2596
R. J. ACKERMANN AND E. G. RAUH
Vol. 67
A THERMODYNAMIC STUDY OF THE TUNGSTEK-OXYGEN SYSTEM AT HIGH TEMPERATURES' BY R. J. ACKERMASK AND E. G. RAUH Argonne -Vational Laboratory, Argonne, Illinois Received Mau $9,1963 The sublimation behavior of the tungsten-oxygen system has been investigated over the temperature range 1300 to 1600°K. by means of mass effusion studies, mass spectrometric observations, chemical analyses, and Xray diffraction examination of the condensed phases. Measurements were carried out on compositions ranging from W01.8Lto WOa. I n all cases the therniodynamically important vapor species are T 4 0 1 2 , WsOs, WaOg, and W20,. Univariant behavior was observed for the solid phases W-WO2, W 0 2 - W 1 8 0 4 g r TT1804g-WzoOj8,TiY2005gW O 2 . 8 6 , and TVOa.96. The composition TT-02.s~ probably represents the aaeotropic composition of the W O S - ~solid solution produced by the vacuum and is the only single phase which evaporates congruently below 1550°K. Except for the W20058-TT02.96 mixture in which the composition of the vapor phase is between those of the solid phases, all other phases and mixtures of two solid phases evaporate incongruently, since the vapor phase is richer in oxygen than the condensed phase. Above 1550'K. there are no congruently evaporating compositions. Standard free energies, enthalpies, and entropies of formation for the four major vapor species and for the Wlg04g,W 2 0 0 s 8 , and W02.9ssolid phases are given.
Introduction The extensive use of tungsten as a refractory material in high temperature studies and applications gerierates a n immediate need for a knowledge of the thermodynamic propert,ies of its compounds. A large number of refractory oxides have been studied in contact wit'h tungsten a t high temperatures, but the lack of consistent thermodynamic data for the solid and gaseous tungsten oxides precludes in some instances an accurate evaluation of the extent of interaction. Previous investigations have shown that the metaloxygen systems of the group VI transition elements are complex and as a result much of the chemistry, especially a t high temperatures, is incomplete. I n addition to the dioxides and trioxides, which are commonly known and whose thermodynamic properties have been studied, intermediate oxides having complex stoichiometries such as Mo80aa, RIo9026, Mo17047,W18049, and w 2 0 0 5 8 ' have been established. For metals showing such multiplicity of valence states, the complexity in the condensed phase is frequently associated with the existence of complex molecules in the vapor phase. Polymeric species, principally trimeric, have been observed in the vapor in equilibrium with molybdenum6J and tungsten8mg oxides. Further, in the case of -a number of transition metal oxides the effect of deviations from ideal stoichiometry upon thermodynamic properties has been observed, e.g., FeOl+z,lo U02+z,11Zr02-z,12 and since the extent of the departure from stoichiometry generally tends to increase with increasing temperature it becomes necessary to (1) Based on work performed under the auspices of the U. 8.Atomic Energy commission. ( 2 ) A. Magneli, A c t a Chem. Scand., 2, 501 (1948). (3) L. Kihlborg, ibid., 14, 1612 (1960). ( 4 ) 4.Magneli, A r k i v Kerni, 1, 223 (1949). (5) A. Magneli. ibid., 1, 513 (1950). '. A . Chupka, J . Chern. Phys., 26, (6) J. Berkowitz, M. G. Inghram, and M 842 (1957). (7) R . P. Burns, Q. DeXIaria, J. Drowart, and R. T. Grimley, ibid., 52, 1303 (1900). (8) J. Berkowitz, K. A. Ciiupka, and 31.G . Inghram, ibid., 27, 85 (1957). (9) R . J. Ackermann, E . G. Rauh, and R. J. Thorn, Argonne Pu'ational Laboratory Annual Report, ANL-6125 (1959). (10) S.M. Ariya, M . P. Morozova, and L. A. Shneider, Zh. Ohschch. Khinz., 24, 41 (1954). (11) L. E. J. Roberts a n d A . J. Walter, J . Inorg. Nucl. Chem., 22, 213 (1961). (12) R. J. Ackermann and R. J. Thorn, Paper presented at the 121st Meeting of the Electrochemical Society, Los Anpeles, California, N a y 7, 1962.
