Thermodynamic analysis of the ternary La–Ni–O system

Journal of Alloys and Compounds 375 (2004) 147–161

Thermodynamic analysis of the ternary La–Ni–O system M. Zinkevich∗ , F. Aldinger Max-Planck-Institut für Metallforschung and Institut für Nichtmetallische Anorganische Materialien, Universität Stuttgart, Heisenbergstraße 3, D-70569 Stuttgart, Germany Received 27 August 2003; received in revised form 20 November 2003; accepted 20 November 2003

Abstract The available literature information on the thermodynamic properties and phase equilibria for the La–Ni–O system has been critically assessed. Based on the known thermodynamics of the boundary systems La–Ni, La–O, and Ni–O models have been defined to describe the Gibbs energy of the individual phases, and the model parameters have been optimized by least-squares fit to the selected experimental information of different kind (phase diagram data, calorimetric data, and equilibrium oxygen pressures) using the CALPHAD-method (calculating phase diagrams). A self-consistent set of Gibbs energy functions describing the La–Ni–O system, which contains four ternary phases La2 NiO4 , La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 that are all treated as stoichiometric compounds has been obtained for the first time. Various phase diagrams and thermodynamic properties have been calculated and are compared with the experimental measurements. Possible directions for the future work are discussed. © 2003 Elsevier B.V. All rights reserved. Keywords: SOFC; Electrode materials; Phase diagram; Thermodynamic modeling

1. Introduction The ternary La–Ni–O system contains Ruddlesden–Popper (RP) phases with the general formula Lan+1 Nin O3n+1 , which possess n layers of perovskite-type LaNiO3 , separated by single rocksalt-type LaO layers. These RP-phases have received considerable attention, because of their close relationship to the superconducting cuprates and interesting electrical, magnetic, and catalytic properties. For example, LaNiO3 and La2 NiO4 were studied as possible cathode materials for solid oxide fuel cells (SOFC) [1,2]. On the other hand, SOFC anodes consist primarily of metallic nickel in a ceramic oxide-ion conducting matrix, such as strontium and magnesium doped lanthanum gallate (LSGM), which has recently been identified as a promising electrolyte material for intermediate temperatures. Several studies describing the formation of interfacial layers between LSGM and Ni-based anodes have been reported, in which lanthanum nickelates have been identified among the reaction products [3,4]. The knowledge of the phase equilibria in the La–Ni–O system ∗ Corresponding author. Tel.: +49-711-68-93-105; fax: +49-711-68-93-131. E-mail address: [email protected] (M. Zinkevich). URL: http://aldix.mpi-stuttgart.mpg.de/zinkevit/home mz.html.

0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.11.138

is essential for the successful preparation of RP-phases as well as for the understanding of possible chemical reactions, which may influence the long-term performance of SOFC with LSGM electrolyte. The topology of the ternary system La–Ni–O is not very well known. Most of the experimental studies are limited to a temperature range 973–1573 K. No measurable solubility of La in NiO and of Ni in La2 O3 has been detected. The solubility of oxygen in solid and liquid La–Ni alloys has not been determined. Numerous works contributed to the experimental study of the RP-phases, which occur in several polymorphic modifications depending on temperature and/or oxygen content. The reported conditions for the preparation of these compounds are, however, not entirely consistent. Furthermore, any experimental study is limited to a certain temperature/composition range, because of the constraints imposed by equipment. On the other hand, by minimizing the Gibbs energy of a system under the given set of conditions using a numerically sophisticated procedure, phase equilibria can be calculated. This technique is known as CALPHAD-method [5,6] and allows the calculation of any kind of phase diagram or thermodynamic property of interest based on the self-consistent thermodynamic description of the system. It also offers a unique possibility to check consistency between different types of experimental data.

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The essence of the CALPHAD-method is the analytical representation of the Gibbs energy of individual phases in a system in terms of state variables, such as temperature, pressure, and composition (thermodynamic description). Some of these expressions contain adjustable coefficients (model parameters). The optimal values of the unknown parameters providing the best match between the calculated quantities and their experimental counterparts are usually obtained by the weighted non-linear least squares minimization procedure (thermodynamic optimization), using experimental thermochemical, constitutional (phase diagram), and crystallographic data as input. The selection of the model for a phase must be based on the physical and chemical properties of that phase, most importantly crystallography, type of bonding, ordering, defect structure, etc. The purpose of the present work is to obtain a self-consistent thermodynamic description of the La–Ni–O system based on the known thermodynamics of the La–Ni, La–O, and Ni–O subsystems and the available literature information on ternary phase equilibria and thermodynamic functions of the stoichiometric RP-phases.

2. Binary systems In the La–Ni system, there are nine intermetallic compounds La3 Ni, La7 Ni3 , LaNi, La2 Ni3 , LaNi2 , La7 Ni16 , LaNi3 , ␣-La2 Ni17 , ␤-La2 Ni17 , and LaNi5 . The compounds La3 Ni, La7 Ni3 , LaNi, and LaNi5 show congruent melting points, while La2 Ni3 , LaNi2 , La7 Ni16 , LaNi3 , ␣-La2 Ni17 , and ␤-La2 Ni17 are formed by peritectic reactions. LaNi5 is the only phase with a measurable homogeneity range. A self-consistent thermodynamic description of the La–Ni system has been obtained by Liu and Jin [7]. Recently, Grundy et al. [8] reported the thermodynamic optimization of the La–O system, which is characterized by a complete miscibility in the liquid phase and by a presence of La2 O3 compound, which exist in three polymorphic modifications, denoted A, H, and X. At high temperatures, hexagonal A-La2 O3 transforms into partially ordered hexagonal H-La2 O3 and then into cubic X-La2 O3 . Solid lanthanum dissolves significant amount of oxygen. La2 O3 is substoichiometric in equilibrium with La-metal. In the Ni–O system, one solid oxide, bunsenite is formed, with the stoichiometry NiO, which is a metal-deficient p-type conductor, with major lattice defects of Ni3+ cations and cation site vacancies. The thermodynamic description of the binary system has been first obtained by Taylor and Dinsdale [9] using the ionic two-sublattice model for the description of the liquid phase and neglecting the oxygen solubility in solid nickel. Kowalski and Spencer [10] re-evaluated the description of the Ni–O liquid phase using the associate model and modeled the oxygen solubility in solid nickel. Both assessments provide excellent reproduction of the experimental data below 2100 K, but result in different high-temperature phase equilibria, so that the cal-

culated phase diagram either shows a restricted miscibility gap in the liquid phase and a congruent melting point of NiO [9] or completely miscible liquid and gas-peritectic formation of NiO [10].

