Thermodynamic assessment of the lanthanum-oxygen ... - Springer Link

Basic and Applied Research: Section I

Thermodynamic Assessment of the Lanthanum-Oxygen System A. Nicholas Grundy, Bengt Hallstedt, and Ludwig J. Gauckler

(Submitted 31 July 2000; in revised form 8 January 2001) The data on the thermodynamic properties of La2O3 have been reviewed and optimized using the CALPHAD method. A consistent set of parameters is presented. Data on this system are scarce and, with the exception of a few datapoints on substoichiometric La2O3ⴚx and one measurement of oxygen solubility in La metal, limited to the properties of pure La and pure La2O3. Using the optimized parameters, a tentative phase diagram and stability diagram have been calculated.

1. Introduction Lanthanum metal exists in three modifications. The double hexagonal close packed (dhcp) structure—also called the Latype structure—with ABAC-stacking sequence at low, facecentered cubic (fcc) at intermediate, and body-centered cubic (bcc) at high temperatures [1961Spe, 1964Jay]. The only stable polymorphic form of La2O3 at lower temperatures is the hexagonal A-type [1969Bra]. Neutron diffraction [1979Ald] and x-ray diffraction [1966Foe] studies at very high temperatures and analysis of cooling curves [1965Foe] show that A-La2O3 transforms to partially ordered hexagonal H-La2O3 at 2313 K, then to cubic X-La2O3 at 2383 K. Although the monoxide LaO has been observed as thin films or stabilized by other components, mixtures of the metal and sesquioxide have failed to produce a stable solid monoxide [1971Ack]. However, mixtures of metallic La and La2O3 have revealed a temperature-dependent substoichiometry (La2O3⫺x) of the oxide phase [1968Mul, 1971Ack]. The compound-energy model [1986And, 1988Hil] is used to describe the Gibbs energy of the substoichiometric La2O3⫺x phase. The Gibbs energy of the liquid is described with the two-sublattice model for ionic liquids [1985Hil, 1991Sun]. The oxygen solubility in La metal is described using interstitial solution models. The thermodynamic properties of lanthanum metal and the gaseous phase are taken from Dinsdale [1991Din] and the SGTE (Scientific Group Thermodata Europe) substance database [1997SGT], respectively, and are not reviewed in this paper.

2. Experimental Data 2.1 The Melting Temperature of La2O3 Several measurements of the melting temperatures of La2O3 are described in the literature (Table 1). As is often the A. Nicholas Grundy, Bengt Hallstedt, and Ludwig J. Gauckler, ETH Zurich, Department of Materials, Institute of Nonmetallic Materials, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland. Contact e-mail: [email protected].

case for refractory oxides, the measured melting temperatures show large variations. The earliest value measured by Ruff et al. [1913Ruf] and also the values of Mordovin et al. [1967Mor] and Noguchi and Mizuno [1967Nog] can be discarded as being too low, probably due to impurities in the La2O3 sample. The remaining three measurements [1932War, 1966Sat, 1975Mor] agree quite well. The average of these three measurements is 2586 K. This is the value adopted by the SGTE substance database [1997SGT] and is used for this study. Remarkably, this value is very close to the early determination by von Wartenberg and Reusch [1932War].

2.2 Heat Capacity, Heat Content, and Entropy of La2O3 Heat capacities were measured using adiabatic calorimetry by Goldstein et al. [1959Gol] from 16 to 300 K, by Justice and Westrum [1963Jus] from 5 to 350 K, and by King et al. [1961Kin] from 54 to 296 K. Heat contents were measured by King et al. [1961Kin] from 300 to 1800 K, by Blomeke and Ziegler [1951Blo] from 30 to 900 K, and from 300 to 1600 K by Yashvili et al. [1968Yas] using drop calorimetry. The heat capacity of the high-temperature H and X polymorphs of La2O3 were assumed to be identical to the heat capacity of the A type. Glushko et al. [1982Glu] used a constant heat capacity of 160 J/(K⭈mol) for H- and X-La2O3, but it seems more realistic to assume that the high-temperature polymorphs have heat capacities similar to the lowtemperature polymorph. Heat capacity measurements were also carried out by Basili et al. [1979Bas] from 400 to 1000 K. These data were not used in this assessment as they showed clear discrepancies compared to the other measurements (Fig. 1 and 2). The cp measurements of La2O3 [1959Gol, 1963Jus, 1961Kin] agree quite well with each other and also with the cp(T ) curve optimized in this study, the equation of which is given below. cP(T ) ⫽ 118 ⫹ 0.016T ⫺ 1.24 ⫻ 106T ⫺2

(Eq 1)

