Critical thermodynamic evaluation and optimization of the Co–Nd, Cu–Nd and Nd–Ni systems

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

Contents lists available at SciVerse ScienceDirect

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad

Critical thermodynamic evaluation and optimization of the Co–Nd, Cu–Nd and Nd–Ni systems Azeem Hussain, Marie-Aline Van Ende, Junghwan Kim, In-Ho Jung n Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, Canada QC H3A 0C5

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 October 2012 Received in revised form 13 December 2012 Accepted 30 December 2012 Available online 25 January 2013

All experimental data on phase equilibria and thermodynamic properties of the Co–Nd, Cu–Nd and Nd–Ni binary systems in literature were reviewed and critically examined. A set of optimized model parameters for all solid stoichiometric compounds and liquid phase was built to reproduce all available reliable thermodynamic properties and phase diagram data within experimental error limits. The Modified Quasichemical Model in the pair approximation was used to describe the thermodynamic properties of the liquid solution accurately. Systematic changes in the phase diagrams and thermodynamic properties between Nd–X binary systems, where X ¼Mn, Fe, Co, Ni and Cu, are presented and discussed. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Rare earth alloys and compounds Thermodynamic modeling CALPHAD Modified Quasichemical Model

1. Introduction Binary RE(Rare Earth element)–X (X¼Fe, Mn, Co, Ni, Cu, etc.) intermetallics have attracted the attention for the magnetic materials [1–4]. In addition, Co, Ni and Cu are frequently used as alloying elements and coating materials for sintered commercial NdFeB permanent magnet [5–7]. In the recycling process of RE from NdFeB magnet using molten metal such as Mg, therefore, the thermodynamic behaviors of Co, Ni and Cu with Nd are important to increase the extraction yield of Nd. In order to understand the chemical interactions of Co, Ni and Cu with NdFeB magnet during the recycling process, the thermodynamic information of both intermetallic phases and liquid phase for the binary Co–Nd, Cu–Nd and Nd–Ni systems are indispensible. The main goal of the present study is to perform a critical evaluation and optimization of the thermodynamic properties and phase diagrams of the Co–Nd, Cu–Nd and Nd–Ni systems. In the thermodynamic ‘‘optimization’’ of a chemical system, all available thermodynamic and phase equilibrium data are evaluated simultaneously in order to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. From these equations, all thermodynamic properties and phase diagrams can be back-calculated. In this way, all the data are rendered self-consistent and consistent with thermodynamic principles. Thermodynamic property data, such as activity data, can aid in the evaluation of the phase diagram, and phase diagram measurements can be used to deduce thermodynamic

n

Corresponding author. Tel.: þ1 514 398 2608; fax: þ1 514 398 4492. E-mail address: [email protected] (I.-H. Jung).

0364-5916/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.calphad.2012.12.003

properties. Discrepancies in the available data can often be resolved, and interpolations and extrapolations can be made in a thermodynamically correct manner. There were several thermodynamic assessments for the Co–Nd [8], Cu–Nd [9–14] and Nd–Ni [15–16] systems. However, the results of the assessments were not quite satisfactory: Although the phase diagram data were well reproduced in most of the assessments, the thermodynamic data of solids and liquid were not well reproduced simultaneously. In addition, an inverse liquid miscibility gap was calculated in several cases [8,12,15,16]. The difficulty in the thermodynamic modeling of these systems mainly resulted from the usage of the Bragg–Williams random mixing model for liquid solutions having a very strong ordering tendency. This will be discussed later. In order to overcome this difficulty, the Modified Quasichemical Model with pair fraction approximation is used for the liquid solutions in the present study. This work is part of a large thermodynamic database development for the recycling of NdFeB magnet waste materials using liquid Mg extraction technique involving Nd–Fe–B–Dy–Tb–Ni– Co–Cu–Mg system. All the thermodynamic calculations in the present study are performed using the FactSage thermochemical software [17].

2. Thermodynamic models 2.1. Liquid phases In order to account for the strong ordering tendency in the liquid phase, the Modified Quasichemical Model [18,19], which accounts for short-range-ordering of nearest-neighbor atoms, was

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

used for the liquid solutions in the present study. As known, the Modified Quasichemical Model can give a more realistic thermodynamic description for liquid solutions, compared with the conventional simple random-mixing Bragg–Williams model especially for liquid solutions with strong ordering tendency. The Modified Quasichemical Model has been successfully applied to many liquid metallic solutions [19–21] and ionic solutions [22,23] exhibiting strong short-range-ordering behavior. Recently, the energy of nearest-neighbor pair formation in the Modified Quasichemical Model is expanded as a polynomial in the pair fractions [18,19] instead of the component fractions [22,24]. In addition, the coordination numbers are now allowed to vary with composition. These modifications provide greater flexibility in reproducing the binary experimental data and in combining optimized binary liquid parameters into a large database for multicomponent solutions [18]. A short description of the model is given below. The details of the model can be found in previous studies [18,19]. Let us consider the case of a binary A–B liquid solution. The atoms A and B are distributed over the sites of a quasi-lattice in the liquid solution. Then, the following pair exchange reaction can be considered:

ðAAÞ þðBBÞ ¼ 2ðABÞ

ð1Þ

where (A–B) represents a first-nearest-neighbor pair of A and B. The non-configurational Gibbs energy change for the formation of two moles of (A–B) pairs according to reaction (1) is Dg AB . Then the Gibbs energy of the solution is given by   Dg AB G ¼ nA GoA þnB GoB T DSconfig þ nAB 2

ð2Þ

where GoA and GoB are the molar Gibbs energies of the pure components A and B, nA and nB are the numbers of moles of A and B atoms, and nAB is the number of moles of (A-B) pairs. The numbers of moles of A–A, B–B and A–B pairs nAA, nBB and nAB are calculated from the mass balance equations in liquid A–B alloys

1700

27

containing nA moles of A and nB moles of B: nA Z A ¼ 2nAA þnAB

ð3Þ

nB Z B ¼ 2nBB þ nAB

ð4Þ

where ZA and ZB are the nearest-neighbor coordination numbers. Table 1 Invariant reactions in the Co–Nd system. Invariant reaction

T (K) (at% Co) Present work Ray et al. [29,30]

L þfcc Co¼ Co17Nd2 L ¼fcc Coþ Co17Nd2 L ¼Co17Nd2 L þCo17Nd2 ¼Co5Nd L þCo5Nd¼ Co19Nd5 L þCo19Nd5 ¼Co7Nd2 L þCo7Nd2 ¼ Co3Nd L þCo3Nd¼ Co2Nd Co5Nd¼Co17Nd2 þCo19Nd5 L ¼CoNd3 L þCo2Nd¼ Co3Nd2 L ¼CoNd3 þ dhcp Nd L þCo3Nd2 ¼ Co3Nd4 L þCoNd3 ¼ Co2Nd5 L ¼Co2Nd5 þ Co3Nd4

– 1572.9 (90.5) 1573.9 1534.5 1426.6 1417.7 1375.3 1238.8 1081.5 914.2 907.6 895.0 (19.2) 865.7 865.6 845.3 (36.3)

1574 7 4 – – 1539 7 5 1439 7 5 1434 7 4 1378 7 4 1238 7 7 – 919 7 2 913 7 9 898 7 3 (20 70.5) 872 7 6 869 7 2 839 7 3 (36 7 0.5)

CoNd3

Co2Nd

Co3Nd

Co7Nd2

Co19Nd5

Co5Nd

Co17Nd2

Tc (K)

14a 4.5

105.3 3.5

392.6 5.5

609 13.1

714 31

911 10.6

1163 33.5

b a

Neel temperature.

Wu et al. (1992): XRD, DTA, EPMA, metallography

1573 1535 1418

1239 1128

1100

1082 914

908 866

300 0.0 Nd

0.1

0.2

0.3

0.4

0.5 0.6 mole fraction

0.7

Fig. 1. Calculated binary phase diagram of the Co–Nd system.

0.8

Co17Nd2

Co19Nd5

Co3Nd Co7Nd2

Co2Nd

Co3Nd2

Co3Nd4

500

Co2Nd5

700

CoNd3

Temperature (K)

1300

Co5Nd

1375

845

– – –

Phase

1500

895

– 1579 7 5 (93)  1643 1539 7 5 1425 7 5 1416 7 5 1373 7 3 1323 7 2 1073 – 923 73 –

Table 2 Measured Curie temperatures (Tc, K) and magnetic moment (b) adopted in the present optimization in SI units per mole.

