Phase equilibria in the Fe-Mo-W-C system containing (Mo0.7W0.3)C carbide

A section of the phase diagram for the Fe-Mo-W-C system at 1273 K has been calculated for compositions which include (Mo_0.7W_0.3)C carbide as a constituent. In this region of the phase diagram, four carbides, namely cementite, MC, M₂C and M₆C (M = Mo, W and Fe) appear as stable phases together with austenite or ferrite, while only three carbides, i.e., cementite, MC and M₆C appear in the Fe-W-C system, and four carbides including Fe₂MoC (ξ) instead of MC in the Fe-Mo-C system. The presence of M₂C carbide in the Fe-(Mo_{0. 7}W_0.3)-C system is in agreement with observations on cemented carbide products with (Mo_0.7W_0.3)C.     

Ortho-equilibrium and para-equilibrium phase diagrams for interstitial / substitutional iron alloys

A mathematical model for the evaluation of compositionally constrained thermodynamic equilibrium has recently been implemented into the computer program MatCalc. This model is applied to the calculation of para-equilibrium phase diagrams for some ternary model iron alloy systems Fe---X---C, with X = Mn, Ni, Cr and Mo. The results are compared to the corresponding full equilibrium (ortho-equilibrium) phase diagrams and the impact of each element on the austenite / ferrite / carbide transformation in steels is analyzed. The para-equilibrium phase diagrams are considerably more simple than the potentially complex ortho-equilibrium phase diagrams, showing cementite formation as the only stable carbide under para-equilibrium conditions. The driving forces for precipitation of cementite and the complex chromium carbides in the Fe---Cr---C system are evaluated as a function of the precipitate composition. The evaluation of the driving forces under para-equilibrium conditions predicts carbide precipitation behavior that agrees with experimental findings.     

CALPHAD modelling of the unmixing of transition metal carbide phases

Phase separation in a pseudo-binary solid solution of the form (M₁,M₂)C where M₁ and M₂ are chosen among minor addition in 9% Cr, martensitic-ferritic steels such as Nb, V, Ta and other transition elements such as Hf and Zr has been studied using the Calphad-Thermocalc approach. Ternary excess parameters accounting for phase equilibria in pseudo-binary sections have been optimised using suitable combinations of already published excess parameters which have been calculated on a physical basis. The ternary parameters obtained by optimisation were checked, when possible, with experimental information on isothermal ternary sections.     

Ferrite — M2C coherent phase equilibrium in AF1410 Steel

A Model for coherent ferrite/M₂C carbide equilibrium is applied to AF1410 steel. The contribution fron coherent elastic energy to the Gibbs free energy has been expressed in a format compatible with the Redlich-Kister-Muggianu extrapolation formula for multicomponent phases. An equilibrium calculation at the standard tempering temperature of 510C predicts a substantial deviation from stoichiometry and a measurable solubility of iron in the M₂C phase, both of which have been verified experimentally.     

Partition and non-partition transition of austenite growth from a ferrite and cementite mixture in hypo- and hypereutectoid Fe-C-Mn alloys

The growth of austenite from a ferrite and cementite mixture in low Mn steel of hypo- and hypereutectoid composition is investigated with focus upon the Mn partitioning between dissolving cementite (or ferrite) and austenite. Under the assumption that austenite is nucleated on cementite, two critical temperatures which characterize the transition between Mn-partitioned and non-partitioned growth of austenite are noticed; below the 1st and lower critical temperature the austenite grows with redistribution of Mn from the beginning, and above the 2nd and higher critical temperature, without Mn redistribution until completion. Between them the growth mode switches from carbon-diffusion to Mn-diffusion control during growth. The influence of carbon and/or Mn diffusion through the matrix becomes progressively more significant with time, but may not affect the growth mode transition temperatures. Above the 2nd critical temperature, which is at most ca. 50 °C higher than Acm or Ae₃ in alloys studied, the distribution of Mn in as-transformed or spheroidized pearlite is preserved at the completion of austenitization irrespective of the last dissolving phase, leading to the formation of an ultrafine mixture of martensite and austenite upon quenching.     

Experimental and thermodynamic study of the influence of the base elements on the carbides natures in {Ni,Co}-based {25Cr, 0.4C, 6Ta}-containing alloys

Primary carbides may be important for the high temperature strength of polycrystalline Cr-rich cast alloys. TaC are among the best carbides for this role. Their presence depends on the base elements of the alloys. This dependence is here studied in the case of a series of Cr-rich alloys based on Ni and/or Co and containing Ta and C in equal molar fractions. Real alloys were cast and exposed at 1400 K and 1510 K, and their as-cast and aged microstructures were characterized. In parallel thermodynamic calculations using Thermo-Calc and a home-made database were carried out. It appears that TaC is the single carbide present in the alloy stabilized at high temperature only if the Co content is higher than the Ni one. Discrepancies appeared between calculations and the experimental results, showing that the used database must be improved. The experimental part of this work provides microstructures data which can be used to test databases and to enrich them if necessary.     

