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A high temperature study of the stoichiometry, phase behavior, vaportization characteristics, and thermodynamic properties of the lanthanum+oxygen system
J. Chem. Thermodynamics 1971, 3, 445-460
A high temperature study of the stoichiometry, phase behavior, vaporization characteristics, and thermodynamic properties of the lanthanum+oxygen systemt R. J. A C K E R M A N N
and E. G. R A U H
Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. (Received 2 July 1970; in revisedform 13 January 1971) The lanthanum + oxygen system has been studied by investigating the vaporization behavior of the sesquioxide phase as a function of temperature and composition, employing mass effusion and mass-spectrometric techniques. The partial pressures of LaO(g) over the sesquioxide phase were measured in the presence of tungsten (1933 to 2408 K) and in the presence of rhenium (1778 to 2427 K). The former were greater by 40 to 80 per cent. The congruently vaporizing composition begins to depart from stoichiometry with increasing temperature and at 2400 K reaches values of La202. 980• 0.002in tungsten and La202.938 ~ 0.002 in rhenium, demonstrating a slight reducing effect of rhenium and a measurably greater reducing effect of tungsten. The following thermochemical quantities were determined: AG['(LaO, g, T)/cal tool- 1 = _ 36940 -- I 1.73 T/K, AH~(LaO, g, 0) = -- (28.6 ± 1.0) kcal tool- 1, and D(LaO, g, 0) = (189.9 ~ 1.0) kcal m o l - 1. The partial pressures of La(g) and LaO(g) over the liquid metal + sesquioxide were measured over the temperature range 1516 to 1904 K. The composition of the sesquioxide phase at the lower phase boundary was determined as a function of temperature from 1660 to 1925 K and appeared to depart from the stoichiometric value above 1400 K. At 1925 K the sesquioxide was reduced to La202.82. The standard Gibbs free energy of formation of the substoichiometric oxide at the lower phase boundary was evaluated as a function of temperature; a calculated value of -- 282.9 kcal mol- ~, corresponding to the composition La202.83, is about 16 kcal tool- 1 less negative than that of the stoichiometric sesquioxide, The standard Gibbs free energy change for the isomolecular reaction, La(g) + YO(g) = LaO(g) + Y(g), was redetermined and compared with the dissociation energies of the monoxides evaluated from the thermochemical data.
1. Introduction The l a n t h a n u m + o x y g e n s y s t e m at first g l a n c e seems r a t h e r simple, t h e o n l y t h e r m o d y n a m i c a l l y stable solid o x i d e b e i n g t h e sesquioxide. (1) M i x t u r e s o f t h e m e t a l a n d sesquioxide h a v e f a i l e d to p r o d u c e a stable solid m o n o x i d e (2) a l t h o u g h a d i f f r a c t i o n pattern f r o m a f.c.c, lattice a n d a s c r i b e d t o L a O has b e e n r e p o r t e d in a h y d r i d e study. (a~ Other l a n t h a n i d e a n d a c t i n i d e m o n o x i d e s h a v e b e e n o b s e r v e d (4~ f o r t h e m o s t p a r t as films or stabilized b y o t h e r c o m p o n e n t s . O n l y E u O has b e e n p r o d u c e d in m a c r o s c o p i c t Work performed under the auspices of the U.S. Atomic Energy Commission.
446
R.J. ACKERMANNAND E. G. RAUH
quantities.(5, 6) The solubility of oxygen in solid lanthanum metal is apparently quite small since the I~---ry transformation at 1137 K is unaffected by oxygen, (~'z) unless the periods of observation were insufficiently long to effect the saturation of the metal by oxygen. The solubility of the oxide in the liquid metal is not known, and due to a rather extensive liquid range (the melting temperature is 1193 K) (v) some of the conventional quenching techniques following saturation at a given temperature may not yield reliable solubilities due to extensive precipitation of the dissolved oxide. (s) A previous investigation by Goldstein, Walsh, and White(9) of the vaporization behavior of lanthanum sesquioxide by means of the effusion method (tungsten cells) established both the principal mode of vaporization: La/O3(s) = 2LaO(g) + O(g), (1) and the thermochemical properties of LaO(g). These authors observed that constant rates of vaporization were obtained after the composition of the sesquioxide phase became La202.96. The temperature(s) at which this composition was obtained was not reported. However, this relatively small sub-stoichiometry was considered insignificant to the thermochemical assessment, and the sesquioxide was assumed to vaporize congruently in accordance with equation (1) at all temperatures. More recent measurements of reaction (1) by Benezech and F6ex (1°) using the transpiration method and solar heating yield vapor pressures that are larger by a factor of 3. An earlier study of the high temperature equilibrium: LazO3(s)+La(g) = 3LaO(g), (2) by Chupka, Inghram, and Porter (~1) was carried out by analyzing mass-spectrometrically the two vapor species effusing from mixtures of the metal and sesquioxide phases contained in an effusion cell. The assumption was made that the compositions of both phases remained invariant and hence did not depart significantly from unit activity. Isomolecular exchange reactions of the type MO(g)+ La(g) = M(g)+ LaO(g) have been used to derive the thermodynamic properties of transition metal and lanthanide metal monoxides based on the existing data for LaO(g), La(g), and M(g). (12' 23) These studies of the reaction involving yttrium have shown a discrepancy of 6 kcal mol -~ in the measured enthalpy change derived from measurements of the temperature dependence of the equilibrium constant. There now exists considerable evidence which shows that the congruently vaporizing compositions and the thermodynamic properties of several refractory binary compounds, UOz, (1.' ~5) PuO2,O6) ZRO2,(17) and YzO3,(~8) are substantially different from those at the lower phase boundary, i.e. the composition in equilibrium with the metal phase, and neither corresponds to the ideal stoichiometric composition of the so-called compound. The existence of a single gaseous molecule in the La + O system, in contrast to the systems cited above, greatly simplifies the evaluation of thermodynamic properties from measurements of vapor pressure. By means of mass effusion and massspectrometric techniques, the vaporization behavior, phase equilibria, and thermodynamic properties of lanthanum + oxygen have been re-examined and extended to remove existing discrepancies and to include the determination of the Gibbs free energy of formation of lanthanum sesquioxide at its lower phase boundary.
THERMODYNAMICS OF La + O
447
An intercomparison of the thermodynamic properties of lanthanum+oxygen and yttrium+ oxygen is presented, including a critical examination of the isomolecular exchange reaction: La(g)+YO(g) = LaO(g)+V(g). (3)
2. Experimental methods and results Mass-spectrometric and mass effusion measurements were made on lanthanum sesquioxide and the two phase system, La(1)+La2Oa(s). The Bendix time-of-flight mass spectrometer, the mass effusion method, and the experimental techniques for each have been described elsewhere. (19~ La203 In order to establish the lower phase boundary of the sub-stoichiometric lanthana La203_x, isopiestic measurements of the type described previously 05~ were performed over the temperature range 1660 to 1925 K. In this procedure a sample of the oxide is equilibrated with the vapor arising from a saturated mixture of the metal and oxide inside a closed container and subsequently analyzed for the mole ratio of O to La by combustion to La203 at 1573 K. The combustion of a 700mg sample of metal containing 910 p.p.m, of oxygen yielded, at this temperature, an increase in mass consistent with the formation of the stoichiometric sesquioxide. The results and a linear least-squares representation of the results in terms of mole fraction of dissolved La in La203 are given in table 1 and are shown in figure 1. A comparison of these results with those obtained previously for YzO3_(~8) is also seen in the figure. The congruently vaporizing composition of sesquioxide from a tungsten effusion cell at 2400 K was determined by evaporating about 20 per cent of a 1 g sample and subsequently analyzing the grayish-black residue by oxidation to white stoichiometric La203 at 1573K. Two such determinations were made. A third determination at 2400K was made on a mixture of 1200mg of La203 and 62mg of lanthanum metal, corresponding to a starting composition of La202.8. The results of the three measurements established the congruently vaporizing composition at 2400 K at La202.980 ± o.oo3. Samples heated in vacuo at 2275 K for 7 h and at 2050 K for 15 h yielded the compositions, La202.992 and La202.998, respectively. Similar measurements made with a rhenium cell yielded, at 2427K, the apparently sub-stoichiometric composition, La202.998 ± o.0o2, showing considerably less reduction of the sesquioxide by rhenium. TABLE 1. The composition of the lower phase boundary of LaaO3- z at temperature T given as the mole ratio n(O)/n(La) and also as the mole fraction x(La) of lanthanum dissolved in stoichiometric La20a
T/K
n(O)/n(La)
x(La)
T/K
n(O)/n(La)
x(La)
1661 1734 1792
1.461 1.455 1.433
0.051 0.058 0.085
1844 1844 1923
1.427 1.421 1.411
0.093 0.099 0.112
logic {x(La)} = (1.21 ~ 0.33) -- (4125 =k 600)K/T
(la)
448
R. J. A C K E R M A N N A N D E. G. R A U H i
i
i
1
[
1
1
1
1
2100 2000 ~d 1900
1800
1700 1600 I
1.40
I
I
r
1
I
1.45 n (O) / n (M)
I
I
I
1.5
FIGURE 1. Variation with temperature of the composition (mole ratio) of the lower phase boundary of lanthana compared with that of yttria. (18> O O, La2Oa- ~; x ×, Y2Oa2 x.
Mass-spectrometric observations on the vaporization behavior of La20 3 in a tungsten cell were made on a 1.1 g sample of the sesquioxide in the form of a cup that had been sintered previously in vacuo for 1 h at 2400K. The sample was heated initially to 2160 K for 24 h. The vapor was almost entirely LaO; no tungsten oxide ions and only a trace ( < 0.1 per cent) of La + were observed. For all observations an ionizing electron energy of 11 eV was used in order to eliminate the formation of La + ions from the fragmentation of LaO; this was established by an appearance potential measurement of the type described previously.(2°) I" The temperature dependence of the LaO ÷ ion current was measured at the end of the 24 h period and after 42 and 48 h at this temperature. The results for each of the three series of measurements were fitted to a straight line by the method of least squares, and the average enthalpies of vaporization, (147.0+2.1), (149.5+ 1.5), and (149.74-1.7) kcal mo1-1, were calculated from the slopes. A closer examination of the plotted values and the residuals revealed a slight positive curvature that suggested a variation of pressure with composition as well as temperature that could be correlated with the measured departure from ideal stoichiometry. Since the average values agreed within the standard deviations, only the results of the second series, covering the temperature range 1933 to 2312K, are reported in section 1 of table 2. The results for a similar series of measurements from a rhenium cell, from which an average enthalpy of vaporization of (139.5 4- t.1)kcal tool -1 was calculated, are given in section 3 of table 2. Again a closer examination of the values reveals a slight positive curvature with increasing temperature. t Throughout this paper eV = 96487 J mop 1, atm = 101.325 kN m- 2, and cal = 4.184 J.
