Thermodynamic assessment of the AlNi system

Journal of

AILOY5

AIND COMPOUblD$ ELSEVIER

Journal of Alloys and Compounds 237 (1996) 20-32

Thermodynamic assessment of the A1-Ni system Yong Du, Narcis Clavaguera Grup de Fisica de l'Estat SOlid, Departament d 'Estructura i Constituents de la Matdria, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain Received 12 September 1995; in final form 19 September 1995

Abstract An optimal set of thermodynamic functions for the A1-Ni system is obtained by means of the CALPHAD (CALculation of PHAse Diagrams) technique applied to almost all the experimental phase diagram and thermodynamic data available. The phases are modeled with the association model (liquid), substitutional solution model (solid solution based on f.c.c. A1-A1 and f.c.c. A1-Ni), as a stoichiometric compound (A13Ni), and with the sublattice model (A13Ni2, A1Ni, A13Nis and A1Ni3). The magnetic contributions to the Gibbs energies are introduced for A1Ni, A1Ni3 and f.c.c. A1 (A1,Ni). Comparison between the calculated and measured phase diagrams and thermodynamic quantities show that most of the experimental information is satisfactorily accounted for by the thermodynamic calculation. Keywords: Thermodynamics; Calculation; Aluminum; Nickel; Phase diagram

1. Introduction Knowledge of the thermodynamic properties in Nibased superalloys is of great importance in many applications such as gas turbines, demolition devices, metal cutting and welding, and emergency beacons and flares. One of the most important Ni-containing superalloy binary systems is the AI-Ni system. There have been a a number of experimental determinations of the phase equilibria and thermodynamic quantities in the A1-Ni system since the pioneering work by Gwyer [1]. However, there is no general agreement among the proposed phase diagram and thermodynamic data. The thermodynamic modeling for the whole system has been performed by Kaufman and Nesor [2] and Ansara et al. [3] by means of the calculation of phase diagrams (CALPHAD) method [4]. The phase relations in the solid solutions have been described by several researchers [5-9] using the cluster variation method [10]. However, their assessments were based on limited experimental data. Furthermore, the A13Ni5 compound reported by Robertson and Wayman [11] was not included in their calculations. Inclusion of a stoichiometric AI3Ni 5 in the modeling has been considered recently [12]. The present work is devoted to the assessment of the experimental phase diagram and thermodynamic 0925-8388/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI 0 9 2 5 - 8 3 8 8 ( 9 5 ) 0 2 0 8 5 - 3

data available for the A1-Ni system by providing an optimal set of thermodynamic functions for this system.

2. Evaluation of experimental data

2.1. Phase diagram data The liquidus has been measured by ten groups of authors [1,13-21]. The data given by Gwyer [1] at 24.97, 40.8, 57.96, and 89.7 at.% Ni, and the liquidus temperatures at 72.5 and 85 at.% Ni published by Alexander and Vaughan [15] were not used in the optimization. The other liquidus data are in reasonable agreement within the estimated experimental errors. In consequence, these data are employed in the optimization. In particular, the experimental data [13,17,18,21] are attached a high weight in the assessment on the grounds that (i) more specimens [13,17,18,21] and higher purity metals [17,18,21] were used compared with the measurements of the other workers [1,14-16,19,20], and (ii) the reported melting temperatures of A1 [13] and Ni [17,18] are in fair agreement with the generally accepted values [22]. Six papers [1,15,17-19,21] have appeared on the solidus. All the experimental values were retained in

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

the optimization, except for one datum given by Gwyer [1] at 89.73 at.% Ni, because it shows significant discrepancy from the recent experimental results [17-19,21]. Information on the homogeneity range of A13Ni 2 is scarce [15,23]. The values reported by Taylor and Doyle [23] are higher by about 1 at.% Ni than those due to Alexander and Vaughan [15]. All the experimental data are retained in the present assessment. The homogeneity range of A1Ni has been the subject of numerous investigations [15-18,21,23-27]. Some experimental values [23-25] show noticeable discrepancy from the others. Consequently, these data are excluded in the optimization procedure. Robertson and Wayman [11] measured the homogeneity range of the A13Ni 5 compound qualitatively. Their results demonstrate that this compound only extends towards the Ni-rich side of the stoichiometric composition (62.5 at.% Ni). In the present assessment, the compositions of A13Ni 5 equilibrating with A1Ni are obtained by eye-fitting the qualitative data of Robertson and Wayman [11] and the assessed datum at 62.5 at.% Ni and 300 K. The assessed compositions are applied a very low weight in the optimization. Plentiful data on the homogeneity range of AINi 3 have been published [15-21,26-31]. All the data are used in the optimization, but the recent experimental data [17-21,30,31] are attached a relatively high weight compared with the previous data [15,16,26-29]. There is much information about the solubility of AI in Ni [15-18,21,24,26-35]. However, the reported data of Bradley and Taylor [24[, Alexander and Vaughan [15] and Schramm [16] at temperatures above 1373 K show some scatter with respect to the overall set of experimental information. In consequence, the solubility data from [15,16,24] are not employed in the optimization. Two groups of investigators [13,36] reported a very low solubility of Ni in A1. These data are used in the optimization but a low weight was applied to them. 2.2. Enthalpy data

By means of water calorimeter, Oelsen and Middel [37] determined the enthalpies of formation of the alloys at 293 K over the entire concentration interval. The calorimetric measurement of direct reaction of pressed metal powders was performed by Kubaschewski [38]. The data of Oelsen and Middel [37] are generally more exothermic than those of Kubaschewski [38] by about 1500-8000 J g at cm -1. Because some oxidation and contamination occurred in the experiment of Oelsen and Middel, as pointed out by Kubaschewski [38], their values are not included in the optimization.

21

The enthalpies of mixing for the liquid have been measured by four groups of researchers [39-42] using high temperature mixing calorimeters. In the initial optimization, all the experimental values were used. It is shown that the data given by Gizenko et al. [40] are not consistent with the majority [39,41,42[. Consequently, they are withdrawn in the final optimization. Using a high temperature calorimeter, Henig and Lukas [43] and Dannohl and Lukas [44] measured the enthalpy of formation of A1Ni phase over the whole range of homogeneity at 1100 K and 1023 K respectively. These data are included in the optimization, since they are consistent within the given experimental errors. Four groups of workers [45-48] contributed to the measurement of the enthalpies of formation for AINi 3 at different temperatures. Within the stated experimental accuracy, the values are in reasonable agreement. All these data are utilized in the optimization. 2.3. Gibbs enecgy data

Partial Gibbs energies of A1 for the liquid have been reported by Schaefer [49] and Schaefer and Gokcen [50] using the electromotive force (EMF) method, by Oforka [51] and Hilpert et al. [47] using Knudsen effusion mass spectrometry (KEMS) technique, and by Vachet et al. [52], who deduced the activity of A1 by determining the distribution of A1 between A1-Ni liquid alloys and liquid Ag. Although there is a certain amount of scatter in the reported partial Gibbs energies, these data are in reasonable agreement and were all retained in the optimization. Using the KEMS technique, Johnston and Palmer [53], Hilpert et al. [47], and Mart and Reid [54] measured the activity of Ni in the liquid at 2000 K, 1728 K and 2000 K respectively. The values published by Johnston and Palmer [53] are not included in the optimization because of the contamination of the alloys in their experiment. The partial Gibbs energies of Ni in the solid phases were measured by the KEMS method. Oforka [51] and Hilpert et al. [47] determined the activities of Ni in the solid phases at 1423 K and 1600 K respectively. Their experimental data are included in the optimization. The partial Gibbs energies of A1 in the solid phases were measured by several workers [47,51,5558]. EMF data are reported by Malkin and Pokidyshev [56], Eskov et al. [57] and Elrefaie and Smeltzer [58], and activity data are given by Steiner and Komarek [55] using the isopiestic method and by Oforka [51] and Hilpert et al. [47] employing the KEMS technique. The activities obtained by Eskov et al. [57] were excluded in the optimization because they are too low, as mentioned by Hilpert et al. ]47]. The other ex-

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

22

perimental data also show a noticeable scatter, but in the absence of further experimental information they were retained in the optimization with a low weight attached to them.

