vanadium chlorides and vanadium silicides include some of the most important species at equilibrium as well as the most uncertain values for enthalpies and entropies of formation. Literature reports of the thermodynamic properties of the vanadium silicides showed great discrepancies and uncertainties, bringing into question the tenability of a computer analysis of the CVD of VsSi. This paper reports a critical assessment of the thermodynamics of the vanadium silicides and develops a consistent set of values. An assessment of the thermodynamics of the vanadium chlorides has been the subject of a separate investigation [ 121. A relatively large number of studies of the thermodynamics of the vanadium silicides have been reported. Golutvin et al. [ 131, Gorelkin et al. [ 14, 151 and Eremenko et al. [ 16 - 181 have reported enthalpies of formation with discrepancies of 15 kcal mol-’ each for VsSi and V&lis and 45 kcal mol-’ for VSiz. An assessment by Chart [ 19, 201 allows for uncertainties of 8 - 19 kcal mol-’ for the enthalpies of formation of the three silicide compounds; an entropy of formation is listed for only one of the three compounds. Table 1 lists the reported experimental and assessed values. Specific heat measurements for various temperature ranges have been reported by Pankratz and Kelley [ 211, Kalishevich et al. [ 22,231, Brock [24], Viswanathan et al. [25], Surikov et al. [26] and Knapp et al. [ 271. The entropies calculated from these heat capacity values do not agree with those reported in the equilibrium e.m.f. study of Eremenko et al. [16 - 181. In a previous study by Spear et al. [ 281 on chemical transport reactions involved in interactions of silica glass with vanadium metal, the ternary V-Si-0 phase equilibria were partially established. They used these data to show the inconsistency of the vanadium silicide thermodynamic data published by Golutvin et al. [ 131. In the present assessment, the same ternary phase relationships are used to show the inconsistency of the currently available thermodynamic properties of the binary vanadium silicide phases.
2. Free energies of formation The V-Si-0 ternary phase diagram and the resulting chemical reactions that can be derived provide much stricter relative limits for the free energies of formation of VsSi, Vr,Si3 and VSiz than those derived from the binary phase diagram.
187 TABLE
1
List of measured and assessed enthalpies of formation at 298 K for the vanadium silicides Source
AH; zaa (V&i) (kcal mol-‘)
Golutvin and Kozlovskaya [13] (1960)
-27
Gorelkin and Mikhailikov [ 141 (1970)
-33.7
f 9
i 2
fW.298 (kcal mol-‘) -96
[~~~!nol-‘)
f 46
-111.0
-112
Gorelkin et al. [15] (1972)
Technique
AH&a
W5Si3)
-75
? 5
-29.8
f 13
-36
+ 21
+3
?r 6
Calorimetric combustion Sintering in an isothermal calorimeter Sintering in an isothermal calorimeter
Eremenko [16] (1974)
-29.6
i 1.2
E.m.f. measurements
Eremenko etal. [17] (1975)
-29.6
2 1.2
E.m.f. measurements
E.m.f. measurements
Eremenko etol. [18] (1976)
-44.4
r 0.1
-104.1
f 2.0
Chart [20] (1973)
-36.0
+ 7.7
-110.3
i 19.1
-30.0
f 8.6
Critical assessment
Present calculations based on free energies of Eremenko
-39.6
+ 2.0
-94.0
+ 3.0
-28.9
+ 3.0
Critical assessment
et al.
