Thermodynamic re-assessment of the ternary system Al-Cr-Ni

Calphad, Vol. 25, No. 2, pp. 279-298, 2001 © 2001 Elsevier Science Ltd All rights reserved 0364-5916/01/$ - see front matter

Pergamon PII: S 0 3 6 4 - 5 9 1 6 ( 0 1 ) 0 0 0 4 9 - 9

Thermodynamic Re-Assessment of the Ternary System AI-Cr-Ni. N. Dupin*, I. Ansara**, B. Sundman + * Calcul Thermodynamique, 3, rue de l'avenir, 63670 Orcet, France, ** L.T.P.C.M., E.N.S.E.E.G., BP 75, 38402 St. Martin d'H~res, France, + Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm, Sweden. (Received May 15, 200~

Abstract A re-assessment of the ternary system A1-Cr-Ni following Dupin's thesis work using a single Gibbs energy function for the 7 and 7' phases is presented taking into account new experimental liquidus temperatures. The disordered bcc A2 and ordered B2 phases are also modelled with a single equation. The existence of vacancies as defects in this structure is described. The other phases are modelled as substitutional solutions, or as stoichiometric or non-stroichiometric binary compounds. The present assessment is limited to the sub-system A1Ni-Cr-Ni where no ternary phase exists. The parameters describing the Gibbs energy of all the assessed phases are given. Extensive comparisons between calculation and experimental data are presented.

Introduction The mechanical properties of the Ni base superalloys are mainly due to the coherency between their constituting phases 9' (A1) and 7' (L12), the L12 structure being an ordered state of the fcc (A1) lattice. The thermodynamic behaviour of both phases can thus be modelled by a single Gibbs energy function which is a sum of two contributions, one corresponding to the Gibbs energy of the disordered phase and the other to the ordering Gibbs energy. This approach leads to constraints between the thermodynamic parameters to ensure the ability of the ordered phase to disorder. For Ni base superalloys, the ternary system AI-Cr-Ni is an important sub-system. The present assessment of this system is a revision of the one presented in Dupin's thesis [95Dup]. It is part of a wider project dedicated to the constitution of a multicomponent thermodynamic database for Ni base superalloys [01Dup]. It introduces a new modelling for the A2 and B2 phases, using also for both of them a single Gibbs energy function and takes into account new experimental liquidus temperatures. An assessment of this ternary system has recently been published by Huang and Chang [99Hua]. It differs mainly from Dupin's thesis work [95Dup] in the modelling of the 7' phase. Arguing that "the description by Dupin seems to be unnecessarily complicated", the two fcc phases 7 and 7' are modelled separetely. The formalism that they used is actually identical to Dupin's but when the ~,' phase disorders, a disordered phases different of the stable 7 is obtained. No real simplification is thus introduced by Huang and Chang's contribution, the fewer number of parameters used for the ordering contribution being largely compensated by the number of the parameters of the new disordered state. Moreover, in multicomponent systems, a possible competition between stable and metastable disordered phases may occur. In the present analysis of the A1-Cr-Ni system, the approach introduced by Ansara et al. [88Ansi is applied not only to the 9' and 7' phases but also to the A2 and B2 phases. It has initially been used by Lacaze and Sundman [91Lac] in the Fe-Si system for the A2 and B2 phases undergoing a second order transformation. Previous studies of the binary AI-Ni [88Ans, 97Arts] and ternary A1 Ni-Cr systems [95Dup, 99Hua] have taken into account vacancies determined experimentally but the B2 was treated independently of the A2 phase. The general conversion of this old model to the one taking into

279

280

N. DUPIN et al.

account the possible second order transition has been presented by Dupin and Ansara [99Dup] and will be applied here. The experimental determination of the B2 phase in the binary system A1-Cr by Helander and Tolochko [99Hel] will be discussed hereunder in the light of the modelling of that phase. Experimental results available for the ternary A1-Cr-Ni concern mainly the sub-system A1Ni-CrNi. The present assessment will be limited to the corresponding composition range. Experimental data The sub-system A1Ni-Cr-Ni exhibits the following phases: • 7, the Ni base fcc (A1) solid solution, • a, the Cr base bcc (A2) solid solution, • 7', the ternary extension of the phase based on NiaA1, • fl, the B2 phase based on A1Ni. Table 1: Experimental Data in the A1Ni-Cr-Ni System. References Exp. Method X-ray, Optical Microscopy [52Tay] [53Kor] [58Bag1] [58Bag2]

Optical Microscopy, Thermal Analysis, Hardness, Resistivity X-ray, Optical Microscopy Optical Microscopy, Hardness, Resistivity

[66Mall

e.m.f.

[82Tu]

EMPA D.T.A. EMPA EMPA Optical Microscopy, X-ray, EMPA, Mass Spectrometry Diffusion Couples D.T.A. EMPA after 26 days of heat treatment D.T.A., Q.A.T.D. Solution calorimetry Optical Microscopy, X-ray, Hardness D.T.A. EPMA Diffusion Couples DTA, EPMA DTA, EPMA hardness, TEM Solution calorimetry

Exp. Data For Ni > 50 % at.: isoth, sect. at 1023, 1123, 1273 and 1423 K, and "tentative" monovaxiant lines of the liquidus Quasi-binary section Cr-A1Ni Isothermal section at 1423 K for A1 < 50 % at. Extension of (Cr) at 1123 and 1523 K TAb AG~X, AS}x, AH~,~ at 1045 K, for Ni <21% at. and

XNi/Xcr=lO.93 [83Lan] [830ch]

[85Ofo] [87Nes] [89Hon]

[90Dav] [90Kek] [92Gor] [93Cot] [94Jia]

[94Yeu] [96Wu] [99Sun] [99Tia] [00Sal]

Isothermal section at 1298 K for A1 < 60 % at. Invariant temperature of 7 + 7' ~ f~ + Isothermal section at 1298 K for A1 < 60 % at. Extension of 7' at 1273 K Isothermal section at 1423 K for A1 < 60 % at. ahl, act, aNi, AGI at 1423 K LimitT/7+flat1473K Solvus 7 / 7 + 7' from 1100 to 1400 K 7+7'+/?at1300K 7 + 7 ' + o ~ a t 1400K Liquidus for Cr < 15, A1 < 27.5 % at. AH! for three L12 compositions Isoplethal sections in the planes containing the reactions: liq. ~ a + ~ a n d l i q . ~7+ Liquidus and solidus in the vicinity of A1Ni 7+7'and•+7'at1473K 7 + f l a t 1473K liq./7 equilibria: Tllq and tie-lines Cr solubility in B2, site occupation of Cr Enthalpy of mixing in the liquid phase

.o

Merchant and Notis in 1984 [84Mer] and Rogl in 1991 [91Rog] have critically assessed the phase diagram data of the ternary system A1-Cr Ni available at that time. Table 1 summarizes the experimental

THERMODYNAMIC

RE-ASSESSMENT

OF THE TERNARY

SYSTEM

AI-Cr-Ni

281

work reported for the sub-system A1Ni-Cr-Ni. Most of the experimental data will be compared hereafter with calculations showing some inconsistencies between the different sets of data as well as uncertainties for single sets.

Thermodynamic modelling of the phases Elements The molar Gibbs energy of a pure element i in the phase % at T and 0.1 MPa, °G~(T), referred to the enthalpy of its stable state at 298.15 K and 0.1 MPa (SER), °HSER(298.15 K), is given by the following equationr: °G~(T) _o HiSEn(298.15 K) = a + b T + c T lnT + . . .

(1)

The value of a, b, c, ... for each i and ~o are from Dinsdale [91Din].

