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To efficiently construct phase diagrams of alloy systems, a machine learning-based method advanced by thermodynamics on phase equilibria is proposed. With the use of uncertainty sampling in active learning, the next point to be synthesized or measured can be recommended to efficiently draw the phase diagram. For appropriate recommendations, two ingenuities are introduced in the machine learning method: training data preparation when the multiphase coexisting region is detected and search space reduction based on the Gibbs’ phase rule. We demonstrate the construction of ternary phase diagrams using our machine learning method by incorporating these ingenuities. The complicated phase diagram of alloy systems could be effectively plotted even when knowing only the information of single-component systems in the initial step. The recommendation made by our machine learning method can help reduce the number of experiments required to construct a phase diagram to approximately 1/8 compared with random sampling.

A critical determination of a phase diagram of the Zn-Fe binary system was carried out by EPMA analysis for skillfully prepared and equilibrated two-phase alloys for solid phases and by EDS areal analysis for the Fe solubility in the heterogeneously solidified liquid phase instead of the conventional diffusion couple method. It was newly confirmed that equilibrium compositions of intermetallic compounds tend to shift toward the Fe side compared to the previous phase diagram on the whole and that the solubility ranges of the Γ-Fe3Zn10 and Γ1-Fe11Zn40 phases are much narrower than those in the literature. The critical composition of the second-order order-disorder transition between δ1k-FeZn7 and δ1p-FeZn10 at high temperature was estimated by Vickers hardness measurement. Furthermore, the phase separation, i.e., the first-order transition, between the δ1k and δ1p phases in the low temperature region was directly found out and its equilibrium compositions were confirmed by EPMA analysis for the two-phase microstructures. The width of the δ1k + δ1p two-phase region at 500 °C is only 0.5 at.% and the δ1p decomposes into the δ1k and ζ-FeZn13 phases via a eutectoid reaction at a temperature between 455 °C and 445 °C. While being mostly coincident with those in the previous literature at temperatures between 1000 °C and 600 °C, the solubility of Fe in the liquid (L) Zn phase is about twenty times larger than the assessed value in the literature at temperatures below 500 °C. A eutectic reaction, L → ζ + (ηZn), was confirmed to occur by precise EPMA analysis and DSC measurement.

In the present study, the formation and growth behaviors of intermetallic compound (IMC) layers in the interfacial reaction of solid Fe and molten Zn during hot dipping at 450 °C were investigated. In the early stage of the interfacial reaction, Γ-Fe4Zn9, δ1k-FeZn7, and ζ-FeZn13 phases were formed, among which the growth of the ζ layer was dominant. Columns of the δ1p-Fe13Zn126 phase were formed on the δ1k/ζ interface at approximately 90 s, and the four IMC layers grew simultaneously until 600 s. Subsequently, a layer of the Γ1-Fe21.2Zn80.8 phase was formed along the Γ/δ1k interface and started growing, after which all the equilibrium IMC phases of Γ/Γ1/δ1k/δ1p/ζ grew competitively. The total thickness of the five IMC layers, dtotal, increased proportionally with the square root of the reaction time, t, i.e., dtotal = d0 t 0.5, which suggested that the growth of the entire IMC layers was controlled by the volume diffusion. However, the values of the time exponent, n, for the individual IMC layers differed depending on their microstructures and chemical concentrations, under equilibrium or nonequilibrium conditions. The formation of the multilayered columnar ζ phase can be attributed to the heterogeneous supersaturation of Fe in the liquid Zn near the columnar ζ / liquid Zn interface during the early stage of the interfacial reaction. The interdiffusion fluxes, J ϕ , of Fe and Zn in the ϕ phase ( ϕ = Γ, δ1k, and ζ) were estimated from the measured concentration profiles of each phase. This suggested that J ϕ caused the growth of each phase as well as the supersaturation of Fe near the interfacial boundaries, thereby resulting in considerable deviations from the equilibrium concentrations. In the later stage of the interfacial reaction, the interfacial concentrations gradually approached the equilibrium concentrations with decreasing J ϕ .

