Database development and Calphad calculations for high entropy alloys

Materials Chemistry and Physics xxx (2017) 1e12

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips Hai-Lin Chen a, *, Huahai Mao a, b, Qing Chen a a b

€gen 18, 16967 Solna, Sweden Thermo-Calc Software AB, Råsundava KTH Royal Institute of Technology, Department of Materials Science and Engineering, 10044 Stockholm, Sweden

h i g h l i g h t s
A 15-element thermodynamic database (TCHEA1) was developed especially for HEAs.
It has 105 binaries, 200 ternaries, and almost all phases in each assessed system.
The development faces new challenges, especially the daunting number of ternaries.
It needs reliable extrapolations into metastable regions and higher order systems.
Examples are made for performing relevant calculations and interpreting the results.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 June 2017 Received in revised form 18 July 2017 Accepted 24 July 2017 Available online xxx

The development of a reliable multicomponent thermodynamic database for high entropy alloys (HEAs) is a daunting task and it faces new challenges comparing to the development of databases for conventional single principal element alloys, such as the assessment of a large number of ternary systems, the proper estimation of phase stability within metastable compositional and temperature ranges, and the reasonable extrapolation into higher order systems. We have recently established a thermodynamic database (TCHEA1) especially for HEAs within a 15-element framework. This work highlights the usage of high throughput density functional theory (DFT) calculations for validating and refining the binary and ternary parameters of the solid solution phases, and having a more reliable extrapolation into metastable regions and higher order systems. TCHEA1 consists of 105 binaries and 200 ternaries and contains nearly all the stable solution phases and intermetallic compounds in each of the assessed systems. Together with Thermo-Calc, this database enables us to predict the stability of the desired multicomponent solid solution relative to intermetallic compounds and other solid solutions. Calculation examples are presented not only for case studies but also for bridging the knowledge gap between Calphadian and people who do not have a background of the Calphad approach. © 2017 Published by Elsevier B.V.

Keywords: High entropy alloys Calphad Thermodynamic database Thermodynamic calculation

1. Introduction High entropy alloys (HEAs) are alloys containing usually more than 5 principal elements and 5 to 35 at.% for each [1]. As the name suggests, it was believed that the high configurational entropy in these alloys should play a prominent role and stabilize solid solution phases against the formation of intermetallic phases, which were considered often detrimental to alloy properties. Theoretically speaking, the high entropy effect could be true only

* Corresponding author. E-mail address: [email protected] (H.-L. Chen).

when the enthalpy effect can be ignored. As a matter of fact, intermetallic phases have been found more and more frequently in recent years in high entropy alloys previously reported as alloys that contained only one single solid solution phase [2]. Some of those intermetallic phases can actually be beneficial and act as strengthening phases to improve significantly the alloy properties. Therefore, considering the proven limitation of the entropy effect and the obvious difference of these alloys from conventional alloys based on a single component, other names, such as “multi-principal element alloys (MPEAs)” or “complex concentrated alloys (CCAs)”, have been proposed for equiatomic [3] or nearequiatomic alloys with or without addition of other minor alloying elements and that are composed of solid solution phase(s)

http://dx.doi.org/10.1016/j.matchemphys.2017.07.082 0254-0584/© 2017 Published by Elsevier B.V.

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

2

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

decorated without any or with some intermetallic phases [2]. While these new names are perhaps more appropriate, “HEAs” is still the most well-known and the most popular one and this will probably not change in future. In the present work, no attempt is made to differentiate one name from the other, and all names are used interchangeably but with some specific intentional focuses: “MPEAs” is used for stressing the fact that this category of alloys contains multiple instead of only one principal component; “CCAs” is used for emphasizing the point that microstructural complexity is common with this type of alloys; and “HEAs” is used broadly in all other situations. The significance of the concept of MPEAs is that for the first time the search of new materials has been switched systematically from the small and relatively-well-explored corner regions to the vast uncharted central fields in the multi-dimensional composition space. This paradigm shift presents us unfathomable opportunities due to enormous possible combinations of the elements from the periodic table. Now more and more alloy researchers and developers are thinking differently and making explorations among these combinatorial alloys. Of course, many of the combinations are doomed based on the knowledge that we have accumulated so far, but some of them are inevitable to yield new alloys with unusual and attractive properties. As the number of possible combinations is immense, even a small fraction of it is still unbelievably large. Apparently, this tremendous potential has driven an explosive increase of interest in HEAs in recent years [2,4]. The immense number of possible HEAs brings us not only huge opportunities but also formidable challenges. It is simply inconceivable to rely on Edisonian approach alone for the exploration of the multi-dimensional composition space of HEAs. To meet the challenges, computational methods are indispensable in this silicon age. Different computational approaches, ranging from empirical rules [5,6] to semi-empirical Calphad method [7e12], and to theoretical first principles method [13,14], have been applied for screening of HEAs. For example, many empirical rules in terms of mixing enthalpy, mixing configurational entropy, total mixing entropy, atomic size mismatch, valence electron concentration, or the like, or a combination of two or more, have been proposed and utilized in order to explore potential alloy systems that could form simple solid solutions. In our opinion, both empirical and theoretical methods suffer from their critical limitations respectively, the former in oversimplification and the latter in expensive computational cost and inadequate accuracy. The semi-empirical Calphad approach is the method of choice. The Calphad method [15,16] has been widely and successfully employed in alloy development and research for decades. With the Calphad approach, the Gibbs energy of each phase (including liquid, solid solutions and intermetallic compounds) as a function of temperature, pressure, and composition can be evaluated by taking into account effects from both enthalpy and entropy, which depend on several physical contributions including that from electronic excitations, lattice vibrations, chemical ordering, and magnetic ordering, etc. The Calphad method has proven to be unique and superior in its capability to describe multicomponent systems due to the fact that the contributions to the Gibbs energy of a phase are mainly from binary and ternary systems in Calphad models. The model parameters of the binary and ternary systems can be assessed by considering all relevant experimental and theoretical information, being thermochemical or phase diagram, stable or metastable equilibrium, and equilibrium or non-equilibrium state. A collection of sets of optimal thermodynamic model parameters for all phases in binary and ternary systems forms a Calphad thermodynamic database. By using a Calphad computational tool, for example Thermo-Calc [17], together with such a database, both thermodynamic properties and phase equilibria in the binary and