Ni are taken from the recent compilation by Dinsdale [22]. That is, no magnetic contribution is introduced for f.c.c. A1-AI, liquid AI and liquid Ni.

2.4. Heat capacity data

3.2. Liquid phase

There are four pieces of information concerning the heat capacities of AINi [59-61] and A1Ni 3 [62]. All these data were included in the optimization. However, a low weight was given to the experimental values of A1Ni, relative to those on A1Ni3, since they show some scatter and depend strongly on heat treatment.

An association model [66] with the associate A1Ni is employed to describe the Gibbs energy of the liquid in view of the fact that viscosity rises to a sharp maximum at the equiatomic A1Ni composition [67] and the enthalpy of mixing [39,41,42] of the liquid shows a minimum at the same composition. The molar Gibbs energy of the liquid is given by the following equation: 0 L G m L - XAIOGAI L -- XNi GNi

3. Thermodynamic models = [YAIOGAI L

3.1. Pure elements

+ R T ( y g l In YA1 + YNi In YNi + YAINiIn YAINi)

The Gibbs energy of f.c.c. A1-Ni is described by resolving it into a non-magnetic contribution °Gnmg and a magnetic contribution AG rag. The non-magnetic contribution is expressed by an equation of the form °Gnmg - H SER

=

A + B T + C T In T + D T 2 + E T 3 + FT

0~ L 0 L YNi IJNi q- 2yAiNi A GAIN i

1 .~_ H T 7 + I T - 9

(1)

where H sER is the stable element reference molar enthalpy, the pure element in its stable state at 298.15 K, and T the temperature in kelvins. The last two terms in Eq. (1) are used only outside the ranges of stability [63], the term H T 7 for liquid below the melting point and I T -9 for solid phases above the melting point. The magnetic contribution to the Gibbs energy is described, according to the Hillert-Jarl-Inden [64,65] model by the following equation: AGmg = R T In(1 + B ) f ( r )

1 +YAINiYNi 0LAINi,Ni] 1 + YAINi

(4)

where YAI, YNi and YAINi are the site fractions of AI, Ni and AINi respectively on the sublattice. The term AOGAINiL represents the Gibbs energy of formation of the associate relative to the liquid Al and liquid Ni. The parameters d e n o t e d °Li,j are the interaction parameters between the species i and j.

3.3. Al3Ni compounds

In view of~the very narrow homogeneity range, this compound is treated as stoichiometric and its molar Gibbs energy is expressed by the following equation:

(2)

in which r = T / T * , with T* the critical temperature for magnetic ordering, i.e. the Curie temperature T c for ferromagnetic ordering or the N6el temperature T N for antiferromagnetic ordering, and B the average magnetic moment per atom. f i r ) is of the following form: f(r) = l - [79r 1/140P + (474/497)(1/P - 1) (r3/6 + ~9/135 + rls/600)]/A - ( r 5/10+ r-15/315 + r-25/1500)/A

0 + YAIYAINi 0LAI,AINi q- YAIYNi LAI,Ni

r~l

~->1

(3) where A = 518/1125 + (11692/15975)(1/P - 1) and P is a parameter essentially determined by the structure of the phase. Inden [65] suggested the value 0.28 for the f.c.c, structure and 0.4 for the b.c.c, structure. In the present work, the Gibbs energies of AI and

GAI3NiFe3C

type

__

0.75 °GAIf..... -- 0.25 °GNif

=A + BT +ClnT

.......

g

(5)

3.4. A I N i c o m p o u n d

The AINi compound is an ordered alloy with the CsCI type of structure [68]. The lattice parameter and density measurements conducted by Taylor and Doyle [23] showed that, on the Al-rich part of the stoichiometric compound, AINi vacancies occur at the Ni sites while, on the Ni-rich side, Ni atoms substitute for AI atoms. This implies that the AINi compound could be modeled with two sublattices: (AI, Ni)os(Ni, Va)0.5. The molar Gibbs energy of the compound is given as follows:

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32 Gmb.C.C. __ XAI 0GAlf.c~c. p

n

XNi 0(-~,VNif.c.c, nmg

_

A0(-~,

b.c.c. +

= [Y mY Ni ~ VAl:Ni +

r

r

rr

,t0 ,,'~

b.c.c.

Y AIY Va /X (JAI:Va

tt

,t0 r-, b.c.c, t tt ,tO..-,, b.c.c. Y ~iY Yi /x (JNi:Ni + Y NiY Va ~ IJNi:Va

+0.5RT(y'AI In Y'AI + Y'NiIn Y'Ni) tt

_~_ tt

+0.SRT(y"Nilny Ni Y valny"va) +

r 0 p t . 0 Y AlY NIY Ni LAI,Ni:Ni + y AIY NiY Va LAI,Ni:Va + , . . 0,Y AlY NiY Va LAI:Ni,Va + , n n 0 ,

,¢

Y hiY N~Y va Lhi:Ni.Va]/(1

-

0"5ynva) + AGmg

(6) in which Y'AI and Y'Ni are the site fractions of A1 and Ni on the first sublattice, and Y"Ni and y"va the site fractions on the second sublattice. The parameters denoted A°G are the Gibbs energies of formation of the compounds per mole of species (including vacancies) :relative to f.c.c. A1-AI and the hypothetical non-magnetic f.c.c. A1-Ni. The comma separates different species on the same sublattice, and the colon separates different sublattices. The magnetic contribution to the Gibbs free energy is calculated by means of Eq. (2), accounting for the composition dependence of the quantities T¢ and B. According to the RedlichKister polynomial, the general formula of T c and B are respectively

t

t¢

??

?t

t

¢

Pf

+Y AlY NiY NiTcA1.Ni:Ni + Y AIY NiY vaTCAI,Ni:Va 21_

?

~

Y AIY YiY valCAI:Ni,Va •

+Y t NiY ??NiY ??vaTcNi:YiNa (7)

B -- Y ' A Y"NiBAI:Ni + Y'AlY"vaBAI:Va + Y'NiYnNiBNi:Ni

+ y'NiY"vaBNi:Va + Y'AlY'NiYnNiB Ai,Ni:Ni

+Y 'AI Y 'Ni YnvaB AI,Ni:Va + Y'A1 Y'Ni Ynva BAI:Ni,Va

+ Y'Ni Y"NiY"vaBNi:Ni,Va

(8)

Owing 1:o the lack of information, only the hypothetical compound f.c.c. A1-Ni'Va is considered magnetic. Accordingly, T c and B are given by

TC = y 'Ni Y"vaTcyi:va B = Y'N YnvaBNi:Va

ing [23,68]. The density measurement by Taylor and Doyle [23] showed that, on the nickel-rich side of the stoichiometric compound AI3Ni:, the sharp rise in density comes from the progressive filling of the vacancies formed by the missing atom planes with nickel atoms and, on the aluminum-rich side, the relatively slow drop in density is due to the substitution of nickel by aluminum. Therefore the A13Ni 2 compound is modeled with the three-sublattice model Alo.5(Ni, A1)o.3333(Va, Ni)oA667. The molar Gibbs energy of this compound is expressed by an equation of the form Gmh.C.p. _ XAI 0GAlf.c.c. _ XNi 0GNif.c.c. nmg

= [Y'NiY"va AOGAI:Ni:Va h'c'p" + Y'AlY"va AOGAI:AI:Va h'c'p

+Y'NiY"Ni AOGAI:Ni:Ni h'cp" + Y'AlYnNi AOGAI:AI:Ni h'cp

+0.3333RT(Y'al In Y'AI + Y'NiIn Y'Ni) +0.1667RT(y"va In Y"va + Y"NiIn Y"Ni) + Y'AlY'NiY"va 0LAI:Ni,AI:Va +Y'AJY'NiY"Ni 0LAI:A1.Ni:Ni +Y'NiY"NiY"va 0LAI:Ni:Va,Ni +

p

n

.

