Thermodynamic evaluation of the Mo–Ru system

Journal of Alloys and Compounds 313 (2000) 115–120

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Thermodynamic evaluation of the Mo–Ru system Chang-Seok Oh*, Hideyuki Murakami, Hiroshi Harada High Temperature Materials 21 Project, National Research Institute for Metals, 1 -2 -1 Sengen, Tsukuba Science City, Ibaraki 305 -0047, Japan Received 26 June 2000; accepted 15 August 2000

Abstract A thermodynamic assessment of the Mo–Ru binary system has been attempted by using the Calphad method. Solution and intermediate s phases were described by regular-type and the compound energy model, respectively, and their Gibbs energy parameters were evaluated through a computerized optimization procedure with available experimental information. The phase diagrams calculated with the obtained thermodynamic parameters are in very good agreements with the reported literature values.  2000 Elsevier Science B.V. All rights reserved. Keywords: Transition metal alloys; Phase diagram; Thermodynamic modelling

1. Introduction The Mo–Ru alloy system has attracted interests in fields of nuclear and materials industries, for example, postirradiation study of oxide nuclear fuels [1] and alloy design of high temperature structural materials, especially Ni-base superalloys [2]. Mo and Ru are two of the major elements in metallic fission product precipitates found in irradiated oxide nuclear fuels. The constitution and thermodynamics of the alloys composed of the Mo, Ru and other elements are closely related to the chemical state of the fuel-fission product system as well as history of the fuel cycle. Mo and other bcc elements whose main characteristics are high melting temperature, high lattice cohesion and low diffusivity have long been served as key alloying elements for g matrix hardener in alloy design of Ni-base superalloys. Recently, platinum group metals (PGMs) such as Ru, Rh, Pd, Pt and Ir have earned potentials as new alloying elements in development of next generation Ni-base superalloys because of their beneficial effects with respect to high temperature oxidation and corrosion resistance, without adversely affecting mechanical properties. Small additions of the PGMs to Ni-base superalloys are also expected to enhance microstructural stability by suppressing or retarding precipitation of topologically closed

*Corresponding author. E-mail address: [email protected] (C.-S. Oh).

packed (TCP) phases, such as s, m, etc., which gives rise to significant deterioration of mechanical properties at elevated temperatures [3,4]. In view of these applications, reliable thermodynamic description of the Mo–Ru system would have an important role in understanding the constitution and stability of the individual phases in the Mo and Ru containing multicomponent alloys. Though calculations of the Mo–Ru phase diagram using simple thermodynamic models have been attempted several times [5–7], it seems that those previous results show much room for improvement for the following reasons. One of the shortcomings of the earlier works is that the existence of the s phase has not been taken into account in the calculation scheme, which has therefore resulted in metastable phase diagrams. In addition, even in the latest work, the lattice stability description for pure elements recommended by the Scientific Group Thermodata Europe (SGTE) organization [8], which has been widely accepted in the construction of current thermodynamic database, was not used. It has been pointed out that the incompatibility of thermodynamic parameters assessed based on different lattice stability values impedes the building up of self-consistent multicomponet thermodynamic databases. For that reason, the use of thermodynamic parameters assessed under the unified lattice stability values is highly recommended. In the present study, a critical assessment of the Mo–Ru system based on the current Calphad approach has been attempted, and attention has been paid to the thermo-

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dynamic description of the s phase, as well as the the extrapolation into higher order systems.

Rothery and by Kleykamp have formed basis to construct the currently accepted Mo–Ru phase diagram [14,15].

