Thermodynamic assessment of the La-Ni system

L

Journal of Alloys and Compounds 264 (1998) 209–213

Thermodynamic assessment of the La-Ni system Z. Du*, D. Wang, W. Zhang Department of Materials Science and Engineering; University of Science and Technology Beijing, Beijing 100083, P.R. China Received 18 April 1997; received in revised form 30 May 1997

Abstract The La-Ni system has been assessed by means of the CALPHAD technique. A consistent set of thermodynamic parameters of individual phases is obtained. The liquid phase is described by the substitutional solution model. All of the intermetallic compounds La 3 Ni, La 7 Ni 3 , LaNi, La 2 Ni 3 , La 7 Ni 16 , LaNi 3 , a La 2 Ni 7 , b La 2 Ni 7 and LaNi 5 have been treated as stoichiometric compounds. The calculated phase diagram and thermodynamic quantities agree with the experiments very well.  1998 Elsevier Science S.A. Keywords: Thermodynamic properties; La-Ni system

1. Introduction The intermetallic compounds formed by rare earth elements and transition metals, are of particular interest regarding to their magnetic properties [1] and reversible absorption of hydrogen gas [2]. Self- consistent thermodynamic descriptions of the alloy systems will be helpful to their design and processing. This work deals with the assessment of the thermodynamic properties of the La-Ni system by means of the CALPHAD (CALculation of PHAse Diagram) technique. In this method, the thermodynamic properties of the alloy systems are analyzed by using thermodynamic models for the Gibbs energy of individual phases. The thermodynamic parameters involved in the models are optimized from the experimental thermodynamic and phase diagram information.

2. Thermodynamic model

f 0 f G fm 5 x 0La G La 1 x Ni G Ni 1 RT(x La lnx La 1 x Ni lnx Ni )

1 E G fm 1 mg G fm

where 0 G fi is the molar Gibbs energy of the element i (i5La, Ni respectively) with the structure in a nonmagnetic state from the compilation by Dinsdale [4]; E G fm is the excess Gibbs energy, expressed in Redlich–Kister polynomials, E

G fm 5 x La x Ni

2.1. Liquid, b.c.c., f.c.c. and d.h.c.p. phases The liquid, b.c.c, f.c.c. and d.h.c.p. phases are treated by a one-sublattice model with the Gibbs energy expressed as *Corresponding author. 0925-8388 / 98 / $19.00  1998 Elsevier Science S.A. All rights reserved. PII S0925-8388( 97 )00269-7

O L (x i

f

La

2 x Ni )i

(2)

i

where i L f is the interaction parameter between elements La and Ni, which is to be evaluated in present work. It’s general form is L f 5 a 1 bT 1 cT lnT 1 dT 2 1 eT 3 1 fT 21 1 gT 7 1 hT 29 (3) but in most cases only the first one or two terms are used. mg f G m is the magnetic contribution to Gibbs energy in solution phases, and expressed as following [5]: mg

The Gibbs energy of individual phases is described by the sublattice model [3] relative to the Standard Element Reference (SER), i.e. the enthalpies of the pure elements in their defined reference phase at 298.15 K.

(1)

G fm 5 RT ln( b f 1 1)f(t f )

(4)

f

where b is a quantity related to the total magnetic entropy, and in most cases is set equal to the Bohr magnetic moment per mole of atoms; t f is defined as T /Tc f , and Tc f is the critical temperature for magnetic ordering, i.e. the Curie temperature (Tc) for ferromagnetic ordering and the Neel temperature(T N ) for antiferromagnetic ordering. They are described by the following expressions, 0 Tc f 5 x 0La Tc fLa 1 x Ni Tc fNi 1 x La x Ni L fTc

(5)

Z. Du et al. / Journal of Alloys and Compounds 264 (1998) 209 – 213

210

f 0 f b f 5 x 0La b La 1 x Ni b Ni 1 x La x Ni L bf f

(6)

f

where L T c and L b are magnetic interaction parameters between the elements La and Ni, here set to be zero due to lack of experimental data. The f(t ) represents the polynomials obtained by Hillert and Jarl [5] based on the magnetic specific heat of iron, i.e. for t , 1: f(t ) 5 1 2 [79t 21 /(140p) 1474 / 497(1 /p 2 1)(t 3 / 6 1 t 9 / 135 1 t 15 / 600)] /A (7) for t . 1: f(t ) 5 2 (t