In particular, the 1273 K V-Si-0 that the reaction
phase diagram, given in Fig. 1, shows
5V5Si3(s) + WO(s) = 4Si02(glass) + 11V3Si(s)
(1)
proceeds from left to right and thus has a negative free energy. The experiments performed by Spear et al. [ 281 in determining this diagram indicated that the same diagram is also valid at the lower temperatures used by Eremenko et al. [ 16 - 181 when measuring the free energies of formation of the silicides. By assuming unit activities for the condensed phases, the standard free energies of formation of these phases must obey the restriction 5AG,“(V,Si3(s)] + 8AGxVO(s))
> 4AGf”(Si02(glass)} + llAGF{V,Si(s)} (2)
V V,Sl
SI
VSiS
VSS’S
Fig. 1. The ternary V-Si-0 phase diagram at 1273 K as given by Spear et al. [28]. The solid lines were determined from their results and the broken lines from the results of other investigators. The shaded areas are two-phase regions. The six V,Og,-1 (n = 3 - 8) phases are represented by their general formula. TABLE
2
Tabulation of auxiliary otherwise noted) Thermodynamic property
data used in assessments
V(s)
A%ss
0
(kcal mol-‘) S&a (e.u.)” J%o-Hi a (kcal mol- P)
6.92b
%OO
5.38 15.50
02(g)
Sits)
0
0
49.00 -
(all data from ref. 29 except
4.68 11.92
SiOg (o-quartz)
VW)
-103.2
4.50b
f 1.5
9.32t -
where
-217.7
0.2
f 0.4
SiOg(l)
-215.7
9.91+ 0.03
t 0.3
11.46+ 0.3
-
-
-170.4
-169.8
(e.u.1'
wJ100
0
0
0
-80.3
(kcal mol-‘) ae.u. = entropy
unit = cal mol-l
K1 .
bData
from Hultgren
et al. [ 301.
Auxiliary data used for the thermodynamic properties of the elements, VO(s) and Si02 are given by JANAF [ 291 and Hultgren et al. [ 301, as shown
189
in Table 2. Since the free energy change for the process SiO,(crystal) = SiO,(liquid) is only 0.6 kcal at 1100 K, it is assumed that AG&,O{SiO, (glass)} is the same as the value given for SiO#quid). The free energy restriction (2) becomes AG,“(V,Si,(s)} The only basis of these energy values the closest fit
> FAG,“{VsSi(s)}
- 7.4 (? 2.5) kcal
(3)
experimental data which approach internal consistency on the limits are those of Eremenko et al. [ 16 - 181 who reported free based on e.m.f. measurements. The data shown in Table 3 give of any of the reported data to the inequality (3)
-93.5(?0.8)
[I71
> -89.7(?3.1)
--89.9(?0.2)> -87.2(+2.6)
(4) El81
TABLE 3 Free energies of formation of vanadium silicides (Eremenko et al. [ 16 - 181) V$i
AGf0.1100(kcal mol-‘)
-37.41 -36.25
VsSi (s)
(6)
f 0.86 f 0.12
-93.51 -89.92
VSiz (s)
f 0.75 5 0.24
-26.51 -26.56 -
Ref.
f 0.84
16 17 18
Taking into account the uncertainties, the inequalities are just barely obeyed. These constraints of the ternary phase equilibria indicate that the free energy of formation of VsSis should be slightly less negative by a few kilocalories, or that the value for VsSi should be more negative. Accordingly, the free energy values of Eremenko et al. [ 16 - 181 have been adjusted and his error limits expanded so that they are consistent with the V-Si-0 phase diagram and yet agree as well as possible with the experimental results. These adjusted values are shown in Table 4. The free energy of formation of VSi2 is more loosely defined by the ternary phase diagram. The following two reactions proceed from left to right: llVSi,(s)
+ 14VO(s) = 7Si02 (glass) + 5V5Si3 (s)
VSi2 (s) + 2VO(s)
= SiOz (glass) + VsSi(s)
These lead to the corresponding z
(5) (6)
free energy limits for VSi, :
AG,“{VSi,(s))
>
AG,“(V,Sis(s)}
- 5.9 kcal
AG,“{VSi,(s))
> AGfO{VsSi(s)} - 9.2 kcal
(7) (8)
190 TABLE 4 Critically assessed thermodynamic Property
properties of the vanadium silicides VaSi (s)
V5Si3
(~1
VSiz (s)
AGf0,lloo (kcal mol-’ )
-38.0
+ 1.5
-90.0
+ 2.0
-26.6
* 2.0
AH&oo
-40.4
* 2.0
-95.2
f 3.0
-29.0
+ 3.0
-39.6
+ 2.0
-94.0
+ 3.0
-28.9
f 3.0
-2.2
f 1.0
-4.8
It 1.0
-2.i
* 1.0
-0.8
?r 0.5
-2.6
+ 0.5
-1.8
f 0.5
(kcal mol-‘)
AHf.298 (kcal mol-‘) WJIOO
(e.u.Y
W.298 (e.u.)* S&o0 (e.u.)” S&J (e.u.)”
