Atomic mobility, diffusivity and diffusion growth simulation for fcc Cu-Mn-Ni alloys

On the basis of the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Cu, Mn and Ni in fcc Cu-Mn-Ni alloys were assessed as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between the calculated results and the experimental data show that a good agreement is obtained for various diffusivities in binary and ternary systems, including impurity diffusion coefficients, tracer diffusion coefficients and interdiffusion coefficients. The atomic mobilities obtained can also be used to describe various diffusion phenomena for a series of binary and ternary diffusion couples, such as concentration profiles, the Kirkendall shift, the interdiffusion flux and diffusion paths.     

A thermodynamic description of the Al–Ca–Zn ternary system

A comprehensive thermodynamic database of the Al–Ca–Zn ternary system is presented for the first time. Critical assessment of the experimental data and re-optimization of the binary Al–Zn and Al–Ca systems have been performed. The optimized model parameters of the third binary system, Ca–Zn, are taken from the previous assessment of the Mg–Ca–Zn system by the same authors. All available as well as reliable experimental data both for the thermodynamic properties and phase boundaries are reproduced within experimental error limits. In the present assessment, the modified quasichemical model in the pair approximation is used for the liquid phase and Al_FCC phase of the Al–Zn system to account for the presence of the short-range ordering properly. Two ternary compounds reported by most of the research works are considered in the present calculation. The liquidus projections and vertical sections of the ternary systems are also calculated, and the invariant reaction points are predicted using the constructed database.     

Atomic mobilities and diffusional growth in solid phases of the V–Nb and V–Zr systems

In conjunction with the thermodynamic parameters in the literature, the atomic mobilities of the V–Nb and V–Zr bcc alloys were assessed from experimental diffusion coefficients. The assessed atomic mobilities are given as functions of temperatures and composition in the CALPHAD format. Comparisons between the calculated and experimental quantities show that the obtained mobility parameters enable most of the experimental diffusion data to be well reproduced. Based on the velocity constructions for lattice planes in V/Nb diffusion couples, the displacements of Kirkendall makers were investigated under various annealing conditions, and the results are in general agreement with experimental values. In addition, computational studies of V/Zr diffusion couples were carried out for the kinetic behaviors of V ₂Zr at various annealing temperatures, from which the temperature dependence of the interdiffusion coefficients for V ₂Zr was evaluated.     

Assessment of atomic mobilities for fcc Co–Ti–V alloys

Based on the experimental interdiffusion coefficients from our previous work and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Co, Ti and V in fcc Co–Ti–V alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software. Askill's empirical relations were utilized to assess the self-diffusion coefficients of fcc Ti and fcc V. Comprehensive comparisons between the DICTRA-calculated diffusivities and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities in binary and ternary systems. In addition, a further verification on the obtained atomic mobilities was carried out through comparing the DICTRA-simulated concentration profiles/diffusion paths of the diffusion couples with the corresponding experimental ones. This work contributes to the establishment of a kinetic database for multi-component cemented carbide.     

Experimental investigation and computational study of atomic mobility in fcc ternary Co–Cr–W alloys

The interdiffusion coefficients in fcc Co–Cr–W alloys at 1373 K have been determined from the concentration profiles across the solid–solid diffusion couples using the Whittle and Green method. On the basis of the experimental interdiffusion coefficients in this work, together with the critically reviewed experimental diffusivities available in the literature, atomic mobilities of Co, Cr and W in fcc Co–Cr–W alloys were assessed as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between the calculated results and the experimental data indicate that the presently obtained atomic mobilities can reasonably reproduce most of the diffusivities, concentration profiles and diffusion paths in binary and ternary systems.     

Assessment of atomic mobilities in fcc Cu-Ni-Zn alloys

On the basis of critically reviewed experimental diffusivities available in the literature, a through assessment of the atomic mobilities of Cu, Ni, and Zn in fcc Cu-Ni-Zn alloys was conducted using the DICTRA software. Comprehensive comparisons show that good agreements between the presently calculated diffusion coefficients and the experimental data were obtained. The reliability of the atomic mobilities obtained was further verified by comparing various model-predicted diffusion phenomena with the experimental information, such as concentration profiles, Kirkendall shift and diffusion paths in a series of binary and ternary diffusion couples.     