recognize the effect of nonstoichiometry upon the thermodynamic properties and subsequent interpretation of high temperature phenomena. In the tungstenoxygen system some evidence of nonstoichiometry has been reported. Glemser and Sauer13 have suggested that the trioxide phase exists over a range of composition from W03 to W 0 z . 9 5 . Hagg and iCIagneli14 suggested the possibility of a new phase a t the composition W O Z . ~ ~In. a preliminary report Ackermann, et a1.,9showed that the trioxide is reduced near 1400'K. in vacuo to a composition near W02,9swhich evaporates congruently. Mass spectrometric identification of the ionic species W20sf,m r 3 0 8 + , and W4OI1+ indicated that vapor species with an oxygen-tungsten ratio of less than 3 may be important in the equilibrium vapor. The principal experimental efforts in the past have dealt largely with determinations of the vapor pressure of the trioxide. The thermodynamic results of these previous measurements are shown in Table I. hlthough the values of the free energy of sublimation, AF'1400, evaluated a t a temperature common to all the investigations are in good agreement, there is considerable disagreement among the values for the heat and entropy of sublimation. In some cases the discrepancies are quite beyond that incurred by the inaccurate assumption of the vapor species, and, although some differences may arise from the usual experimental errors, it would now appear that some result from a lack of knowledge of the composition variable. Some measurements on other than the trioxide phase have been reported; Ackermann, et aLj9 BIackburn,'j and Gilles and Wa11I6 have investigated univariant systems of lower oxides. It is the purpose of the present investigation (1) to examine in greater detail the evaporation behavior of the trioxide phase and univariant systems composed of mixtures of the known solid phases, WOZ, W 1 8 0 4 9 , and W20058,by means of mass effusion studies, mase spectrometric observations, chemical analyses, and Xray diffraction identification of the condensed phases, ( 2 ) to combine the results of the various experimental (13) 0. Glemser a n d H. Sauer, 2. anorg. allgem. chem., 262, 144 (1943). (14) G. Haggand A. Magneli, Arkzv K e m i , Mineral., Ueol., A19, 1 (1944). (15) P. E. Blackburn, W d D C T R 59-575, part 1, section 1, March, 1960; see also Blackburn, et al., part 2, December, 1960. (16) P. W. Gilles and J. G. L. Wall, Paper presented a t the 121st Meeting of the Electrochemical Society, Los Angeles, Calif., May 7, 1962.
THERMODYNAMICS OF TCNGSTEN-OXYGEN AT HIGHTEMPERATURES
Dee., 1963
2597
TABLE I PREVIOUS
DETERMIKATION O F THE
THERMODYNAMICS OF
SUBLIMATION OF TUNGSTEN TRIOXIDE Thermodynamic Properties AH", AS", kcal. mole-' e.u. mole-'
Temperature, Investigator
K. Ueno" Berkowitz, et aLb
,Method
OK.
AF '1400 > kcal. mole-'
1343-1393 1330-1450
112.5 58.4 30.7 130 (trimer) 69.5 32.7 151 (tetramer) 82.5 Blackburn, et al.' Effusion 1314-1581 107.9 54.1 32.2 Meyer, el aLd Transpiration 1373-1523 124.9 66.9 31.2 Blackburne Effusion 1035-1506 123.6 65.5 32.8 See ref. 8. P. E. Blackburn, M. €Koch, and H. L. Johnston, J . Phys. Chem., 62, K. Ueno, J . Chem. SOC.Japan, 62,990 (1941). G. Meyer, J. F. Oosterom, and J. L. DeRoo, Rec. trav. chim., 78,412 (1959). e See ref. 15. 769 (1958). Effusion Mass spectrometer
approaches and calculate a consistent set of standard free energies of formation of the solid phases and the vapor species, and (3) to summarize the evaporation behavior of the tungsten-oxygen system by means of a pressure-composition phase diagram. Experimental Apparatus and Techniques.-The vacuum balance used for the measurement of mass effusion rates and the Bendix Model 12-101 time-of-flight mass spectrometer used for the mass spectrometric observations have been described p r e v i ~ u s l y . ~The ~ characteristics of both apparatus, the control and measurement of the temperature, and the experimental techniques were given in detail. Platinum cells were used for all samples except for W-WOz for which it was possible to use either platinum or tungsten. Samples of tungsten oxides ranging in composition from WOI.SO to WOf were synthesized from mixtures of stoichiometric WO, and tungsten metal prepa,red by reduction of the trioxide with dry hydrogen. The mixtures were heated in an outgassed platinum tube, first in uaczio at about 400' for several hours, then under one atmosphere of purified argon a t 1200' for several days. It was necessary to age the samples further by heating in vacuo at temperatures in the range of the effusion measurements in order to increase the precision of the measurements. Samples and residues were analyzed by measuring the weight increase of a sample after heating in air a t about 700" until the light yellow-green stoichiometric trioxide was produced and constant weight wm achieved.