The two sets of heat content measurements cannot be compared directly, as the older values from Blomeke and Ziegler [1951Blo] are given as H(T ) ⫺ H(303.2), whereas the values

Journal of Phase Equilibria Vol. 22 No. 2 2001

105

Section I: Basic and Applied Research

Fig. 1 Measured heat capacities of La2O3 from the literature compared to the cp function calculated in this work. †Data not used for optimization

Table 1 Melting temperature of La2O3 from literature Reference

Tm (K)

[1913Ruf] [1932War] [1966Sat] [1967Mor] [1967Nog] [1975Cou] [1997SGT], this study

2113(a) 2588 2577 2490(a) 2529(a) 2593 2586

(a) Values discarded as being too low

of King et al. [1961Kin] are given as H(T ) ⫺ H(298.15). However, cp values can be approximated using Eq 2. cp ⫽

H(Tn⫹1) ⫺ H(Tn⫺1) dH → cp(Tn) ⬇ dT Tn+1 ⫺ Tn⫺1

(Eq 2)

where Tn refers to the temperature of the nth heat content measurement. This approximation is only good if the temperatures at which the measurements were performed are evenly distributed and closely spaced. This allows the cp(app.) values,

106

calculated using the heat content measurements, to be compared directly with the measured cp values and the optimized cp(T ) curve. As can be seen in Fig. 2, the fit is quite good, even if the scatter of the data points is rather large. The scatter, however, is not caused by inaccuracies of measurement, but by the above-mentioned unevenness of the distribution of measuring temperatures. The absolute entropy at 298.15 K, S298.15, has been determined by integrating the measured heat capacity. The calculated values are listed in Table 2. The value used for this optimization is the one calculated by Justice and Westrum [1963Jus], as Justice and Westrum’s cp measurements were conducted down to the lowest temperatures, which means that only a small Debye extrapolation down to 0 K was necessary.

2.3 Enthalpy of Formation and Gibbs Energy of Formation of La2O3 The enthalpy of formation was determined by measuring the heat evolved from burning weighed samples of La in bomb calorimeters [1904Mut, 1924Moo, 1940Rot, 1953Hub]. An alternative method is to measure the difference between the heats of solution of La and La2O3 in hydrochloric acid in solution calorimeters and adding the enthalpy of formation of water to this difference according to the BornHaber cycle process listed below.



Fig. 2 Heat capacities of La2O3 from the literature compared to the cp function calculated in this work. †Data not used for calculation. ‡ Approximated cp values calculated from heat content measurements using Eq. 2

Table 2 Calculated entropies at 298.15 K of La2O3 Reference

S298.15 (J/molⴢK)

[1963Jus] [1959Gol] [1961Kin] This study

127.32 127.95 128.57 127.34

Table 3 Enthalpy of formation of La2O3 Reference

ⴚ⌬H 0298 (La2O3) (kJ/mol)

[1904Mut](a) [1924Moo](a) [1940Rot](a) [1953Hub] [1959War](a)

1862.1 1907.4 2255.2 1793.3 1866.1

2La (s) ⫹ 6HCl (aq) → 2LaCl3 (aq) ⫹ 3H2 (g)

⌬H1

La2O3 (s) ⫹ 6HCl (aq) → 2LaCl3 (aq) ⫹ 3H2O (l)

⌬H2

[1965Fit]

1794.5

H2 (g) ⫹ 1.5O2 (g) → 3H2O (l)

⌬H3

[1967Gve]

1797.9

This study

1795.5

2La (s) ⫹ 1.5O2 (g) → La2O3 (s) ⌬H1 ⫹ ⌬H3 ⫺ ⌬H2 ⫽ ⌬H 0298(La2O3) Such determinations of the enthalpies of formation were also performed [1959War, 1965Fit, 1967Gve] and are listed in Table 3. The value measured by Roth et al. [1940Rot] is obviously too high. Von Wartenberg and Reusch [1959War] attributed the high value to additional heats of carbonization and hydration that occurred because of the reaction with the CO2 and H2O that was freed by the burning of the cellophane jacket, used for initial firing of the combustion reaction.

Method Combustion calorimetry Combustion calorimetry Combustion calorimetry Combustion calorimetry Solution calorimetry, Born-Haber cycle Solution calorimetry, Born-Haber cycle Solution calorimetry, Born-Haber cycle Optimized

(a) Values not used for optimization

The most recent value of the enthalpy of formation determined by combustion calorimetry [1953Hub] and the two most recent values determined by solution calorimetry, [1967Gve, 1965Fit], are in almost perfect agreement. These three values were used for this optimization. No measurements of the Gibbs free energy of formation have been performed. The entropy of formation, however,


107

Section I: Basic and Applied Research can be determined with the help of the third law of thermodynamics by integrating the difference between the cp values of La and La2O3 according to Eq 3. 298.15

⌬S298.15 ⫽

冮

⌬cp dT T

(Eq 3)

0

Values of ⌬S298.15 have been determined by King et al. [1961Kin] and Justice and Westrum [1963Jus], the same people who measured the cp values, and are listed in Table 4. The optimized value lies between these two values.

