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Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
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Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system WeiHua Sun, HongHui Xu, Yong Du ∗ , ShuHong Liu, HaiLin Chen, LiJun Zhang, BaiYun Huang State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China
article
info
Article history: Received 13 April 2009 Received in revised form 15 July 2009 Accepted 16 July 2009 Available online 6 August 2009 Keywords: Cu–Mn–Ni system Phase equilibria XRD Thermodynamic modeling
abstract The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ◦ C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ◦ C consists of 4 two-phase regions (cbcc_A12+fcc_A1, cub_A13+fcc_A1, cbcc_A12+ cub_A13, L10 +fcc_A1) and 1 three-phase region (cbcc_A12+cub_A13+fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ (Cu,Ni) and γ (Mn). The L10 phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L10 phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The Cu–Mn–Ni alloys are of great industrial interest because of their good physical, mechanical and corrosion resistance properties. For example, the Cu5−20 Mn65−70 Ni15−20 (in at.%) alloy can be used as resistor materials due to its high value of electrical resistivity with low temperature coefficient [1]. In addition, the alloy with the nominal composition of Cu6 Mn2 Ni2 has a high corrosion resistance strength as well as good ductility and is suitable for producing structural material, such as springs [2,3]. Information on the phase equilibria of the Cu–Mn–Ni system is of great importance for the development of the high quality materials. In order to facilitate reading, the symbols to denote the phases in the Cu–Mn–Ni system are listed in Table 1. Before a literature review on the Cu–Mn–Ni system is conducted, the Mn–Ni binary system is addressed in detail. Gokcen [4] made a critical and comprehensive review on the Mn–Ni system. The phase equilibria above 800 ◦ C are well established. Below 800 ◦ C, however, there exist large discrepancies. The adopted phase diagram below 800 ◦ C by Gokcen [4] is mainly based on the work of Tsiuplakis and Kneller [6]. Ding et al. [7] reinvestigated this system between 500 ◦ C and 800 ◦ C by means of X-ray diffraction (XRD), transmission electron microscopy (TEM) and electron probe microanalysis (EPMA). The reported phase relation between 500 ◦ C and 800 ◦ C is quite different from that due to Tsiuplakis and Kneller [6], but close to that of Coles and Hume-Rothery [8]. In the region between 30 to
∗
Corresponding author. Tel.: +86 731 8836213; fax: +86 731 8710855. E-mail address: [email protected] (Y. Du).
0364-5916/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2009.07.003
60 at.% Ni at 600 ◦ C, there exists only the equilibrium related with L10 and fcc_A1 phases. Liu [9] made a thermodynamic assessment on the Mn–Ni system by taking into account the experimental data from Ding et al. [7]. Both the bcc_B2 and bcc_A2 phases, fcc_A1 and L12 phases were modeled as a single phase, respectively. The L10 phase was described by a symmetric model (Mn, Ni)(Mn, Ni), in which Mn is the major species in the first sublattice while Ni is in the second. In the present work, the experimental result from Ding et al. [7] and binary parameters from Liu [9] were adopted. As for the Cu–Mn–Ni system, there are only a few experimental investigations. By means of thermal analysis (TA) on 36 alloys covering the whole composition range, Parravano [10,11] proposed the liquidus surface, the solidus surface and six vertical sections. Using TA and chemical analysis of the observed phases, Schürmann and Prinz [12,13] investigated the liquidus and solidus in both Curich and Ni-rich corners and established effective functions to express the relations between the alloy composition and the liquidus, solidus temperatures. The data in the above sources [10–13] were considered to be self-consistent in the present assessment. By means of XRD and optical metallography (OM), Zwicker [14] determined the isothermal sections at 1000 ◦ C, 700 ◦ C and 500 ◦ C in the Mn-rich region. The reported phase relations along the Mn–Ni binary side, however, are inconsistent with the reliable Mn–Ni binary phase diagram established by Ding et al. [7]. Using XRD, TA, OM and hardness measurement, Chang [15] constructed a partial Cu–MnNi vertical section and two partial isothermal sections in the Cu rich corner at 350 ◦ C and 450 ◦ C. The experimental phase relation at 450 ◦ C is reasonable, but the relation at 350 ◦ C is questionable while considering the large miscibility gap at 350 ◦ C
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Table 1 List of symbols and crystallographic data of the phases in the Cu–Mn–Ni system. Symbol
Phase
Pearson symbol/Space group/Prototype
Lattice Parameters(Å)
Comments
References
Liquid
Liquid solution
–
–
–
bcc_A2
Solid solution based on (δ Mn) with bcc_A2 structure
– cI2 ¯ Im3m W cF 4 ¯ Fm3m Cu cP20 P41 32 β Mn cI58 ¯ I 43m α Mn cP2 ¯ Pm3m CsCl cP4 Pm3m AuCu3 tP4 P4/mmm AuCu t ∗∗
a = 3.0813
Pure Mn at 1137 ◦ C
fcc_A1
Solid solution based on (γ (Cu,Ni), γ Mn) with fcc_A1 structure
cub_A13
Solid solution based on (β Mn) with cub_A13 structure
cbcc_A12 Solid solution based on (α Mn) with cbcc_A12 structure bcc_B2
Solid solution based on β -MnNi with bcc_B2 structure
L12
Solid solution based on MnNi3 with ordered L12 structure
L10
Solid solution based on θ -MnNi with ordered L10 structure Solid solution based on the MnNi2 compound
MnNi2
in the Cu–Ni boundary [16]. By a combination of XRD, TA, dilatometry and electrical resistivity measurement, Rolland et al. [17,18] investigated the decomposition of fcc_A1 phase in the Cu–MnNi section. Udovenko et al. [19] established the Cu–MnNi quasibinary section at 450–600 ◦ C by means of XRD. Since the data on Cu–MnNi vertical section [15,18,19] are in general agreement with each other, all of these phase equilibria except for those on the partial isothermal section at 350 ◦ C [15] were utilized in the present assessment. The only thermodynamic modeling for the Cu–Mn–Ni system was performed by Miettinen [20]. The Mn–Ni binary boundary adopted by Miettinen [20] disagrees significantly with the recent Mn–Ni phase diagram [7]. The present work is to clarify the phase equilibria at 600 ◦ C in the Mn-rich region by experimental investigation and present a thermodynamic modeling of the Cu–Mn–Ni system by taking into account the reliable data in the literature and incorporating the present experimental data. 2. Experimental procedure Cu blocks (99.9 wt%), electrolytic Mn pieces (99.95 wt%) and Ni blocks (99.95 wt%) were used as starting materials. 12 ternary alloys with weight between 1 and 2g were prepared by arc melting pure elements under high purity argon atmosphere. After being encapsulated in evacuated silica tubes with a residual argon pressure of 10−3 bar, the alloys were annealed at 600 ◦ C for 60 days, followed by water quenching. The phase identification was conducted by means of XRD using Cu Kα radiation. Pure Si powder was added as an internal standard for 2-theta calibration. Only the powder of alloy 1 used for XRD was obtained from grinding the bulk alloy. For the other alloys, powders were obtained via filing the alloys. In order to relieve internal stress caused by filing, the powders were encapsulated with Cu foil in evacuated silica tubes and then annealed at 400 ◦ C for 2 h before being subjected to XRD measurements. After standard metallographic preparation, the samples were investigated using optical microscopy (Leica DMLP, Germany) and scanning electron microscopy (SEM) equipped with energy dispersive X-ray spectroscopy (EDS) (JSM-6360LV, JEOL, Japan) to determine tie-lines or tie-triangle data. Alloy 9 was further examined by EPMA (JXA-8800R, JEOL, Japan) to acquire more accurate data.
