Reassessment of the Ni–V system and a new thermodynamic modeling of the Mo–Ni–V system

Accepted Manuscript Title: Reassessment of the Ni–V system and a new thermodynamic modeling of the Mo–Ni–V system Authors: Yafei Pan, Yong Du, Jian Lv, Tongxiang Liang, Fenghua Luo PII: DOI: Reference:

S0040-6031(18)30029-7 https://doi.org/10.1016/j.tca.2018.01.020 TCA 77929

To appear in:

Thermochimica Acta

Received date: Revised date: Accepted date:

13-7-2017 26-1-2018 29-1-2018

Please cite this article as: Yafei Pan, Yong Du, Jian Lv, Tongxiang Liang, Fenghua Luo, Reassessment of the Ni–V system and a new thermodynamic modeling of the Mo–Ni–V system, Thermochimica Acta https://doi.org/10.1016/j.tca.2018.01.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Reassessment of the Ni–V system and a new thermodynamic modeling of the Mo–Ni–V system Yafei Pana,b,c, Yong Dua,*, Jian Lva,b, Tongxiang Liangb, Fenghua Luoc a

Science and Technology on High Strength Structural Materials Laboratory, Central

b

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South University, Changsha, Hunan, 410083, P.R. China School of Materials Science and Engineering, Jiangxi University of Science and

c

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Technology, Ganzhou, 341000, P.R. China

State Key Laboratory of Powder Metallurgy, Central South University, Changsha,

Hunan, 410083, P.R. China

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* Corresponding author: E-mail: [email protected]; Highlights

The σ phase is described by a three-sublattice (Ni,V)10V4(Ni,V)16.

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The Ni–V and Mo–Ni–V systems have been critically modeled.

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An application of the Mo–Ni–V system as nuclear structural material is discussed.

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Abstract

The Mo–Ni–V system has been assessed by means of the CALPHAD (CALculation

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of PHAse Diagram) approach. The binary system Ni–V was reassessed by considering all available thermochemical and phase diagram data. According to the

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crystallographic data, the σ intermediate compound is described by a three-sublattice (Ni,V)10V4(Ni,V)16. Calculated phase diagram and thermochemical properties of the Ni–V system showed a good agreement with experimental data. A set of self-

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consistent thermodynamic parameter for the Mo–Ni–V system was obtained by considering the phase diagram data in the ternary system. Comprehensive comparisons between the calculated and measured phase diagram and thermodynamic data showed that the experimental information was satisfactorily accounted for by the present thermodynamic description.

Keywords: Ni–V binary system; Mo–Ni–V ternary system; Thermodynamic assessment; Phase equilibria; Material design 1. Introduction Vanadium alloys have been identified as a leading candidate material for fusion reactor structural applications [1–4]. The neutronic properties of vanadium are

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particularly attractive: this element is inherently a low-activation material, and its low neutron absorption characteristics minimize its impact on tritium breeding. In

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addition, vanadium-based alloys possess relatively high thermal conductivities and

low thermal expansion coefficients, which result in lower thermal stresses for a given heat flux compared with most other candidate alloys. The refractory metals, Ti, Cr,

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Ta, Mo, and Nb, are often added in vanadium-based alloys to improve its high

temperature strength. Due to the large solid solubility in vanadium and the favorable

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size factor, nickel is expected to improve the oxidation resistance of the vanadium-

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based alloys [5]. Each element of the Mo–Ni–V ternary system is also the main

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component of Ti(C,N) and WC-based cemented carbides [6–9]. Ni is the important binder phase of Ti(C,N)-based cermets and shows a better corrosion resistance than

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the traditional binder phase Co [10]. The addition of Mo or Mo2C to cermets can improve the wettability between ceramic phase and binder phase [6]. Vanadium is

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often added to the cermets in the form of carbide, which plays an important role in inhibiting the grain growth of the hard phases [7]. As a result, the cermets with a finer

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microstructure and better mechanical properties can be obtained. The CALPHAD (CALculation of PHAse Diagram) approach is a useful tool to

establish thermodynamic databases, which are bases for the prediction of

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thermodynamic properties, phase diagrams, DICTRA (DIffusion Controlled TRAnsformation) [11] and phase-field simulations [12]. In order to optimize V-based alloy compositions and further develop the thermodynamic databases of multicomponent nuclear materials or cemented carbides, knowledge concerning phase equilibria and thermodynamic properties of the Mo–Ni–V ternary system is of fundamental importance. In the present work, the constituent binary systems of the

Mo–Ni–V system were critically assessed, and the Ni–V system was refined by applying a three-sublattice (Ni,V)10V4(Ni,V)16 to the intermediate compound, σ. Due to the reliabilities and extrapolations to the high-order systems [6, 13–15], the thermodynamic descriptions of the Mo–Ni and Mo–V systems were directly taken from Cui et al. [16] and Bratberg and Frisk [17]. Based on all the available experimental phase diagram data, a set of self-consistent thermodynamic parameters

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for the Mo–Ni–V system in the whole range of composition and temperature is obtained by means of CALPHAD approach.

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2. Critical review of the binary systems

The Mo–Ni binary system consists of liquid, bcc, fcc, MoNi4, MoNi3 and MoNi

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phases. Several assessments [16, 18–20] were performed for this binary system. Among the recent assessments, Morishita et al. [19] did not consider MoNi4 and

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MoNi3 phases, which are now confirmed as stable phases [21, 22]. In the assessment

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by Zhou et al. [20], the Gibbs energy descriptions for the phases MoNi2 and MoNi8

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were included. However, MoNi2 and MoNi8 have not been detected in the equilibrated alloys [21–23] and were deduced to be metastable, and so were not considered in the

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present work. The thermodynamic description from Cui et al. [16], which produced well the experimental data [21, 22, 24–26] and is consistent with our previous work

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[6, 14], was adopted in the present modeling. The calculated Mo–Ni phase diagram is

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shown in Figure 1a.