Ray et al. (1973): XRD, DTA, EPMA, metallography

900

Wu et al. [31]

0.9

1.0 Co

28

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

DSconf ig is the configurational entropy of mixing given by a random distribution of the (A–A), (B–B) and (A–B) pairs in the one-dimensional Ising approximation:      X DSconf ig ¼ R nA ln X A þ nB lnX B R nAA ln AA2 Y     A X BB X AB þ nBB ln þ nAB ln ð5Þ 2Y A Y B YB2 where nAA , nBB and nAB are the numbers of moles of each kind of pairs, XA and XB the mole fraction of A and B, and the pair fraction (XAA, XBB and XAB) and coordination equivalent fraction (YA and YB) can be calculated as X AA

¼

nAA nAA þ nBB þ nAB

ð6Þ

X BB

¼

nBB nAA þ nBB þ nAB

ð7Þ

X AB

¼

nAB nAA þ nBB þ nAB

ð8Þ

Y A ¼ X AA þ

1 X AB 2

ð9Þ

Y B ¼ X BB þ

1 X AB 2

ð10Þ

Dg AB is the model parameter to reproduce the Gibbs energy of the liquid phase of the A–B system, which is expanded as a

Fig. 2. (a) Partial and (b) integral enthalpies of mixing of Nd(l) and Co(l) in liquid Co–Nd alloy at 1823 K.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

1.5 and 2, and reproduce the short range ordering in liquid solution of each respective system.

polynomial in terms of the pair fractions, as follows:

Dg AB ¼ Dg oAB þ

X

g iAB0 ðX AA Þi þ

iZ1

Dg oAB ,

g iAB0

X

j g 0j AB ðX BB Þ

ð11Þ

jZ1

2.2. Stoichiometric compounds and elements

g 0ABj

where and are the adjustable model parameters which can be functions of temperature. In the Modified Quasichemical Model, the coordination numbers of A and B, ZA and ZB, can now be varied with composition to reproduce the short-range-ordering as follows:     1 1 2nAA 1 nAB ¼ þ ð12Þ ZA Z AA 2nAA þ nAB Z AB 2nAA þ nAB 1 ZB

¼

    1 2nBB 1 nAB þ Z BB 2nBB þ nAB Z BA 2nBB þnAB

29

ð13Þ

where ZAA is the value of ZA when all nearest neighbors of an A atom are A atoms, and ZAB is the value of ZA when all nearest neighbors are B atoms. ZBB and ZBA are defined in an analogous manner. The nearest-neighbor coordination numbers are adjustable parameters of the Modified Quasichemical Model and do not represent real physical values. The choice of the value of ZXX was discussed by Pelton and Kang [25]. Based on the experience gained by examining and optimizing many metallic systems, the value Z¼6 was found to represent well most binary liquid solutions and predict well the corresponding ternary liquids. The coordination numbers enable to adjust the internal structure of the mixture. When ZAB ¼ZBA (i.e. ZAB/ ZBA ¼1), the maximum short range ordering is set at the composition XA ¼XB ¼0.5. When the composition of maximum short range ordering in the liquid solution is observed at a composition other than XA ¼XB ¼0.5, the former can be varied by the ratio ZAB/ZBA. In the present study, maximum short range ordering was observed at XCo ¼ 0.5 and XCu ¼0.66 based on experimental enthalpy of mixing data in liquid Co–Nd and Cu–Nd alloys, respectively. In the case of the Nd–Ni system where no experimental enthalpy of mixing data in the liquid solution are available, a good fit of the experimental phase diagram data was obtained when the maximum short range ordering is set at XNi ¼0.6. Therefore, ZXNd are set to be 6, 4 and 3 for Co, Ni and Cu, respectively, to have the ratio ZNdX/ZXNd equal to 1,

The Gibbs energies of all pure elements were taken from SGTE database version 5.0 (2009) [26]. The Gibbs energies of stoichiometric intermetallics were optimized based on available experimental data using the standard Gibbs energy expression based on heat capacity, enthalpy and entropy of formation at 298 K. If the heat capacities of stoichiometric compounds were not available, they were typically estimated using the Neumann–Kopp rule. Many stoichiometric intermetallic phases exhibit magnetic transitions associated with Neel or Curie temperature. The magnetic transition below 298 K (typically antiferromagnetic transition with Neel temperature) was taken directly into account in the calculation of S0298 K . The Curie temperature (ferromagnetic transition) occurs typically above 298 K, of which magnetic contribution to the Gibbs energy was considered by an empirical relationship suggested by Inden [27] and modified by Hillert and Jarl [28].

3. Critical evaluation and thermodynamic optimization The thermodynamic optimization of the binary systems was performed based on critical evaluation of all available phase diagram and thermodynamic data for intermetallics and liquid solution. The details of the thermodynamic optimization of each binary system are explained in the following sections. 3.1. The Co–Nd system 3.1.1. Phase diagram data Fig. 1 shows the phase diagram of the Co–Nd system. The system comprises the following phases: liquid, dhcp Nd, bcc Nd, hcp Co, fcc Co, and a number of intermetallic compounds. Ray et al. [29,30] have used x-ray diffraction (XRD), differential thermal analysis (DTA), quantitative electron probe microanalysis (EPMA), and metallography to generate a phase diagram of the

Fig. 3. Optimized heat capacity of Co2Nd.

30

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

entire system. Ten intermediate phases were reported: CoNd3, Co  3Nd  7, Co1.7Nd2, Co3Nd2, Co2Nd, Co3Nd, Co7Nd2, Co19Nd5, Co5Nd and Co17Nd2. Wu et al. [31] employed the same techniques, focusing on the Co-rich region of the system ( Z50 at% Co) where numerous peritectic reactions were reported. They identified seven intermetallic compounds: Co3Nd2, Co2Nd, Co3Nd, Co7Nd2, Co19Nd5, Co5Nd and Co17Nd2. NdCo5 was found to decompose into Co17Nd2 and Co19Nd5 at 800 1C. The liquidus of Co-rich compounds reported by Wu et al. are systematically slightly more enriched with Nd than those of Ray et al. A principal point of disagreement between the two data sets concerns the melting of Co17Nd2. Ray et al. reported it to be peritectic at 130174 1C, whereas Wu et al. reported it to be congruent at about 1370 1C. According to Wu et al., a eutectic reaction between Co17Nd2 and fcc Co occurred at 130675 1C and 92.9 at% Co. The invariant reaction temperatures reported by the two investigations are listed in Table 1. The main divergence concerns the peritectic temperatures of Co2Nd which is 85 K higher in Wu et al.’s study, and those of Co7Nd2 and Co19Nd5, which are, respectively, 18 and 14 K lower in Wu et al.’s study. Liu et al. [8], based on crystallographic data from Moreau and Paccard [32], have concluded that the system contains ten stoichiometric compounds: CoNd3, Co2Nd5, Co3Nd4, Co3Nd2, Co2Nd, Co3Nd, Co7Nd2, Co19Nd5, Co5Nd and Co17Nd2. No study on the stability of the compounds at low temperature has been performed. Thus, there is possibility of dissociation of the compounds at low temperature with a eutectoid reaction. Wu et al. estimated the solid solubility of Nd in Co to be less than 0.03 at% [31] after annealing and quenching at 1000 1C. No experimental data were found regarding the solubility of Co in Nd.

Nikolaenko and Turchanin [35] performed isoperibolic calorimetry to determine the partial enthalpies of mixing of Co and Nd in the liquid solution at 1823 K and then calculate the integral enthalpy of mixing. The experimental and calculated enthalpies of the liquid Co–Nd solution are presented in Fig. 2. Deenadas et al. [36] determined low-temperature heat capacity (Cp) of Co2Nd between 8 and 310 K using adiabatic calorimetry, permitting the elucidation of its entropy of formation. The experimental data are plotted in Fig. 3. The Neel temperature was observed at about 100 K. The estimated entropy of Co2Nd at 298 K (So298 ) including the magnetic effect at 100 K is 140.15 J mol  1 K  1. Although the enthalpies of formation of intermetallic compounds were estimated by Niessen et al. [37]

Table 3 Optimized model parameters for the Co–Nd system (J mol  1 or J mol  1 K  1). Phase

Thermodynamic parameters

Liquid

Dg NdCo ¼ 125521:2552T þ ð20922:092TÞX NdNd 2092X 3CoCo DHo298 ¼ 114000, So298 ¼ 699

Co17 Nd2 Co5Nd Co19Nd5 Co7Nd2 Co3Nd Co2Nd Co3Nd2

3.1.2. Thermodynamic and magnetic properties data Buschow [33] determined Bohr magnetic moments and critical magnetic ordering temperatures of seven intermetallic compounds. Wu et al.’s crystallographic analyses provide the structures and therefore p-factors [31]. Buschow’s magnetic property values, along with a few recent updates [34] are listed in Table 2. These values are used in the present work.

