- Email: [email protected]
Critical evaluation of ternary phase diagram data: Important considerations in the scrutiny of the correctness, coherence, and interpretation
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 68 (2020) 101719
Contents lists available at ScienceDirect
Calphad journal homepage: http://www.elsevier.com/locate/calphad
Invited article
Critical evaluation of ternary phase diagram data: Important considerations in the scrutiny of the correctness, coherence, and interpretation Oleksandr Dovbenko a, b, Liya Dreval a, Yong Du c, *, Yuling Liu c, **, Shuhong Liu c, Svitlana Iljenko a, Günter Effenberg a, 1 a b c
MSI, Materials Science International Services GmbH, 70565, Am Wallgraben 100, Stuttgart, Germany Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Kiev, 03142, Ukraine State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Calphad Critical evaluation Phase diagram Binary system Ternary system
Thermodynamic optimization of ternary phase diagrams via Calphad approach is a complex procedure. The success and quality of such a Calphad optimization depend on the reliability of the experimental data and on the scrutiny of the critical evaluation of the experimental datasets. With this in mind, we provide a set of recom mendations that might facilitate the critical evaluation procedure and improve the quality of the thermodynamic datasets for the calculations of the phase diagrams. The particulars regarding the consistency between binary and ternary phase diagrams as well as the internal agreement between the different ternary datasets, are discussed.
1. Introduction In more than 40 years since the publication of the book Computer Calculation of Phase Diagrams by Larry Kaufman [1], the Calphad approach initially intended to calculate phase diagrams, turned out to be a powerful instrument for solving numerous theoretical and practical questions, from materials development to process control. The successes of this approach have not only paved the way for the breakthrough in materials science, but also have created a false impression that to opti mize a system thermodynamically is a comparatively easy task and that the main obstacles on the way to the self-consistent thermodynamic database are related to the overflow of the experimental data or to a large number of phases to be incorporated in a database. The results of such distorted perception we are witnessing today. We have to stroll through the piles of the published thermodynamic assessments while we are looking for the papers with the published experimental data. This problem has been particularly raised in the paper of Ipser [2] and the Editorial by Watson [3] published in the Journal of Phase Equilibria and Diffusion. In turn, we would like to emphasize that the success of the Calphad optimization along with the selection of the proper models strongly depends upon the reliability of the experimental data, upon the scrutiny of the critical evaluation of the experimental datasets, and the
accuracy of the optimization technique. The fundamentals of the critical evaluation procedure for binary and ternary constitutional data were developed in Refs. [4,5] and applied by the experts from the Materials Science International Team in the critical evaluation of over 4500 ternary and binary systems. The present work intends to provide some guidelines and recom mendations concerning the critical evaluation of the experimental datasets for the ternary systems that may help the users and in particular the postgraduate and young researchers in producing reliable thermo dynamic descriptions. Therefore, the current paper should be considered as a continuation of the previous discussion about this procedure started by Lukas and Fries [6] and by Kumar and Wollants [7] and as an extension in that part which concerns the ternary phase equilibria. The thorough discussion of the accuracy and reliability of the different experimental methods lies outside our scope since this topic is too important and wide to limit it to the size of an article. Those, who are interested in the better experimental practice and its connection to the production of the reliable thermodynamic assessments, we would sug gest to refer to the recently published monography [8] and the paper from Ferro et al. [9]. Since the guidelines about how to avoid the possible pitfalls in the course of the thermodynamic optimization and facilitate this procedure were described by Lukas and Fries [6], Kumar
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Du), [email protected] (Y. Liu). 1 Deceased author. https://doi.org/10.1016/j.calphad.2019.101719 Received 5 August 2019; Received in revised form 28 November 2019; Accepted 29 November 2019 Available online 25 December 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.
O. Dovbenko et al.
Calphad 68 (2020) 101719
and Wollants [7], and lately by Schmid-Fetzer et al. [10] in detail, we shall touch upon this issue only briefly in connection with ternary systems.
ternary system should be started from the thorough exploration of the phase relations in the related binary systems. Moreover, the reasons behind the choice of a particular thermodynamic assessment for a binary system should be thoroughly explained and clear to the readers and users of a database. We can, therefore, conclude that there should not be an internal inconsistency between the binary and ternary data for a particular experimental study providing an isothermal or vertical section. The contradiction between ternary and binary data becomes apparent when one compares a specific section with a binary phase diagram that re sembles a state of the art of the phase relations in this binary system. The inconsistency between the ternary data and binary phase diagrams often arises while a new phase(s) has been discovered, a phase has been proved to be metastable, crystal structure of an intermetallic compound has been re-determined, composition or temperature ranges of stability were re-redetermined for a phase(s) in a binary system. The Co–Ni–Ti system represents an interesting example illustrating such an inconsistency. Kornilov et al. [26] investigated the CoTi–NiTi section and reported that a continuous series of solid solutions [the (Co, Ni)Ti phase] exists between the isostructural NiTi and CoTi binary phases (cP2, the CsCl prototype) along this section as deduced from the XRD and DTA data, (Fig. 1). This conclusion has been confirmed later by other groups [27–30], but the melting temperatures of the NiTi (~1254 � C) and CoTi (~1530 � C) binary compounds reported by Kornilov et al. [26] differ significantly from the currently accepted values. The melting temperature of NiTi is 1310 � C according to Murray’s review [31] or 1311 � C according to the thermodynamic assessments [32,33]. The CoTi compound melts at ~1503 � C according to the DTA data [34] and at 1501 � C according to the thermodynamic evaluation of the same authors published in 2001. Therefore, we have an inconsistency between the maximal temperatures for the NiTi and CoTi phases in the current ver sions of the binary phase diagrams and the data obtained by Kornilov et al. [26]. We would also like to draw the reader’s attention to the fact that the popular handbook [35] published in 1990 gives the value of 1325 � C for the CoTi melting point, which is out of date. This underlines once again the necessity of thorough exploration of the phase equilibria in the binary systems before starting the evaluation of the ternary data. It should be nevertheless mentioned that for a long time the melting point of CoTi was one of the most important issues in the Co–Ti system. The values reported by different research groups [37–41] including those of Kornilov et al. [26] are scattered within the temperature range of 220 � C, as discussed in Ref. [34]. Davydov et al. [34] suggested that
2. Binary phase diagrams and their consistency with ternary phase diagrams To produce a reliable thermodynamic description of the ternary system means in the first place to gain the understanding of the phase equilibria in the related binary systems and to trace how the knowledge on the binary phase diagrams developed with time. It is particularly crucial since the phase relations in the binary systems define the shape and extension of the ternary phase fields in the ternary space. To be able to interpret the ternary data and to construct an isothermal or vertical section properly, one must choose and accept the corresponding binary phase diagrams. The later can be accepted according to handbooks and/ or previous experimental works performed for particular binary systems. Nevertheless, researchers are often forced to study binary systems along with the related ternary system. The common reasons for such studies are: 1) a binary phase diagram has not been investigated in the full composition and temperature ranges; 2) significant contradictions exist between the experimental datasets obtained by different research groups, and none of the experimental datasets can be considered as reliable, or it is hard to give a preference to a particular dataset. The last one case often comprises such issues as accurately establishing a melting temperature or type of melting of an intermetallic compound, number of stable intermetallic compounds in a system and their crystal structure, and character of the liquid phase separation. One of the illustrative examples of such parallel investigations within one work is the Al–Cr–Nb system [11], in which the authors investigated both the ternary system and the Cr–Nb system in order to clarify the phase re lations involving the cubic C15 Laves phase after it was proven by Aufrecht et al. [12] that the frequently observed hexagonal C14 poly type is metastable in this binary system. However, there are still ex amples of the binary systems with the issues remaining unsolved or questionable. For example, a reader can refer to the discussion about the character of the melting point of CuTi2 [13,14], to the literature review parts in the assessments of the Cu–Zr [15,16] and the Na–Sn [17] sys tems comparing the sets of stable intermetallic compounds found in different works or to literature review part of the Turchanin’s assess ment [18] and experimental study by Zhou et al. [19] regarding the liquid miscibility gap of the Cr–Cu system. The unsolved questions are often related to the experimental difficulties arising from high reactivity, high volatility, slow diffusion or high melting points of the constituent elements, low purity of the starting materials, usage of the inappropriate crucible materials etc. and erroneous interpretation of the experimental data affected by these factors. In particular, Aufrecht et al. [12] showed that the previous false conclusions as to the occurrence of the thermo dynamically stable high-temperature C14 Laves phase in the Cr–Nb system are based on the fact that the small amounts of atmospheric contaminations induced the formation of an η-carbide-type phase melting in a temperature range around 1600 � C. It should also be pointed out that unsolved or questionable issues on the phase equilibria observed in a particular binary system give rise to its multiple thermodynamic assessments with phase diagrams differing from each other by the number of intermetallic compounds, their stoi chiometry, type of melting etc. For example, one can find the assessed Cu–Ti phase diagrams with CuTi2 melting peritectically [20] or congruently [14], the assessed Sb–Sn phase diagrams with the Sb2Sn3 phase being stable in a narrow temperature range [21] or with the Sb43Sn47 (considered as a correct stoichiometry for Sb2Sn3) compound stable down to room temperature [22]. For Cu–Zr, up to 4 variants of the phase diagram can be calculated using the thermodynamic datasets from different sources [15,23–25]. With these examples, we just want to draw the attention of our readers that each thermodynamic assessment of a
Fig. 1. Comparison of the schematic quasi-binary CoTi–NiTi sections proposed in Ref. [26] and corrected in the MSI Eureka database [36]. 2