449
T H E R M O D Y N A M I C S OF La + O TABLE 2
SECTION 1: Mass-spectrometric results for the evaporation of La203 from a tungsten cell. Ion currents I(LaO +) in arbitrary units
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
2152 2028 1969 1933 2004
5.25 0.710 0.266 0.136 0.435
2039 2112 2217 2189 2154
0.93 2.98 15.1 10.2 5.4
2038 2058 2076 2186
0.89 1.26 1.68 9.4
T/K 2209 2227 2278 2312
I(LaO +) 14.0 18.6 39.0 74.0
SECTION 2: Mass effusion results for the evaporation of LaaOa from a tungsten cell with orifice area 3.33 × 10 -2 cm 2 and Clausing factor 0.40
T/K
W × 104 gem- 2 s. 1
T/K
W × 104 gem- 2 s- 1
2324 2323 2372
2.40 2.48 4.48
2374 2210 2258
4.91 0.51 1.06
T/K
W / 104 gem- 2 s- 1
T/K
W × 104 gcm_ 2 s- x
2309 2347
2.09 3.38
2408 2381
9.46 5.08
Least-squares representation ofp(LaO) over the sesquioxide in tungsten, combined mass effusion and normalized mass-spectrometric results: log10 {p(LaO)/atm} = (12.311 ~ •.679) -- (4.539 ~ 0.728) × 104K/T +
+ (0.139 :~ 0.079) / 108(K/T) 2.
(2a)
SECTION 3: Mass-spectrometric results for the evaporation of La2Oa from a rhenium cell. Ion currents l(LaO +) in arbitrary units
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
1778 1856 1924 1994
0.0056 0.0265 0.0850 0.304
2084 2•85 2308 2292
1.28 6.30 36.5 31.0
2237 2127 2033 1958
14.2 2.46 0.625 0.180
1900 2033 2144 2242
0.066 0.585 2.50 15.1
SECTION 4: Mass effusion results for the evaporation of La2Os from a rhenium cell with orifice area 2.23 × 10 -2 cm 2 and Clausing factor 0.41
T/K
W × 104 g c m -2 s - i
2374 2389
2.73 3.47
T/K
W × 104 g e m -2 s-Z
T/K
W × 10 ~ g cm -2 s-1
T/K
W × 10a g c m -~ s-1
2321
1.76
2427
5.44
2258
0.53
Least-squares representation ofp(LaO) over the sesquioxide in rhenium, combined mass effusion and normalized mass-spectrometric results: log10 {p(LaO)/atm} = (12.453 -4- 1.048) -- (4,794 -~ 0.427)104K/T + (0.177 ~ 0.043)I08(K/T)L
(2b)
450
R.J. ACKERMANNAND E. G. RAUH
Mass effusion measurements on La203 were carried out in both tungsten and rhenium cells. In order to circumvent the effect of non-cosine distribution of the effusate at low angles from a knife-edge orifice as described by Ward and Fraser, (21) channel-shaped orifices were used, the dimensions and Clausing factors for which are given in table 2. In general, the cell and its contents were held at a selected temperatur6 in the range 2210 to 2427K until the rate of effusion became constant. The results for both tungsten and rhenium cells are given in sections 2 and 4 of table 2. Since LaO(g) and O(g) are the only vapor species present, their partial pressurespi can be calculated from the mass effusion results using the equation: Pi = ZiG(2nMiRT) ÷,
(4)
in which Z i is the molar effusion rate (Wi/Mi) and G is the appropriate geometry factor. The numerically small departures from ideal stoichiometry were not considered since the effect on the magnitude of the coefficients in equation (1) is quite small. Furthermore, if the contribution of oxygen to the mass effusion rate is totally ignored, the calculated values ofp(LaO) are only 5 per cent larger. The two series of mass-spectrometric results, given in table 2, were normalized to the corresponding effusion pressures in the following manner. A three-parameter leastsquares equation was fitted to each series of mass-spectrometric results and a normalizing factor was determined from each of the corresponding pressures calculated from the results in sections 2 and 4. The least-squares equations and the average normalizing factors were combined to yield equations (2a) and (2b) in table 2. The plots of these equations in figure 2 demonstrate a systematic difference in vaporization behavior. The pressures of LaO(g) over stoichiometricallyvaporizing LazOa were calculated from the Gibbs free energies of formation of LazOa(s), O(g), and LaO(g) via equation (1). The standard Gibbs free energy of formation of LazO3(s) was calculated from the enthalpy of formation reported by Huber and Holley(za) and confirmed by Fitzgibbon, Holley, and Wadsoe(23) and the enthalpy and Gibbs free energy functions of La2Oa(s) given by Goldstein et al., (24) and Yashvili and Tsagareishvili, (zS) of atomic oxygen compiled by Stull and Sinke, (zc) and of La(s or 1) compiled by Hultgren et al. (7) Over the temperature range 1600 to 2400 K, AG~(La2Oa,s) can be expressed adequately by a linear equation: AG~(La203, s, T)/cal mol- 1 = _ 425 710 + 66.14 T/K.
(5)
The standard Gibbs free energy of formation of LaO(g) was obtained from the results for the rhenium cell, equation (2b), at 1900 K where the composition of the solid phase is negligibly sub-stoichiometric and consequently the partial pressures of LaO(g) and O(g) are related by the equation, p ( O ) = 0.161p(LaO). The value obtained is AG~(LaO, g) = - 59220 cal mol -I. The temperature dependence of this quantity was calculated from the Gibbs free energy functions for molecular oxygen, (26) solid and liquid lanthanum, (7) and those for LaO(g) which were calculated from the molecular constants and spectroscopic data of Akerlind, (zT) which correspond to the 22 ground state(2s) instead of 4Z,(29) and the low-lying states zA3/z and 2As/2 recently identified by Green. (a°) Derived absolute entropies and Gibbs free energy and enthalpy functions, including anharmonicity corrections, are given in table 3. Previously reported values °3)
THERMODYNAMICS OF La + O
451
TABLE 3. Absolute entropies, and Gibbs free energy and enthalpy functions for LaO(g)
S°(T) T/K
cal K- ~ tool- 1
1800 2000 2200 2400 2600
72.62 73.60 74.51 75.37 76.17
-- {G°(T) -- H°(O)}/T cal K- 1 tool- 1 64.17 65.07 65.88 66.65 67.36
IF(T) --/-/°(0) cal mol- ~ 15220 17080 18980 20920 22900
were calculated f r o m the g r o u n d state only. The Gibbs free energy o f f o r m a t i o n o f LaO(g) is adequately represented by the linear equation, AG~(LaO, g, T)/cal m o l - 1 = _ 3 6 9 0 0 - 1 1 . 7 3 T/K,
(6)
over'the range 1600 to 2400 K. Therefore, the partial pressure p(LaO) o f LaO(g) over stoichiometric La203 is given by, log~o{p(LaO)/atm} = - 30090 K / T + 7.96,
(7)
and is plotted for comparison in figure 2.
T/K 2400 2200
2000
1800
1600
-3.0
N \\
"~ --
equation (7),~ ~ ,
, 0 ove,°
~ ~
\
-7.0
.......
\~xb, ' ~
....
~kb~.fe_quatlon" ~ ~ p(LaO)over ' ~ (2-a) " ~ Xe~La+ La203 ~ p(LaO)over"~ No
~Laps-~(W) \
\
equation { 2 - b ) , - - - - - ~ . . . . . ~ p'(LaO) over "%,N ~ ~k L ~ ) N~xequation (4-d)~ N \
- 8.0
-9'03 5 •
4.0
4.5
5.0 5.5 104 K/T
6.0
6.5
7.0
FIGURE 2. Logl0(pdatm) against 10~K/T for lanthanum + oxygen• Equations (2a) and (2b) p(LaO) over congruently evaporating lanthana in tungsten and rhenimn, respectively; equation (7), calculated p(LaO) over stoichiometric sesquioxide; equation (8), the vapor pressure p°(La) of liquid lanthanum; equations (3d) and (3e), p(La) and p(LaO), respectively, over the two phase system lanthanum + lanthana. 0 , Mass effusion; ©, mass-spectrometric.
452
R.J. ACKERMANN AND E. G. RAUH
The enthalpy of formation of LaO(g) at T = 0, AH~(LaO, g, 0) = (28.6+ 1.0)keal mol-1, is calculated from equation (6) and the Gibbs free energy functions cited above. From this value of AH[(LaO, g, 0), AH~(La, g, 0) = 102.3 kcal mol -~1 (given later), and ½D(O2, 0) = 59.0kcalmol-1, ~31~ one calculates a value of the dissociation energy of LaO(g) at T = 0: D(LaO, g, 0) = (189.9_+ 1.0) kcal m o l - t = (8.24+ 0.04) eV. La(1)+ La203 Mass spectrometric observations on the two phase system: liquid lanthanum+ lanthana, were made on a sample prepared by adding 75 mg of metal to the same lanthana cup that had been used in the previous mass-spectrometric measurements. Both LaO + and La + were observed in the approximate ratio of 3/1 at an ionizing electron energy of lleV. The sample was held at 1810K for a total of 30h. The temperature dependences of the abundance of both ions over the range 1516 to 1870 K were measured 9, 25, and 30h at the set temperature; the enthalpies of vaporization calculated from least-squares analyses of the results were, successively, AH,~(LaO) = (105.9 + 0.3), (107.5 + 0.6), and (106.9_ 0.2) kcal mol-1, and AH~(La) = (94.2__+0.3), (95.8_0.6), and (95.4_ 0.4) kcal mo1-1. The results for the last series are given in section 1 of table 4 with the least-squares representations. Mass effusion measurements of the two-phase system were made on a sample which consisted of 1 g of lanthanum metal added to the same lanthana cup used in the previous mass effusion measurements. The results covering a temp ...... re range of 1713 to 1904K are given in section 2 of table 4, with a linear least-s ..s equation, equation (4c), calculated therefrom; the quantity p~ is that pressure calculated from equation (4) by assuming the vapor to be entirely LaO(g). The vapor pressure-temperature relation for pure lanthanum was derived from the average of the vapor pressures at 2000 K reported by Ackermann and Rauh (19~ and Habermann and Daane (3z) and the absolute entropy at 2000K given by Hultgren et aL ~7) The resulting equation is log1 o{p°(La)}/atm = - 21620 K I T + 5.86, (8) and is shown plotted in figure 2. We estimate an uncertainty of + 20 per cent in the pressure. The derived enthalpy of vaporization at T = 0 is (102.3-t-1.0)kcalmo1-1, and in the temperature range of the present investigation (98.9+l.0)kcalmo1-1, which is to be compared with the enthalpy of vaporization of lanthanum saturated with oxide, (95.4+ 0.4) kcal mo1-1, calculated from equation (4d). The normalization of the mass-spectrometric results in table 4 to yield partial pressures pl of La(g) and LaO(g) requires a knowledge of the instrumental sensitivities k i of these species in accordance with the expression, Pi ~ IiT/ki. Because of the relatively large uncertainties and the limited temperature range in the mass effusion measurements, the previously cited methods (33' 34) for the evaluation of the relative instrumental sensitivities could not be applied. However, Ames et aL (xa) report a value of k(La)/k(LaO) = 1.7 which permits the evaluation of the ratio of the partial pressures, p(La)/p(LaO), from equations (4a) and (4b). The relation between the "effective" pressure and the individual partial pressures is p~ = p(LaO)[1 + {M(LaO)/M(La)}~{p(La)/p(LaO)}].