ternary as well as multicomponent systems can be calculated on the basis of Gibbsian thermodynamics. The credibility of a Calphad calculation is solely dependent on the suitability and quality of the thermodynamic database used. Many thermodynamic databases available today are designed for conventional single principal element alloys. This means that 1) the thermodynamic descriptions included in such a database are mainly for the ternary systems containing the major component; 2) the thermodynamic descriptions may not be complete for a whole system but limited to only the major component rich corner; and 3) phases irrelevant to the targeted type of alloys are deliberately excluded. These databases are apparently not adequate for making predictions for MPEAs, where all ternary systems are in theory equally important. Recently, a new thermodynamic database, TCHEA1 [18], has been developed without the simplifications and omissions pertinent to conventional databases. In this database, all binary and as many as possible complete ternary systems have been included. Since its debut about 2 years ago, TCHEA1 has been applied by many groups interested in HEAs to interpret the experimental phase formation and to explore new alloys and new compositions [19e24]. In this paper, the development of TCHEA1 is reported first. Thermodynamic models for various phases are described. Challenges encountered and strategies used in the database construction are highlighted. Then a few case studies using this database are given to demonstrate the capability of this database in predicting both equilibrium and non-equilibrium phase constitutions in a variety of HEAs. Meanwhile, guidance for making relevant calculations and interpreting calculated 2D sections of a multidimensional phase diagram has been provided also. In the end, a summary of this work is presented. 2. Database development for HEAs: the challenges and strategies The Calphad approach has proven to be useful in materials design and process optimization since it provides an effective and efficient way to map multicomponent phase diagrams by doing mathematical interpolation and extrapolation of the Gibbs energy function of each phase in the composition, temperature, and pressure space. The reliability of a Calphad calculation depends almost entirely on the quality of the database being used. The software for making the calculation can be different in its generality and user-friendliness, but it usually plays no role in the quality of the calculation results. This means that developing a good thermodynamic database is vital for the exploration of new systems and compositions of promising MPEAs. As MPEAs contain multiple principal elements and the selection of elements has no boundaries in the periodic table, the numbers of included elements and assessed systems matter very much in determining whether a database is suitable for MPEAs or not. Needless to say, the database is truly “the bigger, the better” for designing and understanding MPEAs. The development of a big and reliable database for MPEAs is not an easy task and it faces new challenges that do not exist in the development of conventional single component based alloy databases. The two major tasks are the reliable extrapolation of thermodynamic properties of solution phases into metastable compositional ranges and higher order systems and the assessment of a large number of ternary systems. 2.1. Extrapolation into metastable region and higher order systems Calphad approach is intrinsically capable of making extrapolations to metastable regions and to higher order systems. A

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

thermodynamic database is constructed by assessing systems from unary to binary and then to ternary systems. Unary descriptions are generally accepted as a foundation for Calphad assessments, and standard compilations exist such as the earlier work by Dinsdale [25] or the latest SGTE database PURE5 [26] included in ThermoCalc. Quaternary parameters are rarely used since their contributions would be negligible. The major task for developing a database is to model the binary systems and key ternary systems. For substitutional solution phases, such as liquid, Fcc_A1, Bcc_A2, Hcp_A3, the interaction parameters assessed in each individual binary and ternary system are used for calculating the excess energy in multi-component systems. The basic form for the contributions of binary and ternary interactions to the nonmagnetic excess Gibbs energy, E Gm ; of a n-component substitutional solution is given below E

Gm ¼

n1 X n X i¼1 j¼iþ1

xi xj Lij þ

n2 n1 X X

n X

xi xj xk Lijk

(1)

i¼1 j¼iþ1 k¼jþ1

The equation is a sum over binary interactions in all i-j systems and ternary interactions in all i-j-k systems. The mole fractions of each constituent (xi ; xj ; and xk ) are used and there is no assumption that xi þ xj ¼ 1 or xi þ xj þ xk ¼ 1 [15]. Lij and Lijk are binary and ternary interaction parameters respectively. They are constants if the solution is regular, but in general they are functions of composition, temperature, and pressure themselves. The interaction parameters are often evaluated in individual systems based on experimental data on phase equilibria and/or thermodynamic properties. If a solution phase has a very limited homogeneity range, the data available are usually limited to that small range too. This gives no problem in building databases for conventional alloys, but generates large uncertainties for MPEAs. In other words, for conventional alloys, e.g. Al-based alloys, available binary and ternary descriptions can usually be directly used for extrapolation into multi-component systems with satisfied results, but for MPEAs, one needs to be extremely careful in accepting existing binary and ternary parameters. For instance, in the Al-Cu binary system, the maximum Cu solubility in the (Al) solution is only about 2.5 at.% (547.6  C) and the Al solubility in (Cu) is up to 20.5 at.%. The (Al) boundary has been well determined with experiments and the parameters, LAl;Cu , describing the interaction between Al and Cu in the (Al) phase have been obtained by reproducing the experimental phase boundary and the phase equilibria associated with (Al). These binary interaction parameters, together with LAl;Fe and LCu;Fe , have been used successfully for the extrapolation into the Al-Cu-Fe ternary system for the ternary Fcc_A1 (Al) solid solution [27]. This is possible because the ternary (Al) solution is confined to the Al-rich corner, and the compositions, xAl , xCu , and xFe , which are the coefficients used for calculating the contribution of the LAl;Cu /LAl;Fe parameters, vary in a comparable range to that in the Al-Cu/Al-Fe binary system. In this case, the contribution from the LCu;Fe parameters is not significant since both xCu and xFe are very small, which means the accuracy for the interaction between minor elements is not that important for modeling of conventional alloys. Unlike the aluminium alloys, high entropy alloys may have several (typically four or five) principal elements and their compositions are usually equiatomic or near equiatomic. Taking the known Al-Cu-Fe-Ni-Co system as an example, all the xi ði ¼ Al; Cu; Fe; Ni; CoÞ fractions may have values of about 0.2, so all the binary and ternary interaction parameters are equally important and their contributions are all significant and cannot be ignored. At the same time, the existing parameters have to be validated over a wide compositional range, which is often beyond

3

the range where experimental data are available in corresponding binary and ternary systems. For instance, asymmetric descriptions are often derived for binary and ternary solutions, but they may just be a consequence of overfitting although they can be safely used most time for single component rich solution phases. On the other hand, the thermodynamic property of a solution might be truly asymmetric in a system, but a symmetric description was found sufficient to account for the experimental data if they are limited in a very narrow compositional range. In this case, the symmetric description would be an oversimplification. Such unrealistically too complex or too simple descriptions are potentially problematic in the extrapolation into a wider compositional range. In this sense, a database specially developed for high entropy alloys needs more reliable descriptions of individual phases, not only the substitutional solution phases but also intermetallic phases, such as the sigma phase, and their solid solutions. Moreover, the extrapolation of the thermodynamic description of the solution phases into higher order systems demands a proper evaluation of end-member parameters and interaction parameters of the phase in binary and ternary subsystems where it is not stable. This demand exists in the development of databases for conventional alloys as well. For an HEA database, however, the extrapolation to near equiatomic multi-compositions makes a reasonable evaluation of such metastable parameters far more important, and dramatically increases the number of metastable parameters that need to be assessed. Additionally, a reasonable assessment of metastable parameters is more difficult than that of stable ones due to the lack of experimental data. In order to tackle the challenge in the reliable extrapolation of the solution phase descriptions into metastable compositional ranges and higher order systems, high throughput (HT) density functional theory (DFT) calculations are employed to generate mixing enthalpy data for solid solutions (especially in metastable compositional ranges) and formation enthalpy data for intermetallic phases (especially for metastable end-members). High throughput is achieved by using the flowchart with MedeA [28]. Calculations for intermetallic phases are straightforward. To simulate random solid solutions, special quasirandom structures (SQSs) [29,30] are used for binary Fcc_A1, Bcc_A2 and Hcp_A3 and ternary Fcc_A1 [31] and Bcc_A2 [32]. Compared to supercells, SQSs can be chosen to be much smaller thus the calculations with them are much more efficient while the results are of comparable accuracies. The mixing enthalpies are very useful for validating/supporting the descriptions of individual systems and for identifying unrealistic parameters as well as helping to improve the descriptions. It is worth noting that in many alloy systems, the common ordered structures L12 and B2 exist. L12 can be regarded as an ordered structure of Fcc_A1 and B2 as an ordered structure of Bcc_A2. In order to describe the potential second-order transition between an ordered structure and its disordered counterpart, the ordered and disordered structures have to be described with a single continuous Gibbs energy description [33,34] using the so-called partitioning model,