Binary s u b - s y s t e m s The description of the binary sub-systems used are briefly discussed. introduced in the present contribution are presented. 2000

I

18O0 -

I

I

2200 /

2°°°1, 1800 ~

Liq.

,,,, 1600 -

1600 -

.~ 1400 -

~

1200 -

,

]p•

,

m

i1400 -

800 -

600 0

A]

0.2

0.4

0.6

xNi

°

I"*T' "~,

0'.8

I

I

Liq.

a (.42)

~

z:Z~7

\

1000-

4

7i :l,I

I

12o0-

Q

~ 1 o00 -

I

The minor modifications

..

800 -

1.0 Ni

Figure 1: Calculated phase diagram of the binary system AI-Ni compared with most of the phase diagram experimental data. Solid lines: present revision. Dotted lines: [97Ansi.

.....,

600 0

A1

0.2

0.4

0.6

XCr

0.8

1.0

Cr

Figure 2: Calculated phase diagram of A1-Cr. Solid lines: [98Saul. Dotted line: A 2 / B 2 transition with a critical temperature of 1300 K. Broken line: solvus when B2 ordering considered.

The thermodynamic description of the system A1-Ni used was obtained by Ansara et al. [97Anal. A minor revision of the description of the ordering of the 7' phase has been introduced in order to get a better agreement with the experimental solvus at low temperature. This has been made by using the same experimental information as in the previous study by Ansara et al. [97Ansi but assigning a larger weight on the low temperature 7/7' experimental equilibria. The description of the B2 phase has been modified following Dupin and Ansara [99Dup]. The B2 phase (A1,Ni,D)o.5(A1,Ni,D)o.5, where D represents vacancies, is thus treated as an ordered state of the A2 phase which is metastable in this system. This allows to treat second order transition between these two phases in systems where it occurs. The calculated phase diagram is shown in figure 1. The phase diagram derived from the previous description by Ansara et al. [97Ansi is compared with the present one. The slightly better agreement of the solubility of A1 in the 3' phase also induces a change of the invariant temperature involving the A13Nis phase which is not known accurately experimentally.

282

N. DUPIN et al.

The thermodynamic description of the system A1-Cr is due to Saunders [98Sau] and is based on a previous study by Saunders and Rivlin [87San]. The calculated phase diagram is shown in solidlines in figure 2. The intermetallic phases are modelled as stoichiometric phases while in J.L. Murray's [98Mur] assessment of the phase diagram, they are non-stoichiometric. The modelling of the second order transition of the B2 phase, recently determined experimentally by Helander and Tolochko [99Hell, is obtained by adding an order contribution to the Gibbs energy of the A2 phase previously assessed by Saunders and choosing a critical temperature of 1300 K; this transition is well reproduced as shown by the dotted line in figure 2. Nevertheless, it also implies a stabilisation of this phase at low temperature on the Cr rich region with a high retrograde solubility of A1 in Cr leading to the instability of the A1Cr2 phase at low temperatures shown by the broken line in figure 2. Such a result is not satisfactory. A new assessment taking into account the stability of the B2 phase should thus also imply a reassessment of the A1Cr2 phase. But further experiments would first be desirable in order to determine the stable equilibria in this field. In the present study, a much less stable B2 phase has been assumed in order to avoid modifying the actual binary phase diagram. The thermodynamic description of the system Cr-Ni are taken from the SGTE solution database.The calculated phase diagram of the binary system Cr-Ni exhibits a eutectic reaction at 1618 K between the liquid phase (53.8 % at. Cr), the nickel rich fcc solution (49.9 % at. Cr) and the chromium rich bee solution (63.6 % at. Cr).

Ternary solution phases The excess Gibbs energy of the liquid phase and of the disordered solid solutions based on Ni and Cr has been described with the Redlich-Kister-Muggianu [75Mug] expression. Ternary interaction terms have been introduced. The molar Gibbs energy of these phases at a given temperature, is thus expressed as follows:

G~m(xi) = ~-~.xiG~ + R T ~ ~ x , lnxi i

i

xixjLiz + XAIXCrXNiLAI,Cr,Ni

(2)

i j>i

A1 A2 The ternary interaction parameters gliq ~Al,Cr,Ni, LA|,Cr,Ni and LAI,Cr,NI have been optimised in order to reproduce the main features of the liquid-solid equilibria. They have been assumed to be independent of A1 A2 temperature as well as of composition. The value of the parameters LAI,Cr,Ni and LAI,C,,Ni has alSO an influence on the description of the ordered phases 7' and 8.

Ternary 7 and 7' phases The molar Gibbs energy of the 7 and 7' phases has been modelled with a single function based on a two sublattice model (A1,Ni,Cr)a(AI,Ni,Cr) expressed by equation (3). The first term, denoted Gm(xi), depends only on xi, the atomic composition of the phase. It corresponds to the Gibbs energy of the disordered phase 7 and is expressed by equation (2). The second term, denoted AG°rd(y~')), corresponds to the ordering energy. It depends on the site fractions y~S). This term is expressed as a difference of two terms after equation (4). These two terms are calculated using the same function in the sublattice formalism but different site fractions. AG "LI~ (y~')) is function of the site fractions y~) and AG °LI~ (y~) = xi) of the site fractions of the disorder phase of same composition. Both terms are equal when the phase is disordered, the ordering energy being then equal to zero. G ~ or ~' = :

GAI(xi) + AG~d(y},)) aAl(xi)

+ t a ° L 1 2 ( y } s}) -- n a ° L l ' ( y ~ s) = Xi)

(3) (4)

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni The function "A G) ' L) t -2 ('y ~J/mole of atoms.

283

is expressed in the classical sublattice formalism by the following equation, in

Y~' Y' j'AG~:LI"+RT(~Iyiny'+I~y']Iny'j)i

AG°LIz('~')) =

j

L.L12 i

j>i

k

~-~

'

'

~

,, L.L12 Y'kYI'Yj k:iZ

i j>i k

'

"L'LI2

+ E

~ " ~'" °'" I'lL12 YiYAIYCrYNiX~i:AI,Cr,Ni

+ ~ YAIYCrYNiYi AI,Cr,Ni:i i

i

where the interaction parameters depend on the occupation on the sublattice where the interaction takes place as follows: L.LI2

i~:~

=

T*Lt2,0

~,~:~

+ (Y~

-

, xr.Ll2,1 yj)~i~:~

(6)

L.L12 zeL12,0 ,,X L.L12,1 k:ij = ~ k : i j + (Y]' - Yj ) k:ij

(7)

In order to allow the phase to disorder, relations must be introduced between the parameters describing the ordering [8SAns, 95Dup, 97Aus]. A u s a r a e t al. [88Ans] have shown that for this the following equation has to be fulfilled f OG~ ~

(,)

They propose a particular set of constraints between parameters derived from the resolution of this equation. The two sublattice model (A,B,.. ")s (A,B,...), denoted 2SL, mathematically equivalent to the four sublattice model (A,B,...) (A,B,...) (A,B,...) (A,B,...), denoted 4SL, where all sublattices are equivalent [95Dup, 9TAns] also fulfills equation (8). The molar Gibbs energy of a phase in the 4SL model is expressed by: i +

j

k

I

EEE s

o

i

(L°o+ (y}')-y~t))L~j)

(9)

i j>i

be A1, Cr ou Ni on any of the sublattices. The crystallographic equivalence of the four sublattices means that two elements can be interchanged between two sites without change in the Gibbs energy. For the parameters of the reference term, it means: i,j,k

and l can

(lO)

AGi:j:k:z = AGi:j:t:k = AGi:t:h:j . . . . The corresponding chemical formula can also be used as subscripts, i.e. A G A:A~A:B

= AGA3B, A G A:A:B:B

=

A G A~BI, " " .