Co3Nd4 Co2Nd5 CoNd3

Cp ¼2 Cp(Nd(dhcp)) þ17 Cp(Co(hcp)) DHo298 ¼ 49500, So298 ¼ 233 Cp ¼Cp(Nd(dhcp)) þ 5Cp(Co(hcp)) DHo298 ¼ 225372:7, So298 ¼ 996:5 Cp ¼5 Cp(Nd(dhcp)) þ19Cp(Co(hcp)) DHo298 ¼ 90668:8, So298 ¼ 370:5 Cp ¼2Cp(Nd(dhcp)) þ7Cp(Co(hcp)) DHo298 ¼ 41110, So298 ¼ 168:4 Cp ¼Cp(Nd(dhcp)) þ 3Cp(Co(hcp)) DHo298 ¼ 29650, So298 ¼ 143:1 Cp ¼Cp(Nd(dhcp)) þ 2 Cp(Co(hcp)) þ3.7 DHo298 ¼ 45700, So298 ¼ 256 Cp ¼2Cp(Nd(dhcp)) þ3Cp(Co(hcp)) DHo298 ¼ 49900, So298 ¼ 409:45 Cp ¼4 Cp(Nd(dhcp)) þ3 Cp(Co(hcp)) DHo298 ¼ 40100, So298 ¼ 445 Cp ¼5Cp(Nd(dhcp)) þ2Cp(Co(hcp)) DHo298 ¼ 20500, So298 ¼ 260 Cp ¼3Cp(Nd(dhcp)) þCp(Co(hcp))

Fig. 4. Calculated enthalpies of formation at 298 K in the Co–Nd system compared with experimental and predicted values in the Co–Nd, Co–Pr and Co–Sm systems.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

using the Miedema’s technique, no experimental determination has been conducted.

3.1.3. Thermodynamic optimization The Co–Nd system was previously assessed by Okamoto [38] and optimized by Liu et al. [8]. Liu et al. [8] performed the thermodynamic assessment using the Bragg–Williams model for the liquid solution. They used six model parameters including three relatively large temperature-dependent parameters for the liquid solution. Due to the relatively large temperaturedependent parameters, an inverse miscibility gap appears at temperatures above 4000 K. In their assessment, two important key thermodynamic data were not considered: the partial and integral enthalpy of the liquid solution by Nikolaenko and Turchanin [35] and So298 of Co2Nd by Deenadas et al. [36]. These thermodynamic data combined with phase diagram information can effectively constrain the thermodynamic properties of the liquid solution and intermetallic compounds Co2Nd and others. Moreover, Liu et al. assumed the more recent phase diagram data of Wu et al. [31] to be more reliable above 50 at% Co than those of Ray et al. [29,30], who determined the entire phase diagram of the

31

Co–Nd system, without any justification. In the assessment of Liu et al., in fact, the fitting of Wu et al.’s [31] experimental data at the Co-rich side resulted in a large deviation from the liquidus of Co reported by Ray et al. [29,30] which is thermodynamically more reliable in the consideration of the limiting slope rule [39]. In the present study, the thermodynamic properties of the liquid were first roughly fixed based on the partial and integral enthalpy of liquid solution by Nikolaenko and Turchanin [35]. The integral enthalpy of mixing of the liquid Co–Nd solution shows a minimum of about  11 kJ mol  1 at about 50 at% Co (Fig. 2(b)), which is the reason that both coordination numbers ZNdCo and ZCoNd in the Modified Quasichemical Model [18,19] are fixed at the same value, i.e. 6. Then, the thermodynamic properties of solid intermetallic compounds were fixed based on the phase diagram data. Except Co2Nd of which low temperature Cp was reported, Cp of all other intermetallic compounds were estimated using the Neumann–Kopp rule, and So298 were firstly assumed to be the sum of the So298 of their stoichiometric amounts of Co and Nd, and then slightly modified (less than 10% of the original value) to reproduce the phase diagram. The enthalpies of formation at 298 K (DHo298 ) of all intermetallic compounds were adjusted in the aim of reproducing the phase diagram data [29–31]. Both Co and Nd were

Table 4 Invariant reactions in the Cu–Nd system. Invariant reaction

T (K) (at % Cu)

L ¼ Cuþ Cu6Nd L ¼ Cu6Nd L þ Cu6Nd¼ Cu5Nd L þ Cu5Nd¼ Cu4Nd L þ Cu4Nd¼ Cu7Nd2 Cu7Nd2 ¼ Cu2Ndþ Cu4Nd L ¼ Cu2Ndþ Cu7Nd2 L ¼ Cu2Ndþ Cu4Nd L ¼ Cu2Nd L þ Cu2Nd¼ CuNd CuNd ¼CuNd L ¼ NdþCuNd

Present work

Carnasciali et al. [44]

Zheng and Nong [45]

Laks et al. [46]

1149.4 (91) 1193.7 1140.7 1108.9 1099.1 1056.2 1073.8 (73.2) – 1114.9 949.9 743 780.8 (29.5)

1138 7 5 (  90) 1183 7 5 1143 7 5 1118 7 5 1098 75 1058 75 – 1043 75 (73) 1113 7 5 943 75 723–773 793 (30)

1147 (91) 1235 1189 1126 – – – 1033 (74) 1103 875 847 751 (33)

1141 (92) 11907 10 11207 10 1102 – – – 10587 5 (72) 1116 75 – – –

1400

Carnasciali et al. (1983): DTA, XRD, metallography Zheng & Nong (1983): DTA, XRD, metallography Laks et al. (1984): DTA, XRD, metallography, SEM-EDS Efimov et al. (1988): DTA, XRD

1300 1200

Cu7Nd2 1115

1128

1056

1000

950

900 800

781 743

700 600

300 0.0 Nd

0.1

0.2

0.3

0.4

0.5 0.6 mole fraction

0.7

Fig. 5. Calculated binary phase diagram of the Cu–Nd system.

0.8

Cu6Nd

Cu2Nd

400

Cu4Nd Cu5Nd

500 CuNd

Temperature (K)

1149

1074

1100

0.9

1.0 Cu

32

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

assumed to have no mutual solubility in each other. The magnetic property data used in the present study are summarized in Table 2. The phase diagram of the Co–Nd system calculated from the present model parameters is presented in Fig. 1 along with the experimental data. The experimental data of Ray et al. [29,30] were used as primary source for the phase diagram evaluation. It is hard to explain the possible reason of the deviation of Wu et al.’s data [31] from those of Ray et al. The systematic deviation of the liquidus composition may be induced by a wrong calibration of Co and Nd during the EPMA quantification. It is assumed that the mutual solubility of Co and Nd is negligible and all intermetallics are stoichiometric compounds. The result of the present optimization shows that Co17Nd2 and CoNd3 melt congruently. The other compounds show peritectic melting behaviors, as reported in the phase diagram studies [29–31]. According to Ray et al. [29,30], the melting behavior of Co17Nd2 is peritectic. However, this finding seems to be based only on DTA measurements. Though the authors claim to have performed metallography in their experimental section, no metallographic examination was given in the text to support that Co17Nd2 is a peritectic compound. From their reported DTA data, the liquid composition of the peritectic reaction is very close to the stoichiometric Nd2Co17 compound, which causes a difficulty to assert a peritectic or a eutectic reaction. The present optimization reproduces all the experimental liquidus data of Ray et al. [29,30] within experimental error. Based on the simultaneous optimization of the experimental enthalpy of mixing in the liquid, enthalpy of formation of the compounds and experimental phase diagram data, the results of the thermodynamic modeling indicate a congruent melting of Co17Nd2 rather than a peritectic reaction. This is also supported by Wu et al. [31] based on a systematic examination of the samples near the Co17Nd2 compound, although their reported melting temperature is much higher. The calculated partial enthalpies of Co and Nd and integral enthalpy of mixing of liquid Co–Nd solution are presented in Fig. 2 along with experimental data by Nikolaenko and Turchanin [35]. Both experimental data are well reproduced in the present study. As can be seen in Fig. 2(b), the integral enthalpy of mixing predicted by Liu et al.’s optimization [8] is about two times more