0

1

Y A,Y NiY Va LA,:A,:Va.Ni](1 --0.1667y"va )

(11)

3.6. AI3Ni 5 compound

Tc = Y',~lY"NiTCAI:Ni + Y'AIY"vaTCAI:Va + Y ' NiY " Ni T CNi:Ni + Y ' YiY "vaTcNi:Va , t

23

(9)

(10)

The values introduced in the optimization are TcN,:va := 575 K and BNi:Va =0.85/xB (the values of b.c.c. AZ-Ni [22]).

3.5. AI:Ni2 compound The structure of the AI3Ni 2 compound may be considered a modified version of the AINi compound with every third diagonal plane of nickel atoms miss-

The AI3Ni s compound has a Ga3Pts-type structure in which Pt planes consist solely of Pt atoms and Ga planes contain Pt atoms as well. The work due to Robertson and Wayman [11] demonstrated that the A13Ni 5 boundary extends only towards the nickel-rich part of the stoichiometric composition. Considering the above information, this compound is modeled with two sublattices: (AI, Ni)o.375Nio.625. The molar Gibbs energy of the compound is represented by the following equation: GmGa3Pt5 type _ XAI 0GAlf.c.c. _ XN i 0GNif.c.c. nmg = YAI AOGAI:NiGa3Pt5type _.}_YNi A°GNi:NiGa3Pt5type

+0.375RT(yAI In YAI + YNi In Yyi) +YAlYNi[OLAI,Ni:Ni + ( Y A I - - Y Y i ) ILAI,Ni:Ni]

(12)

3.7. AlNi 3 compound AINi 3 has an f.c.c. L12 structure. At the stoichiometric composition, Ni and A1 atoms occupy the face center and cube corner sites respectively. It has been experimentally [69] shown that, on the Ni-rich side of the stoichiometric composition, the AI atoms are replaced by Ni atoms and, on the Al-rich part, Ni atoms are also simply replaced by A1 atoms. With this

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

24

information, the AINi 3 compound is modeled with the two sublattice model (A1, Ni)0.25(Ni, Al)0.75. The Gibbs energy of this phase can be written in a fashion similar to Eq. (6), with a magnetic contribution obtained by using expressions similar to Eqs. (7) and (8) for the composition dependence of T c and B. The values introduced in the optimization are assessed by the trial-and-error method in order to fit the data of Buis et al. [70] and Schrieffer et al. [71]. Table 1 lists the assessed parameters. 3.8. F.c.c. A I ( A I , N i ) p h a s e

The solid solution phase between A1 and Ni is described, in the present work, by the substitutional solution model because both AI and Ni have the same structure. The molar Gibbs energy is given by an equation of the form G m f.c.c. _ XAI 0GAlf.c.c. _ XNi 0 G N i f.c.c, nmg

= RT(XAz lnXAi + XNi lnXNi) +XA~XNi[a o + b o T + (XAj -- XNi)(a ~ + b 1T)] + AGmg

(13) The composition dependence of the parameters T c and B is described by means of the following expressions: 0 T C = X N i T c N i q- XAIXNi

B

(14)

TCAI,Ni

0 = XNiBNi q- XAiXNi

(15)

BAI,N i

The parameter 0TcAt,Ni w a s assessed by fitting the experimentally determined Curie temperature [16,33, 35,72,73]. However, the experimental magnetic moment data available [72,73] on the Ni-rich side were not used in the assessment because the indentification of B with the total magnetic moment riB, even if it agrees reasonably well when used for b.c.c. Fe [74,75], does not hold for other elements, such as Ni [76].

Table 1 P a r a m e t e r s describing the Curie t e m p e r a t u r e T c and magnetic m o m e n t B of f.c.c. A I ( A I , Ni), A1Ni and A1Ni 3 Phase

Tc

B

(K)

(m)

F.c.c. AI(A1, Ni)

TCNi = 633 0Tc.AI.Ni = --2697.83

BNi = 0.52 OBAI,N i = -1.54028

A1Ni

TcN~.v, = 575

BN~.V. = 0.85

A1Ni 3

TCAJN~3 = TCN~:N~= 43 OTc.AI,Ni:NI= 200

BA~Ni3 = BN~:N~= 0.06004 0BAI,Ni:Ni = 0.3

Table 1 lists the parameters describing the T c and B for the A1Ni, A1Ni 3 and f.c.c. AI(A1, Ni) phases.

4. Evaluation of parameters The evaluation of the parameters is conducted by the program developed by Lukas et al. [77], which can accept different types of information in the same operation. For the liquid phase, at least two coefficients should 0 L be introduced for one of the quantities A GAINi ' 0LAI,Ni a n d 0LA|Ni.Ni in Eq. (4) since the experimental enthalpy of mixing [39-42] is temperature dependent. In the present assessment the temperature dependence 0 L is only introduced for A GAINi . As mentioned in the preceding section, f.c.c. AI(AI) and f.c.c. AI(Ni) should be treated as the same phase in the thermodynamic modeling. The Ni solvus has been measured over a large temperature range, which means that the coefficients a~ and b~ of Eq. (13) can be independently adjusted for f.c.c. AI(Ni) solid solution. In the case of the f.c.c. AI(A1) solid solution, the temperature dependence is less well established. This implies that the coefficients a i and bi cannot be reliably obtained from the experimental data. To make the excess enthalpy of f.c.c. AI(Ni) independent of that of f.c.c. AI(A1), at least a 0 and a 1 need to be introduced. In the present work, the relationship between the partial enthalpy of mixing and partial excess entropy of one solute element in infinitely dilute solution [78] is applied to the f.c.c. AI(AI) solid solution. The relationship expressed by the RedlishKister polynomial gives rise to (a o + a 1)/(b o + b l ) = -8485 K as the constrained used in the evaluation of the four coefficients ao, a~, b o and b 1. For AI3Ni, the coefficients A and B of Eq. (5) can be adjusted independently since data on both the enthalpy of formation at room temperature and the phase diagram in a wide range of temperatures are available. In the present work, it was found that the introduction of the coefficient C is necessary in order to describe simultaneously the thermodynamic and phase diagram data. In the calculations by Kaufman and Nesor [2] and Ansara et al. [3], the coefficient C was also introduced. For the compounds A13Ni 2, AINi and AINi 3, the introduction of two coefficients for the parameters denoted °L can describe satisfactorily most of the experimental data. In the case of the A13Ni 5 compound, two coefficients f o r AOGAI:NiGa3Pt5type and one coefficient f o r 0LAI,AI:Ni gave a good compromise to the limited phase diagram and thermodynamic data available. The thermodynamic parameters obtained in the present work are listed in Table 2.