  ord s ord Gm ¼ Gdis m ðxi Þ þ Gm yi  Gm ðxi Þ

(2)

The first term corresponds to the Gibbs energy of the disordered structure, which can be independently assessed on the experimental information of the corresponding disordered phase, and it is described with the substitutional model. The second and the third terms are the contributions from the ordering parameters calculated by using the site fractions ysi and the mole fractions xi respectively. The difference between the second and the third term is the Gibbs energy of ordering. When the phase is fully disordered,

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

4

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

the fractions of each constituent on each site are equal and thus equal to the mole concentration, i.e. ysi ¼ xi , and the second and the third terms cancel out each other so that the total energy is identical to that of the disordered part.

2.2. The need to assess a large number of ternary systems In a database development, the major task is to derive consistent descriptions of binary systems and key ternary systems. Thermodynamic descriptions for most common binary systems are available in literature or existing databases. On one hand, they are usually based on consistent compilations of unary descriptions. On the other hand, incompatibilities might exist due to the different selection of phase models or the different values for certain model parameters. Very often the binary descriptions in literature can be incorporated into a database directly or with moderate modifications. In some cases, a binary system needs to be modeled or remodeled, while in general the modeling or remodeling is relatively simple for a binary system. For ternary systems, however, published descriptions in literature are usually inconsistent. The inconsistencies can be caused by different models or different values for model parameters. Except for the common substitutional solution phases (such as Fcc_A1, Bcc_A2 and Hcp_A3) and a few well known compounds (such as Laves C14, C15 and C36), there are no unique models for other phases. Even for the liquid phase, one may choose between the substitutional solution model or the so-called ionic liquid model or even the (modified) quasi-chemical model. Simple ordered structures based on Fcc_A1 and Bcc_A2 are often (but not always) described with so-called partitioning models. Even if the same model is employed to a phase with a specific crystal structure type, different values are often assigned to the same parameter in different assessments since different binary descriptions have been adopted. Conventional alloys are based on one or two principal metallic element, such as steels, aluminum alloys, a and b titanium alloys and alloys based on g-TiAl. The development of a database for such alloys can be significantly simplified by screening out unimportant ternary systems free of the principal element(s) and being focused on the principal element(s) rich composition ranges. The former means that only the important ternary systems are to be modeled and the latter means that the modeling can be focused on the most important composition range. For a database aiming for HEAs, most elements can be principal ones in any specific unexplored sub-systems. In a given framework, it might be true that certain elements are more frequently used in the development of HEAs than the rest based on the existing investigations and publications. However, the Calphad method is expected to help people who are doing materials design to explore the unknown compositional regions and find new potential alloy systems. The unknown regions could become more important in near future. In general, all the ternary systems can be (although not equivalently) important and shall be properly assessed. Considering a 15 element framework, there are in total 455 ternary systems. To the best of our knowledge, 70 is on average already a good one for number of the ternary descriptions included in a reasonable commercial database of conventional alloys (TCAL4, TCMG4), and few databases (TCNI8) contain more than 200 assessed ternary systems. The main reasons for not having all ternary combinations are (1) the assessments are costly and time-consuming and (2) the quality of a database for conventional alloys can be assured with a good number of assessed ternary systems containing the principal element(s). Private and academic databases are expected to be even smaller.

Considering a 25 element framework, which is a decent but not big number to conventional databases, there would be 300 binary systems and 2300 ternary systems. 300 binary systems are still doable but the assessment of 2300 ternary systems would at least take a very experienced Calphadian 100 years assuming that the person is efficient enough to accomplish the assessment of 23 ternary systems per year. This is almost a mission impossible to most companies, institutes and academic groups that are engaged in Calphad modeling. Despite that increasing the number of elements would exponentially increase the number of systems to be assessed, a comprehensive database developed within a 25 element framework is still desired in order to avoid screening out potential alloy compositions. On one hand, the development has to start with a relatively small framework in order to avoid involving too many systems. On the other hand, the framework should be big enough to enable a meaningful exploration of the MPEA compositions. The strategy is to identify the elements which appear as principal elements in different MPEAs. The non-principal ones, such as B, C, N and Si, might be considered as alloying elements or additives. Certain systems and compositions can then be considered unimportant or less important and screened out from the development temporarily. In the recent work, Miracle and Senkov [2] introduced two parameters, fAB and fAT (which designate the fractions of assessed binary systems and ternary systems, respectively), to evaluate the credibility of Calphad calculations made for HEAs. Based on our experiences in thermodynamic modeling, database developments and Calphad calculations, the binary descriptions are fundamental and fAB should approach 1. This means that in principle all binary systems should be assessed as long as experimental data are sufficient. Ternary descriptions are also important, while it is almost an impossible mission to have all ternary systems assessed within a large multicomponent database. Considering that some ternaries can be reasonably extrapolated based on binary descriptions, and taking into account the fact that roughly 50% ternary systems made of common elements lack experimental data, it is arbitrarily suggested that fAT should be no less than 40e60%. 2.3. The TCHEA database The first version of the thermodynamic database for high entropy alloys, TCHEA1, is developed within a 15 element framework: Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Ta, Ti, V, W and Zr. A relatively small and feasible framework is chosen since the number of ternary systems that need to be assessed increases exponentially with the increase of the number of element. On the other hand, this framework is of a decent size and actually the biggest among the same type of databases to the best of our knowledge. All the 105 binaries and about 200 ternaries (44% of all the possible combinations) have been assessed and included. All the phases in the assessed systems are modeled except for a few solid phases that are controversial or lack experimental data. Appropriate thermodynamic models are used for different types of phases and the selection of the models is published elsewhere [35]. During the course of the review of the paper, TCHEA2 is released. 5 elements are added in the 2nd version of the database, C, N, Si, Re and Ru. Note that all the calculations in this manuscript are performed with TCHEA1. 3. Knowledge gap to bridge Although the reliability of Calphad calculations is to a large extent determined by the quality of the database, it also depends on how they are performed and how the results are interpreted.