1500
1600
T*K
1400
-4.0 6.5
Fig. l.-Mass
7.0
IOfT.
7.5
effusion measurements of univariant W-0 systems.
log wT'l2 = A / T System
a. W-WO2 b. WOz-WI804e C. W18049-W20068 d. WO2.96 e. Wzo068-WOa.Qe
+B
A
B
-31,500 f 320 -27,360 f 2 6 0 - 24,960 f 400 -24,350f130 -23,580 f 530
18.66 f 0.21 16.55 f 0 . 1 8 15.52 f 0.27 15.37f0.09 14.88 i0.37
X-ray diffraction. The reproducibility of the data shows that the proportion of the two solid phases present' does not affect the effusion rate as long as both are present and the surface area of each is large compared t o the area of the oiifice. The systems designated by curves a, b, and c evaporate incongruently a t the expense of the higher oxide and, hence, the composition of the vapor phase is richer in oxygen than either of the two solid phases. In the case of the system W-W02-vapor (curve a) the chemical composition of the vapor phase was determined from the complete evaporation of the dioxide phase t o produce tungsten metal according to the process
Results Mass Effusion Studies.-Measurements of the mass effusion rates of initially stoichiometric trioxide in the temperature range 1300-1500°K. demonstrated that evaporation occurs initially with a preferential loss of oxygen and a concurrent decrease in mass effusion rate by approximately a factor of two, Thereafter, the system evaporates congruently as evidenced by the complete evaporation of an initial 0.2025-g. sample of WOa a t 1498OK. and in a vacuum of approximately mm. The temperature dependence of the effusion rate of the congruently vaporizing composition is shown in curve d, Fig. 1. The composition of the solid WOdS) -+ (2!x)WOz(g) (x - 2/x)W(s) (I) phase was determined from the residues of three difFor three samples of dioxide (100-300 mg.) the average ferent runs by combustion analysis from which oxygenvalue of II: was found to be 2.94 i 0.01. The solubility to-tungsten atom ratios of 2.962, 2.965, and 2.963 were of oxygen or oxide in tungsten metal is probably quite ~ blue and its comobtained. The oxide W O Z .is~ deep small since the lattice parameters of the metal in equiplex crystallographic properties are being studied.I8 librium with the dioxide and metal that had been aged The effusion rates of univariant, three phase ( 2 in a dry hydrogen atmosphere were identical within solid vapor) systems, W-WOz-vapor, T/VOz-W1804gexperimental error. vapor, TiVle049-WZ0068-~apor,and Wzo068-W02.96-vapor, The volatility of the univariant sytem, W20068are given in Fig. 1 by curves a, b, c, and e, respectively. WO~.~~-i-apor, (curve e in Fig. 1) is the highest of the The solid phases present in a given sample before and systems studied. For this system the composition of after the effusion measurements were identified by the vapor phase lies between the compositions of the (17) R. J. Ackermann and E. G. Rauh, J . Chem. Phys., 36,448 (1962). two solid phases, Le., 2.90 < O/W < 2.96. I n order to (18) E Gebert and R. J Ackermann, Arganne National Laboratory, undetermine the vapor composition the effusion rates published results.
+
+
R. J. ACKERMANX ASD E. G. RAW
2598 1450
T’K
1400
1350
I/ 3.0-
k
l-4
-
0,
0
2.0-
1.0
-
I
, I
Fig. 2.--Mass
I
I
ZO
I
I
I
104/T.