Gokcen [4]
a = 3.6146 a = 3.8626 a = 3.5240
Pure Cu at 25 C Pure Mn at 1097 ◦ C Pure Ni at 25 ◦ C
Gokcen [4]
a = 6.3152
Pure Mn at 25 ◦ C
Gokcen [4]
a = 8.9139
Pure Mn at 25 ◦ C
Gokcen [4]
a = 2.977
50 at.% Mn, 50 at.% Ni at 750 ◦ C
Gokcen [4]
a = 3.589
25 at.% Mn, 75 at.% Ni at 25 ◦ C
Gokcen [4]
a = 3.7328 c = 3.5272 –
50 at.% Mn, 50 at.% Ni at 650 ◦ C –
Ding [5]
◦
Gokcen [4]
3. Thermodynamic models The calculated phase diagrams of the Cu–Ni [16], Cu–Mn [21] and Mn–Ni [9] binary systems are shown in Fig. 1. The thermodynamic parameters for liquid, fcc_A1, cub_A13, cbcc_A12 and L10 are optimized in the present work. The Gibbs energy of the solution phase φ (φ = liquid, fcc_A1, cub_A13 and cbcc_A12) is described by the Redlich–Kister polynomial [22]: 0
φ
φ
φ
Gφm = xCu · 0 GCu + xMn · 0 GMn + xNi · 0 GNi
+ R · T · (xCu · ln xCu + xMn · ln xMn + xNi · ln xNi ) φ
φ
+ xCu · xMn · LCu,Mn + xCu · xNi · LCu,Ni φ
φ
+ xMn · xNi · LMn,Ni + ex GCu,Mn,Ni + mag Gφm
(1)
in which R is the gas constant, xCu , xMn and xNi are the molar fractions of Cu, Mn and Ni, respectively. The standard element reference (SER) state [23], i.e. the stable structure of the element at 25 ◦ C and 1 bar, is used as the reference state of Gibbs energy. The φ parameters Li,j (i, j = Cu, Mn, Ni) are the interaction parameters from the binary systems. The excess Gibbs energy expressed as follows: ex
φ
ex
φ
GCu,Mn,Ni is
φ
GCu,Mn,Ni = xCu · xMn · xNi · (xCu · 0 LCu,Mn,Ni φ
φ
+ xMn · 1 LCu,Mn,Ni + xNi · 2 LCu,Mn,Ni ) φ
φ
φ
(2)
where 0 LCu,Mn,Ni , 1 LCu,Mn,Ni and 2 LCu,Mn,Ni are the ternary parameters to be evaluated in the present work. The mag Gm term, which describes the magnetic contribution to the Gibbs energy, is given by the Hillert–Jarl–Inden model [24,25]. For the fcc_A1 and cbcc_A12 phases, it is necessary to introduce mag Gm term, while for the liquid and cub_A13 phases, their mag Gm terms are equal to zero. The L10 phase is modeled with the two sublattice model (Cu, Mn, Ni)0.5 (Cu, Mn, Ni)0.5 in order to describe the solubility of Cu in L10 phase. The boldfaces Mn and Ni are the major species in the first and second sublattices, respectively. Thus, the Gibbs energy for this phase is expressed by the following equation:
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W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
a
b
c
Fig. 1. Calculated binary phase diagrams: (a) Cu–Ni system [16], (b) Cu–Mn system [21], (c) Mn–Ni system [9].
" 0
0 GL1 m
=
XX i
L1 y0i y00j Gi:j 0
+R·T ·
j
1X 0 yi ln y0i 2 i
#
XX X L1 1 X 00 + yi ln y00i y0i y0j + y00k Li,j:0k 2 i i j >i k +
XX i
j >i
y00i y00j
X
L1
y0k Lk:i0,j + · · ·
(3)
k
where y0n and y00n are the site fractions of n (n = i, j or k = Cu, Mn or L1
Ni) on the first and second sublattices, respectively. Gi:j 0 represents L1
L1
the Gibbs energy of the end-member of the L10 phase, Li,j:0k and Lk:i0,j are the interaction parameters within each sublattice 4. Results and discussion 4.1. Experiment All the experimental results for phase identifications, composition measurements and lattice parameter refinements on alloys equilibrated at 600 ◦ C are summarized in Table 2. No ternary phase was obtained at 600 ◦ C. Due to the volatilization of Mn, there was some weight loss during arc melting. That weight loss is about 2 wt% for alloys 1 to 6 in the Mn-corner, and less than 1 wt% for alloys 7 to 12. Since most of the data used for establishing the phase diagram were tie-lines and tie-triangle determined by EDS,
Fig. 2. Presently measured partial isothermal section of the Cu–Mn–Ni system in the Mn-rich region at 600 ◦ C.
the composition deviation from the nominal composition of the alloys would not influence the result and the alloys after arc melting were not subjected to chemical analysis. Fig. 2 presents the constructed partial isothermal section at 600 ◦ C. It is worth noting that the determined phase boundaries are consistent with the latest reported Mn–Ni phase diagram [7].
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Table 2 Summary of the identified phases, their compositions and lattice parameters for the Cu–Mn–Ni alloys annealed at 600 ◦ C for 60 days. No.
Phasea
Nominal composition (at.%) Cu
Mn
1
3
90
7
2
3
86
11
3
3
82
15
4
8
87
5
5
8
83
9
6
13
82
5
7
8
56
36
8 9
3 8
48 48
49 44
10
18
48
34
11 12
26 35
48 48
26 17
a b c
Ni cbcc_A12 cub_A13 fcc_A1 cub_A13 fcc_A1 cub_A13 fcc_A1 cbcc_A12 fcc_A1 cbcc_A12 fcc_A1 cub_A13 (trace) cbcc_A12 fcc_A1 fcc_A1 L10 L10 fcc_A1 L10 fcc_A1 L10 fcc_A1 fcc_A1
Phase compositionb (at.%)
Lattice parameters (Å)c
Cu
Mn
Ni
a
0.6 1.9 10.6 1.6 7.8 3.1 4.3 0.7 18.4 0.5 10.3 1.5 1.2 25.2 8 9.3 3.7 5.4 12.9 27.2 16.3 26.1 34.7
96.4 90.9 77.4 88.8 76 82.3 77.7 97.3 72.9 97 78.8 91.8 97.1 66.7 58.9 52.4 47.9 47.3 48.7 45.2 49.2 47.4 48
3 7.2 12 9.6 16.2 14.6 18 2 8.7 2.5 10.9 6.7 1.7 8.1 33.1 38.3 48.4 47.3 38.4 27.6 34.5 26.5 17.3
– 6.3522(6) 3.728(1) 6.355(4) 3.721(5) 6.333(2) 3.7106(5) 8.936(9) 3.738(2) 8.919(7) 3.724(2) – 8.905(5) 3.751(2) 3.711(3) 3.7381(9) 3.7299(2) – – – – 3.712(1) 3.7166(5)
b
c
3.542(2) 3.5195(4)
The phases were identified by means of XRD. The composition measurement for alloy 9 was conducted with EPMA, and the composition measurements for the other alloys were performed with SEM/EDS. α = β = γ = 90◦ .