(11)

The parameters Li~d:~:z:mare also independent of the sublattice on which the interaction takes place. For sake of simplicity, these parameters have moreover been taken independent of the occupation of the IJ v M M other sublattices. The notation L i1/j thus stands for Lid:k:z:m , Lid:z:,:m , Lij:k:m:i , Li:id:k:m , .... The equivalence of equations (9) and (5) for any occupation yields the following relations to be applied to the parameters of each binary system A-B (eq. 11 to 18) and to the ternary parameters of the system AI-Cr-Ni (eq. 19 to 27). In these relations, the parameters of the 2SL formalism axe expressed as function of the parameters of the 4SL.

284

N. DUPIN et al. =

AGABa

(12)

~-

AGAaB

(13)

L.L12,o A,B:A

----

--3/2 AGA,a + 3/2 AGA2B2 + 3/2 AGAa, + 3LOA.B

(14)

L.L12,0 A,B:B

~

+3/2 AGABa + 3/2 AGA2B2

A r , oLI2 ',.XB: A Age_eLl.2 VA:B

3/2 AGAaB + 3L~, B

(15)

L.LI2,~ A,B:A = +1/2 AGAB3 -- 3/2 AGA2B~ + 3/2 AGA3B+ 3L~ ~

(16)

L.L~,I A,B:B

(17)

=

-3/2 ~,G,~,~+ 3/2 ~ V ~

=

L oA,B

(18)

L.L12,1 = L A,B 1 i:A,B

(19)

L*L12,o i:A,B

1/2 AGAaB+ 3L~

L*L12,0 AI,Cr:Ni

- - 3 / 2 AGAlaNi --

3/2 AGCraNi + 3/2 AGAICr2Ni

L°L12,0 A1,Ni:Cr

+3/2 AGAI2CrNi+ 3LOl,cr --3/2 AGAI3C~-- 3/2 AGcrNi a + 3 / 2 AGAICrNi2 +3/2 AGAI2CrNi+ 3LAI,Ni o

L.L12,0 Cr,Ni:AI ~-~ --3/2 AGhlCra -- 3/2 AGAINi3+ 3/2 AGAICrNi2 +3/2 AGA1Cr2Ni + 3LCr,N o i L.L12,1 AI,Cr:Ni = - 1 / 2 AGhlaNi + 1/2 AGCraNi -- 3/2 AGAICr2Ni +3/2 AGA,2C~Ni+ 3L~a,c~ L.L12,1 A1,Ni:Cr ---- --1/2 AGAI3Cr+ 1/2 AGcrNI3 - 3/2 AGA1CrNi2 1 +3/2 AGAI2CrNi + 3LAI,N i

L.L12,I Cr,Ni:A|

~-

(20)

(21) (22) (23)

(24)

--1/2 AGAICr3+ I/2 AGA~Nia-- 3/2 AGA~CrNi~ +3/2 AGA:Cr2NI+ 3L~r,Ni

(25)

LoLI~,O AI,Cr,Ni:AI

= +AGA:Cr3 -- 3/2 AGAI2C~2-- 3/2 AGAlsC~ +AGAINia -- 3/2 AGAI2Ni2 -- 3/2 AGAIaN i - 3 / 2 AGAICrNi2-- 3/2 AGAICr2Ni+ 6AGAI2CrNi L.L12,0 = --3/2 AGAIc~3-- 3/2 AGA12Cr2+ AGAI3Cr AI,Cr,Ni:Cr + A G C r N i a -- 3/2 AGcr2Ni2 - 3/2 AGCraN i - 3 / 2 AGAICrNi2+ 6AGAIc~2Ni-- 3/2 AGAI2CrNi L°L12,0 -----3/2 AGA~Nia-- 3/2 AGAI2Ni2+ AGAIzNi AI,Cr,Ni:Ni - 3 / 2 i e C r N i a -- 3/2 AGCraNi2 + AGCraN i +6AGAICrNI2 -- 3/2 AGilCr2Ul -- 3/2 AGAI2C~Ni

(26)

(27)

(28)

Due to the use of equation (4), the parameters Li° are not independent and have not been used during this work. Only one Lit parameter has been used, the one assessed in the binary system Al-Ni. The simple and symmetrical set of parameters of the 4SLF is related to complicated relations in the 2SLF. These relations can be simplified when the Gibbs energy of each stoichiometric compound is defined as follows: AGi:j:,:k = Uij + Uik + Uit + Ujk + Uj, + Uk, + oqik,

(29)

For the binary compounds, and for a value zero for the binary variables (~ijk~, their Gibbs energies is expressed as follows: ,~G,~3

=

3U~j

AGi2:/2 = 4U/j AGi3.~ = 3Uij

(3o) (31) (32)

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni

285

and for a ternary compound of the type AGi~:j:k: AVi2:2k = 2Uij + 2Uik + Ujk

(33)

The value of UAINi is obtained from the assessment of the binary system A1-Ni. The variables UAlcr and UCrNi which may contribute to the extension of the L1B field towards the binary systems Al-Cr and Cr-Ni have been assessed during the present work. All the variables aOkt have been kept equal to zero except aAlCrSi2 which has also been assessed during the present work. As already explained, the value of the parameter LAI,cr,Ni has also an influence on the equilibria 7/7'. T e r n a r y a a n d ~ phases The B2 phase had been modelled as (AI,Cr,Ni,D) (AI,Cr,Ni,D) independently of the A2 solid solution by Dupin [95Dup]. In the present work, it has been changed in order to use a single function to describe the Gibbs energy of the A2 and B2 phases similarly to the one used to describe the thermodynamic behaviour of the A1 and L1B phases. G,~ or

~

= GAB(x,) + GoB, (y~,)) _ a,SB(y~,) = x,)

---- 2_.~2..,Y~Y9 ~:j + I / 2 R T i

y~lny~+

(34)

y~'lny~'

(35)

j

The symmetry of the model for the B2 phase has been taken into account by imposing the following relation: B2

B2

(36)

GA..B = GB: A

It has been assumed that no B2 ordering occurs between the vacancies and the Cr leading to: G,B2 Cr:D = 0

(37)

The binary ordering parameters G~:c r and G~:Ni and the ternary interaction parameter of the disordered A2 phase, L AB AI,Cr,Ni have been optimised. As mentioned in the section relative to the binary systems, the ordering parameter used for the system Al-Cr does not account for the results obtained by Helander and Tolochko [99Hel]. A description in agreement with these results keeping the phase diagram unchanged at low temperatures would need a complete reassessment of this binary system which is not within the scope of the present study. A new description is thus desirable but also experimental confirmation of the stability of the B2 phase in this binary system. When a critical temperature of 1300 K for the second ordrer transition A2-B2 is used in r,BB this system, the use of a ternary interaction parameter .r,B2 ~.'cr,sl = ~ Cr,Ni:Al is needed in order to obtain a satisfactory agreement with the available ternary experiments.