I
I
15
I
spectrometric measurements of the major vapor species in equilibrium with 1 v 0 2 . 9 6 .
log IiT
A/T
+B
B
A
Species
-27,020 - 23,490 -24,510 -24,840
a. W 4 0 1 2 b. w7aOg C. TVaos d. WnOs
4.0-
1
\x
f480 f 490 f 510 f 170
21.32 zt 0.34 19.60f0.34 19.58 f 0.36 19.45 zt 0.12
w- wo, 30 e.v. electrons
3.0-
G l-ii
-cz 0
2.0 -
’
of two-phase samples of initial compositions O/W = 2.910, 2.931, 2.943, and 2.956 were measured. -411 compositions except the last ultimately resulted in the system, W18049-W2c0,- vapor, after appreciable evaporation had occurred, whereas the last sample produced w02.96. Therefore, the over-all composition of the vapor phase lies somewhere between the narrower limits, 2.943 < O/W < 2.956, or to sufficient accuracy O/W = 2.96. The data of curve e were obtained from the sample of initial composition O/W = 2.943. The
Vol. 67
equations given in the table of Fig. 1 result from the treatment of the data by the method of least squares; the errors quoted in the constants A and B are standard deviations. The congruency of evaporation of the composition W02.g~ is indicated up to 1480°K. However, at temperatures greater than approximately 1550°K. the evaporation of samples of this composition produced lower oxides and ultimately tungsten metal. Above 1550°K. there are no congruently evaporating phases. Mass Spectrometric Studies.-Mass spectrometric observations were made on samples of three different compositions : W03,wo2.96, and WOl.80. For ionizing electron energies of 40 e.v. or greater the following ions were observed in all cases: WO+, )YO2+, \T7o3+, W20j+, W206+,W30s+, W30g+, W4011+, W40l2+, and W5015+. Of these, WO+, W02+, W03+,and almost all the W205+ disappeared below 30 e.v. and were undoubtedly dissociation fragments of the ionization process. Below 30 e.v. the W205+,W4011+,and TV5015+ were detectable but mere several orders of magnitude and W4012+. less intense than W206+,W308+,W309+, Although a part of the W 2 0 6 + and W308+ ion currents could have resulted from fragmentation of the major species W309,the principal gaseous species above all tungsten oxides studied here appear to be W206, Jv308, W309, and W4012. It was not possible to make quantitative observations on stoichiometric W03 since it is a bivariant system and the ion currents were not constant until the composition of the sample had reached W02.96. In one case a continuous decrease by a factor of almost 3 in the W309+ intensity and a slight increase in the W308+ intensity mere observed, indicating a continuous change in composition of the solid. This behavior clearly demonstrates that a large fraction of the W308+ current results from the primary ionization of Xr308(g) and all is not a fragment of the ionization of W 3 0 9 , otherwise the W308+ and W309+ should have shown parallel behavior. Furthermore, the congruency of eraporation of w02.g6(s) demands the existence of a species having an oxygen-tungsten ratio less than 2.96. The change of log I,T with reciprocal temperature for each species in equilibrium with WO2 96 is shown in Fig. 2 and with a W-W02 mixture in Fig. 3. The data were treated by the method of least squares and the slopes, intercepts, and standard deviations are given in the tables of Fig. 2 and 3. Internal Consistency of the Data.-By combinin? the results of the mass effusion and mass spectrometric measurements it is possible to derive equations for the absolute pressures of the major species in equilibrium with W0296 and W-W02. The effusion equation may be expressed in the form
in which w,, p,, and ;Illare the mass effusion rate, pressure, and molecular weight of a given vapor species. Since the total mass effusion rate is the sum of the mass effusion rates of all the individual species, the pressure in atm. of W309, the major species, can be expressed by the equation p(’cV30~)= (2.256
x
1 0 - 2 ) w ~ 1 ” / ~ ? ’ l (3)
Dee., 1963
THERXIODYXAXUCS O F
TUNGSTEN-OXYGEN AT HIGHTEMPERATURES
TABLE I1 THEPARTIAL PRESSURES O F GASEOUS TUNGSTEN logpi(atm.) = A / T B
+-
-Species
WaOs w308
WlOl2
Iv206
OXIDE8
W0a.w
W-WOa
A
B
eq.