3. Ternary La–Ni–O system 3.1. Solid phases The ternary Ruddlesden–Popper phases in the La–Ni–O system are described as Lan+1 Nin O3n+1 . The existence of La2 NiO4 (n = 1), La3 Ni2 O7 (n = 2), La4 Ni3 O10 (n = 3), and LaNiO3 (n = ∞) has been confirmed in many reports [11–15]. Attempts to obtain single-phase compounds with n ≥ 4 were not successful although they may form on the nanometer scale as intergrowths in the structure of La3 Ni2 O7 and La4 Ni3 O10 [16]. Kitayama reported the synthesis of a compound with the stoichiometry La6 Ni5 O15 [17], but indicated that it might be a solid solution of La4 Ni3 O10 due to the similarity of X-ray diffraction patterns. It can be therefore concluded that the n ≥ 4 members of the Lan+1 Nin O3n+1 series do not belong to the thermodynamically stable phases in the La–Ni–O system. La2 NiO4 can exist with excess, while La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 —with a deficiency of oxygen. The oxidation/reduction occurs in a number of steps through the formation of intermediate phases and has been a topic of many publications. The corresponding phase relations are very complex and difficult to understand without knowledge of the La–Ni–O system in general. Therefore, in the present study, all RP-phases were assumed stoichiometric and the literature information on their oxygen non-stoichiometry is not reviewed here. This simplification is reasonable since the thermodynamic properties of the non-stoichiometric phases can be derived from those of the stoichiometric compounds and the topology of the La–Ni–O system will not change significantly, if the effect of variable oxygen content is taken into account. This is being considered as a possible topic for further work. The assessed literature information on the stoichiometric ternary phases of the La–Ni–O system is compiled in Table 1. A summary of the available relevant experimental data on phase equilibria in the La–Ni–O system is given in Table 2. In addition, values, which are assessed or obtained from the equilibrium calculations in this work, are provided. At high temperatures, La2 NiO4 adopts the tetragonal K2 NiF4 -type structure with only Ni2+ -ions and shows the successive phase transitions (HTT → LTO → LTLO) upon decreasing temperature [18,19]. HTT, LTO, and LTLO stand for the high-temperature tetragonal, low-temperature orthorhombic and low-temperature less orthorhombic phase, respectively. The difference between two lattice parameters of the LTLO phase is very small, so that it can also be considered as tetragonal within the limits of experimental errors: the refinement of diffraction patterns gave the same results for the space groups Pccn and P42 /ncm [18,19,30].

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149

Table 1 Stoichiometric ternary phases in the La–Ni–O system Phase (stability range)

Pearson symbol

Space group

Prototype

Lattice parameters

Reference

La2 NiO4 –LTLO (T < 74 ± 6 K)

oP28 or tP28

Pccn or P42 /ncm

–

–

[18,19]

La2 NiO4 –LTO (74 ± 6 < T < 700 ± 10 K)

oC28

Cmca

–

a = 0.54619(8) nm b = 1.26797(6) nm c = 0.54555(8) nm at 300 K

[20]

La2 NiO4 –HTT (T > 700 ± 10 K)

tI14

I4/mmm

K2 NiF4

–

[19]

La3 Ni2 O7

oC48

Cmcm

Sr3 Ti2 O7

a = 2.0502(1) nm b = 0.54494(7) nm c = 0.53981(7) nm at 300 K

[20]

La4 Ni3 O10

oC68

Cmca

Sr4 Ti3 O10

a = 0.5413(1) nm b = 2.8033(3) nm c = 0.5441(1) nm at 300 K

[20]

LaNiO3

hR30

R3c

LaNiO3

a = 0.54573(1) nm c = 1.31462(3) nm at 298 K

[21]

La2 NiO4 is antiferromagnetic with TN = 328 ± 1 K and magnetic moment of 1.58 ± 0.1µB per Ni-atom. Table 2 Selection of experimental information for the La–Ni–O system: phase diagram data Data description

Experimental techniques

Measured quantity

LTLO ⇔ LTO phase transition in La2 NiO4

ACa

Use

Reference

AC XRD, NMR XRD MPa ND XRD, NDa RSa IRa RSa NDa Assessed

T T T T T T T T T T T T

5K 0.5 K 5K 5K 10 K 10 K 10 K 5K 5K 10 K 0.5 K 6K

+ − + + + + + + + − +

[22] [23] [24] [19] [25] [18] [26] [27] [28] [29] [30] This work

LTO ⇔ HTT phase transition in La2 NiO4

XRD ND Assessed

T = 700 ± 10 K T = 770 ± 20 K T = 700 ± 10 K

+ −

[19] [18] This work

Invariant reaction: 4LaNiO3 = La4 Ni3 O10 + NiO + 0.5O2

TG (pO2 = 0.21 bar) TG, DTA (pO2 = 0.21 bar) TG, DTA (pO2 = 1 bar) XRD (pO2 = 0.21 bar) Calculated (pO2 = 0.21 bar)

T T T T T

20 K 20 K 20 K 20 K

+ − − −

[31] [32] [32] [15] This work

Invariant reaction: 2LaNiO3 = La2 NiO4 + NiO + 0.5O2

TG (pO2 = 0.21 bar) TG (pO2 = 1 bar) Unknown

T = 1323 ± 50 K T = 1393 K T = 1073 K

− − −

[33] [34] [35]

Invariant reaction: La4 Ni3 O10 = 2La2 NiO4 + NiO + 0.5O2

TG, EMF (pO2 = 0.21 bar)

T = 1485 ± 5 K

+

[36]

Eutectic reaction: liquid = NiO + La2 NiO4

Unknown Calculated

T = 1923 ± 50 K; x(NiO) ≈ 0.7 T = 1908 K; x(NiO) = 0.64

+

[37] This work

Melting point of La2 NiO4

Unknown Unknown Calculated

T = 1943 ± 50 K T = 2023 ± 50 K T = 1957 K

+ −

[38] [39] This work

= 80 = 56 = 75 = 75 = 70 = 80 = 75 = 73 = 65 = 60 = 70 = 74

± ± ± ± ± ± ± ± ± ± ± ±

= 1253 ± = 1367 ± = 1405 ± = 1120 ± = 1253 K

The column “Use” indicates whether the values were used (+) or not used (−) in the assessment. AC: adiabatic calorimetry, DTA: differential thermal analysis, EMF: electromotive force measurement, IR: infrared spectroscopy, MP: study of magnetic properties, ND: neutron diffraction, NMR: nuclear magnetic resonance, RS: Raman spectroscopy, TG: thermogravimetry, XRD: X-ray diffraction. a Measurements on single crystal.