56.3 f l.Ob
108.5 * 1.5
37.3 * l.ob
24.4 * 0.5b
45.5 f 1.0
14.1 ? 0.5b
*e.u. = entropy unit = cal mol-’ K-l. bThe origins of these data are given in Table 5.
As seen in eqns. (9) and (lo), the free energy values of Eremenko et al. [ 171 fall well within the range of these limits from the ternary diagram: -26.6
> -48.4
(9)
-26.6
> -46.6
(10)
The free energy of formation of VSi2 given by Eremenko et al. [ 171 could be greatly in error without violating the ternary phase equilibria constraints, but the fact that their value is in good general agreement with the enthalpies of formation determined for VSi2 by Gorelkin et al. [ 14, 151 supports its accuracy. (Table 1 lists these enthalpy values.)
3. Entropies
and enthalpies
of formation
Although the free energies of formation given by Eremenko et al. [ 171 are close to internal consistency, their calculated enthalpy and entropy of formation values appear to be too negative, particularly for V3Si and VgSi3. This could easily result from systematic temperature errors which cause relatively large errors in the slopes and intercepts of free energy uersus temperature plots. As discussed below, we have calculated enthalpy and entropy of formation values using the free energies given in Table 4 and absolute entropies derived from low and high temperature heat capacity data given in the literature. 3.1. Entropies of formation, Absolute entropies for V3Si and VSi2 have been determined from the heat capacity studies indicated in Table 5. High temperature incremental entropies were combined with the 298 K entropies to give figures at 1100 K. An average of the two S&s(V3Si) values was chosen for use in subsequent calculations.
191 TABLE 5 Absolute entropies reported for V&Z(s) and VSiz(s) Entropy increment (cal mol-l K-l)
ST3 SO 298
0.23a 24.47
-&
S&l
- f&
VSia(s)
Ref.
14.13
22
23.19
23
24 26
0.72’
24
23.34a
27
24.06
G98
Go0
Ref.
24.70
G98
G98
V$i(s)
-
G98
31.9
21
aValues calculated by graphical integration of reported heat capacity data.
By using the entropies for vanadium and silicon given in Table 2 and making the assumption that AS” = 0 at all temperatures for the solid state reaction : 7VsSi + 4VSiz = 5V,Sis
(11)
the absolute entropies and entropies of formation of all three vanadium silicides could be calculated. These figures are shown in Table 4. The entropies of formation at 298 K given in Table 4 range from -0.2 to -0.6 cal (g atom))’ K-l. These compare with an average of -0.28 cal (g atom)-’ K-l for the entropies of formation for a total of nine silicides listed in Hultgren et al. [30] and Kubaschewski et al. [31]. The similar 298 K values calculated from the 1073 K listed values of Eremenko et al. [18] are -1.4 and -1.3 cal (g atom)-’ K-l for VsSi and V&s, respectively. Eremenko et al. [16] list a 298 K value for VSi2 of -0.88 cal (g atom)-’ K-l. 3.2. Enthalpies of formation Using the above calculated entropies of formation along with the assessed free energies (Table 4), the enthalpies of formation at 1100 K were calculated. Enthalpies of formation at 298 K are obtained from the 1100 K values using enthalpy data for the compounds [21, 231 and the elements [ 291. The differences are small since the AC: values are small. By assuming that ACE is zero in eqn. (ll), an incremental enthalpy may be calculated for the formation of VgSi3. Since these enthalpies of formation were derived in a direct manner from the assessed free energies of formation given in Table 4, they fulfil the thermodynamic restrictions of the ternary phase diagram. A larger spread between the heats of formation of VsSi and VBSi,, such as we find in the
192
values (given in Table 1) of Golutvin et al. [ 131, Gorelkin et al. [ 141, Eremenko et al. [16 - 181 and Chart [20], cannot satisfy the restrictions of the phase diagram. It may be noted that the error limits of the critical assessment by Chart [ 19,20 ] fall within the acceptable range of eqn. (3). However, the narrower limits provided by this assessment make these figures of much greater usefulness for the thermodynamic analysis of the CVD of VsSi.