There is no intermediate phase in the Mo–V system. Thermodynamic modeling

of the system was attempted by several investigators [17, 27]. In the present optimization, the thermodynamic parameters of the Mo–V system were directly taken

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from the work of Bratberg and Frisk [17], since the thermodynamic parameters [17] have been successfully used to build the thermodynamic databases for cemented carbides [15, 28]. According to their modeling [17], there is a miscibility gap in the bcc phase field below 884 °C, which is considered in the description of the Mo–Ni–V ternary system. The calculated Mo–V phase diagram is shown in Figure 1b.

The Ni–V system is composed of liquid, bcc, fcc, Ni3V, Ni2V, σ and Ni2V7 phases. This binary system was previously assessed by Watson and Hayes [29], and the σ phase was modeled by four kinds of thermodynamic models (substitutional model, (Ni,V)18(V)4(Ni)8, (Ni,V)10V4(Ni,V)16 and (Ni,V)10(Ni,V)4(Ni,V)16). The sublattices (Ni,V)18(V)4(Ni)8, (Ni,V)10V4(Ni,V)16 and (Ni,V)10(Ni,V)4(Ni,V)16 could well produce the phase boundary for the σ phase and the sub-lattice

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(Ni,V)10V4(Ni,V)16 was the most succinct and appropriate model to reflect the crystal structure and solubility information of the σ phase. In their modelling [29], however,

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the temperature terms for both Gibbs energies and interaction parameters of the end

members were excessively large. Recently, Kabanova et al. [30] reassessed the Ni–V system. They used a three-sublattice model of (Ni,V)18V4Ni8 to model the σ phase.

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Such a model could not represent its crystal structure. The σ phase has the Cr0.49Fe0.51-

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type [31] crystal structure with five different atomic sites: 2a, 8i1, 8i2, 8j and 4f. The

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2a (CN=12) and 8i1(CN=12) sites are essentially occupied by Ni atoms due to its fcc structure, while the 4f (CN=15) site is mainly occupied by V atoms with a bcc

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structure. In addition, the remaining sublattices 8i2 (CN=14) and 8j (CN=14) can be

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occupied by both Ni and V atoms [32, 33]. In order to simplify the model for σ, we can merge the sites with the same coordination numbers and make the stoichiometry 10:4:16. Considering its homogeneity range of 55.0 to 73.5 at.% V [5, 34, 35], the

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three sublattice model (Ni,V)10V4(Ni,V)16 was adopted in the present optimization, which has been successfully applied to the description of the AlTa2 phase in the Al–

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Ta system [36]. Accordingly, the Ni–V system was reassessed in the present work. To facilitate reading, it is necessary to give a brief introduction about the

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available experimental information for the Ni–V system. It is characterised by the existence of a large fcc phase field, which extends almost half-way across the diagram [29]. There is also appreciable dissolution of Ni in V (bcc), up to a maximum of 24 at.% Ni at 1280 °C [29]. Between the fcc and bcc phases, there is a large σ phase field spanning about 20 at.% at 900 °C. Three other intermetallic phases, Ni3V, Ni2V and Ni2V7, are present in the system [29]. The first phase shows a homogeneity range of 4

at.% at 900 °C [29]. The phase diagram is well constructed across the whole composition range due to a series of measurements [5, 34, 35, 37, 38]. Stevens and Carlson [5] determined the V-rich solidus and liquidus curves by differential thermal analysis (DTA). Pearson and Hume-Rothery [34] determined the solidus and liquidus curves in the region 0 to 70 at.% V by means of a series of heating and cooling curves. The phase boundaries of the fcc phase were investigated by Pearson and

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Hume-Rothery [34], Khlomov et al. [35], Moreen et al. [37] and Miyazaki [38]. In the region 36.7 to 42.7 at.% V, the data for the boundary of fcc/(fcc+σ) from Khlomov et

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al. [35] shifted to the V side by about 1 at.%, compared to those from Pearson and

Hume-Rothery [34]. The phase boundary of the bcc phase was constructed by Stevens and Carlson [5] and Khlomov et al. [35]. The data on the boundary of bcc/(bcc+σ)

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from Khlomov et al. [35] shifted to the V side, compared to those from Stevens and

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Carlson [5] and the deviation reached about 6.8 at.%. The data from Khlomov et al.

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[35] was obtained by the diffusion couples method, which had larger experimental errors than the equilibrium alloys method adopted by Stevens and Carlson [5] and

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Pearson and Hume-Rothery [34]. So the data from Stevens and Carlson [5] and

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Pearson and Hume-Rothery [34] was used to describe the boundaries of the bcc and fcc phases and the data from Khlomov et al. [35] was not used. The other experimental data [37, 38] were self-consistent and reasonable to construct the phase

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diagram of the Ni-V system and given the equivalent weight in the optimization process. Enthalpies of mixing of the liquid phase [39] and enthalpies of formation of

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the solid solution phases [40] have been measured by means of calorimetry. Thermodynamic data also exist for the intermetallic compounds

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ΔHf for Ni3V [41], ΔHTr for Ni3Vfcc [42], ΔHTr for Ni2Vfcc [42], ΔHdecomp for Lfcc+σ [30], ΔHdecomp for Ni2V7bcc+σ [5].