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Kyomen et al. suggested the existence of additional incommensurate polymorphic modification of La2 NiO4 between 80 and 150 K [22]. It should be noted, however, that their conclusion is based on the observation of a wide tail on the high-temperature side of the sharp heat capacity peak, which corresponds to the LTO ⇔ LTLO phase transition. The amplitude of the anomaly is not significantly larger than the experimental noise, and, whatever effect is responsible for it, there is no evidence that the crystal structure of La2 NiO4 is different just below and above 150 K. Thus, at present, only three phases (HTT, LTO, and LTLO) can be considered as polymorphic forms of the stoichiometric La2 NiO4 . The LTO ⇔ LTLO transformation was interpreted as a first-order phase transition with a characteristic wide hysteresis. The transition temperature determined by different techniques spreads between 56 and 80 K (Table 2). Owing to the absence of the normal statistical distribution the values ≤60 K [23,29] were not included in the present analysis because of the possible systematic errors. This is in agreement with more recent studies using the same method [22,27]. The assessed equilibrium temperature of the LTO ⇔ LTLO phase transformation (74 ± 6 K) was obtained as a weighted average of the remaining data. The HTT ⇔ LTO phase transition was determined to be of second order [19]. This transformation has been reported to occur at 770 ± 20 K [18] or 700 ± 10 K [19]. Tavares [40] observed a sharp rise (570–640 K) and then a sharp fall (640–680 K) in heat capacity of the air-prepared La2 NiO4 . However, this phenomenon can hardly be associated with the HTT ⇔ LTO phase transition, because the oxygen content in the sample has not been measured and it is well-known that the stoichiometric La2 NiO4 can only be obtained by annealing in reducing atmospheres [41]. The absence of magnetic ordering down to 4 K reported in [40] also indicates the significant deviation from the stoichiometric composition. The assessed temperature for the HTT ⇔ LTO phase transition is 700 ± 10 K. This choice is supported by the careful X-ray diffraction examination [19], while the value of 770 K reported by Rodriguez-Carvajal et al. [18] appears to be overestimated. In the latter study, the orthorhombic strain in La2 NiO4 has been investigated as a function of temperature, but little attention has been paid to the high-temperature range, where measurements have only been conducted at 600, 700, and 750 K. At the same time, extrapolating the data of [18] results in zero orthorhombic strain already at 720 K. The stoichiometric La2 NiO4 is antiferromagnetic with the Néel point (TN ) at 328 ± 1 K [18,22,23,25]. Earlier studies indicated TN around 650 K [30,42,43], but later [25] this was shown to be caused by the presence of metallic Ni, which has a Curie point at 633 K. The value of the magnetic moment per Ni-atom is assessed as 1.58 ± 0.1µB based on neutron diffraction measurements [18,25,30]. Both the La3 Ni2 O7 and La4 Ni3 O10 phases crystallize in the orthorhombic cell (Table 1). First structure refinements resulted in Fmmm space group [44,45]. Recently, the crystal structure of the lanthanum nickelates Lan+1 Nin Oy (n = 1,

2, 3) has been re-investigated by means of neutron and X-ray powder diffraction, synchrotron radiation and EXAFS spectroscopy [20,46]. The lattice symmetry was found to be orthorhombic. However, two parameters of the unit cell differ only slightly and thus, all phases can be regarded as distorted tetragonal structures. The orthorhombic unit cell of La2 NiO4 is formed from the tetragonal K2 NiF4 -type structure by inclination and rotation of the oxygen octahedron around the c-axis, so that two different Ni–O bond lengths are present. The oxygen octahedrons in La3 Ni2 O7 are significantly distorted and show four different interatomic distances. In La4 Ni3 O10 , there are two types of oxygen octahedrons: practically ideal octahedrons centered by Ni3+ and distorted octahedrons centered by Ni2+ ions. The proposed space groups (Cmcm and Cmca for La3 Ni2 O7 and La4 Ni3 O10 , respectively) allowed the better fit to observed data than the Fmmm model suggested previously. LaNiO3 crystallizes in the rhombohedrally distorted perovskite-type structure, where all Ni ions are trivalent. The existence of the tetragonal and cubic modifications of LaNiO3 at certain values of oxygen deficiency has been mentioned in the literature [32,34,47]. It is stressed however, that the effect of oxygen non-stoichiometry is not taken into account in the present study. Therefore, only rhombohedral LaNiO3 is assumed to exist. Unlike La2 NiO4 , the low-temperature measurements revealed no evidence for symmetry lowering or magnetic/charge ordering in La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 [21,44–46,48]. 3.2. Phase diagram Phase diagrams of the La–Ni–O system are available as partial isothermal sections at 1373 and 1473 K [17,36,49], a pseudobinary section La2 O3 –NiO [50–52], and a vertical section along the La2 NiO4 –LaNiO3 join [14,49]. The La–Ni–O liquidus surface is unknown. The reported isothermal sections are mutually consistent assuming that the La6 Ni5 O15 phase found by Kitayama [17] is identical to La4 Ni3 O10 and show the presence of five stable phases: Ni, NiO, La2 O3 , La2 NiO4 , and La4 Ni3 O10 . The existence of the three-phase equilibria Ni + NiO + La2 NiO4 , Ni + La2 O3 + La2 NiO4 , and NiO + La2 NiO4 + La4 Ni3 O10 has been indicated. Neither La3 Ni2 O7 , nor LaNiO3 have been observed at temperatures from 1173 to 1673 K and oxygen pressures (pO2 ) between 1 and 10−14 bar [17,36,49]. Odier et al. determined phase relations in the La–Ni–O system in air between LaNiO3 and La2 NiO4 at temperatures ranging from 1073 to 1573 K [14]. The authors observed rhombohedral LaNiO3 , orthorhombic La3 Ni2 O7 , tetragonal La2 NiO4 , NiO, and a mixture of unresolved phases of the series Lan+1 Nin O3n+1 . Above 1473 K, the various phases were found to transform into La2 NiO4 and NiO. These results are consistent with the work of Cherepanov et al. [49], except for the presence of La3 Ni2 O7 . The absence of visible variation of the unit cell parameters of La2 NiO4 with the La/Ni ratio in the range 1.925–1.99 seems to exclude the possibility of

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151

a solid solution of NiO in La2 NiO4 at least for air-annealed compounds in agreement with Foëx et al. [39]. Recently, Bannikov and Cherepanov (the same group as in [49,36]) reported the synthesis and investigation of the thermodynamic stability of La4 Ni3 O10 , La3 Ni2 O7 , and LaNiO3 [31]. Thus, the existence of La2 NiO4 , La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 as thermodynamically stable phases in air in the vertical section La2 NiO4 –LaNiO3 is now well established. Their stability decreases in the order La2 NiO4 > La3 Ni2 O7 > La4 Ni3 O10 > LaNiO3 implying the following sequence of decomposition reactions (T1 < T2 < T3 ):

et al. studied the binary system La2 O3 –NiO at 973, 1073, and 1173 K in air [51]. LaNiO3 was the only intermediate phase found at 1073 and 973 K and La4 Ni3 O10 was the only intermediate phase at 1173 K. Contrary to previous work neither La2 NiO4+δ , nor La2−x NiO4+δ were found. This was interpreted as being due to the incomplete equilibration of samples in earlier studies. However, both the LaNiO3 and La4 Ni3 O10 compositions are outside the tie-line La2 O3 –NiO and hence, the results obtained in [51] cannot be used to construct the pseudobinary section La2 O3 –NiO.

4LaNiO3 = La4 Ni3 O10 + NiO + 0.5O2 ;

(1)

3.3. Thermodynamics

(2)