2.4 Enthalpies and Temperature of Transformation La2O3 shows two reversible polymorphic transformations [1965Foe, 1966Foe, 1979Ald]. Hexagonal A-La2O3 transforms into partially ordered hexagonal H-La2O3 at intermediate temperatures, then into cubic X-La2O3 at high temperatures (Table 5). The A → H transition is accompanied by a discontinuity in the c/a ratio of the crystallographic axis. A first indication of these three polymorphic phases was given when Foe¨x [1965Foe] found three distinctive steps in the cooling curves of molten lanthanum oxide, one at 2583 K corresponding to the solidification and two more at 2383 and 2313 K corresponding to the X → H and H → A transitions, respectively. Subsequent x-ray measurements by Foe¨x and Traverse [1966Foe] and neutron diffraction studies by Aldebert and Traverse [1979Ald] at high temperatures resolved the structures of the H and X phases: the hexagonal H form belongs to the P63 /mmc space group, and the X form to the Im3m space group. No measurements of the enthalpies of transition have been reported. Du et al. [1995Du] estimated the enthalpy of the H-La2O3 → X-La2O3 transition to be 60 kJ/mol by applying the Van’t Hoff equation to the ZrO2-La2O3 phase diagram. They estimated the enthalpy of the A-La2O3 → H-La2O3 transition to be 46 kJ/mol, equal to the enthalpy of the H-Y2O3 → C-Y2O3 transition [1976Shp]. This assumption is questionable as the transition in Y2O3 is from cubic (low temperature) to hexagonal (high temperature), whereas in La2O3, it is from hexagonal (low temperature) to disordered Table 4 Entropy of formation of La2O3 Reference

ⴚ⌬S298.15 (J/molⴢK)

[1961Kin] [1963Jus] This study

294.56 292.88 294.02

hexagonal (high temperature). In spite of this shortcoming, we have accepted this estimation due to the lack of other data. Du et al. [1995Du] estimated the enthalpy of melting by plotting the enthalpy of melting of Y2O3 (measured by [1976Shp]) and Pr2O3 (tabulated by [1991Kna]) versus ionic radius and extrapolating to La2O3. The value thus found is ⌬H ⫽ 93.6 kJ/mol. Now, Knacke et al. [1991Kna] gave the entropy of melting of Pr2O3 as ⌬S ⫽ 36.0 J/(mol⭈K) (i.e., ⌬H ⫽ 92.5 kJ/mol) citing Samsonov [1982Sam], who in addition to the enthalpy of melting of Pr2O3 (⌬H ⫽ 92.1 kJ/ mol) also gives the enthalpy of melting of La2O3 as ⌬H ⫽ 75.4 kJ/mol. The origin of this datum is unclear, but it is most probably not based on measurement, but on an estimate. Du et al. [1995Du] also applied the Van’t Hoff equation to the melting of La2O3, although with large uncertainty, and found ⌬H ⫽ 70 kJ/mol. Glushko et al. [1982Glu] also made an estimation based on comparison with Sc2O3 and Y2O3 and arrived at ⌬H ⫽ 125 kJ/mol. We choose ⌬H ⫽ 75 kJ/mol for the enthalpy of melting of La2O3 which is close to the Van’t Hoff evaluation from Du et al. [1995Du] and the value from Samsonov [1982Sam].

2.5 Solubility of Oxygen in Lanthanum Metal There is no direct measurement of the oxygen solubility in Lanthanum metal, but Okabe et al. [1998Oka2] have measured the oxygen content in fcc-La at the oxygen partial pressure defined by the Y/Y2O3 equilibrium at 1093 K. Under these conditions, the oxygen content in fcc-La was found to be 80 ⫾ 10 mass ppm. Okabe and co-workers [1998Oka1, 1998Oka2] also made measurements of oxygen content as a function of oxygen partial pressure for other rare earths (Pr, Nd, Gd, Tb, Dy, and Er) up to about 2000 mass ppm and found them to obey Sievert’s law reasonably well. Extrapolating the oxygen content in La up to the La/La2O3 equilibrium, using Sievert’s law, results in an oxygen solubility of xO ⬇ 0.06 in fcc-La at 1093 K. Of course, the uncertainty of this value is large.

2.6 Liquid There are no measurements of the heat capacity or enthalpy of liquid lanthanum oxide. The cp of the liquid has been estimated to be a constant value of 200 J/(K⭈mol) following the estimation of Glushko et al. [1982Glu] (also adopted by the SGTE [1997SGT]).