4. Summary
and conclusions
In conclusion, calorimetric studies of the heats of formation of these compounds have not yielded sets of values which are consistent with the ternary V-Si-0 phase diagram. The e.m.f. studies of Eremenko et al. [16 - 181 yielded values for the free energy of formation which fall just within the thermodynamic constraints, but their calculated enthalpy and entropy of formation values appear to be too negative. The combination of the assessed free energy values and the entropies derived from low temperature heat capacity studies yields a set of thermodynamic values for the free energies, enthalpies and entropies of formation which is in agreement with the constraints imposed by the V-Si-0 ternary phase diagram. This application of thermodynamic constraints derived from phase diagrams provides a powerful tool when assessing the reliability of published equilibrium data. The present study helps to exemplify the fact that a phase diagram is just a graphical representation of the chemistry and thermodynamics of a chemical system. When evaluating any thermochemical data, the exact relationships between phase equilibria and thermodynamics should be used routinely to determine the internal consistency of the properties of the system.
Acknowledgments This work was made possible National Science Foundation.
by grant DMR75-05813
from the
References 1 G. Hardy and J. Hulm, Phys. Rev., 93 (1954) 1004 - 1016. 2 L. Testardi, in W. P. Mason and R. N. Thurston (eds.), Physical Acoustics, Vol. 10, Academic Press, New York, 1973, pp. 193 - 296. 3 R. Kieffer, F. Benesovsky and H. Schmid, Z. Metallkd., 47 (1956) 247 - 253. 4 W. Fbstoker and A. Yamamoto, Trans. Am. Sot. Met., 46 (1954) 1136 - 1167. 5 H. Nowotny, B. Lux and H. Kudielka, Monatsh. Chem., 87 (1956) 447 - 470. 6 H. Bruning, Philips Res. Rep., 22 (1967) 349 - 354. 7 Yu. Efimov, Russ. J. Inorg. Chem., 8 (1963) 790 - 792. 8 Yu. Kochenhinksii, 0. Kulik and E. Shishkin, Proc. Acad. Sci. USSR, 209 (1973) 333 - 335.
193 9 J. Hallais, Ann. Chim. (Paris), 6 (1971) 321 - 330. 10 T. M. Besmann and K. E. Spear, J. Electrochem. Sot., 124 (5) (1977) 786 - 790. 11 C. F. Wan and K. E. Spear, in L. F. Donaghey, P. Rai-Choudhury and R. N. Tauber (eds.), Proc. 6th Int. Conf. Chemical Vapor Deposition, The Electrochemical Society, Princeton, New Jersey, 1977, pp. 47 - 58. 12 P. F. Freund, G. M. Rosenblatt and K. E. Spear, to be published. 13 Yu. Golutvin and T. Kozlovskaya, Russ. J. Phys. Chem., 34 (1960) 1116 - 1118. 14 0. Gorelkin and S. Mikhailikov, Russ. J. Phys. Chem., 45 (1971) 1523 - 1524. 15 0. Gorelkin, A. Dubrovin, 0. Kolesnikova and N. Chirkov, Russ. J. Phys. Chem., 46 (1972) 431- 432. 16 V. Eremenko, Dopov. Akad. Nauk Ukr. RSR Ser. B, 36 (1974) 712. 17 V. Eremenko, G. Lukashenko and V. Sidorko, Rev. Int. Hautes Temp. Refract., 12 (1975) 237 - 240. 18 V. Eremenko, G. Lukashenko, V. Sidorko and 0. Kulik, Dopov. Akad. Nauk Ukr. RSR Ser. A, (1976) (4) 365 - 368. 19 T. Chart, Natl. Phys. Lab. (U.K.) Rep., 18 (1972). 20 T. Chart, High Temp.-High Pressures, 5 (1973) 241 - 252. 21 L. Pankratz and K. Kelley, U.S. Bur. Mines Rep. Invest., 6241 (1963). 22 G. Kalishevich, P. Gel’d and R. Krentsis, Russ. J. Phys. Chem., 42 (1968) 675 - 676. 23 G. Kalishevich, P. Gel’d and Yu. Putintsev, High Temp. (USSR), 6 (1968) 959 - 962. 24 J. Brock, Solid State Commun., 7 (1969) 1789 - 1792. 25 R. Viswanathan and H. Luo, Solid State Commun., 9 (1971) 1733 - 1736. 26 V. Surikov, G. Kalishevich and P. Gel’d, Russ. J. Phys. Chem., 49 (1975) 326 - 327. 27 G. Knapp, S. Bader, H. Culbert, F. Fradin and T. Klippert, Phys. Rev. B, 11 (1975) 4331- 4338. 28 K. Spear, P. Gilles and H. Schafer, J. Less-Common Met., 14 (1968) 69 - 75. 29 JANAF Thermochemical Tables, Dow Chemical Co., Midland, Mich., 1971; 1974 suppl. and 1975 suppl. 30 R. Hultgren, P. Desai, D. Hawkins, M. Gleiser, K. Kelley and D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, Am. Sot. Metals, Metals Park, Ohio, 1973. 31 0. Kubaschewski, E. Evans and C. Alcock, Metallurgical Thermochemistry, Pergamon Press, Oxford, 1967.