(9)
453
THERMODYNAMICS OF La + O
TABLE 4 SECTION I: Mass spectrometric results for the evaporation of La q- La203. Ion currents I in arbitrary units
T/K
I(La +)
I(LaO +)
1813 1702 1623 1544 1516
4.95 0.910 0.246 0.056 0.031
17.8 2.74 0.615 0.119 0.062
T/K 1579 1664 1756 1835 1870
l(La +)
l(LaO +)
0.112 0.475 2.12 6.60 I0.0
0.252 1.31 6.95 25.0 41.5
loglo {I(La+)T/K } = -- (20850 ± 90)(K/T) q- (15.44 :~ 0.06), loglo {I(LaO+)T/K } = -- (23360 ± 50)(K/T) + (17.39 ~ 0.03),
(4a)
(4b)
SECTION 2: Mass effusion results on the evaporation of La -]- La203 W × 105
W × 105
T/K
g cm_as_ x
T/K
1773 1786 1810
2.93 4.46 7.11
1804 1750
g cm_2s_ i 6.60 3.09
W x 105
T/K
g cm_2s_ ~
T/K
1904 1902
22.1 23.6
1848 1713
W × 105 g cm_2s_ 1,
11.0 1.38
loglo {po/atm } = -- (21000 ± 980)(K/T) + (6.30 ~ 0.54). (4c) Least-squares representation of the normalized mass-spectrometric results on the evaporation of La + La203: loglo {p(La)/atm } = -- (20850 =~ 90)(K/T) + (5.35 ~ 0.08), (4d) log~o{p(LaO)/atm } = -- (23360 i 50)(K/T) + (7.53 ~ 0.08). (4e) From this equation and the ratio p(La)/p(LaO) the partial pressures o f La(g) and LaO(g) were calculated at each temperature o f measurement o f Pc. The results are given by equations (4d) and (4e) in table 4 and are plotted in figure 2. T h e p a r t i a l pressure o f La(g) in equilibrium with La(1)+ LazO3(s), equation (4d), is shown to be less than the vapor pressure o f pure liquid lanthanum, equation (8), at all temperatures but tends towards the latter at the lowest temperature suggesting that the solubility o f the oxide in liquid l a n t h a n u m becomes insignificant below approximately 1600 K. The results o f this study therefore appear to be quite consistent with the instrumental sensitivities reported by Ames et aL °3) La(g) + YO(g) = LaO(g) ~- Y(g) The mass-spectrometric measurements o f the isomolecular exchange reaction given by equation (3) were carried out on two samples of widely differing constitution. The first sample consisted o f 370 m g each of L a 2 0 3 and Y203 in the form o f a small cup in which was placed 80 m g of each metal. The second consisted o f 56 mg o f Y203, 50 m g of Y, and 27 mg o f La contained in a single crystal tantalum cup. The measured ion currents in the two cases differed considerably; in the former the intensities were always in the order L a O > La > Y > Y O whereas in the latter Y > La > L a O > YO.
454
R.J. ACKERMANN AND E. G. RAUH
The equilibrium constant for reaction (3) in terms of partial pressures Pi, ion currents li, and instrumental sensitivities ki is
Kv = {p(Y)p(LaO)}/{p(YO)p(La)} = [{I(Y)I(LaO)}/{I(YO)I(La)}][{k(La)k(YO)}/{k(LaO)k(Y)}].
(10)
The relative instrumental sensitivities, k(La)/k(LaO) = 1.7 and k ~ ) / k ( Y O ) = 1.5 are those given by Ames et aL °3) The results of the measurements of Kp at various temperatures in the range 1783 to 2184 K are shown in figure 3. The agreement between the two sets of values suggests that both samples lie in a bivariant region of the phase diagram where the (Y, La)
T/K" 2200
2100 J
2000 --
1900
I
1800
r
I
2.4 "q
2.3 ~" 2.2 e~
+ ~++ •
o•o/"
2.1 2.0 1.9 1,8
I
4.6
4.7
4.8
4.9
5.0 5.1 104 K/~r
5.2
5.3
I
t
5.4 5.5
t
5.6
FIGURE 3. LogioK, against 104KIT for the isomolecular reaction: La(g) + YO(g) = LaO(g) + Y(g). +, First sample; ©, second sample. - - , logloK, = -- (0.506 -t- 0.047) + (5260 i 90)KIT. liquid phase coexists with a (Y203, La203) phase; the vapor compositions can vary at constant temperature and still represent the equilibrium state of the system. A leastsquares treatment of the results yields the equation for the change in standard Gibbs free energy of equation (3) as a function of temperature,
AG~ = - R T l n K v
= {-(24070-t-410)+(2.32___0.22) T/K} calmol ~1.
(11)
As previously cited, the mass-spectrometric observations were carried out using 11 eV ionizing electrons in order to minimize fragmentation of monoxide species. The effect of fragmentation was particularly noticeable in the first of the two samples for which the intensity of the LaO was greater, by a factor of about three, than the La intensity. For ionizing electron energies of 25 eV the measured equilibrium constant was approximately one-half that measured at 11 eV. For the second sample this effect was not observed. The explanation of this behavior can be seen from the relative ion
THERMODYNAMICS OF La + O
455
intensities and from equation (10). If the intensity ofMO ÷ is greater than or comparable with M +, fragmentation of MO + will increase the observed intensity of M+, but little or no measurable effect will be observed when M + > MO +.
3. Discussion The difference between the thermodynamic properties of LaO(g) reported herein and those previously given by Ames et al. (13) is due principally to the reduction of the oxide by the tungsten effusion cell used in the earlier study. For example the dissociation energy of LaO(g) reported in the earlier study was 193.2kcalmol -~ compared with the value (189.9 + 1.0)kcal mo1-1 reported in the present study. The role of chemical reduction played by the tungsten is represented by the difference in equations (2a) and (2b) and the correlated change in the congruently vaporizing composition with temperature which effectively causes a decrease in the partial pressure of oxygen and an increase in the partial pressure of LaO(g) as is seen in the equilibrium constant for equation (1), Kp = {p(LaO)}Zp(O). Thus the experimental results indicate that the partial pressure of oxygen is rather sharply dependent on the composition variable near the stoichiometric sesquioxide. The thermodynamic data for LaO(g) derived from the measurements ofp(LaO) using the rhenium cell which can be considered inert at temperatures less than about 2250 K are internally consistent with the total vaporization behavior of the system. Equations (5) and (6) may be used to calculate the partial pressure p°(LaO) in equilibrium with pure liquid lanthanum a n d stoichiometric sesquioxide according to the reaction, ½LazOa(s, a = 1)+½La(1, a = 1) = LaO(g). (12) The resultant values are approximately 20 per cent greater than these calculated from equation (4e) which corresponds to the mutually saturated two phase system. The activity of the component (La203) in LazOa - , at the lower phase boundary at 1800 K, where the mole fraction of La203 is 0.9, is a(La203) = p(LaO)3/{a(La)p°(LaO) 3} ~ 0.7 which suggests a small negative deviation from ideality. On the other hand, the use of the measured values for p(LaO) obtained via the tungsten cell gives rise to a Gibbs free energy of formation of LaO(g) that is approximately 2.5 kcal mol- x more negative and leads to a value of a(La203) g 0.1, which is unreasonably small. Furthermore, the isomolecular reaction, equation (3), can be used to derive the Gibbs free energy of formation of LaO(g) from the known values for y(g),(ls) YO(g),(zo) and La(g) from equation (8). The resultant quantity is consistent within experimental uncertainty (1 to 2kcalmol -~) with the mass effusion results obtained from the La203(Re) system but not with those from the La2Oa(W) system. The mechanism of the reduction of LazO a by tungsten is not completely understood. The effect of the reduction is to increase the measured partial pressure of LaO(g) by approximately 60 per cent buf no corresponding volatile oxides of tungsten were observed. Actually a number of earlier studies have reported definite evidence of "reaction" between La2Oa and tungsten. Ackermann and Thorn (35) have reviewed the earlier work, and Goldstein, Walsh, and White(36) report that 0.1 tool of tungsten per mole of La/O a is vaporized. From the absence of any tungsten containing vapor species effusing through the orifice it was concluded that the oxygen diffuses into the
456
R.J. ACKERMANN AND E. G. RAUH
massive tungsten effusion cell and subsequently vaporizes from the relatively large exterior surface. A more pronounced example of this behavior and its interpretation has been observed in the case of tantalum cells. (37) It is known that tantalum will dissolve substantial amounts of oxygen at high temperatures, (3s) and the evidence of the present study suggests that tungsten and oxygen also form a stable solid solution. Inspection of equation (7) and equation (2b) in figure 2 suggests that at temperatures above 2300 K rhenium also becomes somewhat reducing. The earlier study by Chupka e t al. (11) of the equilibrium given by equation (2) provides a useful basis of comparison and discussion with the present study. A systematic difference was observed by these investigators between mixtures of La(1, excess) + La203(s ) and La(1) + La203(s, excess), the former yielding partial pressures of La(g) approximately a factor of three greater than the latter. The former system yielded values of the partial pressures of both LaO(g) and La(g) that are in close agreement with those of the present study after a correction for the relative instrumental sensitivities is made. Two explanations were offered to account for the factor of three. The first involved the formation of a LaO solid phase. This explanation was discarded because X-ray diffraction studies showed no evidence of a new phase in the residue of the vaporization studies. The second explanation suggested a diffusion process resulting from the covering of the liquid metal phase by the excess of the oxide. The results of the present study offer a third and perhaps more likely explanation, namely, the reaction of all the lanthanum metal with the excess oxide to form a sub-stoichiometric sesquioxide having a composition lying to the right of the phase boundary shown in figure 1, that is, only a single phase may have been present. The partial pressure of LaO(g) is seen from equations (7) and (4e) in figure 2 to increase more than a thousand-fold as the composition of the sesquioxide changes from stoichiometric to that at the lower phase boundary. Even a small sub-stoichiometric departure from the ideal sesquioxide composition produces an increase in the partial pressure of LaO(g) and this effect is seen by comparing equation (7) with equations (2b) and (2a). The apparent increase in the enthalpy of vaporization {equations (2b) and (2a)} with increasing temperature and increasing sub-stoichiometry is numerically opposite to that reported by Goldstein e t al. (9) Their mass effusion data at higher temperatures yield an enthalpy of vaporization of LaO(g) of (130.9___ 4.7) kcal mol-t whereas at lower temperatures their mass-spectrometrically determined value is (139.5 4.2) kcalmo1-1. The vapor pressure of liquid lanthanum is reduced by the presence of oxide as is seen from the plot of equations (8) and (4d) of figure 2. However, the difference between these curves suggests that the solubility of La203 in liquid lanthanum is smaller than the corresponding effect in the yttrium+ oxygen system. °s) It should be pointed out that the measured enthalpy of vaporization of La(g) from the two phase system, La(1) + La203(s), equation (4d), is smaller by (4.5___1.1) kcal mol-1 than that for the system of pure liquid lanthanum (equation (8)) demonstrating that the effect, though smaller, is nevertheless real. The standard Gibbs free energy of formation of the sub-stoichiometric sesquioxide phase at the lower phase boundary can be evaluated from the reaction: La203_x(S)+(1-x)La(g ) = (3-x)LaO(g), (13)
THERMODYNAMICS OF La + O
457
and the equation:
AG~(La~O~-x) = ( 3 - x)R r In {p(LaO)} + (3 - x)AG°f(LaO, g ) - (1 - x)R T In {p(La)} - (1 - x)AG~(La, g).