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

5

3.1. Applicable regions Before calculations are made, one should be aware of the limit of a database. It is a common mistake to misuse a reliable database beyond its applicable region. Every database has its own applicable regions and inapplicable ones. The applicable regions are the composition and temperature ranges in which a database has been validated. In principle, calculations can be reliably performed within only these regions. Calculations beyond these regions are sometimes necessary due to the lack of a more suitable database and the “extrapolation” is also allowed, but one has to be aware of the risks and be able to evaluate the reliability of the results. As a general rule, an Al alloy database shall be used only for aluminum alloys and an Mg alloy database only for magnesium alloys. If necessary, an Al alloy database (e.g. TCAL4) might be reasonably used for making predictions for the phase formation in AZ91 magnesium alloys since the Al-Mg-Zn system has been well assessed and many Mn- and Si- containing systems are included there. As elucidated in Section 2, however, most alloy databases1 that have been developed for conventional alloys are considered inapplicable for HEAs. 3.2. Vertical sections A vertical section, which is sometimes referred to as an “isopleth”, is a diagram showing the phase equilibria along a specific composition line and over a temperature range. Vertical sections are diagrams of phase equilibria, in which metastable phases could be involved if necessary. They are often employed to interpret the impact of the variation of a composition on the phase equilibria over a wide temperature range or comparing the phase formation in a series of compositions during heating or cooling. Phase regions and boundaries among them are shown in such two-dimensional (2D) diagrams. Such a 2D diagram appears to be similar to a binary phase diagram, but there is a very important difference: the level rule does not hold there. In other words, the phase boundaries of a two-phase region at specific temperatures in an ordinary isopleth do not correspond to the equilibrium compositions of the two phases. As marked in the vertical section Cr0.5Ni0.5 to Cr (Fig. 1a), the alloy Co0.25Ni0.25Cr0.50 is located in Fcc_A1 þ Sigma two-phase region at 1200  C, which is adjacent to the Fcc_A1 and Sigma singlephase regions. The boundaries merely mark the end of the two phase region, and their compositions are different from the equilibrium compositions of the two phases. The tie-line, which stands for the composition line connecting the two equilibrium phases, is not confined within the vertical section. This can be clearly illustrated with an isothermal section at the same temperature (see Fig. 1b). The phase boundary varies in different vertical sections which cut the tie-lines. There are an unlimited number of such sections. The tie-line, however, is unique for a specific composition at a specific temperature. In the isothermal section, e.g. Fig. 1b, one may always find a particular composition line, which goes in the same direction as the tie-line does. However, the tie-line rotates in ternary and high order systems as the temperature changes. The vertical section along that particular line would be still invalid for predicting the equilibrium compositions in that two phase region at different temperatures, not to mention the other multi-phase

1 The Ni-based superalloy database, TCNI8, contains a great number of binary and ternary systems. It is the basis of the first version of the TCHEA database. It is almost equally good for TCHEA1 at making calculations for HEAs, but its usage in HEAs is not suggested since TCHEA2 is available.

Fig. 1. Calculations for the Co-Cr-Ni system (a) vertical section from Cr0.5Ni0.5 to Cr and (b) isothermal section at 1200  C.

regions in that section. Only in rare cases, tie-lines can be tentatively drawn in a vertical section. Such a vertical section is known as a pseudo binary phase diagram and the composition line that the section is based on can be considered as a pseudo binary system. Pseudo binary phase diagrams cannot be arbitrarily drawn, unless such systems truly exist. Fig. 2 presents the calculated vertical section for the Co1Cr1Fe1Ni1Alx (0 < x < 2) alloys. The base alloy Co1Cr1Fe1Ni1 is made of transitional metals. In general, the Al addition not only stabilizes the Bcc structures and but also result in the formation of the ordered Bcc_B2 phase. In fact the Bcc_B2 phase is stable at the central areas of the Al-Co [36] and Al-Ni [33,37] binary systems. Unlike Co and Ni, Bcc_A2 Cr and Fe are stable and can have large solubilities of Al. The dissolution of Al, however, may transform disordered

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

6

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

Fig. 2. Calculated phase equilibria in the Co1Cr1Fe1Ni1Alx (0 < x < 2) system.

Bcc_A2 to ordered Bcc_B2, respectively, in the Al-Fe [38] and Al-Ni binary systems. Even though the general trend in the multicomponent alloy can be postulated from the features in the individual binary systems, more reliable predictions on the transition temperatures and compositions can be made only with Calphad calculations. Without Al, the phase formed in as-cast Co1Cr1Fe1Ni1 alloy is dominated by Fcc_A1. Adding about 11.11 at.% Al (x ¼ 0.5) could result in the formation of B2, which forms after Fcc_A1. According to Fig. 2, eutectic composition is reached around 13.98 at.% Al (x ¼ 0.65). Further increasing the Al content causes the exchange of the solidification sequence and the primary formation of B2. When the Al content increased up to more than 18.37 at.% Al (x ¼ 0.9), Fcc_A1 might be absent during the fast solidification. The compositional range from 11 to 18 at.% Al can be considered as a near-eutectic region, where both Fcc_A1 and B2 can form in as-cast alloys. The region can be further divided into a hypo-eutectic region and a hyper-eutectic region. The compositions corresponding to the start of B2 and the vanishing of Fcc_A1are marked with dashed lines in Fig. 2. They are estimated based on the present calculation and can well account for the experimental observations in literature [39]. The as-cast alloy compositions investigated by Ref. [39] are imposed on the top of the diagram and different symbols are used for indicating the identified phases in individual alloys.

while that in solid phases is negligible. Such simulations correspond to local-equilibrium solidifications. A real solidification may significantly deviate from a Scheil simulation due to several reasons. To name but a few, (1) The diffusion in liquid is not sufficiently high either because the cooling rate is too high or the temperature is too low; (2) the back diffusion in solid phases is not always negligible; (3) phases that have high nucleation barriers may not be able to form. Experimental solidifications may be better accounted for by equilibrium calculations, depending on alloy systems and compositions as well as the experimental conditions (especially the cooling rate). It is a good practice to always consider both types of simulations. Generally speaking, the more the solidification deviates from the equilibrium state, the higher the possibility for an additional phase to form at late stages. Fig. 3 presents the phase formation sequence during a Scheil solidification simulation of the alloy with an Al content of 21.57 at.% (i.e. the alloy Co1Cr1Fe1Ni1Al1.1). As one can see, the Fcc_A1 phase could form at the end of the simulation. Additional data show that its amount can be up to 4%. The experimental solidification is expected to proceed to this stage at relatively high cooling rates. The data imposed on the bottom of Fig. 2 are from Ref. [40] and they give the composition limits for the formation of Bcc, Fcc_A1 and Bcc þ Fcc_A1, respectively. The as-cast results well accord with the present estimation. The Fcc_A1/Bcc þ Fcc_A1 boundary, determined from the alloys treated at 1100  C for 24 h, is in good agreement with the present calculation. The Bcc þ Fcc_A1/Bcc boundary was determined at two different compositions from the alloys treated at 1100  C for 24 h and those homogenized at 1100  C for 24 h and then cold rolled. The discrepancy in whether or not Fcc_A1 is to form depends on how far the experimental solidification deviates from the equilibrium conditions, as discussed above. If Fcc_A1 occurs, then the question is if it can be fully dissolved during such short homogenization. The calculated Bcc þ Fcc_A1/Bcc boundary is located between the two data and considered reasonable. Despite of the agreement, it is also worth noting that [40] probably did not distinguish the ordered B2 phase from the disordered Bcc_A2 phase, which is predicted in the present calculation