3. Critical review of the Mo–Ni–V system The major contribution to the measurement of the Mo–Ni–V ternary phase diagram comes from the extensive work by Prima et al. [43, 44]. According to their study, no ternary compound was detected in the temperature range from 900 °C up to the melting temperatures of alloys. Based on the optical microscopy (OM), X-ray

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diffraction (XRD) and micro-X-ray spectral methods, Prima and Tretyachenko [43] constructed the isothermal sections at 1150 °C and 900 °C. For the isothermal section at 1150 °C, the phase equilibria are characterized by the coexistence of the σ and δ

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solid solutions with the fcc-(Ni) and bcc-(Mo,V) solid solutions. The homogeneity region of the δ-based phase is very small. The maximum solubility of Mo in σ is about 12 at.%. The extremely narrow fields of the three-phase equilibria

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(Ni)+δ+(Mo,V) and (Ni)+σ+(Mo,V) lead to the wide composition range in which the

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(Ni) and (Mo,V) phases coexist. For the isothermal section at 900 °C, Prima and

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Tretyachenko [43] did not present the experimental detail or original experimental

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data. From their descriptions of the phase equilibria at 900 °C, it can be concluded that the solubility of V and Mo in fcc-(Ni) diminishes with decreased temperature,

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and so the (Ni) phase region sharply narrows. Its boundary in the ternary system determined by Prima et al. [43] has an obvious discontinuity at the composition of

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10.0Mo-58.2Ni-35.8V (at.%). The alloys containing 75 at.% Ni at 900 °C are located in the stability range of MoNi3 and Ni3V phases. The homogeneity regions of the

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phases MoNi3 and Ni3V are elongated along the vertical section at 75 at.% Ni. The composition range of solid solutions based on the Ni3V compound is about 3 at.%. In MoNi3, vanadium replaces up to 20 at.% Mo. In addition, the presence of the broad

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two-phase regions in which the MoNi3 and σ phase coexist with bcc-(Mo,V) solid solutions is found at 900 °C. The liquidus projection of the Mo–Ni–V system was investigated by using 43 cast alloys [44]. The compositions were located in the vertical sections at 15, 55, 67, 75 at.% Ni and over the vertical section Ni48Mo52Ni–Ni40V60. The alloys were melted in an arc furnace under argon atmosphere using a non-consumable tungsten electrode

and the weight change of each sample after arc-melting was less than 1 wt.%, which guaranteed that the compositions of the alloys were very close to their nominal ones. These alloys were also subjected to homogenization annealing at 1150 °C for 50 h. All samples were investigated by means of OM, XRD analysis and the PiraniAlterthum method. The Pirani-Alterthum method [45] was used to determine the incipient melting temperature by observing the initial formation of liquid inside a

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small hole (~1 mm diameter × 1.5 mm deep) located at the center of the specimen (~2.5 mm diameter × 25 mm length) through a glass window with the aid of a

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calibrated disappearing-filament type pyrometer focused at the bottom of the hole. For the alloys located in the region of invariant equilibria, the melting temperatures were determined by DTA [44]. The liquidus projection in the ternary system is dominated

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by two liquid transition reactions: L + δ = (Ni) + (Mo,V) at 1290 °C and L + (Mo,V)

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= (Ni) + σ at 1230 °C [44].

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Without specific explanation, all the phase diagram and thermodynamic data

the Ni–V and Mo–Ni–V systems.

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evaluated presented in Sections 2 and 3 were utilized in the present optimization for

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4. Thermodynamic models

The SGTE compilation by Dinsdale [46] is widely used to describe the Gibbs

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energies of the pure elements. The subsequent updates [47, 48] are the extensions of

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the SGTE data [46] from 298 K to zero Kelvin temperature. In addition, many systems involving Mo , Ni and V use these data from Dinsdale [46], such as Co–Mo– Ni [14], Al–Mo–V [49] and so on. The Gibbs energy functions for Mo, Ni and V from the SGTE compilation by Dinsdale [46] are adopted in the present work, since we are

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only interested in the thermodynamic descriptions above room temperature (298 K). The thermodynamic parameters for the Mo–Ni and Mo–V binary sub-systems were taken from Cui [16] and Bratberg and Frisk [17], respectively. In the present work, the Ni–V binary system was reassessed by considering the crystallographic data on the σ phase, phase diagram and thermodynamic data in the literature [5, 30, 34, 35, 37–42].

The thermodynamic parameters obtained for the Ni–V system were then applied to describe the phase equilibria of the Mo–Ni–V system. 4.1 Liquid and solid solution phases The Gibbs energy of the ternary liquid was described by the Redlich-Kister-

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Muggianu polynomial [50, 51]: L GmL  xMo  0GMo + xNi  0GNiL + xV  0GVL

0

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+ RT  ( xMo  ln xMo + xNi  ln xNi + xV  ln xV )

(1)

+ xMo  xNi  LLMo , Ni + xMo  xV  LLMo,V + xNi  xV  LLNi ,V L + exGMo , Ni ,V

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where R is the gas constant, and xMo, xNi and xV are molar fractions of the elements

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Mo, Ni and V, respectively. The standard element reference (SER) state [46], i.e. the

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stable structure of the element at 25 °C and 1 bar, was used as the reference state of Gibbs energy. The parameters LLi, j (i, j  Mo, Ni,V ) are the interaction parameters

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expressed as follows:

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L from the binary constituent systems. The ternary excess Gibbs energy exGMo , Ni ,V is

L 0 L 1 L 2 L GMo , Ni ,V  xMo  xNi  xV   xMo  LMo , Ni ,V + xNi  LMo , Ni ,V + xTi  LMo , Ni ,V 

(2)

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ex

in which the interaction parameters 0 LLMo, Ni ,V , 1LLMo, Ni ,V and 2 LLMo, Ni ,V are linearly

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temperature-dependent. These parameters were evaluated, or determined in the present work if they did not exist before. For the (Ni), (Mo) and (V) phases, the Gibbs energy of each phase is described by a non-magnetic ( 0Gnmg ) and a magnetic contribution ( G mg ). 0Gnmg is given by an

equation similar to Eq. (1). Gmag is described by the Hillert-Jarl model [52]. The (Ni) is modeled as the fcc phase, while (Mo) and (V) modeled as the bcc phase. 4.2 Intermetallic phases in the Ni–V binary sub-system

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The Ni3V phase, which exhibits a range of nonstoichiometric alloys, was modeled with a two-sublattice model [53], which has a general formula described by

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(Ni,V)3(Ni,V)1. The Gibbs energy of the phase per mole of formula unit is represented as follows:

GmNi 3V  yNi  yNi  0GNiNi:3NiV + yNi  yV  0GNiNi:V3V + yV  yNi  0GVNi:Ni3V + yV  yV  0GVNi:V3V + 3  RT  ( yNi  ln yNi + yV  ln yV ) + RT  ( yNi  ln yNi + yV  ln yV)