Journal of the Less-Common Metals, 60 (1978) 185 - 193 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
ASSESSMENT OF THE THERMODYNAMIC VANADIUM SILICIDES UTILIZING TERNARY
PROPERTIES OF PHASE EQUILIBRIA
PETER F. FREUND and KARL E. SPEAR Materials Research Laboratory, 16802 (U.S.A.)
The Pennsylvania
State
University,
University
Park, Pa.
(Received February 14,1978)
Summary
The ternary V-Si-0 phase equilibria and auxiliary oxide data are used to set relative limits on the free energies of formation of the condensed vanadium silicide phases VsSi, Vr,Si3, and VSiz. The assessed free energies of formation are then used with entropies derived from heat capacity data to calculate a set of enthalpies of formation for these silicide phases which is also consistent with the ternary phase equilibria constraints. The thermodynamic values reported in the literature are compared with the consistent set of values derived in the present study.
1. Introduction
Considerable interest has been shown in the vanadium silicides since Hardy and Hulm [l] found a superconducting transition temperature of 17.1 K for VsSi in 1954. A sample-dependent martensitic transformation from cubic to tetragonal occurring at about 21 K and anomalous temperature dependences of the Knight shift, magnetic susceptibility and elastic behaviour [ 21 have made this Al5 compound of special interest. The cubic VsSi is one of three intermediate solid phases that were identified in the V-Si system in the early work of Kieffer et al. [3] and Rostoker et al. [ 41. The other phases are a tetragonal V&Z& phase and a hexagonal VSis phase. An impurity-stabilized hexagonal form of VaSis has been characterized by Nowotny et al. [ 51. More recent phase equilibria studies by Bruning [ 61, Efimov [ 71 and Kocherzhinskii et al. [ 81 have confirmed the existence of the three binary solid phases. A study by Hallais [9] reports the formation of an orthorhombic VsS&, compound as well, but others have not confirmed its existence as a stable binary phase. The present study is part of a research program on the crystal growth and chemical vapor deposition of niobium and vanadium superconducting compounds with the Al5 structure type. A computerized thermodynamic analysis of the chemical vapor deposition (CVD) of VsSi(s) from a mixture of
186
gaseous chlorides and hydrogen has been undertaken following the work of Besmann and Spear [lo] on the CVD of titanium borides and of Wan and Spear [ 111 on the CVD of niobium germanides. The analysis of the high temperature equilibrium behavior of the V-Si-H-Cl system requires accurate knowledge of the thermodynamic properties of the reacting species. Relatively small changes in thermodynamic values of species in this fourcomponent system can cause the equilibrium to shift from favoring the deposition of VsSi to not favoring its deposition. The binary vanadium chlorides and vanadium silicides include some of the most important species at equilibrium as well as the most uncertain values for enthalpies and entropies of formation. Literature reports of the thermodynamic properties of the vanadium silicides showed great discrepancies and uncertainties, bringing into question the tenability of a computer analysis of the CVD of VsSi. This paper reports a critical assessment of the thermodynamics of the vanadium silicides and develops a consistent set of values. An assessment of the thermodynamics of the vanadium chlorides has been the subject of a separate investigation [ 121. A relatively large number of studies of the thermodynamics of the vanadium silicides have been reported. Golutvin et al. [ 131, Gorelkin et al. [ 14, 151 and Eremenko et al. [ 16 - 181 have reported enthalpies of formation with discrepancies of 15 kcal mol-’ each for VsSi and V&lis and 45 kcal mol-’ for VSiz. An assessment by Chart [ 19, 201 allows for uncertainties of 8 - 19 kcal mol-’ for the enthalpies of formation of the three silicide compounds; an entropy of formation is listed for only one of the three compounds. Table 1 lists the reported experimental and assessed values. Specific heat measurements for various temperature ranges have been reported by Pankratz and Kelley [ 211, Kalishevich et al. [ 22,231, Brock [24], Viswanathan et al. [25], Surikov et al. [26] and Knapp et al. [ 271. The entropies calculated from these heat capacity values do not agree with those reported in the equilibrium e.m.f. study of Eremenko et al. [16 - 181. In a previous study by Spear et al. [ 281 on chemical transport reactions involved in interactions of silica glass with vanadium metal, the ternary V-Si-0 phase equilibria were partially established. They used these data to show the inconsistency of the vanadium silicide thermodynamic data published by Golutvin et al. [ 131. In the present assessment, the same ternary phase relationships are used to show the inconsistency of the currently available thermodynamic properties of the binary vanadium silicide phases.