3.3. Non-equilibrium phase formation The observed phase formation in a practical process, such as solidification, is more or less a result of non-equilibrium phase transformation due to the kinetic factors. There exist two kinds of typical mistakes in the application of Calphad calculations. One is that equilibrium calculations are always used to interpret the phase formation, even if it obviously deviates from the equilibrium conditions. The other, to the opposite extreme, is that Scheil simulations are always used to account for the formation of as-cast microstructures. It should be emphasized that Scheil simulations hold the following assumption: the diffusion in liquid is sufficient

Fig. 3. Equilibrium (in dashed line) and Scheil (in solid line) solidification simulations of the Co1Cr1Fe1Ni1Al1.1 alloy (21.57 at.% Al).

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

7

and has been observed in experiments [41]. The equilibrium diagram in Fig. 2 shows that Bcc_A2 could form in alloys with more than 20 at.% Al via a decomposition of the B2 phase. The simulation (Fig. 3) even suggests that Bcc_A2 could form during nonequilibrium solidifications even though B2 is the only phase that forms under equilibrium conditions. The phase formation in the Co-Cr-Fe-Ni-Al HEAs is worth a detailed discussion, which is beyond the scope of this paper. 3.4. Solidification of eutectic alloys Very recently, a new eutectic-type HEA was successfully designed to form a mixture of soft Fcc_A1 and hard Bcc_A2 phases, to achieve the balance of high fracture strength and high ductility in the pioneering work by Ref. [42]. Near eutectic compositions are desired in the alloy design, since a narrow solidification temperature range alleviates the segregation and shrinkage cavity and improve castability. It needs to be pointed out that, according to the Gibbs phase rule, a two-phase eutectic is not an invariant reaction in a multicomponent system. As an example, the near eutectic composition Co1Cr1Fe1Ni1Al0.65 (13.98 at.% Al) in Fig. 2 was subjected for solidification simulations. The results are shown in Fig. 4. Note that the selection of an exact eutectic composition is impossible for a numerical simulation. Except for the negligible first stage of the formation of the B2 phase, B2 and Fcc_A1 form concurrently during the whole solidification process. The composition being used can be regarded as a eutectic one. The absence of a horizontal plateau indicates the non-invariant feature of the solidification. The variation of the reaction temperature is attributed to the fact that the averaged composition of the two solid phases differs from that of the liquid. The solidification of the eutectic phases consequently causes a continuous accumulation of certain solutes, especially Ni and Cr, in the residual liquid, as seen in Fig. 4b. The change in the liquid composition lowers the solidification temperature. This widens the solidification window and causes compositional and microstructure segregations, especially in the Scheil simulation. The Scheil simulation noticeably deviates from the equilibrium one after 40% solid phases. The slope of the curve of the solid phase fraction becomes steeper as the solidification proceeds, especially after the solid phase reaches 70%. The solidification of the residual liquid is expected to be completed at a rather low temperature. Considering 1% residual liquid, the solidification window can be up to 30 K. It should be added that the liquid composition constantly changes during the solidification, as shown in Fig. 4b. The compositions below the dashed-dotted line all correspond to the same reaction of L ¼ Bcc_B2 þ Fcc_A1. In other words, a two-phase eutectic reaction does not occurs at a constant temperature nor at a fixed composition in a multicomponent system. The change in the eutectic composition provides an opportunity for the alloy design, even if the formation of a specific type of eutectic microstructure is desired. The impact of the composition variation on the phase formation, microstructure formation and potential segregation and how to optimize the eutectic composition is to be discussed in a separate paper. 3.5. Phase formation in Cantor alloys The Co1Cr1Fe1Mn1Ni1 equiatomic alloy had been investigated by Cantor et al. [3] for the first time and is known as one of the “Cantor alloys”. The melt-spun microstructure is of the Fcc_A1 single phase. Otto et al. [43] recently reinvestigated the alloy with prolonged heat treatments. The alloys were annealed at 500  C, 700  C and 900  C, respectively, for 500 days.

Fig. 4. Solidification simulation of the eutectic alloy Co1Cr1Fe1Ni1Al0.65 (13.98 at.% Al): (a) phase formation sequence and solid phase fractions from equilibrium (in dashed line) and Scheil simulation (solid line); and (b) liquid phase composition from Scheil simulation.

Figs. 5e8 present the results of an equilibrium stepping from liquidus temperature down to 400  C. Fig. 5 shows that Fcc_A1 would be the only phase that can form during the solidification and the single phase state remains for a wide temperature range. This can well account for the observation of single Fcc_A1 phase in the as-cast alloy [3] and in the alloy annealed at 900  C [43]. In this case, no Scheil simulations are performed, since the formation of an additional phase during non-equilibrium is highly unlikely considering the high stability of Fcc_A1 over other phases at high temperatures. The precipitation of the Cr-rich sigma phase was observed at 700  C [43]. The calculation (Figs. 5 and 6) does predict the

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

8

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

Fig. 7. Calculated composition of Bcc_B2 in alloy Co1Cr1Fe1Mn1Ni1. Fig. 5. Stepping equilibrium calculation of Co1Cr1Fe1Mn1Ni1. The dashed line was recalculated by adding 1200 J/mole-atoms to the energy of Sigma.