This isothermal section is characterized with the continuous disordered fcc_A1 solution phase between γ (Cu,Ni) and γ (Mn). All of the alloys except for alloy 8 contribute to determining the homogeneity range of the fcc_A1 solution, and this phase is in equilibrium with the cub_A13, cbcc_A12 and ordered L10 phases. Alloys 7, 9 and 10 are located in the two-phase region of ordered L10 phase and the disordered fcc_A1 solution phase. Figs. 3a and 4a show the XRD pattern and BSE micrograph of alloy 7, respectively. The BSE micrograph in Fig. 4a clearly indicates that alloy 7 shows a two-phase equilibrium microstructure. As presented in Fig. 3a, the XRD pattern of fcc_A1 phase almost overlaps with those of L10 phase. This feature is caused by the following two reasons. Firstly, the L10 phase is an ordered state of fcc_A1 phase, so all the four peaks from 0 to 90 ◦ C in the XRD pattern of fcc_A1 phase will be very close to those of L10 phase. Secondly, the powder for XRD was obtained from filing the bulk alloy. The filing process inevitably caused great internal stress in the powder, which would severely broaden the peaks. The powder had been annealed at 400 ◦ C for 2 h for stress relief and the quality of the XRD pattern was improved. It should be mentioned that although the patterns are still not as good as the pattern of the powder from grinding the alloy, they are acceptable for phase identification. After peak decomposition by fitting peak profile, lattice parameters of both fcc_A1 and L10 phases were calculated: a = b = c = 3.711 Å for fcc_A1 phase, a = b = 3.7381 Å and c = 3.542 Å for L10 phase. The L10 phase dissolves a considerable amount of Cu up to 16 at.% in alloy 10 according to the EDS measurement. The XRD pattern in Fig. 3b indicates that alloy 1 is in the threephase equilibrium region of cbcc_A12 + cub_A13 + fcc_A1, the existence of which is confirmed by the SEM/EDS measurement as shown in Fig. 4b. Alloys 2 and 3 are located in the two-phase region of cub_A13+fcc_A1, and alloys 4 and 6 are in the cbcc_A12+fcc_A1 region. Fig. 4c and 4d present the corresponding BSE micrographs for alloys 3 and 4, respectively. 4.2. Thermodynamic modeling The thermodynamic parameters were evaluated by the optimization module PARROT of the program Thermo-Calc, which
Table 3 Optimized thermodynamic parameters in the Cu–Mn–Ni system. Liquid: (Cu, Mn, Ni)1 0 L LCu,Mn,Ni
= −42 780
1 L LCu,Mn,Ni
= −67 310
2 L LCu,Mn,Ni
= −56 060
fcc_A1: (Cu, Mn, Ni)1 (Va)1 a
0 fcc_A1 LCu,Mn,Ni
= −67 000
1 fcc_A1 LCu,Mn,Ni
= −49 000
2 fcc_A1 LCu,Mn,Ni
= −49 000
cub_A13: (Cu, Mn, Ni)1 (Va)1 1 cub_A13 LCu,Mn,Ni
= −80 000
L10 : (Cu, Mn, Ni)0.5 (Cu, Mn, Ni)0.5 L1
0
GCu0:Cu = 0 Gfcc_A1 + 10 Cu L1
L1
0
GCu0:Mn = 0 GMn0:Cu = 0.5 · 0 Gfcc_A1 + 0.5 · 0 Gfcc_A1 + 7400 Cu Mn
0
L1 GCu0:Ni
0
L1 GCu0,Ni:Mn
0
L1
=
0
L1 GNi:0Cu
=
0
= 0.5 · 0 Gfcc_A1 + 0.5 · 0 Gfcc_A1 + 7100 Cu Ni
L1 GMn0:Cu,Ni
= −20 630 + 10 · T
L1
GCu0,Mn:Ni = 0 GNi:0Cu,Mn = −46 650 + 50 · T In J mole-atoms−1 ; temperature (T ) in Kelvin. The Gibbs energies for the pure elements are from the SGTE compilation [23]. The binary parameters are from Refs. [9,16,21]. a The magnetic contribution to the Gibbs energy is described by the Hillert–Jarl–Inden model [24,25].
works by minimizing the square sum of the differences between measured and calculated values. The experimental data considered in the optimization are listed below: liquidus and solidus from Parravano [10,11] and Schürmann and Prinz [12,13], partial isothermal section at 450 ◦ C [15], current experimental isothermal section at 600 ◦ C, Cu–MnNi vertical section [15,18,19]. The total amount of data is about 70 and the ratio between the amount of data and the number of final optimized parameters is about 8:1. The optimized parameters are listed in Table 3. As for the modeling process, five critical points are mentioned below. Firstly, the optimization began with the fcc_A1 and L10 phases. L1 The 0 GCu0:Cu and parameters of four hypothetic end members
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W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
a
b
Fig. 3. XRD patterns of the alloys annealed at 600 ◦ C for 60 days: (a) Alloy 7 (Cu8 Mn56 Ni36 ) (b) Alloy 1 (Cu3 Mn90 Ni7 ). Si powder was added as the internal standard for the 2-theta calibration.
a
b
c
d
Fig. 4. BES images of the alloys annealed at 600 ◦ C for 60 days: (a) Alloy 7 (Cu8 Mn56 Ni36 ), (b) Alloy 1 (Cu3 Mn90 Ni7 ), (c) Alloy 3 (Cu3 Mn82 Ni15 ), and (d) Alloy 4 (Cu8 Mn87 Ni5 ). L1
L1
L1
L1
(0 GCu0:Mn , 0 GMn0:Cu , 0 GCu0:Ni , 0 GNi:0Cu ) were fixed with values, which cause the L10 phase to not influence the stable binary phase diagrams [9,16,21]. Secondly, it was found that the two interaction parameters L1 L1 (0 GMn0:Cu,Ni , 0 GCu0,Mn:Ni ) were critical for the optimization of solubility of Cu in L10 phase and fcc_A1/L10 boundary. We assumed that L1 L1 L1 0 L10 GCu,Ni:Mn = 0 GMn0:Cu,Ni and 0 GNi:0Cu,Mn = 0 GCu0,Mn:Ni . According to the experimental Cu–MnNi vertical section [15,18,19], the fcc_A1/L10 boundary changes significantly with temperature, the parameters b describing temperature dependence of the interaction parameters for L10 phase were introduced. L1 L1 Thirdly, 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni make the single L10 phase region and fcc_A1/L10 boundary extend along Mn0.5 Ni0.5 –Cu0.5 Mn0.5
line, while
0
L1
GCu0,Mn:Ni and
0
L1
GNi:0Cu,Mn make them extend along L1
L1
L1
L1
Mn0.5 Ni0.5 –Cu0.5 Ni0.5 line. At 600 ◦ C, both 0 GCu0,Mn:Ni and 0 GNi:0Cu,Mn are equal to −3000 J/mol, much less than 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni with the value of −11 900 J/mol. This is in agreement with the experimental phenomenon that the experimental isothermal section at 600 ◦ C shows that L10 single phase region does not extend along Mn0.5 Ni0.5 –Cu0.5 Ni0.5 line. The present experimental fcc_A1/L10 boundary at 450 ◦ C is symmetric with reference to Cu–Mn0.5 Ni0.5 L1 line. This feature could be satisfied by the condition that 0 GCu0,Mn:Ni L1
and 0 GNi:0Cu,Mn with the value of −10 500 J/mol keeps in balance L1
L1
with the 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni with the value of −13 400 J/mol at 450 ◦ C.
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a
647
b
c
d
e
f
Fig. 5. Calculated liquidus and solidus along the sections of 10 wt% Cu (a), 20 wt% Cu (b), 10 wt% Mn (c), 20 wt% Mn (d), 10 wt% Ni (e), and 20 wt% Ni (f). The experimental data [10,11] and the values calculated from well derived functions [12,13] are plotted for comparisons.