2. Free energies of formation The V-Si-0 ternary phase diagram and the resulting chemical reactions that can be derived provide much stricter relative limits for the free energies of formation of VsSi, Vr,Si3 and VSiz than those derived from the binary phase diagram.
187 TABLE
1
List of measured and assessed enthalpies of formation at 298 K for the vanadium silicides Source
AH; zaa (V&i) (kcal mol-‘)
Golutvin and Kozlovskaya [13] (1960)
-27
Gorelkin and Mikhailikov [ 141 (1970)
-33.7
f 9
i 2
fW.298 (kcal mol-‘) -96
[~~~!nol-‘)
f 46
-111.0
-112
Gorelkin et al. [15] (1972)
Technique
AH&a
W5Si3)
-75
? 5
-29.8
f 13
-36
+ 21
+3
?r 6
Calorimetric combustion Sintering in an isothermal calorimeter Sintering in an isothermal calorimeter
Eremenko [16] (1974)
-29.6
i 1.2
E.m.f. measurements
Eremenko etal. [17] (1975)
-29.6
2 1.2
E.m.f. measurements
E.m.f. measurements
Eremenko etol. [18] (1976)
-44.4
r 0.1
-104.1
f 2.0
Chart [20] (1973)
-36.0
+ 7.7
-110.3
i 19.1
-30.0
f 8.6
Critical assessment
Present calculations based on free energies of Eremenko
-39.6
+ 2.0
-94.0
+ 3.0
-28.9
+ 3.0
Critical assessment
et al.
In particular, the 1273 K V-Si-0 that the reaction
phase diagram, given in Fig. 1, shows
5V5Si3(s) + WO(s) = 4Si02(glass) + 11V3Si(s)
(1)
proceeds from left to right and thus has a negative free energy. The experiments performed by Spear et al. [ 281 in determining this diagram indicated that the same diagram is also valid at the lower temperatures used by Eremenko et al. [ 16 - 181 when measuring the free energies of formation of the silicides. By assuming unit activities for the condensed phases, the standard free energies of formation of these phases must obey the restriction 5AG,“(V,Si3(s)] + 8AGxVO(s))
> 4AGf”(Si02(glass)} + llAGF{V,Si(s)} (2)
V V,Sl
SI
VSiS
VSS’S
Fig. 1. The ternary V-Si-0 phase diagram at 1273 K as given by Spear et al. [28]. The solid lines were determined from their results and the broken lines from the results of other investigators. The shaded areas are two-phase regions. The six V,Og,-1 (n = 3 - 8) phases are represented by their general formula. TABLE
2
Tabulation of auxiliary otherwise noted) Thermodynamic property
data used in assessments
V(s)
A%ss
0
(kcal mol-‘) S&a (e.u.)” J%o-Hi a (kcal mol- P)
6.92b
%OO
5.38 15.50
02(g)
Sits)
0
0
49.00 -
(all data from ref. 29 except
4.68 11.92
SiOg (o-quartz)
VW)
-103.2
4.50b
f 1.5
9.32t -
where
-217.7
0.2
f 0.4
SiOg(l)
-215.7
9.91+ 0.03
t 0.3
11.46+ 0.3
-
-
-170.4
-169.8
(e.u.1'
wJ100
0
0
0
-80.3
(kcal mol-‘) ae.u. = entropy
unit = cal mol-l
K1 .
bData
from Hultgren
et al. [ 301.