Fig. 8. Calculated composition of Bcc_A2 in Co1Cr1Fe1Mn1Ni1. Fig. 6. Calculated composition of sigma in alloy Co1Cr1Fe1Mn1Ni1.

formation of a Cr-rich sigma phase but at temperatures slightly lower than 600  C. Apparently the sigma phase is underestimated. The discrepancy seems quite big in terms of the temperature difference. However, the underestimation should be evaluated in terms of Gibbs energy. With Thermo-Calc, the driving force (-DG/ RT) of the Sigma phase is calculated at 700  C to be 0.1291, which corresponds to energy of about 1044 J/mole-atoms. This means that Sigma can be stabilized at 700  C if its energy is lowered by that amount or more. Thus the formation of Sigma was recalculated by adding an additional energy term of 1200 J/mole-atoms and was presented in dashed line in Fig. 5. The energy addition is in the

same magnitude of the experimental uncertainty in typical calorimetric measurements. The sample equilibrated at 500  C even consists of three phases at the Fcc_A1 grain boundaries, Mn and Ni-rich L10, Cr-rich Bcc_A2 and Fe and Co-rich Bcc_B2. Both Bcc phases were predicted even though they are also a bit underestimated. The driving forces of A2 and B2 are calculated at 500  C to be at 0.0676 and 0.1671, respectively, corresponding to an energy term of 435 and 1074 J/ mole-atoms. As shown in Fig. 7, the B2 phase is rich in Co and Fe. The Co and Fe contents are calculated to be about 42 at.% and 47 at.%, which agree well with the experimental values of 45.9 at.% and 46.0 at.%, respectively. As shown in Fig. 8, the A2 phase is rich in

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

Cr and the Cr content is calculated to be 84 at.%, which is in a good agreement with the experimental value of 86.3 at.%. The calculated Fe and Co contents are also comparable with the experimental reports. The L10 phase is not predicted in the present calculation. This phase was treated as an independent phase from Fcc_A1 in the Mn-Ni binary system. The experimental results suggest that it can dissolve a small but noticeable amount of Co, Cr and Fe. L10 might be stabilized by considering the solubilities of these elements. Note that L10 is an ordered structure of the Fcc_A1 phase and it can be treated as the same phase as Fcc_A1 and L12 if the so-called 4sublattice portioning model [33] is used in the thermodynamic modeling. The failure in predicting L10 might account for the calculated high Mn content in Bcc_A2. Despite of the discrepancies, the agreement shall be considered remarkable in predicting the phase formation and the phase compositions, since the calculation is based on the extrapolation to the center region of the five-component system and that half of the ternary subsystems are missing in the very first database. As explained, the discrepancies are not significant in terms of Gibbs energy, though a refinement is needed in future development. Cantor et al. [3] also investigated the Co1Cr1Cu1Fe1Mn1Ni1 alloy prepared by means of melt spinning. They reported that “there was interdendritic segregation with no second phase” in the as-cast microstructures. The conclusion of the existence of single phase was drawn based on the results from XRD, but the interdendritic phase shall be considered as a second phase even though both the dendritic and interdendritic phases are of the Fcc_A1 type. From the thermodynamic point of view, the formation of two Fcc_A1 phases can be considered as the existence of a miscibility gap in the Fcc_A1 solution. The immiscibility is caused by the Cu addition. Cu is not miscible with Co, Cr and Fe in the Fcc lattice. At high temperatures a continuous homogeneous Fcc_A1 solid solution forms in the Cu-Mn [44] and Cu-Ni [45] binary systems, while it decomposes at low temperatures. The decomposition in Cu-Mn can be revealed in a metastable phase diagram, which can be readily calculated and thus not presented here in order to save space.

9

Fig. 10. The composition of the Cu-lean Fcc_A1 dendritic phase from the Scheil simulation of Co1Cr1Cu1Fe1Mn1Ni1.

Direct calculations were made for the multicomponent alloy composition Co1Cr1Cu1Fe1Mn1Ni1. Fig. 9 presents the total solid phase fractions from an equilibrium calculation and a Scheil simulation. Individual phase fractions of minor phases are imposed in the same plot and enclosed with dashed-dotted lines. The solidification starts with the formation of a Cu-lean Fcc_A1 phase (Figs. 9 and 10), corresponding to the dendrites observed in the ascast alloy. The second Fcc_A1 phase (labelled as Fcc_A1#2), which is Cu-rich (Fig. 11) starts to form when only about 30% liquid remains. Among the minor alloying elements, Mn and Ni have noticeably higher contents than Co, Cr and Fe, which makes sense according to our analyses on the binary phase diagrams above. The equilibrium solidification ends at the concurrent formation of the two Fcc phases, while the Scheil simulation even predicts the formation of a Cr-rich Bcc_A2. No Bcc_A2 phase was reported, either its amount was too little to be detected with XRD, or its formation was suspended by the rapid cooling.

3.6. Phase formation and compositional segregation

Fig. 9. Total solid phase fraction from the Scheil simulation (in solid lines) and equilibrium calculation (in dashed lines) of Co1Cr1Cu1Fe1Mn1Ni1. The phase fractions of the minor phases (Fcc_A1#2 and Bcc_A2) are imposed and enclosed with the dasheddotted lines.

Ma et al. [46] investigated as-cast equiatomic Al1Co1Cr1Fe1Ni1Nbx alloys with different amounts of Nb (x ¼ 0.1, 0.25, 0.50 and 0.75), which had been prepared with Cu-mould suction casting. In such cases, a vertical section, as shown in Fig. 12, is useful for systematically understanding the impact of the Nb addition on the phase formation. A two-phase eutectic point between Bcc_A2 and Laves_C14 is shown around x ¼ 0.4. The primary phase in the hypoeutectic alloys, such as those at x ¼ 0.1 and 0.25, is Bcc_A2. It changes to C14_laves phase in the hypereutectic alloys, such as those at x ¼ 0.50 and 0.75, The change of the primary phase with the increasing of the Nb content was supported by the as-cast microstructures, but C14 was experimentally observed as the primary phase only in the alloy x ¼ 0.75. This might indicate that the C14 phase needs to be destabilized a bit in the database. It should be noted, however, that the discrepancy might also be explained (or at least partly) by the potential nucleation difficulty at high cooling rate. As a topologically close packaged (TCP) phase, the nucleation

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

10

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

Fig. 11. The composition of the Cu-rich Fcc_A1 interdendritic phase from the Scheil simulation of Co1Cr1Cu1Fe1Mn1Ni1.

Fig. 13. Equilibrium stepping calculation for the alloy Al1Co1Cr1Fe1Ni1Nb0.25.

stages, the primary solidification of Bcc_A2 and the concurrent solidification of C14 and Bcc_A2. The second stage starts below 1270  C and the eutectic reaction accounts for the formation of the interdendritic structure in the as-cast alloy [46]. Figs. 14 and 15, respectively, show the compositions of Bcc_A2 and C14 for the alloy Al1Co1Cr1Fe1Ni1Nb0.25. Bcc_A2 is Al-rich while Laves_C14 Nb-rich, which is reflected by the dark contrast of the dendrites and the white contrast of the interdendritic phases. The microstructures published by Ma et al. [46] clearly evidence a severe composition segregation of the dendritic Bcc_A2 phase, since the center of each dendrite is much darker than its outer rim, but they did not investigate or even mention the segregation at all.

Fig. 12. Vertical section of Al1Co1Cr1Fe1Ni1Nbx (0 < x < 0.8) calculated with TCHEA1. The extension of the Bcc_A2 liquidus is in thick dashed line.

of C14 from liquid is expected to be more difficult than that of the simple Bcc_A2 phase. If the liquid phase could be sufficiently undercooled before C14 crystallizes, Bcc_A2 could probably start to form as a primary phase. A vertical section shows the phases that form and the formation sequence, and roughly gives the transition temperatures. For more details, such as the phase amounts and the phase compositions as well as the exact transition temperatures, one can run equilibrium stepping calculations for individual alloy compositions. Fig. 13 presents the phase formation sequence and the fraction of each phase in alloy with x ¼ 0.25. The solidification consists of two

Fig. 14. Calculated compositions of the Bcc_A2 phase from equilibrium stepping calculation for the alloy Al1Co1Cr1Fe1Ni1Nb0.25.