negative than the experimental data. Moreover, the shape of the integral enthalpy of mixing curve at Nd and Co-rich alloys is thermodynamically peculiar and the resultant partial enthalpies of Co and Nd are completely off from the experimental data in Fig. 2(a): This integral enthalpy shape is typical for a liquid solution having miscibility gaps, and clearly in order to suppress the miscibility gap formation due to this unreasonable enthalpy of mixing, they used several large entropy terms. The low-temperature Cp data for Co2Nd by Deenadas et al. [36] were used to determine the Cp and So298 of the compound. As can be seen in Fig. 3, the Cp calculated from the Neumann–Kopp rule of Co2Nd are slightly lower than the experimental data, so the Cp calculated from the Neumann–Kopp rule was shifted up by 3.7 J mol  1 K  1 to line up with the experimental data. The entropy of Co2Nd at 298 K (So298 ) estimated from the low-temperature Cp data [36] including the anti-ferro magnetic transition at 100 K is 140.15 J mol  1 K  1, which is about 9 J mol  1 K  1 higher than the summation of So298 of hcp Co (30.04 J mol  1 K  1 including magnetic contribution) and dhcp Nd (71.09 J mol  1 K  1). In the present optimization, the So298 of Co2Nd was increased by 3 J mol  1 K  1, which can be close to typical experimental error range, to reproduce the phase diagram data. For other intermetallic compounds, Cp was estimated using the Neumann–Kopp rule, and So298 was firstly assumed to be the sum of the So298 of their stoichiometric amounts of Co and Nd, and then slightly modified (less than 10% of the original value) to reproduce the phase diagram. The enthalpies of formation at 298 K (DHo298 ) of all intermetallic compounds were adjusted in the aim of reproducing the phase diagram data [29–31]. The optimized enthalpy of formation at 298 K of solid compounds are plotted in Fig. 4 along with the estimated data by Niessen et al. [37] using Miedema’s technique for the Co–Nd. Niessen et al. also estimated the enthalpies for the compounds in Co–Pr and Co–Sm systems using the same technique. It is expected that the enthalpies of formation of these RE (rare earth element) binary systems should be in similar range considering the similarity in the electro-magnetic properties of Nd, Sm and Pr. In order to evaluate the accuracy of the estimation of Niessen et al., the available experimental data for the Co–Pr and Co–Sm

Fig. 6. Calculated enthalpies of formation at 298 K in the Cu–Nd system compared with experimental and predicted values.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

systems were collected from literature and compared in Fig. 4. The enthalpies of formation in the Co–Pr system were measured by Deodhar and Ficalora [40] using DTA and by Bar and Schaller [41] using electromotive force (EMF), and in the Co–Sm system by Meyer-Liautaud et al. [42] using solution calorimetry and by Shilov [43] using DTA technique. As can be seen in Fig. 4, the estimation of enthalpy of formation by Niessen et al. using Miedema’s technique are two times more negative than the experimental data for the Co–Pr and Co–Sm systems. In addition, the enthalpies of formation estimated by Niessen et al. for the Co–Nd system is about twice more negative than the enthalpy of mixing of liquid Co–Nd solution, which seems to be a too large difference from the experience of the authors. Thus, we believe that the estimated value by Niessen et al. is unreasonably negative. As can be seen in Fig. 4, the optimized enthalpies of formation of the compounds in

33

the present study are similar to the experimental enthalpies of formation of the compounds in the Co-Pr and Co-Sm systems. It should be noted that Liu et al. [8] used Niessen et al.’s estimated data for their thermodynamic assessment, which also induced wrong assessment results. The optimized model parameters for the intermetallic compounds and liquid solution are listed in Table 3. All the invariant reactions in the Co–Nd system calculated using the present model parameters are compared with the experimental data in Table 1. 3.2. The Cu–Nd system 3.2.1. Phase diagram data There is a total of 10 equilibrium phases in the Cu–Nd system: liquid, fcc Cu, dhcp Nd, bcc Nd, and intermetallic compounds

Fig. 7. (a) Partial and (b) integral enthalpies of mixing of Nd(l) and Cu(l) in liquid Cu–Nd alloy at (a) 1523 K and (b) 1473 K.

34

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

CuNd, Cu2Nd, Cu7Nd2, Cu4Nd, Cu5Nd, and Cu6Nd. Extensive phase diagram study was carried out by Carnasciali et al. [44] and Zheng and Nong [45] using metallography, DTA, and XRD. They determined the phase diagram of the entire Cu–Nd system. The DTA data of the two studies are, however, rather different in the liquidii of Nd, Cu2Nd, Cu4Nd, Cu5Nd, and Cu6Nd. In particular, the congruent melting temperature of Cu6Nd and the liquidii reported by Zheng and Nong is about 40 K higher than that of Carnasciali et al. Later, Laks et al. [46] determined the phase diagram of the Cu-rich side of the system using DTA and classical equilibration/quenching technique followed by SEM–EDS analysis. They confirmed the melting temperatures of Cu6Nd and Cu2Nd by Carnasciali et al. Gu and Song [47] reported, based on DTA and XRD phase determination, similar melting temperature for Cu6Nd and liquidii as Carnasciali et al. Efimov et al. [48] investigated the phase diagram between 0 and 20 at% Nd based on DTA, EPMA, microstructural and X-ray phase analysis data. However, they did not report the existence of Cu6Nd and found a eutectic between Cu and Cu5Nd at 1156 K and 90.3 at% Cu. While the existence of the compounds Cu6Nd, Cu5Nd, Cu4Nd, Cu2Nd and CuNd are well ascertained by several investigators [44–47], the presence of Cu7Nd2 is only reported by Carnasciali et al. According to them, this compound is stable in the temperature range between 1058 K and 1098 K. The various invariant reactions reported for the Cu–Nd system are summarized in Table 4. The experimental phase diagram data are plotted in Fig. 5. As can be seen in Table 4 and Fig. 5, there are large discrepancies between the experimental data for this system. Compared to the usage of very high purity starting materials (99.9% or higher) of Nd and Cu by Carnasciali et al. and Laks et al., lower grade starting materials were used by Zheng and Nong, which can explain the rather scattered liquidus data and transition temperatures of peritectic and eutectic reactions compared with other studies. Regarding the mutual solubility of Nd and Cu, Carnasciali et al. reported negligible solid solubility of Nd in Cu and of Cu in a-Nd (less than 0.5 at% Cu) from XRD data. Zheng and Nong reported no mutual solubility between Nd and Cu in the system. No homogeneity range of the intermetallic phases has been reported.

3.2.2. Thermodynamic data Contrary to the phase diagram data, experimental thermodynamic data on the intermetallic compounds are scarce. By means of direct synthesis calorimetry, Fitzner and Kleppa [49] determined the enthalpy of formation of Cu2Nd and Cu6Nd. No other enthalpies of formation and no heat capacities for the intermetallic compounds have been ascertained by experiments to date. First principal calculations have been performed by Wang et al. [9] to estimate the enthalpy of formation of CuNd, Cu2Nd, Cu5Nd and Cu6Nd at 298 K. The calculated results for Cu2Nd and Cu6Nd are slightly more negative than the experimental data of Fitzner and Kleppa, as can be seen in Fig. 6. Carnasciali et al. [44] determined the heat of transformation from a-CuNd to b-CuNd to be 1.7 kJ mol  1 at about 743 K using DTA technique. The only compound with magnetic transition in the Cu–Nd system is CuNd. Chen [50] has performed AC electrical

Table 5 Optimized model parameters for the Cu–Nd system (J mol  1 or J mol  1 K  1). Phase

Thermodynamic parameters

Liquid

Dg NdCu ¼ 19246:4 þ ð10501:84 þ 4:6024TÞX NdNd

Cu6Nd

¼ 87500, So298 ¼ 269:986 Cp ¼Cp(Nd(dhcp)) þ 6Cp(Cu(fcc)) DHo298 ¼ 81600, So298 ¼ 236:836 Cp ¼Cp(Nd(dhcp)) þ 5Cp(Cu(fcc)) DHo298 ¼ 74400, So298 ¼ 203:686 Cp ¼Cp(Nd(dhcp)) þ 4Cp(Cu(fcc)) DHo298 ¼ 107091:8, So298 ¼ 405 Cp ¼2Cp(Nd(dhcp)) þ 7Cp(Cu(fcc)) DHo298 ¼ 56000, So298 ¼ 137:386 Cp ¼Cp(Nd(dhcp)) þ 2Cp(Cu(fcc)) DHo298 ¼ 33900, So298 ¼ 102:236 Cp ¼Cp(Nd(dhcp)) þ Cp(Cu(fcc))

6276X CuCu þ 4309:52X 3NdNd 4184X 3CuCu

DHo298

Cu5Nd Cu4Nd Cu7Nd2 Cu2Nd

a-CuNd

-b DHatrans ¼ 2500, T ¼ 743K

b-CuNd

50 Qi et al. (1989): calorimetry

45

88.4 at.% Cu

Enthalpy Increment (kJ/mol)

85.7 at.% Cu

40

71.1 at.% Cu 66.7 at.% Cu 60.2 at.% Cu

35

88.4 at.% Cu 66.7 at.% Cu 71.1 at.% Cu

85.7 at.% Cu

30 60.2 at.% Cu

25 20 15 10 800

900

1000 1100 Temperature (K)