(14)
The partial pressures of LaO(g) and La(g) are given by equations (4e) and (4d); the standard Gibbs free energies of formation of LaO(g) and La(g) are calculable from equations (6) and (8). At a temperature of 1750K the value of x in equation (13) is 0.11 as seen from the data in table 1. The calculated value of AG~(La202.89) !s _300.3kcalmo1-1 which appears to be numerically reasonable since it is more negative than that, - 2 9 8 . 6 kcal t o o l - a obtained from a linear interpolation between the integral molar Gibbs free energies of the pure metal, AG~ = 0, and stoichiometric LazOa, AG~ = - 3 1 0 . 0 kcal tool -1, equation (5). That is to say, the Gibbs free energy of formation of single phase La202.89(s ) from 0.074mol of lanthanum metal and 0.963 tool of LazO3(s) is approximately - 1.7 kcal tool-1. Inspection of equation (14) indicates that errors in the two terms which are multiplied by the quantity (3 - x) have
n(O)/n(La) of lower phase boundary 1.5 /[- i
1.49 1.48 1.47 1.46 t
t
i
~
1.44" i
[
1.42 I
J
1.40 J
I
/- /
27O 7'
280 t
~
-
I 31o
L o3
320
330 z ~ : : ~ ' ' ~ 340 I i 1400
i 1500
l 1600
~ 1700
i 1800
r 1900
2000
T/K FIGURE 4. Comparison of the standard Gibbs free energies of formation as a function of temperature of the lanthanum sesquioxide phase at ideal stoichiometry and at its lower phase boundary. the greater influence on the numerical value of AG~(La203-x). An error of 20 per cent in the measurement o f the partial pressure of LaO(g) given by equation (4e) generates an error of 2kcal tool -1 in the Gibbs free energy of formation and an uncertainty of 1 keal tool -1 in AG~(LaO) generates nearly 3 kcal tool -1. Hence, the numerical values calculated from equation (14) and shown in figure 4 have uncertainties that may be several kcal mo1-1. Such an error, of course, is large by calorimetric standards, but on the other hand, direct calorimetric studies of sub-stoichiometric materials such as La2Oa-x would be quite difficult to perform; quenched samples are generally difficult to obtain since they rapidly disproportionate at lower temperatures to mixtures of
458
R.J. ACKERMANN AND E. G. RAUH
metal and oxide, as was the case in the present study. The composition of the lower phase boundary approaches the stoichiometric composition below about 1450 K, as seen from figure 1, and the standard Gibbs free energy shows parallel behavior. A summary of the present and previous results of the measurements of the iso. molecular reaction, equation (3), is given in table 5. The first and third columns give t h e enthalpy of reaction at the absolute zero of temperature and the entropy change at 2000 K derived from t h e experimental measurements via the so-called second-law method. The second and fourth columns give the same quantities via the so-called third-law method as defined in the footnotes of the table. The value in the fourth column has been calculated from the absolute entropies of the gaseous metals taken TABLE 5. Comparison of thermodynamic quantities of the isomolecular reaction: La(g) q- YO(g) = LaO(g) -t- Y(g), obtained in the present study with those of previous studies -- AH°(0, II): kcal mol- 1
-- AH°(0, III)b kcal mol- 1
AS°(2000K, II) cal K- 1 mol- ~
16.5 :d: 2.7 22.7 q- 1.0 21.4 ± 0.4
19.3 -4- 0.7 19.6 ± 0.2 19.6 ± 0.1 21.1 :k 1.5~
-- 0.40 -- 3.7 ± 1.4 -- 2.32 ± 0.22
AS°(2000K, III) cal K- ~mol- 1 "~ ) - - 1.4
Reference
12 13 This study = Do(YO)(2°) -- Do(LaO)
a AHo(0,II) = AH°(T) -- A {H°(T) -- H°(0) }. b AHO(0,I I I ) = AG°(T) -- A (G°(T) -- H°(0) } = -- R T l n Kp -- A {G°(T) -- H°(0) ]. c Computed from the results in reference 12. a The error is estimated from uncertainties of • 1 kcal mol- 1 in each value of D0(MO); all other errors are standard deviations. from the compilation of Hultgren e t aL, (7) of YO(g) from the thermal functions given by Ames e t aL, O3) and of LaO(g) from table 3. The last entry in the second column is the enthalpy of the reaction calculated from the difference of the dissociation energies of YO(g) (2°) and LaO(g) obtained in the present study. The error quoted is that which is consistent with an uncertainty of + 10 to _ 15 per cent in each of the Vapor pressure measurements. The isomolecular reaction is a very sensitive method for measuring this difference in dissociation energies and is also quite accurate insofar as the relative instrumental sensitivities of monoxide to metal cancel in equation (10). The relatively more precise measurements of the present study reduce the nominal discrepancy between the second-law and third-law values to less than 2 kcal mo1-1. The agreement of the present results with those of the previous studies, with the exception of the value of AH°(0, II) of Smoes e t aL, (12) is generally good and demonstrates that equilibrium can be achieved under a variety of experimental conditions. The thermodynamic and molecular properties of the oxides of the Group III transition metals have been intercompared previously (2°) and show the relatively greater stability in the vapor phase of the + 2 valence state of lanthanum compared with yttrium. This fact is quantitatively reflected in the results in table 5, notably by the negative values in the second column. The difference in the vaporization behavior
THERMODYNAMICS OF La + O
459
of mixtures o f La(1)+LazO3(s) and Y(1)+Y203(s) is due largely to the relatively greater stability o f LaO(g); in contrast to the results o f this study, the partial pressure of YO(g) is unimportant above liquid yttrium saturated with its oxide. (18) However, the + 3 valence state o f yttrium in the solid phase is more stable in view o f the m o r e negative Gibbs free energy o f formation o f the sesquioxide. The extent o f the departure of both sesquioxides f r o m ideal stoichiometry appears to be related to these trends in that at the lower phase b o u n d a r y the La203 phase at a given temperature is substantially more easily reduced than Y2Oa, as seen in figure 1, suggesting that the + 2 valence state o f l a n t h a n u m is also relatively more stable in th~ solid phase. The behavior of both phases is similar with respect to deviation f r o m non-ideality. The metal component shows a strong positive deviation f r o m R a o u l t ' s law. The partial pressure o f La(g) increases by a factor o f 109 at 1900K as the composition o f the sesquioxide changes f r o m stoichiometric to La202.82, The authors are grateful to M r R. R. Waiters, formerly o f the Chemistry Division, for his assistance in carrying out some o f the experimental measurements.
