Thermodynamic and kinetic modeling of the Cr-Ti-V system

A synergistic approach of thermodynamic and kinetic modeling is applied to the Cr-Ti-V system. To assist the design of (α+β) and β titanium alloys for structural applications and vanadium alloys for fusion reactor applications, a set of self-consistent and optimized thermodynamic model parameters is presented to describe the phase equilibria of the Cr-Ti, Cr-V, Ti-V, and Cr-Ti-V systems. The Laves phases, α-Cr₂Ti, β-Cr₂Ti, and γ-Cr₂Ti, are described by a two-sublattice model assuming antistructure atoms on both sublattices. The calculated thermodynamic quantities and phase diagrams are in good accord with the corresponding experimental data. To assist the simulation of the kinetics of diffusional transformations in bodycentered cubic (bcc) alloys, the atomic mobilities of Cr, Ti, and V are modeled. A set of optimized mobility parameters is given. Very good agreement between the calculated and experimental diffusivities was found.     

Effect ofβ volume fraction on the dynamic grain growth during superplastic deformation of Ti3Al-based alloys

The superplastic deformation behavior of Ti₃Al based(α ₂+β alloy was studied with respect to the volume fraction of α₂/β. Three alloys containing 21, 50 and 77% in volume fractions ofβ exhibited large tensile elongations of over 500% at 970°C with a strain rate of 2.5x10^-4 sec^-1. The largest elongation was observed in the alloy with 21% ofβ. As the volume fraction ofβ phase increased, the flow stress and correspondingly, the strain-rate sensitivity values decreased. Due to the higher diffusivity of Ti in,β phase than in α₂ phase, the increase inβ volume fraction from 21 % to 77% accelerated the dynamic grain growth, and degraded the superplasticity of the Ti₃Al-based alloys. The strain-based grain growth behavior was quantitatively analyzed and incorporated into a constitutive equation. The calculated flow curves are in agreement with the experimental ones in the stable deformation region.     

Thermodynamic optimization of the Ti-C system

The condensed Ti-C system was assessed using a computerized least squares optimization method. The solid phases—αTi, βTi, and TiC—were modeled as interstitial solid solutions or by the compound energy formalism with two sublattices, respectively. The liquid phase was described by a Redlich-Kister polynomial. All phase diagram data and thermodynamic values available in the literature were critically assessed before the optimization. An optimized thermodynamic parameter set is presented, and the resulting calculations are compared with experimental and estimated data from the literature.     

Experimental determination and thermodynamic calculation of phase equilibria in the Fe−Mn−Al system

The phase equilibria among the face-centered cubic (fcc), body-centered cubic (bcc), and βMn phases at 800, 900, 1000, 1100, and 1200 °C were examined by electron probe microanalysis (EPMA), and the A2/B2 and B2/D0₃ ordering temperatures were also determined using the diffusion couple method and differential scanning calorimetry (DSC). The critical temperatures for the A2/B2 and B2/D0₃ ordering were found to increase with increasing Mn content. Thermodynamic assessment of the Fe−Mn−Al system was also undertaken with use of experimental data for the phase equilibria and order-disorder transition temperatures using the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs energies of the liquid, αMn, βMn, fcc, and ε phases were described by the subregular solution model and that of the bcc phase was represented by the two-sublattice model. The thermodynamic parameters for describing the phase equilibria and the ordering of the bcc phase were optimized with good agreement between the calculated and experimental results. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Densities of solid aluminum-magnesium (Al-Mg) alloys

Densities of solid Al and Al-Mg alloys were measured by the dilatometric method for seven compositions at mole fractions of magnesium: 0.015, 0.05, 0.1, 0.125, 0.15, 0.20, and 0.25. A curvilinear dependence of density on temperature (room temperature up to 800 K) was observed for all investigated alloys. Results are described by polynomials of the second degree. The molar volumes of Al-Mg alloys were calculated from the density measurements. It has been found that the densities of solid Al-Mg alloys show negative deviations from linearity and the molar volumes exhibit positive deviations from ideal behavior for all samples in the experimental concentration range. The density of the β(Al₃Mg₂) phase along the (α(Al) + β)/β boundary was calculated and is described by a temperature-dependent polynomial.     