3. Thermodynamic Models The thermodynamic description of La2O3 has been optimized using the data discussed in Section 2.

Table 5 Temperatures and enthalpies of polymorphic transitions and melting Transition A-type → H-type H-type → X-type X-type → Liquid

108

Temperature (K)

Reference

⌬H (kJ/mol)

Reference

2313 2383 2586

[1966Foe] [1966Foe] Section 2.1

46 60 75

[1995Du] [1995Du] Section 2.4



Fig. 3 Square diagram for nonstoichiometric lanthanum oxide

The two-sublattice model is used to describe the ionic liquid [1985Hil, 1991Sun2]. All solid phases are modeled using the compound energy model [1986And, 1988Hil]. Oxygen solubility in La is modeled using interstitial solution models. The standard elements reference state (SER), i.e., the most stable states of the elements at 298.15 K and 1 bar, has been chosen as the reference state of the system.

3.1 Stoichiometric Lanthanum Sesquioxide The thermodynamic description of the A-, H-, and Xtype La2O3 has been optimized using the above-mentioned experimental data and Eq 4. GLa2O3(T ) ⫺ H SER(298.15) ⫽ A ⫹ BT ⫹ CT ln (T )

0

⫹ DT 2 ⫹ ET ⫺1

(Eq 4)

The parameters A and B were optimized using values for ⫺⌬H 0298 (A-La2O3) and S 0298.15 for A-La2O3. The A and B parameters of the H and X phases were optimized using the respective transition enthalpies and temperatures. The parameters C, D, and E are assumed to be identical for the A, H, and X phases and were optimized using cp and heat content values.

3.2 Substoichiometric Lanthanum Oxide La2O3ⴚx Ackermann and Rauh [1971Ack] suggest that in a mixture with lanthanum metal the equilibrium composition of the lanthanum oxide is substoichiometric. Density and x-ray diffraction studies carried out by Miller and Daane [1965Mil] on Gd2O3, Er2O3, Y2O3, and Lu2O3 led them to conclude that these show substoichiometry due to the formation of oxygen vacancies, Va, in the anion sublattice. We have assumed an analogous model for the substoichiometry of lanthanum oxide. The lack of negative charge in the anion sublattice due to oxygen vacancies is compensated by substitution of La2+ for La3+ in the cation sublattice giving the average chemical formula (La3+,La2+)2(O2⫺,Va)3. The molar Gibbs energy 0GLa2O3⫺x of the substoichiometric phase can then be calculated using the compound-energy model [1986And], which has already been successfully applied to other nonstoichiometric ionic phases [1988Hil] and is given by: 0

GLa2O3⫺x ⫽ yLa⫹3yO⫺2 0GLa⫹3:O⫺2 ⫹ yLa⫹3yVa 0GLa⫹3:Va ⫹ yLa⫹2yO⫺2 0GLa⫹2:O⫺2 ⫹ yLa⫹2yVa 0GLa⫹2:Va ⫹ RT [2( yLa⫹3 ln yLa⫹3 ⫹ yLa⫹2 ln yLa⫹2) ⫹ 3( yO⫺2 ln yO⫺2 ⫹ yVa ln yVa)]⫹ (EGm)


(Eq 5)

109

Section I: Basic and Applied Research The excess term EGm has been set equal 0 to this assessment, which is reasonable, as the value of x in La2O3⫺x is small. The model can be visualized by the composition square in Fig. 3. Each corner represents a 0G parameter, three of which refer to compounds that are not neutral and can therefore not exist on their own. Only compounds along the neutral line can exist on their own. The Gibbs energy of the two end points of the neutral line, La2O3 and La2O2, can be given by Eq 6 and 7, respectively. GLa⫹3:O⫺2 ⫽ 0GLa2O3

0

(Eq 6)

and

冢

冣

20 1 2 2 1 1 GLa⫹2:O⫺2 ⫹ 0GLa⫹2:Va ⫹ 3RT ln ⫹ ln 3 3 3 3 3 3 ⫽ 2 0GLaO

(Eq 7)

From these equations, two of the four 0G parameters can be determined. Two more equations are still needed to determine the other two 0G parameters. We choose 0GLa⫹3:Va as reference and give it the value:

GLa⫹3:Va ⫽ 0GLa2O3 ⫺

0

30 GO2 2

(Eq 8)

The last 0G finally can be determined using the reciprocal relation: GLa⫹3:Va ⫺ 0GLa⫹3:O⫺2 ⫺ 0GLa⫹2:Va ⫹ 0GLa⫹2:O⫺2 ⫽ ⌬Gr