2.2. Thermodynamic data 2. Literature information

2.1. Phase equilibrium data The earlier constitution studies on the Mo–Ru system date back to the mid-1950s. By X-ray diffraction and microstructure examination, Raub [9] made investigation on the alloys containing 28.8–89.5 at.% Ru, annealed and quenched from temperatures between 1073 and 1873 K. He reported that the solubility of Mo in Ru in the temperature range 1073–1873 K was about 35 at.% Mo, whereas that of Ru in Mo was negligible at 1473 K but increased with temperature, and an intermediate phase homogeneous at the composition of Mo 5 Ru 3 with a complex X-ray diffraction pattern existed. Later, the intermediate phase, designated to ‘Mo 5 Ru 3 ’ phase, was identified as s phase with a narrow composition range around 30 at.% by Bloom [10], who performed X-ray diffraction studies on the sintered powder compacts with compositions of Mo-25, 33, 50 and 70 at.% Ru. Greenfield and Beck [11] supported the existence of the s phase from X-ray diffraction and microstructure observation on five alloys prepared by arc-melting and annealed at 1473 K. However, they claimed that the s phase was stable in a composition range of about 1 at.% around 40 at.% Ru. Anderson and Hume-Rothery [12] established the equilibrium phase diagram from 14508C to melting temperatures of the components, over a whole range of composition by X-ray diffraction study and microstructure examination. They determined the liquidus and solidus curves by microscopical observation of quenched specimen, and reported that Mo dissolved 30.5 at.% Ru, whereas Ru dissolved 51 at.% Mo at eutectic temperature of 2218610 K, and that both solubility limits decreased with decreasing temperature. They reported that the s phase was stable in the region of 37.061 at.% Ru and formed through a peritectoid reaction occurring slightly below the eutectic horizontal between the solid solutions of Mo and Ru. Using metallography, X-ray diffraction, X-ray microanalysis, differential thermal analysis and dilatometry, Kleykamp [13] investigated the constitution of the Mo–Ru system between 1173 and 2273 K. The alloy system was characterized as eutectic type with a reaction temperature of 2228 K and a liquid with about 42 at.% Ru, which is in close agreement with the earlier work by Anderson and Hume-Rothery. The maximum solubility of Ru in Mo was 32.4 at.% Ru and that of Mo in Ru was 51.5 at.% Mo at 2208 K. The only intermediate s phase occurring between 36.7 and 39.4 at.% Ru was formed by a peritectoid reaction at 2188 K, and was decomposed by a eutectoid reaction at 1416 K. The studies by Anderson and Hume-

Brewer and Lamoreaux [16] estimated partial molar enthalpy of solution of Ru in the bcc solid solution from the corresponding value for Rh and the relative number of non-bonding 4d-electrons in pure Ru and Rh. During optimization these values were used only for reference because they are not measured. By e.m.f. (electromotive force) measurements using solid galvanic cell, Kleykamp [17] and Cornish and Pratt [7] obtained partial molar Gibbs energies of Mo in bcc and hcp solid solutions in the composition ranges 0.04#x Ru #0.98 between 1174 and 1356 K, and 0.1#x Ru #0.9 at 1406 K, respectively, and derived related thermodynamic quantities. Admitting that the measurements were carried out at different temperatures, two results show quite a different tendency and are in significant disagreement with each other, which will be discussed in detail later. By using Miedema’s semi-empirical model, de Boer et al. [18] estimated the limiting heats of solution for Mo in Ru and Ru in Mo, the heat of mixing of liquid phase at the equiatomic composition and the heat of formation for various hypothetical ordered compositions in the solid state.

3. Thermodynamic models

3.1. Solution phases The liquid, bcc and hcp phases were described by non-magnetic substitutional solution model. The Gibbs energy function of the solution phase F for 1 mol of atoms was expressed as follows: o F o F GF m 5 x Mo G Mo 1 x Ru G Ru 1 RT(x Mo ln x Mo 1 x Ru ln x Ru )

1 Dxs G F m

(1)

where 0 F 1 F Dxs G F m 5 x Mo x Ru [ L Mo,Ru 1 (x Mo 2 x Ru ) L Mo,Ru ]

(2)

The parameter o G F i (i5Mo,Ru) denotes the Gibbs energy of the element i with the structure F in a nonmagnetic state. The excess Gibbs energy parameters, i L F Mo,Ru , represent interaction energies between Mo and Ru, and they may in general depend upon temperature.

3.2. s Phase Though the s phase present in the Mo–Ru system shows a narrow range of homogeneity, i.e., smaller than 2.7 at.%, considering the possibility of extrapolation into higher order systems in future works, the s phase was