Densities of solid aluminum-magnesium (Al-Mg) alloys

Densities of solid Al and Al-Mg alloys were measured by the dilatometric method for seven compositions at mole fractions of magnesium: 0.015, 0.05, 0.1, 0.125, 0.15, 0.20, and 0.25. A curvilinear dependence of density on temperature (room temperature up to 800 K) was observed for all investigated alloys. Results are described by polynomials of the second degree. The molar volumes of Al-Mg alloys were calculated from the density measurements. It has been found that the densities of solid Al-Mg alloys show negative deviations from linearity and the molar volumes exhibit positive deviations from ideal behavior for all samples in the experimental concentration range. The density of the β(Al₃Mg₂) phase along the (α(Al) + β)/β boundary was calculated and is described by a temperature-dependent polynomial.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

Strengthening behavior of beta phase in lamellar microstructure of TiAl alloys

β phase can be introduced to TiAl alloys by the additions of β stabilizing elements such as Cr, Nb, W, and Mo. The β phase has a body-centered cubic lattice structure and is softer than the α₂ and γ phases in TiAl alloys at elevated temperatures, and hence is thought to have a detrimental effect on creep strength. However, fine β precipitates can be formed at lamellar interfaces by proper heat treatment conditions and the β interfacial precipitate improves the creep resistance of fully lamellar TiAl alloys, since the phase interface of γ/β retards the motion of dislocations during creep. This paper reviews recent research on high-temperature strengthening behavior of the β phase in fully lamellar TiAl alloys.     

Thermodynamic optimization of the Na2O-B2O3 pseudo-binary system

The Na₂O-B₂O₃ system is thermodynamically optimized by means of the CALPHAD method. A two-sublattice ionic solution model, (Na⁺¹)_P(O⁻²,BO₃ ⁻³,B₄O₇ ⁻²,B₃O_4.5)_Q, has been used to describe the liquid phase. All the solid phases were treated as stoichiometric compounds. A set of thermodynamic parameters, which can reproduce most experimental data of both phase diagram and thermodynamic properties, was obtained. Comparisons between the calculated results and experimental data are presented.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic Assessment of the Mn-B System

The phase equilibrium and thermodynamic data on the Mn-B system are critically reviewed. Based on the experimental data, a thermodynamic modeling is performed on this system. A set of self-consistent thermodynamic parameters is obtained and the calculated results are in general agreement with the experimental data. A parameter ξ is introduced to compare the degree of flatness of the δMn/L liquidus with those in other metal-boron systems. It is found that the δMn/L liquidus is the flattest, which causes difficulties in its modeling. An effective approach to evaluate the thermodynamic parameters for o-Mn₂B_0.982 phase is developed. Such an approach is valid for evaluating thermodynamic parameters of the phases with limited phase diagram data.     

Corrosion behavior of Ti-Ag alloys used in dentistry in lactic acid solution

The purpose of this study was to evaluate the corrosion resistance of experimental Ti-Ag alloys used as dental materials. An elution test and a rest-potential measurement of alloys with 5–30 mass.% Ag were performed in a 1 % lactic acid solution. The amount of Ti ions released from the α phase of the Ti-Ag alloys decreased as the Ag concentration increased. TiAg present in the alloys dissolved preferentially, but Ti₂Ag did not. The rest potentials of the Ti-Ag alloys were significantly higher than that of pure titanium. The elution test and the rest-potential measurement revealed that the Ti-Ag alloys, which formed a single α-titanium structure or contained a titanium and Ti₂Ag, had excellent corrosion resistance that was comparable or superior to that of pure titanium.     

The 1400°C isothermal section of the Ti-Al-Nb ternary system

The 1400‡C isothermal section of Ti-Al-Nb system was determined using the diffusion couple technique, along with optical microscopy and electron probe microanalysis (EPMA). Equilibrated alloys were employed to identify the phase regions using XRD. The isothermal section consists of seven single-phase regions including Β(ΒTi,Nb), α(αTi), γ(TiAl), η((Ti,Nb)Al₃), σ(Nb₂Al), δ(Nb₃Al), and γ₁. The detailed studies on the γ₃₁ phase were made by XRD, DTA, and DSC.     

Critical assessment and thermodynamic calculation of the ternary system C-Hf-Zr (Carbon-Zirconium-Hafnium)

Based on an assessment of the available experimental thermochemical and phase diagram information available, the phase equilibria of the C-Hf-Zr system were calculated. The G of the individual phases was described with thermodynamic models. The liquid phase was described as a substitutional solution using the Redlich-Kister formalism for excess G. Graphite was treated as a stoichiometric phase. The solid solutions of carbon in α(Hf,Zr) and β(Hf,Zr), as well as the non-stoichiometric phase (Hf,Zr)C_1−x, were represented as interstitial solid solutions using the compound energy model with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data. A detailed comparison was made between calculation and experimental data.