There are extensive thermodynamical studies of the La–Ni–O system, which are compiled in Table 3. Equilibrium oxygen pressures for the reaction La2 NiO4 ⇔ La2 O3 + Ni + 0.5O2 have been determined in a wide range of temperatures from 1073 to 1573 K [17,36,41,49,53]. Sreedharan et al. measured the free energy of formation of the La2 NiO4 from La2 O3 and NiO using the EMF method [54]. Good agreement exists between [49], [36], and [17]. Those data were used in the present study to evaluate the Gibbs energy function of the La2 NiO4 . The thermodynamic characteristic of the La4 Ni3 O10 compound has been obtained by the EMF method [36,49]. The cell reaction was 2La2 NiO4 + NiO + 0.5O2 ⇔ La4 Ni3 O10 due to the very slow formation of La3 Ni2 O7 (see above). Attempts to measure the EMF of the cell La2 NiO4 , La4 Ni3 O10 , La2 O3 , O2 (Pt)|O2− |(Pt)O2 , where the corresponding reaction is 3La2 NiO4 + 0.5O2 = La4 Ni3 O10 + La2 O3 [36] resulted in values, which cannot be reconciled with the thermodynamic properties of La2 NiO4 and La4 Ni3 O10 . Kitayama determined the standard Gibbs energy of the reaction 2NiO + 3La2 NiO4 + 0.5O2 = La6 Ni5 O15 at 1473 K [17]. However, the existence of the La6 Ni5 O15 compound is questionable and therefore, these data do not contribute to the equilibrium thermodynamics of the La–Ni–O system. Bannikov and Cherepanov [31] studied the decomposition thermodynamics of La4 Ni3 O10 and La3 Ni2 O7 using the EMF technique (Table 3). From their data, the free energy function of La3 Ni2 O7 can be evaluated. Nakamura et al. measured the equilibrium oxygen partial pressure for the reaction (1) by thermogravimetry at 1273 K [53], from which the Gibbs energy of the LaNiO3 can be calculated. Lazarev et al. measured the heat content of La2 NiO4 and detected no phase transitions between 298 and 1273 K [55]. This is in apparent contradiction with the results of structural studies, where the HTT ⇔ LTO phase transition has been found [18,19]. Since the sample investigated in [55] has been prepared in air, it can hardly be associated with the stoichiometric La2 NiO4 . Low-temperature heat capacity of La2 NiO4 has been measured by Castro and Burriel [23] and Kyomen et al. [22] with the use of an adiabatic calorimeter. The differences of 3–4% between the results of [22] and [23] could originate from the presence of a weakly bound

T1

3La4 Ni3 O10 = 4La3 Ni2 O7 + NiO + 0.5O2 ; 2La3 Ni2 O7 = 3La2 NiO4 + NiO + 0.5O2 ;

T2 T3

(3)

The decomposition of LaNiO3 at elevated temperatures is described in several publications [12,15,31–35], partially with rather conflicting results concerning the stability range and decomposition products (Table 2). The temperature of the reaction (1) in air has been measured as 1120 K [15], 1367 K [32], and 1253 K [31]. The sample of Byun et al. [15], however, contained significant amount of La2 O3 that might result in the lower apparent decomposition temperature due to the possible reaction: La2 O3 + 6LaNiO3 = 2La4 Ni3 O10 + 0.5O2 . The decomposition temperatures of 1367 K in air and 1405 K in oxygen [32] are inconsistent with the thermodynamic study of Nakamura et al. [53] (see below). Therefore, in the present work, the equilibrium temperature for the reaction (1) has been taken as 1253 ± 20 K. Reactions (2) and (3) have been observed directly [12,14,15] and indirectly confirmed in the thermodynamic study [31]. However, their equilibrium temperatures have not been accurately determined. Compared to La2 NiO4 and LaNiO3 , the compounds La3 Ni2 O7 and La4 Ni3 O10 form only very slowly [12], probably due to the complex layered structures. This explains the frequent observation of La2 NiO4 and NiO as the decomposition products of LaNiO3 and La4 Ni3 O10 [11,32–36,49]. As long as the equilibrium phases have not been formed, LaNiO3 and La4 Ni3 O10 can be in equilibrium with La2 NiO4 and NiO. In the present work, the temperature of the decomposition reaction La4 Ni3 O10 = 2La2 NiO4 + NiO + 0.5O2 in air [36] supported by the thermodynamic data (see below) has been utilized to evaluate the free energy function of the La4 Ni3 O10 compound. The pseudobinary section La2 O3 –NiO in air contains only one compound, La2 NiO4 [50,52], which melts congruently at 1943 K according to Timofeeva and Romanovich [38], while Foëx et al. indicated the melting point of La2 NiO4 around 2023 K [39]. Both values are in fair agreement taking into account the accuracy of such measurements (±50 K). Solid solutions based on La2 O3 , La2 NiO4 , or NiO have not been observed [50]. Revcolevschi [37] pointed out the existence of an eutectic in the system La2 O3 –NiO near 70 mol% NiO (i.e., between NiO and La2 NiO4 ) around 1923 K. Li

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Table 3 Selection of experimental information for the La–Ni–O system: thermodynamic data Data description

Experimental techniques

Measured quantity

Use

Reference

Equilibrium O2 pressure, La2 NiO4 + La2 O3 + Ni

EMF (T = 1073–1473 K) EMF (T = 1373 K) TG (T = 1473 K) TG (T = 1273 K) Annealing and quenching (T = 1173–1573 K)

pO2 pO2 pO2 pO2 pO2

+ + + − −

[36] [49] [17] [53] [41]

Equilibrium O2 pressure, La2 NiO4 + La4 Ni3 O10 + NiO

EMF (T = 1203–1473 K) EMF (T = 1373 K)

pO2 pO2

+ +

[36] [49]

Equilibrium O2 pressure, La2 NiO4 + La4 Ni3 O10 + La2 O3 Equilibrium O2 pressure, La2 NiO4 + La6 Ni5 O15 + NiO Equilibrium O2 pressure, La3 Ni2 O7 + La4 Ni3 O10 + NiO Equilibrium O2 pressure, La2 NiO4 + La3 Ni2 O7 + NiO Equilibrium O2 pressure, La4 Ni3 O10 + LaNiO3 + NiO Gibbs energy of formation of La2 NiO4 from oxides (NiO + La2 O3 = La2 NiO4 ) Heat content of La2 NiO4

EMF (T = 1203–1473 K) TG (T = 1473 K) EMF (T = 1370 K) EMF (T = 1368 K) TG (T = 1273 K) EMF (T = 1136–1259 K)

pO2 pO2 pO2 pO2 pO2 G

– – + + + –

[36] [17] [31] [31] [53] [54]

DC (T = 298–1273 K)

H − H298

–

[55]

Heat capacity of La2 NiO4

AC (T = 14–500 K) AC (T = 2–350 K) DSC (T = 300–800 K)

CP CP CP

+ – –

[22] [23] [40]

The column “Use” indicates whether the values were used (+) or not used (−) in the assessment. AC: adiabatic calorimetry, DC: drop calorimetry, DSC: differential scanning calorimetry, EMF: electromotive force measurement, TG: thermogravimetry.

oxygen in as-prepared samples, which have been studied in [23]. This results in a heat evolution above room temperature, while this effect disappears after annealing at 400 K and the heat capacity values obtained after the annealing were smaller than those obtained before the annealing [22]. Tavares studied the heat capacity of La2 NiO4 between 300 and 800 K [40]. However, as mentioned above, the sample was probably non-stoichiometric and therefore, these data are not taken into account.