A thermal fluctuation-based nucleation model for use in a phase-field model is proposed. In the model, a normally distributed random temperature fluctuation is imposed on a calculation system, and if a given grid temperature is lower than the average, the undercooling is converted to an increase in the crystallized/precipitated phase fraction. The conversion coefficient is derived as a function of a phase-field critical value for nucleation. The idea of a threshold of nucleation for the phase field, i.e., a critical value, is introduced first in the present study. The model is applied to homogeneous nucleation during solidification in a supercooled pure metal, and a reasonable nucleation probability curve is successfully obtained from the numerical calculations. An application to the homogeneous nucleation of an Al-Cu alloy is also demonstrated.

Phase equilibria in multi-phase Zn–Fe–Al alloys were experimentally measured using a field-emission electron probe micro-analyzer for alloy samples, and a precise iso-thermal phase diagram at 450 °C in the entire composition range of the Zn–Fe–Al ternary system, except for the Fe-rich corner, was determined. The ternary solubility ranges of the Γ-Fe4Zn9, Γ1-Fe21.2Zn80.8, δ1k-FeZn7, and ζ-FeZn13 on the Fe–Zn side and of the ζ-FeAl2, η-Fe2Al5, and θ-Fe4Al13 on the Fe–Al side were consistent with the latest corresponding binary data, whereas no δ1p-Fe13Zn126 phase was detected. The single-phase region of the Γ2-Fe8Zn87Al4 ternary intermetallic compound phase is significantly narrower than that reported in the previous studies. The solubility of Fe in the liquid phase increased consistently and continuously from the value in the Zn–Fe binary system (0.6 at.%) up to 1.2 at.% at 31 at.% Al with increasing Al content. In the Al-rich portion of the phase diagram at 450 °C, the Fe(Al, Zn)6 intermetallic compound phase was newly discovered, and confirmed to be an isomorph extended from the FeAl6 phase which is metastable in the Fe–Al binary system.

Al-rich portion of the Al–Fe binary phase diagram was determined by conventional heat-treatment for equilibration, the diffusion couple method and thermal analysis. Equilibrium compositions are mostly coincident with the generally accepted phase diagram in the literature up to 1000 °C, except the solubility range of θ-Fe 4 Al 13 phase. The solubility ranges of the η-Fe 2 Al 5 and the θ-Fe 4 Al 13 phases were confirmed to increase and incline to the Fe-rich side with increasing temperature. Phase boundaries and the eutectoid composition of the e-Fe 5 Al 8 phase were determined from the diffusion couple method and heating curves of DSC measurement, which were slightly shifted to a higher Fe concentration. Transformation temperatures of liquidus, solidus and invariant reactions determined from heating curves of DSC measurement were mostly lower than those in the phase diagram evaluated by Kattner and Burton. An invariant reaction related to the formation of the θ-Fe 4 Al 13 phase was confirmed as the peritectic reaction of Liquid + η-Fe 2 Al 5 = θ-Fe 4 Al 13 in this study taking equilibrium compositions of the η-Fe 2 Al 5 + θ-Fe 4 Al 13 phases and solidus temperatures of the θ-Fe 4 Al 13 phase into consideration.

Phase equilibria in the Ir–W, Ir–Al and Ir–W–Al systems at temperatures between 1100 °C and 1600 °C were experimentally investigated using diffusion couples and two- or three-phase alloys, and the mechanical properties of γ′ (L12) strengthened Ir–W–Al alloys were examined by hardness and compression tests at room and elevated temperatures. The phase boundaries between the γ(A1)/e′(D019), e′/e(A3) and e/e″(B19) in the Ir–W system at 1400 °C–1600 °C and those between the γ/β(B2) and β/Al2.7Ir in the Ir–Al system at 1100 °C–1400 °C were determined. The phase diagrams in the Ir-rich corner of the Ir–W–Al ternary system at 1300 °C and 1400 °C were also determined. The existence of the γ′ phase of the Ir3(W,Al) ternary compound was confirmed, and this system was found to consist of the γ, γ′, e, e′ and β phases in the Ir-rich portion. It was also found from hardness and compression tests up to 1200 °C that Ir–Al–W alloys having the γ + γ′ structure with a small lattice misfit show high hardness and strength at room and high temperatures.