1200

1300

Fig. 8. Calculated and experimental enthalpy increments as a function of temperature of Cu–Nd mixtures containing 60.2, 66.7, 71.1, 85.7 and 88.4 at% Cu.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

resistivity and DC magnetization measurements and reported the Ne´el temperature for CuNd to be 10 K. Fitzner and Kleppa [49] measured the integral enthalpy of mixing of the liquid at 1473 K using direct synthesis calorimetry. Turchanin et al. [51] measured the partial enthalpy of mixing of Cu and Nd in Nd- and Cu-rich regions, respectively, at 1523 K by a high temperature isoperibolic calorimeter and reported the estimated integral enthalpy of mixing of the liquid at 1523 K. The enthalpy data are plotted in Fig. 7. The calculated enthalpy of mixing by Turchanin et al. is slightly more positive than the experimental data of Fitzner and Kleppa, but the results are in reasonable agreement. The minimum of the integral enthalpy of mixing is about  15 kJ mol  1 at about 65 at% Cu. Qi et al. [52] measured the change in heat content of five Cu–Nd alloys at the Cu-rich region from room temperature to temperatures in the range between 850 K and 1250 K by using a drop calorimeter. The experimental heat content data of Qi et al. are plotted in Fig. 8.

3.2.3. Thermodynamic optimization Okamoto [53] reviewed the experimental data of the Cu–Nd system until 1998. A number of thermodynamic assessments on the system have been performed [9–14]. In all the previous assessments, the liquid solution was modeled using the Bragg–Williams random mixing model with many model parameters. Wang [11] used nine model parameters for the liquid solution, including three linear temperature-dependent parameters (entropy parameters; T) and three excess heat capacity parameters (TlnT). The calculated phase diagrams by Zhuang et al. [13] and Lysenko [14] are not very accurate in comparison with experimental data. The assessments of Du and Clavaguera [12] and Zhuang et al. [13] used large positive temperature-dependent parameters, which induce an inverse miscibility gap above about 1400 K in Du and Clavaguera’s optimized phase diagram [12]. In order to resolve this shortcoming of the previous thermodynamic optimizations, Wang et al. [9] intentionally added two excess heat capacity parameters (TlnT) along with two linear temperature-dependent parameters for the liquid solution, which becomes similar to the previous assessment of Wang [11]. However, these TlnT parameters for the liquid solution are

35

rather artificial parameters for the Bragg–Williams random mixing model to prevent an inverse miscibility gap in the liquid solution having a strong short-range ordering behavior. This problem of inverse miscibility gap can easily be resolved with the Modified Quasichemical Model [18,19], which is used in the present study. As seen in Fig. 7(a), the partial enthalpies of Cu and Nd calculated from other assessments [10,13] are not quite well reproducing the experimental data. The enthalpies of formation of the compounds by Subramanian and Laughlin [10] deviate significantly from the experimental data by Fitzner and Kleppa [49] in Fig. 6. In the present thermodynamic optimization, the model parameters of the liquid solution were first roughly fixed with the enthalpy of mixing data in Fig. 7. In order to reproduce the minima of the enthalpy of mixing, the coordination numbers ZNdCu and ZCuNd in the Modified Quasichemical Model [18,19] are fixed to be 6 and 3, respectively. All the reported intermetallic compounds, including Cu7Nd2, were considered in the optimization. As no heat capacity data of the intermetallic compounds have been determined, the heat capacities of all the compounds were estimated using the Neumann–Kopp rule. The entropies at 298 K (So298 ) of the

Table 6 Invariant reactions in the Nd–Ni system. Invariant reaction

T (K) (at% Ni)

L ¼Nd2Ni17 þNi L þNdNi5 ¼ Nd2Ni17 Nd2Ni17 ¼NdNi5 þ Ni L ¼NdNi5 L þNdNi5 ¼ Nd2Ni7 L þNd2Ni7 ¼NdNi3 L þNdNi3 ¼ NdNi2 L ¼NdNi2 þ NdNi L ¼NdNi L ¼NdNi þ Nd7Ni3 L þNd3Ni¼ Nd7Ni3 L ¼Nd3Ni L ¼Nd3Niþ dhcp Nd

Present work

Pan and Zheng [62]

Huang et al. [16]

1555.2 (92.6) 1577.1 1503.6 1677.6 1465.2 1340.8 1234.8 1044.0 (56.1) 1090.6 867.3 (32.1) 868.6 891.4 874.1 (19.3)

1563 (90) 1573 1523 1693 1407 1303 1213 993 1053 813 ( 35) 838 863 843 ( 19)

1558 1559 1555 1678 1466 1341 1237 1046 1092 858 871 891 884

1900

Pan & Zheng (1985): XRD, DTA

1678

Qi et al. (1989): quenching, EPMA, OM, ICP Huang et al. (2005): DTA, DSC

1700

1577

Nd2Ni17

1465

1500

1100

1235 1128

1089 1044

900

891

874

867

300 0.0 Nd

0.1

0.2

0.3

0.4

0.5 0.6 mole fraction

0.7

Fig. 9. Calculated binary phase diagram of the Nd–Ni system.

NdNi5

NdNi3 Nd2Ni7

NdNi2

NdNi

500

Nd7Ni3

700

Nd3Ni

Temperature (K)

1341

1300

1555 1504

0.8

0.9

1.0 Ni

36

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

intermetallic compounds were firstly approximated from the summation of So298 of their stoichiometric amounts of fcc-Cu and dhcpNd and changed slightly to reproduce the phase diagram. The enthalpy of formation at 298 K (DHo298 ) of Cu2Nd and Cu6Nd were fixed using the experimental data by Fitzner and Kleppa [49]. The enthalpies of formation calculated with the first principles calculations by Wang et al. [9] were used to estimate the DHo298 of a-CuNd and Cu5Nd with the possibility that the actual DHo298 of the compounds are slightly more positive than the calculated values, as witnessed for Cu2Nd and Cu6Nd. In order to reproduce the phase diagram, the thermodynamic model parameters of the compounds and liquid solution were optimized all together. The experimental phase diagram data by

Carnasciali et al. [44] and Laks et al. [46] were considered more reliable in the present optimization. The results of the optimization are in good agreement with the experimental data as can be seen in Figs. 5–8. In the present optimization, a-CuNd and b-CuNd are assumed to have the same heat capacity function. The adopted transition temperature is 743 K and the optimized heat of transformation is 2.5 kJ mol  1, which is in fair agreement with the value of 1.7 kJ mol  1 measured by Carnasciali et al. [44]. In order to reproduce the thermal stability of Cu7Nd2 (forming peritectically at 1098 K and decomposing eutectoidally at 1058 K [44]), DHo298 and So298 of the compound were adjusted. The calculated heat contents for the Cu–Ni alloys were compared with experimental data by Qi et al. [52] in Fig. 8. Although the

100 90

Heat capacity of NdNi2 (J/mol-K)

80 70 60 50 40 30 Wallace et al. (1970): calorimetry

20 10 0

0

100

200

300 Temperature (K)

400

500

600

200 180

Heat capacity of NdNi5 (J/mol-K)

160 140 120 100 80 60 40

Marzouk et al. (1973): calorimetry Radwanski et al. (1994): adiabatic calorimetry

20 0

0

75

150

225

300 375 Temperature (K)

450

Fig. 10. Optimized heat capacity of (a) NdNi2 and (b) NdNi5.