0

(Eq 9) where ⌬Gr represents deviations from ideality, but since the nonstoichiometry is rather small, ⌬Gr can be set equal to 0. The only function to be optimized is 0GLaO and is given by:

GLaO ⫽

0

10 1 G ⫹ 0G ⫹ A ⫹ BT 3 La2O3 3 La

(Eq 10)

3.3 Lanthanum Metal We describe oxygen solution in lanthanum metal using interstitial solution models. For dhcp-La, we use (La)1(Va,O)0.5; for fcc-La, (La)1(Va,O)1; and for bcc-La, (La)1(Va,O)1.5. The fcc structure has one octahedral interstitial site per metal atom and the interstitial sublattice can in principle be fully occupied as is the case for, e.g., fcc carbides. The hcp (hexagonal close packed) structure has one octahedral interstitial site per metal atom as well, but shows pairwise shorter distances between the interstitial sites. It is therefore usually assumed that only one-half of the interstitial sites can be occupied, which is very nicely illustrated by the Ti–O system where the solubility limit of oxygen in hcp-Ti is almost exactly xO ⫽ 1/3 [1999Wal]. The situation in the dhcp structure is the same as in the hcp structure. The bcc structure is more complex in that it has distorted octahedral and tetrahedral interstitial sites. The octahedral sites are somewhat smaller, but can, to a certain degree, be more easily distorted to accommodate interstitial atoms. Traditionally, interstitial solution in the bcc structure is modeled using the formula (Me)1(Va,X)3, but as for the hcp structure, the occupation of certain interstitial sites excludes the occupation of others. There are octahedral interstitial sites at the cube face and cube edges of the unit cell, in total three per metal atom, but the occupation of a cube face site excludes the occupation of adjacent cube edge sites. In this way, the maximum occupation is 1.5 per metal atom. For the tetrahedral interstitial sites, the situation is similar. There are four sites very close to each other at each cube face or a total of six sites per metal atom, Table 6 Thermodynamic parameters of the La-O system. All parameter values are given in SI units (J, mol, K; and R ⴝ 8.31451 Jⴢ(molⴢK)ⴚ1) Dhcp-La: (La)1(Va,O)0.5 1 0 dhcp GLaO0.5 ⫽ 0GLa ⫹ 0GO2 ⫺ 285,000 ⫹ 42.4T 4 Fcc-La: (La)1(Va,O)1 1 fcc 0 GLaO ⫽ 0GLa ⫹ 0GO2 ⫺ 570,000 ⫹ 91.4T 2 Bcc-La: (La)1(Va,O)1.5 3 0 bcc GLaO1.5 ⫽ 0GLa ⫹ 0GO2 ⫺ 855,000 ⫹ 142.5T 4 A-La2O3: (La3+,La2+)2(O2ⴚ,Va)3 0 A GLa2O3(T ) ⫺ H SER ⫽ ⫺1,835,600 ⫹ 674.72T ⫺ 118T ln (T ) ⫺ 0.008T 2 ⫹ 620,000T ⫺1 1 A 1 0 GLaO ⫽ 0GLa ⫹ 0GLa ⫹ 62,000 ⫹ 0 ⭈ T 2O3 3 3 H-La2O3: (La3+,La2+)2(O2ⴚ,Va)3 0 H G La2O3(T ) ⫺ H SER ⫽ ⫺1,789,600 ⫹ 654.83T ⫺ 118T ln (T ) ⫺ 0.008T 2 ⫹ 620,000T ⫺1 10 A 1 GLaO ⫽ GLa2O3 ⫹ 0GLa ⫹ 62,000 ⫹ 0 ⭈ T 3 3 X-La2O3: (La3+,La2+)2(O2ⴚ,Va)3 0 X GLa2O3(T ) ⫺ H SER ⫽ ⫺1,729,600 ⫹ 629.65T ⫺ 118T ln (T )

0

The parameters A and B were optimized using the experimental data from Ackermann and Rauh [1971Ack]. Although these measurements only concern A-La2O3, there is no reason to believe that the high-temperature polymorphs show a much smaller nonstoichiometry. Lacking further information, we choose the same model for H- and X-La2O3 as for A-La2O3 and use the same parameters for 0GLaO.