Fourthly, it should be mentioned that the current experimental boundary between L10 and fcc_A1 phases at 600 ◦ C, which is the ternary extension from the Mn–Ni binary side, is very curvaceous and asymmetric. The thermodynamic parameters on the binary Mn–Ni system [9], however, is symmetric. Thus there are no parameters, which can adjust the exact shape of the L10 /fcc_A1 boundary at 600 ◦ C. Consequently, a compromise was made in the assessment of the experimental data from different sources. Fifthly, since there is a small amount of data about the solid phases, the b values for the parameters of the fcc_A1 phase were not used. In addition, the a values were controlled during the optimization procedure to make the miscibility gap of fcc_A1 phase
not appear above 450 ◦ C. Finally, the liquid phase was considered in the optimization. There are no experimental thermodynamic data for the liquid phase, so only the ternary parameters a were used for the measured solidus and liquidus. Fig. 5a–f present the calculated liquidus and solidus along the sections of x = 10 wt.% Cu, 20 wt% Cu, 10 wt% Mn, 20 wt% Mn, 10 wt% Ni and 20 wt% Ni, compared with the experimental data [10,11] and the values calculated from well derived functions [12,13]. Most experimental data were reasonably accounted for by the present calculations except for the data in the Cu and Mn corners from Parravano [10,11]. These data in the Cu and Mn corners [10,11] were considered to be inaccurate, because they do
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a
b
1150
1100
1050
1000
950 950
c
1000
1050
1100
1150
d
Fig. 6. Comparison between the calculated liquidus/solidus and the experimental data [12,13]: (a) liquidus in the Cu-rich corner, (b) solidus in the Cu-rich corner, (c) liquidus in the Ni-rich corner, (d) solidus in the Ni-rich corner.
not accord with the well-determined Mn-rich and Cu-rich liquidus and solidus in the binary systems [9,16,21], if being extrapolated into the binary boundaries. A comparison between the calculated liquidus/solidus and the experimental data [12,13] is shown in Fig. 6. As indicated in Fig. 6a and b, the data in the Cu corner are well reproduced, while in the Ni corner, the consistency is moderate but acceptable as shown in Fig. 6c and d. Since the calculated results in the Cu and Ni corners are mainly determined by the binary parameters, it can be concluded that the experimental data [12,13] are very accurate, while most of the data [10,11] are acceptable except for the data in the Cu and Mn corners [10,11]. Fig. 7 shows the calculated liquidus surface projection. There are only two preliminary phases of fcc_A1 and bcc_A2 solutions. Fig. 8 presents the calculated Cu–MnNi vertical section, compared with experimental data from Refs. [15,18,19]. The presently calculated boundary of fcc_A1/fcc_A1 + L10 is well consistent with the data of Udovenko et al. [19], while a little lower than that from Refs. [15,18]. Fig. 9 presents the calculated isothermal section at 450 ◦ C compared with experimental data of Chang [15]. The presently calculated fcc_A1/fcc_A1 + L10 boundary is in general agreement with that determined by Chang [15]. Fig. 10 compares the calculated isothermal section at 600 ◦ C compared
Fig. 7. Calculated projection of the liquidus surface and the isothermal liquidus in the Cu–Mn–Ni system.
W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
649
Fig. 10. Calculated isothermal section at 600 ◦ C, compared with the present experimental data. Fig. 8. Calculated Cu–MnNi vertical section, compared with the experimental data [15,18,19].
was measured to be up to about 16 at.%. No ternary compound was found. • A thermodynamic modeling of this system was carried out in the whole composition range by taking into account both reliable literature data and the current experimental data. Comprehensive comparisons show that the present calculations are generally in agreement with the critically assessed experimental data. Acknowledgements The financial support from the Creative Research Group of National Natural Science Foundation of China (Grant No. 50721003) and the National Outstanding Youth Science Foundation of China (Grant No. 50425103) is acknowledged. The Thermo-Calc Software AB is acknowledged for the provision of Thermo-Calc software. Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.calphad.2009.07.003.
Fig. 9. Calculated isothermal section at 450 ◦ C, compared with the experimental data [15].
with the present experimental data. The present calculation well accounts for the Mn-rich experimental data, but does not well reproduce the phase equilibria between fcc-A1 and L10 . It is probably because the parameters describing the binary Mn–Ni phase diagram [9] are symmetric, which have negative effect on the modeling of the very curvaceous and asymmetric L10 + fcc_A1 phases boundary in the ternary system. At last, it is worth noting that few experimental data were reported below 900 ◦ C, not only for the Cu–Mn–Ni system, but also for the M (M = Al, Fe et al.)-Mn–Ni systems. Furthermore, most of reported data do not coincide with the Mn–Ni binary phase diagram [7]. Therefore, further experiments need to be performed for the investigation of the M (M = Al, Fe, Cu et al.)-Mn–Ni systems below 900 ◦ C. 5. Conclusion
• A partial isothermal section at 600 ◦ C of the Cu–Mn–Ni system in the Mn-rich region was constructed. The three-phase equilibrium of cbcc_A12 + cub_A13 + fcc_A1 was determined. The solubility of Cu in the MnNi compound with L10 structure
References [1] R.I. Agladze, V.M. Mokhov, L.I. Topchiashvili, Splavy Margantsa s Med’yu, Nikelem, i Tsinkom, Tbilisi, Akad. Nauk Gruz. (1954) 51–65. [2] K. Dies, Metall 15 (1961) 1161–1172. [3] G. Groma, Proc. 4th Conf on Dimensioning, Acad. Kiado, Budapest, Hungary, 1973, pp. 417–422. [4] N.A. Gokcen, J. Phase Equilib. 12 (1991) 313–321. [5] L. Ding, Master Thesis, University of Wisconsin-Madison, USA, 2001. [6] K.E. Tsiuplakis, E. Kneller, Z. Met.kd. 60 (1969) 433–438. [7] L. Ding, P.F. Ladwig, X.Y. Yan, Y.A Chang, Appl. Phys. Lett. 80 (2002) 1186–1188. [8] B.R. Coles, W. Hume-Rothery, J. Inst. Met. (London) 80 (1951–1952) 85–92. [9] S.H. Liu, Master Thesis, Central South University, China, 2008. [10] N. Parravano, Gazz. Chim. Ital. 42 (1913) 385–394. [11] N. Parravano, Intern. Z. Metallog. 4 (1913) 171–202. [12] E. Schürmann, B. Prinz, Z. Metallkd. 65 (1974) 535–539. [13] E. Schürmann, B. Prinz, Z. Metallkd. 65 (1974) 593–598. [14] U. Zwicker, Z. Metallkd. 42 (1951) 331–335. [15] B.C. Chang, Izv. Vyss. Uchebn. Zaved. Tsvetn. Metall. 5 (1958) 107–115. [16] S. Mey, CALPHAD 16 (1992) 255–260. [17] J. Rolland, D. Whitwham, Mem. Sci. Rev. Met. 67 (1970) 607–614. [18] J. Rolland, P. Priester, D. Whitwham, Compt. Rend. Acad, Sci. Paris, Ser. C 270 (1970) 1777–1780. [19] V.A. Udovenko, V.V. Sanadze, N.A. Polyakova, E.D. Chichua, L.D. Gogua, Soobshch. Akad. Nauk Gruz. SSR 134 (1989) 73–76. [20] J. Miettinen, CALPHAD 27 (2003) 147–152. [21] C.Y. He, Y. Du, H.L. Chen, S.H. Liu, H.H. Xu, Y.F. Ouyang, Z.K. Liu, J. Alloys Compounds. 457 (2008) 233–238. [22] O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [23] A.T. Dinsdale, CALPHAD 15 (1991) 317–425. [24] G. Inden, The proceedings of CALPHAD V project meeting, Max-Planck Institute for Metal Research, Dusseldorf, 1976, pp. 1–13. [25] M. Hillert, M. Jarl, CALPHAD 2 (1978) 227–238.