4. Thermodynamic modeling The thermodynamic description of a ternary system is based on the Gibbs energy functions describing the individual phases in binary and unary subsystems. The Gibbs energy of the pure elements is taken from the SGTE (Scientific Group Thermodata Europe) unary database [56], while the description of the binary phases La3 Ni, La7 Ni3 , LaNi, La2 Ni3 , LaNi2 , La7 Ni16 , LaNi3 , ␣-La2 Ni17 , ␤-La2 Ni17 , LaNi5 , A-La2 O3 , H-La2 O3 , and X-La2 O3 is adopted from the corresponding binary systems [7,8]. Since the enthalpies cannot be defined absolutely, the Gibbs energy is referred to the constant enthalpy values of the so-called Stable Element References, HSER , at 298.15 K and 1 bar as recommended by SGTE [57]. The reference states are one mole of dhcp-La (double hexagonal close-packed structure), fcc-Ni (face-centered cubic structure) and 1/2 mol of O2 gas. The Gibbs energy of stoichiometric solid phases and end-members of solutions is represented as a power series in terms of temperature in the form:

◦

G(T) = G(T) − H SER = a + bT + cT ln(T) + dT2 + eT3 +

f
gn T n + T n (4)

where a to f and gn are coefficients and n stands for a set of integers. The stoichiometric compounds La2 NiO4 , La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 are represented by the formulas (La3+ )2 (Ni2+ )1 (O2− )4 , (La3+ )3 (Ni2+ )1 (Ni3+ )1 (O2− )7 , (La3+ )4 (Ni2+ )1 (Ni3+ )2 (O2− )10 , and (La3+ )1(Ni3+ )1 (O2− )3 , respectively. The gas phase is described as an ideal mixture containing the gaseous species La, La2 O, La2 O2 , LaO, Ni, NiO, O, O2 , and O3 . The Gibbs energy of the gas phase is given as  

P ◦ gas gas G = (5) xi Gi + RT xi ln xi + RT ln P0 i

i

where xi is the mole fraction of the specie i in the gas phase, the standard Gibbs energy of the gaseous specie i [58], R the gas constant, and P0 the standard pressure of 1 bar. The liquid phase is described by the two-sublattice model for ionic liquids [59], assuming that the anions and cations occupy separate lattices and are allowed to mix freely on their respective sublattice. Hypothetical vacancies (Va) are introduced on the anion sublattice to maintain charge neutrality and to allow a description towards a metallic liquid containing cations only. In the La–Ni–O system, the liquid is represented as (La3+ , Ni2+ )p(O2− , Vaq − )q, where the number of sites on the respective sublattice, p and q, vary with composition in order to maintain electroneutrality. The molar Gibbs energy is given by ◦ Ggas i

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161 ϕ

Gliq = yLa3+ yO2− ◦ GLa2 O3 + yNi2+ yO2− ◦ GNi2 O2 liq

liq

+ q(yLa3+ yVaq− ◦ GLa + yNi2+ yVaq− ◦ GNi ) liq

liq

+ pRT(yLa3+ ln yLa3+ + yNi2+ ln yNi2+ ) + qRT(yO2− ln yO2− + yVaq− ln yVaq− ) + E Gliq ,

(6)

where yi represents the site fraction of the specie i on the liq liq liq liq respective sublattice, ◦ GLa2 O3 , ◦ GNi2 O2 , ◦ GLa , and ◦ GNi are equal to the Gibbs energy of the liquid binary oxides and metals, respectively, and E Gliq is the excess Gibbs energy, which can be expressed as Redlich–Kister type polynomial [60] using the compound energy formalism [61]: E

Gliq = yLa3+ yO2− yVaq−

n


ν liq LLa3+ :O2− ,Vaq− (yO2−

− yVaq− )ν

ν liq L 2+ 2− q− (yO2− Ni :O ,Va

− yVaq−)ν

ν=0 n


+ yNi2+ yO2− yVaq−

ν=0 n


+ yLa3+yNi2+yVaq−

ν=0

ν liq L 3+ 2+ q−(yLa3+ La ,Ni :Va

n


+ yLa3+ yNi2+yO2−

ν=0

ν liq L 3+ 2+ 2−(yLa3+ La ,Ni :O

− yNi2+)ν

− yNi2+)ν. (7)

The colons separate species on different sublattices. The liq liq terms ν Li:j,k and ν Li,j:k are so-called interaction parameters, which account for the deviation from the ideal mixing behavior between the species in the same sublattice. The valliq liq liq liq ues of ◦ GLa2 O3 , ν L 3+ 2− q− ,◦ GNi2 O2 , ν L 2+ 2− q− , and ν L

La :O ,Va liq are taken La3+ ,Ni2+ :Vaq−

Ni

:O

,Va

from the corresponding bi-

nary systems [7–9], while the parameters ν L 3+ 2+ 2− , La ,Ni :O ν = 0, 1 are evaluated in the present work. Oxygen occupies interstitial sites in lanthanum and nickel metals. The oxygen solubility is then represented by a two-sublattice model based on the compound energy formalism [61] with one sublattice fully occupied by La and/or Ni and the other one where oxygen and vacancies mix randomly, i.e., (La, Ni)1 (O, Va)x . The maximum number of interstitial sites per metal atom, which are available for oxygen (x) is taken as 0.5, 1.0, and 1.5 for dhcp-, fcc-, and bcc-lattices (bcc: body-centered cubic) as suggested by Grundy et al. [8] for the La–O system. The molar Gibbs energy is given by ϕ

liq

ϕ

ϕ

Gϕ = yLa yVa ◦ GLa:Va + yNi yVa ◦ GNi:Va + yLa yO ◦ GLa:O ϕ

+ yNi yO ◦ GNi:O + RT(yLa ln yLa + yNi ln yNi )

ϕ

+ xRT(yO ln yO + yVa ln yVa ) + yLa yNi yVa 0 LLa,Ni:Va ϕ

+ yLa yNi yO 0 LLa,Ni:O . ◦ Gϕ Me:Va

ϕ

(8)

and ◦ GMe:O are the expressions for the Gibbs energy of the dhcp-, fcc-, or bcc-modifications of pure elements and hypothetical compounds MeOx (Me stands for

153 ϕ

ϕ

La or Ni). The parameters ◦ GLa:Va , ◦ GNi:Va , and ◦ GLa:O are taken from the SGTE unary database [56] and from the asϕ sessment of the La–O system [8], respectively, while ◦ GNi:O are evaluated in the present study. The mixing of oxygen and vacancies is assumed to be ideal [8]. The interaction paϕ rameters 0 LLa,Ni:Va are adopted from the description of the ϕ La–Ni system [7] and 0 LLa,Ni:O are set to zero in view of the low oxygen solubility and a lack of experimental measurements. A two-sublattice model for the bunsenite phase (NiO) is taken from the binary Ni–O description [9] and one additional term corresponding to the Gibbs energy of the compound LaO with rocksalt-type structure [62] has been added. In the ternary system, the bunsenite phase (halite) is then represented by the formula (Ni2+ , Ni3+ , La3+ , Va)1 (O2− )1 and the molar Gibbs energy is given by Ghal = yNi2+ yO2− ◦ Ghal + yNi3+ yO2− ◦ Ghal Ni2+ O2− Ni3+ O2− + yLa3+ yO2− ◦ Ghal + yVa yO2− ◦ Ghal La3+ O2− VaO2− + RT(yNi2+ ln yNi2+ + yNi3+ ln yNi3+ + yLa3+ ln yLa3+ + yVa ln yVa + yO2− lnyO2− ).

(9)

Note that the compounds (Ni3+ )1 (O2− )1 , (La3+ )1 (O2− )1 , and (Va)1 (O2− )1 are not electrically neutral and will be only present in neutral combinations 2/3 [(Ni3+ )1 (O2− )1 , (La3+ )1 (O2− )1 ] + 1/3[(Va)1 (O2− )1 ]. Magnetic ordering results in additional contribution to the Gibbs energy. For a phase with the magnetic moment β (Bohr’s magnetons per mole of atoms) and the ordering (Curie or Néel) temperature TC (K) the magnetic contribution to its Gibbs energy is expressed as [63,64]   T Gmag = RT ln(β + 1)f , (10) TC where f(T/TC ) represents the polynomial function [64]. The corresponding parameters for bcc, fcc, and halite are taken from the literature [9,56]. The energetic contribution from the antiferromagnetic ordering in the La2 NiO4 phase cannot be described within this simple model (see below).