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0

(3)

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3V    Ni 3V + yNi  yV  yNi  LNNii 3,VV:Ni + yNi  yV  yV  LNi Ni ,V :V + y Ni  y Ni  yV  LNi:Ni ,V

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3V + yV  yNi  yV  LVNi:Ni ,V

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where yNi and yV are the site fractions of Ni and V in the first sublattice,

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3V respectively, and yNi and yV the same in the second sublattice. 0GiNi (i, j = Ni or V) :j

denotes the Gibbs energy of the fictitious compounds i3j1 (i, j = Ni or V). The

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parameter LiNi, j3:Vk or LiNi: j3,Vk (i, j, k = Ni or V) is the interaction parameter between unlike

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atoms on the same sublattice. According to the Pearson and Hume-Rothery [34] and Stevens and Carlson [5],

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the compounds Ni2V and Ni2V7 have a homogeneity ranges of about 0.5 and 1.0 at.%, respectively, and were treated as pure binary stoichiometric phases in the present work. Ni2V7 was shown to exist at the composition of 77.0 to 78.0 at.% V [5], and the atomic ratio of Ni to V was set to 1:3.5 rather than 1:3 to agree better with the compositions. Their Gibbs energy per mole formula is given by:

GNiNi:mVVn  m  0GNifcc  n  0GVbcc  a  bT

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in which a and b are the parameters which were optimized in this work. The σ phase is described with the three sublattice model (Ni,V)10V4(Ni,V)16, and

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its Gibbs energy per mole of formula can be expressed as follows:    0    0    0  Gm  yNi  yNi  0GNi :V :Ni + y Ni  yV  GNi:V :V + yV  y Ni  GV :V :Ni + yV  yV  GV :V :V +10  RT  ( yNi  ln yNi + yV  ln yV ) +16  RT  ( yNi  ln yNi + yV  ln yV)

0

(5)

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+ yNi  yV  yNi  LNi ,V :V :Ni + yNi  yV  yV  LNi ,V :V :V + yNi  yNi  yV  LNi:V :Ni ,V + yV  yNi  yV  LV :V :Ni ,V

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4.3 Binary phases with ternary solubilities

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The MoNi3 phase forms homogeneous fields extending in the ternary at almost

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constant Ni at 900 °C [43], indicating that V tends to substitute for Mo. Thus, V was permitted to be on the first and second sublattices to replace Mo, which led to a two-

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sublattice model (Mo,Ni,V)3(Mo,Ni,V)1 for its description. Similar to MoNi3, the

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Ni3V phase was also described by the two-sublattice model (Mo,Ni,V)3(Mo,Ni,V)1. Considering that V preferentially replaces the atomic occupation of Mo in the

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Mo–Ni–V system [43], the thermodynamic model for the δ phase was developed to be Ni6(Mo,Ni,V)5(Mo,V)3, which is sufficient to cover the homogeneity range of δ in the

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ternary system.

The three-sublattice model (Ni,V)10V4(Ni,V)16, which is used in Ni–V binary

sub-system was applied to the Mo–Ni–V ternary system for the σ phase. Based on the crystal structure [31] and solubility information [43], we considered that Mo tends to

substitute for V and introduced Mo into the second and third sublattices, for the reason that Mo and V are both inclined to occupy the lattices which have the higher coordination numbers [32]. The resulting model is thus (Ni,V)10(Mo,V)4((Mo,Ni,V)16. The binary phases MoNi4, Ni2V and Ni2V7 were treated as pure binary

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stoichiometric compounds due to the lack of experimental data on its solubility of the

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third component.

All phases in this system and the corresponding thermodynamic models used in

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the present work are listed in Table 1.

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5. Results and discussion

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The evaluation of the model parameters was carried out using the optimization

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program PARROT [54], which works by minimizing the sum of the square of the

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differences between measured and calculated values. The step-by- step optimization procedure described by Du et al. [55] was utilized in the present assessment. Each

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piece of selected information was given a certain weight based on the uncertainties of

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the experimental data. The weights were changed by trial and error during the assessment until most of the selected experimental information was reproduced within

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the expected uncertainty limits. During optimization, we want to describe all the reliable data well. However, this is basically impossible. Our aim is to reduce the deviations or errors between the calculated and experimental results. In the optimization process, each piece of selected information was given a certain weight. Sometimes one experimental data was given too much weight, and this data could be

fit well. But the other data could not fit well. So we should decrease the weight of this data. The optimization is a process to adjust the weight of each data and to reduce the total deviations. In addition, the focus of this article is to provide the parameters of the Mo–Ni–V system to the readers. So we did not spend too much vigor to describe the

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optimization processes and methods.

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The optimization of the Ni–V binary system began with the liquid, fcc and bcc phases using the phase diagram data [5, 34, 35, 37, 38], the enthalpy of mixing for liquid [39] and the enthalpy of formation for fcc and bcc [40]. For the intermediate

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phase σ, the experimental enthalpy of formation [40], phase boundary information and

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invariant equilibria [5, 34, 35, 37, 38] were employed to obtain a reliable

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thermodynamic description. Next, the parameters for Ni3V, Ni3V and Ni2V7 were obtained to reproduce the enthalpies and the phase transition temperatures [5, 34, 35,

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37, 38, 41, 42]. The final optimization was done with all experimental data of all

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phases simultaneously, and the assessed parameters were then used to model the Mo– Ni–V ternary system. The optimization procedure for the ternary system proceeded

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with solid phases using the experimental isothermal sections at 1150 °C and 900 °C [43]. The model parameters for the liquid phase were evaluated with the primary

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crystallization fields and invariant equilibria [44]. Subsequently, the thermodynamic parameters for liquid, fcc and bcc phases were refined using the experimental phase relations in solid states [43, 44]. All the parameters were finally evaluated together to obtain the best set of parameter values, that minimised the reduced sum of squares of error.