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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad
Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system WeiHua Sun, HongHui Xu, Yong Du ∗ , ShuHong Liu, HaiLin Chen, LiJun Zhang, BaiYun Huang State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China
article
info
Article history: Received 13 April 2009 Received in revised form 15 July 2009 Accepted 16 July 2009 Available online 6 August 2009 Keywords: Cu–Mn–Ni system Phase equilibria XRD Thermodynamic modeling
abstract The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ◦ C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ◦ C consists of 4 two-phase regions (cbcc_A12+fcc_A1, cub_A13+fcc_A1, cbcc_A12+ cub_A13, L10 +fcc_A1) and 1 three-phase region (cbcc_A12+cub_A13+fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ (Cu,Ni) and γ (Mn). The L10 phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L10 phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The Cu–Mn–Ni alloys are of great industrial interest because of their good physical, mechanical and corrosion resistance properties. For example, the Cu5−20 Mn65−70 Ni15−20 (in at.%) alloy can be used as resistor materials due to its high value of electrical resistivity with low temperature coefficient [1]. In addition, the alloy with the nominal composition of Cu6 Mn2 Ni2 has a high corrosion resistance strength as well as good ductility and is suitable for producing structural material, such as springs [2,3]. Information on the phase equilibria of the Cu–Mn–Ni system is of great importance for the development of the high quality materials. In order to facilitate reading, the symbols to denote the phases in the Cu–Mn–Ni system are listed in Table 1. Before a literature review on the Cu–Mn–Ni system is conducted, the Mn–Ni binary system is addressed in detail. Gokcen [4] made a critical and comprehensive review on the Mn–Ni system. The phase equilibria above 800 ◦ C are well established. Below 800 ◦ C, however, there exist large discrepancies. The adopted phase diagram below 800 ◦ C by Gokcen [4] is mainly based on the work of Tsiuplakis and Kneller [6]. Ding et al. [7] reinvestigated this system between 500 ◦ C and 800 ◦ C by means of X-ray diffraction (XRD), transmission electron microscopy (TEM) and electron probe microanalysis (EPMA). The reported phase relation between 500 ◦ C and 800 ◦ C is quite different from that due to Tsiuplakis and Kneller [6], but close to that of Coles and Hume-Rothery [8]. In the region between 30 to
∗
Corresponding author. Tel.: +86 731 8836213; fax: +86 731 8710855. E-mail address: [email protected] (Y. Du).
0364-5916/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2009.07.003
60 at.% Ni at 600 ◦ C, there exists only the equilibrium related with L10 and fcc_A1 phases. Liu [9] made a thermodynamic assessment on the Mn–Ni system by taking into account the experimental data from Ding et al. [7]. Both the bcc_B2 and bcc_A2 phases, fcc_A1 and L12 phases were modeled as a single phase, respectively. The L10 phase was described by a symmetric model (Mn, Ni)(Mn, Ni), in which Mn is the major species in the first sublattice while Ni is in the second. In the present work, the experimental result from Ding et al. [7] and binary parameters from Liu [9] were adopted. As for the Cu–Mn–Ni system, there are only a few experimental investigations. By means of thermal analysis (TA) on 36 alloys covering the whole composition range, Parravano [10,11] proposed the liquidus surface, the solidus surface and six vertical sections. Using TA and chemical analysis of the observed phases, Schürmann and Prinz [12,13] investigated the liquidus and solidus in both Curich and Ni-rich corners and established effective functions to express the relations between the alloy composition and the liquidus, solidus temperatures. The data in the above sources [10–13] were considered to be self-consistent in the present assessment. By means of XRD and optical metallography (OM), Zwicker [14] determined the isothermal sections at 1000 ◦ C, 700 ◦ C and 500 ◦ C in the Mn-rich region. The reported phase relations along the Mn–Ni binary side, however, are inconsistent with the reliable Mn–Ni binary phase diagram established by Ding et al. [7]. Using XRD, TA, OM and hardness measurement, Chang [15] constructed a partial Cu–MnNi vertical section and two partial isothermal sections in the Cu rich corner at 350 ◦ C and 450 ◦ C. The experimental phase relation at 450 ◦ C is reasonable, but the relation at 350 ◦ C is questionable while considering the large miscibility gap at 350 ◦ C
W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
643
Table 1 List of symbols and crystallographic data of the phases in the Cu–Mn–Ni system. Symbol
Phase
Pearson symbol/Space group/Prototype
Lattice Parameters(Å)
Comments
References
Liquid
Liquid solution
–
–
–
bcc_A2
Solid solution based on (δ Mn) with bcc_A2 structure
– cI2 ¯ Im3m W cF 4 ¯ Fm3m Cu cP20 P41 32 β Mn cI58 ¯ I 43m α Mn cP2 ¯ Pm3m CsCl cP4 Pm3m AuCu3 tP4 P4/mmm AuCu t ∗∗
a = 3.0813
Pure Mn at 1137 ◦ C
fcc_A1
Solid solution based on (γ (Cu,Ni), γ Mn) with fcc_A1 structure
cub_A13
Solid solution based on (β Mn) with cub_A13 structure
cbcc_A12 Solid solution based on (α Mn) with cbcc_A12 structure bcc_B2
Solid solution based on β -MnNi with bcc_B2 structure
L12
Solid solution based on MnNi3 with ordered L12 structure
L10
Solid solution based on θ -MnNi with ordered L10 structure Solid solution based on the MnNi2 compound
MnNi2
in the Cu–Ni boundary [16]. By a combination of XRD, TA, dilatometry and electrical resistivity measurement, Rolland et al. [17,18] investigated the decomposition of fcc_A1 phase in the Cu–MnNi section. Udovenko et al. [19] established the Cu–MnNi quasibinary section at 450–600 ◦ C by means of XRD. Since the data on Cu–MnNi vertical section [15,18,19] are in general agreement with each other, all of these phase equilibria except for those on the partial isothermal section at 350 ◦ C [15] were utilized in the present assessment. The only thermodynamic modeling for the Cu–Mn–Ni system was performed by Miettinen [20]. The Mn–Ni binary boundary adopted by Miettinen [20] disagrees significantly with the recent Mn–Ni phase diagram [7]. The present work is to clarify the phase equilibria at 600 ◦ C in the Mn-rich region by experimental investigation and present a thermodynamic modeling of the Cu–Mn–Ni system by taking into account the reliable data in the literature and incorporating the present experimental data. 2. Experimental procedure Cu blocks (99.9 wt%), electrolytic Mn pieces (99.95 wt%) and Ni blocks (99.95 wt%) were used as starting materials. 12 ternary alloys with weight between 1 and 2g were prepared by arc melting pure elements under high purity argon atmosphere. After being encapsulated in evacuated silica tubes with a residual argon pressure of 10−3 bar, the alloys were annealed at 600 ◦ C for 60 days, followed by water quenching. The phase identification was conducted by means of XRD using Cu Kα radiation. Pure Si powder was added as an internal standard for 2-theta calibration. Only the powder of alloy 1 used for XRD was obtained from grinding the bulk alloy. For the other alloys, powders were obtained via filing the alloys. In order to relieve internal stress caused by filing, the powders were encapsulated with Cu foil in evacuated silica tubes and then annealed at 400 ◦ C for 2 h before being subjected to XRD measurements. After standard metallographic preparation, the samples were investigated using optical microscopy (Leica DMLP, Germany) and scanning electron microscopy (SEM) equipped with energy dispersive X-ray spectroscopy (EDS) (JSM-6360LV, JEOL, Japan) to determine tie-lines or tie-triangle data. Alloy 9 was further examined by EPMA (JXA-8800R, JEOL, Japan) to acquire more accurate data.