Optimisation p r o c e d u r e The optimisation of the thermodynamic parameters of the various phases was performed with P A I ~ O T [84Jan] part of the ThermoCalc package [85Sun]. In a first step, in order to accelerate the optimisation procedure, a selected set of experimental data has been used: the invariant equilibria, a few liquidus temperatures, 7 solvns data, and solubility limits in the 7' and/~ phases. They have been progressively taken into account in order to get a better agreement between calculations and experimental data. In addition, a systematic comparison of all the available experimental data with the calculated results has been made at each step of the optimisation. Some experiments have not been possible to reproduce precisely, in particular the A 2 / B 2 equilibria and the use of more experiments involving these phases has not given any better agreement. The experimental points concerning the extension of the primary field of the 7' phase beyond 10 at. % Cr was given

N. DUPIN et al.

286

an important weight in the previous assessment [95Dup]. It affected too much the calculated liquid-7 equilibria as found when comparing new liquidus temperature data at higher Cr content [96Wu, 99Sun]. These experiments [90Dav] have thus been given a lower weight in the present work. Finally, a satisfactory agreement has been obtained for most of the available experimental data. The optimised parameters obtained in the present work are listed in the appendix as well as those originating from previous studies. Comparisons of calculation with experimental data will be presented and discussed in the next section. Results

Liquid-solid equilibria Figure 3 compares the calculated projection of the monovariant lines of the liquidus with those proposed by Taylor and Floyd [52Tay] and Kornilov and Mints [54Kor] and the nature of the primary phase experimentally identified by David [90Dav]. The projection suggested by Taylor and Floyd [52Tay] is tentative; no experimental details is given on this part of their study and no experimental composition contains less than 50 % Ni except a couple on the line between A1Ni and Cr. Kornilov and Mints [54Kor] presented the monovariant lines between the a, f~ and 7 fields in the sub-system A1Ni-Cr-Ni as function of the mole % of Ni, Cr and A1Ni. The lines drawn in figure 3 derive from a conversion to molar fraction of A1, Cr and Ni done by Merchant and Notis [84Mer]. A1

A1 5Zrav

.....

Cu × ~gSun +

Ni

0

0.2

0.4

0.6

0.8

1.0

Cr

XCr

Figure 3: Calculated monovariant lines of the liquidus in the sub-system system Ni-A1Ni-Cr compared with experimental data.

Ni

0

0.2

0.4

0.6

0.8

1.0

Cr

x~ Figure 4: Isothermal lines of the liquidus each 50 K beetwen 1600 and 2150 K.

The calculated projection shows four primary crystallisation fields of 7, 7', ~ and a. The primary field of the 7' phase is less extended than indicated by David's [90Dav] results. It is one of the main difference with the previous assessment [95Dup]. This discrepancy could be explained by the experimental difficulty to keep the first solid formed when quenching. The calculated monovariant lines between the phases 7 and a, and fl and ~ are not in very good agreement with Taylor and Floyd [52Tay] and Kornilov and Mints [54Kor] results. Due to the relative inaccuracy of these experiments, it is difficult to put more weight on them during the optimisation. A careful study of the invariant eutectic reaction liq. ~.. o~ + fl + 7, of the liquidus surface of the phases c~ and f~ and of the equilibria a+/5 is highly desirable. The calculated monovariant line between the 7 and ~ phases is in very good agreement with all the experiments. Figure 4 presents the isothermal lines of the liquidus calculated each 50 K between 1600 and 2150 K in the sub-system Ni-A1Ni-Cr. The dotted line corresponds to the monovariant lines of the liquidus

THERMODYNAMIC

RE-ASSESSMENT

OF THE TERNARY

SYSTEM

AI-Cr-Ni

287

in this area. The curvature of the 7 liquidus surface is much less than the one calculated in the previous assessment [95Dup] and falls between those reported by David [90Day] and Kornilov and Mints [54Kor]. The curvature of the surface in the /5 and o~ field is in agreement with the ones from Kornilov and Mints [54Kor]. I

1740

I

I

I

I

XCr=0.05 • 54Kor A90Day XCr=0.10 • 54Kor m 90Day X 99Sun XCr=0.15 • 54Kor O 90Dav

°'"

1720 1700 "-

~

1680 1660

O O

&&

t~

1640 1620 1600

1580

oh5

0

0' 5 0 ,0 oh5 0.30 xA1

Figure 5: Calculated liquidus temperatures for xcr

=

0.05, 0.10, 0.15 compared to the experimental ones.

Figure 5 represents the liquidus temperatures calculated for 5, 10 and 15 at.% Cr together with the experimental values from David [90Day] and Sung and Poirier [99Sun]. The points labelled 54Kor [54Kor] are the intersection of the sections studied by David and the isothermal lines of the liquidus surface drawn by Merchant after conversion of Kornilov and Mints's results [54Kor] from weight % in the AINi-Cr-Ni section into the atomic % in the system A1-Cr-Ni. There is a difference of about 40 K between the sets from Kornilov and Mints [54Kor] and David's [90Dav], the calculated values lying between them. The difference between experimental and calculated values in these sections are similar to the ones in the binary system A1-Ni. The agreement obtained is satisfactory. 1750

I

0.50

I

i

I

I

.°

0.45-

1700 -

~= 1 6 ~ -

1600-

..."

,b.v'~ •~"

1550

lYOO Exp.Tliq./ K

.B

OA1

175o

OCt-

.."

0'15 0.10 t .1~" 0.05 ..o 0

mCr 96Wu

& 90Day + 96Wu

16'oo

oAI

0.350.30~ 0.250.20 -

X 99Sun 1550

99Sun

0.40-

"

0

011

90Day

..

AAI •

012

013

014

Cr

0.5

Exp.

Figure 6: Comparison of experimental and cal- Figure 7: Comparison of experimental and calculated culated liquidus temperatures. compositions of the primary .y phase.

288

N. DUPIN et aL

The comparison of the experimental liquidus temperatures with the ones calculated for compositions studied by David [90Dav] is also presented in figure 6 with those obtained for the compositions studied by Wu [96Wu] and Sung et al. [99Sun]. The agreement with Wu [96Wu] and Sung and Poirier [99Sun] is better than with David [90Dav]. The comparison of the calculated composition of the first solid formed with the experimental values for these three sets [90Dav, 96Wu, 99Sun] is given in figure 7. The agreement is very satisfactory for all of them. Invariant r e a c t i o n s Table 2 presents the calculated invariant equilibria in the sub-system A1Ni-Cr-Ni. A relatively large difference (37 K) is obtained for the eutectic reaction liq. ~ a +/~ + 9'. Nevertheless, it shows the same tendency that was found with the liquidus temperature in the 7 field where other experiments are closer to the calculation (fig. 5). A satisfactory agreement with the experimental invariant temperatures has thus been obtained.

Table 2: Calculated Invariant Reaction in the Sub-System A1Ni-Cr-Ni. Reaction

Tc~c.

Phase I

Te.p [Ref.] liq. + 9" ~- 9" + ~

1622K 1613± 10 K [52Tay]

liq. 9" 9'

liq ~- 9' + ~ + a

1556 K 1593 • 10 K [52Tay] 1573 K [55Kor]

liq. 9'

9'+~-9"+a

1269 K 1273 g [52Tay] 1263 ± 3 K [82Tu]

"7 9"

L

Composition A1 Cr 23.6 4.5 23.4 2.9 20.4 4.2 28.4 2.4 17.4 32.5 12.9 36.2 30.2 1 4 . 5 3.1 79.9 11.7 2 8 . 1 30.5 9.6 21.2 10.8 0.2 96.3