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

Fig. 15. Calculated compositions of the Laves_C14 phase from equilibrium stepping calculation for the alloy Al1Co1Cr1Fe1Ni1Nb0.25.

Fortunately, with the aid of the Calphad calculations, it is still possible to examine the microsegregations. Fig. 14 presents the Bcc_A2 composition, which changes noticeably and constantly during the solidification. It is much richer in Al (as well as Ni) at the early stage than the late stage, which accounts for the contrast within the dendrites. Note that there is sharp change in the slopes from the solidification of the Bcc_A2 single phase to that of Bcc_A2 and C14. Despite of the segregation, Ma et al. [46] reported only one set of composition for the dendritic phase in this alloy, which is in a general agreement with the calculated composition of Bcc_A2 at the early stage and indicates that they probably did a single point measurement on the center of the dendrite. It is interesting to notice that the calculated composition of Bcc_A2 maintains almost unchanged after the completion of the solidification and the five principal elements are nearly in equal amounts, i.e. close to the nominal composition of the alloy. The C14 phase was calculated to be Nb-rich (Fig. 15), which accounts for the white contrast of the interdendritic structure, but the calculated value is noticeably different from the as-measured composition Al12.20Co20.05Cr22.23Fe20.30Nb10.70Ni14.51. This is because the measurement was performed on the interdendritic structure or the “region B” in Ma et al. [46], which is not of the C14 single phase. The calculated liquid composition is calculated in order for interpreting the eutectic composition. As shown in Fig. 16, the liquid composition changes constantly during the course of solidification. It is the liquid composition during the stage of eutectic reaction (i.e. the late stage of the solidification as shown in Fig. 13) that shall be used for accounting for the composition of the eutectic structure. Note that the liquid composition also varies during the eutectic reaction. On one hand, a large uncertainty from the experimental measurements could be expected for the comparison. On the other hand, the composition of a mixture shall be measured in sufficiently big areas, if it had been appropriately performed, the as-measured value can be considered as the averaged value of the compositions at different locations. In this sense, one is suggested to use the liquid composition at the start of the eutectic solidification, as indicated with the thick dashed line in Fig. 16, since the

11

Fig. 16. Calculated compositions of the liquid phase from equilibrium stepping calculation for the alloy Al1Co1Cr1Fe1Ni1Nb0.25.

liquid at that moment will all transform to the eutectic structure despite of the segregation that occurs. It has been demonstrated in this example that Calphad calculations can make predictions for an alloy with given chemical composition, in the phase formation, the phase formation sequence, the transition temperatures, the phase amounts and the phase compositions. It highlights that the micro-segregation and the eutectic composition can be accounted for with proper interpretation of the calculated results.

4. Summary We have recently developed a thermodynamic database (TCHEA1) especially for HEAs within a 15-element framework. In order to have a proper estimation of phase stability within metastable compositional and temperature ranges and a reasonable extrapolation of thermodynamic properties into higher order systems, high throughput density functional theory (DFT) calculations of the enthalpy of mixing were used extensively for validating and refining the binary and ternary parameters for the solid solution phases. To have a full and precise picture of the phase competition in multicomponent systems, the formation energies of endmembers of intermetallic phases have also been calculated and utilized in the database construction. TCHEA1 consists of 105 binary and 200 ternary descriptions and contains almost all the stable solution phases and intermetallic compounds in each of the assessed systems. This database enables us to predict the stability of the desired multicomponent solid solution in relation to intermetallic compounds and other solid solutions. A few examples were given to show the good agreements between predictions and experimental observations. While it is undeniable that there are still rooms to improve, such as the underestimated stability of the sigma phase, favorable comparisons about the type and amount of phases formed and the microsegregation in non-equilibrium ascast state provides clear evidences for the capacity of this database. The importance of making right calculations that are relevant to experimental conditions was stressed. The meaning of a section phase diagram cut from a multidimensional composition space has also been discussed.

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082

12

H.-L. Chen et al. / Materials Chemistry and Physics xxx (2017) 1e12

References [1] J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299e303. [2] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. (2016) 1e64. [3] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375e377 (2004) 213e218. [4] M. Tsai, J. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett. 2 (2014) 107e123. [5] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10 (2008) 534e538. [6] S. Guo, C.T. Liu, Phase stability in high entropy alloys: formation of solidsolution phase or amorphous phase, Prog. Nat. Sci. Mater. Int. 21 (6) (2011) 433e446. [7] C. Zhang, F. Zhang, S. Chen, W. Cao, Computational thermodynamics aided high-entropy alloy design, JOM 64 (2012) 839e845. € lkl, U. Glatzel, [8] A. Manzoni, H. Daoud, S. Mondal, S. van Smaalen, R. Vo N. Wanderka, Investigation of phases in Al23Co15Cr23Cu8Fe15Ni16 and Al8Co17Cr17Cu8Fe17Ni33 high entropy alloys and comparison with equilibrium phases predicted by Thermo-Calc, J. Alloys Compd. 552 (2013) 430e436. [9] O.N. Senkov, J.D. Miller, D.B. Miracle, C. Woodward, Accelerated exploration of multi-principal element alloys with solid solution phases, Nat. Commun. 6 (2015) 6529. [10] H. Yao, J.-W. Qiao, M.C. Gao, J.A. Hawk, S.-G. Ma, H. Zhou, MoNbTaV mediumentropy alloy, Entropy 18 (2016) 189. [11] R. Feng, M.C. Gao, C. Lee, M. Mathes, T. Zuo, S. Chen, J.A. Hawk, Y. Zhang, P.K. Liaw, Design of light-weight high-entropy alloys, Entropy 18 (2016) 333. [12] C. Zhang, M.C. Gao, Calphad modeling of high-entropy alloys, in: M.C. Gao, J.W. Yeh, P.K. Liaw, Y. Zhang (Eds.), High-entropy Alloys: Fundamentals and Applications, Springer International Publishing, Cham, 2016, pp. 399e444. [13] W.P. Huhn, M. Widom, Prediction of A2 to B2 phase transition in the high entropy alloy MoNbTaW, JOM 65 (2013) 1772e1779. [14] F. Tian, L.K. Varga, N. Chen, J. Shen, L. Vitos, Ab initio design of elastically isotropic TiZrNbMoVx high-entropy alloys, J. Alloys Compd. 599 (2014) 19e25. [15] H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: the Calphad Method, Cambridge University Press, New York, 2007. [16] N. Saunders, A.P. Miodownik, Calphad - Calculation of Phase Diagrams: a Comprehensive Guide, Pergamon Press, Elsevier Science, Ltd., Oxford, 1998. [17] B. Sundman, Thermo-Calc, a general tool for phase diagram calculations, in: M. Doyama, T. Suzuki, J. Kihara, R. Yamamoto (Eds.), Computer Aided Innovation of New Materials, North Holland, 1991. [18] Thermo-Calc High Entropy Alloy Database, TCHEA1, Thermo-Calc Software AB, Stockholm, Sweden, 2015. [19] J.Y. He, H. Wang, Y. Wu, X.J. Liu, H.H. Mao, T.G. Nieh, Z.P. Lu, Precipitation behavior and its effects on tensile properties of FeCoNiCr high-entropy alloys, Intermetallics 79 (2016) 41e52. [20] D. Choudhuri, B. Gwalani, S. Gorsse, C.V. Mikler, R.V. Ramanujan, M.A. Gibson, R. Banerjee, Change in the primary solidification phase from Fcc to Bcc-based B2 in high entropy or complex concentrated alloys, Scr. Mater. 127 (2017) 186e190. [21] G. Bracq, M. Laurent-Brocq, L. Perriere, R. Pires, J.-M. Joubert, I. Guillot, The fcc solid solution stability in the Co-Cr-Fe-Mn-Ni multi-component, Acta Mater. 128 (2017) 327e336. [22] T.M. Butler, M.L. Weaver, Investigation of the phase stabilities in AlNiCoCrFe high entropy alloys, J. Alloys Compd. 691 (2017) 119e129. [23] A. Takeuchi, T. Wada, Y. Zhang, MnFeNiCuPt and MnFeNiCuCo high-entropy alloys designed based on L10 structure in Pettifor map for binary compounds, Intermetallics 82 (2017) 107e115.