Auxiliary data used for the thermodynamic properties of the elements, VO(s) and Si02 are given by JANAF [ 291 and Hultgren et al. [ 301, as shown
189
in Table 2. Since the free energy change for the process SiO,(crystal) = SiO,(liquid) is only 0.6 kcal at 1100 K, it is assumed that AG&,O{SiO, (glass)} is the same as the value given for SiO#quid). The free energy restriction (2) becomes AG,“(V,Si,(s)} The only basis of these energy values the closest fit
> FAG,“{VsSi(s)}
- 7.4 (? 2.5) kcal
(3)
experimental data which approach internal consistency on the limits are those of Eremenko et al. [ 16 - 181 who reported free based on e.m.f. measurements. The data shown in Table 3 give of any of the reported data to the inequality (3)
-93.5(?0.8)
[I71
> -89.7(?3.1)
--89.9(?0.2)> -87.2(+2.6)
(4) El81
TABLE 3 Free energies of formation of vanadium silicides (Eremenko et al. [ 16 - 181) V$i
AGf0.1100(kcal mol-‘)
-37.41 -36.25
VsSi (s)
(6)
f 0.86 f 0.12
-93.51 -89.92
VSiz (s)
f 0.75 5 0.24
-26.51 -26.56 -
Ref.
f 0.84
16 17 18
Taking into account the uncertainties, the inequalities are just barely obeyed. These constraints of the ternary phase equilibria indicate that the free energy of formation of VsSis should be slightly less negative by a few kilocalories, or that the value for VsSi should be more negative. Accordingly, the free energy values of Eremenko et al. [ 16 - 181 have been adjusted and his error limits expanded so that they are consistent with the V-Si-0 phase diagram and yet agree as well as possible with the experimental results. These adjusted values are shown in Table 4. The free energy of formation of VSi2 is more loosely defined by the ternary phase diagram. The following two reactions proceed from left to right: llVSi,(s)
+ 14VO(s) = 7Si02 (glass) + 5V5Si3 (s)
VSi2 (s) + 2VO(s)
= SiOz (glass) + VsSi(s)
These lead to the corresponding z
(5) (6)
free energy limits for VSi, :
AG,“{VSi,(s))
>
AG,“(V,Sis(s)}
- 5.9 kcal
AG,“{VSi,(s))
> AGfO{VsSi(s)} - 9.2 kcal
(7) (8)
190 TABLE 4 Critically assessed thermodynamic Property
properties of the vanadium silicides VaSi (s)
V5Si3
(~1
VSiz (s)
AGf0,lloo (kcal mol-’ )
-38.0
+ 1.5
-90.0
+ 2.0
-26.6
* 2.0
AH&oo
-40.4
* 2.0
-95.2
f 3.0
-29.0
+ 3.0
-39.6
+ 2.0
-94.0
+ 3.0
-28.9
f 3.0
-2.2
f 1.0
-4.8
It 1.0
-2.i
* 1.0
-0.8
?r 0.5
-2.6
+ 0.5
-1.8
f 0.5
(kcal mol-‘)
AHf.298 (kcal mol-‘) WJIOO
(e.u.Y
W.298 (e.u.)* S&o0 (e.u.)” S&J (e.u.)”
56.3 f l.Ob
108.5 * 1.5
37.3 * l.ob
24.4 * 0.5b
45.5 f 1.0
14.1 ? 0.5b
*e.u. = entropy unit = cal mol-’ K-l. bThe origins of these data are given in Table 5.
As seen in eqns. (9) and (lo), the free energy values of Eremenko et al. [ 171 fall well within the range of these limits from the ternary diagram: -26.6
> -48.4
(9)
-26.6
> -46.6
(10)
The free energy of formation of VSi2 given by Eremenko et al. [ 171 could be greatly in error without violating the ternary phase equilibria constraints, but the fact that their value is in good general agreement with the enthalpies of formation determined for VSi2 by Gorelkin et al. [ 14, 151 supports its accuracy. (Table 1 lists these enthalpy values.)