(% at) Ni 71.9 73.7 75.4 69.2 50.1 50.9 55.2 16.9 60.2 59.8 68.0 3.5

Isoplethal sections The calculated isoplethal section Cr-A1Ni is presented in figure 8. It is not of the quasi-binary nature reported by Kornilov and Mints [53Kor] and Bagaryatskiy [58Bag2]. Rogl's points [91Rog] result from the critical assessement of all the available publications on the system. The overall agreement is satisfactory. Tian et al. [99Tia] propose a solubility of 8 at. % at 1563 K reported on figure 8. However, this conclusion yields from two conflicting results: the microstructural examinations show that the solubility is less than this value while the hardness measurements during ageing at lower temperature indicates that it is higher. Their arguments for the latter is not very convincing. The calculated solubility limit is not very far from this point but no attempt has been made to obtain a better agreement. Comparisons with the experiments near this section can also be seen on the isothermal sections (fig. 14 and 18). They show a consistent agreement with the solubility of Cr in the B2 phase but not for the A1Ni in the A2 phase. The calculated solubility in the A2 phase is in agreement with the one reported by Bagaryatskiy et al. [58Bag] but not with DeLancrolle and Seigle [83Lan] or Oforka and Argent [85Ofo]. Attempts have been made to put more weight on those later, but it has not been possible to get a more satisfactory agreement. It would be interesting to understand if these discrepancies are due to high experimental uncertainties in this field or to a weakness of the model used. The influence of the stability of a B2 phase on the A1-Cr system could partially explain this problem. The change of the binary second order-disorder transi-

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni

289

tion to the first order ternary transition would be of particular interest. A better experimental knowledge of this area is desirable. Tian et al. [99Tia] have used the Atom Location by CHanneling Enhanced MIcroanalysis (ALCHEMI) technique in order to determined the site preference of Cr. The value of F c r = y(cAr1) / (y(cArl) + y(CNi)) where ~Cr° (0 is the fraction of Cr on the site mainly occupied by i is reported for three compositions but the article does not indicate at which temperature it corresponds. The treatment of the experiments does not take into account the presence of vacancies (y~)=0) or reciprocal substitution of Ni and AI (y(Ail) = y(ANi) = 0) which are modelled by the present description. Figure 9 compares the values obtained by Tian with Fcv calculated at 1563 and 1273 K. A qualitative agreement is obtained. The change of the preference of Cr with composition is well described. Such experimental results are particularly valuable in the choice of a thermodynamic modelling and are to be generalized.

2400

I

I

I

2200

I

I

53Kor: nsinglcphase Iltwophases 58Bag: O single phase Stwophases

I

~1273 K 1

0.8-

2000

g

1.0

|

0.6-

1800 1600

0.4-

14oo 0.2-

1200 1000

0 AINi

0'.2

0'.4

0'.6

0'.8

~Cr

1.0 Cr

0 0.45

0.50 XAt

0.55

Figure 8: Calculated isoplethal section AINi--Cr Figure 9: Calculated Cr occupancy of A1 site in the compared with experiments ([53Kor], [58Bag], B2 phase, at 1563 and 1273 K for Xcr = 2 at. % [91Rog], [99Tia]). compared with experimental results.

1800

I

I

52Tay r~

1600

I

t

=

i

I

i

89Hon

1600 ~1400

?'

1200

~ 1400 -~/

mXAI=0'15

90DDaCA ~twoi~lses 89rI°IY{A

i 1300 " VO0 1 1[ ~ ~, 1200-[/ _~

XXAl=0.11 OXAl=0'13 v XAl=0.09 + XAl=0.07

00\°

1000 8O0

~onOChph~e

0

Ni3AI

0.1 XCr

1000 /

0.2 Ni3Cr

0

÷ g

0.1

0.2

0.3

014

0.5

XCr

Figure 10: Isoplethal section calculated for Figure 11: Calculated solvns temperature for constant. xNi ----0.75 compared with experimental data. composition in A1 compared with experimental data. Figure 10 compares the calculated isoplethal section for XNi = 0.75 with experimental data in this ection. Taylor and Floyd [5~I'ay] have used X-ray diffraction and optical microscopy, Ochai et al. [83Och]

290

N. DUPIN et aL

electronic microscopy and EMPA, Hong et aL [89Hon] DTA and EPMA and David [90Dav] DTA. The calculated diagram is significantly different of the one drawn by Taylor and Floyd [52Tay] but supported by the studies of Hong et al. [89Hon] and Ochiai [83Och]. The 7 solvus temperatures measured by Hong et al. [89Hon] by DTA are compared with the calculated ones for different compositions in M in figure 11. The agreement is satisfactory considering that the experiments refers to solid transformations studied by DTA. Isothermal sections Figure 12 compares the calculated isothermal section at 1573 K with the experimental tie-lines from Jia et al. [94Jia] between the 7' and the B2 or 7 phases. The agreement is very good for all the tie-lines except for the one with the highest Cr content which maybe due to non-equilibrium. It is also the case at 1473 K (fig. 13) for at least one tie-line which is inconsistent with the other sets of experiments. The calculated section at 1473 K is in agreement with the different sets [94Yeu, 98Qia, 84Carl within the experimental uncertainties. Figure 14 compares the isothermal section calculated at 1423 K and the experimental points from Oforka and Argent [85Ofo]. The calculated equilibria are in good agreement except for the c~+ fl equilibria. The calculated solubility of A1 and Ni in the bcc A2 phase is much lower than those measured by these authors and the calculated solubility of Cr in the B2 phase highly decreases for A1 compositions higher than 50 at. % while they also reported an almost constant value. As their measured solubility for the alpha phase in the binary system Cr-Ni is also inconsistent with the calculated value, it could be due to experimental uncertainties. The discrepancies on the solubility in Cr reflects the inconsistencies between experimental data in the isothermal sections [85Ofo, 83Lan] and in the isoplethal section A1Ni-Cr (fig. 8). The composition of the samples studied by Oforka and Argent [85Ofo] and DeLancrolle and Seigle[83Lan] being in the middle of the a + fl field, the uncertainty on the composition measured for the a phase are thought to be higher than the one from Kornilov and Mints [53Kor] who analysed compositions in the two and single phase fields, in the vicinity of the phase boundary. The almost constant solubility of Cr in A1Ni found by Oforka and Argent [85Ofo] is in disagreement with Cotton [93Cot] which reports a decrease of the solubility in Cr for the highest aluminium composition. Cotton concludes that Cr preferencially substitutes A1. The decrease of the solubility of Cr would thus be correctly described. The calculated shape of the fl phase field is supported by the comparison of the isothermal section calculated at 1298 K with the results from DeLancrolle [83Lan] (fig. 18). At 1423 K, the calculated 7 solvus is in disagreement with Taylor and Floyd's data [52Tay] in this area. It could be argued that this is due to a bad fitting of the binary A1-Ni system. But this is not the case as the comparison of the calculated isothermal section at 1400 K with the experimental solvus by Hong et al. [89Hon] confirms the good description of the solvus of the 7 phase in this region. Figures 16 and 17 compare the isothermal sections calculated at 1373 and 1300 K with the experimental data available at these temperatures. The agreement is very satisfactory. However, in figure 17, the tie-line from Hong et al. [89Hon] is experimentally reported as an edge of a tie-triangle 7+fl÷~. Such an equilibrium at this temperature (1300K) would be inconsistent with the temperature of the experimental invariant temperature involving the a, ~, 7 and 7 r phases (see table 2). Figures 18 and 19 compare the isothermal section calculated at 1298 and 1273 K with the experimental data available. An overall good agreement is obtained. At 1298 K (fig. 18), the calculated Cr solubility in the ~,' phase is lower than the experimental one which may be due to experimental uncertainties. At 1273 K (fig. 19), the data from Taylor and Floyd are only qualitatively reproduced while those from Ochai et al. [83Och] agree well with the calculations. The latter has been preferred during the optimisation procedure because of longer heat treatment time (5 days against 4) and higher purity. The binary tie-line determined by Jia [94Jia] is perfectly reproduced but the ternary one shows differences about 2 at. %. Such discrepancies have also been found for this set of experimental data at higher temperature (fig. 12 and 13) and also in other systems, for instance A1 C ~ N i [95Dup].