REFERENCES 1. Eliott, R. P. Constitution of Binary Alloys, First Supplement, McGraw-Hill Book Company, New York, 1965. 2. Daane, A. H.; Spedding, F. H. U.S. At. Energy Comm. Rep. ISC-530, 1954 (declassified 1955); quoted by Gschneider, K. A., Jr, Rare Earth Alloys, D. Van Nostrand Company, Inc., Princeton N.J., 1961, p. 251. 3. Korst, W. L.; Waft, J. C. Abstracts of Papers for the 129th Meeting, American Chemical Society 4Q, April 1956. 4. Westrum, E. F. Jr.; Lyon, W. G. In Proceedings of a Symposium on Thermodynamics of Nuclear Materials, International Atomic Energy Agency, Vienna, 1968, p. 239. 5. Haschke, J. M. ; Eick, H. A. or. Phys. Chem. 1969, 73, 374. 6. Huber, E. J. Jr. ; Holley, C. E. Jr. J. Chem. Thermodynamics 1969, 1, 30•. 7. Hultgren, R. R.; Orr, L.; Anderson, P. D.; Kelley, K. K. Selected Valuesfor the Thermodynamic Pivperties of Metals and Alloys, John Wiley and Sons, Inc. : New York. 1963. 8. See for example, Guinet, P.; Vaugoyeau, H.; Blum, P. Commissariat a l'Energy Atomique Report CEA-R 3060, November, 1966. 9. Goldstein, H. W.; Walsh, P. N.; White, D. J. Phys. Chem. 1961, 65, 1400. 10. Benezech, Gilbert; and Foex, Mark, C.R.H. Aead. SeL Ser. C 1969, 268, 2315. 11. Chupka, W. A.; Inghram, M. G.; Porter, R. F. J. Chem. Phys. 1956, 24, 792. 12. Smoes, S.; Drowart, J.; Verhaegen, G. J. Chem. Phys. 1965, 43, 732. 13. Ames, L. L.; Walsh, P. N.; White, D. J. Phys. Chem. 1967, 71, 2707. 14. Edwards, R. K.; Chandrasekharaiah, M. S.; Danielson, P. M. High Temp. Sci. 1969, 1, 98. 15. Ackermann, R. J. ; Rauh, E. G.; Chandrasekharaiah, M. S. J. Phys. Chem. 1969, 73, 762. 16. The Plutonium-Oxygen and Uranium-Plutonium-Oxygen Systems; A Thermoehemieal Assessment, Technical Reports Series No. 79. International Atomic Energy Agency, Vienna, Austria, 1967. 17. Ackermann, R. J.; Thorn, R. J. Chemical Bonding from High Temperature Studies; Sublimation of Refractory Compounds, reprinted from High Temperature Technology, International Union of Pure and Applied Chemistry, Butterworth and Co., Ltd., London, 1964. 18. Ackermann, R. J. ; Rauh, E. G.; Walters, R. R. J. Chem. Thermodynamics 1970, 2, 139. 19. Ackermann, R. J. ; Rauh, E. G. Y. Chem. Phys. 1962, 36, 448. 20. Ackermann, R. J. ; Rauh, E. G. ; Thorn, R. J. J. Chem. Phys. 1964, 40, 883. 21. Ward, John; Fraser, M. V. J. Chem. Phys. 1968, 49, 3743. 22. Huber, E. J. Jr. ; Holley, C. E. Jr. J. Amer. Chem. Soe. 1953, 75, 3594. 23. Fitzgibbon, G. C.; Holley, C. E. Jr.; and Wadsoe, Imgemar; J. Phys. Chem. 1965, 69, 2464. 24. Goldstein, H. W.; Neilson, E. F.; Walsh, P. N.; White, D. J. Phys. Chem, 1959, 63, 1445. 25. Yashvili, T. S.; and Tsagareishvili, D. Sh.; Teplofiz. Vys. Temp. 1968, 6, 817. 31
460
R. J. ACKERMANN AND E, G. RAUH
26. Stull, D. R.; Sinke, G. C. Thermodynamic Properties of the Elements. American Chemical Society, Washington, D.C. 1956. 27. A.kerlind, L. Ark. Fys. 1962, 22, 65. 28. Weltner, W., Jr.; McLeod, D., Jr.; Kasai, P. H. d. Chem. Phys. 1967, 46, 3172. 29. Brewer, L.; Walsh, R. M. d. Chem. Phys. 1965, 42, 4055. 30. Green, D. W. J. Phys. Chem., to appear. 31. Brix, P.; Herzberg, G. Can. J. Phys. 1954, 32, 110. 32. Habermann, C. E.; Daane, A. H. J. Chem. Phys. 1964, 41, 2818. 33. Cater, E. D.; Thorn, R. J. J. Chem. Phys. 1966, 44, 1342. 34. Ackermann, R. J.; Rauh, E. G. d. Phys. Chem. 1969, 73, 769. 35. Ackermann, R. J. ; Thorn, R. J. Progr. Ceram. ScL 1961, 1. 36. Goldstein, Harold W. ; Walsh, P. N. ; White, D. d. Phys. Chem. 1961, 65, 1400. 37. Goldstein, H. W. ; Walsh, P. N. ; White, D. J. Phys. Chem. 1960, 64, 1087. 38. Gebhardt, E.; Seghezzi, H. D. Z. Metallk. 1957, 48, 503
A high temperature study of the stoichiometry, phase behavior, vaporization characteristics, and thermodynamic properties of the lanthanum+oxygen systemt R. J. A C K E R M A N N
and E. G. R A U H
Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. (Received 2 July 1970; in revisedform 13 January 1971) The lanthanum + oxygen system has been studied by investigating the vaporization behavior of the sesquioxide phase as a function of temperature and composition, employing mass effusion and mass-spectrometric techniques. The partial pressures of LaO(g) over the sesquioxide phase were measured in the presence of tungsten (1933 to 2408 K) and in the presence of rhenium (1778 to 2427 K). The former were greater by 40 to 80 per cent. The congruently vaporizing composition begins to depart from stoichiometry with increasing temperature and at 2400 K reaches values of La202. 980• 0.002in tungsten and La202.938 ~ 0.002 in rhenium, demonstrating a slight reducing effect of rhenium and a measurably greater reducing effect of tungsten. The following thermochemical quantities were determined: AG['(LaO, g, T)/cal tool- 1 = _ 36940 -- I 1.73 T/K, AH~(LaO, g, 0) = -- (28.6 ± 1.0) kcal tool- 1, and D(LaO, g, 0) = (189.9 ~ 1.0) kcal m o l - 1. The partial pressures of La(g) and LaO(g) over the liquid metal + sesquioxide were measured over the temperature range 1516 to 1904 K. The composition of the sesquioxide phase at the lower phase boundary was determined as a function of temperature from 1660 to 1925 K and appeared to depart from the stoichiometric value above 1400 K. At 1925 K the sesquioxide was reduced to La202.82. The standard Gibbs free energy of formation of the substoichiometric oxide at the lower phase boundary was evaluated as a function of temperature; a calculated value of -- 282.9 kcal mol- ~, corresponding to the composition La202.83, is about 16 kcal tool- 1 less negative than that of the stoichiometric sesquioxide, The standard Gibbs free energy change for the isomolecular reaction, La(g) + YO(g) = LaO(g) + Y(g), was redetermined and compared with the dissociation energies of the monoxides evaluated from the thermochemical data.
1. Introduction The l a n t h a n u m + o x y g e n s y s t e m at first g l a n c e seems r a t h e r simple, t h e o n l y t h e r m o d y n a m i c a l l y stable solid o x i d e b e i n g t h e sesquioxide. (1) M i x t u r e s o f t h e m e t a l a n d sesquioxide h a v e f a i l e d to p r o d u c e a stable solid m o n o x i d e (2) a l t h o u g h a d i f f r a c t i o n pattern f r o m a f.c.c, lattice a n d a s c r i b e d t o L a O has b e e n r e p o r t e d in a h y d r i d e study. (a~ Other l a n t h a n i d e a n d a c t i n i d e m o n o x i d e s h a v e b e e n o b s e r v e d (4~ f o r t h e m o s t p a r t as films or stabilized b y o t h e r c o m p o n e n t s . O n l y E u O has b e e n p r o d u c e d in m a c r o s c o p i c t Work performed under the auspices of the U.S. Atomic Energy Commission.
446
R.J. ACKERMANNAND E. G. RAUH
quantities.(5, 6) The solubility of oxygen in solid lanthanum metal is apparently quite small since the I~---ry transformation at 1137 K is unaffected by oxygen, (~'z) unless the periods of observation were insufficiently long to effect the saturation of the metal by oxygen. The solubility of the oxide in the liquid metal is not known, and due to a rather extensive liquid range (the melting temperature is 1193 K) (v) some of the conventional quenching techniques following saturation at a given temperature may not yield reliable solubilities due to extensive precipitation of the dissolved oxide. (s) A previous investigation by Goldstein, Walsh, and White(9) of the vaporization behavior of lanthanum sesquioxide by means of the effusion method (tungsten cells) established both the principal mode of vaporization: La/O3(s) = 2LaO(g) + O(g), (1) and the thermochemical properties of LaO(g). These authors observed that constant rates of vaporization were obtained after the composition of the sesquioxide phase became La202.96. The temperature(s) at which this composition was obtained was not reported. However, this relatively small sub-stoichiometry was considered insignificant to the thermochemical assessment, and the sesquioxide was assumed to vaporize congruently in accordance with equation (1) at all temperatures. More recent measurements of reaction (1) by Benezech and F6ex (1°) using the transpiration method and solar heating yield vapor pressures that are larger by a factor of 3. An earlier study of the high temperature equilibrium: LazO3(s)+La(g) = 3LaO(g), (2) by Chupka, Inghram, and Porter (~1) was carried out by analyzing mass-spectrometrically the two vapor species effusing from mixtures of the metal and sesquioxide phases contained in an effusion cell. The assumption was made that the compositions of both phases remained invariant and hence did not depart significantly from unit activity. Isomolecular exchange reactions of the type MO(g)+ La(g) = M(g)+ LaO(g) have been used to derive the thermodynamic properties of transition metal and lanthanide metal monoxides based on the existing data for LaO(g), La(g), and M(g). (12' 23) These studies of the reaction involving yttrium have shown a discrepancy of 6 kcal mol -~ in the measured enthalpy change derived from measurements of the temperature dependence of the equilibrium constant. There now exists considerable evidence which shows that the congruently vaporizing compositions and the thermodynamic properties of several refractory binary compounds, UOz, (1.' ~5) PuO2,O6) ZRO2,(17) and YzO3,(~8) are substantially different from those at the lower phase boundary, i.e. the composition in equilibrium with the metal phase, and neither corresponds to the ideal stoichiometric composition of the so-called compound. The existence of a single gaseous molecule in the La + O system, in contrast to the systems cited above, greatly simplifies the evaluation of thermodynamic properties from measurements of vapor pressure. By means of mass effusion and massspectrometric techniques, the vaporization behavior, phase equilibria, and thermodynamic properties of lanthanum + oxygen have been re-examined and extended to remove existing discrepancies and to include the determination of the Gibbs free energy of formation of lanthanum sesquioxide at its lower phase boundary.
THERMODYNAMICS OF La + O
447
An intercomparison of the thermodynamic properties of lanthanum+oxygen and yttrium+ oxygen is presented, including a critical examination of the isomolecular exchange reaction: La(g)+YO(g) = LaO(g)+V(g). (3)
2. Experimental methods and results Mass-spectrometric and mass effusion measurements were made on lanthanum sesquioxide and the two phase system, La(1)+La2Oa(s). The Bendix time-of-flight mass spectrometer, the mass effusion method, and the experimental techniques for each have been described elsewhere. (19~ La203 In order to establish the lower phase boundary of the sub-stoichiometric lanthana La203_x, isopiestic measurements of the type described previously 05~ were performed over the temperature range 1660 to 1925 K. In this procedure a sample of the oxide is equilibrated with the vapor arising from a saturated mixture of the metal and oxide inside a closed container and subsequently analyzed for the mole ratio of O to La by combustion to La203 at 1573 K. The combustion of a 700mg sample of metal containing 910 p.p.m, of oxygen yielded, at this temperature, an increase in mass consistent with the formation of the stoichiometric sesquioxide. The results and a linear least-squares representation of the results in terms of mole fraction of dissolved La in La203 are given in table 1 and are shown in figure 1. A comparison of these results with those obtained previously for YzO3_(~8) is also seen in the figure. The congruently vaporizing composition of sesquioxide from a tungsten effusion cell at 2400 K was determined by evaporating about 20 per cent of a 1 g sample and subsequently analyzing the grayish-black residue by oxidation to white stoichiometric La203 at 1573K. Two such determinations were made. A third determination at 2400K was made on a mixture of 1200mg of La203 and 62mg of lanthanum metal, corresponding to a starting composition of La202.8. The results of the three measurements established the congruently vaporizing composition at 2400 K at La202.980 ± o.oo3. Samples heated in vacuo at 2275 K for 7 h and at 2050 K for 15 h yielded the compositions, La202.992 and La202.998, respectively. Similar measurements made with a rhenium cell yielded, at 2427K, the apparently sub-stoichiometric composition, La202.998 ± o.0o2, showing considerably less reduction of the sesquioxide by rhenium. TABLE 1. The composition of the lower phase boundary of LaaO3- z at temperature T given as the mole ratio n(O)/n(La) and also as the mole fraction x(La) of lanthanum dissolved in stoichiometric La20a
T/K
n(O)/n(La)
x(La)
T/K
n(O)/n(La)
x(La)
1661 1734 1792
1.461 1.455 1.433
0.051 0.058 0.085
1844 1844 1923
1.427 1.421 1.411
0.093 0.099 0.112
logic {x(La)} = (1.21 ~ 0.33) -- (4125 =k 600)K/T
(la)
448
R. J. A C K E R M A N N A N D E. G. R A U H i
i
i
1
[
1
1
1
1
2100 2000 ~d 1900
1800
1700 1600 I
1.40
I
I
r
1
I
1.45 n (O) / n (M)
I
I
I
1.5
FIGURE 1. Variation with temperature of the composition (mole ratio) of the lower phase boundary of lanthana compared with that of yttria. (18> O O, La2Oa- ~; x ×, Y2Oa2 x.