-14,840 f 610 -27,190f610 -25,180f610
11.76f0.38 1 1 . 7 6 f 0.40 13.27 f 0.40 11.81f 0.40
a b
-23,800 f 590
in which the four values of r for W309, W3OS,Wz06, and W4012 are given by ri = piMil"/p(W,Og) = li~(W309)Mi"~//l(W309) ci. By substituting into eq. 3 the appropriate values of wT1I2from eq. a or d of Fig. 1, the corresponding ion ratios evaluated from the eq. of Fig. 2 and 3, and assumed ionization cross sections of U(W30g) U(W308) "4 U ( W 4 0 1 2 ) % "2 U(W&), the pressures of W309(g) were calculated a t the extremities of the temperature range and equations of the form, log p(WaO9) = A / T B, were obtained for the systems 1v02.96and W-W02. From these equations and the pressure ratios, pi/p(W309), equations for the ~ derived. From pressures of W308, WZO,and w 4 0 were the error aiialysis of the equations given in Fig. 1, 2, and 3, the standard deviation in the quantities IiT and wTIIa a,t any temperature is less than f5%. With this estimate, eq. 3, and the law of propagation of errors it is possible to estimate the standard deviations in the constants A and B for log p(W309). Uncertainties in these constants for the other species are estimated by the method given by Birge.lg The results are given in Table 11. I n Table I11 the consistency of the mass effusion and mass spectrometric dais is demonstrated by the agreement of the heats of sublimation, AH',.,, measured mass spectrometrically with those calculated, A H o C a l o d , from eq. a through h, Table 11. Although the former are involved in the calculation of the latter, the major factor in determining p(W309) in eq. 3 and its heat of sublimation is the quantity wTIIaand its temperature dependence. The agreement can be further demonstrated by comparison of the over-all composition of the vaplor phase determined mass spectrometrically with that demanded by the congruency of evaporation of WO2.90. At 104/T = 7.5 the ratio of the total pressure of trioxide polymers (W,03,)to the pressure of W 3 0 , calculated from the equations in Table I1 is 7.2 compared to a value of 7.3 demanded by the congruency of evaporation, whereas a t 104/T = 6.7 the ratio is 6.5. The change in the ratio between the upper and lower extremities of the temperature range corresponds to a change in the atom ratio in the solid phase of only 0.003. Similarly, the composition of the vapor phase for the system W-W02 agrees within experimental error with that actually determined according to eq. 1 and changes insignificantly over the temperature range of the mass effusion measurements. This small change of vapor composition with temperature reduces the likelihood of systematic errors resulting from temperature gradients within the cell. It would appear, therefore, that the interpretation of the mass spectrometric data, based on the assumption that the observed ion currents result principally from primary ionization and the estimates of ionization crosssections, is consistent with the mass effusion data and
+
(19) R. J. Birge, P h ~ 8Rev., . 40, 224 (1932).
2599
B
eq.
15.24 f 0.43 15.18 f 0.44 17.42f0.44 14.21f0.44
e
A
-31,280 f 670 - 3 2 , 2 8 0 f 690 -36,560 =!= 690 -30,380 1690
C
d
f g
h
the measured stoichiometries of evaporation. However, since the system is quite complex, the possible cancellation of errors incurred by these operative assumptions must be kept in mind and the apparent agreement could be partly fortuitous. For example, if the composition of the congruently evaporating trioxide phase were W02.$*,the stoichiometry of evaporation would require that the ratio of the pressures of trioxide polymers to that of W308(g)be doubled. However, the estimates of cross sections could be uncertain by the same factor. The point to be emphasized in this section is the good experimental agreement between the mass effusion data and the mass spectrometric measurements of the principal rapor species, W309(g). Agreement among the other species is less obvious but will become apparent in the thermodynamic calculations that follow. TABLE I11 COMPARISON OF CALCULATED AND MASS SPECTROMETRICALLY MEASURED HEATSOF SUBLIMATION woa.9s Speciea
w-woz
r
AHOm.s.