525

600

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

melting temperatures of the samples measured by Qi et al. [52] are about 25 K higher than those in the phase diagram proposed by Carnasciali et al. [44] and Laks et al. [46], the calculated enthalpy changes (HT–H298 K) are in fair agreement with the experimental data. All the optimized thermodynamic properties of the liquid solution and compounds are available in Table 5. All the invariant reactions in the Cu–Nd system calculated using the present model parameters are compared with the experimental data in Table 4. 3.3. The Nd–Ni system 3.3.1. Phase diagram data Fig. 9 shows the phase diagram of the Nd–Ni system. There is a total of 12 equilibrium phases in the Nd–Ni system: liquid, fcc Ni, dhcp Nd, bcc Nd, and eight intermetallic compounds: Nd3Ni, Nd7Ni3, NdNi, NdNi2, NdNi3, Nd2Ni7, NdNi5, and Nd2Ni17 [54–61]. Pan and Zheng [62] mapped the entire phase diagram by means of DTA and XRD. Later, Qi et al. [63] performed classical quenching experiments followed by EPMA to determine the liquidii of NdNi5, Nd2Ni7 and NdNi3. Huang et al. [16] focused on the invariant reactions of several intermetallic phases and in-between alloys using both DSC and DTA techniques to validate the results of Pan and Zheng [62]. The measured data are in fair agreement with the results of Pan and Zheng, but in some cases the discrepancy is more than 40 K. The compound Nd2Ni17 was found to exist over a very limited temperature range. Virkar and Raman [60] and Pan and Zheng [62] determined the stability range between 1523 K and 1573 K, whereas the results of Huang et al. [16] suggested a much narrower temperature range between 1555 K and 1559 K. Pan and Zheng [62] reported no detectable solubility of Ni in Nd or of Nd in Ni based on their XRD pattern analysis. All the experimental invariant reactions are summarized in Table 6.

temperature heat capacities for NdNi2 and NdNi5, respectively. The entropy at 298 K (So298 ) calculated from these data are 135.65 and 233.54 J mol  1 K  1, respectively. The entropy values are very similar (about 1.48 and 2.66 J mol  1 K  1 difference, respectively) to the summed So298 of stoichiometric amounts of Nd and Ni, confirming the applicability of the Neumann–Kopp rule. The heat capacity of NdNi2 and NdNi5 are plotted in Fig. 10. Guo and Kleppa [66,67] determined the enthalpy of formation of NdNi5 at 298 K by direct synthesis calorimetry and the enthalpy of formation of NdNi using the same method a few years later. The experimental data are plotted in Fig. 11.

3.3.3. Thermodynamic optimization The Nd–Ni system was previously reviewed by Okamoto [68,69] and thermodynamic assessment of this system was

Table 7 Optimized model parameters for the Nd–Ni system (J mol  1 or J mol  1 K  1). Phase

Thermodynamic parameters

Liquid Nd3Ni

Dg NdNi ¼ 334725020:8X NdNd 13388:8X NiNi DHo298 ¼ 69420, So298 ¼ 246:281

Nd7Ni3

DHo298 ¼ 206900, So298 ¼ 590

Cp ¼ 3Cp(Nd(dhcp)) þ Cp(Ni(fcc))

NdNi NdNi2 NdNi3 Nd2Ni7 NdNi5

3.3.2. Thermodynamic data No thermodynamic data is available for the liquid solution. Wallace et al. [64] and Marzouk et al. [65] measured the low-

37

Nd2Ni17

Cp ¼ 7Cp(Nd(dhcp)) þ 3Cp(Ni(fcc)) DHo298 ¼ 61400, So298 ¼ 104:7 Cp ¼ Cp(Nd(dhcp)) þ Cp(Ni(fcc)) DHo298 ¼ 96500, So298 ¼ 137:13 Cp ¼ Cp(Nd(dhcp)) þ 2Cp(Ni(fcc)) DHo298 ¼ 122000, So298 ¼ 167:58 Cp ¼ Cp(Nd(dhcp)) þ 3Cp(Ni(fcc)) DHo298 ¼ 265000, So298 ¼ 366:2 Cp ¼ 2Cp(Nd(dhcp)) þ 7Cp(Ni(fcc)) DHo298 ¼ 151200, So298 ¼ 233:541 Cp ¼ Cp(Nd(dhcp)) þ 5Cp(Ni(fcc)) DHo298 ¼ 166616, So298 ¼ 780 Cp ¼ 2Cp(Nd(dhcp)) þ 17Cp(Ni(fcc))

Fig. 11. Calculated enthalpies of formation at 298 K in the Nd–Ni system compared with experimental and predicted values.

38

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

previously performed by Du and Clavaguera [15] and Huang et al. [16] using the Bragg–Williams random mixing model for the liquid solution. In Du and Clavaguera’s assessment [15], the liquidus of NdNi5, Nd2Ni7 and NdNi3 determined by Qi et al. [63] was not well described. Their optimized DHo298 of NdNi was about 10 kJ g-atom  1 more negative than the experimental value by Guo and Kleppa [66,67]. Unfortunately, our attempt to reproduce the Gibbs energy of their liquid solution failed due to a misprint in the numbers given in their article. However, an inverse miscibility gap in the liquid is expected to appear around 2500 K due to the relatively large temperature-dependent parameters for the liquid solution. Huang et al.’s assessment [16] showed an even more significant deviation of the DHo298 of NdNi from the experimental data. Their evaluated value is  46.9 kJ gatom  1 compared to the experimental value of 25 kJ g-atom  1

by Guo and Kleppa [67]. Their calculated liquidus of Nd also largely deviated from the experimental data of Pan and Zheng [62]. Due to the relatively large temperature-dependent parameters for the liquid solution, an inverse miscibility gap was found in the liquid solution at around 8000 K. In the present optimization, the thermodynamic properties of the solid compounds NdNi5 and NdNi were firstly roughly fixed based on the available experimental data. In the case of NdNi5, both DHo298 and So298 were fixed from the experimental data of Guo and Kleppa [66] and Marzouk et al. [65], respectively. For NdNi, DHo298 was fixed by the experimental data of Guo and Kleppa [67] and So298 was obtained from the summation of the So298 of its stoichiometric amount of Ni and Nd. The heat capacity of both compounds was estimated by the Neumann–Kopp rule. Then, the model parameters of the liquid solution were roughly optimized

0 -10

Partial enthalpy of mixing (kJ/mol)

-20 -30 -40 -50 -60 -70 -80 -90 -100 -110 T = 1800 K

-120 -130 -140 -150 0.0 Nd

0.1

0.2

0.3

0.4

0.5 0.6 mole fraction

0.7

0.8

0.9

1.0 Ni

0.9

1.0 Ni

0 T = 1800 K

Enthalpy of mixing (kJ/mol)

-5 -10 -15 -20 -25 -30 -35 -40 0.0 Nd

0.1

0.2

0.3

0.4

0.5 0.6 mole fraction

0.7

0.8

Fig. 12. (a) Partial and (b) integral enthalpies of mixing of Nd(l) and Ni(l) in liquid Nd–Ni alloy at 1800 K.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

to reproduce the liquidus of NdNi5, NdNi and the two terminal elements (Nd and Ni). The final optimization was done with the consideration of all compounds together. The So298 of the compounds Nd3Ni, Nd7Ni3, NdNi2, NdNi3, Nd2Ni7 and Nd2Ni17 were firstly estimated as the sum of the So298 of its stoichiometric amount of Ni and Nd, then they were slightly modified to reproduce the phase diagram along with the optimization of DHo298 . The heat capacities of the compounds were all estimated by the Neumann–Kopp rule. The calculated phase diagram and the enthalpy of formation of the compounds at 298 K are plotted in Figs. 9 and 11 along with the experimental data. The more recent experimental phase diagram data determined by Huang et al. [16] were weighted

39

more in the present optimization rather than those by Pan and Zheng [62] and Qi et al. [63]. As can be seen in Fig. 9, the calculated phase diagram is in good agreement with experimental data. According to Pan and Zheng [62], the Nd7Ni3 compound shows a congruent melting behavior, while the assessed phase diagram by Huang et al. [16] indicated possible incongruent melting of NdNi3 from their DTA results near the Nd7Ni3 composition. In the present optimization, it is found that Nd7Ni3 melts peritectically. Regarding the stability of the Nd2Ni17 compound, the temperature range given by Huang et al. [16] is extremely narrow (only 4 K) and might only reflect the eutectic reaction between that compound and fcc Ni. In the present assessment, the stability range of Nd2Ni17 determined by Pan and Zheng [62]

8 4

Nd-Mn

Enthalpy of mixing (kJ/mol)

0

Nd-Fe

-4 -8 -12

Nd-Co

-16

Nd-Cu

-20 -24 -28 -32

Nd-Ni

-36 -40 0.0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Mole fraction of Co, Cu, Ni, Mn and Fe

0.8

0.9

1.0

0.9

1.0

1600

e Nd-F -Co Nd

-N

1000

Nd

Temperature (C)

1200

i

1400

n

Nd-M

Nd-C

u

800 600 400 200 0 0.0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Mole fraction of Co, Cu, Ni, Mn and Fe

0.8

Fig. 13. (a) Enthalpy of mixing at 1800 K and (b) liquidus curves of the binary systems Nd–X, where X ¼ Mn, Fe, Co, Ni and Cu.