O. Dovbenko et al.
Calphad 68 (2020) 101719
the potential overestimation of the melting point might be due to the contamination of samples with oxygen or other interstitial elements, while the underestimation was linked to the shift in the composition of a sample under investigation from stoichiometry. Since the experimental procedure has been very briefly described in the article [26] (for example, neither material of crucible nor details of thermal analysis measurements are provided), it is hard to give reasons for significant deviation of the data experimentally measured by Kornilov et al. [26] from the currently accepted. Another example is the Hf–Pd–Pt system for which the isothermal section at 1000 � C was established by Kuznetsov et al. [42] using X-ray diffraction analysis (XRD), electron probe microanalysis (EPMA), and metallography. The authors suggested that a continuous solid solution should exist between the HfPd and HfPt phases, presumably having the CsCl structure (cP2). The later investigations of the Hf–Pd [43] and Hf–Pt [44] systems by Stalick and Watersrat nevertheless disprove this suggestion. In particularly, Stalick and Watersrat found out that the cubic CsCl modification of the HfPt phase transforms to the ortho rhombic CrB-type phase at around 1660 � C while the HfPd phase with the CsCl modification is stable from 1610 � C down to 600 � C. At 600 � C, a transition to a B190 -type phase occurs. The original isothermal section and its corrected version based on the recent Hf–Pd and Hf–Pt phase diagrams by Refs. [43,44] are compared in Fig. 2. The inconsistency between the ternary data and binary phase dia grams raises a question whether the whole isothermal or vertical section should be discarded. The final decision depends on many factors, including the total amount of experimental data points available for a system. One also should bear in mind a recommendation formulated by Kumar and Wollants [7], who underlined that the usage of all critically evaluated data is not recommended as too many data could be difficult to handle. In the case of the Co–Ni–Ti system, the liquidus and solidus temperatures by Kornilov et al. [26] cannot be used for the thermody namic calculation. At least, the usage of the data related to the NiTi part is not advisable. Moreover, several new experimental works [27–29,46, 47], including the liquidus data [48], were published since 1975. Therefore, there is no sense to fit the ternary phase data by Kornilov et al. [26] as this can appear harmful for the reliability of the thermo dynamic parameters. In the case of the Hf–Pd–Pt system, the experi mental reinvestigation of the phase equilibria should be recommended to ascertain the character of the phase equilibria at least between the HfPt and HfPd phases. There is also a case that the thermodynamic parameters of the three binary subsystems can well reproduce the available phase diagram and thermodynamic properties, and this binary thermodynamic description seems to be reasonably accurate. Still, the ternary system cannot be well modeled unless certain modifications are implemented in the
thermodynamic parameters of one or more of the binary subsystems. Some illustrative examples can be found in the literature [49–51]. One of the examples is the thermodynamic assessment for the U–Nb–Zr system [49]. The reported thermodynamic parameters of three binary subsystems seem to be reliable due to the general consistency with the measured data. However, a preliminary assessment shows that the bi nary parameters cannot yield satisfactory description of the experi mental data on the phase equilibria in the U–Nb–Zr system. An unusual widening of γ4þγ5 miscibility gap was found in the calculation, which was hardly influenced by ternary parameters. Such a behavior of the miscibility gap was found to be very sensitive to binary parameters of the U–Nb subsystem. Hence, the thermodynamic modeling of the U–Nb system was revised by slightly adjusting parameters of stable phases. If the ternary experimental data cannot be reasonably fitted using the ternary parameters, it might be reasonable to modify the thermody namic parameters in the binary subsystem. It should be kept in mind that all accurately measured data in binary subsystems should be considered during the modification. With such modification of the parameters for the binary subsystem, a satisfactorily calculated result in the ternary system could be obtained. 3. Comments on the evaluation of the experimental procedure Accuracy and reliability of the experimental results depend on different factors: purity of starting materials, reliable sample prepara tion technique, the correct condition of heat treatment for the investi gated material and experimental methods which were used for the phase equilibrium investigations. It is also important to check whether the materials of crucibles and containers used for the sample preparation, heat treatment or measurements are suitable for the materials and alloys under investigation. The correct interpretation of the experimental data and experience also play an important role by producing reliable experimental datasets. For these reasons, it should be kept in mind that the papers, which do not provide detailed descriptions of the experi mental procedure, should be considered as less reliable until their cor rectness is justified by other independent measurements of the same quantity. For a reliable experimental investigation of the phase equilibria, it is best to use a combination of different methods: crystallographic methods for the identification of the phases (for example, XRD), methods for the determination of the phase compositions (for example, EPMA or energy-dispersive X-ray spectroscopy (EDX)), metallographic methods (for example, optical (OM) or scanning electron microscopy (SEM)), methods and techniques for the measurement of the phase transformation temperatures (such as differential thermal analysis or differential scanning calorimetry) etc. The number of methods, which
Fig. 2. Isothermal section of the Hf–Pd–Pt system at 1000 � C after original work [42] and after critical evaluation from the MSI Eureka database [45]. 3
O. Dovbenko et al.
Calphad 68 (2020) 101719
should be used for the determination of the phase equilibria, must be sufficient to obtain reliable and sound results. It is highly objectionable to use only one or two experimental methods while investigating the phase equilibria in a ternary system characterized by the formation of many intermetallic compounds. Examples justifying this advice can be found among the papers reporting the experimentally studied isothermal sections of the Co–Ni–Ti system. A number of isothermal sections at 800, 900, 1000 � C were investigated in Refs. [52–55] using the diffusion couples and EPMA only. As a result, a continuous solution between Ni3Ti and Co3Ti binary phases was reported for all tempera tures (see, for example, the isothermal section at 800 � C in Fig. 3a) which is impossible as these binary compounds possess different crys tallographic structures – cubic AuCu3 for Co3Ti and hexagonal Ni3Ti [56]. Such kind of experimental data also reflects the investigators’ knowledge of the system, and it will have detrimental effect on the thermodynamic assessment, if such results are used in the optimization. As it was later found out in the numerous works [27–30,46,48], in which the XRD analysis together with SEM, EPMA techniques was applied, three compounds, namely binary Ni3Ti, Co3Ti and the ternary τ with the hexagonal Co3V structure, exist in the Co3Ti–Ni3Ti composition region (Fig. 3b). These compounds exhibit large homogeneity ranges and the same orientation relations, as has been stated by Van Loo and Bastin [46]. It is therefore impossible to distinguish between three compounds by relying only on the EPMA technique as the crystallographic structures of the phases must also be identified to obtain reliable results. For the same reasons, the authors [52–55] failed to correctly establish the phase equilibria involving the hexagonal and cubic modifications of the CoTi Laves phase as can be seen from Fig. 3. It should also be noted that the usage of the XRD and metallographic techniques only is not advisable for the investigation of phase equilibria at a constant temperature (an isothermal section) if a ternary system is characterized with the formation of a large number of intermetallic compounds with wide homogeneity ranges. For such systems, the pre cise establishment of tie-lines and tie-triangles would be complicated if the EPMA or EDX methods were not involved in the investigation. Special care should be paid by evaluating the experimental proced ure and results of the investigation reporting the so-called quasi-binary vertical sections in the metallic systems or systems containing such nonmetallic elements as B, C or N. The term “quasi-binary” implies that all tie-lines are located along an investigated section and that no ternary fields appear inside the plane of the section. The quasi-binary sections may be read like a binary system, and they will provide the full infor mation on the type, composition, and fraction of phases. Such a vertical section can be most probably expected in two cases. The first case is a system in which two compounds without the homogeneity ranges in the binary systems are isostructural and form a continuous solid solution in
the whole temperature-composition range. The second case is a section between either a pure element and a strictly stoichiometric compound or between two strictly stoichiometric compounds. Nevertheless, the sec tion, which is truly quasi-binary in the whole temperature-composition range, is a rare case. The sections, which are only partially quasi-binary (usually at high temperatures), are more often when some of the com pounds are not strictly stoichiometric, for example, the carbide systems containing compounds with a deficiency in carbon. It is therefore advisable to accurately evaluate the data reported for the quasi-binary sections between the intermetallic compounds showing wide homogeneity ranges in binary and ternary systems. One should pay attention to two conditions: 1) whether the section passes through the so-called distectic points, e.g. melting point of a pure element, congruent melting points of binary compounds, maxima in the ternary system; 2) whether all the investigated compositions lie inside the investigated composition plane. In the Cu–Mg–Zn, two quasi-binary sections were €ster and Müller [57] and Mikheeva and Kryukova [58]. proposed by Ko These are the section from pure Mg to the peritectic composition of the γ phase (so-called γ-brass phase with approximate stoichiometry Cu5Zn8) [57] and the section from pure Mg to the Cu50Zn50 (at.%) composition (the Mg–β section) [58]. The Mg–γ section is a result of the interpolation between the experimental points since the composition of the investi gated samples lies somewhat outside the vertical plane, and it is there fore only approximately a quasi-binary. The plane of the Mg–β section intersects no distectic points in the binary Cu–Zn system. The β (disor dered b.c.c. solution) phase has a wide homogeneity range in the Cu–Zn system and dissolves a certain amount of Mg that most certainly results in a change of the direction of the tie-lines with temperature thus ruling out the quasi-binary nature of the Mg–β section near the Cu–Zn system. 4. On the consistency between isothermal and vertical sections Before starting to compile a dataset, the internal consistency be tween the isothermal sections, vertical sections must be carefully checked to avoid the possible difficulties during the optimization pro cedure. It should be noted that the experimentally established isothermal sections are usually more trustworthy than the vertical one as far as the accuracy of the phase boundaries representation is concerned. The only exception from this rule is quasi-binary sections which have been already discussed in Section 3. In case of an isothermal section, not only the phase assemblages in a particular part of the concentration triangle can be determined but also the composition of the phases in equilibrium can be comparatively easy established since all tie-lines and tie-triangles are lying in the plane of the section. In case of a vertical section, most of the tie-lines lie outside the plane of the section. Therefore, the precise determination of the phase boundaries requires
Fig. 3. Experimentally established isothermal section of the Co–Ni–Ti system at 800 � C according to Refs. [52,53] (a) and [29] (b). 4
O. Dovbenko et al.
Calphad 68 (2020) 101719
the XRD, EPMA, and metallographic examination of several samples equilibrated at different temperatures and subsequently quenched. As it has been mentioned in Refs. [4,5], the best way to construct a vertical section is to use a set of well-determined isothermal sections, liquidus and solidus surfaces, and the DTA data. The situation in which an isothermal section contradicts to a vertical section is not rare. As an example, a vertical and isothermal sections (redrawn for atomic per cent) of the Mo–Ni–Zr system are compared in Fig. 4. The experimentally determined vertical section with weight ratio of Mo:Ni ¼ 1:1 in the Zr-rich region (~65–100 at.% Zr) was constructed by Gruzdeva and Tararaeva [59]. In this work, the samples were pre liminarily homogenized at 1000–1200 � C, annealed within different periods, 340 to 2 h, depending on annealing temperature, and subse quently quenched. The annealing temperatures were chosen at 50 � C intervals between 700 and 1000 � C. The prepared samples were analyzed using microscopy, hardness, and microhardness
measurements. As can be seen from Fig. 4a, the vertical section shows (βZr) and (βZr) þ NiZr2 phase regions for very low Mo and Ni contents and the three-phase (βZr) þ NiZr2 þ Mo2Zr region for zirconium content more than 90 at.% at 900 � C. However, two ternary compounds τ1 (cF96, the NiTi2 prototype) and τ2 (hP28, the Hf9Mo4B prototype) were reported to be in equilibrium with the (βZr) phase at 900 � C in the later experimental work by Wang et al. [60] (Fig. 4b). The isothermal section [60] was established based on the XRD and EPMA investigations of the samples prepared from high purity materials (99.99 mass%), annealed for 40 days and quenched in cold water. According to this isothermal section, the Mo:Ni ¼ 1:1 vertical section should cross the (βZr) þ NiZr2 þ τ1 region instead of the (βZr) þ NiZr2 þ Mo2Zr phase field at 900 � C. Materials and methods, which were used for investigation by Wang et al. [60], should give more reliable results than those reported by Gruzdeva and Tararaeva [59]. Consequently, the later experimental dataset should not be included in the optimization procedure as it has been done in the assessment of the Mo–Ni–Zr system performed Wang et al. [61]. 5. On the consistency among isothermal, vertical sections and liquidus projection The information on the phase equilibria involving the liquid phase, which is often presented in the form of a liquidus projection and rarer in the form of a melting diagram, is important for the establishment of a physically sound thermodynamic description. The usage of the co ordinates of the invariant reactions in an experimental dataset is espe cially beneficial for the optimization procedure as such data are more suggestive than the tie-lines in the isothermal sections or the tempera tures of the monovariant reactions. For a ternary system characterized by the formation of many intermetallic compounds, the establishment of liquidus or solidus projection is a complicated and time-consuming task, and it requires considerable expertise and significant effort. Exemplary works providing an extensive explanation of the construction of the liquidus and solidus projections were conducted by Prima and Petyukh [62,63] for Mo–Ni–Zr, by Palm et al. [64] for Al–Co–Nb, and by Stein et al. [11] for Al–Cr–Nb. Before the coordinates of an invariant reaction will be included in an experimental dataset for a further optimization, one should decide: 1) whether a particular reaction is relevant or not for a quantitative vali dation of the phase equilibria in a ternary system; 2) what kind of the coordinates (temperature or compositions of the phases) have been actually measured. As to the relevance of the invariant reactions, Janz et al. [65] pointed out that the degenerated reactions, which are typi cally the reactions showing at least one of the phase fractions close to zero and having the reaction temperature close to a corresponding invariant reaction in a low-order system, should be considered as irrel evant since they essentially provide the information for one of the sub-systems. Therefore, it is advisable to include the degenerated re actions in the experimental dataset after a workable thermodynamic description of a system is produced. In the case of the coordinates of the invariant reactions, one should clearly distinguish between the measured and deduced data. As a rule, the temperature of an invariant reaction can be relatively precisely measured by DTA or DSC methods if the invariant composition field is wide enough and the kinetics of the reaction is fast. For each measured invariant reaction, the type and compositions of the phases could be established. The eutectic and per itectic reactions can be identified by the corresponding types of micro structure in the as-cast samples. The transition-type (Lþ α ¼ β þ γ) and sometimes peritectic-type (Lþ αþ β ¼ γ) reactions can be revealed after careful analysis of the preceding and succeeding phase fields which appear in the microstructure of the as-cast samples or samples annealed for a short time at the sub-solidus temperatures. The hardest task is the measurement of the phase compositions involved in a particular invariant reaction. Theoretically, the compositions of a eutectic and all the involved phases can be measured in the as-cast samples if the size of the eutectic and the grains of the precipitated products are large enough
Fig. 4. Partial vertical section at weight ratio of Mo:Ni ¼ 1:1 after [59] (a) and partial isothermal section at 900 � C after [60] (b) of the Mo–Ni–Zr system. Both sections are redrawn for atomic per cent. 5