Gokcen [4]
a = 3.6146 a = 3.8626 a = 3.5240
Pure Cu at 25 C Pure Mn at 1097 ◦ C Pure Ni at 25 ◦ C
Gokcen [4]
a = 6.3152
Pure Mn at 25 ◦ C
Gokcen [4]
a = 8.9139
Pure Mn at 25 ◦ C
Gokcen [4]
a = 2.977
50 at.% Mn, 50 at.% Ni at 750 ◦ C
Gokcen [4]
a = 3.589
25 at.% Mn, 75 at.% Ni at 25 ◦ C
Gokcen [4]
a = 3.7328 c = 3.5272 –
50 at.% Mn, 50 at.% Ni at 650 ◦ C –
Ding [5]
◦
Gokcen [4]
3. Thermodynamic models The calculated phase diagrams of the Cu–Ni [16], Cu–Mn [21] and Mn–Ni [9] binary systems are shown in Fig. 1. The thermodynamic parameters for liquid, fcc_A1, cub_A13, cbcc_A12 and L10 are optimized in the present work. The Gibbs energy of the solution phase φ (φ = liquid, fcc_A1, cub_A13 and cbcc_A12) is described by the Redlich–Kister polynomial [22]: 0
φ
φ
φ
Gφm = xCu · 0 GCu + xMn · 0 GMn + xNi · 0 GNi
+ R · T · (xCu · ln xCu + xMn · ln xMn + xNi · ln xNi ) φ
φ
+ xCu · xMn · LCu,Mn + xCu · xNi · LCu,Ni φ
φ
+ xMn · xNi · LMn,Ni + ex GCu,Mn,Ni + mag Gφm
(1)
in which R is the gas constant, xCu , xMn and xNi are the molar fractions of Cu, Mn and Ni, respectively. The standard element reference (SER) state [23], i.e. the stable structure of the element at 25 ◦ C and 1 bar, is used as the reference state of Gibbs energy. The φ parameters Li,j (i, j = Cu, Mn, Ni) are the interaction parameters from the binary systems. The excess Gibbs energy expressed as follows: ex
φ
ex
φ
GCu,Mn,Ni is
φ
GCu,Mn,Ni = xCu · xMn · xNi · (xCu · 0 LCu,Mn,Ni φ
φ
+ xMn · 1 LCu,Mn,Ni + xNi · 2 LCu,Mn,Ni ) φ
φ
φ
(2)
where 0 LCu,Mn,Ni , 1 LCu,Mn,Ni and 2 LCu,Mn,Ni are the ternary parameters to be evaluated in the present work. The mag Gm term, which describes the magnetic contribution to the Gibbs energy, is given by the Hillert–Jarl–Inden model [24,25]. For the fcc_A1 and cbcc_A12 phases, it is necessary to introduce mag Gm term, while for the liquid and cub_A13 phases, their mag Gm terms are equal to zero. The L10 phase is modeled with the two sublattice model (Cu, Mn, Ni)0.5 (Cu, Mn, Ni)0.5 in order to describe the solubility of Cu in L10 phase. The boldfaces Mn and Ni are the major species in the first and second sublattices, respectively. Thus, the Gibbs energy for this phase is expressed by the following equation:
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W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
a
b
c
Fig. 1. Calculated binary phase diagrams: (a) Cu–Ni system [16], (b) Cu–Mn system [21], (c) Mn–Ni system [9].
" 0
0 GL1 m
=
XX i
L1 y0i y00j Gi:j 0
+R·T ·
j
1X 0 yi ln y0i 2 i
#
XX X L1 1 X 00 + yi ln y00i y0i y0j + y00k Li,j:0k 2 i i j >i k +
XX i
j >i
y00i y00j
X
L1
y0k Lk:i0,j + · · ·
(3)
k
where y0n and y00n are the site fractions of n (n = i, j or k = Cu, Mn or L1
Ni) on the first and second sublattices, respectively. Gi:j 0 represents L1
L1
the Gibbs energy of the end-member of the L10 phase, Li,j:0k and Lk:i0,j are the interaction parameters within each sublattice 4. Results and discussion 4.1. Experiment All the experimental results for phase identifications, composition measurements and lattice parameter refinements on alloys equilibrated at 600 ◦ C are summarized in Table 2. No ternary phase was obtained at 600 ◦ C. Due to the volatilization of Mn, there was some weight loss during arc melting. That weight loss is about 2 wt% for alloys 1 to 6 in the Mn-corner, and less than 1 wt% for alloys 7 to 12. Since most of the data used for establishing the phase diagram were tie-lines and tie-triangle determined by EDS,
Fig. 2. Presently measured partial isothermal section of the Cu–Mn–Ni system in the Mn-rich region at 600 ◦ C.
the composition deviation from the nominal composition of the alloys would not influence the result and the alloys after arc melting were not subjected to chemical analysis. Fig. 2 presents the constructed partial isothermal section at 600 ◦ C. It is worth noting that the determined phase boundaries are consistent with the latest reported Mn–Ni phase diagram [7].
W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
645
Table 2 Summary of the identified phases, their compositions and lattice parameters for the Cu–Mn–Ni alloys annealed at 600 ◦ C for 60 days. No.
Phasea
Nominal composition (at.%) Cu
Mn
1
3
90
7
2
3
86
11
3
3
82
15
4
8
87
5
5
8
83
9
6
13
82
5
7
8
56
36
8 9
3 8
48 48
49 44
10
18
48
34
11 12
26 35
48 48
26 17
a b c
Ni cbcc_A12 cub_A13 fcc_A1 cub_A13 fcc_A1 cub_A13 fcc_A1 cbcc_A12 fcc_A1 cbcc_A12 fcc_A1 cub_A13 (trace) cbcc_A12 fcc_A1 fcc_A1 L10 L10 fcc_A1 L10 fcc_A1 L10 fcc_A1 fcc_A1
Phase compositionb (at.%)
Lattice parameters (Å)c
Cu
Mn
Ni
a
0.6 1.9 10.6 1.6 7.8 3.1 4.3 0.7 18.4 0.5 10.3 1.5 1.2 25.2 8 9.3 3.7 5.4 12.9 27.2 16.3 26.1 34.7
96.4 90.9 77.4 88.8 76 82.3 77.7 97.3 72.9 97 78.8 91.8 97.1 66.7 58.9 52.4 47.9 47.3 48.7 45.2 49.2 47.4 48
3 7.2 12 9.6 16.2 14.6 18 2 8.7 2.5 10.9 6.7 1.7 8.1 33.1 38.3 48.4 47.3 38.4 27.6 34.5 26.5 17.3
– 6.3522(6) 3.728(1) 6.355(4) 3.721(5) 6.333(2) 3.7106(5) 8.936(9) 3.738(2) 8.919(7) 3.724(2) – 8.905(5) 3.751(2) 3.711(3) 3.7381(9) 3.7299(2) – – – – 3.712(1) 3.7166(5)
b
c
3.542(2) 3.5195(4)
The phases were identified by means of XRD. The composition measurement for alloy 9 was conducted with EPMA, and the composition measurements for the other alloys were performed with SEM/EDS. α = β = γ = 90◦ .