Y, Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

25

Table 2 Summary

of the thermodynamic

parameters

(in joules per gram-atom)

f o r t h e A 1 - N i s y s t e m (where the temperature is in k e l v i n s )

Liquid phase: (Al, AlNi, NO ()GAI I -- /q"AI s E R = 3 0 2 8 . 8 7 9 + 1 2 5 . 2 5 1 1 7 1 T - 2 4 . 3 6 7 1 9 7 6 T In T - 0 . 0 0 1 8 8 4 6 6 2 T 2

7T3+74092/T+7.934x10

-8.77664×10

298.15K
2°T7

= - 2 7 1 . 2 1 + 2 1 1 . 2 0 6 5 7 9 T - 3 8 . 5 8 4 4 2 9 6 T In T + 0 . 0 1 8 5 3 1 9 8 2 T 2 5 . 7 6 4 2 2 7 × 10 6T~ + 7 4 0 9 2 / T + 7 . 9 3 4 × 1 0 - 2 ~ T 7

- - 7 9 5 . 9 9 6 + 1 1 7 . 4 3 0 1 7 8 T - 3 1 . 7 4 8 1 9 2 T In T

700 K < T < 933.47 K

933.47 K < T < 2 9 0 0 K

°GNi~ -- /~'Ni s~R = 11235.527 + 1 0 8 . 4 5 7 T - 2 2 . 0 9 6 T In T - 0 . 0 0 4 8 4 0 7 T ~ - 3 . 8 2 3 1 8 x 10 :~ T 7 - 9 5 4 9 . 7 7 5 + 2 6 8 . 5 9 8 T - 4 3 . 1 T In T

298.15 K < T < 1728.3 K

(1728.3 K < T < 3000 K

A°GAINi L = G A I N i I -- 0.5 °GALL -- 0.5 ()GNi t" -- - - 7 3 0 0 2 . 9 7 5 + 2 7 . 2 7 4 8 8 T ~)LA~,myi =: - - 3 1 1 3 3 . 4 9

~)LA~,N i -- - - 4 2 7 7 9 . 6

OLAty~,~~=

25312.13

F.c.c. AI(AI, Ni) phase: (Al, NO °GAll "; - H A l s E R = - 7 9 7 6 . 1 5 + 1 3 7 . 0 9 3 0 3 8 T - 2 4 . 3 6 7 1 9 7 6 T In T - 0 . 0 0 1 8 8 4 6 6 2 T 2 - 8 . 7 7 6 6 4 × 10 7T3 + 7 4 0 9 2 / T - 1 1 2 7 6 . 2 4 + 2 2 3 . 0 4 8 4 4 6 T - 3 8 . 5 8 4 4 2 9 6 T In T + 0 . 0 1 8 5 3 1 9 8 2 T 2 - 5 . 7 6 4 2 2 7 × 1 0 - 6 T 3 + 7 4 0 9 2 / T 1 1 2 7 8 . 3 7 8 + 1 8 8 . 6 8 4 1 5 3 T - 3 1 . 7 4 8 1 9 2 T In T - 1.231 × 1028T -9 C'GN/ ......... g -- H s , s ~ = - 5 1 7 9 . 1 5 9 + 1 1 7 . 8 5 4 T - 2 2 0 9 6 T In T - 0 . 0 0 4 8 4 0 7 T 2

700 K < T < 933.47 K

933.47 K < T < 2 9 0 0 K

298.15 K < T < 1728.3 K

- 2 7 8 4 0 . 6 5 5 + 2 7 9 . 1 3 5 T - 4 3 . 1 T In T + 1 . 1 2 7 5 4 x 103t T -9 0LAI,N i = - 1 5 7 2 4 5 . 9 + 3 7 . 4 3 0 5 8 T

298.15 K < T < 700 K

1728.3 K < T < 3 0 0 0 K

ILAI,Ni = 4 3 2 4 8 . 7 8 -- 2 3 . 9 9 5 4 5 T

Al3Ni phase: Al~Ni AOGAI3NiI:e3 C type = GAHNiFe3 C type __ 0.75 OGAIf..... -- 0.25 OGNif. . . . . . . g = - - 4 9 3 7 3 . 5 1 -- 3 1 . 7 7 3 5 3 T + 6 . 7 5 6 9 2 6 T In T

AI3Ni: phase: AI~(Ni, Al)2(Va, Ni)~ A°GAI:Ni:Xah'cp" = GApyi:v, h cP -- 0 . 5 ° G A l f cc - - 0 . 3 3 3 3 °GNif . . . . . . . . g = - - 5 7 3 6 8 . 5 9 + 1 6 . 4 8 6 1 1 T A O G A I : A I : v a h c.p = G A I : A I yah c p __ 0 . 8 3 3 3 °GAif ..... = 4 5 6 7 . 5 _ 1 5 T . AOGal:Ni:r~i hcp

= GAl:Ni:Nih.~.p. _ 0 . 5 ° G A I f ' c ' P

-- 0 . 5 °GN,f . . . . . . . g = 4 1 6 6 . 7

AOGAI:AI:t,li h'ep = GAI:AI:Ni hc P - - 0 . 8 3 3 3 ° G A l l cP -- 0 . 1 6 6 7 °GN~f . . . . . . . g = 6 6 1 0 2 . 7 6 -- 17.98611 T OLAI:Ni,AI:W a = (ILAPNi.AI:Ni - - - 2 5 8 2 7 . 4 7

+ 20.18962T

OLAI:Ni:Va.~i = ¢)LAL:Ab:W.Ni = - - 6 8 6 5 0 . 8 4

+ 11.28426T

AINi phase: (Al, Ni)i(Ni, Va)1 A O G A I : N i b .... __ G A I : N i b ..... -- 0 . 5 0 G A l l . . . . -- 0.5 ° G N ~ . . . . . . .

g = --67686.38 + 15.66362T

AOGA~:vah ~ c = G A l : v a b c c __ 0 . 5 ( ) G A I l ..... = 2 5 0 0 " AOGN~:N h ~

= Gyi

Nib ..... _ OGNf ........ g = 8 7 1 5 . 0 8 - 3 . 5 5 6 T "

AOGNi:v b .... = GNi:vab .... -- 0.5 (JGNI f . . . . . . g = 7 8 9 0 1 . 4 5 -- 1 9 . 2 1 9 6 2 T IILAI.Ni:Ni = I~Lai,Ni:Va = I)LAI ,~i.v a -

19365.67 + 6.9194T

OLNi:NiV a = --28611.76

+ 16.54069T

AI~Ni5 p~ase: (AI, Ni)~Ni5 AOGAI:AI(~a3Pt5type = I)GAI:AIGa3Pt 5 type __ 0.375

OGAif'c'c -- 0.625 OGNif . . . . . . . . g = - - 5 6 7 1 6 . 0 9 + 1 4 . 6 7 3 7 3 T

AOGNi:Ni( a3P15 type = 0GNi:Ni(;aaPt5 type __ OGNif . . . . . . . . g = 5 0 0 0 t'

AIN(~ pk.ase: (AI. Ni),(Ni, AI).~ A O G h l : N i t c c = O G A I : N i f . . . . -- 0.25 °Gal t.....

- - 0.75 °GNif . . . . . . . .

0LAt.Ni:Ni = - - 8 8 7 7 . 5

g = -38683

+ 8.18241T

A~GN~:A/ ~c = 0GNi:A/ ..... -- 0.75 °GAff .... -- 0.25 °GNIf . . . . . . . . g = 4 8 6 8 3 -- 8 . 1 7 2 4 1 T AtIGxl:All

cc

I , G A I All c c _ O G A t f . c c = 5 0 0 0 b

0 L A i , N i . N i = ('LAI.Ni A t = - - 7 5 1 0 . 0 7 8

+ 0.1591275T

° L A I Ni,A I -- OLNi:Ni,AI = - - 1 5 5 7 0 4 . 5

+ 57.47359T

A O G N i : N i f. . . . . .

0 G N i : N i l ..... _ 0 G N i f . . . . . . .

T h i s v a l u e is t a k e n f r o m [22]. b I n the present w o r k these values are placed at 5 0 0 0 J g - a t o m

g = 5000 b

t.

5. Results and discussion The calculated Curie temperature of f.c.c. AI(Ni), which is shown in Fig. 1, falls within the experimental scatter band [16,33,35,72,73,79]. In Fig. 2 the computed magnetic moment of f.c.c. AI(Ni) is compared with the experimental data of Marian [72] and Crangle and

Martin [73]. Except for the two data points in the Ni-rich part, the experimental values are well described by the present assessment. The A1-Ni phase diagram calculated using the present set of thermodynamic parameters is shown in Fig. 3. Comparison between the experimental and calculated invariant equilibria is presented in Table 3.