Mass-spectrometric observations on the vaporization behavior of La20 3 in a tungsten cell were made on a 1.1 g sample of the sesquioxide in the form of a cup that had been sintered previously in vacuo for 1 h at 2400K. The sample was heated initially to 2160 K for 24 h. The vapor was almost entirely LaO; no tungsten oxide ions and only a trace ( < 0.1 per cent) of La + were observed. For all observations an ionizing electron energy of 11 eV was used in order to eliminate the formation of La + ions from the fragmentation of LaO; this was established by an appearance potential measurement of the type described previously.(2°) I" The temperature dependence of the LaO ÷ ion current was measured at the end of the 24 h period and after 42 and 48 h at this temperature. The results for each of the three series of measurements were fitted to a straight line by the method of least squares, and the average enthalpies of vaporization, (147.0+2.1), (149.5+ 1.5), and (149.74-1.7) kcal mo1-1, were calculated from the slopes. A closer examination of the plotted values and the residuals revealed a slight positive curvature that suggested a variation of pressure with composition as well as temperature that could be correlated with the measured departure from ideal stoichiometry. Since the average values agreed within the standard deviations, only the results of the second series, covering the temperature range 1933 to 2312K, are reported in section 1 of table 2. The results for a similar series of measurements from a rhenium cell, from which an average enthalpy of vaporization of (139.5 4- t.1)kcal tool -1 was calculated, are given in section 3 of table 2. Again a closer examination of the values reveals a slight positive curvature with increasing temperature. t Throughout this paper eV = 96487 J mop 1, atm = 101.325 kN m- 2, and cal = 4.184 J.
449
T H E R M O D Y N A M I C S OF La + O TABLE 2
SECTION 1: Mass-spectrometric results for the evaporation of La203 from a tungsten cell. Ion currents I(LaO +) in arbitrary units
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
2152 2028 1969 1933 2004
5.25 0.710 0.266 0.136 0.435
2039 2112 2217 2189 2154
0.93 2.98 15.1 10.2 5.4
2038 2058 2076 2186
0.89 1.26 1.68 9.4
T/K 2209 2227 2278 2312
I(LaO +) 14.0 18.6 39.0 74.0
SECTION 2: Mass effusion results for the evaporation of LaaOa from a tungsten cell with orifice area 3.33 × 10 -2 cm 2 and Clausing factor 0.40
T/K
W × 104 gem- 2 s. 1
T/K
W × 104 gem- 2 s- 1
2324 2323 2372
2.40 2.48 4.48
2374 2210 2258
4.91 0.51 1.06
T/K
W / 104 gem- 2 s- 1
T/K
W × 104 gcm_ 2 s- x
2309 2347
2.09 3.38
2408 2381
9.46 5.08
Least-squares representation ofp(LaO) over the sesquioxide in tungsten, combined mass effusion and normalized mass-spectrometric results: log10 {p(LaO)/atm} = (12.311 ~ •.679) -- (4.539 ~ 0.728) × 104K/T +
+ (0.139 :~ 0.079) / 108(K/T) 2.
(2a)
SECTION 3: Mass-spectrometric results for the evaporation of La2Oa from a rhenium cell. Ion currents l(LaO +) in arbitrary units
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
T/K
I(LaO +)
1778 1856 1924 1994
0.0056 0.0265 0.0850 0.304
2084 2•85 2308 2292
1.28 6.30 36.5 31.0
2237 2127 2033 1958
14.2 2.46 0.625 0.180
1900 2033 2144 2242
0.066 0.585 2.50 15.1
SECTION 4: Mass effusion results for the evaporation of La2Os from a rhenium cell with orifice area 2.23 × 10 -2 cm 2 and Clausing factor 0.41
T/K
W × 104 g c m -2 s - i
2374 2389
2.73 3.47
T/K
W × 104 g e m -2 s-Z
T/K
W × 10 ~ g cm -2 s-1
T/K
W × 10a g c m -~ s-1
2321
1.76
2427
5.44
2258
0.53
Least-squares representation ofp(LaO) over the sesquioxide in rhenium, combined mass effusion and normalized mass-spectrometric results: log10 {p(LaO)/atm} = (12.453 -4- 1.048) -- (4,794 -~ 0.427)104K/T + (0.177 ~ 0.043)I08(K/T)L
(2b)
450
R.J. ACKERMANNAND E. G. RAUH
Mass effusion measurements on La203 were carried out in both tungsten and rhenium cells. In order to circumvent the effect of non-cosine distribution of the effusate at low angles from a knife-edge orifice as described by Ward and Fraser, (21) channel-shaped orifices were used, the dimensions and Clausing factors for which are given in table 2. In general, the cell and its contents were held at a selected temperatur6 in the range 2210 to 2427K until the rate of effusion became constant. The results for both tungsten and rhenium cells are given in sections 2 and 4 of table 2. Since LaO(g) and O(g) are the only vapor species present, their partial pressurespi can be calculated from the mass effusion results using the equation: Pi = ZiG(2nMiRT) ÷,
(4)
in which Z i is the molar effusion rate (Wi/Mi) and G is the appropriate geometry factor. The numerically small departures from ideal stoichiometry were not considered since the effect on the magnitude of the coefficients in equation (1) is quite small. Furthermore, if the contribution of oxygen to the mass effusion rate is totally ignored, the calculated values ofp(LaO) are only 5 per cent larger. The two series of mass-spectrometric results, given in table 2, were normalized to the corresponding effusion pressures in the following manner. A three-parameter leastsquares equation was fitted to each series of mass-spectrometric results and a normalizing factor was determined from each of the corresponding pressures calculated from the results in sections 2 and 4. The least-squares equations and the average normalizing factors were combined to yield equations (2a) and (2b) in table 2. The plots of these equations in figure 2 demonstrate a systematic difference in vaporization behavior. The pressures of LaO(g) over stoichiometricallyvaporizing LazOa were calculated from the Gibbs free energies of formation of LazOa(s), O(g), and LaO(g) via equation (1). The standard Gibbs free energy of formation of LazO3(s) was calculated from the enthalpy of formation reported by Huber and Holley(za) and confirmed by Fitzgibbon, Holley, and Wadsoe(23) and the enthalpy and Gibbs free energy functions of La2Oa(s) given by Goldstein et al., (24) and Yashvili and Tsagareishvili, (zS) of atomic oxygen compiled by Stull and Sinke, (zc) and of La(s or 1) compiled by Hultgren et al. (7) Over the temperature range 1600 to 2400 K, AG~(La2Oa,s) can be expressed adequately by a linear equation: AG~(La203, s, T)/cal mol- 1 = _ 425 710 + 66.14 T/K.
(5)
The standard Gibbs free energy of formation of LaO(g) was obtained from the results for the rhenium cell, equation (2b), at 1900 K where the composition of the solid phase is negligibly sub-stoichiometric and consequently the partial pressures of LaO(g) and O(g) are related by the equation, p ( O ) = 0.161p(LaO). The value obtained is AG~(LaO, g) = - 59220 cal mol -I. The temperature dependence of this quantity was calculated from the Gibbs free energy functions for molecular oxygen, (26) solid and liquid lanthanum, (7) and those for LaO(g) which were calculated from the molecular constants and spectroscopic data of Akerlind, (zT) which correspond to the 22 ground state(2s) instead of 4Z,(29) and the low-lying states zA3/z and 2As/2 recently identified by Green. (a°) Derived absolute entropies and Gibbs free energy and enthalpy functions, including anharmonicity corrections, are given in table 3. Previously reported values °3)
THERMODYNAMICS OF La + O
451
TABLE 3. Absolute entropies, and Gibbs free energy and enthalpy functions for LaO(g)
S°(T) T/K
cal K- ~ tool- 1
1800 2000 2200 2400 2600
72.62 73.60 74.51 75.37 76.17
-- {G°(T) -- H°(O)}/T cal K- 1 tool- 1 64.17 65.07 65.88 66.65 67.36
IF(T) --/-/°(0) cal mol- ~ 15220 17080 18980 20920 22900
were calculated f r o m the g r o u n d state only. The Gibbs free energy o f f o r m a t i o n o f LaO(g) is adequately represented by the linear equation, AG~(LaO, g, T)/cal m o l - 1 = _ 3 6 9 0 0 - 1 1 . 7 3 T/K,
(6)
over'the range 1600 to 2400 K. Therefore, the partial pressure p(LaO) o f LaO(g) over stoichiometric La203 is given by, log~o{p(LaO)/atm} = - 30090 K / T + 7.96,
(7)
and is plotted for comparison in figure 2.
T/K 2400 2200
2000
1800
1600
-3.0
N \\
"~ --
equation (7),~ ~ ,
, 0 ove,°
~ ~
\
-7.0
.......
\~xb, ' ~
....
~kb~.fe_quatlon" ~ ~ p(LaO)over ' ~ (2-a) " ~ Xe~La+ La203 ~ p(LaO)over"~ No
~Laps-~(W) \
\
equation { 2 - b ) , - - - - - ~ . . . . . ~ p'(LaO) over "%,N ~ ~k L ~ ) N~xequation (4-d)~ N \
- 8.0
-9'03 5 •
4.0
4.5
5.0 5.5 104 K/T
6.0
6.5
7.0
FIGURE 2. Logl0(pdatm) against 10~K/T for lanthanum + oxygen• Equations (2a) and (2b) p(LaO) over congruently evaporating lanthana in tungsten and rhenimn, respectively; equation (7), calculated p(LaO) over stoichiometric sesquioxide; equation (8), the vapor pressure p°(La) of liquid lanthanum; equations (3d) and (3e), p(La) and p(LaO), respectively, over the two phase system lanthanum + lanthana. 0 , Mass effusion; ©, mass-spectrometric.