O. Dovbenko et al.
Calphad 68 (2020) 101719
to be measured by the beam of the energy-dispersive or wavelength-dispersive spectrometer. However, only the composition of the eutectic liquid can be usually established with a high accuracy. For the peritectic- and transition-type reactions, the composition of the liquid phase lies in the apex of the equilibrium composition space and does not correspond to the point where all the educts are fully converted to the product phases. Often, the composition of the equilibrium liquid phase cannot be measured directly in an as-cast sample, and it is usually deduced by interpolating between the experimental points. In principle, additional investigation using the samples annealed for a short time at the sub-solidus temperatures is required to accurately determine the compositions of all equilibrium phases participating in the peritectic- or transition-type reaction. Therefore, the temperature and type of an invariant reaction and eutectic composition should be considered as more reliable data than the reported compositions of the solid phases or liquid phase involved in the peritectic- and transition-type reaction. The cases described above are only general recommendations. For a better understanding of the possible pitfalls in the critical evaluation of the liquidus and solidus data, the interested reader could refer to Refs. [7,8,
11,64,65]. It is also mandatory to check whether the reported invariant equi libria and adjoining equilibrium phase relations agree with the experi mentally established isothermal and vertical sections available in other sources. It is not rare that a temperature of the invariant reaction has been measured accurately, but the phase equilibria have been errone ously interpreted. Mikheeva and Kryukova [58] studied a number of the vertical sections in the Cu–Mg–Zn system using the thermal analysis (TA) and metallographic examination of the samples after TA. The projection of the liquidus surface was constructed based on these experimental data. As the authors used metallography and thermal analysis only, they were unable to determine the stoichiometry of a ternary phase τ experimentally. It was assumed that this phase had no homogeneity range and lied outside the Cu2Mg–MgZn2 section, which was drawn as a typical isopleth (Fig. 5a). Therefore, the corresponding maxima in the monovariant L þ Cu2Mg↔τ (610 � C) and Lþτ↔MgZn2 (720 � C) lines appeared to be outside the plane of the section and the invariant reaction L þ Cu2Mg↔τþ MgZn2 at 602 � C (U3 in Fig. 5c) was proposed for this section. This finding contradicts to the data of Lieser
Fig. 5. The Cu–Mg–Zn system: the Cu2Mg–MgZn2 section after [58] (a) and after [66] (b); liquidus projection after [58] (c). 6
O. Dovbenko et al.
Calphad 68 (2020) 101719
and Witte [66], who reported the Cu2Mg–MgZn2 section to be a quasi-binary with the MgZn2 (C14), Cu2Mg (C15), and τ (CuMg2Zn3, C36) Laves phases appearing in the plane of the section (Fig. 5b). Furthermore, the C15 and C36 Laves phases exhibit wide homogeneity ranges. Both Mikheeva and Kryukova [58] and Lieser and Witte [66] used the thermal analysis and the reported temperatures of the maxima in the Lþτ↔MgZn2 (720 � C (p2, max in Fig. 5c) [58] and 716 � C [66]) and L þ Cu2Mg↔τ (610 � C (p1, max in Fig. 5c) [58] and 600 � C [66]). But the section proposed by Lieser and Witte [66] is more accurate as it is also based on the examination of the equilibrated samples using XRD and metallography. By comparison of the data, the evaluation of the experimental pro cedure always plays a vital role as can be seen, for example, by comparing the results of Prima and Petyukh [63] and Wang et al. [61] for the Mo–Ni–Zr system. Prima and Petyukh [63] investigated the liq uidus surface projection and melting diagram in the Zr–ZrNi–Mo region using the DTA, XRD, EPMA methods. The samples for the investigation were prepared by arc melting under argon atmosphere purified by melting Ti–Zr getter. The samples in as-cast state and annealed at sub-solidus temperatures were used for the experimental examination. According to Prima and Petyukh [63], only one ternary compound τ1 exists on the liquidus surface and is formed by the peritectic reaction, Lþ (Zr)þMo2Zr↔τ1 at 1020 � C. Later, Wang et al. [61] established the isothermal section at 1100 � C by analyzing the samples annealed at this temperature for 20 days in the evacuated quartz capsules with the XRD, EPMA, and SEM methods. They found that the τ2 phase equilibrates with the (βZr) and Mo2Zr phases. The appearance of the τ2 phase at such a high temperature also indicates that it equilibrates with the liquid phase and, therefore, should also appear on the liquidus surface. The experi mental methods and samples preparation procedure were accurate enough to obtain reliable results. However, there are differences in the purity of the starting materials. Wang et al. [61] used molybdenum, zirconium, and nickel with a purity of 99.99 wt%. Prima and Petyukh [63] used zirconium with a purity of 99.96 wt%, moulding compact molybdenum 99.9% Mo, nickel 99.9%, which contains up to 0.1 wt% Co. Considering the purity of the starting materials and annealing time, it could be concluded that the results of Wang et al. [61] are more preferable than the data of Prima and Petyukh [63]. Thus, the later re sults can be used for the thermodynamic assessment only partially, as it has been done in the work of Wang et al. [61]. In Fig. 6, the partial liquidus projection after Prima and Petyukh [63], in which a suggested primary crystallization field of τ2 is marked with a grey dashed line, is shown. Nevertheless, the Zr-rich part of the liquidus surface requires additional experimental verification.
Fig. 6. Corrected partial liquidus projection after [63] of the Mo–Ni–Zr system.
work. Acknowledgement The financial support from National Natural Science Foundation of China (Grant no. 51671219) is acknowledged. Both Dr. Oleksandr Dovbenko and Dr. Liya Dreval thank the grant from Department of In ternational Cooperation and Exchanges of Central South University, China. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.calphad.2019.101719. References [1] L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams: with Special Reference to Refractory Metals, Acad. Press, New York, 1970. [2] H. Ipser, Who will do the necessary experiments? J. Phase Equilibria Diffusion 38 (2017) 1–2. [3] A. Watson, Editorial, J. Phase Equilib. Diffus. 29 (2008) 1. [4] G. Cacciamani, G. Effenberg, R. Ferro, S. Ilyenko, P. Perrot, A. Pisch, P. Rogl, R. Schmid-Fetzer, Critical Evaluation of Binary Phase Diagram Data. Best Practice Guidelines for Evaluation & Notes for Authors, 3rd. ed., MSI, Materials Science International, Stuttgart, 2012. http://www.msiport.com/fileadmin/content/res earch/binary_evaluations/docs/notes_authors_binary.pdf. [5] G. Effenberg, R. Schmid-Fetzer, Critical Evaluation of Ternary Phase Diagram Data. Best Practice Guidelines for Evaluation & Notes for Authors, sixth ed., MSI, Materials Science International, Stuttgart, 2012. http://www.msiport.com/fileadm in/content/research/ternary_evaluations/docs/notes_author_ternary.pdf. [6] H.L. Lukas, S.G. Fries, Demonstration of the use of “BINGSS” with the Mg-Zn system as example, J. Phase Equilibria 13 (1992) 532–542. [7] K.C. Hari Kumar, P. Wollants, Some guidelines for thermodynamic optimisation of phase diagrams, J. Alloy. Comp. 320 (2001) 189–198. [8] J.C. Zhao (Ed.), Methods for Phase Diagram Determination, Elsevier, 2007. [9] R. Ferro, G. Cacciamani, G. Borzone, Remarks about data reliability in experimental and computational alloy thermochemistry, Intermetallics 11 (2003) 1081–1094. [10] R. Schmid-Fetzer, D. Andersson, P.Y. Chevalier, L. Eleno, O. Fabrichnaya, U. R. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, M. Zinkevich, Assessment techniques, database design and software facilities for thermodynamics and diffusion, Calphad 31 (2007) 38–52. [11] F. Stein, C. He, I. Wossack, The liquidus surface of the Cr–Al–Nb system and reinvestigation of the Cr–Nb and Al–Cr phase diagrams, J. Alloy. Comp. 598 (2014) 253–265. [12] J. Aufrecht, A. Leineweber, A. Senyshyn, E.J. Mittemeijer, The absence of a stable hexagonal Laves phase modification (NbCr2) in the Nb–Cr system, Scr. Mater. 62 (2010) 227–230. [13] J.L. Murray, Cu-Ti (Copper-Titanium), in: P.R. Subramanian (Ed.), Phase Diagrams of Binary Copper Alloys, ASM International, Materials Park, OH, 1994, pp. 447–460. [14] M.A. Turchanin, P.G. Agraval, A.R. Abdulov, Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system, Powder Metall. Met. Ceram. 47 (2008) 344–360.