AHOcalod
107.5 f 2 . 3 112.1 f 2 . 3 123.6 f 2.2 113.610.8
143.1 f 3.1 147.7 f 3 . 2 167.3 f 3 . 2 139.0f3.2
A H *calcd
WaOs 108.9 f 2 . 7 Jv30, 1 1 3 . 7 f 2.8 W 4 0 ~1 2 4 . 4 f 2.8 WzOe 1 1 5 . 2 f 2 . 8
>
>
AH'm.s.
142.1 f 2.2 146.4 f 1.3 166.2 f 2 . 5 137.4f2.4
Thermodynamic Calculations.-From consideration of the equation representing the various equilibria
WO,(s) = aW,O,(g)
+ bW(s)
(4)
for which
-RT In p"(W,O,) = aAF,'(W,O,) - AFl0(WO2) (5) it is possible to calculate the standard free energies of formation of W,O,(g) since the partial pressures of W309, WgOs, W4012, and W206 are given by eq. a through h, Table 11,and the standard free energy of formation of tungsten dioxide [AFfo(W02) = -137,150 40.00T (1200 < T < 17OO0K.)]is evaluated from the compilation of King, et d 2 0 The results of these calculations are given in 'Table IV. From consideration of the equation
+
W0*.9&)
=
~ ~ n o , , ( gf ) L? Wsos(g)
(6)
for which
-RT In K =
CY
AF10(W,03,)
+
fi
- AF,O(WOi,gs)
(7) it is possible to calculate the standard free energy of formation for the W02.ge phase, AF,0(W02.96), by evalua,ting the equilibrium constant, K = p"(W,03,)/ AFy'(W308)
(20) E. G. King, W. W. Weller, ant1 A. U. Christensen, "Thermodynamics of Some Oxides of Molybdenum and Tungsten," U. S. Dept. of the Interior, Bureau of Mines, Washington, I>. C., 1960.
R. J. ACKERMANN AND E. G. RAUH
2600
TABLE IV STANDARD FREEENERGIES OF FORMATION OF GASEOUS TUNGSTEN OXIDES AF,' = A BT (cal. mole-') (1300-1600°K.)
+
W& w 4 0 1 2
waos
A
B
-655 ,600 -474 ,100
160.29 110.26 90.54 54.98
-400,900 -272,500
W 3 0 8
WZ08
p P ( W 3 0 8 ) , from eq. a through d, Table 11, and the standard free energies of formation of the gaseous species given in Table IV. The results of these calculations are given in Table V. The agreement of the three free energy equations demonstrates good internal
+
A
B
2 3 4 Average values
- 191,100 -191,400 - 192,200 - 191,600
53.70 53.85 54.39 54 00
results given in Fig. 1, 2, and 3 one calculates that the mass effusion rate of W309is approximately 65% of the total measured rate for both W02.96 and W-W02. Furthermore, in both cases the temperature depend~ log I T for W309are nearly identiences of log W T ' /and cal. Therefore, it is possible to estimate sufficiently reliably the partial pressure of W,Og(g), and its temperature dependence, in equilibrium with the systems W02-W18049-vapor, W18049-MT20068-vapor, and W2,,068-Nr02.96-vaporby means of eq. 2 in which M i is the molecular weight of W309(g) and W ~ T "is~0.65 the appropriate value of wT'IZevaluated from eq. b, e, and e of Fig. 1. The standard free energy formation of V t ' 0 2 . 7 2 ( W18049)can be calculated from the partial pressure of W309corresponding to curve b of Fig. 1 [log p(at1-n.) = -27,36O/T 13.291and the standard free energies of formation of W309(g) and WOz(s). The standard (1/20 W2,,OsS)can be free energy of formation of T.I~OZ.~O calculated (1) from the partial pressure of Wa09(g) corresponding to curve e of Fig. 1 [logp(atm.) = -24,960/ T 12.261 and the standard free energies of formation of W309(g)and W02.72(s), or (2) from the partial pressure of W3OS(g) corresponding to curve e of Fig. 1 [log p(atm.) = -23,58O/T 11.621 and the standard free energies of formation of W309(g) and W 0 2 . 9 6 ( 8 ) . The resultant linear equations for all solid tungsten oxides are shown in Table VI. It should be noted that the method of calculation of these free energies is one in which inherent errors are compounded. It is, therefore, estimated that the uncertainty in the values of AF,' is approximately 2 to 5 kcal. mole-l. The relatively good agreement between the two nominal values of AHo and AXo for WOz,go(s)would suggest that any effects of nonstoichiometry or systematic experimental errors are minimal and lie outside the sensitivity of the present techniques of measurement.