C.-S. Oh et al. / Journal of Alloys and Compounds 313 (2000) 115 – 120

described by the compound energy model proposed by ˚ Sundman and Agren [19]. In general, the s phase contains five independent crystallographic sites (sublattices) having 2, 4, 8, 8 and 8 atoms per site with coordination numbers of CN512, 15, 14, 12 and 14, respectively. Because the ideal description of the s phase, (A,B) 2 (A,B) 4 (A,B) 8 (A,B) 8 (A,B) 8 , would have to evaluate 32 Gibbs energy parameters for hypothetical end member phases with a s phase structure, several simplifications taking into account preferential occupation of elements to each site have been attempted. The sublattice model (A,B) 8 (A) 4 (A,B) 18 was originally applied to modeling of the s phase in the Fe–Cr system by Andersson and Sundman [20], subsequently it has been used in the assessments of the Co–Cr [21], Cr–Mn [22], Fe–Mo [23] and Mn–V [24] systems. The alternative sublattice model (A,B) 10 (A) 4 (A,B) 16 proposed by Hertzman and Sundman [25] has been used in assessments of the Al–Nb [26], Al–Ta [27], Fe–Mo [25] and Fe–V [28] systems. Though these two models have been successfully described thermodynamic behavior of the s phase as well as the preferential occupations of specific crystallographic sites in each system, the incompatibility between two models have become an issue when assessing higher order systems, such as the alloy system of stainless steels containing high Cr and Mo. In the recent Ringberg workshop on thermodynamic modeling of solutions and alloys, Ansara et al. [29] thoroughly examined the models and recommended to use the second description or its simplified version. However, the first formula, (A,B) 8 (A) 4 (A,B) 18 has been commonly used in metallic systems and the use of the second formula still encounter problems according to stoichiometry and composition range of the s phase in various alloy systems. Therefore, in recent assessments of the Co–Mo [30], Cr–Re [31], Re–Ta and Re–W [32] systems which are important subsystems in single crystal Ni-base superalloys, both models were employed to allow flexibility for extrapolations into higher order systems. In the present work, both models were used to describe the s phase in the Mo–Ru system, where the normal ordering scheme proposed by Kasper and Waterstrat [33] was assumed. Mo and Ru were assigned to A and B type atoms, respectively, where A and B are located in positions left and right of group VIIA elements in the periodic table, respectively. Further simplifications were made in order to determine the model parameters because of the lack of experimental information. The Gibbs energy functions for the s phase described as Ru 8 Mo 4 (Mo,Ru) 18 (model I, s 1 ) and Ru 10 Mo 4 (Mo,Ru) 16 (model II, s 2 ) can be written as follows: III o s1 III o s1 G sm1 5 y Ru G Ru:Mo:Ru 1 y Mo G Ru:Mo:Mo III III III III III 1 18RT( y III Ru ln y Ru 1 y Mo ln y Mo ) 1 y Ru y Mo L Ru:Mo:Ru,Mo

(3) and

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o s2 III o s2 G sm2 5 y III Ru G Ru:Mo:Ru 1 y Mo G Ru:Mo:Mo III III III III III 1 16RT( y III Ru ln y Ru 1 y Mo ln y Mo ) 1 y Ru y Mo L Ru:Mo:Ru,Mo

(4) respectively, where the colon and comma denote interactions between elements in different and in the same sublattices, respectively, and y III is the site fraction of Mo or Ru in the third sublattice. The L parameters have the same physical meaning as in the solution phase. The expressions for Gibbs energies of the end members in the two models are expressed as follows [34]: s

o

fcc

o

bcc

o

bcc

s

o

1 G Ru:i :k 5 8 G Ru 1 4 G i

o

o fcc o bcc s2 2 G sRu:i 1 16 o G kbcc 1 DG Ru:i :k 5 10 G Ru 1 4 G i :k

1 1 18 G k 1 DG Ru:i :k

(5) (6)

where i and k represent either Mo or Ru, and DG sRu:i :k in Eqs. (5) and (6) may have linear temperature dependence.

4. Results and discussion The entire optimization procedure is known as the Calphad method and consists of the choice of thermodynamic models for the Gibbs energy of the individual phases as previously described, compilation and analysis of experimental data, and finally computer-aided nonlinear regression of minimizing square error sum with the model parameters. In this study, the thermodynamic parameters for the bcc and hcp phases were evaluated at the first stage of optimization with e.m.f. data and phase boundary information. The liquid and s phases were subsequently included, and finally all the parameters were simultaneously optimized. In the optimization procedure, the model parameters describing phases were changed while weightings imposed to the selected experimental information were adjusted and some experimental data were not used until the error sum of square of weighted residuals was reduced to a certain level. During the course of optimization, the weights for the e.m.f. data from Kleykamp [17] and Cornish and Pratt [7] were set to lower values than phase equilibrium data, since thermodynamic quantities derived from e.m.f. data were in conflict with each other and not consistent with phase boundary data at high temperatures. In addition, small weights were given to the estimated thermodynamic properties such as the enthalpy of the liquid phase calculated using Miedema’s semi-empirical model. The optimization of the model parameters, calculations of the phase diagram and thermodynamic properties have been performed using the PARROT and POLY-3 modules of the Thermo-Calc program [35]. The assessed Gibbs energy parameter values of the individual phases in the system are given in Table 1 and the Mo–Ru phase diagram calculated with the optimized parameters (Model I for the s phase) is presented in Fig. 1.

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Table 1 The thermodynamic parameters of the Mo–Ru system (all values in SI units for one formula unit) Parameters

Model I, Ru 8 Mo 4 (Mo,Ru) 18

Model II, Ru 10 Mo 4 (Mo,Ru) 16

0

240 115.617.201T 9029.0211.302T 8.738T 9759.2212.972T 108 084.72160.723T 2288 549.2124.328T

239 547.416.907T 8930.2211.263T 8.637T 9837.0213.055T 89 340.62190.433T 2227 720.0178.114T

liq

L L bcc 1 bcc L 0 hcp L D o G sRu:Mo:Mo D o G sRu:Mo:Ru 0

Fig. 1. The calculated Mo–Ru phase diagram using the present thermodynamic description.