110

⫺ 0.008T 2 ⫹ 620,000T ⫺1 10 A 1 GLaO ⫽ GLa2O3 ⫹ 0GLa ⫹ 62,000 ⫹ 0 ⭈ T 3 3 Liquid: (La3+)P(O2ⴚ,VaⴚQ)Q 0 GLa2O3(l)(T ) ⫺ H SER ⫽ ⫺1,812,300 ⫹ 1285.34T ⫹ ⫺200T ln (T ) 0


Basic and Applied Research: Section I but since only one out of four sites can be occupied, the maximum occupation is 1.5 per metal atom here as well. That is, the same model can be used for the bcc structure regardless of the actual occupation (octahedral or tetrahedral sites). Waldner and Eriksson [1999Wal] used the model (Ti)1(Va,O)3 to describe dissolution of oxygen in bcc-Ti and had problems with the end point TiO3 becoming too stable when they tried to fit the solution data. Using the model (Ti)1(Va,O)1.5 could possibly resolve this problem. For some metals (e.g., Ag [1997Ass], Cu [1994Hal], and Fe [1991Sun1]), a substitutional solution model has been used to describe the oxygen solubility. This was tried for La as well, but this resulted either in strong deviations from Sievert’s law even at very low oxygen content or in fcc-O becoming much more stable than oxygen gas, neither of which is acceptable. The only actual experimental data point concerns oxygen in fcc-La (Section 2.5). There are no data on dhcp-La or bcc-La. In Y-O, the solubility of oxygen is slightly larger in bcc-Y than in hcp-Y [1998Swa]; in Ti-O, the solubility in hcp-Ti is a factor 4 to 5 larger than in bcc-Ti [1999Wal]; and in Fe-O, the solubility is twice as large in bcc-Fe as in fccFe [1991Sun1]. It does not seem to be possible a priori to say whether the oxygen solubility in dhcp-La and bcc-La should be smaller or larger than in fcc-La. It does seem that the difference should not be extremely large, though. We thus assume that the oxygen solubility is similar in dhcp-La, fcc-La, and bcc-La. This is to some extent supported by the

results from Okabe et al. [1998Oka2], who found similar Gibbs energies for oxygen dissolution in fcc-La, dhcp-Pr, and dhcp-Nd. As for the temperature dependence, we assume ⌬S ⫽ ⫺70 J/(mol⭈K) for the reaction 1/2O2 (1 bar) → O (1 mass.%). Okabe et al. [1998Oka1] found similar values in their study of Gd, Tb, Dy, and Er.

3.4 Liquid Phase The two-sublattice model for ionic liquids [1985Hil, 1991Sun2], used for melts containing species with different tendencies for ionization, assumes that the cations mix on one sublattice, and the anions on the other. For the La-O system, the liquid can be represented by the formula (La+3)P(O⫺2,Va⫺Q)Q , where each set of parentheses surround one sublattice. Charged vacancies are introduced to allow a continuous description toward the pure metallic liquid. The values of P and Q must vary with the composition of the liquid in order to maintain electroneutrality and are given by: P ⫽ yO⫺2 ⭈ 2 ⫹ yVa⫺Q ⭈ Q

(Eq 11)

and Q ⫽ 3 ⭈ yLa⫹3

(Eq 12)

where y denotes the respective site fractions. The end points

Fig. 4 Tentative binary phase diagram of the La-O system


111

Section I: Basic and Applied Research

Fig. 5 Stability diagram of La2O3

of the described liquid are given by La2O3 (for yVa ⫽ 0 and yO⫺2 ⫽ 1) and La3Va3 (for yVa ⫽ 1 and yO⫺2 ⫽ 0). The molar Gibbs energy is then given by: 0 Liq 0 Liq GLiq m ⫽ 3yVa⫺Q GLa ⫹ yO⫺2 GLa2O3 ⫹ 3RT(yO⫺2 ln yO⫺2

⫹ yVa⫺Q ln yVa⫺Q) ⫹ EGLiq m

(Eq 13)

Due to lack of data, the excess parameter EGLiq m is set equal to 0, so that the liquid is described as an ideal solution between liquid La and liquid La2O3. The molar Gibbs energy of pure liquid La, 0GLa(1), is taken from [1991Din]; 0GLa2O3(1) represents the molar Gibbs energy of ideal nondissociated liquid La2O3 and was optimized using Eq 14. GLa2O3(1)(T ) ⫺ H SER(298.15) ⫽ A ⫹ BT ⫹ CT ln (T )

0

(Eq 14) The parameters A and B were calculated using the melting temperature of La2O3 and the enthalpy of melting estimated at 75 kJ/mol (Section 2.4). The heat capacity of the liquid was set equal to a constant value of 200 J/(mol⭈K).

112

3.5 Gaseous Phase The gas phase is described as an ideal mixture containing the species La, LaO, LaO2, La2O, La2O2, O, O2, and O3. The description of La, LaO, LaO2, La2O, and La2O2 is taken from the SGTE substance database [1997SGT] (originating from Glushko et al. [1982Glu]). The description of O and O3 is taken from [1992SGT], and the description of O2 from Dinsdale [1991Din]. These data are not reviewed here.