T H E R M O D Y N A M I C RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni

0.50/-~

°4V \ o4o/~ /\ 0.35/

°-3°2~-,---~

~ o.~,~:

94Jia +.-. +

0.50/~

0.45/ 0.40/

L\

O.lO/ °o°~ N,O

o~

a 94Yeu

~\

+ 94.1ia

o4

~

~

ao25~/: \ \ o2o~~ \ \ 0,5Ho °~'~ ~'~s~---%~ O.lO/ °°%\

\

o~

I~

0'30 t ~ . ~ ~ , .

~

~

o,

O 98Qia

'~

0.35~ B2

o.2o/,_,,_~_ \~,~,

o~/

291

o,

°o°7

Ni 0

~

0.1

~

~

0.2

XCr

~ \~

0.3

0.4

0.5

XCr

Figure 12: Partial isothermal section of the Figure 13: Partial isothermal section of the ternary ternary system A1-Cr-Ni calculated at 1573 K system AI-Cr-Ni calculatedat 1473 K compared with compared with experimental data. experimental data•

A1 1.0

0

0.50/~

~

0.8 ~ i i i ! . ~ "

0~~~

x overall composition

x.o..o~,A

.. - ~ - - k

Ni

0X 0

^ 0.2

e~q'

"~ ... -'::~--

^ x ,, 0.4 0.6 XCr

"B2+7'

^-"~-----,4,2,0.8 1.0 Cr

89H?nDTA , _ o x

\

o.3oy . ~ - ~ . _ ~

°~or

• / r x ~ ! : ' . : ~ ' . k

04"~no Ix` .~xx

0.::7 0.35/,, ~2[

85Ofo

~ o~~/~

\~

o.2o2~~ J ~ \ ~:;\ o.15/----__~_____~\ O.lO/ \--~

o:7 Ni

o

, o71

0?2

0?3

0?4

o.5

Xcr

Figure 14: Partial isothermal section of the ternary system Figure 15: Partial isothermal section of th( AI-Cr Ni calculated at 1423 K compared with experimen- ternary system A1-Cr-Ni calculated at 1400 B tal data. compared with experimental data.

292

N. DUPIN et 0.50'

94Jia

a/.

0.50/~

+--- +

°.4°7~2 r \ ° 35z% \

0 ° 357~,,, I

~,:,,\

o2ot~\\ 0.15J ~

\

o.~oj

0.1

0.2

0.3

0.4

\

0.20?, ~ \ \ ~ ; ~ , \ 0 . 1 5 ~ . '

\--\

OoO Ni 0

89Hon

\

o.~o!

OoO 0.5

Ni 0

0.1

0.2

XCr

0.3

0.4

0.5

XCr

Figure 16: Partial isothermal section calculated at 1373 K with experimental data.

Figure 17: Partial isothermal section calculated at 1300 K with experimental data.

Al 1.0 0~

0.50/~

...'~~:

O

0.4V/ 0.4V /

83Lan

0.8 0.7 0.6

0.3% 0;~ 0 . 2 0 ~

0.4 0.3 0.2 0

Ni

0

94Jia

+...+

~

83OCh 0 one phase • two phases

[

Yr

~,

52Tay 0~'

OT

@3q-7"

@

B2+'t'

©82+~, oA2+~

\.

OA2+B2+y~' ¢B2+7"t~'

; 0.2

0.4

0.6 XCr

0.8

1.0

O ~ P~

Ni o

0.1

0.3

o.2

P~

0.4

~

O A2+B2 A

0.5

XCr

Figure 18: Partial isothermal section calculated Figure 19: Partial isothermal section calculated at 1273 K with experimental data. at 1298 K with experimental data.

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni

293

A1 0.50 A

94Jia

1.0~

+-.. +

92Gor lIA2+-/

0 9 ~_.:.:~i~

'/~:~iii.:k.

0.40~ / \ °.3V: ~._ \

;:::::::....=....=...:::::::: . . . . ~,

Ni 0

0.1

0

0

'

w

0.2

0.3

0.4

0.5

Ni

2 - Y ~

• ~/ ~ ~ ' " ~

. A

7

~

0.2

e'r~t'

Os2~lt" oA2,,~

~

~

e

X

A 0.4

A

0

"~

'

0

" ~::, .:". ~:"=- d !::::~, ":::i !!!~!!i!~}~. '~::~:: !i::':....

/ "~ o.3,~/2,---~. ~r

~

ay

:::E EEEE EEriE E;~EiEiE~Ei.

II 0 4 -)( /

o.~o!~ ~ _ ~ _ _ . _ ~

°0°7

VA2+B2+lt'

.~EEEEEEEEEEE:

o.~o~.. /

o.1o!

=A2+~'

0 8 ,~..~::gi::iL~-

0.~+~,

k¢..

8)

e~2+~/'

\

~'A2+B2+'

,

.A2+B2

A

A 1.0

~

0.6

0.8

Cr

XCr

XCr

Figure 20: Partial isothermal section calculated at 1173 K with the experimental data.

Figure 21: Partial isothermal section calculated at 1123 K with the experimental data.

A1 0.50/~

94Jia

1.0 ~

+- • - +

°~k/X \ o.4o,,v,:/ °~V 7"---~\ ~,~ o~%,~____~, \ o~o~ \ % . ~ o~k - ~-_~.._~

0o7 Ni

0

~A 2 + ' /

n a ~:iii~

~,~

vA2+s2+x'

:: ::::::::::::::::: :::::::::::::::::::::::::

°3°L / ..... ,,~

o.lo/ ~

~o~

::::X

~,

0.4-// °"~:c~- v

\

52Tay

/':i!!EEh'IL'~aii~iii!i!iiiiii!i~ •::~:~!~!!iiiiii::F:::::::::::i::i.

• wr =================================== ~--'

~

~ ":~i@i!i!iiiiiii~

~2+~,'

/ 0.1

0.2

0.3

0.4

0.5

XCr

Figure 22: Partial isothermal section of the ternary system A 1 - C r - N i calculated at 1073 K compared with experimental data.

Ni

0

0.2

0.4

0.6

0.8

1.0

Xcr Figure 23: Partial isothermal section of the ternary system A1-Cr-Ni calculated at 1023 K compared with experimental data•

Cr

294

N. DUPIN

et al.

Figures 20 and 22 compare the isothermal sections calculated at 1173 and 1123 K with the experimental results [94Jia]. The agreement with the 9'/9" tie-line is not satisfactory as observed for this experimental set of data [94Jia] at 1573, 1473 and 1273 K (fig. 12, 13 and 19). For this particular set, Huang and Chang [99Hua] compared their calculated results at only two temperatures and in a composition range where a satisfactory agreement was obtained. At 1123 K (fig. 21), the calculated extension of the 9" phase field is less than shown by Taylor and Floyd [52Tay]. Attempts to obtain a better agreement at this temperature had lead to differences with the data at higher temperature and in particular with those of Ochai [83Och] at 1273 K (fig. 19 and 10). The same trend is obtained for the isothermal section at 1023 K (fig. 23). These discrepancies could be explained by experimental difficulties to reach equilibrium at low temperatures. Another explanation could be the difficulties reported by Taylor and Floyd [52Tay] in their analysis of specimens quenched from "low" temperatures. Unfortunately, the more recent studies performed in this temperature range [92Gor, 94Jia] give no information on the extension of the 9" phase towards the A1-Cr system. More experimental information would be desirable. Thermodynamics