Construction of modified embedded atom method potentials for the study of the bulk phase behaviour in binary Pt–Rh, Pt–Pd, Pd–Rh and ternary Pt–Pd–Rh alloys

A first attempt is made to simulate the solid part of the phase diagram of the ternary Pt–Pd–Rh system. To this end, Monte Carlo (MC) simulations are combined with the Modified Embedded Atom Method (MEAM) and optimised parameters entirely based on Density Functional Theory (DFT) data. This MEAM potential is first validated by calculating the heat of mixing or the demixing phase boundary for the binary subsystems Pt–Rh, Pt–Pd and Pd–Rh. For the disordered alloy systems Pt–Rh and Pt–Pd, the MC/MEAM simulation results show a slightly exothermic heat of mixing, thereby contradicting any demixing behaviour, in agreement with other theoretical results. For the Pd–Rh system the experimentally observed demixing region is very well reproduced by the MC/MEAM simulations. The extrapolation of the MEAM potentials to ternary systems is next validated by comparing DFT calculations for the energy of formation of ordered Pt–Pd–Rh compounds with the corresponding MEAM energies. Finally, the validated potential is used for the calculation of the ternary phase diagram at 600 K.     

Assessment of diffusion mobilities in FCC Cu–Ni alloys

On the basis of the available thermodynamic parameters and experimental data of tracer diffusivity, intrinsic diffusivity and chemical diffusivity in the Cu–Ni binary system, the atomic mobilities of Cu and Ni in face-centered cubic (fcc) Cu–Ni alloys have been assessed as a function of temperature and composition using the CALPHAD approach and DICTRA software package. Comparisons between the calculated and measured diffusion coefficients show that most of the experimental information can be reproduced satisfactorily in the present work. The obtained mobility parameters can also predict reasonably the concentration profiles of the diffusion zone in binary Cu–Ni diffusion couple.     

First-principles calculations assisted thermodynamic assessment of the Pt–Ga–Ge ternary system

The Pt–Ga–Ge ternary system was thermodynamically assessed by the CALPHAD (CALculaton of PHAse Diagram) approach with help of first-principles calculations. Firstly, the formation enthalpies of the Pt–Ge and Pt–Ga compounds were calculated by the first-principles method. Subsequently, the Pt–Ge system was modeled and the Pt–Ga system was re-assessed. The solution phases, Liquid, Diamond_A4 (Ge) and Fcc_A1 (Pt), were modeled as substitutional solutions, of which the excess Gibbs energy was formulated with the Redlich–Kister polynomial. The binary intermetallics, Ga₇Pt₃, Ga₂Pt, Ga₃Pt₂, GaPt, Ga₃Pt₅, GaPt₂, Ge₂Pt, Ge₃Pt₂, GePt, Ge₂Pt₃ and GePt₂, were treated as stoichiometric compounds while GePt₃ was described with a two-sublattice model. Finally, based on the currently optimized Pt–Ga and Pt–Ge binary systems along with the already assessed Ga–Ge system, phase equilibria in the Pt–Ga–Ge ternary system were extrapolated. The isothermal sections at 473 K, 973 K and 1073 K of the ternary system were calculated, showing good agreement with the experimental data. In addition, the liquidus projection of the Pt–Ga–Ge ternary system was predicted using the obtained model parameters.     

Assessment of the atomic mobility in fcc Al–Cu–Mg alloys

Various experimentally measured diffusivities of fcc Al–Mg, Cu–Mg and Al–Cu–Mg alloys available in the literature are critically reviewed in the present work. The first-principles calculations coupled with a semi-empirical correlation is employed to derive the temperature dependence of impurity diffusivity for Mg in fcc Cu. Atomic mobilities for the above fcc alloys are then evaluated as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between calculated and measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. The concentration profiles and diffusion paths are predicted with the mobility parameters in a series of binary and ternary diffusion couples. A good agreement is obtained between experiment and simulation.     

Thermodynamic modeling of the Mg–Ge–Pb system

All available thermodynamic and phase diagram data of the Mg–Ge and Mg–Pb binary systems, and the Mg–Ge–Pb ternary system have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. The liquid phase was modeled using the Modified Quasichemical Model in order to describe the strong ordering in Mg–Ge and Mg–Pb liquid. Mg₂Ge–Mg₂Pb solid solution phase was modeled with consideration of a solid miscibility gap. All calculations were performed using the FactSage thermochemical software.     