6. Conclusion Some guidelines concerning the critical evaluation of the experi mental phase diagram in the ternary system and related binary systems are presented. We hope that these recommendations will be helpful to a novice user of the software packages for thermodynamic optimizations of the phase diagrams using the Calphad method. These guidelines are rather general, and a reader should realize that there are always specific issues associated with a critical evaluation of the experimental results for a particular system. Nevertheless, the authors feel that these hints will be useful for postgraduates, young researchers and experts in pro ducing a self-consistent experimental dataset for a thermodynamic optimization of a targeted system. Although the present work is focused on the critical evaluation of ternary phase diagram data, we would like to stress that thermochemical data of the ternary and related binary phases, if available, are also crucial for accurate Calphad assessment and proper optimization of the model parameters. Declaration of competing interest The authors declared that they have no conflicts of interest to this 7
O. Dovbenko et al.
Calphad 68 (2020) 101719
[15] M.A. Turchanin, P.G. Agraval, A.R. Abdulov, Thermodynamic assessment of the Cu-Ti-Zr system. II. Cu-Zr and Ti-Zr systems, Powder Metall. Met. Ceram. 47 (2008) 428–446. [16] N. Wang, C. Li, Z. Du, F. Wang, W. Zhang, The thermodynamic re-assessment of the Cu–Zr system, Calphad 30 (2006) 461–469. [17] L. Dreval, M. Zschornak, W. Münchgesang, O. Fabrichnaya, D. Rafaja, M. L. Martine, L. Giebeler, M. Motylenko, Thermodynamic assessment and first principle calculations of the Na Sb Sn system, J. Alloy. Comp. 695 (2017) 1725–1742. [18] M.A. Turchanin, Phase equilibria and thermodynamics of binary copper systems with 3d-metals. III. Copper-chromium system, Powder Metall. Met. Ceram. 45 (2006) 457–467. [19] Z.M. Zhou, J. Gao, F. Li, Y.P. Wang, M. Kolbe, Experimental determination and thermodynamic modeling of phase equilibria in the Cu–Cr system, J. Mater. Sci. 46 (2011) 7039–7045. [20] K.H. Kumar, I. Ansara, P. Wollants, L. Delaey, Thermodynamic optimisation of the Cu-Ti system, Z. Metallkd. 87 (1996) 666–672. [21] COST531 Thermodynamic Database Version 3.0, 10 June 2008. [22] S.W. Chen, C.-C. Chen, W. Gierlotka, A.R. Zi, P.Y. Chen, H.J. Wu, Phase equilibria of the Sn-Sb binary system, J. Electron. Mater. 37 (2008) 992–1002. [23] K.J. Zeng, M. H€ am€ al€ ainen, H.L. Lukas, A new thermodynamic description of the Cu-Zr system, J. Phase Equilibria 15 (1994) 577–586. [24] K. Yamaguchi, Y.-C. Song, T. Yoshida, K. Itagaki, Thermodynamic investigation of the Cu–Zr system, J. Alloy. Comp. 452 (2008) 73–79. [25] D.H. Kang, I.-H. Jung, Critical thermodynamic evaluation and optimization of the Ag–Zr, Cu–Zr and Ag–Cu–Zr systems and its applications to amorphous Cu–Zr–Ag alloys, Intermetallics 18 (2010) 815–833. [26] I.I. Kornilov, E.V. Kachur, O.K. Belousov, Investigation of the TiNi-TiCo system, Russ. Metall. (1975) 162–163. [27] P. Riani, K. Sufryd, G. Cacciamani, Critical assessment and experimental investigation of Co–Ni–Ti phase equilibria, Calphad 44 (2014) 26–38. [28] C. Zhou, C. Guo, C. Li, Z. Du, Experimental determination and thermodynamic assessment of the Co–Ni–Ti system, Calphad 63 (2018) 61–76. [29] Y. Yuan, L. Yang, D. Li, A. Tang, F. Pan, H. Seifert, N. Moelans, Diffusion multiple study of Co-Ni-Ti system at 1073 K, Calphad 63 (2018) 156–163. [30] H. Li, P. Zhou, Y. Du, Z. Jin, Isothermal sections of the Co–Ni–Ti system at 950 and 1 000 � C, Int. J. Mater. Res. 109 (2018) 105–112. [31] J.L. Murray, Ni-Ti, in: P. Nash (Ed.), Phase Diagrams of Binary Nickel Alloys, ASM International, Materials Park, Ohio, 1991, pp. 342–355. [32] K.C.H. Kumar, P. Wollants, Thermodynamic assessment of the Ni-Ti phase diagram, Z. Metallkd. 87 (1996) 972–978. [33] J. de Keyzer, G. Cacciamani, N. Dupin, P. Wollants, Thermodynamic modeling and optimization of the Fe–Ni–Ti system, Calphad 33 (2009) 109–123. [34] A.V. Davydov, U.R. Kattner, d. Josell, R.M. Waterstrat, W.J. Boettinger, J. E. Blendell, A.J. Shapiro, Determination of the CoTi congruent melting point and thermodynamic reassessment of the Co-Ti system, Metall. Mater. Trans. A 32 (2001) 2175–2186. [35] T.B. Massalski, H. Okamoto (Eds.), Binary Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1990. [36] G. Cacciamani, P. Riani, in: M.S.I. Eureka, G. Effenberg (Eds.), Co-Ni-Ti Ternary Phase Diagram Evaluation, MSI, Materials Science International Services GmbH, MSI Eureka, Stuttgart, 2004. http://www.msi-eureka.com/preview-html/10.117 39.1.6/Co-Ni-Ti_Ternary-Phase-Diagram-Evaluation/. [37] A. Iannucci, A.A. Johnson, E.J. Hughes, P.W. Barton, Study of the solubility limits of the compound TiCo using high-temperature X-ray diffractometry, J. Appl. Phys. 39 (1968) 2222–2224. [38] V.V. Pet’kov, M.V. Kireev, Intermediate phases in the titanium-cobalt system, Metallofizika 33 (1971) 107–115. [39] H. Huthmann, G. Inden, High-temperature neutron diffraction on FeTi and CoTi, Phys. Status Solidi 28 (1975) K129–K130. [40] S.R. Butler, J.E. Hanlon, R.J. Wasilewski, Electric and magnetic properties of TiCo and related compositions, J. Phys. Chem. Solids 30 (1969) 281–286. [41] H.J. Wallbaum, The systems of the iron-group metals with titanium, zirconium, niobium, and tantalum, Arch. Eisenhuettenwes. 10 521–526.
[42] V.N. Kuznetsov, G.P. Zhmurko, E.M. Sokolovskaya, Phase equilibria and structural stability of intermetallics in the Pt-Pd-Hf and Pt-Pd-Zr systems, J. Less Common. Met. 163 (1990) 1–8. [43] J.K. Stalick, R.M. Waterstrat, Crystal structures and phase equilibria in the hafnium-palladium system, J. Phase Equilibria Diffusion 37 (2016) 416–422. [44] J.K. Stalick, R.M. Waterstrat, The hafnium-platinum phase diagram, J. Phase Equilibria Diffusion 35 (2014) 15–23. [45] K. Korniyenko, Hafnium - palladium - platinum, in: M.S.I. Eureka, G. Effenberg (Eds.), MSI, Materials Science International Services GmbH, MSI Eureka, Stuttgart, 2018. http://www.msi-eureka.com/full-html/10.15360.1.4/Hf-Pd-Pt_Ternary-Ph ase-Diagram-Evaluation/#Text0. [46] F.J.J. van Loo, G.F. Bastin, Phase relations and diffusion paths in the Ti-Ni-Co system at 900 � C, J. Less Common. Met. 81 (1981) 61–69. [47] Y. Du, Z.P. Jin, P.Y. Huang, Determination of the 850 � C isothermal section in the Co-Ni-Ti system, J. Phase Equilibria 14 (1993) 348–353. [48] C. Zhou, C. Guo, J. Li, C. Li, Z. Du, Experimental investigations of the Co–Ni–Ti system: liquidus surface projection and isothermal section at 1373 K, J. Alloy. Comp. 754 (2018) 268–282. [49] P. Zhou, Y. Peng, Y. Du, L. Zhang, W. Mo, T. Fa, B. Bai, X. Wang, Thermodynamic modeling of the U-Nb-Zr ternary system, J. Nucl. Mater. 523 (2019) 157–171. [50] Y. Peng, P. Zhou, M. Bu, W. Zhang, Y. Du, A thermodynamic evaluation of the C–Cr–Nb system, Calphad 53 (2016) 10–19. [51] Y. Liu, P. Zhou, S. Liu, Y. Du, Experimental investigation and thermodynamic description of the Cu-Cr-Zr system, Calphad 59 (2017) 1–11. [52] A.S. Sagyndykov, M.V. Raevskaya, E.M. Sokolovskaya, B.I. Gryzunov, Co-Ni-Ti system, komplecs, Ispol. Mineral. Sypiya (1979) 193–195. [53] V.I. Gryzunov, A.S. Sagyndykov, Mutual diffusion in the system Ti-Ni-Co, Phys. Met. Metallogr. 49 (1980) 178–182. [54] V.I. Gryzunov, A.S. Sagyndykov, Y.M. Sokolovskaya, Temperature dependence of mutual diffusion coefficients in the Ti-Ni-Co system, Phys. Met. Metallogr. 54 (1982) 69–74. [55] V.I. Gryzunov, G.V. Shcherbedinskiy, B.K. Sokolovskaya, Kinetics of phase growth during interdiffusion in ternary multiphase metallic systems, Phys. Met. Metallogr. 56 (1983) 183–186. [56] P. Paufler, P. Villars, L.D. Calvert, ’s Pearson, Handbook of Crystallographic Data for Intermetallic Phases. American Society for Metals. Metals Park. Ohio, 1–3, 1986, p. 3258. [57] W. K€ oster, F. Müller, The ternary copper-zinc-magnesium system, Z. Metallkd. 39 (1948) 352–359. [58] V.I. Mikheeva, O.N. Kryukova, Melting diagram of the system Cu-Mg-Zn, Izv. Sekt. Fiz.-Khim. Anal., Akad. Nauk. SSSR 20 (1950) 76–93. [59] N.M. Gruzdeva, E.M. Tararaeva, Zr corner of the Zr-Mo-Ni system phase diagram, in: O.S. Ivanov (Ed.), Fiz. Khim. Splavov Tsirkoniya, Nauka, Moscow, 1968, pp. 189–195. [60] S. Wang, C. Zhang, C. Lin, Y. Peng, Y. Du, Measurement of 900 � C isothermal section in the Mo-Ni-Zr system, J. Phase Equilibria Diffusion 37 (2016) 672–679. [61] S. Wang, C. Zhang, Y. Du, Y. Peng, Y. Pan, P. Zhou, L. Dreval, Experimental investigation and thermodynamic assessment of the Mo–Ni–Zr ternary system, Calphad 58 (2017) 128–137. [62] S.B. Prima, V.M. Petyukh, Phase ratios of solidification of alloys of the Ni-Zr-Mo system in the ZrNi-Ni-Mo region, Russ. Metall. (1991) 149–155. [63] S.B. Prima, V.M. Petyukh, Phase transformations during solidification of nickelzirconium-molybdenum alloys in the Zr-ZrNi-Mo region, Russ. Metall. (1993) 149–156. [64] M. Palm, C. He, O. Dovbenko, F. Stein, J.C. Schuster, Liquidus projection and reaction scheme of the Co-Al-Nb system, J. Phase Equilibria Diffusion 33 (2012) 210–221. [65] A. Janz, J. Gr€ obner, R. Schmid-Fetzer, Thermodynamics and constitution of Mg-AlCa-Sr-Mn alloys: Part II. Procedure for multicomponent key sample selection and application to the Mg-Al-Ca-Sr and Mg-Al-Ca-Sr-Mn systems, J. Phase Equilibria Diffusion 30 (2009) 157–175. [66] K.H. Lieser, H. Witte, Investigation on ternary systems of Mg-Cu-Zn, Mg-Ni-Zn, and Mg-Cu-Ni, Z. Metallkd. 43 (1952) 396–401.