+
TABLE V STANDARD FREEENERGY OF FORMATION OF WOz sa(s) CALCULATED FROM Ea. 7 AF,' = A BT (eal. mole-') (1300-1550'K.) n
Vol. 67
+
+
consistency among the free energies of formation of the polymeric trioxides, since the magnitude of the stoichiometric constant /3 is quite small compared to CY and therefore, the free energy of formation of w 0 2 . 9 6 is principally determined by the free energies of formation of the W,Os,(g) and the magnitude of the equilibrium constant. It is instructive to compare the thermodynamic properties of W02.9e(s) with those of stoichiometric trioxide in terms of the partial pressures of the polymeric trioxides in equilibrium with the respective solid phases. From the thermodynamic data given in Tables IV and V and the standard free energy of formation of stoichiometric trioxide [AF,' = - 196,400 56.63T (1200 < T < 17OO0K.)] evaluated from the 0 can show that the compilation of King, et ~ 1 . , ~one partial pressures of the trimer, tetramer, and dimer are factors of 2.6, 2.4, and 1.5, respectively, greater than the partial pressures (eq. a through d, Table 11) corresponding to the solid phase w 0 2 . 9 6 . These results (particularly that of the trimer) are thus in agreement with the experimental observations that the total mass effusion rate decreased by a t least a factor of two and that the intensity of the W 3 0 g + decreased by nearly a factor of three in traversing the change in composition from W O 3 . 0 0 to WO2.96. Although mass effusion data are reported in Fig. 1for the univariant systems W02-W18049-vapor, w18049WzoOci8-vapor, and W2005s-WOz.g6-vapor, these systems were not analyzed mass spectrometrically. If the phases m T 1 8 0 4 g and W2,,058 deviate significantly from stoichiometry as previously suggested,13l5 then an accurate thermodynamic description of these phases cannot be obtained from the data of this investigation alone. However, it is instructive to evaluate from the available information and to make a systematic comparison of the resultant standard free energies of formation of the solid phases WO2.72 (l/lB W18049) and W02.90 ( l / 2 0 W20058). One would hope to detect some evidence of extensive nonstoichiometry from a thermodynamic inconsistency from the following treatment. From the
+
TABLE VI STAXDARD FREEENERGIES OF FORMATION OF SOLID TUNGSTEX OXIDES( 1300-1600'K.) AFfa = AH," - TAS,' (cal. mole-")" Oxide -AH," - AS, W03b 196,400 56 63 wos 98 191,600 54.00 190,900 { 54.27 IT02 90 188,000 \ 53 28 J3'02 72 812,200 52.26 WOzh 137,150 40 00 a The uncertainties in AF,' for W02 and 1%703 are estimated to be from 1 to 2 kcal. mole-1 and for the other oxides 2 to 5 kcal. mole-'. * Equations derived from the compilation of King, et ai.*"
{
Discussion The evaporation behavior of the entire tungstenoxygen system a t 1450'K. as interpreted from the experimental observations is summarized schematically in the phase diagram shown in Fig. 4. The minimum in the pressure represents the congruently evaporating composition w 0 2 . 9 6 which results from the preferential loss of oxygen from the stoichiometric trioxidez1in high vacuum. Although this composition a t room temperature has a crystal structure in many respects similar to (21) The conclusion b y King, et aZ.,*othat "WOa gives a negligible pressure of oxygen a t 2000°K." is based on a calculation of a n assumed decomposition of WOs to WOz. Since these phases do not coexist in equilibrium the calculated pressures are hypothetical.
Dec., 1963
TIIERMODYZTAMICS OF TUNGSTES-OXYGEIY AT HIGHTEMPERATURES
that of the stoichiometric trioxide, there are significant differences,I* however, a t high temperatures it is likely that W02.96represents the lower boundary of a WOs-, solid solution rather than a t,hermodynamic phase physically distinct from W03. The inset of Fig. 4 shows the incongruent evaporation of the W O S - ~phase above approximately 1550"1