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

26

800 3~

700

i

G e n t r y mnd [] Q u e n c h e d

2100

I

Fine(IgT2): n~mptes

I

1800

/

G00

I

t_ O

~- lseo'

500 ~-400

L

I

I

~

i

~N,~-

Llquld

t

1200

300 L~

200

+

100 0

A

~

0.85

X *

900

C r a n g l e and M a r ~ i n ( 1 9 5 9 ) Schr~mm(i941) Marlan(Ig37) Manders(~936) i

600

L

0.90 0.95 Atomic Traction Mi

1.00

M~

Fig. 1. Calculated Curie temperature of f.c.c. AI(Ni) together with the experimental data [16,33,35,72,73,79]. 0.8

©0.7 :~'.0 . 6 C

~' Cr~ngle ~nd Marttn(ig59) X Marian(ig37) VX

~0.5 O

E u

0.4

-o

u0.3 c

~-0.2

0.1 0

0.85

I

I

0.90 0. 95 Atomic Traction Ni

i. 00 M[

Fig. 2. The Ni content dependence of the B parameter for the f.c.c. AI(Ni) phase according to the present mathematics representation. Experimental data [72,73] on the total magnetic moment in Bohr magneton (tzB) are also shown.

The experimental invariant equilibria are well reproduced by the calculation. Fig. 4 compares the calculated Al-rich part of the phase diagram with the experimental data [1,1315,36]. Except for one liquidus temperature reported by Nishimura [14] at 4.5 at.% Ni, the experimental data are well reproduced by the calculation. Fig. 5 shows a comparison between the calculated and measured [1,13-15,23-25,36] AI-A1Ni phase diagram. Taking into account the scatter of the experimental data, the agreement is very good. The calculated phase diagram in the range 60-90 at.% Ni and 1600-1700 K is shown in Fig. 6(a) together with the experimental data [1,15-21]. Fig. 6(b) is the enlarged central part of

A

300 0

1 (Al)+AI~N|

At

L 0.~ 0.4 0.6 0.8 Atomic Fraction

1.0

IN] M[

Fig. 3. Calculated A1-Ni phase diagram according to the present optimization.

Fig. 6(a). If the scatter between the different experimental values is considered, the calculated curves agree with the experimental data. The calculated solubility of A1 in Ni is a little higher than the experimental value. In the present work, it was found that any attempt to improve the fit to the solubility results in a worse agreement with the thermodynamic data concerning A1Ni 3. Fig. 7 gives a comparison between the computed and measured [1,11,15-21,2335,61] phase diagram in the comparison range 50 at.% Ni to Ni. The experimental data are rather well reproduced by the calculation within the scatter of the experimental values. Fig. 8 shows the calculated enthalpy of mixing in the liquid phase at four different temperatures together with the experimental data [39-42]. Apart from the data of Gizenko et al. [40], the experimental values are well reproduced by the calculation within the estimated experimental errors. The calculated activities of AI and Ni in the liquid at 2000 K are shown in Fig. 9 compared with the experimental data available [47,5154]. To enable a comparison among the experimental data given at different temperatures in one diagram, the measured data points were shifted by the calculated term ai (2000 K ) - - a i (Texp) , where a i is the activity of component i (i -- AI on Ni) and Texp is the experimental temperature. As can be seen in Fig. 9, the calculated values agree with the experimental data except for the AI values published by Vachet et al. [52] and Johnston and Palmer [53]. It should be noted that Vachet et al. [52] studied the partition of A1 between AI-Ni liquid alloys and liquid Ag to determine the A1 activity at 1873 K. Their calculation relied on the activity of AI in Ag at a much lower temperature (973-1253 K). The values of Johnston and Palmer [53] are under caution because of the possible contamina-

27

Y. Du, N. Clavaguera I Journal of Alloys and Compounds 237 (1996) 20-32 Table 3 Comparison between the calculated and experimental invariant equilibria Source

Ni concentration (at.%)

Temperature (K)

Present work Schramm [ 16] Bremer et al. [18] Hilpert et al. [17] Verhoeven et al? [21]

Liquid + f.c.c.(A1, N i ) o A I N i 3 75.83 81.28 76.44 76.70 80.00 77.00 76.08 79.59 77.02 75.50 78.50 76.16 76.00 78.80 77.00

1643.17 1635.00 1636.90 1645.00 1649.00

Present wcrk Schramm [16] Bremer et al. [18] Hilpert et al. [17] Verhoeven et al." [21]

LiquidoA1Ni 75.71 69.46 75.87 69.90 75.50 70.90 75.20 71.00 75.55 71.80

+ AINi3 76.47 76.90 76.97 76.00 76.60

1642.97 1633.00 1635.00 1642.00 1646.00

Present work Gwyer [1] Alexander and Vaughan [15]

Liquid + AINi, 26.51 41.25 24.97 26.84 41.82

oAI3Ni5 40.14 33.33 40.30

1405.00 1405.00 1406.00

Present work Gwyer [1] Nishimura [14] Alexander and Vaughan [15]

Liquid + AI3Ni 2 16.43 32.82 15.00 33.33 14.50 15.40 35.96

oAI3Ni 25 25 25 25

1124.00 1115.00 1097.00 1127.00

Present work Gwyer [1] Fink and Willey [13] Nishimura [14]

Liquid~A13Ni 2.58 25 3.00 25 2.70 25 2.36 25

+ f.c.c. (AI, Ni) 0.30 0.0 0.023 0.0

916.00 913.00 913.00 912.00

Present work Robertson and Wayman b [11]

AINi + AINi 3 59.89 70.84 60.50 72.80

~-~AI3Ni 5 66.10 67.00

993.00 973 -+ 30

The invadant equilibrium temperatures reported by Verhoeven et al. [21] extrapolated to zero solidification rate. b Assessed values.

10@@

. . . .

at

three different solidification rates, 61, 80, and 100 ~ m s-', are

2100

,

I

i~ ,(

I

)

~> Fink

&_~

/ r~/

~//w

~nd Wille~(1934)

~)001

L D

{2_ E 8J F-

I

Tawlor and Dogle(Ig72) Alexander and Vaughan(IgB7) 0 Bradley and T~ylor(1937) ~

Gww~r(IgOB) [] Ronigen and Koch(1933) Fink and Willew(i934) X

600

Ninhimura(1936) @[exander a n d

V

1200 g_ E

V~ugh~n(1937)

500

~0i

400 300 0

A]

i 0.01

i 0.02

Atomic

i 0.03

I 0.04

fraction

N]

X Nishimurm(193G)

390

0.05

Fig, 4. Comparison between the calculated phase diagram and experimental values [1,13-15,36] for the Al-rich side below 1000 K.

~

~ A[

G~W~i(ae~8) I [~.l

0.2

Atomic

If

J

f

~.3

[~.4

fraction

~.5

Hi

Fig. 5. Comparison between the calculated diagram and experimental data [1,13-15,23-25,36] from AI to 50 at.% Ni.

Y. Du, N. Clavaguera I Journal of Alloys and Compounds 237 (I996) 20-32

28

]

I

XSmndokov Udov~kll et

1680 I

I

I

al.([971).

mt. (tggl)

--18

1670~

~

rnG|zenko

et

K

19E3

¢Sudavt,ov~ et ai.(1990),

¢i.(19gi)

Verhoeven i t

e't

xi

iaee

1773 K

a1.(1983),

N Oremer et at.clUB) Htlpmr~ e* ~ ] , ( t g S ? ) Schr a~/n(L541)

~i~50 I

Qlexa~d~r ~md V~g~(1~@7)

6~er (1~08J

~1~4o~1.620

A

0.60

0.65

0,70

0.75

Atomic

0.80

0.85

fractlon

-48

0.90

,

(a)

-58

1655.0

_~

i

"

1658.0

-

~

-68

, rnO

1652.5

n 0

W

i t a l . (1~$11 Ilh~r=~dkor e l e1.(19909

Atomic

N ~e~r

et a1,(1~8)

1.0

M]

Mi

i

- - - , 1700 K.