Experimental investigation and thermodynamic evaluation of the Co–Ta binary phase diagram was carried out. Equilibrium compositions obtained in two-phase alloys and diffusion couples were measured by electron probe microanalyzer (EPMA). A very narrow λ3(C36) + λ2(C15) two-phase region is confirmed to be present around 26.5 at.% Ta at temperatures between 950 °C and 1448 °C. Equilibrium relationships above 1500 °C among the liquid, Laves (λ1(C14), λ2 and λ3, whose stoichiometry is described by Co2Ta), μ(D8b) and CoTa2(C16) phases were investigated by microstructural examination in as-cast Co-(24–60 at.%)Ta alloys. The solvus temperature of the γ′ Co3Ta (L12) phase precipitated in the 5.8 at.%Ta γ(Co) and the peritectoid temperature of the Co7Ta2 phase in an 8.5 at.%Ta alloy were determined to be 1013 °C and 1033 °C, respectively, by differential scanning calorimeter (DSC). Fine precipitates of the γ′ phase precipitated in the γ (A1) matrix were observed by transmission electron microscope (TEM). Analyzing the present experimental results synthetically, the γ′ Co3Ta phase was identified to be a metastable phase, of which the γ/γ′ transition temperature of the stoichiometric Co3Ta alloy was estimated to be 2000 °C. Thermodynamic assessment of the Co–Ta binary system was carried out based on the present results as well as on experimental data in the literature. Calculated results of not only stable but also metastable equilibria were found to be in good agreement with the revised phase diagram. The evaluated stability of the metastable γ′ Co3Ta coincides with the enthalpy of formation (ΔH(γ'Co3Ta) = −23.44 kJ/mol) calculated by the ab initio method.

The phase equilibria among γ (A1), γ′ (L12), χ (D019), β (B2) and μ (D85) phases and the γ′ solvus and γ solidus temperatures were investigated in the Co–Al–W-based quaternary systems with alloying elements of Ti, V, Nb, Ta, Cr, Mo, Mn, Fe, Ni, Si, Zr, Hf, Ru and Ir by electron probe microanalysis (EPMA) using multiphase alloys and by differential scanning calorimetry (DSC). It was found that Ta, Nb, Ti, V, Mo and W are partitioned to the γ′ or χ phase rather than to the γ phase, while Cr, Mn and Fe tend to be distributed to the γ phase. The correlation between the partition coefficient of alloying elements between γ/γ′, γ/χ and γ/β phases and ab initio formation energy of Co3X (L12), Co3X (D019) and CoX (B2) was respectively obtained. It was also found that the γ′ solvus temperature increases by the addition of the γ′ former elements such as Ta, Nb and Ti, which decreases the γ solidus temperature.

The normal grain growth behaviors at 750, 800 and 900°C in block and sheet samples of Cu­Al­Mn shape memory alloy with the bcc single-phase structure were investigated. The grain growth exponents, n, evaluated in the two- and three-dimensional grain growths were found to be larger than those in most other metals and were located between 10 and 18. Furthermore, the two-dimensional growth in thin sheet samples was much slower than the three-dimensional growth in block samples due to the grooves formed along grain boundaries on the specimen surface, these grooves constituting a hindrance to the movement. [doi:10.2320/matertrans.M2013167]

Phase equilibria in the Fe–Si binary system were investigated experimentally and thermodynamic assessment was carried out. The αFe (A2) + α"Fe3Si (D03) two-phase microstructures at 600°C and 650°C were obtained, whose grain sizes were sufficiently coarsened to be analyzed by FE-EPMA with a spatial resolution below 0.5 μm under the condition of 6 kV accelerating voltage. α'FeSi (B2) + α"Fe3Si (D03) two-phase equilibria above 700°C were detected for the first time and equilibrium compositions were determined by the diffusion couple method. The horn-shaped two-phase miscibility gap extends from the low temperature αFe + α"Fe3Si equilibrium along the B2/D03 second-order transition boundary and closes below 1000°C. Four-sublattice split compound energy formalism was applied to calculate the Gibbs energy of the bcc phases, A2(αFe), B2(α'FeSi) and D03(α"Fe3Si), and the thermodynamic parameters in the Fe–Si binary system were evaluated. Equilibrium relations in the binary system were well reproduced, especially the effect of the B2 and D03 ordering on the liquidus and solidus curves and the miscibility gap between bcc phases. Optimized thermodynamic parameters as well as the experimental results are expected to be helpful for developing higher multi-component systems for practical steels.