significant, which leads to overall features of phase diagrams and invariant reactions (Table 2) calculated with the two sets of parameters which are almost identical. The differences between the phase diagrams calculated using the optimized parameters of models I and II is beyond recognition. Therefore, the phase diagram calculated using model II for the s phase is not presented nor overlapped. Fig. 2 represents the calculated phase diagram above 1600 K together with the experimental data reported by Anderson and Hume-Rothery [12]. As shown in the figure, the calculated phase diagram reproduces the measured data within experimental error. One can show that the calculated liquidus line in the Mo-rich composition range is located at higher temperature than the experimental data, which is more pronounced in the composition region around 18 at.% Ru. Introducing more model parameters to the liquid or bcc phase to get a better fit was not successful to improve the results but leads to distortion of solidus line (appearance of kink). Considering that the experimental data were not obtained from direct measurement of liquidus points but from an indirect method, it would be thought that there is certain amount of errors in estimating

The calculated compositions and temperatures for three invariant reactions occurring in the system are compared with the values from the literature in Table 2. As shown in the Table 1, differences between the values of two sets of parameters for the liquid, bcc and hcp phases are not

Table 2 The experimental and calculated invariant reactions of the Mo–Ru system Composition (at.% Ru)

Temp. (K)

Experimental Calculated (Model I) Calculated (Model II)

Liq5bcc1hcp 42.0 32.4 48.5 42.5 32.3 48.8 42.5 32.1 48.8

2228 2229 2230

Experimental Calculated (Model I) Calculated (Model II)

bcc1hcp5s 32.4 48.5 37.5 31.3 48.8 38.1 31.1 48.8 38.0

2188 2190 2190

Experimental Calculated (Model I) Calculated (Model II)

s5bcc1hcp 37.5 11.0 59.0 37.8 11.0 56.8 37.6 11.1 56.8

1416 1414 1414

Fig. 2. The calculated Mo–Ru phase diagram in the high temperature region, compared with experimental data by Anderson and Hume-Rothery [12].

C.-S. Oh et al. / Journal of Alloys and Compounds 313 (2000) 115 – 120

liquidus temperatures, which might be due to failure of the bcc phase to nucleate during quenching. In general, it has been pointed out that the fewer assessed parameters used in the low order system the fewer problems occur in calculation of higher order systems. In the present work, as a consequence, the liquid and hcp phases were described by simple regular type model and the bcc phase by the sub-regular type model. Fig. 3 is the calculated phase diagram compared with the experimental data below eutectic temperature by Kleykamp [13]. The agreement between calculated and measured phase boundaries is quite satisfactory. Calculated range of homogeneity for the s phase is about 2.2 at.% around 1850 K which is comparable to the reported data of 2.7 at.%. Fig. 4 presents the calculated activities of Mo and Ru at 1200 and 1400 K compared with the measured activities of Mo reported by Kleykamp [17] at 1200 K and Cornish and Pratt [7] at 1406 K, respectively. As shown in the figure, these experimental data points do not show consistency over all composition range and this tendency is more pronounced in the Ru-rich composition region. It would be thought that incompatibility between two experimental data should be relieved by further experimental work. In Fig. 5 the metastable phase diagram calculated by suspending s phase is presented. The calculated phase diagram with the parameters obtained in the present work (solid line) is compared with the one calculated with the parameters reported by Cornish and Pratt [7] (dotted line). Considering that fewer model parameters were introduced to describe liquid, bcc and hcp phases than the previous work, it would be regarded that an improvement on the calculated result has been achieved in the present evaluation.

Fig. 3. The calculated Mo–Ru phase diagram compared with experimental data by Kleykamp [13].

119

Fig. 4. The calculated activities of Mo and Ru at 1200 and 1400 K, compared with experimental data by Cornish and Pratt [7] and Kleykamp [13].

5. Summary Two sets of self-consistent thermodynamic descriptions for the Mo–Ru binary system were obtained through a thermodynamic analysis of the system. Though thermodynamic models employed were simple and a limited number of parameters were used, the calculated phase

Fig. 5. The calculated metastable Mo–Ru phase diagram where s phase is suspended. The solid lines and dotted lines are phase diagrams calculated with the parameters obtained in the present work and in the work of Cornish and Pratt [7], respectively.

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diagram satisfactorily reproduce the experimental information available in the literature. Though some disagreement is noted between reported thermodynamic properties of bcc and hcp phases, the evaluated thermodynamic parameters could be served as a part of the thermodynamic database for the next generation Ni-base superalloys.

[7] [8] [9] [10] [11] [12] [13] [14]

Acknowledgements The present study has been carried out in the framework of ‘High Temperature Materials 21 Project’ at National Research Institute for Metals. One of the authors (C.-S. Oh) would like to express his gratitude to Japan Science and Technology Corporation for financial support through the Science and Technology Agency (STA, Japan) Fellowship Program.

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