8
Contents lists available at ScienceDirect
Calphad journal homepage: http://www.elsevier.com/locate/calphad
Invited article
Critical evaluation of ternary phase diagram data: Important considerations in the scrutiny of the correctness, coherence, and interpretation Oleksandr Dovbenko a, b, Liya Dreval a, Yong Du c, *, Yuling Liu c, **, Shuhong Liu c, Svitlana Iljenko a, Günter Effenberg a, 1 a b c
MSI, Materials Science International Services GmbH, 70565, Am Wallgraben 100, Stuttgart, Germany Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Kiev, 03142, Ukraine State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Calphad Critical evaluation Phase diagram Binary system Ternary system
Thermodynamic optimization of ternary phase diagrams via Calphad approach is a complex procedure. The success and quality of such a Calphad optimization depend on the reliability of the experimental data and on the scrutiny of the critical evaluation of the experimental datasets. With this in mind, we provide a set of recom mendations that might facilitate the critical evaluation procedure and improve the quality of the thermodynamic datasets for the calculations of the phase diagrams. The particulars regarding the consistency between binary and ternary phase diagrams as well as the internal agreement between the different ternary datasets, are discussed.
1. Introduction In more than 40 years since the publication of the book Computer Calculation of Phase Diagrams by Larry Kaufman [1], the Calphad approach initially intended to calculate phase diagrams, turned out to be a powerful instrument for solving numerous theoretical and practical questions, from materials development to process control. The successes of this approach have not only paved the way for the breakthrough in materials science, but also have created a false impression that to opti mize a system thermodynamically is a comparatively easy task and that the main obstacles on the way to the self-consistent thermodynamic database are related to the overflow of the experimental data or to a large number of phases to be incorporated in a database. The results of such distorted perception we are witnessing today. We have to stroll through the piles of the published thermodynamic assessments while we are looking for the papers with the published experimental data. This problem has been particularly raised in the paper of Ipser [2] and the Editorial by Watson [3] published in the Journal of Phase Equilibria and Diffusion. In turn, we would like to emphasize that the success of the Calphad optimization along with the selection of the proper models strongly depends upon the reliability of the experimental data, upon the scrutiny of the critical evaluation of the experimental datasets, and the
accuracy of the optimization technique. The fundamentals of the critical evaluation procedure for binary and ternary constitutional data were developed in Refs. [4,5] and applied by the experts from the Materials Science International Team in the critical evaluation of over 4500 ternary and binary systems. The present work intends to provide some guidelines and recom mendations concerning the critical evaluation of the experimental datasets for the ternary systems that may help the users and in particular the postgraduate and young researchers in producing reliable thermo dynamic descriptions. Therefore, the current paper should be considered as a continuation of the previous discussion about this procedure started by Lukas and Fries [6] and by Kumar and Wollants [7] and as an extension in that part which concerns the ternary phase equilibria. The thorough discussion of the accuracy and reliability of the different experimental methods lies outside our scope since this topic is too important and wide to limit it to the size of an article. Those, who are interested in the better experimental practice and its connection to the production of the reliable thermodynamic assessments, we would sug gest to refer to the recently published monography [8] and the paper from Ferro et al. [9]. Since the guidelines about how to avoid the possible pitfalls in the course of the thermodynamic optimization and facilitate this procedure were described by Lukas and Fries [6], Kumar
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Du), [email protected] (Y. Liu). 1 Deceased author. https://doi.org/10.1016/j.calphad.2019.101719 Received 5 August 2019; Received in revised form 28 November 2019; Accepted 29 November 2019 Available online 25 December 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.
O. Dovbenko et al.
Calphad 68 (2020) 101719
and Wollants [7], and lately by Schmid-Fetzer et al. [10] in detail, we shall touch upon this issue only briefly in connection with ternary systems.
ternary system should be started from the thorough exploration of the phase relations in the related binary systems. Moreover, the reasons behind the choice of a particular thermodynamic assessment for a binary system should be thoroughly explained and clear to the readers and users of a database. We can, therefore, conclude that there should not be an internal inconsistency between the binary and ternary data for a particular experimental study providing an isothermal or vertical section. The contradiction between ternary and binary data becomes apparent when one compares a specific section with a binary phase diagram that re sembles a state of the art of the phase relations in this binary system. The inconsistency between the ternary data and binary phase diagrams often arises while a new phase(s) has been discovered, a phase has been proved to be metastable, crystal structure of an intermetallic compound has been re-determined, composition or temperature ranges of stability were re-redetermined for a phase(s) in a binary system. The Co–Ni–Ti system represents an interesting example illustrating such an inconsistency. Kornilov et al. [26] investigated the CoTi–NiTi section and reported that a continuous series of solid solutions [the (Co, Ni)Ti phase] exists between the isostructural NiTi and CoTi binary phases (cP2, the CsCl prototype) along this section as deduced from the XRD and DTA data, (Fig. 1). This conclusion has been confirmed later by other groups [27–30], but the melting temperatures of the NiTi (~1254 � C) and CoTi (~1530 � C) binary compounds reported by Kornilov et al. [26] differ significantly from the currently accepted values. The melting temperature of NiTi is 1310 � C according to Murray’s review [31] or 1311 � C according to the thermodynamic assessments [32,33]. The CoTi compound melts at ~1503 � C according to the DTA data [34] and at 1501 � C according to the thermodynamic evaluation of the same authors published in 2001. Therefore, we have an inconsistency between the maximal temperatures for the NiTi and CoTi phases in the current ver sions of the binary phase diagrams and the data obtained by Kornilov et al. [26]. We would also like to draw the reader’s attention to the fact that the popular handbook [35] published in 1990 gives the value of 1325 � C for the CoTi melting point, which is out of date. This underlines once again the necessity of thorough exploration of the phase equilibria in the binary systems before starting the evaluation of the ternary data. It should be nevertheless mentioned that for a long time the melting point of CoTi was one of the most important issues in the Co–Ti system. The values reported by different research groups [37–41] including those of Kornilov et al. [26] are scattered within the temperature range of 220 � C, as discussed in Ref. [34]. Davydov et al. [34] suggested that
2. Binary phase diagrams and their consistency with ternary phase diagrams To produce a reliable thermodynamic description of the ternary system means in the first place to gain the understanding of the phase equilibria in the related binary systems and to trace how the knowledge on the binary phase diagrams developed with time. It is particularly crucial since the phase relations in the binary systems define the shape and extension of the ternary phase fields in the ternary space. To be able to interpret the ternary data and to construct an isothermal or vertical section properly, one must choose and accept the corresponding binary phase diagrams. The later can be accepted according to handbooks and/ or previous experimental works performed for particular binary systems. Nevertheless, researchers are often forced to study binary systems along with the related ternary system. The common reasons for such studies are: 1) a binary phase diagram has not been investigated in the full composition and temperature ranges; 2) significant contradictions exist between the experimental datasets obtained by different research groups, and none of the experimental datasets can be considered as reliable, or it is hard to give a preference to a particular dataset. The last one case often comprises such issues as accurately establishing a melting temperature or type of melting of an intermetallic compound, number of stable intermetallic compounds in a system and their crystal structure, and character of the liquid phase separation. One of the illustrative examples of such parallel investigations within one work is the Al–Cr–Nb system [11], in which the authors investigated both the ternary system and the Cr–Nb system in order to clarify the phase re lations involving the cubic C15 Laves phase after it was proven by Aufrecht et al. [12] that the frequently observed hexagonal C14 poly type is metastable in this binary system. However, there are still ex amples of the binary systems with the issues remaining unsolved or questionable. For example, a reader can refer to the discussion about the character of the melting point of CuTi2 [13,14], to the literature review parts in the assessments of the Cu–Zr [15,16] and the Na–Sn [17] sys tems comparing the sets of stable intermetallic compounds found in different works or to literature review part of the Turchanin’s assess ment [18] and experimental study by Zhou et al. [19] regarding the liquid miscibility gap of the Cr–Cu system. The unsolved questions are often related to the experimental difficulties arising from high reactivity, high volatility, slow diffusion or high melting points of the constituent elements, low purity of the starting materials, usage of the inappropriate crucible materials etc. and erroneous interpretation of the experimental data affected by these factors. In particular, Aufrecht et al. [12] showed that the previous false conclusions as to the occurrence of the thermo dynamically stable high-temperature C14 Laves phase in the Cr–Nb system are based on the fact that the small amounts of atmospheric contaminations induced the formation of an η-carbide-type phase melting in a temperature range around 1600 � C. It should also be pointed out that unsolved or questionable issues on the phase equilibria observed in a particular binary system give rise to its multiple thermodynamic assessments with phase diagrams differing from each other by the number of intermetallic compounds, their stoi chiometry, type of melting etc. For example, one can find the assessed Cu–Ti phase diagrams with CuTi2 melting peritectically [20] or congruently [14], the assessed Sb–Sn phase diagrams with the Sb2Sn3 phase being stable in a narrow temperature range [21] or with the Sb43Sn47 (considered as a correct stoichiometry for Sb2Sn3) compound stable down to room temperature [22]. For Cu–Zr, up to 4 variants of the phase diagram can be calculated using the thermodynamic datasets from different sources [15,23–25]. With these examples, we just want to draw the attention of our readers that each thermodynamic assessment of a
Fig. 1. Comparison of the schematic quasi-binary CoTi–NiTi sections proposed in Ref. [26] and corrected in the MSI Eureka database [36]. 2