This isothermal section is characterized with the continuous disordered fcc_A1 solution phase between γ (Cu,Ni) and γ (Mn). All of the alloys except for alloy 8 contribute to determining the homogeneity range of the fcc_A1 solution, and this phase is in equilibrium with the cub_A13, cbcc_A12 and ordered L10 phases. Alloys 7, 9 and 10 are located in the two-phase region of ordered L10 phase and the disordered fcc_A1 solution phase. Figs. 3a and 4a show the XRD pattern and BSE micrograph of alloy 7, respectively. The BSE micrograph in Fig. 4a clearly indicates that alloy 7 shows a two-phase equilibrium microstructure. As presented in Fig. 3a, the XRD pattern of fcc_A1 phase almost overlaps with those of L10 phase. This feature is caused by the following two reasons. Firstly, the L10 phase is an ordered state of fcc_A1 phase, so all the four peaks from 0 to 90 ◦ C in the XRD pattern of fcc_A1 phase will be very close to those of L10 phase. Secondly, the powder for XRD was obtained from filing the bulk alloy. The filing process inevitably caused great internal stress in the powder, which would severely broaden the peaks. The powder had been annealed at 400 ◦ C for 2 h for stress relief and the quality of the XRD pattern was improved. It should be mentioned that although the patterns are still not as good as the pattern of the powder from grinding the alloy, they are acceptable for phase identification. After peak decomposition by fitting peak profile, lattice parameters of both fcc_A1 and L10 phases were calculated: a = b = c = 3.711 Å for fcc_A1 phase, a = b = 3.7381 Å and c = 3.542 Å for L10 phase. The L10 phase dissolves a considerable amount of Cu up to 16 at.% in alloy 10 according to the EDS measurement. The XRD pattern in Fig. 3b indicates that alloy 1 is in the threephase equilibrium region of cbcc_A12 + cub_A13 + fcc_A1, the existence of which is confirmed by the SEM/EDS measurement as shown in Fig. 4b. Alloys 2 and 3 are located in the two-phase region of cub_A13+fcc_A1, and alloys 4 and 6 are in the cbcc_A12+fcc_A1 region. Fig. 4c and 4d present the corresponding BSE micrographs for alloys 3 and 4, respectively. 4.2. Thermodynamic modeling The thermodynamic parameters were evaluated by the optimization module PARROT of the program Thermo-Calc, which
Table 3 Optimized thermodynamic parameters in the Cu–Mn–Ni system. Liquid: (Cu, Mn, Ni)1 0 L LCu,Mn,Ni
= −42 780
1 L LCu,Mn,Ni
= −67 310
2 L LCu,Mn,Ni
= −56 060
fcc_A1: (Cu, Mn, Ni)1 (Va)1 a
0 fcc_A1 LCu,Mn,Ni
= −67 000
1 fcc_A1 LCu,Mn,Ni
= −49 000
2 fcc_A1 LCu,Mn,Ni
= −49 000
cub_A13: (Cu, Mn, Ni)1 (Va)1 1 cub_A13 LCu,Mn,Ni
= −80 000
L10 : (Cu, Mn, Ni)0.5 (Cu, Mn, Ni)0.5 L1
0
GCu0:Cu = 0 Gfcc_A1 + 10 Cu L1
L1
0
GCu0:Mn = 0 GMn0:Cu = 0.5 · 0 Gfcc_A1 + 0.5 · 0 Gfcc_A1 + 7400 Cu Mn
0
L1 GCu0:Ni
0
L1 GCu0,Ni:Mn
0
L1
=
0
L1 GNi:0Cu
=
0
= 0.5 · 0 Gfcc_A1 + 0.5 · 0 Gfcc_A1 + 7100 Cu Ni
L1 GMn0:Cu,Ni
= −20 630 + 10 · T
L1
GCu0,Mn:Ni = 0 GNi:0Cu,Mn = −46 650 + 50 · T In J mole-atoms−1 ; temperature (T ) in Kelvin. The Gibbs energies for the pure elements are from the SGTE compilation [23]. The binary parameters are from Refs. [9,16,21]. a The magnetic contribution to the Gibbs energy is described by the Hillert–Jarl–Inden model [24,25].
works by minimizing the square sum of the differences between measured and calculated values. The experimental data considered in the optimization are listed below: liquidus and solidus from Parravano [10,11] and Schürmann and Prinz [12,13], partial isothermal section at 450 ◦ C [15], current experimental isothermal section at 600 ◦ C, Cu–MnNi vertical section [15,18,19]. The total amount of data is about 70 and the ratio between the amount of data and the number of final optimized parameters is about 8:1. The optimized parameters are listed in Table 3. As for the modeling process, five critical points are mentioned below. Firstly, the optimization began with the fcc_A1 and L10 phases. L1 The 0 GCu0:Cu and parameters of four hypothetic end members
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W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
a
b
Fig. 3. XRD patterns of the alloys annealed at 600 ◦ C for 60 days: (a) Alloy 7 (Cu8 Mn56 Ni36 ) (b) Alloy 1 (Cu3 Mn90 Ni7 ). Si powder was added as the internal standard for the 2-theta calibration.
a
b
c
d
Fig. 4. BES images of the alloys annealed at 600 ◦ C for 60 days: (a) Alloy 7 (Cu8 Mn56 Ni36 ), (b) Alloy 1 (Cu3 Mn90 Ni7 ), (c) Alloy 3 (Cu3 Mn82 Ni15 ), and (d) Alloy 4 (Cu8 Mn87 Ni5 ). L1
L1
L1
L1
(0 GCu0:Mn , 0 GMn0:Cu , 0 GCu0:Ni , 0 GNi:0Cu ) were fixed with values, which cause the L10 phase to not influence the stable binary phase diagrams [9,16,21]. Secondly, it was found that the two interaction parameters L1 L1 (0 GMn0:Cu,Ni , 0 GCu0,Mn:Ni ) were critical for the optimization of solubility of Cu in L10 phase and fcc_A1/L10 boundary. We assumed that L1 L1 L1 0 L10 GCu,Ni:Mn = 0 GMn0:Cu,Ni and 0 GNi:0Cu,Mn = 0 GCu0,Mn:Ni . According to the experimental Cu–MnNi vertical section [15,18,19], the fcc_A1/L10 boundary changes significantly with temperature, the parameters b describing temperature dependence of the interaction parameters for L10 phase were introduced. L1 L1 Thirdly, 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni make the single L10 phase region and fcc_A1/L10 boundary extend along Mn0.5 Ni0.5 –Cu0.5 Mn0.5
line, while
0
L1
GCu0,Mn:Ni and
0
L1
GNi:0Cu,Mn make them extend along L1
L1
L1
L1
Mn0.5 Ni0.5 –Cu0.5 Ni0.5 line. At 600 ◦ C, both 0 GCu0,Mn:Ni and 0 GNi:0Cu,Mn are equal to −3000 J/mol, much less than 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni with the value of −11 900 J/mol. This is in agreement with the experimental phenomenon that the experimental isothermal section at 600 ◦ C shows that L10 single phase region does not extend along Mn0.5 Ni0.5 –Cu0.5 Ni0.5 line. The present experimental fcc_A1/L10 boundary at 450 ◦ C is symmetric with reference to Cu–Mn0.5 Ni0.5 L1 line. This feature could be satisfied by the condition that 0 GCu0,Mn:Ni L1
and 0 GNi:0Cu,Mn with the value of −10 500 J/mol keeps in balance L1
L1
with the 0 GCu0,Ni:Mn and 0 GMn0:Cu,Ni with the value of −13 400 J/mol at 450 ◦ C.
W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
a
647
b
c
d
e
f
Fig. 5. Calculated liquidus and solidus along the sections of 10 wt% Cu (a), 20 wt% Cu (b), 10 wt% Mn (c), 20 wt% Mn (d), 10 wt% Ni (e), and 20 wt% Ni (f). The experimental data [10,11] and the values calculated from well derived functions [12,13] are plotted for comparisons.