452
R.J. ACKERMANN AND E. G. RAUH
The enthalpy of formation of LaO(g) at T = 0, AH~(LaO, g, 0) = (28.6+ 1.0)keal mol-1, is calculated from equation (6) and the Gibbs free energy functions cited above. From this value of AH[(LaO, g, 0), AH~(La, g, 0) = 102.3 kcal mol -~1 (given later), and ½D(O2, 0) = 59.0kcalmol-1, ~31~ one calculates a value of the dissociation energy of LaO(g) at T = 0: D(LaO, g, 0) = (189.9_+ 1.0) kcal m o l - t = (8.24+ 0.04) eV. La(1)+ La203 Mass spectrometric observations on the two phase system: liquid lanthanum+ lanthana, were made on a sample prepared by adding 75 mg of metal to the same lanthana cup that had been used in the previous mass-spectrometric measurements. Both LaO + and La + were observed in the approximate ratio of 3/1 at an ionizing electron energy of lleV. The sample was held at 1810K for a total of 30h. The temperature dependences of the abundance of both ions over the range 1516 to 1870 K were measured 9, 25, and 30h at the set temperature; the enthalpies of vaporization calculated from least-squares analyses of the results were, successively, AH,~(LaO) = (105.9 + 0.3), (107.5 + 0.6), and (106.9_ 0.2) kcal mol-1, and AH~(La) = (94.2__+0.3), (95.8_0.6), and (95.4_ 0.4) kcal mo1-1. The results for the last series are given in section 1 of table 4 with the least-squares representations. Mass effusion measurements of the two-phase system were made on a sample which consisted of 1 g of lanthanum metal added to the same lanthana cup used in the previous mass effusion measurements. The results covering a temp ...... re range of 1713 to 1904K are given in section 2 of table 4, with a linear least-s ..s equation, equation (4c), calculated therefrom; the quantity p~ is that pressure calculated from equation (4) by assuming the vapor to be entirely LaO(g). The vapor pressure-temperature relation for pure lanthanum was derived from the average of the vapor pressures at 2000 K reported by Ackermann and Rauh (19~ and Habermann and Daane (3z) and the absolute entropy at 2000K given by Hultgren et aL ~7) The resulting equation is log1 o{p°(La)}/atm = - 21620 K I T + 5.86, (8) and is shown plotted in figure 2. We estimate an uncertainty of + 20 per cent in the pressure. The derived enthalpy of vaporization at T = 0 is (102.3-t-1.0)kcalmo1-1, and in the temperature range of the present investigation (98.9+l.0)kcalmo1-1, which is to be compared with the enthalpy of vaporization of lanthanum saturated with oxide, (95.4+ 0.4) kcal mo1-1, calculated from equation (4d). The normalization of the mass-spectrometric results in table 4 to yield partial pressures pl of La(g) and LaO(g) requires a knowledge of the instrumental sensitivities k i of these species in accordance with the expression, Pi ~ IiT/ki. Because of the relatively large uncertainties and the limited temperature range in the mass effusion measurements, the previously cited methods (33' 34) for the evaluation of the relative instrumental sensitivities could not be applied. However, Ames et aL (xa) report a value of k(La)/k(LaO) = 1.7 which permits the evaluation of the ratio of the partial pressures, p(La)/p(LaO), from equations (4a) and (4b). The relation between the "effective" pressure and the individual partial pressures is p~ = p(LaO)[1 + {M(LaO)/M(La)}~{p(La)/p(LaO)}].
(9)
453
THERMODYNAMICS OF La + O
TABLE 4 SECTION I: Mass spectrometric results for the evaporation of La q- La203. Ion currents I in arbitrary units
T/K
I(La +)
I(LaO +)
1813 1702 1623 1544 1516
4.95 0.910 0.246 0.056 0.031
17.8 2.74 0.615 0.119 0.062
T/K 1579 1664 1756 1835 1870
l(La +)
l(LaO +)
0.112 0.475 2.12 6.60 I0.0
0.252 1.31 6.95 25.0 41.5
loglo {I(La+)T/K } = -- (20850 ± 90)(K/T) q- (15.44 :~ 0.06), loglo {I(LaO+)T/K } = -- (23360 ± 50)(K/T) + (17.39 ~ 0.03),
(4a)
(4b)
SECTION 2: Mass effusion results on the evaporation of La -]- La203 W × 105
W × 105
T/K
g cm_as_ x
T/K
1773 1786 1810
2.93 4.46 7.11
1804 1750
g cm_2s_ i 6.60 3.09
W x 105
T/K
g cm_2s_ ~
T/K
1904 1902
22.1 23.6
1848 1713
W × 105 g cm_2s_ 1,
11.0 1.38
loglo {po/atm } = -- (21000 ± 980)(K/T) + (6.30 ~ 0.54). (4c) Least-squares representation of the normalized mass-spectrometric results on the evaporation of La + La203: loglo {p(La)/atm } = -- (20850 =~ 90)(K/T) + (5.35 ~ 0.08), (4d) log~o{p(LaO)/atm } = -- (23360 i 50)(K/T) + (7.53 ~ 0.08). (4e) From this equation and the ratio p(La)/p(LaO) the partial pressures o f La(g) and LaO(g) were calculated at each temperature o f measurement o f Pc. The results are given by equations (4d) and (4e) in table 4 and are plotted in figure 2. T h e p a r t i a l pressure o f La(g) in equilibrium with La(1)+ LazO3(s), equation (4d), is shown to be less than the vapor pressure o f pure liquid lanthanum, equation (8), at all temperatures but tends towards the latter at the lowest temperature suggesting that the solubility o f the oxide in liquid l a n t h a n u m becomes insignificant below approximately 1600 K. The results o f this study therefore appear to be quite consistent with the instrumental sensitivities reported by Ames et aL °3) La(g) + YO(g) = LaO(g) ~- Y(g) The mass-spectrometric measurements o f the isomolecular exchange reaction given by equation (3) were carried out on two samples of widely differing constitution. The first sample consisted o f 370 m g each of L a 2 0 3 and Y203 in the form o f a small cup in which was placed 80 m g of each metal. The second consisted o f 56 mg o f Y203, 50 m g of Y, and 27 mg o f La contained in a single crystal tantalum cup. The measured ion currents in the two cases differed considerably; in the former the intensities were always in the order L a O > La > Y > Y O whereas in the latter Y > La > L a O > YO.
454
R.J. ACKERMANN AND E. G. RAUH
The equilibrium constant for reaction (3) in terms of partial pressures Pi, ion currents li, and instrumental sensitivities ki is
Kv = {p(Y)p(LaO)}/{p(YO)p(La)} = [{I(Y)I(LaO)}/{I(YO)I(La)}][{k(La)k(YO)}/{k(LaO)k(Y)}].
(10)
The relative instrumental sensitivities, k(La)/k(LaO) = 1.7 and k ~ ) / k ( Y O ) = 1.5 are those given by Ames et aL °3) The results of the measurements of Kp at various temperatures in the range 1783 to 2184 K are shown in figure 3. The agreement between the two sets of values suggests that both samples lie in a bivariant region of the phase diagram where the (Y, La)
T/K" 2200
2100 J
2000 --
1900
I
1800
r
I
2.4 "q
2.3 ~" 2.2 e~
+ ~++ •
o•o/"
2.1 2.0 1.9 1,8
I
4.6
4.7
4.8
4.9
5.0 5.1 104 K/~r
5.2
5.3
I
t
5.4 5.5
t
5.6
FIGURE 3. LogioK, against 104KIT for the isomolecular reaction: La(g) + YO(g) = LaO(g) + Y(g). +, First sample; ©, second sample. - - , logloK, = -- (0.506 -t- 0.047) + (5260 i 90)KIT. liquid phase coexists with a (Y203, La203) phase; the vapor compositions can vary at constant temperature and still represent the equilibrium state of the system. A leastsquares treatment of the results yields the equation for the change in standard Gibbs free energy of equation (3) as a function of temperature,
AG~ = - R T l n K v
= {-(24070-t-410)+(2.32___0.22) T/K} calmol ~1.
(11)
As previously cited, the mass-spectrometric observations were carried out using 11 eV ionizing electrons in order to minimize fragmentation of monoxide species. The effect of fragmentation was particularly noticeable in the first of the two samples for which the intensity of the LaO was greater, by a factor of about three, than the La intensity. For ionizing electron energies of 25 eV the measured equilibrium constant was approximately one-half that measured at 11 eV. For the second sample this effect was not observed. The explanation of this behavior can be seen from the relative ion
THERMODYNAMICS OF La + O
455
intensities and from equation (10). If the intensity ofMO ÷ is greater than or comparable with M +, fragmentation of MO + will increase the observed intensity of M+, but little or no measurable effect will be observed when M + > MO +.
3. Discussion The difference between the thermodynamic properties of LaO(g) reported herein and those previously given by Ames et al. (13) is due principally to the reduction of the oxide by the tungsten effusion cell used in the earlier study. For example the dissociation energy of LaO(g) reported in the earlier study was 193.2kcalmol -~ compared with the value (189.9 + 1.0)kcal mo1-1 reported in the present study. The role of chemical reduction played by the tungsten is represented by the difference in equations (2a) and (2b) and the correlated change in the congruently vaporizing composition with temperature which effectively causes a decrease in the partial pressure of oxygen and an increase in the partial pressure of LaO(g) as is seen in the equilibrium constant for equation (1), Kp = {p(LaO)}Zp(O). Thus the experimental results indicate that the partial pressure of oxygen is rather sharply dependent on the composition variable near the stoichiometric sesquioxide. The thermodynamic data for LaO(g) derived from the measurements ofp(LaO) using the rhenium cell which can be considered inert at temperatures less than about 2250 K are internally consistent with the total vaporization behavior of the system. Equations (5) and (6) may be used to calculate the partial pressure p°(LaO) in equilibrium with pure liquid lanthanum a n d stoichiometric sesquioxide according to the reaction, ½LazOa(s, a = 1)+½La(1, a = 1) = LaO(g). (12) The resultant values are approximately 20 per cent greater than these calculated from equation (4e) which corresponds to the mutually saturated two phase system. The activity of the component (La203) in LazOa - , at the lower phase boundary at 1800 K, where the mole fraction of La203 is 0.9, is a(La203) = p(LaO)3/{a(La)p°(LaO) 3} ~ 0.7 which suggests a small negative deviation from ideality. On the other hand, the use of the measured values for p(LaO) obtained via the tungsten cell gives rise to a Gibbs free energy of formation of LaO(g) that is approximately 2.5 kcal mol- x more negative and leads to a value of a(La203) g 0.1, which is unreasonably small. Furthermore, the isomolecular reaction, equation (3), can be used to derive the Gibbs free energy of formation of LaO(g) from the known values for y(g),(ls) YO(g),(zo) and La(g) from equation (8). The resultant quantity is consistent within experimental uncertainty (1 to 2kcalmol -~) with the mass effusion results obtained from the La203(Re) system but not with those from the La2Oa(W) system. The mechanism of the reduction of LazO a by tungsten is not completely understood. The effect of the reduction is to increase the measured partial pressure of LaO(g) by approximately 60 per cent buf no corresponding volatile oxides of tungsten were observed. Actually a number of earlier studies have reported definite evidence of "reaction" between La2Oa and tungsten. Ackermann and Thorn (35) have reviewed the earlier work, and Goldstein, Walsh, and White(36) report that 0.1 tool of tungsten per mole of La/O a is vaporized. From the absence of any tungsten containing vapor species effusing through the orifice it was concluded that the oxygen diffuses into the
456
R.J. ACKERMANN AND E. G. RAUH
massive tungsten effusion cell and subsequently vaporizes from the relatively large exterior surface. A more pronounced example of this behavior and its interpretation has been observed in the case of tantalum cells. (37) It is known that tantalum will dissolve substantial amounts of oxygen at high temperatures, (3s) and the evidence of the present study suggests that tungsten and oxygen also form a stable solid solution. Inspection of equation (7) and equation (2b) in figure 2 suggests that at temperatures above 2300 K rhenium also becomes somewhat reducing. The earlier study by Chupka e t al. (11) of the equilibrium given by equation (2) provides a useful basis of comparison and discussion with the present study. A systematic difference was observed by these investigators between mixtures of La(1, excess) + La203(s ) and La(1) + La203(s, excess), the former yielding partial pressures of La(g) approximately a factor of three greater than the latter. The former system yielded values of the partial pressures of both LaO(g) and La(g) that are in close agreement with those of the present study after a correction for the relative instrumental sensitivities is made. Two explanations were offered to account for the factor of three. The first involved the formation of a LaO solid phase. This explanation was discarded because X-ray diffraction studies showed no evidence of a new phase in the residue of the vaporization studies. The second explanation suggested a diffusion process resulting from the covering of the liquid metal phase by the excess of the oxide. The results of the present study offer a third and perhaps more likely explanation, namely, the reaction of all the lanthanum metal with the excess oxide to form a sub-stoichiometric sesquioxide having a composition lying to the right of the phase boundary shown in figure 1, that is, only a single phase may have been present. The partial pressure of LaO(g) is seen from equations (7) and (4e) in figure 2 to increase more than a thousand-fold as the composition of the sesquioxide changes from stoichiometric to that at the lower phase boundary. Even a small sub-stoichiometric departure from the ideal sesquioxide composition produces an increase in the partial pressure of LaO(g) and this effect is seen by comparing equation (7) with equations (2b) and (2a). The apparent increase in the enthalpy of vaporization {equations (2b) and (2a)} with increasing temperature and increasing sub-stoichiometry is numerically opposite to that reported by Goldstein e t al. (9) Their mass effusion data at higher temperatures yield an enthalpy of vaporization of LaO(g) of (130.9___ 4.7) kcal mol-t whereas at lower temperatures their mass-spectrometrically determined value is (139.5 4.2) kcalmo1-1. The vapor pressure of liquid lanthanum is reduced by the presence of oxide as is seen from the plot of equations (8) and (4d) of figure 2. However, the difference between these curves suggests that the solubility of La203 in liquid lanthanum is smaller than the corresponding effect in the yttrium+ oxygen system. °s) It should be pointed out that the measured enthalpy of vaporization of La(g) from the two phase system, La(1) + La203(s), equation (4d), is smaller by (4.5___1.1) kcal mol-1 than that for the system of pure liquid lanthanum (equation (8)) demonstrating that the effect, though smaller, is nevertheless real. The standard Gibbs free energy of formation of the sub-stoichiometric sesquioxide phase at the lower phase boundary can be evaluated from the reaction: La203_x(S)+(1-x)La(g ) = (3-x)LaO(g), (13)
THERMODYNAMICS OF La + O
457
and the equation:
AG~(La~O~-x) = ( 3 - x)R r In {p(LaO)} + (3 - x)AG°f(LaO, g ) - (1 - x)R T In {p(La)} - (1 - x)AG~(La, g).