O. Dovbenko et al.
Calphad 68 (2020) 101719
the potential overestimation of the melting point might be due to the contamination of samples with oxygen or other interstitial elements, while the underestimation was linked to the shift in the composition of a sample under investigation from stoichiometry. Since the experimental procedure has been very briefly described in the article [26] (for example, neither material of crucible nor details of thermal analysis measurements are provided), it is hard to give reasons for significant deviation of the data experimentally measured by Kornilov et al. [26] from the currently accepted. Another example is the Hf–Pd–Pt system for which the isothermal section at 1000 � C was established by Kuznetsov et al. [42] using X-ray diffraction analysis (XRD), electron probe microanalysis (EPMA), and metallography. The authors suggested that a continuous solid solution should exist between the HfPd and HfPt phases, presumably having the CsCl structure (cP2). The later investigations of the Hf–Pd [43] and Hf–Pt [44] systems by Stalick and Watersrat nevertheless disprove this suggestion. In particularly, Stalick and Watersrat found out that the cubic CsCl modification of the HfPt phase transforms to the ortho rhombic CrB-type phase at around 1660 � C while the HfPd phase with the CsCl modification is stable from 1610 � C down to 600 � C. At 600 � C, a transition to a B190 -type phase occurs. The original isothermal section and its corrected version based on the recent Hf–Pd and Hf–Pt phase diagrams by Refs. [43,44] are compared in Fig. 2. The inconsistency between the ternary data and binary phase dia grams raises a question whether the whole isothermal or vertical section should be discarded. The final decision depends on many factors, including the total amount of experimental data points available for a system. One also should bear in mind a recommendation formulated by Kumar and Wollants [7], who underlined that the usage of all critically evaluated data is not recommended as too many data could be difficult to handle. In the case of the Co–Ni–Ti system, the liquidus and solidus temperatures by Kornilov et al. [26] cannot be used for the thermody namic calculation. At least, the usage of the data related to the NiTi part is not advisable. Moreover, several new experimental works [27–29,46, 47], including the liquidus data [48], were published since 1975. Therefore, there is no sense to fit the ternary phase data by Kornilov et al. [26] as this can appear harmful for the reliability of the thermo dynamic parameters. In the case of the Hf–Pd–Pt system, the experi mental reinvestigation of the phase equilibria should be recommended to ascertain the character of the phase equilibria at least between the HfPt and HfPd phases. There is also a case that the thermodynamic parameters of the three binary subsystems can well reproduce the available phase diagram and thermodynamic properties, and this binary thermodynamic description seems to be reasonably accurate. Still, the ternary system cannot be well modeled unless certain modifications are implemented in the
thermodynamic parameters of one or more of the binary subsystems. Some illustrative examples can be found in the literature [49–51]. One of the examples is the thermodynamic assessment for the U–Nb–Zr system [49]. The reported thermodynamic parameters of three binary subsystems seem to be reliable due to the general consistency with the measured data. However, a preliminary assessment shows that the bi nary parameters cannot yield satisfactory description of the experi mental data on the phase equilibria in the U–Nb–Zr system. An unusual widening of γ4þγ5 miscibility gap was found in the calculation, which was hardly influenced by ternary parameters. Such a behavior of the miscibility gap was found to be very sensitive to binary parameters of the U–Nb subsystem. Hence, the thermodynamic modeling of the U–Nb system was revised by slightly adjusting parameters of stable phases. If the ternary experimental data cannot be reasonably fitted using the ternary parameters, it might be reasonable to modify the thermody namic parameters in the binary subsystem. It should be kept in mind that all accurately measured data in binary subsystems should be considered during the modification. With such modification of the parameters for the binary subsystem, a satisfactorily calculated result in the ternary system could be obtained. 3. Comments on the evaluation of the experimental procedure Accuracy and reliability of the experimental results depend on different factors: purity of starting materials, reliable sample prepara tion technique, the correct condition of heat treatment for the investi gated material and experimental methods which were used for the phase equilibrium investigations. It is also important to check whether the materials of crucibles and containers used for the sample preparation, heat treatment or measurements are suitable for the materials and alloys under investigation. The correct interpretation of the experimental data and experience also play an important role by producing reliable experimental datasets. For these reasons, it should be kept in mind that the papers, which do not provide detailed descriptions of the experi mental procedure, should be considered as less reliable until their cor rectness is justified by other independent measurements of the same quantity. For a reliable experimental investigation of the phase equilibria, it is best to use a combination of different methods: crystallographic methods for the identification of the phases (for example, XRD), methods for the determination of the phase compositions (for example, EPMA or energy-dispersive X-ray spectroscopy (EDX)), metallographic methods (for example, optical (OM) or scanning electron microscopy (SEM)), methods and techniques for the measurement of the phase transformation temperatures (such as differential thermal analysis or differential scanning calorimetry) etc. The number of methods, which
Fig. 2. Isothermal section of the Hf–Pd–Pt system at 1000 � C after original work [42] and after critical evaluation from the MSI Eureka database [45]. 3
O. Dovbenko et al.
Calphad 68 (2020) 101719
should be used for the determination of the phase equilibria, must be sufficient to obtain reliable and sound results. It is highly objectionable to use only one or two experimental methods while investigating the phase equilibria in a ternary system characterized by the formation of many intermetallic compounds. Examples justifying this advice can be found among the papers reporting the experimentally studied isothermal sections of the Co–Ni–Ti system. A number of isothermal sections at 800, 900, 1000 � C were investigated in Refs. [52–55] using the diffusion couples and EPMA only. As a result, a continuous solution between Ni3Ti and Co3Ti binary phases was reported for all tempera tures (see, for example, the isothermal section at 800 � C in Fig. 3a) which is impossible as these binary compounds possess different crys tallographic structures – cubic AuCu3 for Co3Ti and hexagonal Ni3Ti [56]. Such kind of experimental data also reflects the investigators’ knowledge of the system, and it will have detrimental effect on the thermodynamic assessment, if such results are used in the optimization. As it was later found out in the numerous works [27–30,46,48], in which the XRD analysis together with SEM, EPMA techniques was applied, three compounds, namely binary Ni3Ti, Co3Ti and the ternary τ with the hexagonal Co3V structure, exist in the Co3Ti–Ni3Ti composition region (Fig. 3b). These compounds exhibit large homogeneity ranges and the same orientation relations, as has been stated by Van Loo and Bastin [46]. It is therefore impossible to distinguish between three compounds by relying only on the EPMA technique as the crystallographic structures of the phases must also be identified to obtain reliable results. For the same reasons, the authors [52–55] failed to correctly establish the phase equilibria involving the hexagonal and cubic modifications of the CoTi Laves phase as can be seen from Fig. 3. It should also be noted that the usage of the XRD and metallographic techniques only is not advisable for the investigation of phase equilibria at a constant temperature (an isothermal section) if a ternary system is characterized with the formation of a large number of intermetallic compounds with wide homogeneity ranges. For such systems, the pre cise establishment of tie-lines and tie-triangles would be complicated if the EPMA or EDX methods were not involved in the investigation. Special care should be paid by evaluating the experimental proced ure and results of the investigation reporting the so-called quasi-binary vertical sections in the metallic systems or systems containing such nonmetallic elements as B, C or N. The term “quasi-binary” implies that all tie-lines are located along an investigated section and that no ternary fields appear inside the plane of the section. The quasi-binary sections may be read like a binary system, and they will provide the full infor mation on the type, composition, and fraction of phases. Such a vertical section can be most probably expected in two cases. The first case is a system in which two compounds without the homogeneity ranges in the binary systems are isostructural and form a continuous solid solution in
the whole temperature-composition range. The second case is a section between either a pure element and a strictly stoichiometric compound or between two strictly stoichiometric compounds. Nevertheless, the sec tion, which is truly quasi-binary in the whole temperature-composition range, is a rare case. The sections, which are only partially quasi-binary (usually at high temperatures), are more often when some of the com pounds are not strictly stoichiometric, for example, the carbide systems containing compounds with a deficiency in carbon. It is therefore advisable to accurately evaluate the data reported for the quasi-binary sections between the intermetallic compounds showing wide homogeneity ranges in binary and ternary systems. One should pay attention to two conditions: 1) whether the section passes through the so-called distectic points, e.g. melting point of a pure element, congruent melting points of binary compounds, maxima in the ternary system; 2) whether all the investigated compositions lie inside the investigated composition plane. In the Cu–Mg–Zn, two quasi-binary sections were €ster and Müller [57] and Mikheeva and Kryukova [58]. proposed by Ko These are the section from pure Mg to the peritectic composition of the γ phase (so-called γ-brass phase with approximate stoichiometry Cu5Zn8) [57] and the section from pure Mg to the Cu50Zn50 (at.%) composition (the Mg–β section) [58]. The Mg–γ section is a result of the interpolation between the experimental points since the composition of the investi gated samples lies somewhat outside the vertical plane, and it is there fore only approximately a quasi-binary. The plane of the Mg–β section intersects no distectic points in the binary Cu–Zn system. The β (disor dered b.c.c. solution) phase has a wide homogeneity range in the Cu–Zn system and dissolves a certain amount of Mg that most certainly results in a change of the direction of the tie-lines with temperature thus ruling out the quasi-binary nature of the Mg–β section near the Cu–Zn system. 4. On the consistency between isothermal and vertical sections Before starting to compile a dataset, the internal consistency be tween the isothermal sections, vertical sections must be carefully checked to avoid the possible difficulties during the optimization pro cedure. It should be noted that the experimentally established isothermal sections are usually more trustworthy than the vertical one as far as the accuracy of the phase boundaries representation is concerned. The only exception from this rule is quasi-binary sections which have been already discussed in Section 3. In case of an isothermal section, not only the phase assemblages in a particular part of the concentration triangle can be determined but also the composition of the phases in equilibrium can be comparatively easy established since all tie-lines and tie-triangles are lying in the plane of the section. In case of a vertical section, most of the tie-lines lie outside the plane of the section. Therefore, the precise determination of the phase boundaries requires
Fig. 3. Experimentally established isothermal section of the Co–Ni–Ti system at 800 � C according to Refs. [52,53] (a) and [29] (b). 4
O. Dovbenko et al.
Calphad 68 (2020) 101719
the XRD, EPMA, and metallographic examination of several samples equilibrated at different temperatures and subsequently quenched. As it has been mentioned in Refs. [4,5], the best way to construct a vertical section is to use a set of well-determined isothermal sections, liquidus and solidus surfaces, and the DTA data. The situation in which an isothermal section contradicts to a vertical section is not rare. As an example, a vertical and isothermal sections (redrawn for atomic per cent) of the Mo–Ni–Zr system are compared in Fig. 4. The experimentally determined vertical section with weight ratio of Mo:Ni ¼ 1:1 in the Zr-rich region (~65–100 at.% Zr) was constructed by Gruzdeva and Tararaeva [59]. In this work, the samples were pre liminarily homogenized at 1000–1200 � C, annealed within different periods, 340 to 2 h, depending on annealing temperature, and subse quently quenched. The annealing temperatures were chosen at 50 � C intervals between 700 and 1000 � C. The prepared samples were analyzed using microscopy, hardness, and microhardness
measurements. As can be seen from Fig. 4a, the vertical section shows (βZr) and (βZr) þ NiZr2 phase regions for very low Mo and Ni contents and the three-phase (βZr) þ NiZr2 þ Mo2Zr region for zirconium content more than 90 at.% at 900 � C. However, two ternary compounds τ1 (cF96, the NiTi2 prototype) and τ2 (hP28, the Hf9Mo4B prototype) were reported to be in equilibrium with the (βZr) phase at 900 � C in the later experimental work by Wang et al. [60] (Fig. 4b). The isothermal section [60] was established based on the XRD and EPMA investigations of the samples prepared from high purity materials (99.99 mass%), annealed for 40 days and quenched in cold water. According to this isothermal section, the Mo:Ni ¼ 1:1 vertical section should cross the (βZr) þ NiZr2 þ τ1 region instead of the (βZr) þ NiZr2 þ Mo2Zr phase field at 900 � C. Materials and methods, which were used for investigation by Wang et al. [60], should give more reliable results than those reported by Gruzdeva and Tararaeva [59]. Consequently, the later experimental dataset should not be included in the optimization procedure as it has been done in the assessment of the Mo–Ni–Zr system performed Wang et al. [61]. 5. On the consistency among isothermal, vertical sections and liquidus projection The information on the phase equilibria involving the liquid phase, which is often presented in the form of a liquidus projection and rarer in the form of a melting diagram, is important for the establishment of a physically sound thermodynamic description. The usage of the co ordinates of the invariant reactions in an experimental dataset is espe cially beneficial for the optimization procedure as such data are more suggestive than the tie-lines in the isothermal sections or the tempera tures of the monovariant reactions. For a ternary system characterized by the formation of many intermetallic compounds, the establishment of liquidus or solidus projection is a complicated and time-consuming task, and it requires considerable expertise and significant effort. Exemplary works providing an extensive explanation of the construction of the liquidus and solidus projections were conducted by Prima and Petyukh [62,63] for Mo–Ni–Zr, by Palm et al. [64] for Al–Co–Nb, and by Stein et al. [11] for Al–Cr–Nb. Before the coordinates of an invariant reaction will be included in an experimental dataset for a further optimization, one should decide: 1) whether a particular reaction is relevant or not for a quantitative vali dation of the phase equilibria in a ternary system; 2) what kind of the coordinates (temperature or compositions of the phases) have been actually measured. As to the relevance of the invariant reactions, Janz et al. [65] pointed out that the degenerated reactions, which are typi cally the reactions showing at least one of the phase fractions close to zero and having the reaction temperature close to a corresponding invariant reaction in a low-order system, should be considered as irrel evant since they essentially provide the information for one of the sub-systems. Therefore, it is advisable to include the degenerated re actions in the experimental dataset after a workable thermodynamic description of a system is produced. In the case of the coordinates of the invariant reactions, one should clearly distinguish between the measured and deduced data. As a rule, the temperature of an invariant reaction can be relatively precisely measured by DTA or DSC methods if the invariant composition field is wide enough and the kinetics of the reaction is fast. For each measured invariant reaction, the type and compositions of the phases could be established. The eutectic and per itectic reactions can be identified by the corresponding types of micro structure in the as-cast samples. The transition-type (Lþ α ¼ β þ γ) and sometimes peritectic-type (Lþ αþ β ¼ γ) reactions can be revealed after careful analysis of the preceding and succeeding phase fields which appear in the microstructure of the as-cast samples or samples annealed for a short time at the sub-solidus temperatures. The hardest task is the measurement of the phase compositions involved in a particular invariant reaction. Theoretically, the compositions of a eutectic and all the involved phases can be measured in the as-cast samples if the size of the eutectic and the grains of the precipitated products are large enough
Fig. 4. Partial vertical section at weight ratio of Mo:Ni ¼ 1:1 after [59] (a) and partial isothermal section at 900 � C after [60] (b) of the Mo–Ni–Zr system. Both sections are redrawn for atomic per cent. 5