The phase equilibria at 200 °C, 250 °C, 300 °C, and 400 °C and the phase transformation of the Sn-Au-Bi system were investigated by using the electron probe micro-analyzer (EPMA) and differential scanning calorimeter (DSC), respectively. It is found that there is a new ternary intermetallic compound with a possible AuSn structure (called the ϕ phase in the present work), which has a limited solubility of Au in the Au-rich portion, and the ϕ phase decomposes peritectically at about 313 °C. Based on the experimental data reported in the previous papers and new experimental data determined by the present work, thermodynamic assessments of the Sn-Au-Bi system were carried out by the calculation of phase diagrams (CALPHAD) method. The thermodynamic parameters for describing the Gibbs free energy of each phase were optimized, and reasonable agreement between the calculated results and experimental data was obtained in the Sn-Au-Bi ternary system.

Mechanical properties of Fe-20Mn-(10-14)Al-(0-1.8)C (mass%) quaternary and Fe-20Mn-(10-14)Al-(0.75-1.8)C-5Cr (mass%) quinary alloys were investigated by hardness, cold-workability and tensile tests at room temperature. The γ(fcc) alloys in both quaternary and quinary systems with a low density of less than 7.0 g/cm 3 showed an excellent ductility and their hardness and tensile strength increased with increasing Al and C contents. The γ+α(bcc) duplex alloys also exhibited a high tensile strength by controlling the α volume fraction. TEM observation confirmed that high hardness and tensile strength of the alloys with high Al and C contents are caused by the precipitation of nano-size κ-carbide with perovskite structure during cooling from the annealing temperature. Fe-20Mn-11Al-1.8C-5Cr alloy with a density of 6.51 g/cm 3 showed a high specific strength of more than 180 MPa · cm 3 /g with a good tensile elongation of 40 %. The present Fe-20Mn-Al-C(-5Cr) alloys showed a higher specific strength than conventional steels.

The National Natural Science Foundation of China [50425101, 50571084]; The Ministry of Science and Technology of China [2004CCA04200]; The Ministry of Education of China [20050384003, 105100, 707037]; Grant-Aid Core Research for Evolution Science and Tech

The phase equilibria at 300, 400, 500, and 600 °C in the Ag–Bi–Ni system and 300, 400, and 500 °C in the Cu–Bi–Ni system were experimentally determined by metallography and electron probe microanalysis on equilibrated alloys and diffusion couples. Differential scanning calorimetry was used to measure the temperatures of phase transformations. All the experimental results show that the solubilities of the ternary elements of the binary intermetallic compounds in the Ag–Bi–Ni system are limited. However, the binary intermetallic compounds have some solubilities of the ternary elements in the Cu–Bi–Ni system. No ternary intermetallic compound was found in the Ag–Bi–Ni and Cu–Bi–Ni systems. On the basis of the determined results, the phase equilibria in the Ag–Bi–Ni and Cu–Bi–Ni systems were thermodynamically assessed, and reasonable agreement between the calculated results and experimental data was obtained.

Phase equilibria between the α (A2), α' (B2) and γ (A1 ) phases in the Fe-Rh binary system were investigated using electron probe micro-analysis (EPMA) and differential scanning calorimetry (DSC) techniques. The A2/B2 order-disorder transformation temperature was also examined by a transmission electron microscope (TEM) observations and high-temperature X-ray diffraction (HTXRD). It was confirmed that while the transition temperature from the α (A2) phase to the γ (A1 ) phase decreases with increasing Rh content up to about 20 at% Rh, the b.c.c. region is stabilized by further Rh addition in the composition range between about 20 and 50 at% Rh, and then again the stability of b.c.c. phase decreases in the composition region over 50 at% Rh. It was also shown by TEM observation and HTXRD examination that the compositions of the phase boundary of the A2/B2 ordering at 500°C and 600°C were determined to be 16.5 and 19.1 at% Rh, respectively. On the basis of those experimental results, a thermodynamic analysis was carried out. The results of the thermodynamic calculation suggest that the anomalous behavior of the stability of the b.c.c. phase is caused by the A2/B2 ordering.