5. Results and discussion The thermodynamic model parameters were evaluated using the optimization module PARROT of the multicomponent software for thermodynamic calculations “Thermo-Calc” [65]. They are given in Table 4. Firstly, the description of the Ni–O system was modified to account for the solubility of oxygen in solid fcc-nickel. For this purpose, most recent data have been used [66], which show a reasonable increase of the solubility with temperature contrary to the previous measurements [67,68] indicating the opposite temperature dependence. The calculated solubility of oxygen in fcc-nickel in equilibrium with NiO is shown

154

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

Table 4 Summary of the thermodynamic parameters describing the La–Ni–O system referred to stable element reference HSER (T = 298.15 K, P = 1 bar) Parameter Liquid

(La3+ ,

Ni2+ )p(O2− ,

Equation

Reference

(6)

[56]

(6)

[8]

(6)

[9]

(7)

[8]

(7)

[9]

(7)

[7]

(7)

This work

(7)

This work

(8)

[56]

(8)

[7]

(8)

[8]

(8)

This work

(8)

[7]

(8)

This work

(8) and (10)

[56]

(8)

[8]

(8)

This work

Vaq− )q

◦ Gliq , ◦ Gliq La Ni ◦ Gliq La2 O3 ◦ Gliq Ni2 O2 0 Lliq La3+ :O2− ,Vaq− liq liq 0 Lliq , 1 L 2+ 2− q− , 2 L 2+ 2− q− Ni2+ :O2− ,Vaq− Ni :O ,Va Ni :O ,Va liq 0 Lliq , 1 L 3+ 2+ q− 2+ 3+ q− La ,Ni :Va La ,Ni :Va 0 Lliq = −51990.25 2+ 2− 3+ La ,Ni :O 1 Lliq = −92164.39 La3+ ,Ni2+ :O2−

dhcp (La, Ni)1 (O, Va)0.5 ◦ Gdhcp La:Va ◦ Gdhcp Ni:Va ◦ Gdhcp La:O ◦ Gdhcp = +30000 Ni:O 0 Ldhcp La,Ni:Va 0 Ldhcp La,Ni:O = 0

dhcp + ◦ GNi:Va

gas + 0.25◦ GO2

fcc (La, Ni)1 (O, Va)1 ◦ Gfcc , ◦ Gfcc , (T )fcc , βfcc C Ni:Va La:Va Ni:Va Ni:Va ◦ Gfcc La:O ◦ Gfcc = −178600 + 105.1T + ◦ Gfcc Ni:O Ni:Va 0 Lfcc La,Ni:Va 0 Lfcc La,Ni:O = 0

+ 0.5◦ GO2

gas

(8)

[7]

(8)

This work

(8) and (10)

[56]

(8)

[8]

(8)

This work

bcc (La, Ni)1 (O, Va)1.5 ◦ Gbcc , ◦ Gbcc , (T )bcc , βbcc C Ni:Va La:Va Ni:Va Ni:Va ◦ Gbcc La:O ◦ Gbcc = +30000 + ◦ Gbcc + 0.75◦ Ggas O2 Ni:O Ni:Va 0 Lbcc La,Ni:Va 0 Lbcc La,Ni:O = 0

(8)

[7]

(8)

This work

(9) and (10)

[9]

(9)

[62]

(9)

[9]

(4)

This work

(4)

This work

(4)

This work

(4)

This work

Halite (Ni2+ ,Ni3+ ,La3+ ,Va)1 (O2− )1 ◦ Ghal , ◦ Ghal3+ 2− , Ni2+ O2− Ni O hal ◦G La3+ O2− ◦ Ghal VaO2−

(TC )hal2+ Ni

:O2−

, βhal2+ Ni

:O2−

, (TC )hal3+ Ni

:O2−

, βhal3+ Ni

:O2−

La2 NiO4 (La3+ )2 (Ni2+ )1 (O2− )4 ◦G

= −2099565.1 + 1040.99436T − 178.837619T ln T − 0.00640046346T 2 + 1231924.12T −1

La2 NiO4

La3 Ni2 O7 (La3+ )3 (Ni2+ )1 (Ni3+ )1 (O2− )7 ◦G

La3 Ni2 O7

= −488.5 + 0.5◦ GLa2 NiO4 + 0.5◦ GLa4 Ni3 O10

La4 Ni3 O10 (La3+ )4 (Ni2+ )1 (Ni3+ )2 (O2− )10 ◦G

La4 Ni3 O10

= −4339518.9 + 816.35899T + 4◦ GLa:Va + 3◦ GNi:Va + 5◦ GO2

gas

fcc

dhcp

LaNiO3 (La3+ )1 (Ni3+ )1 (O2− )3 ◦G

LaNiO3

= −1157180.9 + 234.67466T + ◦ GLa:Va + ◦ GNi:Va + 1.5◦ GO2 dhcp

fcc

gas

Values are given in SI units (Joule, mole, and Kelvin). “Equation” indicates the equation number in the text. Parameters for binary phases, which are not listed here can be found in the descriptions of the La–Ni [7] and La–O [8] systems.

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

Fig. 1. Oxygen solubility in solid nickel according to the present work as compared with the experimental data [66].

in Fig. 1 in comparison with experimental measurements of Park and Altstetter [66], which are well fitted, when ◦ Gfcc − ◦ Gfcc ◦ gas Ni:O Ni:Va − 0.5 GO2 is expressed as linear function of temperature (Table 4). A similar solubility curve was obtained by Kowalski and Spencer [10], but they fixed ◦ Gfcc and adjusted the interaction parameter 0 Lfcc Ni:O Ni:O,Va . In view of the low solubility it appears reasonably, however, to assume ideal mixing of oxygen atoms and vacancies. dhcp The parameters ◦ GNi:O and ◦ Gbcc Ni:O are estimated by adding a positive enthalpy term (30 kJ/mol) to the Gibbs energy of a mechanical mixture of the hypothetical dhcp- or bcc-Ni with oxygen gas to make the corresponding end-members unstable. Parameters describing the ternary La–Ni–O system were obtained on the base of the selected experimental data (“+” in column “Use” of Tables 2 and 3). The polymorphism of the La2 NiO4 compound is not taken into account in the thermodynamic calculations for the following reasons: (i) The LTO ⇔ LTLO phase transition temperature (74 ± 6 K) is well below the lower limit for the equilibrium calculations, usually 298.15 K. (ii) The HTT ⇔ LTO phase transition at 700 ± 10 K is believed to be of second order, but no accurate measurements of the heat capacity have been made around the transition temperature, where both the enthalpy and entropy of HTT and LTO phases are equal and the knowledge of the transition temperature only is not sufficient to evaluate the Gibbs energy function of both polymorphs. Thus, in the present thermodynamic modeling, only one phase with the stoichiometry La2 NiO4 is taken into account and it is represented with five non-zero coefficients of Eq. (4) (Table 4) by fitting the heat capacity measurements of Kyomen et al. [22] (Fig. 2) and the entropy obtained by integra-