Figure 24 compares the calculated molar enthalpy of mixing with the ones measured by Saltykov [00Sal]. The agreement is satisfactory. Some systematic deviation when Cr increases seems to originates from the description of the binary system Cr-Ni. Figure 25 compares the calculated activities measured by Oforka and Argent [85Ofo] in the ternary system A1-Cr-Ni as well as in the limiting binary systems. The experimental points with highest composition in A1 are not compared on this figure as experimental difficulties are reported for them. The point showing a large disagreement for the nickel activity corresponds to the highest Al content taken into account in the present work (42.8at.%). The Gibbs energy value derived by Oforka and Argent [85Ofo] for this point also seems inconsistent with the trend shown with increasing A1 in the a ÷/~ field. However, an overall satisfactory agreement is obtained. q0 /

I

,

I

I

'

.~

00Sal

101

I

I

I

85Ofo

X Cr-Ni

""

AI-Cr-Ni • ata • acz Oa~

10 ° c~ - 1 0

O AI-Ni0.g5Cr0.t5 I'1 A1.Ni0.70Cr0.30

1 /'°1

-50/"' -50

, -40

, -30

[o.-.o..o 'w AI.Ni0.20Cr0.80

, -20

HExp.

, -10

, 0

F F /

10

10-1

AI-Ni A aAi A*'

10 .2 .-

A 10 .3

Cr-Ni lib ac~

<>

"

AI-Cr acz

10.4

10'

16~

16'

161

lb °

1

Exp.

Figure 24: Comparison of the calculated enthalpy Figure 25: Comparison of the calculated activity of mixing of the liquid phase with experimental re- with the values measured by Oforka and Argent sults ([00Sail). ([850fo]). Table 3 compares the calculated molar Gibbs energy of the phases participating in the monovariant equilibria 9" + 9' + fl and 9' + /~ + o~ at 1423 K to the values derived by Oforka and Argent [85Ofo] from the measurements of the activities of the elements. The agreement is satisfactory except for the a phase. Some inconsistencies between different experimental results have been noted in this region and could explain these differences.

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni

295

Table 3: Molar Gibbs Energy of Formation of the Phases Envolved in the Three Phase Equilibria at 1423 K, Referred to the Pure Elements A1 Liquid, Cr bcc and Ni fcc at 1423 K. Equilibrium 7+7'+~

7 + fl + c~

Phase 7 7' 7 /~

Calc. AG~ / kJ -25.3 -31.1 -37.8 -20.7 -38.3 -2.9

Exp. AG ~ / kJ [85Ofo] -24.9 -30.3 -34.7 -23.6 -37.9 -9.2

Table 4 presents the enthalpy of formation of solid alloys at room temperature calculated considering the 7' alone, the 7 and 7' phases and the 7, ~' and a phases. This table also shows the values measured by Kek et al. for these compositions where only the ~ phase was thought to be present. The agreement between calculation and experiments is better when considering the 7 and a phases. It seems that the measurement have been made on samples containing the different phases and not only the ~ phase. This result is particularly clear on the alloy containing 12 at. % Cr. Table 4: Calculated Molar Enthapy of Formation of the Solid Alloys Studied by Kek et al. [90Kek] Referred to the Pure Elements A1 fcc, Cr bcc and Ni fcc at Room Temperature. Composition A1 Cr 23 5 22 8 21 12

(% at) Ni 72 70 67

7' -36.7 -34.7 -32.4

Calc. A H I / kJ 7' + 7 7' + 7 + a -36.7 -36.7 -35.0 -35.6 -32.8 -34.0

Exp. AH! / kJ [90Kek] -36.7 + 1.4 -35.2 4- 1.4 -34.9 4- 1.3

Conclusion

Taking into account a selected set of experimental data in the optimisation procedure, a satisfactory description of the ternary system A1-Cr-Ni has been obtained. The study has mainly been focused on the equilibria involving the 7, 7' and liquid phases in particular because of the interest of these phases for Ni superalloys. The results have been obtained using thermodynamic models adapted to the phases under consideration to analyse experimental data on the phase diagram as well as the thermodynamic behaviour in this field. The extrapolation of this description over the entire range of composition of this ternary system is hoped to be helpful in planning the desirable experiments in the region which are not yet sufficiently known i.e. the A1 rich corner and the equilibria involving the a and ~ phases. Huang and Chang [99Hua] have critized the modelling used in the previous assessment by Dupin [95Dup] because of an unsatisfactory agreement observed for the 7/liquid equilibria. The experimental data under discussion [96Wu, 99Sun] were not available at the time of Dupin's original assessment. The present revision shows that taking them into account the agreement becomes satisfactory. This work shows that the modelling of the ordered phases L12 and B2 with the same Gibbs energy function for the corresponding A1 and A2 disordered phases allows a satisfactory description. Moreover the description of the B2 has largely been simplified and the metastability problems shown with the previous version seem to be solved.

Acknowlegment P. Saltykov is acknowledged for providing his rough experimental data. ThermoCalc AB is acknowledged for supporting the present work.

296

N. DUPIN et al.

References [52Tay]