25

/ 10 1 t 215 / 315 1 t 225 / 1500) /A

(8)

where A5519 / 1125111692 / 15975(1 /p21) and p depends on the structure, 0.4 for b.c.c. structure and 0.28 for the others.

diagram from LaNi to LaNi 5 , and specified the compound formerly called LaNi 2 to be La 7 Ni 16 . Minor differences for several invariant temperatures were given compared to the results of Buschow and van Mal [10]. Based mainly on these results, the La-Ni phase diagram was reviewed by Pan and Nash [13], and later updated by Okamoto [14]. The enthalpies of mixing liquid lanthanum with solid nickel for liquid alloys in the range 0–65 at %Ni at 1376 K and the enthalpies of formation of the intermetallic compounds La 3 Ni, LaNi and LaNi 5 at 298.15 K were measured by Watanabe and Kleppa [15]. Rezukhina and Kutsev [16], Semenenko et al. [17–19], Colinet et al. [20], Chatillon–Colinet et al. [21], Hubbard et al. [22] and Pasturel et al. [23] determined the enthalpies of formation of the La-Ni intermetallic compounds, respectively. The magnetic properties of the intermetallic compounds in the La-Ni system were summarized by Buschow [1].

4. Optimization and discussion

2.2. Intermetallic compounds There are eight stable intermetallic compounds in the La-Ni system, i.e. La 3 Ni, La 7 Ni 3 , LaNi, La 2 Ni 3 , La 7 Ni 16 , LaNi 3 , La 2 Ni 7 , and LaNi 5 . They are treated by a twosublattice model with La on one sublattice and Ni on the other one. Owing to lack of experimental measurements, it is assumed that the Neumann–Kopp rule applies to the heat capacity, i.e. DCp50. Thus the Gibbs energy for per mole of formula unit LaA Ni B can be expressed as following: La Ni B

Gm A

0

d.h.c.p.

5 A G La

0

f.c.c.

1 B G Ni 1 a 1 bT

(9)

Because the Curie temperature of all eight compounds is below 298.15 K [1], the magnetic contribution to Gibbs A Ni B A Ni B energy mg G La is included in the term G La expressed m m by Eq. (9).

Most of the experimental information mentioned above was selected for the optimization of thermodynamic model parameters. The experimental data of the phase diagram are based mainly on the results of Okamoto [14]. As the d.h.c.p. structure is not stable for pure Ni, its lattice stability had to be estimated. According to the estimation of Fernandez Guillermet and Huang [24] for high melting b.c.c. metals V, Nb and Ta, the following lattice stability was chosen, 0

d.h.c.p. G Ni 5 0 G f.c.c. 1 5000 J / mol Ni

(10)

The optimization was done by means of the ThermoCalc software [25] which can take various kinds of experimental data. The program works by minimizing an error sum where each of the selected data values is given a certain weight.The weight is chosen by personal judgment and changed by trial and error during the work until most

3. Experimental information The phase diagram of the La-Ni system was first investigated systematically by Vogel [6], who found six intermetallic compounds, and called them La 3 Ni, LaNi, LaNi 2 , LaNi 3 , LaNi 4 and LaNi 5 . Later Gschneidner [7] and Virkar and Raman [8] corrected the composition of LaNi 4 to La 2 Ni 7 , it has a Ce 2 Co 7 -type structure at room temperature and Gd 2 Co 7 -type structure at high temperature. The compound La 7 Ni 3 was first observed by Kissel et al. [9]. Buschow and van Mal [10] reinvestigated the La-Ni system in the range 50–100 at %Ni and observed the compound LaNi 1.4 , which was later found to be La 2 Ni 3 [11]. Ivanchenko et al. [12] also studied the La–Ni system. Later Zhang et al. [13] redetermined the La-Ni phase