On the basis of the CALPHAD (Calculation of Phase Diagrams) method, the compositional range of stable miscibility gap and volume fractions of the two liquid phases in the Cu–Fe–Cr–Ni system were predicted, which can provide the guidance for design of self-formed composite materials. Based on such information, the self-formed pencil-like bulk composite materials consisting of copper alloy and two kinds of stainless steels were prepared by controlling the compositions of Cu-rich and Fe-rich phases in immiscible liquid system by the conventional casting process. The experimental results are in good agreement with the ones predicted by calculation. This study indicates that it is possible to develop the pencil-like bulk composite materials consisting of copper alloy and stainless steels by the conventional casting process.

Phase equilibria between the y and y' phases at 900°C in the Co-(10-70)Ni-Al-W system were determined by electron probe microanalysis (EPMA) and X-ray diffractometry (XRD). It was found that the "/ phase with L1 2 structure continuously exists from the Co side to the Ni side in Co-Ni-Al-W system and that it widens to the low W region with increasing Ni content. The partition of Al into the y' phase increased with Ni content, while the W changed from a y' former to a y former by increase of Ni content. Differential scanning calorimetry (DSC) measurements also revealed that the y' solvus temperature increases with Ni content, while the solidus temperature is hardly affected by such content. The lattice parameter of the y and y' phases and the mismatch decreased with increasing Ni content, which caused the morphologic change of the γ' precipitates from cubes to spheres.

The recrystallization and grain growth characteristics of pre-deformed Fe–1.9vol%Bi alloy specimens in the two-phase region of αFe and liquid Bi were investigated by microstructural observation. Precipitate-free zones (PFZs) were mainly formed in the vicinity outside of the curved grain boundaries. Furthermore, large Bi particles were also observed on the grain boundaries of the matrix along the PFZs. These results suggest that the intragranular liquid Bi particles were trapped and dragged by grain boundaries. The grain growth of the matrix phase was extremely retarded by the effect of this dragging.

The phase equilibria, A2/B2 and B2/L21 order–disorder transitions and ferromagnetic/paramagnetic transition on the Co–Fe side of the Co–Fe–Ga system were examined by electron probe microanalysis (EPMA), differential scanning calorimetric (DSC) measurement and vibrating sample magnetometer (VSM). The equilibrium compositions of interrelations mainly among γ (A1: disordered fcc-Co), α (A2: disordered bcc-Fe), β (B2: ordered bcc-CoGa or FeGa) and β′ (L21 or D03: ordered bcc-Co2FeGa or Fe3Ga) phases were determined using diffusion couples and two-phase bulk specimens. It was confirmed that a bcc single-phase region composed of α, β and β′ at 700–1000° C exists in a wide composition range and that the ferromagnetic region appearing on the Co–Fe side extends to the center of the Gibbs triangle with decreasing temperature. On the other hand, the β′ phase appears along the Fe3Ga–Co3Ga section and the maximal critical temperature of the B2/L21 order–disorder transformation was determined to be 825 °C at a stoichiometric composition expressed as Co2FeGa. The obtained phase diagram was examined in comparison with that of the Co–Fe–Al system.

The carbide dispersion carburizing process was applied to Fe-based high-speed steels, which contained multiple carbide-forming elements, Mo and V. Fine carbides precipitated during the carburization and the dispersed particles in the Fe–Mo–V–C alloys heat-treated at 1 200°C were identified as VC, (Mo, V)2C, and (Fe ,Mo)6C, which behave as effective inhibitors against the grain growth of austenite and as reinforcers resulting in increased hardness of the martensitic matrix. The maximum Vickers hardness of the Fe–10Mo–5V–2.05C alloy quenched from 1 200°C and tempered at 600°C achieved values of 1 100 and 1 000, respectively. Thermodynamic calculation of the Fe–Mo–V–C quaternary system proved to be useful for optimizing the composition of carbide forming elements, the carburizing conditions, and the microstructure of carburized and solution-treated alloys.