The present thermodynamic parameters obtained for the Ni–V and Mo–Ni–V systems are given in Table 2. Using this set of parameters, all the phase equilibrium data, i.e., isothermal sections, vertical sections, solubility ranges, invariant reactions and thermodynamic properties, were calculated to show the rationality of the present

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modeling.

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Figure 2a presents the calculated Ni–V phase diagram according to the final

treatment, in comparison with the available experimental data [5, 34, 35, 37, 38]. It can be seen from the figure that the calculated liquidus and solidus agreed with the

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measured results [5, 34]. For the bcc-(V) solidus, the data point at 82.2 at.% V and

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1441 °C [5] did not fit well. The data deviated from the trend of other data, probably

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due to the experimental errors. The bcc-(V) solidus can only be affected by the parameters of the liquid and bcc phases. The other models (substitutional model,

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(Ni,V)18(V)4(Ni)8 and (Ni,V)10(Ni,V)4(Ni,V)16) for the σ phase would also led to this

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deviation. As shown in Table 3, the calculated equilibria were in excellent agreement with the measured ones. The differences between the calculated and measured

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temperatures were less than 8 °C. The calculated boundary for the σ phase agreed with the experimental data [5, 34, 35]. According to the present calculation, there are

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phase decompositions of the Ni2V phase at 291 K and a phase separation of the liquid phase at 6011 K, as can be seen in Figure 2. Considering that the Gibbs energy functions for Mo, Ni and V from the SGTE compilation by Dinsdale [46] are in the temperature range of 298.15 K to 6000 K, the present results are reasonable and acceptable.

Figure 3 shows the calculated enthalpies of mixing at 2020 K and 2320 K, compared with the experimental data by Schaefers [39]. Most of the experimental data agreed with the present calculations, although the fit was less good for the higher Ni content data at 2320 K. When we adjust the parameters of liquid to fit the measured

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enthalpies of mixing at 2320 K near 60 at.% Ni, the temperature for the phase separation of liquid would be reduced to below 6000 K. By controlling the

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temperature for the phase separation slightly above 6000 K, we have made efforts to

reduce the deviations between the calculated and measured [39] enthalpies of mixing

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at 2320 K. The calculated enthalpies of formation for the fcc, σ and bcc phases at

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1473 K in comparison with the measured data reported by Watson and Hayes [40] are

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presented in Figure 4.

The calculated thermodynamic data for the intermetallic compounds Ni3V, Ni2V,

ED

(σ), and Ni2V7 are also presented in Table 3. The calculated result for

PT

ΔHdecomp(Ni2V7bcc+σ) fitted well with the experimental value from Stevens and Carlson [5]. There were some differences between the calculated and experimental

CC E

data for ΔHdecomp(Lfcc+σ) [30], ΔHTr(Ni3Vfcc) [42], ΔHTr(Ni2Vfcc) [42]. For ΔHdecomp(Lfcc+σ), the deviation between the calculation and measured results

A

reached 4.1 kJ/mol, since the liquid, fcc and σ phases were basically fixed by Schaefers et al. [39] and Watson and Hayes [40], their data were more reliable than the only one data from Kabanova et al. [30]. The deviations for ΔHTr(Ni3Vfcc) [42] and ΔHTr(Ni2Vfcc) [42] were 0.57 kJ/mol and 0.7 kJ/mol, respectively. Much effort has been devoted to improve the results. It was felt that excessive pursuit of the good

fit for the enthalpies of transition would deteriorate the present phase equilibria. After all, the phase equilibrium information involving the types, compositions and temperatures of the invariant reactions showed higher accuracies than the enthalpies of transition [40], and was thus attached a higher weight in the optimization process.

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The enthalpy of formation of the Ni3V phase calculated using the resulting

SC R

parameters (-12.1 kJ/mole of atoms) was larger than the measured data from Guo et al. [41] (-5.4 kJ/mole of atoms) and seemed to be reasonable for two reasons: (1) it showed the similar value to the calculated result by Kabanova et al. [30] (-10.67

U

kJ/mole of atoms); and (2) it agreed with the enthalpy of the phase transition for the

A

N

Ni3V (order)  fcc (disorder) (-2.44 kJ/mole of atoms [42]).

M

The calculated isothermal section of the Mo–Ni–V system at 1150 °C, compared with the experimental data from Prima and Tretyachenko [43] is shown in Figure 5,

ED

and was in good agreement with the experimental data. The maximum solubility of

PT

Mo in σ reached 12 at.%. The fields of the three-phase equilibria (Ni)+δ+(Mo,V) and (Ni)+σ+(Mo,V) coexisted with the wide two-phase region of (Ni) and (Mo,V). For the

CC E

boundary of the fcc-(Ni) phase, the blue line is compiled by Prima and Tretyachenko [43] according to their experimental data [43] and the black line is calculated by the

A

present modeling. The measured phase boundary for fcc phase by Prima and Tretyachenko [43] had an obvious discontinuity at the composition of 10.0Mo58.2Ni-35.8V (at.%) and varied sharply adjacent to the Ni–V side. Such an overestimated stability of the fcc phase would lead to the disappearance of the Ni3V phase at 900 °C. To ensure the phase relationships at 900 °C, the calculated phase

boundary of the fcc phase (the black line) in the Ni–V side at 1150 °C slightly deviated from that measured by Prima and Tretyachenko [43] (the blue line). In Figure 6, the calculated 900 °C isothermal section of the Mo–Ni–V system is presented. The calculated solubilities of V in MoNi3 and Mo in Ni3V at 75 at.% Ni

IP T

reached up to ~23 and 3 at.%, respectively. The broad two-phase regions of MoNi3+bcc-(Mo,V) and (σ)+bcc-(Mo,V) coexisted at 900 °C, which was in

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accordance with the work by Prima and Tretyachenko [43]. Figure 6b is the local magnification of the 900 °C isothermal section, which clearly revealed the phase

U

relationship in Ni-rich corner. In the present results (Figure 6a), a miscibility gap of

N

the bcc phase was calculated, which is also present in the Mo-V binary system [17].