40

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

appeared more realistic. The calculated stability range based on the present optimization is slightly larger than the experimental data to reproduce the eutectic temperature. The calculated enthalpy of formation at 298 K for the system is presented in Fig. 11 along with experimental data of Guo and Kleppa [66,67] and the results from other assessments [15,16]. Clearly, the DHo298 of NdNi calculated from the present study is much closer to the experimental data by Guo and Kleppa [67]. The model parameters are listed in Table 7. It is found that the phase diagram in Fig. 9 and thermodynamic data of solid phases in Fig. 11 were better reproduced with the use of the coordination numbers ZNdNi ¼6 and ZNiNd ¼4 in the Modified Quasichemical Model [18,19]. This means that the short range ordering in the liquid solution is occurring at about 60 at% Ni. When the coordination number ZNiNd is set at 3 or 6 instead of 4, it became more difficult to reproduce the DHo298 of NdNi. The calculated integral enthalpy of mixing and partial enthalpies of the liquid Nd–Ni solution are plotted in Fig. 12.

4. Trend in the Nd–X system (X ¼Mn, Fe, Co, Ni and Cu) Recently, critical evaluations and optimizations of the Mn–Nd and Fe–Nd binary systems were performed by the present authors [70,71] using the Modified Quasichemical Model for the liquid solution. Accurate optimizations of the binary systems between Nd and the transition metals from Mn to Cu are therefore available. Fig. 13 presents the changes in the enthalpy of mixing at 1800 K (Fig. 13(a)) and the liquidus curves (Fig. 13(b)) for the binary systems Nd–X, where X¼Mn, Fe, Co, Ni and Cu. The liquid enthalpy of mixing between Nd and transition metals become more negative in the following order: Mn, Fe, Co, Cu and Ni. Also, the maximum ordering composition in the liquid solution is shifting toward the transition metal side following the same order. In the phase diagram, as can be seen in Fig. 13(b), the number of compounds with congruent melting behavior increases in the same order: none in the Mn–Nd and Fe–Nd systems, two in the Co–Nd and Cu–Nd systems and three in the Nd–Ni system. The reason for this trend is not clear. Thermochemical and/or electronic properties of these elements are possibly at the origin of the changes observed in the phase diagrams and thermodynamic properties. However, the Modified Quasichemical Model, where the maximum ordering composition can be flexibly changed for each binary system, can easily reproduce the thermodynamic properties of the liquid solution as shown in the present study.

5. Summary A complete critical evaluation of all available phase diagram and thermodynamic data for the Co–Nd, Cu–Nd and Nd–Ni systems has been carried out, and a database of optimized model parameters has been developed. The Gibbs energies of many binary compounds were properly described based on all available thermodynamic properties data with the help of phase diagrams. The thermodynamic properties of the liquid solution are easily reproduced with the Modified Quasichemical Model. Experimental thermodynamic property data for stoichiometric compounds and liquid solutions which were not considered in previous optimizations were taken into account and successfully reproduced. Investigation of the trend in the binary systems Nd–X, where X ¼Mn, Fe, Co, Ni and Cu, revealed more negative enthalpy of mixing of the liquid solution, a shift of the maximum ordering composition in the liquid toward the transition metal side and stronger compounds in the order: Mn, Fe, Co, Cu and Ni.

Acknowledgments The authors wish to express their gratitude to the Korean Institute of Technology (KITECH) South Korea and the Gerald Hatch Faculty Fellowship (I.-H. Jung) from McGill University for the financial support.

Appendix. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/http://dx.doi.org/10.1016/j. calphad.2012.12.003.

References [1] K.J. Strnat, Rare-earth magnets in present production and development, J. Magn. Magn. Mater. 7 (1978) 351–360. [2] M. Sagawa, S. Fujimura, N. Togawa, H. Yamamoto, Y. Matsuura, New material for permanent magnets on a base neodymium and iron, Sumitomo Tokushu Kinzoku Giho 8 (1985) 17–23. [3] K.H.J. Buschow, New permanent magnet materials, Mater. Sci. Rep. 1 (1986) 1–63. [4] J.M.D. Coey, Permanent magnet applications, J. Magn. Magn. Mater. 248 (2002) 441–456. [5] H.H. Man, H.C. Man, L.K. Leung, Corrosion protection of NdFeB magnets by surface coatings - Part 2: Electrochemical behaviour in various solutions, J. Magn. Magn. Mater. 152 (1996) 47–53. [6] J. Jakubowicz, M. Giersig, Structure and magnetic properties of Nd2(Fe,Co,Al,Cr)14B/a-Fe nanocomposite magnets, J. Alloys Compd. 349 (2003) 311–315. [7] A. Ali, A. Ahmad, K.M. Deen, Multilayer ceramic coating for impeding corrosion of sintered NdFeB magnets, J. Rare Earths 27 (2009) 1003–1007. [8] X.B. Liu, Z.M. Du, C.P. Guo, C.R. Li, Thermodynamic assessment of the Co-Nd system, J. Alloys Compd. 439 (2007) 97–102. [9] P. Wang, L. Zhou, Y. Du, H. Xu, S. Liu, L. Chen, Y. Ouyang, Thermodynamic optimization of the Cu-Nd system, J. Alloys Compd. 509 (2011) 2679–2683. [10] P.R. Subramanian, D.E. Laughlin, The Cu–Nd (Copper–Neodymium) system, Bull. Alloy Phase Diagrams 9 (1988) 362–369. [11] J.X. Wang, Evaluation of the thermodynamics for copper-praseodymium, copper-neodymium systems, CALPHAD 16 (1992) 87–92. [12] Y. Du, N. Clavaguera, Thermodynamic assessment of the Cu–Nd system, Scr. Mater. 34 (1996) 1609–1613. [13] W. Zhuang, Z.-Y. Qiao, S. Wei, J. Shen, Thermodynamic evaluation of the Cu–R (R: Ce, Pr, Nd, Sm) binary systems, J. Phase Equilibria 17 (1996) 508–521. [14] V.A. Lysenko, Thermodynamic calculations of phase equilibria in the bariumcopper-neodymium system, Zh. Fiz. Khim. 77 (2003) 1556–1560. [15] Y. Du, N. Clavaguera, Thermodynamic calculation of the Nd–Ni system, CALPHAD 20 (1996) 289–296. [16] M. Huang, R.W. McCallum, T.A. Lograsso, Experimental investigation and thermodynamic modeling of the Nd–Ni system, J. Alloys Compd. 398 (2005) 127–132. [17] C.W. Bale, E. Belisle, P. Chartrand, S.A. Decterov, G. Eriksson, K. Hack, I.H. Jung, Y.B. Kang, J. Melancon, A.D. Pelton, C. Robelin, S. Petersen, FactSage thermochemical software and databases - recent developments, CALPHAD 33 (2009) 295–311. [18] A.D. Pelton, S.A. Degterov, G. Eriksson, C. Robelin, Y. Dessureault, The modified quasichemical model I—Binary solutions, Metall. Mater. Trans. B 31 (2000) 651–659. [19] A.D. Pelton, P. Chartrand, The modified quasi-chemical model: Part II. Multicomponent solutions, Metall. Mater. Trans. A 32 (2001) 1355–1360. [20] I.H. Jung, D.H. Kang, W.J. Park, N.J. Kim, S. Ahn, Thermodynamic modeling of the Mg–Si–Sn system, CALPHAD 31 (2007) 192–200. [21] D. Nassyrov, I.H. Jung, Thermodynamic modeling of the Mg–Ge–Pb system, CALPHAD 33 (2009) 521–529. [22] A.D. Pelton, M. Blander, Thermodynamic analysis of ordered liquid solutions by a modified quasi-chemical approach—application to silicate slags, Metall. Trans. B 17 (1986) 805–815. [23] P. Wu, G. Eriksson, A.D. Pelton, M. Blander, Prediction of the thermodynamic properties and phase-diagrams of silicate systems—evaluation of the FeO– MgO–SiO2 system, ISIJ Int. 33 (1993) 26–35. [24] A.D. Pelton, M. Blander, Computer-assisted analysis of the thermodynamic properties and phase diagrams of slags, in: Proceedins of the Second International Symposium on Metallurgical Slags and Fluxes, Lake Tahoe, NV, Metallurgical Society of AIME, 1984, pp. 281–294. [25] A.D. Pelton, Y.B. Kang, Modeling short-range ordering in solutions, Int. J. Mat. Res. 98 (2007) 907–917. [26] A.T. Dinsdale, SGTE data for pure elements, CALPHAD 15 (1991) 317–425. [27] G. Inden, in: Project meeting CALPHAD V, Dusseldorf, Germany, Max-PlanckInstitute, Eisenforschung, G.m.b.H., 1976, p. 111.