A. Taylor, R.W. Floyd, J. Inst. Met., 1952, 81,451. I. I. Kornilov, R. S. Mints, Ivz. Sekt. Fiz.- Khim. Anal., Inst. Obschch. Neorg. Khim., Akad. Nank. SSSR, 1953, 22, 111. [54Kor] I. I. Kornilov, R. S. Mints, Dolk. Akad. Nank. SSSR, 1954, 94, 1085. [55Kor] I. I. Kornilov, Izv. Sekt. Fiz. Khim. Anal. Inst. Obschch. Neorg. Khim. Akad. Nank. SSSR, 1955, 26, 62. [58Bag] Yu. A. Bagaryatskiy, Russ. J. Inorg. Chem., 1958, 3, 247. [58Bagl] Yu. A. Bagaryatskiy, Z. M. Petrova, L. M. Utevski, Problema Metalloved i Fizika Metalloyy, 1958, 5, 235. [58Bag2] Yu. A. Bagaryatskiy, Zh. Neorg. Khim., 1958, 3, 722. [66Mall V. I. Malkin, V. V. Pokidyskev, Izv. Akad. Nank S.S.S.R., Neorg. Mater., 1966, 2, 166. [75Mug] Y. M. Muggianu, M. Gambino, J. P. Bros, J. Chim. Phys., 1975, 72, 83. [82Tu] D. C. Tu, Thesis, Univ. of New York, Stony Brook, USA, 1982. [83Lan] N. DeLancrolle, L. L. Seigle, Univ. of New York, Stony Brook, USA, 1983. [83Och] S. Ochiai, Y. Oya, T. Suzuki, Bull. P.M.E. (T.LT.), 1983, 52, 1. [84Car] L.A. Carol, Thesis, Michigan Technological University, USA, 1984. [84Jan] B. Jansson, Thesis, Royal Institute of Technology, Stockholm, Sweden, 1984. [84Mer] S. M. Merchant, M. R. Notis, Mater. Sci. Eng., 1984, 66, 47. [85Ofo] N. C. Oforka, B. B. Argent, J. Less Common Met., 1985, 114, 97. [85Sun] B. Sundman, B. Jansson, J.-O. Anderson, Calphad, 1985, 2, 153. [86Din] A. Dinsdale, T. Chart, MTDS NPL, Unpublished work 1986; SGTE SSOL. [87Nes] J.A. Nesbitt, R.W. Heckel, Metall. Trans., 1987, 18A, 2061. [87Sau] N. Saunders, V.G. Rivlin, Z. Metallkde, 1987, 78, 795. [88Ans] I. Ansara, B. Sundman, P. Willemin, Acta Metall., 1988, 36, 977. [89Hon] Y. M. Hong, Y. Mishima, T. Suzuki, Mat. Res. Soc. Symp. Proc., 1989, 133, 429. [90Dav] D. David, Thesis, INPG, Grenoble, France, 1990. [90Kek] S. Kek, C. Rzyman, F. Sommer, Anales de fisica B, 1990, 86, 31. [91Din] A. Dinsdale, SGTE Data for Pure Elements, Calphad, 1991, 15, 317. [91Lac] J. Lacaze, B. Sundman, Met. Trans., 1991, 22A, 2211. [91Lee] B.-J. Lee, unpublished revision 1991; C-Cr-Fe-Ni, SGTE SSOL [91Rog] P. Rogl, Ternary Alloys, A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams, Ed. G. Petzow and G. Effenberg, 1991, 4, 400. Publ. VCH (Germany). [92Gor] G. P. Goretskii, Russ. Akad. Nank. Met, 1992, 199. [93Cot] J.D. Cotton, R.D. Noebe, M.J. Kanfman, J. Phase Equil., 1993, 14, 579. [94Jia] C. C. Jia, K. Ishida, T. Nishizawa, Met. and Mater. Trans. A, 1994, 25A, 473. [94Yeu] C. W. Yeung, W. D. Hopfe, J. E. Mortal, A. D. Romig Jr., In: Experimental methods of phase diagram determination, Warrendale,J. E. Morral, R.. S. Schiffman, S. M. Merchant, editors, Warrendale, PA: The Minerals, Metals and Materials Society, 1994, 39-44. [95Dup] N. Dupin, Thesis, Institut National Polytechnique de Grenoble, France, 1995. [96Wu] R. Wu, Report to investment casting cooperative arrangement, Madison, WI: University of Wisconsin, 1996. [97Ans] I. Ansara, N. Dupin, H. L. Lukas, B. Sundman J. Alloys and Comp., 1997, 247, 20. [98Mur] J. L. Murray, J. Phase Equil., 1998, 19, 368. [98Qia] Q. M. S. Qiao, Thesis, Interdiffusion microstructure in "y-}-~/'y-t-~ diffusion couples. University of Connecticut, 1998. [98Sau] N. Saunders, "COST 507 : Thermochemical Database for Light Metal Alloys", Vol. 2, p. 23-27, Ed. I. Ansara, A. Dinsdale and M.H. Rand, 1998, Eur 18499 EN. [99Dup] N. Dupin, I. Ansara Z. Metallkde, 1999, 90, 76. [99Hel] T. Helander, O. Tolochko, J. Phase Equil., 1999, 20, 57. [99Hua] W. Huang, A. Chang, Intermetallics, 1999, 7, 863. [99Sun] P.K. Sung, D.R. Poirier, Metall. Mater. Trans. A, 1999, 30 A, 2173.

[53Kor]

THERMODYNAMIC RE-ASSESSMENT OF THE TERNARY SYSTEM AI-Cr-Ni [99Tia] [00Sal] [01Dup]

W.H. Tian, C.S. Han, M. Nemoto, Intermetallics, 1999, 7, 59. P. Saltykov, T h e r m o d y n a m i c s of Alloys 2000, Stockholm, Sweden, May 2000. N. Dupin, B. Sundman, Scand. J Metall., 2001, 30 (3), 184.

Appendix:

Thermodynamic

d e s c r i p t i o n o f t h e p h a s e s (in S I

units)

Liquid phase -29000

Lllq,o AI Cr : rliq"l ~ A | Cr

[98Sau] [98Sau] [9TAns] [97Ans] [97Ans] [97Ansi [97Ans] [91Lee] [91Lee]

--11000

rliq"0 -207109 + 41.315 T ~AI,Ni Lliq,1 AI Ni = --10186 + 5.871 T /- liq',2 ~AINi = 81205 -- 31.957T /- liq',3 "AI,Ni = 4365 -- 2.516T /-[iq,4 ~ A I Ni = --22101.64 + 13.163 T /- liq',0

"Cr,Ni = 318 -- 7.33T Lliq,1 16941 - 6.37T Cr,Ni : Lllq AI,C~,Ni = 16000 fcc-A1 phase L~ = -45900 + 6 T LAAA}'.~i= -162408 + 16.213T LAA~',~i= + 7 3 4 1 8 - 34.914T LAnai = +33471 - 9.837T = -30758

+ 10.2

3T

TC]~N, =

--1112 + 1745 (XA, -- x.i) Lcr'~i : +8030 -- 12.880 T Af 1 Lc~'~i = + 3 3 0 8 0 - 16.036 T T ~1 A1 CCr.NI = --3605 /?Cr,Ni-----1.91 A1,0 LA1,Cr,Ni ----30300

[98Sau] [97Ans] [97Ans] [97Ans] [97Ans] [97Ans] [91Lee] [91Lee] [86Din]

fcc-L12 p h a s e a (A1,Cr,Ni)0.75(A1,Cr,Ni)0.25 The parameters of the two sublattice model are expressed as function of the parameters of the four sublattice model with the relations (11-27). The values of the parameters of the four sublattice model are given by the following expression:

AGijlk : Ulij + Ulil + Ulik + Ulj! + Uljk + Ullk except for AGAlcrNi2 given by: AGAIcrNi2 = +U1AICr + 2 U1A1Ni + 2 UlcrNi + 6650 with U1AINi : 2 ( - 2 2 2 1 3 + 4.396T) 1 i = +7204 -- 3.743 T LAI,N U1CrNi :

--1980

U1AICr =

-830

bcc-A2 phase C~Al,O = + 1 0 0 0 0 - T C~Ni,[] = +162397 -- 27.406 T C~A1,Ni= --152397 + 26.406 T G~ ~ = 0.0

LA2,O

AI [] :

rA~'O = ~Cr,D

+OZAI, D + /~A1,D

100000

AAI,D = 150000 ANI,[] = --64024 + 26.494 T "~AI,Ni = -52441 + 11.301 T

[97Ans] [97Ans] [97Ans] [99Dup] [99Dup] [99Dup]

297

298

N. DUPIN et al. ,0 ~---

LA:i~ L A:,

= -54900 + 10T

+C~Ni,O+

LA:I

= +OIAI,Ni + AAI,Ni

/~Ni,D

LA; = + 1 7 1 7 0 - 11.82T LAr2 -- + 3 4 4 1 8 - 11.858T TC~ qi : 2373 + 617 (XCr - LA2,¢ AI,Cr,Ni = 42500

XNi)

~CAr2,Ni= 4

bcc-B2 phase 2 (A1,Cr,Ni,D)o.5(A1,Cr,Ni,D)o.~ G°~] = 0.0 for i = A1, Cr, Ni, [] G.B2 _ ~re.s2 _ I / 2 aAl,o -- 1/2/~AI,O AI:O-O:AI-GoB2 _ ~,B2 _ 0 Cr:O--

1/2 ANi,o

~ f2.B2 ~-~ AhNi = 1 / 2 ~AI,Ni - - i / 2 "~AI Ni /.u_,B2 _ 4000 Ni:Cr-- ~'~ Cr:Ni--

G.B2

_

[99Dup] [99Dup]

~'~ O : C r - -

G.B2 _ "-I ~ . mNi:O-_ 1/2 ~Ni.n D:Ni-G.m 2000 Cr:AI --~ ~.B2 u.~ AhCr G,B2 Ni:AI

[99Dup] [98Sau] [99Dup] [91Lee] [91Lee] [86Din]

[99Dup] [99Dup]