3. Entropies
and enthalpies
of formation
Although the free energies of formation given by Eremenko et al. [ 171 are close to internal consistency, their calculated enthalpy and entropy of formation values appear to be too negative, particularly for V3Si and VgSi3. This could easily result from systematic temperature errors which cause relatively large errors in the slopes and intercepts of free energy uersus temperature plots. As discussed below, we have calculated enthalpy and entropy of formation values using the free energies given in Table 4 and absolute entropies derived from low and high temperature heat capacity data given in the literature. 3.1. Entropies of formation, Absolute entropies for V3Si and VSi2 have been determined from the heat capacity studies indicated in Table 5. High temperature incremental entropies were combined with the 298 K entropies to give figures at 1100 K. An average of the two S&s(V3Si) values was chosen for use in subsequent calculations.
191 TABLE 5 Absolute entropies reported for V&Z(s) and VSiz(s) Entropy increment (cal mol-l K-l)
ST3 SO 298
0.23a 24.47
-&
S&l
- f&
VSia(s)
Ref.
14.13
22
23.19
23
24 26
0.72’
24
23.34a
27
24.06
G98
Go0
Ref.
24.70
G98
G98
V$i(s)
-
G98
31.9
21
aValues calculated by graphical integration of reported heat capacity data.
By using the entropies for vanadium and silicon given in Table 2 and making the assumption that AS” = 0 at all temperatures for the solid state reaction : 7VsSi + 4VSiz = 5V,Sis
(11)
the absolute entropies and entropies of formation of all three vanadium silicides could be calculated. These figures are shown in Table 4. The entropies of formation at 298 K given in Table 4 range from -0.2 to -0.6 cal (g atom))’ K-l. These compare with an average of -0.28 cal (g atom)-’ K-l for the entropies of formation for a total of nine silicides listed in Hultgren et al. [30] and Kubaschewski et al. [31]. The similar 298 K values calculated from the 1073 K listed values of Eremenko et al. [18] are -1.4 and -1.3 cal (g atom)-’ K-l for VsSi and V&s, respectively. Eremenko et al. [16] list a 298 K value for VSi2 of -0.88 cal (g atom)-’ K-l. 3.2. Enthalpies of formation Using the above calculated entropies of formation along with the assessed free energies (Table 4), the enthalpies of formation at 1100 K were calculated. Enthalpies of formation at 298 K are obtained from the 1100 K values using enthalpy data for the compounds [21, 231 and the elements [ 291. The differences are small since the AC: values are small. By assuming that ACE is zero in eqn. (ll), an incremental enthalpy may be calculated for the formation of VgSi3. Since these enthalpies of formation were derived in a direct manner from the assessed free energies of formation given in Table 4, they fulfil the thermodynamic restrictions of the ternary phase diagram. A larger spread between the heats of formation of VsSi and VBSi,, such as we find in the
192
values (given in Table 1) of Golutvin et al. [ 131, Gorelkin et al. [ 141, Eremenko et al. [16 - 181 and Chart [20], cannot satisfy the restrictions of the phase diagram. It may be noted that the error limits of the critical assessment by Chart [ 19,20 ] fall within the acceptable range of eqn. (3). However, the narrower limits provided by this assessment make these figures of much greater usefulness for the thermodynamic analysis of the CVD of VsSi.
4. Summary
and conclusions
In conclusion, calorimetric studies of the heats of formation of these compounds have not yielded sets of values which are consistent with the ternary V-Si-0 phase diagram. The e.m.f. studies of Eremenko et al. [16 - 181 yielded values for the free energy of formation which fall just within the thermodynamic constraints, but their calculated enthalpy and entropy of formation values appear to be too negative. The combination of the assessed free energy values and the entropies derived from low temperature heat capacity studies yields a set of thermodynamic values for the free energies, enthalpies and entropies of formation which is in agreement with the constraints imposed by the V-Si-0 ternary phase diagram. This application of thermodynamic constraints derived from phase diagrams provides a powerful tool when assessing the reliability of published equilibrium data. The present study helps to exemplify the fact that a phase diagram is just a graphical representation of the chemistry and thermodynamics of a chemical system. When evaluating any thermochemical data, the exact relationships between phase equilibria and thermodynamics should be used routinely to determine the internal consistency of the properties of the system.
Acknowledgments This work was made possible National Science Foundation.
by grant DMR75-05813
from the
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