A. Hussain et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 41 (2013) 26–41

[28] M. Hillert, M. Jarl, A model for alloying in ferromagnetic metals, CALPHAD 2 (1978) 227–238. [29] A.E. Ray, A.T. Biermann, R.S. Harmer, J.E. Davison, Revised phase diagrams for the binary systems cerium–cobalt, praseodymium–cobalt, and neodymium– cobalt, in: Engl (Ed.), Cobalt, 1973, pp. 103–106. [30] A.E. Ray, Review of the binary rare earth-cobalt alloy systems, in: Engl (Ed.), Cobalt, 1974, pp. 13–20. [31] C.H. Wu, Y.C. Chuang, X.M. Jin, X.H. Guan, Phase diagram of the cobalt-rich portion of the neodymium-cobalt binary system, Z. Metallkd. 83 (1992) 162–164. [32] J.M. Moreau, D. Paccard, The monoclinic crystal structure of rare earth-cobalt R5Co2 (R ¼ Pr, Nd, Sm) with the manganese carbide (Mn5C2) structure type, Acta Cryst. B32 (1976) 1654–1657. [33] K.H.J. Buschow, Intermetallic compounds of rare earth and 3d transition metals, Rep. Prog. Phys. 40 (1977) 1179–1256. [34] Y. Fasasi, E.I. Obiajunwa, Thermomagnetic properties of Nd–Co magnetic alloy, Mater. Eng. (Modena, Italy) 14 (2003) 181–188. [35] I.V. Nikolaenko, M.A. Turchanin, Heats of mixing of cobalt with neodymium, samarium, and gadolinium, Rasplavy (1989) 77–79. [36] C. Deenadas, R.S. Craig, N. Marzouk, W.E. Wallace, The heat capacity of PrCo2 and NdCo2 between 8 and 300 K, J. Solid State Chem. 4 (1972) 1–3. [37] A.K. Niessen, FR de Boer, R. Boom, PF de Chatel, W.C.M. Mattens, A.R. Miedema, Model predictions for the enthalpy of formation of transition metal alloys II, CALPHAD 7 (1983) 51–70. [38] H. Okamoto, Co–-Nd (cobalt–neodymium), J. Phase Equilibria 14 (1993) 122–124. [39] A.D. Pelton, On the slopes of phase boundaries, Metall. Trans. A 19A (1988) 1819–1825. [40] S.S. Deodhar, P.J. Ficalora, A study of the reaction kinetics for the formation of rare earth-transition metal laves compounds, Metall. Trans. A 6A (1975) 1909–1914. [41] S. Bar, H.J. Schaller, Thermodynamic properties of cobalt–praseodymium alloys, Thermochim. Acta 314 (1998) 131–136. [42] F. Meyer-Liautaud, C.H. Allibert, R. Castanet, Enthalpies of formation of samarium-cobalt alloys in the composition range 10–22 at% samarium, J. Less-Common Met. 127 (1987) 243–250. [43] A.L. Shilov, Heats of formation of intermetallic compounds, Zh. Fiz. Khim. 61 (1987) 1384–1385. [44] M.M. Carnasciali, G.A. Costa, E.A. Franceschi, Phase equilibriums in the neodymium–copper system, J. Less-Common Met. 92 (1983) 97–103. [45] J.X. Zheng, L.Q. Nong, Phase diagram of the binary neodymium–copper alloy system, Wuli. Xuebao. (Acta Phys. Sin.) 32 (1983) 1449–1454. [46] C. Laks, J. Pelleg, L. Zevin, Notes on the neodymium–copper system, J. LessCommon Met. 102 (1984) 23–28. [47] H.Z. Gu, J.Q. Song, Neodymium–copper system, 26, Ziran Kexueban, Beijing Daxue Xuebao, 1990, pp. 136–140. [48] V.V. Efimov, L.A. Ryabtsev, E.V. Lysova, T.M. Frolova, Phase diagram and properties of copper-neodymium alloys, Izv Vyssh Uchebn Zaved, Tsvetn. Metall. (1988) 85–90. [49] K. Fitzner, O.J. Kleppa, thermochemistry of binary alloys of transition metals: the systems Cu–Ce, Me–Pr, and Me–Nd (Me ¼Cu, Ag, Au), Metall. Mater. Trans. A 25A (1994) 1495–1500. [50] J.W. Chen, Electrical and magnetic properties of RCu (R ¼La, Ce, Pr, and Nd) systems, J. Magn. Magn. Mater. 137 (1994) 134–138.

41

[51] M.A. Turchanin IV, Nikolaenko, G.I. Batalin, Calorimetric study of thermodynamic properties of molten alloys of copper with praseodymium and neodymium, Rasplavy 2 (1988) 118–119. [52] G. Qi, K. Itagaki, A. Yazawa, High-temperature heat content measurements of copper–RE (RE ¼yttrium, lanthanum, cerium, praseodymium, neodymium) binary systems, Mater. Trans., JIM 30 (1989) 273–282. [53] H. Okamoto, Cu–Nd (Copper–Neodymium), J. Phase Equilibria 19 (1998) 181. [54] J.H. Wernick, S. Geller, Rare earth compounds with the MgCu2 structure, Trans. Metall. Soc. AIME 218 (1960) 866–868. [55] S.C. Abrahams, J.L. Bernstein, R.C. Sherwood, J.H. Wernick, H.J. Williams, The crystal structure and magnetic properties of the rare-earth nickel (RNi) compounds, Phys. Chem. Solids 25 (1964) 1069–1080. [56] A.E. Dwight, R.A. Conner Jr., J.W. Downey, Equiatomic compounds of the transition and lanthanide elements with Rh, Ir, Ni, and Pt, Acta Crystallogr. 18 (1965) 835–839. [57] R. Lemaire, D. Paccard, Crystallographic structure of rare earth intermetallic compounds of the type T3Ni, where T is a rare earth or yttrium atom, Bull. Soc. Fr. Miner. Cristallogr. 90 (1967) 311–315. [58] D. Paccard, R. Pauthenet, Crystallographic and magnetic properties of alloys with the formula TNi3, where T is yttrium or a rare earth metal, C. R. Acad. Sci., Ser. A B 264B (1967) 1056–1059. [59] R.C. Mansey, G.V. Raynor, I.R. Harris, Rare-earth intermediate phases. V. The cubic Laves phases formed by rare-earth metals with iron and nickel, J. LessCommon Met. 14 (1968) 329–336. [60] A.V. Virkar, A. Raman, Crystal structures of AB3 and A2B7 rare earth-nickel phases, J. Less-Common Met. 18 (1969) 59–66. [61] G.L. Olcese, Crystal structure and magnetic properties of some 7:3 binary phases between lanthanides and metals of the 8th Group, J. Less-Common Met. 33 (1973) 71–81. [62] Y. Pan, J. Zheng, Phase diagram of the neodymium–nickel binary system, Wuli Xuebao 34 (1985) 384–389. [63] G. Qi, Z. Li, K. Itagaki, A. Yazawa, High-temperature phase relations in nickelrare earth (lanthanum, cerium, praseodymium, neodymium) binary and ternary alloy systems, Mater. Trans., JIM 30 (1989) 583–593. [64] W.E. Wallace, R.S. Craig, A. Thompson, C. Deenadas, M. Dixon, M. Aoyagi, N. Marzouk, Heat capacity studies of intermetallic compounds containing rare earth elements, Colloq. Int. Cent. Nat. Rech. Sci. 180 (1970) 427–441. [65] N. Marzouk, R.S. Craig, W.E. Wallace, Heat capacity and electrical resistivity of some lanthanide-nickel (LnNi5) compounds between 5 and 300 1K, J. Phys. Chem. Solids 34 (1973) 15–21. [66] Q. Guo, O.J. Kleppa, Standard enthalpies of formation of neodymium alloys, NdþMe (Me  Ni, Ru, Rh, Pd, Ir, Pt), by high-temperature direct synthesis calorimetry, Metall. Mater. Trans. B 26B (1995) 275–279. [67] Q. Guo, O.J. Kleppa, Standard enthalpies of formation of CeNi5 and of RENi (RE¼ Ce, Pr, Nd, Sm, Gd, Tb, Ho, Tm and Lu), determined by high-temperature direct synthesis calorimetry, J. Alloys Compd. 270 (1998) 212–217. [68] H. Okamoto, Nd–Ni (Neodymium–Nickel), J. Phase Equilibria 13 (1992) 218–220. [69] H. Okamoto, Nd–Ni (Neodymium–Nickel), J. Phase Equilibria 19 (1998) 290. [70] J. Kim, I.H. Jung, Critical systematic evaluation and thermodynamic optimization of the Mn–RE system: RE¼ La, Ce, Pr, Nd and Sm, J. Alloys Compd. 525 (2012) 191–201. [71] M.A. Van Ende, I.H. Jung, Critical thermodynamic evaluation and optimization of the Fe–B, Fe–Nd, B–Nd and Nd–Fe–B systems, J. Alloys Compd. 548 (2013) 133–154.