O. Dovbenko et al.
Calphad 68 (2020) 101719
to be measured by the beam of the energy-dispersive or wavelength-dispersive spectrometer. However, only the composition of the eutectic liquid can be usually established with a high accuracy. For the peritectic- and transition-type reactions, the composition of the liquid phase lies in the apex of the equilibrium composition space and does not correspond to the point where all the educts are fully converted to the product phases. Often, the composition of the equilibrium liquid phase cannot be measured directly in an as-cast sample, and it is usually deduced by interpolating between the experimental points. In principle, additional investigation using the samples annealed for a short time at the sub-solidus temperatures is required to accurately determine the compositions of all equilibrium phases participating in the peritectic- or transition-type reaction. Therefore, the temperature and type of an invariant reaction and eutectic composition should be considered as more reliable data than the reported compositions of the solid phases or liquid phase involved in the peritectic- and transition-type reaction. The cases described above are only general recommendations. For a better understanding of the possible pitfalls in the critical evaluation of the liquidus and solidus data, the interested reader could refer to Refs. [7,8,
11,64,65]. It is also mandatory to check whether the reported invariant equi libria and adjoining equilibrium phase relations agree with the experi mentally established isothermal and vertical sections available in other sources. It is not rare that a temperature of the invariant reaction has been measured accurately, but the phase equilibria have been errone ously interpreted. Mikheeva and Kryukova [58] studied a number of the vertical sections in the Cu–Mg–Zn system using the thermal analysis (TA) and metallographic examination of the samples after TA. The projection of the liquidus surface was constructed based on these experimental data. As the authors used metallography and thermal analysis only, they were unable to determine the stoichiometry of a ternary phase τ experimentally. It was assumed that this phase had no homogeneity range and lied outside the Cu2Mg–MgZn2 section, which was drawn as a typical isopleth (Fig. 5a). Therefore, the corresponding maxima in the monovariant L þ Cu2Mg↔τ (610 � C) and Lþτ↔MgZn2 (720 � C) lines appeared to be outside the plane of the section and the invariant reaction L þ Cu2Mg↔τþ MgZn2 at 602 � C (U3 in Fig. 5c) was proposed for this section. This finding contradicts to the data of Lieser
Fig. 5. The Cu–Mg–Zn system: the Cu2Mg–MgZn2 section after [58] (a) and after [66] (b); liquidus projection after [58] (c). 6
O. Dovbenko et al.
Calphad 68 (2020) 101719
and Witte [66], who reported the Cu2Mg–MgZn2 section to be a quasi-binary with the MgZn2 (C14), Cu2Mg (C15), and τ (CuMg2Zn3, C36) Laves phases appearing in the plane of the section (Fig. 5b). Furthermore, the C15 and C36 Laves phases exhibit wide homogeneity ranges. Both Mikheeva and Kryukova [58] and Lieser and Witte [66] used the thermal analysis and the reported temperatures of the maxima in the Lþτ↔MgZn2 (720 � C (p2, max in Fig. 5c) [58] and 716 � C [66]) and L þ Cu2Mg↔τ (610 � C (p1, max in Fig. 5c) [58] and 600 � C [66]). But the section proposed by Lieser and Witte [66] is more accurate as it is also based on the examination of the equilibrated samples using XRD and metallography. By comparison of the data, the evaluation of the experimental pro cedure always plays a vital role as can be seen, for example, by comparing the results of Prima and Petyukh [63] and Wang et al. [61] for the Mo–Ni–Zr system. Prima and Petyukh [63] investigated the liq uidus surface projection and melting diagram in the Zr–ZrNi–Mo region using the DTA, XRD, EPMA methods. The samples for the investigation were prepared by arc melting under argon atmosphere purified by melting Ti–Zr getter. The samples in as-cast state and annealed at sub-solidus temperatures were used for the experimental examination. According to Prima and Petyukh [63], only one ternary compound τ1 exists on the liquidus surface and is formed by the peritectic reaction, Lþ (Zr)þMo2Zr↔τ1 at 1020 � C. Later, Wang et al. [61] established the isothermal section at 1100 � C by analyzing the samples annealed at this temperature for 20 days in the evacuated quartz capsules with the XRD, EPMA, and SEM methods. They found that the τ2 phase equilibrates with the (βZr) and Mo2Zr phases. The appearance of the τ2 phase at such a high temperature also indicates that it equilibrates with the liquid phase and, therefore, should also appear on the liquidus surface. The experi mental methods and samples preparation procedure were accurate enough to obtain reliable results. However, there are differences in the purity of the starting materials. Wang et al. [61] used molybdenum, zirconium, and nickel with a purity of 99.99 wt%. Prima and Petyukh [63] used zirconium with a purity of 99.96 wt%, moulding compact molybdenum 99.9% Mo, nickel 99.9%, which contains up to 0.1 wt% Co. Considering the purity of the starting materials and annealing time, it could be concluded that the results of Wang et al. [61] are more preferable than the data of Prima and Petyukh [63]. Thus, the later re sults can be used for the thermodynamic assessment only partially, as it has been done in the work of Wang et al. [61]. In Fig. 6, the partial liquidus projection after Prima and Petyukh [63], in which a suggested primary crystallization field of τ2 is marked with a grey dashed line, is shown. Nevertheless, the Zr-rich part of the liquidus surface requires additional experimental verification.
Fig. 6. Corrected partial liquidus projection after [63] of the Mo–Ni–Zr system.
work. Acknowledgement The financial support from National Natural Science Foundation of China (Grant no. 51671219) is acknowledged. Both Dr. Oleksandr Dovbenko and Dr. Liya Dreval thank the grant from Department of In ternational Cooperation and Exchanges of Central South University, China. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.calphad.2019.101719. References [1] L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams: with Special Reference to Refractory Metals, Acad. Press, New York, 1970. [2] H. Ipser, Who will do the necessary experiments? J. Phase Equilibria Diffusion 38 (2017) 1–2. [3] A. Watson, Editorial, J. Phase Equilib. Diffus. 29 (2008) 1. [4] G. Cacciamani, G. Effenberg, R. Ferro, S. Ilyenko, P. Perrot, A. Pisch, P. Rogl, R. Schmid-Fetzer, Critical Evaluation of Binary Phase Diagram Data. Best Practice Guidelines for Evaluation & Notes for Authors, 3rd. ed., MSI, Materials Science International, Stuttgart, 2012. http://www.msiport.com/fileadmin/content/res earch/binary_evaluations/docs/notes_authors_binary.pdf. [5] G. Effenberg, R. Schmid-Fetzer, Critical Evaluation of Ternary Phase Diagram Data. Best Practice Guidelines for Evaluation & Notes for Authors, sixth ed., MSI, Materials Science International, Stuttgart, 2012. http://www.msiport.com/fileadm in/content/research/ternary_evaluations/docs/notes_author_ternary.pdf. [6] H.L. Lukas, S.G. Fries, Demonstration of the use of “BINGSS” with the Mg-Zn system as example, J. Phase Equilibria 13 (1992) 532–542. [7] K.C. Hari Kumar, P. Wollants, Some guidelines for thermodynamic optimisation of phase diagrams, J. Alloy. Comp. 320 (2001) 189–198. [8] J.C. Zhao (Ed.), Methods for Phase Diagram Determination, Elsevier, 2007. [9] R. Ferro, G. Cacciamani, G. Borzone, Remarks about data reliability in experimental and computational alloy thermochemistry, Intermetallics 11 (2003) 1081–1094. [10] R. Schmid-Fetzer, D. Andersson, P.Y. Chevalier, L. Eleno, O. Fabrichnaya, U. R. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, M. Zinkevich, Assessment techniques, database design and software facilities for thermodynamics and diffusion, Calphad 31 (2007) 38–52. [11] F. Stein, C. He, I. Wossack, The liquidus surface of the Cr–Al–Nb system and reinvestigation of the Cr–Nb and Al–Cr phase diagrams, J. Alloy. Comp. 598 (2014) 253–265. [12] J. Aufrecht, A. Leineweber, A. Senyshyn, E.J. Mittemeijer, The absence of a stable hexagonal Laves phase modification (NbCr2) in the Nb–Cr system, Scr. Mater. 62 (2010) 227–230. [13] J.L. Murray, Cu-Ti (Copper-Titanium), in: P.R. Subramanian (Ed.), Phase Diagrams of Binary Copper Alloys, ASM International, Materials Park, OH, 1994, pp. 447–460. [14] M.A. Turchanin, P.G. Agraval, A.R. Abdulov, Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system, Powder Metall. Met. Ceram. 47 (2008) 344–360.