A

The calculated vertical sections Ni75Mo25–Ni75V25, Ni67Mo33–Ni67V33, Ni55Mo45–

M

Ni55V45 and Ni48Mo52–Ni40V60 of the Mo–Ni–V system together with the

ED

experimental data by Prima et al. [44] are shown in Figure 7a-d. Most of the

PT

experimental data agreed with the present calculations. The calculated liquidus projection of the Mo–Ni–V system is given in Figure 8 together with measured

CC E

primary crystallization phases of individual alloys [44], while Figure 9 presents the reaction scheme in the range of melting/solidification for this system. In Figure 8, the

A

primary crystallization region of the σ phase was too small to involve one alloy with a composition of 6.0Mo-41.1Ni-52.9V. When we adjust the parameters to enlarge the crystallization region of the σ phase, a phase separation of the bcc phase and an invariant reaction L + bcc-(V)#1 = bcc(V)#2 + σ would occur above 1150 °C, as can be seen in Figure 10. This phase relationship has not been reported by Prima et al. [43,

44]. In the present modeling, we narrowed the crystallization region of the σ phase, and eliminated the phase separation and the invariant reaction. The calculated invariant equilibria along with the experimental ones [44] are listed in Table 4. The reaction types, and temperatures of the invariant reactions reported by Prima et al.

IP T

[44] were well reproduced by the present modeling, and the difference between the calculated and measured temperatures was within 9 °C. Such a small difference is

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rarely realized for most thermodynamic modeling of ternary systems reported in the literature. Table 5 presents the predicted solid invariant reactions according to the

U

present calculations.

A

A reassessment of the Ni–V has been performed by taking into account recent

M



N

6. Conclusions

experimental data, and a consistent set of thermodynamic parameters was obtained.

ED

The σ phase was modeled as (Ni,V)10V4(Ni,V)16 on the basis of the crystallographic

PT

data. The invariant equilibria, enthalpy of mixing of the liquid and the phase boundary of the Ni3V and σ were well reproduced in the present work. The phase equilibria in the Mo–Ni–V ternary system were modelled based on the

CC E



critical review of the experimental data. The thermodynamic calculation for the

A

ternary Mo–Ni–V system was presented in the form of isothermal and vertical sections, and the liquidus projection, with appropriate comparisons with available experimental data. The reaction scheme of Mo–Ni–V system was also generated, which is of interest for practical applications as well as basic materials research. The thermodynamic parameters obtained for the Mo–Ni–V ternary system have

been incorporated into the thermodynamic databases for multicomponent cemented carbides [28] and nuclear materials. Acknowledgments The financial support from the Science Challenge Project of China (Grant No.

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tz2016004) and National Natural Science Foundation of China (Grant No. 51371199)

A

CC E

PT

ED

M

A

N

U

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is greatly acknowledged.

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[38] T. Miyazaki, Private communication. [39] K. Schaefers, J. Qin, M. Rösner-Kuhn, M.G. Frohberg, Mixing enthalpies of liquid Ni–V, Ni–Nb and Ni–Ta alloys measured by levitation alloying calorimetry, Can. Metall. Quart. 35 (1996) 47–51.

[40] A. Watson, F.H. Hayes, Enthalpies of formation of solid Ni–Cr and Ni–V alloys by direct reaction calorimetry, J. Alloys Compd. 220 (1995) 94–100. [41] Q. Guo, O.J. Kleppa, Standard enthalpies of formation of Ni3V, Ni3Hf, Pd3Hf, and Pt3Sc and systematics of ΔHof for Ni3Me (Me = La, Hf, Ta), Pd3Me (Me = La, Hf, Ta), and Pt3Me (Me = Sc, Ti, V or Y, Zr, Nb) alloys, J. Phys. Chem. 99 (1995) 2854–

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2856. [42] J. H. Perepezko, Private Commun. (Department of Metallurgical and Mineral

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Engineering, Univ. of Wisconsin-Madison, 1983).

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USSR (1985) 19–24.

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in the solidification region of alloys, Izv. Akad. Nauk SSSR, Met. 1 (1980) 212–217.

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[45] A.A. Silva, G.C. Coelho, C.A. Nunes, P.A. Suzuki, J. M. Fiorani c, N. David, M.

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Vilasi, Experimental determination of the Ta–Ge phase diagram, J. Alloys Compd.

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[46] A.T. Dinsdale, SGTE data for pure elements, CALPHAD 15 (4) (1991) 317–425. [47] I. Roslyakova, B. Sundman, H. Dette, L.J. Zhang, I. Steinbach, Modeling of

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Gibbs energies of pure elements down to 0 K using segmented regression, CALPHAD 55 (2016) 165–180. [48] J. Vřešt’ál, J. Štrof, J. Pavlů, Extension of SGTE data for pure elements to zero

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Kelvin temperature—A case study, CALPHAD 37 (2012) 37–48. [49] B. Hu, B. Yao, J. Wang , J.R. Zhao, F.F. Min, Y. Du, Thermodynamic assessment of the Al–Mo–V ternary system, J. Min. Metall. Sect. B-Metall. 53 (2) B (2017) 95–106.

[50] O. Redlich, A.T. Kister, Thermodynamics of nonelectrolytic solutions. Algebraic representation of thermodynamic properties and the classification of solutions, Ind. Eng. Chem. 40 (1948) 84–88. [51] Y.M. Muggianu, M. Gambino, and J.P. Bros, Enthalpies of Formation of Liquid Alloys Bismuth-Gallium-Tin at 723.deg.K. Choice of an Analytical Representation of

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Integral and Partial Excess Functions of Mixing, J. Chim. Phys. Phys. Chim. Biol. 72 (1) (1975) 83–88.

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[52] M. Hillert, M. Jarl, A model for alloying effects in ferromagnetic metals, CALPHAD 2 (1978) 227–238.

[53] M. Hillert, L.I. Staffansson, Regular solution model for stoichiometric phases

U

and ionic melts, Acta Chem. Scand. 24 (1970) 3618–3626.