[24] F. Tancret, I. Toda-Caraballo, E. Menou, P.E.J.R. Diaz-Del-Castillo, Designing high entropy alloys employing thermodynamics and Gaussian process statistical analysis, Mater. Des. 115 (2017) 486e497. [25] A.T. Dinsdale, SGTE data for pure elements, Calphad 15 (1991) 317e425. [26] SGTE Pure Element Database, SGTE, Scientific Group Thermodata Europe, 2009, Version 5.0. . [27] H.L. Chen, Y. Du, H. Xu, W. Xiong, Experimental investigation and thermodynamic modeling of the ternary Al-Cu-Fe system, J. Mater. Res. 24 (10) (2009) 3154e3164. [28] A. France-Lanord, D. Rigby, A. Mavromaras, V. Eyert, P. Saxe, C. Freeman, E. Wimmer, MedeA: atomistic simulations for designing and testing materials for micro/nano electronics systems, in: 15th International Conference on Thermal, Mechanical and Multi-physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2014. [29] A. Zunger, S. Wei, L. Ferreira, J. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65 (1990) 353e356. [30] S. Wei, L. Ferreira, J.E. Bernard, A. Zunger, Electronic properties of random alloys: special quasirandom structures, Phys. Rev. B 42 (15) (1990) 9622e9651. [31] D. Shin, A. van de Walle, Y. Wang, Z. Liu, First-principles study of ternary fcc solution phases from special quasirandom structures, Phys. Rev. B 76 (2007) 144204. [32] C. Jiang, First-Principles study of ternary bcc alloys using special quasirandom structures, Acta Mater. 57 (2009) 4716e4726. [33] I. Ansara, N. Dupin, H.L. Lukas, B. Sundman, Thermodynamic assessment of the Al-Ni system, J. Alloys Comp. 247 (1e2) (1997) 20e30. [34] N. Dupin, I. Ansara, B. Sundman, Thermodynamic re-assessment of the ternary system Al-Cr-Ni, Calphad 25 (2) (2001) 279e298. [35] H. Mao, H.-L. Chen, Q. Chen, TCHEA1: a thermodynamic database not limited for “high entropy” alloys, J. Phase Equilib. Diffus. 38 (4) (2017) 353e368. [36] H. Ohtani, M. Yamano, M. Hasebe, Thermodynamic analysis of the Co-Al-C and Ni-Al-C systems by incorporating Ab initio energetic calculations into the Calphad approach, Calphad 28 (2004) 177e190. [37] H.-L. Chen, E. Doernberg, P. Svoboda, R. Schmid-Fetzer, Thermodynamics of the Al3Ni phase and revision of the Al-Ni system, Thermochim. Acta 512 (1e2) (2011) 189e195. [38] B. Sundman, I. Ohnuma, N. Dupin, U.R. Kattner, S.G. Fries, An assessment of the entire Al-Fe system including D03 ordering, Acta Mater. 57 (2009) 2896e2908. [39] W.R. Wang, W.-L. Wang, S.-C. Wang, Y.-C. Tsai, C.-H. Lai, J.-W. Yeh, Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi highentropy alloys, Intermetallics 26 (2012) 44e51. [40] Y.-F. Kao, S.-K. Chen, T.-J. Chen, P.-C. Chu, J.-W. Yeh, S.-J. Lin, Electrical, magnetic, and Hall properties of AlxCoCrFeNi high-entropy alloys, J. Alloy Compd. 509 (2011) 1607e1614. [41] Y. Ma, B. Jiang, C. Li, Q. Wang, C. Dong, P.K. Liaw, F. Xu, L. Sun, The BCC/B2 morphologies in AlxNiCoFeCr high-entropy alloys, Metals 7 (2017) 57e68. [42] Y. Lu, Y. Dong, S. Guo, L. Jiang, H. Kang, T. Wang, B. Wen, Z. Wang, J. Jie, Z. Cao, H. Ruan, T. Li, A promising new class of high-temperature alloys: eutectic high-entropy alloys, Sci. Rep. 4 (2014) 6200. nov [43] F. Otto, A. Dlouhý, K.G. Pradeep, M. Kube a, D. Raabe, G. Eggeler, E.P. George, Decomposition of the single-phase high-entropy alloy CrMnFeCoNi after prolonged anneals at intermediate temperatures, Acta Mater. 112 (2016) 40e52. [44] C. He, Y. Du, H.-L. Chen, S. Liu, H. Xu, Y. Ouyang, Z.K. Liu, Thermodynamic modeling of the Cu-Mn system supported by key experiments, J. Alloys Compd. 457 (2008) 233e238. [45] B. Markovic, D. Zivkovic, J. Vrest’al, D. Manasijevic, D. Minic, N. Talijan, J. Stajic Trosic, R. Todorovic, Experimental study and thermodynamic remodeling of the Bi-Cu-Ni system, Calphad 34 (2010) 294e300. [46] S.G. Ma, Y. Zhang, Effect of Nb addition on the microstructure and properties of AlCoCrFeNi high-entropy alloy, Mater. Sci. Eng. A 532 (2012) 480e486.

Please cite this article in press as: H.-L. Chen, et al., Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips, Materials Chemistry and Physics (2017), http://dx.doi.org/10.1016/j.matchemphys.2017.07.082