The phase equilibria of the In-Ag-Bi and In-Ag-Sb systems were determined by differential scanning calorimetry (DSC) and electron probe microanalysis (EPMA). Thermodynamic calculations of these systems were also carried out by taking the experimental results into account. The Gibbs energies of the liquid and solid solution phases are described on the basis of the sub-regular solution model, and that of the intermetallic compounds are based on the two-sublattice model. A consistent set of thermodynamic parameters was optimized for describing the Gibbs energy of each phase, which leads to a good fit between calculated and experimental results. In addition, the surface tension and viscosity of liquid phase were calculated on the basis of the thermodynamic parameters obtained in the present assessment.

The morphologies and growth of e(Cu 3 Sn) and η(Cu 6 Sn 5 ) intermetallic compounds (IMCs) between a molten Sn base solder and a Cu substrate were experimentally investigated. It is shown that the thickness of the e(Cu 3 Sn) and η(Cu 6 Sn 5 ) compounds decreases with deceasing Sn content and that the order of the growth rate of the compounds on the Cu substrate are as follows: Sn-57(mass%)Bi < Sn-37Pb < Sn-3.5Ag < Sn < Sn-6.7Sb. The growth of these phases basically obeys the parabolic law, but the growth behavior is divided into two stages, the growth rate and morphology of the η(Cu 6 Sn 5 ) compound are differing from each other in the two-stage. It is suggested that the grooving effect is at least one of the origins of the formation of the scallop morphology of the η(Cu 6 Sn 5 ) compound.

Microstructure and grain growth characteristics of pre-deformed Al-Bi alloys annealed at 773 K were investigated mainly by scanning electron microscopic (SEM) observation. In addition to very fine liquid-Bi particles in the grains, large Bi particles were observed on the grain boundaries, and non-precipitation zones are mainly formed in the vicinity outside of the curved grain boundaries. This result suggests that the Bi particles on the grain boundaries were dragged by the grain boundaries. The grain growth is significantly retarded by the effect of this dragging, the origin of which can be explained by the decrease of the interfacial energy of the intragranular Bi particles. Quantitative analysis showed that the diffusion of Al atoms in the liquid Bi particles on the grain boundaries is the rate-determining process of this dragging.

A thermodynamic description of the Bi–In–Sb ternary system of lead-free solder alloys using the CALPHAD (Calculation of Phase Diagram) method is presented. Phase equilibria information such as vertical sections, liquidus projection and thermochemical quantities were calculated and compared with the experimental data. The calculated and experimental data are in excellent agreement in most cases.

The evolution of sulfide morphology in the Fe-(0.3-18)mass%Cr-(0.05-0.3)mass%S alloys during solidifi-cation and heat treatment was investigated by means of optical microscopy, scanning electron microscopy, analytical electron microscopy and X-ray diffraction. In situ observation of the formation of the fine particle sulfide was also conducted at elevated temperatures by confocal scanning laser microscopy. The morphology of sulfide in the Fe-Cr-S ternary alloys was found to change from a cell wall type to a globular type with increasing Cr content. Accompanying the phase transformation of the matrix from the δ phase to the γ phase, two types of transgranular fine particle sulfide were formed. One is a fine spherical sulfide formed from the FeS-rich liquid phase through the remelting reaction of δ→γ+Liq. in less than 5 mass% Cr alloys, and the other is a fine rod-like sulfide formed through the eutectoid reaction of δ→γ+sulfide in 5 to 13 mass% Cr alloys. The formation mechanism of various types of sulfide morphology was examined based on phase diagram information.