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[54] B. Sundman, B. Jansson, J.O. Andersson, The thermo-calc databank system,

A

CALPHAD 9 (1985) 153–190.

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[55] Y. Du, R. Schmid-Fetzer, H. Ohtani, Thermodynamic assessment of the V–N

A

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PT

ED

system, Z. Met. 88 (1997) 545–556.

A ED

PT

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SC R

U

N

A

M

Figure Caption

A ED

PT

CC E Fig. 1

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SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

A ED

PT

CC E Fig 2

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SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

A Fig 3

ED

PT

CC E

IP T

SC R

U

N

A

M

Fi

A ED

PT

CC E Fig 4

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SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

Fig 5

A ED

PT

CC E

IP T

SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

Fig 6

A ED

PT

CC E

IP T

SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

A ED

PT

CC E

IP T

SC R

U

N

A

M

Fig 7

A ED

PT

CC E

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SC R

U

N

A

M

Fig 8

A ED

PT

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U

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Fig 9

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Fig 10

Table 1 List of the symbols to denote stable phases in the Mo–Ni–V ternary system. Prototype

Pearson symbol

Space group

Designation Phase description

Liquid

–

–

–

–

–

(Mo),(V) W

cI2

Im-3m

bcc

Solid solution based on bcc-(Mo) and bcc-(V)

(Ni)

Cu

cF4

Fm-3m

fcc

Solid solution based on fcc-(Ni)

MoNi

Mo3(Mo0.8Ni0.2)5Ni6

oP56

P212121

δ

Solid solution based on MoNi

MoNi3

Cu3Ti

oP8

Pmmn

MoNi3

Solid solution based on Mo0.25Ni0.75

MoNi4

MoNi4

tI10

I4/m

Ni3V

Al3Ti

tI8

Ni2V

Pt2Mo

Sigma Ni2V7

SC R

A

U

Stoichiometric phase based on Mo0.2Ni0.8

I4/mmm

Ni3V

Solid solution based on Ni3V

oI6

Immm

Ni2V

Stoichiometric phase based on Ni0.6667V0.3333

(Cr0.49Fe0.51)

tP30

P42/mnm

σ

Solid solution based on Ni0.3V0.7 phase

Cr3Si

cP8

Pm3n

Ni2V7

Solid solution based on Ni0.2222V0.7778

PT

ED

M

N

MoNi4

CC E A

IP T

Phase

IP T SC R U N A M ED

Table 2

Summary of the optimized thermodynamic parameters in the Mo–Ni–V systema.

0 Liquid Ni ,V

L

PT

Liquid: Model (Mo, Ni, V)1

 –69727.75+23.10T

0 Liquid Mo , Ni ,V

L

 –3537.34–1.02T 2 LLiquid Ni ,V  +4613.66–5.77T

2 Liquid  +318346.57–120.43T 1LLiquid LMo, Ni ,V  +244716.92– Mo , Ni ,V  +124455.61–131.82T

CC E

L

1 Liquid Ni ,V

107.65T

A

fcc_A1: Model (Mo, Ni, V)1 0

LNifcc,V  –42546.16+4.60T 1LNifcc,V  –66881.70+36.46T 2 LNifcc,V  +36212.36–25.52T

0

fcc 1 fcc fcc LMo LMo, Ni ,V  –84646.05+26.82T 2 LMo , Ni ,V  + 464046.45–128.13T , Ni ,V  + 498569.59–

229.48T bcc_A2: Model (Mo, Ni, V)1 0 bcc Ni ,V

L

 –7835.86–5.88T 1Lbcc Ni ,V  + 38301.81–28.07T

0 bcc Mo , Ni ,V

L

2 bcc  –240021 1Lbcc LMo, Ni ,V  –427903.21 Mo , Ni ,V  + 2303567.82–248.91T

Ni3V: Model (Mo, Ni, V)3(Mo, Ni, V)1 Ni Ni V GNiNi:3NiV  4 0G fcc  0Gbcc + 5862.49–0.94T 0GNiNi:V3V  3 0G fcc –53663.32+4.33T

0

Ni V V GVNi:Ni3V  0G fcc  3 0Gbcc +53663.32–4.33T 0GVNi:V3V  4 0Gbcc +1453.42+28.80T

0

Ni 3V 0 Mo 0 Ni 0 Ni 3V Mo V GMo +250000 GMo:V  3 0Gbcc  0Gbcc :Ni  3 Gbcc  G fcc +250000

0

V Ni Mo 3V V Mo GNiNi:3Mo  3 0G fcc  0Gbcc +325.65+19.59T 0GVNi:Mo +150000  3 0Gbcc  0Gbcc

0

L

 –49532.70

Ni2V: Model (Ni)0.6667(V)0.3333 0 V GNiNi:V2V  0.6667 0G Ni fcc  0.3333 Gbcc –13256.43+0.22T

U

Ni2V7: Model (Ni)0.2222(V)0.7778

SC R

0 Ni 3V Ni:Mo ,V

IP T

Ni 3V 0 Mo GMo :Mo  4 Gbcc +20000

0

σ: Model (Ni, V)10(Mo, V)4(Mo, Ni, V)16

N

0 V GNiNi:V2V 7  0.2222 0G Ni fcc  0.7778 Gbcc –9702.34+1.33 T

A

 0 Ni 0 V 0  Ni V GNi GNi:V :V  10 0G fcc  20 0Gbcc –429589.12+97.23T :V :Ni  26 G fcc  4 Gbcc –244766.91+40.82T

M

0

Ni V V GV:V :Ni  16 0G fcc  14 0Gbcc +673423.39–89.53T 0GV:V :V  30 0Gbcc +63966.36+25.82T

0

 0 Mo 0 Ni 0  Mo Ni V GNi GNi:Mo:V  4 0Gbcc  10 0G fcc  16 0Gbcc –110000 :Mo:Mo  20 Gbcc  10 G fcc +100000

ED

0

 0 Mo 0 Ni 0 V GNi :V :Mo  16 Gbcc  10 G fcc  4 Gbcc –81540.10+150.26T

0

Mo V Mo V +10000 0GV:Mo:V  4 0Gbcc +200000 GV:Mo:Mo  20 0Gbcc  10 0Gbcc  26 0Gbcc