4. Results and Discussion The parameters of the 0G(T ) functions optimized in this study are listed in Table 6. The optimization was performed using the PARROT [1984Jan] program included in the Thermo-Calc database system [1985Sun]. The optimization of 0GLaO delivered a negative B parameter. This made the solid LaO-phase more stable than the liquid at high temperatures. This result seemed unreasonable and the B parameter was therefore set equal to zero. A tentative calculated phase diagram is presented in Fig. 4. This diagram was calculated using the optimized parameters. Of course, it is highly speculative due to the lack of binary data. A stability diagram was also calculated for the


Basic and Applied Research: Section I La-O system (Fig. 5). This suggests that lanthanum metal is only stable at extremely low oxygen partial pressures. Including the thermodynamic description of the gas phase in the calculation of the stability diagram presented problems, as, contrary to experimental observations, the gas phase became stable below the melting temperature of La2O3 (in air atmosphere). The dominating species turned out to be LaO2 and not the experimentally observed LaO species [1971Ack]. The data for LaO2 have only been estimated, whereas the data for the other species (La, LaO, La2O, and La2O2) are based on experimental measurement [1982Glu], and excluding LaO2 from the dataset solves the problem. Acknowledgment Financial support under grant number 20-53542.98 from the Swiss National Science Foundation is gratefully acknowledged. References 1904Mut: W. Muthmann and L. Weiss: Justus Liebig’s Annalen der Chemie, 1904, vol. 331, pp. 1-50 (in German). 1913Ruf : O. Ruff, H. Seiferheld, and J. Suda: Z. Anorg. Allg. Chem., 1913, vol. 82, pp. 373-400 (in German). 1924Moo: J.E. Moose and S.W. Parr: J. Am. Chem. Soc., 1924, vol. 46, pp. 2656-61. 1932War]: H. von Wartenberg and H.J. Reusch: Z. Anorg. Allg. Chem., 1932, vol. 207, pp. 1-20 (in German). 1940Rot: W.A. Roth, U. Wolf, and O. Fritz: Z. Elektrochem., 1940, vol. 46, pp. 42-45 (in German). 1951Blo: J.O. Blomeke and W.T. Ziegler: J. Am. Chem. Soc., 1951, vol. 73, pp. 5099-102. 1953Hub: E.J. Huber and C.E. Holley: J. Am. Chem. Soc., 1953, vol. 75, pp. 3594-95. 1959Gol: H.W. Goldstein, E.F. Neilson, P.N. Walsh, and D. White: J. Phys. Chem., 1959, vol. 63, pp. 1445-49. 1959War: H. Von Wartenberg: Z. Anorg. Allg. Chem., 1959, vol. 299, pp. 227-31 (in German). 1961Kin: E.G. King, W.W. Weller, and L.B. Pankratz: “Thermodynamic Data for Lanthanum Sesquioxide,” Report of Investigation 5857, United States Bureau of Mines, Washington, DC, 1961. 1961Spe: F.H. Spedding, J.J. Hanak, and A.H. Daane: J. LessCommon Met., 1961, vol. 3, pp. 110-24. 1963Jus: B.H. Justice and E.F. Westrum: J. Phys. Chem., 1963, vol. 67, pp. 339-45. 1964Jay: A. Jayaraman and R.C. Sherwood: Phys. Rev. Lett., 1964, vol. 12 (1), pp. 22-23. 1965Fit: G.C. Fitzgibbon, C.E. Holley, and I. Wadso¨: J. Phys. Chem., 1965, vol. 69, pp. 2464-66. 1965Foe¨: M. Foe¨x: Z. Anorg. Allg. Chem., 1965, vol. 337, pp. 31324 (in German). 1965Mil: A.E. Miller and A.H. Daane: J. Inorg. Nucl. Chem., 1965, vol. 27, pp. 1955-60. 1966Foe¨: M. Foe¨x and J.-P. Traverse: Rev. Int. Hautes Tempe´r. Re´fract., Fr., 1966, vol. 3, pp. 429-53 (in French). 1966Sat: T. Sata: Rev. Hautes Tempe´r. Re´fract., 1966, vol. 3, pp. 337-41 (in French). 1967Gve: G.G. Gvelesiani and T.S. Yashvili: Russ. J. Inorg. Chem., 1967, vol. 12, pp. 1711-12. 1967Mor: O.A. Mordovin, N.I. Timofeeva, and L.N. Drozdova: Inorg. Mater., 1967, vol. 3, pp. 159-62.