6. Conclusion Some guidelines concerning the critical evaluation of the experi mental phase diagram in the ternary system and related binary systems are presented. We hope that these recommendations will be helpful to a novice user of the software packages for thermodynamic optimizations of the phase diagrams using the Calphad method. These guidelines are rather general, and a reader should realize that there are always specific issues associated with a critical evaluation of the experimental results for a particular system. Nevertheless, the authors feel that these hints will be useful for postgraduates, young researchers and experts in pro ducing a self-consistent experimental dataset for a thermodynamic optimization of a targeted system. Although the present work is focused on the critical evaluation of ternary phase diagram data, we would like to stress that thermochemical data of the ternary and related binary phases, if available, are also crucial for accurate Calphad assessment and proper optimization of the model parameters. Declaration of competing interest The authors declared that they have no conflicts of interest to this 7
O. Dovbenko et al.
Calphad 68 (2020) 101719
[15] M.A. Turchanin, P.G. Agraval, A.R. Abdulov, Thermodynamic assessment of the Cu-Ti-Zr system. II. Cu-Zr and Ti-Zr systems, Powder Metall. Met. Ceram. 47 (2008) 428–446. [16] N. Wang, C. Li, Z. Du, F. Wang, W. Zhang, The thermodynamic re-assessment of the Cu–Zr system, Calphad 30 (2006) 461–469. [17] L. Dreval, M. Zschornak, W. Münchgesang, O. Fabrichnaya, D. Rafaja, M. L. Martine, L. Giebeler, M. Motylenko, Thermodynamic assessment and first principle calculations of the Na Sb Sn system, J. Alloy. Comp. 695 (2017) 1725–1742. [18] M.A. Turchanin, Phase equilibria and thermodynamics of binary copper systems with 3d-metals. III. Copper-chromium system, Powder Metall. Met. Ceram. 45 (2006) 457–467. [19] Z.M. Zhou, J. Gao, F. Li, Y.P. Wang, M. Kolbe, Experimental determination and thermodynamic modeling of phase equilibria in the Cu–Cr system, J. Mater. Sci. 46 (2011) 7039–7045. [20] K.H. Kumar, I. Ansara, P. Wollants, L. Delaey, Thermodynamic optimisation of the Cu-Ti system, Z. Metallkd. 87 (1996) 666–672. [21] COST531 Thermodynamic Database Version 3.0, 10 June 2008. [22] S.W. Chen, C.-C. Chen, W. Gierlotka, A.R. Zi, P.Y. Chen, H.J. Wu, Phase equilibria of the Sn-Sb binary system, J. Electron. Mater. 37 (2008) 992–1002. [23] K.J. Zeng, M. H€ am€ al€ ainen, H.L. Lukas, A new thermodynamic description of the Cu-Zr system, J. Phase Equilibria 15 (1994) 577–586. [24] K. Yamaguchi, Y.-C. Song, T. Yoshida, K. Itagaki, Thermodynamic investigation of the Cu–Zr system, J. Alloy. Comp. 452 (2008) 73–79. [25] D.H. Kang, I.-H. Jung, Critical thermodynamic evaluation and optimization of the Ag–Zr, Cu–Zr and Ag–Cu–Zr systems and its applications to amorphous Cu–Zr–Ag alloys, Intermetallics 18 (2010) 815–833. [26] I.I. Kornilov, E.V. Kachur, O.K. Belousov, Investigation of the TiNi-TiCo system, Russ. Metall. (1975) 162–163. [27] P. Riani, K. Sufryd, G. Cacciamani, Critical assessment and experimental investigation of Co–Ni–Ti phase equilibria, Calphad 44 (2014) 26–38. [28] C. Zhou, C. Guo, C. Li, Z. Du, Experimental determination and thermodynamic assessment of the Co–Ni–Ti system, Calphad 63 (2018) 61–76. [29] Y. Yuan, L. Yang, D. Li, A. Tang, F. Pan, H. Seifert, N. Moelans, Diffusion multiple study of Co-Ni-Ti system at 1073 K, Calphad 63 (2018) 156–163. [30] H. Li, P. Zhou, Y. Du, Z. Jin, Isothermal sections of the Co–Ni–Ti system at 950 and 1 000 � C, Int. J. Mater. Res. 109 (2018) 105–112. [31] J.L. Murray, Ni-Ti, in: P. Nash (Ed.), Phase Diagrams of Binary Nickel Alloys, ASM International, Materials Park, Ohio, 1991, pp. 342–355. [32] K.C.H. Kumar, P. Wollants, Thermodynamic assessment of the Ni-Ti phase diagram, Z. Metallkd. 87 (1996) 972–978. [33] J. de Keyzer, G. Cacciamani, N. Dupin, P. Wollants, Thermodynamic modeling and optimization of the Fe–Ni–Ti system, Calphad 33 (2009) 109–123. [34] A.V. Davydov, U.R. Kattner, d. Josell, R.M. Waterstrat, W.J. Boettinger, J. E. Blendell, A.J. Shapiro, Determination of the CoTi congruent melting point and thermodynamic reassessment of the Co-Ti system, Metall. Mater. Trans. A 32 (2001) 2175–2186. [35] T.B. Massalski, H. Okamoto (Eds.), Binary Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1990. [36] G. Cacciamani, P. Riani, in: M.S.I. Eureka, G. Effenberg (Eds.), Co-Ni-Ti Ternary Phase Diagram Evaluation, MSI, Materials Science International Services GmbH, MSI Eureka, Stuttgart, 2004. http://www.msi-eureka.com/preview-html/10.117 39.1.6/Co-Ni-Ti_Ternary-Phase-Diagram-Evaluation/. [37] A. Iannucci, A.A. Johnson, E.J. Hughes, P.W. Barton, Study of the solubility limits of the compound TiCo using high-temperature X-ray diffractometry, J. Appl. Phys. 39 (1968) 2222–2224. [38] V.V. Pet’kov, M.V. Kireev, Intermediate phases in the titanium-cobalt system, Metallofizika 33 (1971) 107–115. [39] H. Huthmann, G. Inden, High-temperature neutron diffraction on FeTi and CoTi, Phys. Status Solidi 28 (1975) K129–K130. [40] S.R. Butler, J.E. Hanlon, R.J. Wasilewski, Electric and magnetic properties of TiCo and related compositions, J. Phys. Chem. Solids 30 (1969) 281–286. [41] H.J. Wallbaum, The systems of the iron-group metals with titanium, zirconium, niobium, and tantalum, Arch. Eisenhuettenwes. 10 521–526.
[42] V.N. Kuznetsov, G.P. Zhmurko, E.M. Sokolovskaya, Phase equilibria and structural stability of intermetallics in the Pt-Pd-Hf and Pt-Pd-Zr systems, J. Less Common. Met. 163 (1990) 1–8. [43] J.K. Stalick, R.M. Waterstrat, Crystal structures and phase equilibria in the hafnium-palladium system, J. Phase Equilibria Diffusion 37 (2016) 416–422. [44] J.K. Stalick, R.M. Waterstrat, The hafnium-platinum phase diagram, J. Phase Equilibria Diffusion 35 (2014) 15–23. [45] K. Korniyenko, Hafnium - palladium - platinum, in: M.S.I. Eureka, G. Effenberg (Eds.), MSI, Materials Science International Services GmbH, MSI Eureka, Stuttgart, 2018. http://www.msi-eureka.com/full-html/10.15360.1.4/Hf-Pd-Pt_Ternary-Ph ase-Diagram-Evaluation/#Text0. [46] F.J.J. van Loo, G.F. Bastin, Phase relations and diffusion paths in the Ti-Ni-Co system at 900 � C, J. Less Common. Met. 81 (1981) 61–69. [47] Y. Du, Z.P. Jin, P.Y. Huang, Determination of the 850 � C isothermal section in the Co-Ni-Ti system, J. Phase Equilibria 14 (1993) 348–353. [48] C. Zhou, C. Guo, J. Li, C. Li, Z. Du, Experimental investigations of the Co–Ni–Ti system: liquidus surface projection and isothermal section at 1373 K, J. Alloy. Comp. 754 (2018) 268–282. [49] P. Zhou, Y. Peng, Y. Du, L. Zhang, W. Mo, T. Fa, B. Bai, X. Wang, Thermodynamic modeling of the U-Nb-Zr ternary system, J. Nucl. Mater. 523 (2019) 157–171. [50] Y. Peng, P. Zhou, M. Bu, W. Zhang, Y. Du, A thermodynamic evaluation of the C–Cr–Nb system, Calphad 53 (2016) 10–19. [51] Y. Liu, P. Zhou, S. Liu, Y. Du, Experimental investigation and thermodynamic description of the Cu-Cr-Zr system, Calphad 59 (2017) 1–11. [52] A.S. Sagyndykov, M.V. Raevskaya, E.M. Sokolovskaya, B.I. Gryzunov, Co-Ni-Ti system, komplecs, Ispol. Mineral. Sypiya (1979) 193–195. [53] V.I. Gryzunov, A.S. Sagyndykov, Mutual diffusion in the system Ti-Ni-Co, Phys. Met. Metallogr. 49 (1980) 178–182. [54] V.I. Gryzunov, A.S. Sagyndykov, Y.M. Sokolovskaya, Temperature dependence of mutual diffusion coefficients in the Ti-Ni-Co system, Phys. Met. Metallogr. 54 (1982) 69–74. [55] V.I. Gryzunov, G.V. Shcherbedinskiy, B.K. Sokolovskaya, Kinetics of phase growth during interdiffusion in ternary multiphase metallic systems, Phys. Met. Metallogr. 56 (1983) 183–186. [56] P. Paufler, P. Villars, L.D. Calvert, ’s Pearson, Handbook of Crystallographic Data for Intermetallic Phases. American Society for Metals. Metals Park. Ohio, 1–3, 1986, p. 3258. [57] W. K€ oster, F. Müller, The ternary copper-zinc-magnesium system, Z. Metallkd. 39 (1948) 352–359. [58] V.I. Mikheeva, O.N. Kryukova, Melting diagram of the system Cu-Mg-Zn, Izv. Sekt. Fiz.-Khim. Anal., Akad. Nauk. SSSR 20 (1950) 76–93. [59] N.M. Gruzdeva, E.M. Tararaeva, Zr corner of the Zr-Mo-Ni system phase diagram, in: O.S. Ivanov (Ed.), Fiz. Khim. Splavov Tsirkoniya, Nauka, Moscow, 1968, pp. 189–195. [60] S. Wang, C. Zhang, C. Lin, Y. Peng, Y. Du, Measurement of 900 � C isothermal section in the Mo-Ni-Zr system, J. Phase Equilibria Diffusion 37 (2016) 672–679. [61] S. Wang, C. Zhang, Y. Du, Y. Peng, Y. Pan, P. Zhou, L. Dreval, Experimental investigation and thermodynamic assessment of the Mo–Ni–Zr ternary system, Calphad 58 (2017) 128–137. [62] S.B. Prima, V.M. Petyukh, Phase ratios of solidification of alloys of the Ni-Zr-Mo system in the ZrNi-Ni-Mo region, Russ. Metall. (1991) 149–155. [63] S.B. Prima, V.M. Petyukh, Phase transformations during solidification of nickelzirconium-molybdenum alloys in the Zr-ZrNi-Mo region, Russ. Metall. (1993) 149–156. [64] M. Palm, C. He, O. Dovbenko, F. Stein, J.C. Schuster, Liquidus projection and reaction scheme of the Co-Al-Nb system, J. Phase Equilibria Diffusion 33 (2012) 210–221. [65] A. Janz, J. Gr€ obner, R. Schmid-Fetzer, Thermodynamics and constitution of Mg-AlCa-Sr-Mn alloys: Part II. Procedure for multicomponent key sample selection and application to the Mg-Al-Ca-Sr and Mg-Al-Ca-Sr-Mn systems, J. Phase Equilibria Diffusion 30 (2009) 157–175. [66] K.H. Lieser, H. Witte, Investigation on ternary systems of Mg-Cu-Zn, Mg-Ni-Zn, and Mg-Cu-Ni, Z. Metallkd. 43 (1952) 396–401.
8