PT

0

Mo V +80000 GV:V :Mo  16 0Gbcc  14 0Gbcc

CC E

0

δ: Model (Ni)0.4286(Mo, Ni, V)0.3571(Mo, V)0.2143  0 Mo 0 Ni 0 V GNi :V :Mo  0.2143 Gbcc  0.4286 G fcc  0.3571 Gbcc –8772.83

A

0

0  Ni:Ni ,V :Mo

L

 +47356.90

MoNi3: Model (Mo, Ni, V)0.75(Mo, Ni, V)0.25 MoNi 3 0 Mo 0 V 0 MoNi 3 Ni V GMo GNi:V  0.75 0G fcc  0.25 0Gbcc –12084.55 :V  0.75 Gbcc  0.25 Gbcc +30000

0

3 V 3 GVMoNi  0Gbcc +15000 0 LMoNi Ni:Mo ,V  –12194.96+8.19T :V

0

a

A

CC E

PT

ED

M

A

N

U

SC R

IP T

All parameters are given in J/mole and temperature (T) in K. The Gibbs energies for the pure elements are taken from the compilation of Dinsdale [46]. The thermodynamic parameters for the Mo–Ni and Mo–V binary sub-systems were taken from Cui [16] and Bratberg and Frisk [17], respectively. The thermodynamic parameter for the Ni–V binary system was obtained by the present modeling.

Table 3 Comparison between the calculated and measured phase equilibria [5, 34, 35, 37, 38] and thermodynamic data [5, 30, 39–42] in the Ni–V system. The experimental information is in parenthesis.

(61.5)

1204 (1202)

76.0 (76)

68.0 (67)

1276 (1280)

fcc-

31.0

26.7

(Ni)=Ni3V+Ni2V

(32.5)

(28.5)

fcc-(Ni)= Ni3V

89.5

(73.5)

(89.5)

24.7 (25) 33.3

(33.3)

CC E

33.3 (33)

53.2 (55) 77.8

24.7 (25) 33.3

(33.3)

-12.3 (-8.2)

904 (908)

882 (890)

900 (900)

-1.35 (-1.48)

—

1052 (1045)

-1.87 (-2.44)

—

933 (>922)

-2.24 (-1.54)

A

74.2

PT

fcc-(Ni)=Ni2V

33.3 (33)

(38.5)

M

σ+bcc-(V)= Ni2V7

36.7

ED

fcc-(Ni)=Ni2V+σ

A

55.6 (55)

transition, kJ/mol

IP T

62.9

42.7 (43)

Enthalpy of

SC R

L+bcc-(V)=σ

50.6 (51)

T, °C

U

L=fcc-(Ni)+σ

Phase composition, at.% of V

N

Invariant rection

(77.8)

IP T SC R U N A M ED

Table 4

CC E

PT

Comparison between the calculated and measured invariant reactions in the Mo–Ni–V system. Liquid composition

Invariant rection

T, °C

Source

at.% Ni

at.% V

U1: L+δ=

25.5

65.1

9.4

1281

This work

fcc-(Ni)+bcc-(Mo,V)

—

—

—

1290

[40]

U2: L+bcc-(Mo,V)=

7.2

54.1

38.7

1223

This work

fcc-(Ni)+σ

—

—

—

1230

[40]

A

at.% Mo

IP T SC R U N A M ED PT CC E A

Table 5 Predicted solid invariant reactions according to the present calculations. Reaction

T (°C)

fcc-(Ni)+bcc-(Mo,V)=δ+MoNi3

1064

817

fcc-(Ni)+Ni3V=MoNi3+Ni2V

806

fcc-(Ni)=σ+MoNi3+Ni2V

798

σ+MoNi3=bcc-(Mo,V)+Ni2V

751

MoNi3+Ni2V=bcc-(Mo,V)+Ni3V

733

A

CC E

PT

ED

M

A

N

U

SC R

IP T

fcc-(Ni)+bcc-(Mo,V)=σ+MoNi3

Figure captions Fig. 1. Calculated binary phase diagrams: (a) Mo–Ni system [16] and (b) Mo–V system [17]. Fig. 2. Calculated Ni–V phase diagram at the temperature ranges (a) from -200 to 200 °C, along with experimental data [5, 34, 35, 37, 38] used in the thermodynamic optimization and (b) from 0 to 7000 °C.

IP T

Fig. 3. Calculated and measured enthalpies of mixing [39] at (a) 2020 K and (b) 2320 K.

SC R

Fig. 4. Calculated and measured enthalpies of formation [40] at 1473 K (standard states: Ni, fcc; V, bcc). The color lines represent the calculated results and the symbols represent the measured ones.

Fig. 5. Calculated isothermal section of the Mo–Ni–V system at 1150 °C compared with the experimental data reported by Prima and Tretyachenko [43].

A

N

U

Fig. 6. Calculated isothermal section of the Mo–Ni–V system at 900 °C compared with the experimental data reported by Prima and Tretyachenko [43], (a) the whole compositions and (b) local magnification.

M

Fig. 7. Calculated vertical sections of the Mo–Ni–V system: (a) Ni75Mo25–Ni75V25, (b) Ni67Mo33–Ni67V33, (c) Ni55Mo45–Ni55V45 and (d) Ni48Mo52–Ni40V60 together with with the experimental data reported by Prima et al. [44].

ED

Fig. 8. Calculated liquidus projection of the Mo–Ni–V system according to the present thermodynamic modeling, together with the experimental data considering primary crystallization phases determined by Prima et al. [44].

CC E

PT

Fig. 9. Reaction scheme for the Mo–Ni–V system including liquid phase according to the present calculations with temperature in °C. The invariant reactions of solid phases are not included.

A

Fig. 10. Calculated isothermal section of the Mo–Ni–V system at 1296 °C: (a) the whole compositions and (b) the V-rich side.