1967Nog: T. Noguchi and M. Mizuno: Solar Energy, 1967, vol. 11, pp. 90-94. 1968Mu¨l: H.K. Mu¨ller-Buschbaum: J. Inorg. Nucl. Chem., 1968, vol. 30, p. 895 (in German). 1968Yas: T.S. Yashvili, D.S. Tsagareishvili, and G.G. Gvelesiani: Teplofizika Vys. Temp., 1968, vol. 6 (5), pp. 817-20 (in Russian). 1969Bra: G. Brauer and A. Siegert: Z. Anorg. Allg. Chem., 1969, vol. 371, pp. 263-73 (in German). 1971Ack: R.J. Ackermann and E.G. Rauh: J. Chem. Thermodyn., 1971, vol. 3, pp. 445-60. 1975Cou: J.-P. Coutures, R. Verges, and M. Foe¨x: Rev. Int. Hautes Tempe´r. Re´fract., Fr., 1975, vol. 12, pp. 181-85 (in French). 1976Shp: E.E. Shpil’rain, D.N. Kagan, L.S. Barkhatov, and V.V. Koroleva: High Temp.—High Pressures, 1976, vol. 8, pp. 183-86. 1979Ald: P. Aldebert and J.P. Traverse: Mater. Res. Bull., 1979, vol. 14 (3), pp. 303-23 (in French). 1979Bas: R. Basili, A. El-Sharkawy, and S. Atalla: Rev. Int. Hautes Tempe´r. Re´fract., Fr., 1979, vol. 16, pp. 331-38. 1982Glu: V.P. Glushko, L.V. Gurvich, G.A. Bergman, G.A. Khachkuruzov, V.A. Medvedev, I.V. Veyts, and V.S. Yungman: Thermodynamic Properties of Individual Substances, Nauka, Moscow, 1982, vol. 4 (in Russian). 1982Sam: The Oxide Handbook, G.V. Samsonov, ed., IFI/Plenum, New York, NY, 1982. The Russian edition was published by Metallurgiya Press, Moscow, 1978. 1984Jan: B. Jansson: “A General Method for Calculating Phase Equilibria under Different Types of Conditions,” TRITA-MAC 233, Royal Institute of Technology, Stockholm, 1984. ˚ gren: Metall. 1985Hil: M. Hillert, B. Jansson, B. Sundman, and J. A Trans. A, 1985, vol. 16A, pp. 261-66. 1985Sun: B. Sundman, B. Jansson, and J.-O. Andersson: CALPHAD, 1985, vol. 9 (2), pp. 153-90. 1986And: J.-O. Andersson, A.F. Guillermet, M. Hillert, B. Jansson, and B. Sundman: Acta Metall., 1986, vol. 34 (3), pp. 437-45. 1988Hil: M. Hillert, B. Jansson, and B. Sundman: Z. Metallkd., 1988, vol. 79 (2), pp. 87-87. 1991Din: A.T. Dinsdale: CALPHAD, 1991, vol. 15 (4), pp. 317-425. 1991Kna: Thermochemical Properties of Inorganic Substances, 2nd ed., O. Knacke, O. Kubaschewski, and K. Hesselemann, eds., Springer, Berlin, 1991. 1991Sun1: B. Sundman: J. Phase Equilibrium, 1991, vol. 12 (1), pp. 127-40. 1991Sun2: B. Sundman: CALPHAD, 1991, vol. 15 (2), pp. 109-19. 1992SGT: The SGTE substance database, version 1992, SGTE (Scientific Group Thermodata Europe), Grenoble, France, 1992. 1994Hal: B. Hallstedt, D. Risold, and L.J. Gauckler: J. Phase Equilibrium, 1994, vol. 15 (5), pp. 483-99. 1995Du: Y. Du, M. Yashima, T. Koura, M. Kakihana, and M. Yoshimura: J. Eur. Cera. Soc.,1995, vol. 15 (6), pp. 503-11. 1997Ass: J. Assal, B. Hallstedt, and L.J. Gauckler: J. Am. Ceram. Soc., 1997, vol. 80 (12), pp. 3054-60. 1997SGT: The SGTE substance database, version 1997, SGTE (Scientific Group Thermodata Europe), Grenoble, France, 1997. 1998Oka1: T.H. Okabe, K. Hirota, E. Kasai, F. Saito, Y. Waseda, and K.T. Jacob: J. Alloys Compounds, 1998, No. 279, pp. 184-91. 1998Oka2: T.H. Okabe, K. Hirota, Y. Waseda, and K.T. Jacob: J. Mining Mater. Processing Inst. Jpn. (Shigen-to-Sozai), 1998, vol. 114 (11), pp. 813-18. 1998Swa: V. Swamy, H.J. Seifert, and F. Aldinger: J. Alloys Compounds, 1998, vol. 269, pp. 201-07. 1999Wal: P. Waldner and G. Eriksson: CALPHAD, 1999, vol. 23 (2), pp. 189-218.


113