'.r' OL

8.9 8.72

fraction

1 0.[]

Fig. 8. Calculated enthalpy of mixing of the liquid with the experimental data [39-42]: -,1923 K; - - - 1800 K; . . . . . ,1773 K;

1.8

0.70

i 0.6

I_= V e r h = ~

"z&" H l l p e P t e~ el.(ig~?Pl 5¢hr&nm ( 1541 ) -~ ~lexandoP ~ d VsugP~n(L~3?)

(b)

/

N g~/ ~ g-~,

t 0.4

8.2

At

1635,8 A

-i

Ml

Ni

MI

'

N i l p e r t et a i . ( 1 9 9 0 ) O~orka(I986)

./ w~ X/~

-

8.8

Q.80

. . . . . . . . . .

Atomic ¢ractlon

X

HI

8,7

Fig. 6. (a) Comparison of the calculated phase diagram and experimental data [1,15-21] from 60 to 90 at.% Ni in the temperature range 1600-1700 K. (b) Enlarged central part of Fig. 6(a).

33

"~8,6 b

"4J~ 0 . 5 (J

2120p

f

i

i

O

r

Watana~e

et a l . t15'~4)

• U l l o v S k l l ei a1.(19~11) d~ rJh4pwadk4r e* 4L, ( ~ 9 ~ ;

1800H

A

~ .rla I l S g e l

~

|M

Bremer et

c~8.4 ~.3 Al

al.(l~@)

~, H | i p l p I i~< ~). (tglBT] R o b ~ z o n ~d WmWI~In(I~4); 0

One phase r ~ I o n

¢

J'~.N~I tg~dl Ta ]or ana DOyle(Z~F'd)

AN

0.1 L~00

A

N

~ Kuch~ko ~ma T r o ~ l ' ~ l n a ( I ~ , ' i ) + Ra$togt al~d A r ~ e l l ( t ~ 9 )

tq

v A~d~lt (LgGG~ * HQ,n~9~ ~ d Kre~e(19~) ~r TsWIoP ~,d rloud(19~) X Gu|eVa(l~L ) Sohr41wn(1~411

@ •

A

0.5

0.6

0.7Qtomic

--O.8 0.9 f r a c t i o n N[

Alexander ana V~ugh~n(l~) I i r a d l e W and T~NIoP(19~17)

1, MI

Fig. 7. Comparison of the calculated phase diagram and experimental data [1,11,15-21,23-35,61[ from 50 at.% Ni to Ni above 300 K.

tion of alloys. In Fig. 10 the calculated activity of AI in the liquid at 1100 K is compared with the values of Schaefer [49] and Schaefer and Gokcen [50]. Within the estimated experimental errors, the agreement is excellent. The calculated enthalpy of formation at 298.15 K in the whole composition range, shown in Fig. 11, is compared with the data from two groups of workers [37,38]. The full and broken lines correspond to the calculation with and without introducing the parameter C in Eq. (5). Taking into account the accuracy and

0 0

0.Z

0.4 Atomic

0.6

0.8

fraction

Ni

.8 Hi

Fig. 9. Calculated activities of AI and Ni vs. Ni content for the liquid at 2000 K with the experimental data [47,51-54]. The reference states for both AI and Ni are the liquid.

scatter of the experimental data [38] for the A13Ni and AI3Ni 2 compounds, the fit to the experimental values is reasonable. In particular, the agreement is improved by introducing the parameter C into the expression for the Gibbs energy of A13Ni. The calculated partial Gibbs energies of AI and Ni for the solid phases at 1350 K are presented in Fig. 12 with the experimental data [47,51,55-58]. The computed curves fall within the large experimental scatter band. In Fig. 13 the calculated enthalpy of formation of the A1Ni phase at 1100 K is compared with the data from two groups of researchers [43,44]. As shown in this figure, the fit to the experimental data is excellent. The calculated and measured heat capacity [59-61]

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

0

•

o

0 9

\

0

8

3~

~

7

l

I

A1 X

Ni AI

-50

A1

Ni

29

N£

/

At

-%

:3D

nl

m -100 L

37

~

6

A

}

S~

Sch~eTmr(1975) S c h e ~ T ~ r and G o k c ~ n ( 1 9 7 9 )

s

-t50

U

D

0,4

-200 0.3

S ~3.

4 -250

H i l p e r t et a 1 . ( 1 9 9 0 ) OTorka(t986) Elre~ale and Smeltzer(1981; E s k o v et a 1 . ( 1 9 7 4 3 [] M a t k ~ n a n d P o k i d y s h e v ( 1 9 6 5 ) + Sterner and Komarek(lg64)

x

n I

0 0

I

0.05

0. 1 0

Atomic

fraction

0.15 Ni

I

I

&

0.B

0.4

~.5

I

I

0.6

Atomic

Fig. 10, Calculated activity of A1 vs. Ni content for the liquid at 1100 K with the experimental data [49,50].

I

I

-300

0.7

I

I

0.8

fraction

0.9 Hi

1.0 Mi

Fig. 12. Comparison of the calculated partial Gibbs energies of AI and Ni vs. Ni content for the solid phases at 1350 K with the experimental data [47,51,55-58]. The reference states for A1 and Ni are liquid and f.c.c, respectively.

I

(

-10

-54

[]

-20 -57

-30

I

I

D Heni 9 and Lukas(ig75) B~nnohl end Luka=(1974)

0

\E

-40

-60 0

-50

E \ -6B 5£

~-~ - 6 o <1

Al3Mi - 78 0 f

l

L-aa

~3

T

AI3MI2 AIMI i (t958)

-6g

Kubnschewsk

-90

Oelsen and

-100

AI

J

I

0.2

0.4 Atomic

Middel(1937) I

-72

I

O.G

0.8

1.0

fraction

Ni

Mi

Fig. 11. Comparison between the calculated enthalpy of formation of the alloys at 298.15 K and the experimental values [37,38]: - - , the calculations with coefficient for the excess heat capacity; , calculations without introducing the coefficient for the excess heat capacity.

of the AINi phase is shown in Fig. 14. The experimental data below about 700 K are reasonably described by the calculation within the estimated experimental errors. However, above this temperature the computed results deviate noticeably from the experimental data. In order to improve the fit at high temperatures, probably a chemical ordering contribution should be introduced in the Gibbs energy, since chemical ordering for A1Ni phase occurs at about 723 K [59,61]. A comparison of the calculated enthalpy of formation for AINi 3 as a function of temperature with the experimental data [37,45-48] is made in Fig. 15. The calculated curve fits the experimental data within the

-75 0.44

I 0.48 Atomic

I 0.52

k 0.56

fraction

Fig. 13. C a l c u l a t e d e n t h a l p y o f f o r m a t i o n o f t h e K withtheexperimentaldata[43,44].

0.60

Hi

AlNiphaseatll00

range of experimental errors. The heat capacity for the AINi 3 calculated as a function of the temperature is compared with the experimental values for the 76.6 at.% Ni alloy of Kovalev et al. [62], in Fig. 16. Good agreement between the experimental data and calculated values is obtained. The calculated partial Gibbs energy of A1 in the two phase regions vs. temperature is plotted in Fig. 17 with the experimental data [49,50,55-57]. The experimental values are reasonably well described by the calculation except for the data of Eskov et al. [57], which were not used in the optimization. In Fig. 18, the model-predicted partial Gibbs energy of Ni in the two-phase regions vs. temperature is compared with the ex-

30

Y. Du, N. Clavaguera I Journal of Alloys and Compounds 237 (1996) 20-32 40

i

f

r

t

i

i

2100 A Schaefer and Gokcen(1979) X Malkln and Pokld~sheu(1965)

K u c ~ ' ~ r l n k Q an~ T r a l h k l ~ t ( l ~ 7 ~ )

? Stelner a

~l.(igTt) & TPa~hkln~ ~md KhQm~akovCl~L~ O ~nd~kov$

e~

n

~

8

~

_

1800

~4

[] Schaefer(t975)

g

\

~o

AT

\

~50o

L 1200 E

~4

900,

20

I

300

I

400

500

I

[

600

I

700

I

800

TempePa~uPe,

900

1000

600

I1 / ~ ~ ~

K

Fig. 14. Comparison between the calculated heat capacity of the A1Ni phase (Al05Ni05) with the experimental values [59-61].