Phase stability of the BCC phases with A2, B2 and D03 structures and phase equilibria among these phases in the Fe-rich portion of the Fe–Al binary system were examined using diffusion couples, transmission electron microscopy (TEM), energy dispersion spectroscopy (EDS) and Vickers hardness (VH) measurement. TEM observations of the diffusion couples annealed at the temperatures between 300 and 700 °C were performed to identify the crystal structure of the ordered phases and to measure the average size of the B2 and D03 ordered domains. Phase boundaries between A2 and B2 or D03 phases were then evaluated by comparison between the concentration profile and the profiles of the ordered phase domain size or Vickers hardness. It was clarified that the present results in the high temperature range over 450 °C are in agreement with the previous data, while the A2+D03 two-phase field extends beyond the A2/D03 phase boundary in the currently available phase diagram into a lower Al range at temperatures below 450 °C. The A2→B2, B2→D03 and para→ferro continuous ordering temperatures were also measured by differential scanning calorimetry (DSC).

A thermodynamic description of the In–Sn–Zn ternary system, which is of technical importance to optimize lead-free solder alloys, is presented using the CALPHAD method. Phase equilibria, such as isothermal and vertical sections, liquidus projection and mole fractions of the phase constitution, and thermochemical quantities were calculated and compared with the experimental data. They are in excellent agreement in most cases.

The stability region of the B2 phase at 1000°C in the Ti-rich part of the Ti–Al–Cr and Ti–Al–Fe ternary systems are investigated by energy dispersive spectroscopy (EDS) and transmission electron microscopy (TEM) using two-phase alloys and diffusion couples. It is established that the critical boundaries of the A2/B2 continuous ordering transition are functions of both the Al and Fe or Cr contents, and the phase equilibria between the α2 and the β and between the β and FeTi (B2) phases are strongly affected by the A2/B2 order–disorder transition. By extrapolating these ternary data to the Ti–Al binary and using the Bragg–Williams–Gorsky approximation a metastable A2/B2 ordering boundary is postulated to exist at 1000°C in the vicinity of 23.5 at%Al in the Ti–Al binary system.

Microstructural investigation of the Co–11.0Ge–5.7W (at.%) ternary alloy was conducted. Fine cuboidal precipitates were observed in this alloy annealed at 1173 K and the crystal structure of the precipitate phase was identified as an L12 structure with a composition of Co–12.6Ge–8.2W (at.%). The solvus temperature of this phase was about 1180 K. Since a stable L12 phase has not been reported in the Co–W and Co–Ge binary systems, this ternary compound is a new L12 phase designated as γ′-Co3(Ge, W).

Investigations relating to the phase equilibria involving the α, γ, σ and liquid phases and the ordering reactions in the bcc aluminides of the Fe–Ni–Si system in the temperature interval 800∼1200°C have been carried out by energy dispersion X-ray spectroscopic (EDS) analysis and transmission electron microscopy (TEM). The equilibrium compositions of the γ (A1: fcc-Fe), α (A2: bcc-Fe), σ (σ phase) and liquid phases and the critical boundaries of the continuous ordering transition in the α phase region have been determined. It is observed that the critical temperatures of the continuous ordering transitions α(A2)/α′(B2) and α′/α″(D03) are mainly functions only of Si content, and not of Ni. It is also found that the tie-line configurations and the partition behavior of the constituents at the α/γ phase equilibrium are strongly affected by the order–disorder transitions in the α phase. Results pertaining to these phase equilibria and the stability of the ordered bcc aluminides are presented and discussed.

The solubility product of TiN in an austenitic steel was experimentally determined using a diffusion couple technique. Diffusion couples consisting of Ti–N steels with various compositions were annealed at temperatures between 1 473 and 1623 K, taking special care to exclude the oxygen contamination during the annealing. The solubility limit of TiN was determined from the break points of iso-activity lines for nitrogen. A thermodynamic analysis was also carried out to arrive at solubility products by considering the wide range of temperature dependence of the TiN formation energy. Solubility products in austenite (γ), ferrite (α or δ) and liquid phases were determined as log(mass%Ti)(mass%N)γ=4.35–14 890/T, log(mass%Ti)(mass%N)α(δ)= 4.65–16310/T and log(mass%Ti)(mass%N)liq=4.46–13500/T respectively.