(14)
The partial pressures of LaO(g) and La(g) are given by equations (4e) and (4d); the standard Gibbs free energies of formation of LaO(g) and La(g) are calculable from equations (6) and (8). At a temperature of 1750K the value of x in equation (13) is 0.11 as seen from the data in table 1. The calculated value of AG~(La202.89) !s _300.3kcalmo1-1 which appears to be numerically reasonable since it is more negative than that, - 2 9 8 . 6 kcal t o o l - a obtained from a linear interpolation between the integral molar Gibbs free energies of the pure metal, AG~ = 0, and stoichiometric LazOa, AG~ = - 3 1 0 . 0 kcal tool -1, equation (5). That is to say, the Gibbs free energy of formation of single phase La202.89(s ) from 0.074mol of lanthanum metal and 0.963 tool of LazO3(s) is approximately - 1.7 kcal tool-1. Inspection of equation (14) indicates that errors in the two terms which are multiplied by the quantity (3 - x) have
n(O)/n(La) of lower phase boundary 1.5 /[- i
1.49 1.48 1.47 1.46 t
t
i
~
1.44" i
[
1.42 I
J
1.40 J
I
/- /
27O 7'
280 t
~
-
I 31o
L o3
320
330 z ~ : : ~ ' ' ~ 340 I i 1400
i 1500
l 1600
~ 1700
i 1800
r 1900
2000
T/K FIGURE 4. Comparison of the standard Gibbs free energies of formation as a function of temperature of the lanthanum sesquioxide phase at ideal stoichiometry and at its lower phase boundary. the greater influence on the numerical value of AG~(La203-x). An error of 20 per cent in the measurement o f the partial pressure of LaO(g) given by equation (4e) generates an error of 2kcal tool -1 in the Gibbs free energy of formation and an uncertainty of 1 keal tool -1 in AG~(LaO) generates nearly 3 kcal tool -1. Hence, the numerical values calculated from equation (14) and shown in figure 4 have uncertainties that may be several kcal mo1-1. Such an error, of course, is large by calorimetric standards, but on the other hand, direct calorimetric studies of sub-stoichiometric materials such as La2Oa-x would be quite difficult to perform; quenched samples are generally difficult to obtain since they rapidly disproportionate at lower temperatures to mixtures of
458
R.J. ACKERMANN AND E. G. RAUH
metal and oxide, as was the case in the present study. The composition of the lower phase boundary approaches the stoichiometric composition below about 1450 K, as seen from figure 1, and the standard Gibbs free energy shows parallel behavior. A summary of the present and previous results of the measurements of the iso. molecular reaction, equation (3), is given in table 5. The first and third columns give t h e enthalpy of reaction at the absolute zero of temperature and the entropy change at 2000 K derived from t h e experimental measurements via the so-called second-law method. The second and fourth columns give the same quantities via the so-called third-law method as defined in the footnotes of the table. The value in the fourth column has been calculated from the absolute entropies of the gaseous metals taken TABLE 5. Comparison of thermodynamic quantities of the isomolecular reaction: La(g) q- YO(g) = LaO(g) -t- Y(g), obtained in the present study with those of previous studies -- AH°(0, II): kcal mol- 1
-- AH°(0, III)b kcal mol- 1
AS°(2000K, II) cal K- 1 mol- ~
16.5 :d: 2.7 22.7 q- 1.0 21.4 ± 0.4
19.3 -4- 0.7 19.6 ± 0.2 19.6 ± 0.1 21.1 :k 1.5~
-- 0.40 -- 3.7 ± 1.4 -- 2.32 ± 0.22
AS°(2000K, III) cal K- ~mol- 1 "~ ) - - 1.4
Reference
12 13 This study = Do(YO)(2°) -- Do(LaO)
a AHo(0,II) = AH°(T) -- A {H°(T) -- H°(0) }. b AHO(0,I I I ) = AG°(T) -- A (G°(T) -- H°(0) } = -- R T l n Kp -- A {G°(T) -- H°(0) ]. c Computed from the results in reference 12. a The error is estimated from uncertainties of • 1 kcal mol- 1 in each value of D0(MO); all other errors are standard deviations. from the compilation of Hultgren e t aL, (7) of YO(g) from the thermal functions given by Ames e t aL, O3) and of LaO(g) from table 3. The last entry in the second column is the enthalpy of the reaction calculated from the difference of the dissociation energies of YO(g) (2°) and LaO(g) obtained in the present study. The error quoted is that which is consistent with an uncertainty of + 10 to _ 15 per cent in each of the Vapor pressure measurements. The isomolecular reaction is a very sensitive method for measuring this difference in dissociation energies and is also quite accurate insofar as the relative instrumental sensitivities of monoxide to metal cancel in equation (10). The relatively more precise measurements of the present study reduce the nominal discrepancy between the second-law and third-law values to less than 2 kcal mo1-1. The agreement of the present results with those of the previous studies, with the exception of the value of AH°(0, II) of Smoes e t aL, (12) is generally good and demonstrates that equilibrium can be achieved under a variety of experimental conditions. The thermodynamic and molecular properties of the oxides of the Group III transition metals have been intercompared previously (2°) and show the relatively greater stability in the vapor phase of the + 2 valence state of lanthanum compared with yttrium. This fact is quantitatively reflected in the results in table 5, notably by the negative values in the second column. The difference in the vaporization behavior
THERMODYNAMICS OF La + O
459
of mixtures o f La(1)+LazO3(s) and Y(1)+Y203(s) is due largely to the relatively greater stability o f LaO(g); in contrast to the results o f this study, the partial pressure of YO(g) is unimportant above liquid yttrium saturated with its oxide. (18) However, the + 3 valence state o f yttrium in the solid phase is more stable in view o f the m o r e negative Gibbs free energy o f formation o f the sesquioxide. The extent o f the departure of both sesquioxides f r o m ideal stoichiometry appears to be related to these trends in that at the lower phase b o u n d a r y the La203 phase at a given temperature is substantially more easily reduced than Y2Oa, as seen in figure 1, suggesting that the + 2 valence state o f l a n t h a n u m is also relatively more stable in th~ solid phase. The behavior of both phases is similar with respect to deviation f r o m non-ideality. The metal component shows a strong positive deviation f r o m R a o u l t ' s law. The partial pressure o f La(g) increases by a factor o f 109 at 1900K as the composition o f the sesquioxide changes f r o m stoichiometric to La202.82, The authors are grateful to M r R. R. Waiters, formerly o f the Chemistry Division, for his assistance in carrying out some o f the experimental measurements.
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26. Stull, D. R.; Sinke, G. C. Thermodynamic Properties of the Elements. American Chemical Society, Washington, D.C. 1956. 27. A.kerlind, L. Ark. Fys. 1962, 22, 65. 28. Weltner, W., Jr.; McLeod, D., Jr.; Kasai, P. H. d. Chem. Phys. 1967, 46, 3172. 29. Brewer, L.; Walsh, R. M. d. Chem. Phys. 1965, 42, 4055. 30. Green, D. W. J. Phys. Chem., to appear. 31. Brix, P.; Herzberg, G. Can. J. Phys. 1954, 32, 110. 32. Habermann, C. E.; Daane, A. H. J. Chem. Phys. 1964, 41, 2818. 33. Cater, E. D.; Thorn, R. J. J. Chem. Phys. 1966, 44, 1342. 34. Ackermann, R. J.; Rauh, E. G. d. Phys. Chem. 1969, 73, 769. 35. Ackermann, R. J. ; Thorn, R. J. Progr. Ceram. ScL 1961, 1. 36. Goldstein, Harold W. ; Walsh, P. N. ; White, D. d. Phys. Chem. 1961, 65, 1400. 37. Goldstein, H. W. ; Walsh, P. N. ; White, D. J. Phys. Chem. 1960, 64, 1087. 38. Gebhardt, E.; Seghezzi, H. D. Z. Metallk. 1957, 48, 503