B00 -200

-150 Partial

-30

I

I

/ ~ / i i

-I00 Gibbs

0

-50

energw , K]/mol

Fig. 17. Calculated two-phase equilibrium partial Gibbs energies of AI vs. temperature with the experimental data [49,50,55-57]: region 1, f.c.c. A1 (Ni); region 2, AINi3; region 3, A13Nis; region 4, AINi; region 5, A13Ni2; region 6, A13Ni; region 7, f.c.c. A1 (AI); region 8, liquid.

I

A Monet and Rzym~n(1995) Hllperl et ai.(1990) Sommer(1988) @ Mogutnov el a).(1984) Oelmen and Middel(1937)

-35i

/

0

E \

2100 -40

g

,

,

[] O~orka(1986) &

/

~

A

2: 1 8 0 0 1 A

H. . . . . . . . .

d Seybo]t(l 7

X

-45

-50

I 0

J

500

I

1000

1500

Temperature,

2000

K

Fig. 15. Calculated enthalpy of formation of the AINi3 phase with the experimental data [37,45-48]. 300~/

40

1

I

I

-E00

Partial

B8 36

A

Kovalev

et at. (1976) &

30

&

m_

26 A

22 20 B00

t

i

i

-100 Gibbs

i

I

-50

il

0

e n e r g y , K_T/mol

Fig. 18. Calculated two-phase equilibrium partial Gibbs energies of Ni vs. temperature with the experimental data of Oforka [51] and the assessed values of Hanneman and Seybolt [80]. For the meanings of the numerals see Fig. 17.

A

~-28 24

J

-150

I

I

600

900 Temperature,

I 1200

1500

K

Fig. 16. Comparison between the calculated heat capacity of the AINi3 phase (Aloz34Nio766) and the experimental data [62].

perimental datum of Oforka [51] and the assessed data from Hanneman and Seybolt [80]. Except for one value [80], corresponding to the A1Ni + AI3Ni 2 phase region, the experimental data are well reproduced by the calculation. Using the experimental A1 activity at 1273 K published by Steiner and Komarek [55], Hanneman and Seybolt [80] evaluated the Ni activity by means of the Gibbs-Duhem equation. The assessed Ni activity data are not used in the optimization. A further check on the reliability of the thermodynamic modeling is provided by Fig. 19, where the

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

8.58 0.45

I

I

I

6. Conclusions

I

r ~ y l o r ~nd B o y l e ( 1 9 7 Z ) , ~4@S K Guneva ~nd Makorou(1951), IS13 K

@ 48 gO

35

u@

30

~0

25

@

~0

,,

y" /

2@

O]

@ 15 0 10

0.4@

0.45

0.50

Atomic

0.55

0.60

~raction

Mi

31

8.65

Fig. 19. ~.alculated site fractions of Ni (Y'N~) and vacancies (Y"v,) on the first and second sublattices respectively of (A1, Ni)l(Ni, Va)l. The experimental data [23,81] are not used in the evaluation of the

All the phase diagram and thermodynamic data available for the AI-Ni system have been carefully evaluated. An optimal set of thermodynamic functions for the system has been obtained from the selected phase diagram and thermodynamic data by using the CALPHAD technique. The comprehensive comparison show that most of the experimental information is reasonably well accounted for by the present description of the AI-Ni system. It is also demonstrated that the currently optimized parameters can reasonably predict the experimental data (site fractions of the species on the sublattice (A1, Ni)l(Ni, Va)l for AINi for long-range order parameter for AINi3), which are not used in the thermodynamic modeling.

Acknowledgments

parameters.

currenlly predicted site fractions of Ni and vacancy on the first and second sublattices of the two-sublattice model (A1, Ni) 1(Ni, Va) 1 used for AINi agree well with the experimental data [23,81], which are not included in the optimization. In Fig. 20, the model-predicted long-range order parameter for A1Ni 3 is compared with the experimental data taken from three groups of workers [69,82,83]. The predicted curve gives a good compromise to the experimental values [69,82,83].

i

0

0 9

n 0 C rv 0 7

Aoki and Izumi(1975) [] Clark and Mohanty(1974) Corey and P o t t e r ( 1 9 6 7 )

0 6

0 5 0.73

I 0.7,4 Atomic

I 021.75

I 0.76

~raction

0.77

Ni

Fig. 20. Calculated long-range order parameter (LROP) of AINi 3 with the experimental data [69,82,83]. The definition used is LROP := [(PAl -- XAI)/(1 -- XAI) + (PNi -- Xr~i)/(1 -- XNi)]/2, where PAl and Psi are the probabilities that AI atom sites and Ni atom sites are filled by AI atoms and Ni atoms respectively, and Xa~ and xN~ are the mole fractions of AI and Ni respectively.

One of the authors (Y. Du) gratefully acknowledges the grant released by the Ministry of Education and Science of Spain. Thanks are also due to Dr. H.L. Lukas for the provision of his program, to Professor I. Ansara for his critical advice and for the supply of his unpublished results, and to Professor M.T. Clavaguera-Mora and Dr. C. Comas for their help.

References [1] A.G.C. Gwyer, Z. Anorg. Chem., 57 (1908) 133. [2] L. Kaufman and H. Nesor, C A L P H A D , 2 (1978) 325. [3] I. Ansara, B. Sundman and P. Willemin, Acta Metall., 36 (1988) 977. [4] L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, New York, 1970. [5] J.M. Sanchez, J.R. Barefoot, R.N. Tarret and J.K. Tien, Acta Metall., 32 (1984) 1519. [6] C. Sigli and J.M. Sanchez, Acta Metall., 33 (1985) 1097. [7] C. Colinet, P. Hicter and A, Pasturel, Phys. Rev. B, 45 (1992) 1571. [8] A. Pasturel, C. Colinet, A.T. Paxton and M.v. Schilfgaarde, J. Phys.: Condens. Matter, 4 (1992) 945. [9] M. Sluiter, P.E.A. Turchi, F.J. Pinski and G.M. Stocks, J. Phase Equilib., 13 (1992) 605. [10] R. Kikuchi, Phys. Rev., 81 (1951) 988. [11] I.M. Robertson and C.M. Wayman, Metallography, 17 (1984) 43. [12] N. Dupin, Th~se, Institut National Polytechnique de Grenoble, 1995; I. Ansara, N. Dupin, H.L. Lukas and B. Sudman, in press. [13] W.L. Fink and L.A. Willey, Trans. Am. Inst. Min. Metall. Eng., 111 (1934) 293. [14] H. Nishimura, J. Min. Inst. Jpn., 614 (1936) 381. [15] W.O. Alexander and N.B.Vaughan, J. Inst. Met., 61 (1937) 247. [16] J. Schramm, Z. Metallkd., 33 (1941) 347. [17] K. Hilpert, D. Kobertz, V.Venugopal, M. Miller, H. Gerads, F.J. Bremer and H. Nickel, Z. Naturforsch., 42a (1987) 1327. [18] F.J. Bremer, M. Beyss, E. Karthaus, A. Hellwig, J. Schober, J.-M. Welter and H. Wenzl, J. Cryst. Growth., 87 (1988) 185.