Fourthly, it should be mentioned that the current experimental boundary between L10 and fcc_A1 phases at 600 ◦ C, which is the ternary extension from the Mn–Ni binary side, is very curvaceous and asymmetric. The thermodynamic parameters on the binary Mn–Ni system [9], however, is symmetric. Thus there are no parameters, which can adjust the exact shape of the L10 /fcc_A1 boundary at 600 ◦ C. Consequently, a compromise was made in the assessment of the experimental data from different sources. Fifthly, since there is a small amount of data about the solid phases, the b values for the parameters of the fcc_A1 phase were not used. In addition, the a values were controlled during the optimization procedure to make the miscibility gap of fcc_A1 phase
not appear above 450 ◦ C. Finally, the liquid phase was considered in the optimization. There are no experimental thermodynamic data for the liquid phase, so only the ternary parameters a were used for the measured solidus and liquidus. Fig. 5a–f present the calculated liquidus and solidus along the sections of x = 10 wt.% Cu, 20 wt% Cu, 10 wt% Mn, 20 wt% Mn, 10 wt% Ni and 20 wt% Ni, compared with the experimental data [10,11] and the values calculated from well derived functions [12,13]. Most experimental data were reasonably accounted for by the present calculations except for the data in the Cu and Mn corners from Parravano [10,11]. These data in the Cu and Mn corners [10,11] were considered to be inaccurate, because they do
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a
b
1150
1100
1050
1000
950 950
c
1000
1050
1100
1150
d
Fig. 6. Comparison between the calculated liquidus/solidus and the experimental data [12,13]: (a) liquidus in the Cu-rich corner, (b) solidus in the Cu-rich corner, (c) liquidus in the Ni-rich corner, (d) solidus in the Ni-rich corner.
not accord with the well-determined Mn-rich and Cu-rich liquidus and solidus in the binary systems [9,16,21], if being extrapolated into the binary boundaries. A comparison between the calculated liquidus/solidus and the experimental data [12,13] is shown in Fig. 6. As indicated in Fig. 6a and b, the data in the Cu corner are well reproduced, while in the Ni corner, the consistency is moderate but acceptable as shown in Fig. 6c and d. Since the calculated results in the Cu and Ni corners are mainly determined by the binary parameters, it can be concluded that the experimental data [12,13] are very accurate, while most of the data [10,11] are acceptable except for the data in the Cu and Mn corners [10,11]. Fig. 7 shows the calculated liquidus surface projection. There are only two preliminary phases of fcc_A1 and bcc_A2 solutions. Fig. 8 presents the calculated Cu–MnNi vertical section, compared with experimental data from Refs. [15,18,19]. The presently calculated boundary of fcc_A1/fcc_A1 + L10 is well consistent with the data of Udovenko et al. [19], while a little lower than that from Refs. [15,18]. Fig. 9 presents the calculated isothermal section at 450 ◦ C compared with experimental data of Chang [15]. The presently calculated fcc_A1/fcc_A1 + L10 boundary is in general agreement with that determined by Chang [15]. Fig. 10 compares the calculated isothermal section at 600 ◦ C compared
Fig. 7. Calculated projection of the liquidus surface and the isothermal liquidus in the Cu–Mn–Ni system.
W. Sun et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 642–649
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Fig. 10. Calculated isothermal section at 600 ◦ C, compared with the present experimental data. Fig. 8. Calculated Cu–MnNi vertical section, compared with the experimental data [15,18,19].
was measured to be up to about 16 at.%. No ternary compound was found. • A thermodynamic modeling of this system was carried out in the whole composition range by taking into account both reliable literature data and the current experimental data. Comprehensive comparisons show that the present calculations are generally in agreement with the critically assessed experimental data. Acknowledgements The financial support from the Creative Research Group of National Natural Science Foundation of China (Grant No. 50721003) and the National Outstanding Youth Science Foundation of China (Grant No. 50425103) is acknowledged. The Thermo-Calc Software AB is acknowledged for the provision of Thermo-Calc software. Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.calphad.2009.07.003.
Fig. 9. Calculated isothermal section at 450 ◦ C, compared with the experimental data [15].
with the present experimental data. The present calculation well accounts for the Mn-rich experimental data, but does not well reproduce the phase equilibria between fcc-A1 and L10 . It is probably because the parameters describing the binary Mn–Ni phase diagram [9] are symmetric, which have negative effect on the modeling of the very curvaceous and asymmetric L10 + fcc_A1 phases boundary in the ternary system. At last, it is worth noting that few experimental data were reported below 900 ◦ C, not only for the Cu–Mn–Ni system, but also for the M (M = Al, Fe et al.)-Mn–Ni systems. Furthermore, most of reported data do not coincide with the Mn–Ni binary phase diagram [7]. Therefore, further experiments need to be performed for the investigation of the M (M = Al, Fe, Cu et al.)-Mn–Ni systems below 900 ◦ C. 5. Conclusion
• A partial isothermal section at 600 ◦ C of the Cu–Mn–Ni system in the Mn-rich region was constructed. The three-phase equilibrium of cbcc_A12 + cub_A13 + fcc_A1 was determined. The solubility of Cu in the MnNi compound with L10 structure
References [1] R.I. Agladze, V.M. Mokhov, L.I. Topchiashvili, Splavy Margantsa s Med’yu, Nikelem, i Tsinkom, Tbilisi, Akad. Nauk Gruz. (1954) 51–65. [2] K. Dies, Metall 15 (1961) 1161–1172. [3] G. Groma, Proc. 4th Conf on Dimensioning, Acad. Kiado, Budapest, Hungary, 1973, pp. 417–422. [4] N.A. Gokcen, J. Phase Equilib. 12 (1991) 313–321. [5] L. Ding, Master Thesis, University of Wisconsin-Madison, USA, 2001. [6] K.E. Tsiuplakis, E. Kneller, Z. Met.kd. 60 (1969) 433–438. [7] L. Ding, P.F. Ladwig, X.Y. Yan, Y.A Chang, Appl. Phys. Lett. 80 (2002) 1186–1188. [8] B.R. Coles, W. Hume-Rothery, J. Inst. Met. (London) 80 (1951–1952) 85–92. [9] S.H. Liu, Master Thesis, Central South University, China, 2008. [10] N. Parravano, Gazz. Chim. Ital. 42 (1913) 385–394. [11] N. Parravano, Intern. Z. Metallog. 4 (1913) 171–202. [12] E. Schürmann, B. Prinz, Z. Metallkd. 65 (1974) 535–539. [13] E. Schürmann, B. Prinz, Z. Metallkd. 65 (1974) 593–598. [14] U. Zwicker, Z. Metallkd. 42 (1951) 331–335. [15] B.C. Chang, Izv. Vyss. Uchebn. Zaved. Tsvetn. Metall. 5 (1958) 107–115. [16] S. Mey, CALPHAD 16 (1992) 255–260. [17] J. Rolland, D. Whitwham, Mem. Sci. Rev. Met. 67 (1970) 607–614. [18] J. Rolland, P. Priester, D. Whitwham, Compt. Rend. Acad, Sci. Paris, Ser. C 270 (1970) 1777–1780. [19] V.A. Udovenko, V.V. Sanadze, N.A. Polyakova, E.D. Chichua, L.D. Gogua, Soobshch. Akad. Nauk Gruz. SSR 134 (1989) 73–76. [20] J. Miettinen, CALPHAD 27 (2003) 147–152. [21] C.Y. He, Y. Du, H.L. Chen, S.H. Liu, H.H. Xu, Y.F. Ouyang, Z.K. Liu, J. Alloys Compounds. 457 (2008) 233–238. [22] O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [23] A.T. Dinsdale, CALPHAD 15 (1991) 317–425. [24] G. Inden, The proceedings of CALPHAD V project meeting, Max-Planck Institute for Metal Research, Dusseldorf, 1976, pp. 1–13. [25] M. Hillert, M. Jarl, CALPHAD 2 (1978) 227–238.