Thermodynamic modeling of the C–Pu–U system

The ternary C–Pu–U system is thermodynamically assessed to pursue the development of a thermodynamic database for future nuclear fuels. The substitution model was used for the liquid phase, and a two-sublattice model for the PuC–UC monocarbide, PuC₂–UC₂ dicarbide and Pu₂C₃–U₂C₃ sesquicarbide phases. Ternary interaction parameters were adjusted on the experimental information for the phase relationships. Isoplethal and isothermal ternary sections, as well as some liquidus temperatures are calculated and compared with the experimental data. The overall agreement is discussed, and shows that experimental uncertainties still remain.     

The phase equilibria in the Mg–Ni–Ca system

The three binary systems Mg–Ni, Ca–Ni and Mg–Ca have been re-optimized. A self-consistent thermodynamic database of the Mg–Ni–Ca system is constructed by combining the optimized parameters of these three constituent binaries. Lattice stability values are not added to the pure elements Mg-hcp, Ni-fcc, Ca-fcc and Ca-bcc to construct this database. The Redlich–Kister polynomial model is used to describe the liquid and the terminal solid solution phases, and the sublattice model is used to describe the non-stoichiometric phase, in this system. The constructed database is used to calculate the three binary and the ternary systems. The calculated binary phase diagrams along with their thermodynamic properties such as Gibbs energy, enthalpy, entropy and activities are found to be in good agreement with experimental data from the literature. This is the first attempt to construct the ternary phase diagram of the Mg–Ni–Ca system. The established database for this system predicted three ternary eutectic, five ternary quasi-peritectic, two ternary peritectic and two saddle points.     

Assessment of the diffusional mobilities in the face-centred cubic Ag–Zn alloys

Based on the available thermodynamic information and diffusion coefficient data of the Ag-Zn binary system, the atomic mobilities of Ag and Zn in face-centred cubic (fcc) Ag-Zn alloys have been assessed as a function of temperature and composition in terms of the CALPHAD method using the DICTRA software package. Optimized mobility parameters are presented. Comparisons between the calculated and measured diffusion coefficients show that most of the experimental information can be satisfactorily reproduced in the present work. The obtained mobility parameters can also predict reasonable concentration profiles of the diffusion zone in the binary Ag-Zn diffusion couples.     

Mobilities and diffusivities in fcc Co–X (X=Ag,Au, Cu,Pd and Pt) alloys

The mobilities and diffusivities in fcc Co–X (X=Ag, Au, Cu, Pd and Pt) alloys have been critically assessed by the CALPHAD method, based on the reported experimental data and published thermodynamic parameters. The atomic mobilities are expressed as functions of temperature and compositions in the CALPHAD format. Comprehensive comparisons between the calculated and measured diffusivities, such as self-diffusivities, impurity diffusivities, intrinsic diffusivities, and interdiffusivities, are made, where the proposed mobility parameters for Ag, Au, Co, Cu, Pd and Pt enable most of the experimental values to be reproduced. The effect of magnetic ordering on diffusion in fcc Co–Pd and Co–Pt alloys is discussed. This work contributes to the establishment of a Co mobility database, which can aid the computational study of microstructure evolution in Co-based alloys at high temperatures.     

Numerical modelling of moving interfaces under local equilibrium conditions

A new method is presented to simulate moving interfaces during diffusion-controlled growth under local equilibrium conditions. The position and compositions of the interface are obtained directly from the equilibrium state of the subsystem around the moving interface, without iterative calculation between diffusion fluxes and solute balance conditions. The method is applicable to general multi-component systems, and it ensures the consistency in compositions and solute balance at the interfaces; Those are ascribed to the presented consideration of subsystem around the interface region in a discretized form. Explicit equations of interface compositions and position in discretized variables are also presented for the simplified ternary systems of two-solution and compound/solution. The validity and usefulness of the method is demonstrated by simulations of the two important ternary systems; The simulation results illustrate the features of diffusion-controlled growth with different alloy compositions and diffusivities of solutes in both systems.     

Computer-aided thermodynamics of fcc solid ternary Fe–Co–Cr alloys by Knudsen cell mass spectrometry

The fcc solid ternary Fe–Co–Cr alloys have been investigated thermodynamically by means of computer-aided Knudsen cell mass spectrometry. The “Digital Intensity Ratio” (DIR) method has been applied for the determination of the thermodynamic excess properties. The ternary thermodynamically adapted power (TAP) series concept is used for the algebraic representation of the molar excess properties. The corresponding TAP parameters as well as the values of the molar excess Gibbs energies G^E, of the molar heats of mixing H^E, of the molar excess entropies S^E, and of the thermodynamic activities at 1673 K are presented.