32

Y. Du, N. Clavaguera / Journal of Alloys and Compounds 237 (1996) 20-32

[19] S.R. Dharwadkar, K. Hilpert, D. Kobertz, V. Venugopal and H. Nickel, High Temp. Sci., 28 (1990) 203. [20] A.L. Udovskii, I.V. Oldakovskii, V.G. Moldavskii and V.Z. Turkevich, Dokl. Acad. Nauk SSSR, 317 (1991) 161. [21] J.D. Verhoeven, J.H. Lee, F,C. Laabs and L.-L. Jones, J. Phase Equilib., 12 (1991) 15. [22] A.T. Dinsdale, C A L P H A D , 15 (1991) 317. [23] A. Taylor and N.J. Doyle, J. Appl. Crystallogr., 5 (1972) 201. [24] A.J. Bradley and A. Taylor, Proc. Roy. Soc., London, Ser. A, 159 (1937) 56. [25] L.N. Guseva, Dokl. Akad. Nauk SSSR, 77 (1951) 415. [26] M.M.P. Janssen, Metall. Trans., 4 (1973) 1623. [27] P. Nash and D,R.F. West, Met. Sci., 17 (1983) 99. [28] A. Taylor and R.W. Floyd, J. Inst. Met., 81 (1952/1953) 25. [29] E. Hornbogen and H. Kreye, Z. Metallkd., 57 (1966) 122. [30] C.C. Jia, Ph.D. Thesis, Tohoku University, Japan, 1990. [31] M. Watanabe, Z. Horita, D.J. Smith, M.R. McCartney, T. Sano and M. Nernoto, Acta Metall. Mater., 42 (1994) 3381. [32] R.O. Williams, Trans. Metall. Soc. AIME, 215 (1959) 1026. [33] A.J. Ardell, Acta Metall., 16 (1968) 511. [34] P.K. Rastogi and A.J. Ardell, Acta Metall., 17 (1969) 595. [35] W.O. Gentry and M.E. Fine, Acta Metall., 20 (1972) 181. [36] P. Rontgen and W. Koch, Z. Metallkd., 25 (1933) 182. [37] W. Oelsen and W. Middel, Mitt. Kaiser-Wilhelm-Inst. Eisenforsch. Dusseldorf, 19 (1937) 1. [38] O. Kubaschewski, Trans. Faraday Soc., 54 (1958) 814. [39] V.M. Sandakov, Yu.O. Esin and P.V. Gel'd, Russ. J. Phys. Chem., 45 (1971) 1020. [40] N.V. Gizenko, S.N. Kilesso, D.V. Ilinkov, B.I. Emlin and A.L. Zavyalov, Izv. Vyssh. Uchebn. Zaved., Tsvetn. MetaU., 4 (1983) 21. [41] V.S. Sudavtsova, A.V. Shuvalov and N.O. Sharkina, Rasplavy, 4 (1990) 97. [42] U.K. Stolz, I. Arpshofen, F. Sommer and B. Predel, J. Phase Equilib., 14 (1993) 473. [43] E.-Th. Henig and H.L. Lukas, Z. Metallkd. 66 (1975) 98. [44] H.-D. Dannohl and H.L. Lukas, Z. Metallkd,, 65 (1974) 642. [45] B.M. Mogutnov, I.A. Tomilin and L.A. Shvartsman, Thermodynamics of Iron Alloys, Metallurgiya, Moscow, 1984, 208 pp. [46] F. Sommer, J. Therm. Anal., 33 (1988) 15. [47] K. Hilpert, M. Miller, H. Gerads and H. Nickel, Ber. Bunsenges. Phys. Chem., 94 (1990) 40. [48] Z. Moser and K. Rzyman, personal communication, 1995. [49] S.C. Schaefer, Rep. Invest. 7993, 1975, 15 pp (US Bureau of Mines). [50] S.C. Schaefer and N.A. Gokcen, High Temp. Sci., 11 (1979) 31. [51] N.C. Oforka, Indian J. Chem. A, 25 (1986) 1027. [52] F. Vachet, P. Desre and E. Bonnier, C.R. Acad. Sci., Paris, .260 (1965) 453. [53] G.R. Johnston and L.D. Palmer, High Temp. High Pressures, 12 (1980) 261. [54] P.L. Mart and W.D. Reid, Fech.. Rep. MRL-TR-91-15, A R NO. 006-366, 1991, p. 33. [55] A. Steiner and K.L. Komarek, Trans. Metall. Soe. AIME., 230 (1964) 786. [56] V.I. Malkin and V?V..Pokidyshev, lzv. Akad. Nauk SSSR, Neorg. Mater., 1 (1965) 1747.

[57] V.M. Eskov, V?V~.Samokhval and A.A. Vecher, lzv. Akad. Nauk SSSR, Met., 2 (1974) 199. [58] F.A. Elrefaie and W.W. Smeltzer, J. Electrochem. Soc., 128 (1981) 2237. [59] V.A. Troshkina and K.G. Khomyakov, Russ. J. lnorg. Chem., 6 (1961) 1233. [60] M.I. Sandakova, V.M. Sandakov, G.I. Kalishevich and P.V. Geld, Russ. J. Phys. Chem., 45 (1971) 901. [61] L.A. Kucherenko and V.A. Troshkina, Russ. Metall., 1 (1971) 115. [62] A.I. Kovalev, M.B. Bronfin, Yu.V. Loshchinin and V.A. Vertogradskii, High Temp. High Pressures, 8 (1976) 581. [63] J.-O. Andersson, A.F. Guillermet, P. Gustafson, M. Hillert, B. Jansson, B. Jonsson, B. Sundman and J. Argen, C A L P H A D , 11 (1987) 93. [64] M. Hillert and M. Jarl, C A L P H A D , 2 (1978) 227-238. [65] G. Inden, Proc. Project Meet. C A L P H A D V, Max-Planck Institute for Metal Research, Diisseldorf, 1976, Chapter 111, (4), 1-13. [66] F. Sommer, Z. Metallkd., 73(2) (1982) 72-86. [67] E.S. Levin and G.D. Ayushina, lzv. Akad. Nauk SSSR, Met., 1 (1971) 227-229. [68] A.J. Bradley, Philos. Mag., 23(158) (1937) 1049-1067. [69] K. Aoki and O. Izumi, Phys. Status Solidi A, 32(82) (1975) 657-664. [70] N. Buis, J.J.M. Franse and P.E. Brommer, Physica B-C, 106 (1981) 1-8. [71] J.R. Schrieffer, F.R. de Boer, C.J. Schinkel, J. Biesterbos and S. Proost, J. Appl. Phys., 40(3) (1969) 1049-1055. [72] V. Marian, Ann. Phys., NY, 7 (1937) 459-527. [73] J. Crangle and M.J.C. Martin, Philos. Mag., 8(4) (1959) 10061012. [74] A.F. Guillermet and P. Gustafson, High Temp. High Pressures, 16 (1984) 591-610. [75] G.T. Rado and H. Suhl, Magnetism, Vol. IV, Academic Press, New York, 1966, pp. 118-145. [76] T. Chart, unpublished research, National Physical Laboratory, UK, 1985. [77] H.L. Lukas, E.-Th. Henig and B. Zimmermann, C A L P H A D , •(3) (1977) 225-236. [78] T. Tanaka, N.A. Gokcen and Z.-I. Morita, Z. Metallkd, 8•(5) (1990) 349-353. [79] C. Manders, Ann. Phys., NY, 11(5) (1936) 167-231. [80] R.E. Hanneman and A.U. Seybolt, Trans. Metall. Soc. A1ME, 245(2) (1969) 434-435. [81] L.N. Guseva and E.S. Makorov, Dokl. Akad. Nauk SSSR, 77 (1951) 615-616. [82] C.L. Corey and D.I. Potter, J. Appl. Phys., 38 (1967) 3894. [83] J.P. Clark and G.P. Mohanty, Ser. Metall., 8 (1974) 959.