155

Fig. 2. Calculated heat capacity of La2 NiO4 (solid curve) with experimental measurements superimposed. The dashed curve shows the hypothetical heat capacity of antiferromagnetic La2 NiO4 with the magnetic contribution calculated from Eq. (10).

tion from 0 K in conjunction with other data [17,36–38,49]. Note that the magnetic ordering in La2 NiO4 is anomalous in the sense that most of the magnetic entropy is consumed in a short-range ordering process over a broad temperature range resulting in a very small peak of CP at TN [23] as shown in Fig. 2. Therefore, a separation of the magnetic part from the total heat capacity by subtracting the other physically identifiable contributions [69] becomes a challenging task. Although the magnetic properties of such systems can be modeled using a spin-wave theory [23,70] this treatment is incompatible with the phenomenological model used in thermodynamic calculations (Eq. (10)). The dashed line in Fig. 2 shows the expected anomaly on the heat capacity curve calculated with this model using the assessed value for the magnetic moment per Ni-atom of 1.58µB and TN = 328 K as input. Therefore, all contributions to the heat capacity of La2 NiO4 are approximated together by Eq. (4). Fig. 3 shows the calculated Gibbs energy of formation of La2 NiO4 from La2 O3 and NiO in comparison with the measurements of Sreedharan et al. [54], which have been discarded in the optimization (Table 3). Although the calculated and experimental values nearly coincide around 1350 K, the measurements result in too high entropy of formation, so that the La2 NiO4 compound would be unstable against decomposition into La2 O3 and NiO below 850 K. For the compounds La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 no heat capacity measurement are available from the literature and thus, their Gibbs energies are described relative to the mechanical mixture of elements (Table 4) by applying the Neumann–Kopp rule, i.e., assuming the heat capacity of formation equal to zero. The Gibbs energy of the La4 Ni3 O10 compound is represented by two coefficients a and b of Eq. (4), which are related to the enthalpy and entropy of formation to fit the measurements of equilibrium oxygen pressure [36,49]. The experimental data concerning La3 Ni2 O7 and LaNiO3 [31,53] are available in a very limited temperature range (Tables 2 and 3). Therefore, the

156

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161 Table 5 Calculated thermodynamic functions of La4 Ni3 O10 at 298.15 K

Fig. 3. Calculated Gibbs energy of formation of the La2 NiO4 from La2 O3 and NiO in comparison with the measurements of Sreedharan et al. [54].

Gibbs energy of the La3 Ni2 O7 compound is taken as an average of the Gibbs energies of La2 NiO4 and La4 Ni3 O10 plus a constant (Table 4). In the case of LaNiO3 , the situation is more complicated as it represents the end-member of the RP-series Lan+1 Nin O3n+1 and either enthalpy or entropy had to be fixed. In the present work, the enthalpy of formation of LaNiO3 from elements has been estimated by the method suggested by Yokokawa et al. [71] based on correlation between the tolerance factor for perovskite compounds and their enthalpy of formation, while the entropy parameter was allowed to vary.

◦ Hf (kJ mol−1 )

◦S

−4478.6 −4508 −4334.0

390.0 – 535.5

(J mol−1 K−1 )

◦ Gf (kJ mol−1 )

Reference

−4194.7 – −4093.5

[73] [72] This work

In Fig. 4, the calculated and experimental equilibrium oxygen pressures for different three-phase regions are presented. The thermodynamic parameters of the La2 NiO4 phase are best fitted to the data of Petrov et al. [36]. There is no significant deviation from the van’t Hoff dependence, which gives a straight line in the log(pO2 ) − 1/T coordinates. Also the metastable equilibrium La4 Ni3 O10 = 2La2 NiO4 + NiO + 0.5O2 [36] is well accounted for (Fig. 4b). The lines in Fig. 4 do not intersect, which indicates the sequence of decomposition reactions (1) → (2) → (3) considered above upon increasing temperature or decreasing oxygen pressure. As it can be seen in Fig. 4b, the reaction 3La4 Ni3 O10 = 4La3 Ni2 O7 + NiO + 0.5O2 is characterized by the equilibrium oxygen pressure, which is in fair agreement with the measurements of Bannikov and Cherepanov [31]. As for the reaction 2La3 Ni2 O7 = 3La2 NiO4 + NiO + 0.5O2 , the deviation is inevitably larger, since the corresponding line should be in any case below one, which represents the metastable equilibrium La2 NiO4 + La4 Ni3 O10 + NiO, while the measurement [31] is above (Fig. 4b). To resolve the contradiction further experimental studies of the equilibrium oxygen pressures for the reactions (2) and (3) over a range of temperatures are necessary.

Fig. 4. Calculated and experimental equilibrium oxygen pressures for different three phase regions: (a) full range and (b) enlarged view at high oxygen pressures.

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

Reznitskii calculated the standard enthalpy of formation of La4 Ni3 O10 at 298 K using an empirical relationship between the enthalpy of formation and the corresponding change of the cation coordination numbers in oxides [72], while Yokokawa et al. [73] estimated both the enthalpy of formation and entropy. The results are compared with calculations of this work in Table 5. It can be seen that the present thermodynamic description results in more positive enthalpy of formation and more positive entropy, while the difference in the Gibbs energy of formation is smaller. It is believed that the thermodynamic properties of La4 Ni3 O10 evaluated in this work are closer to reality since they come directly from the equilibrium La2 NiO4 + La4 Ni3 O10 + NiO. Even though it is metastable, the measured equilibrium oxygen pressures are always between those, which correspond to the true equilibria (Fig. 4b). Although the Gibbs energy description of the LaNiO3 compound is based on the single experimental measurement [53] and the estimated enthalpy of formation, the calculations show (Fig. 4b) that oxygen pressures higher than 1 bar are required to stabilize this phase at high temperature (above 1500 K) in agreement with many observations [17,36,49]. Fig. 5 shows the calculated vertical section of the La–Ni–O phase diagram along the La2 NiO4 –LaNiO3 join in air compared to experimental results from different reports. This diagram can be constructed from Fig. 4 by drawing the horizontal line at pO2 = 0.21 bar. As mentioned before, the temperature of the invariant reaction (1) is selected as 1253 K [31], which lies between the values from other

157

Fig. 5. Calculated vertical section of the La–Ni–O phase diagram along the La2 NiO4 –LaNiO3 join in air superimposed with experimental measurements.

Fig. 6. Calculated stability diagrams of the La–Ni–O system along the La2 NiO4 –LaNiO3 join at (a) 1373 K and (b) 1473 K as compared with the experimental data.

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M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

Fig. 7. (a) Pseudobinary section La2 O3 –NiO according to the present work calculated with regular and subregular solution parameters in comparison with the available literature data. Dashed line show the same diagram optimized with only regular solution parameter. (b) Central part of (a) showing the invariant equilibria.

studies [15,32]. The calculated section (Fig. 5) is in general agreement with the data of Cherepanov et al. [49] except for the existence of the La3 Ni2 O7 and LaNiO3 compounds, so that the metastable two-phase fields La2 NiO4 + La4 Ni3 O10 and La4 Ni3 O10 + NiO (at lower temperatures) appear instead of the stable phase equilibria La2 NiO4 + La3 Ni2 O7 , La3 Ni2 O7 + La4 Ni3 O10 , and LaNiO3 + NiO. The data of Odier et al. [14] are reproduced very well.