Thermodynamic description of the Sn–Ag–Au ternary system

Gibbs energy of hcp_A3 phase in the Ag–Sn binary system has been reassessed using compatible lattice stability. Combined with previous assessments of the Ag–Au and Au–Sn binary systems, the Sn–Ag–Au ternary system has been thermodynamically optimized using the CALPHAD method on the basis of available experimental information. The solution phases including liquid, fcc_A1, hcp_A3 and bct_A5, are modeled as substitutional solutions, while the intermediate compound Ag₃Sn is treated using a 2-sublattice model because Au can be dissolved to a certain degree. The solubility of Ag in the Au–Sn intermediate phases, D0₂₄, Au₅Sn, AuSn, AuSn₂ and AuSn₄, is not taken into account. Thermodynamic properties of liquid alloys, liquidus projection and several vertical and isothermal sections of this ternary system have been calculated, which are in reasonable agreement with the reported experimental data.     

An assessment of Fe-Nb-B melts using the two-state liquid model

Amorphous alloys of the (Fe-Co-Ni)-(Cr-Mo-Nb)-B system are promising materials to supply the demands for higher wear resistance components in the petrochemical industry. Since the development of the CALPHAD method, the development of new metallic alloys has been accompanied by thermodynamic modelling and calculations. The prediction of the formation of amorphous alloys requires special care with the modeling of the liquid and or an amorphous phase. As a initial stage in the more complex system, the basic Fe-Nb-B ternary system was selected. In order to predict the stability and tendencies of transformations of these amorphous alloys, the Fe-Nb-B system was reassessed using Ågren's two-state model to describe the liquid phase. The results of the present assessment show very good agreement with the recently reported stable phase diagram. Furthermore, the use of the two-state model for the liquid is more accurate and physically consistent when evaluating transformations from supercooled liquid, as shown it the present work.     

Thermodynamic studies and the phase diagram of the Mg---Cd system

EMF measurements of the cell reaction: Mg(s)¦MgCl₂ in(LiCl-KCl)_eut(l)¦Mg---Cd (1) have been used to measure the partial molar free energies of Mg---Cd liquid alloys in the composition range 0.042Mg<0.703 and at temperatures between 740 and 890 K. Partial molar enthalpies of cadmium measured in a Calvet calorimeter at 918 and 942 K were used for calculation of both the partial molar enthalpy of magnesium and integral molar enthalpies. The data from emf studies were also employed for phase diagram calculations. The emf results were coupled with independent calorimetric data to derive integral excess entropies which illustrate a correlation between the thermodynamic character and the structure of the liquid Mg---Cd alloys.     

Experimental and thermodynamic study of the high temperature microstructure of tantalum containing nickel-based alloys

Experiments and thermodynamic calculations were performed on three nickel-based alloys containing chromium, carbon and tantalum. Solidus and liquidus temperatures, and natures and surface fractions of the carbides after exposure for 100 h at 1000, 1100 and 1200 ^∘C were determined for each alloy. These results are compared with calculated results, using a thermodynamic database. Good agreement was generally found for the solidus temperatures but less good agreement for the liquidus ones. For alloys containing chromium carbides alone, carbide fractions and matrix compositions correspond to calculation results. But the presence of tantalum carbides in the third alloy was not predicted by calculations.     

Solidification structure of CaO–SiO2–MgO–Al2O3 (–CaF2) systems and computational phase equilibria: Crystallization of MgAl2O4 spinel

The solidification behaviour of the CaO–SiO₂–Al₂O₃–CaF₂–10% MgO system, which is similar to the inclusion compositions in the stainless steel and the crystallization of spinel have been investigated using XRD, SEM-EDS, and an image analyser. The solidification mode and the phase equilibria were computed by employing thermochemical software. The liquidus temperature of the oxides containing 5% CaF₂ increases with increasing alumina content from 10% to 30%, while the solidus temperature has little dependence on alumina content. The size of spinel crystals in the final microstructure increases on increasing the content of alumina, resulting from that the oxides spending more time at higher temperatures below the liquidus temperature, where crystal growth is generally faster than nucleation, during slow cooling. The liquidus temperature of the oxides containing 30% Al₂O₃ is scarcely varied, while the solidus temperature decreases by increasing the content of CaF₂ to 10%. The size of spinel crystals decreases as the content of CaF₂ increases, resulting from the fact that the oxides could spend more time at relatively lower temperatures, where nucleation is faster than growth, during the cooling process.     

Ab-initio calculations of the formation energies of BCC-based superlattices in the Fe---Al system

First-principles calculations of the total energies of A2 iron and aluminum, B2 (FeAl), B32 (FeAl) and D0₃ (Fe₃Al and FeAl₃) compounds were performed in the frame of density functional theory (DFT) using the Full Potential - Linear Augmented Plane Wave method (FP-LAPW). These results have been used to obtain formation energies of the respective ground states. The calculated formation energies of the D0₃ (Fe₃Al) and B2 (FeAl) compounds show excellent agreement with available calorimetric data on standard enthalpies of formation of Fe---Al alloys up to 50 at.% aluminum. As the Fe---Al system has a controversial magnetic behavior when described by ab-initio methods in the DFT, this agreement is remarkable.     

Tetrahedron treatment of the fcc lattice

A computer program for calculating the disorder-order phase diagrams of FCC-based binary alloys is presented. The cluster variation method is used, with the tetrahedron as the basic cluster. Ordered phases are the Cu₃Au type (L1₂) and the CuAu type (L1₀). Energy parameters are independent of temperature and composition, and include the many-body effect within a tetrahedron. A detailed explanation of the computer program is presented in the main body of the paper. Three example calculations are shown.