Table 1 Optimized thermodynamic parameters of the La-Ni system, in SI units liquid: 0 L liquid 5 2116299119.815T 1 liquid L 563813240.941T b.c.c: 0 L b.c.c. 5100 000 f.c.c.: 0 L f.c.c. 5100 000 d.h.c.p.: 0 L d.h.c.p. 5100 000 3 Ni La 3 Ni: G La 2 3 0 G d.h.c.p. 2 G f.c.c. 5 2 60909 2 0.702T m La Ni La 7 Ni 3 0 d.h.c.p. f.c.c. La 7 Ni 3 : G m 2 7 G La 2 3 0 G Ni 5 2 180100 1 1.054T 0 d.h.c.p. 0 f.c.c. LaNi:G LaNi 2 G 2 G 5 2 51390 2 0.055T m La Ni d.h.c.p. f.c.c. 2 Ni 3 La 2 Ni 3 : G La 2 2 0 G La 2 3 0 G Ni 5 2 138509 1 14.109T m 0 d.h.c.p. 0 f.c.c. 7 Ni 16 La 7 Ni 16 : G La 2 7 G 2 16 G Ni 5 2 639390 1 91.778T m La d.h.c.p. f.c.c. 3 LaNi 3 : G LaNi 2 0 G La 2 3 0G Ni 5 2 108154 1 15.857T m d.h.c.p. f.c.c. aLa 2 Ni 7 : G maLa 2 Ni 7 2 2 0 G La 2 7 0 G Ni 5 2 239869 1 37.356T bLa 2 Ni 7 0 d.h.c.p. 0 f.c.c. bLa 2 Ni 7 :G m 2 2 G La 2 7 G Ni 5 2 237259 1 35.267T 5 LaNi 5 : G LaNi 2 0 G d.h.c.p. 2 5 0 G f.c.c. 5 2 154674 1 30.622T m La Ni

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211

Fig. 1. The La-Ni phase diagram calculated by the optimized parameters in present work.

of the selected experimental information is reproduced within the expected uncertainty limits. The thermodynamic description of the La-Ni system obtained in present work is presented in Table 1. The La-Ni phase diagram calculated by means of the optimized thermodynamic parameters is shown in Fig. 1. Fig. 2 compares the calculated phase diagram with the experimental data [6,10,12,13]. It agrees very well with the invariant temperatures measured by Zhang et al. [13], and

updated by Okamoto [14], the liquidus fits with the results of Buschow and van Mal [10]. Fig. 3 and Fig. 4 present the calculated enthalpies of formation at 298.15 K in the entire composition range and enthalpy of mixing of the liquid at 1376 K relative to liquid La and Ni with f.c.c. structure respectively. Satisfactory agreement is shown between the calculations and experimental results [15–23]. The special points of the La-Ni phase diagram are listed in Table 2.

Fig. 2. Comparison of the calculated phase diagram and the experimental data [6,10,12,13].

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Z. Du et al. / Journal of Alloys and Compounds 264 (1998) 209 – 213

Table 2 The special points of the La-Ni system Reaction

liq.→La 3 Ni1f.c.c.(La) liq.→La 3 Ni liq.→La 3 Ni1La 7 Ni 3 liq.→La 7 Ni 3 liq.→La 7 Ni 3 1LaNi liq.→LaNi liq.→LaNi1La 2 Ni 3 liq.1La 7 Ni 16 →La 2 Ni 3 liq.1LaNi 3 →La 7 Ni 16 liq.1aLa 2 Ni 7 →LaNi 3 aLa 2 Ni 7 →bLa 2 Ni 7 liq.1LaNi 5 →bLa 2 Ni 7 liq.→LaNi 5 liq.→LaNi 5 1f.c.c.(Ni)

Composition (at % Ni in liquid)

21.06 25.00 27.86 30.00 35.48 50.00 55.73 57.17 58.10 60.46 – 65.85 83.33 91.28

Temperature (K) Present work

Okamoto ref.14

797 805 801 803 784 988 949 960 987 1084 1249 1287 1622 1543

800 805 – – 790 988 948 961 987 1084 1249 1287 1623 1543

Fig. 4. Enthalpy of mixing of the liquid at 1376 K relative to liquid La and f.c.c. Ni with the experimental data [15].

Fig. 3. Comparison of the calculated enthalpy of formation and the experimental data [15–23].

Acknowledgements The authors would like to express their gratitude to Royal Institute of Technology, Sweden for supplying the Thermo-Calc software. This work was supported by National Natural Science Foundation of China (NSFC).

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