In Fig. 6, two stability diagrams along the La2 NiO4 – LaNiO3 join at 1373 and 1473 K are presented. They can be again constructed from Fig. 4 by drawing the vertical line at the corresponding temperatures. When discussing the agreement between calculations and experiments, the same comments can be given with respect to [49] as for Fig. 5 above. The data of Kitayama [17] are well accounted for and, according to the calculation, the highest measured oxygen

Fig. 8. Calculated isothermal sections of the La–Ni–O system at 1373 K (a) and 1473 K (b) (pO2 = 1 bar) with the corresponding experimental points [17,49].

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

pressure corresponds to the equilibrium between La3 Ni2 O7 , La2 NiO4 and NiO (Fig. 6b). This may be an indication that the La6 Ni5 O15 compound [17] should be considered as La3 Ni2 O7 . The interaction parameters for the liquid phase are obtained from the limited information on the pseudobinary

159

section La2 O3 –NiO [37,38]. Fig. 7 shows the calculated La2 O3 –NiO phase diagram along with the experimental measurements. The congruent melting point of La2 NiO4 as well as the eutectic temperature and composition are well reproduced (Table 2). Another eutectic in this system (liquid = La2 O3 + La2 NiO4 ) is calculated at 1954 K,

Fig. 9. Evolution of the topology of the La–Ni–O system with increasing temperature or oxygen pressure. Phase regions: I = La2 O3 + La2 NiO4 + Ni; II = La2 NiO4 + NiO + Ni; III = La2 O3 + La3 Ni2 O7 + La2 NiO4 ; IV = La2 NiO4 + La3 Ni2 O7 + NiO; V = La2 O3 + La4 Ni3 O10 + La3 Ni2 O7 ; VI = La3 Ni2 O7 + La4 Ni3 O10 + NiO; VII = La2 O3 + LaNiO3 + La4 Ni3 O10 ; VIII = La4 Ni3 O10 + LaNiO3 + NiO; IX = La2 O3 + gas + LaNiO3 ; X = LaNiO3 + gas + NiO; XI = La2 O3 + gas + La4 Ni3 O10 ; XII = La4 Ni3 O10 + gas + LaNiO3 ; XIII = La3 Ni2 O7 + gas + La4 Ni3 O10 ; XIV = La2 O3 + gas + La3 Ni2 O7 ; XV = La2 O3 + gas + La2 NiO4 ; XVI = La4 Ni3 O10 + gas + NiO; XVII = La3 Ni2 O7 + gas + NiO; XVIII = La2 NiO4 + gas + NiO.

160

M. Zinkevich, F. Aldinger / Journal of Alloys and Compounds 375 (2004) 147–161

just below the melting point of La2 NiO4 (Fig. 7b). Although the use of a non-zero subregular solution parameter 1 Lliq may be questioned because of the sparse La3+ ,Ni2+ :O2− experimental data, it is justified by the fact that these data could not be well fitted with only the regular solution parameter. The dashed line in Fig. 7a illustrates such a case: apart from the significantly worse agreement, the congruent transformation of La2 NiO4 is then replaced by a peritectic reaction. The congruent melting behavior of La2 NiO4 is strongly corroborated, however by the possibility to grow large and pure single crystals from the melt [22,74,75]. Nevertheless, the calculated liquidus, especially in the NiO-region is rather speculative. Fig. 8 shows the calculated isothermal sections of the La–Ni–O system at 1373 and 1473 K for 1 bar oxygen pressure. The experimentally observed phase relations within the triangle La2 O3 –Ni–NiO are exactly reproduced by calculations. On the other hand, there are discrepancies regarding phase equilibria involving La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 due to the missing La3 Ni2 O7 and LaNiO3 compounds and the observance of the La6 Ni5 O15 phase [17,49]. These discrepancies are also reflected in the vertical section along the La2 NiO4 –LaNiO3 join (Figs. 5 and 6) and have already been discussed. Phase relations in the metallic part of the La–Ni–O system (i.e., within the triangle La–La2 O3 –Ni) have not been studied experimentally so far. They are predicted for the first time in this work. As can be seen in Fig. 8, La2 O3 forms the tie-lines with the compound LaNi5 and the metallic liquid of the La–Ni system. Furthermore, there is a small miscibility gap in the La-rich region, which is formed by the La–O and La–Ni liquids and expands with increasing temperature (Fig. 8). The existence of such miscibility gap can be understood since the liquid in the La–O system dissolves an appreciable amount of oxygen and miscibility gaps are quite common between metallic and oxide melts (slags). It should be noted that the topology of the La–Ni–O system in the composition range where the RP-phases Lan+1 Nin O3n+1 are formed may change significantly through the variations of temperature and oxygen pressure. In Fig. 9 seven partial isothermal sections are shown, which represent all possible phase equilibria at different conditions, except for extremely low oxygen pressures or very high temperatures, at which La2 NiO4 , NiO, or La2 O3 decomposes. The pO2 − T dependencies, which separate the individual diagrams can be easily calculated using the parameters from Table 4. At high oxygen pressures and low temperatures all RP-phases are in equilibrium with La2 O3 and NiO and only LaNiO3 forms tie-lines with the gas phase. When decreasing pO2 or increasing temperature, the equilibria with La2 O3 are successively replaced by those with the gas phase, while the equilibria with NiO persist. Further increase in temperature or decrease in oxygen pressure results in a successive decomposition of LaNiO3 , La4 Ni3 O10 , and La3 Ni2 O7 until only the La2 NiO4 compound coexisting with La2 O3 , NiO, Ni and gas remains.

6. Conclusions Thermodynamic properties of the ternary La–Ni–O system are analyzed by means of the CALPHAD-method. Parameters describing the boundary systems La–Ni, La–O, and Ni–O are taken from the literature. The description of the Ni–O system is modified to include the solubility of oxygen in fcc-nickel. The gas phase is treated as an ideal solution of the species La, La2 O, La2 O2 , LaO, Ni, NiO, O, O2 , and O3 . The liquid phase is described by the two-sublattice model for partially ionic liquids. Oxygen solubility in the dhcp, fcc, and bcc phases is represented by the interstitial solution model, while for the halite phase (NiO), the two-sublattice model for ionic compounds is used. The ternary phases La2 NiO4 , La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 are treated as stoichiometric compounds. Neither different polymorphs of the La2 NiO4 compound nor the magnetic contribution to its Gibbs energy could be described separately. The relevant literature information is critically assessed and the inconsistencies are ascertained. A self-consistent set of Gibbs energy functions describing the phases in the La–Ni–O system is obtained for the first time by least-squares fit to the selected experimental data. The backward compatibility of the refined parameters with the preferred datasets is demonstrated by calculation of various phase diagrams and thermodynamic properties, such as isothermal sections, vertical sections, equilibrium oxygen pressure, Gibbs energy, enthalpy, entropy, and heat capacity, which are compared with all available literature data. It is shown that the topology of the La–Ni–O system may change significantly through the variations of temperature and oxygen pressure. Further refinement of the present thermodynamic description would be possible if the oxygen non-stoichiometry of La2 NiO4 , La3 Ni2 O7 , La4 Ni3 O10 , and LaNiO3 were taken into account, provided that more information on their thermodynamic properties become available.

Acknowledgements The authors wish to express their thanks to Dr. Toru Kyomen, Materials and Structures Laboratory, Tokyo Institute of Technology for providing original heat capacity data.

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