Thermodynamic assessments of the Ni–Pt and Al–Ni–Pt systems

The Ni–Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni₃Pt–L1₂, NiPt–L1₀ and NiPt₃–L1₂, are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al–Ni and Al–Pt, the Al–Ni–Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.     

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.     

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.     

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.     

Thermodynamic description of the Pb–Yb binary system

Thermodynamic modelling of the Pb–Yb binary system was carried out with the help of the CALPHAD method. The liquid phase has been described with the association solution model with ‘ Pb₁Y b₂’ as an associated complex. The solution phases BCC_A2 and FCC_A1 were modelled with the sublattice formalism. The αPbYb_LT and βPbYb_HT Pb sub-stoichiometric intermetallic compounds, which have a homogeneity range, were treated with the formula (Pb,Y b)_0.5(Y b)_0.5 by a two-sublattice model with Pb and Yb on the first sublattice and Yb on the second one. Pb₃Y b, Pb₃Y b₅ and PbY b₂ have been treated as stoichiometric compounds. The calculations based on the thermodynamic modelling are in good agreement with the phase diagram data and experimental thermodynamic values.     

Ab initio calculation of the BCC Fe–Al–Mo (Iron–Aluminum–Molybdenum) phase diagram: Implications for the nature of the phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe–Al–Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order–disorder equilibrium between Fe₃Al–D0₃ and FeAl–B2 is increased by Mo additions, while the critical temperature for the FeAl–B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2–(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the τ₂ phase, stable at high temperatures in overstoichiometric B2–FeAl.     

Analysis of interface states of metal–insulator–semiconductor photodiode with n-type silicon by conductance technique

A metal–insulator–semiconductor photodiode (MIS-PD) as active layer with n-type silicon as interdigitated Schottky electrodes has been fabricated. The current–voltage characteristics, density of interface states and photovoltaic properties of the MIS-PD diode have been investigated. The diode has a metal–insulator–semiconductor configuration with ideality factor higher than unity. The electronic parameters (ideality factor, series resistance and barrier height) of the diode were found to be 1.94, 2.23 × 10⁴ Ω and 0.74, respectively. At voltages between 0.13 and 0.50 V, the charge transport mechanism of the diode is controlled by space charge-limited current mechanism. The interface state density of the diode was found to vary from 5.54 × 10¹² to 5.67 × 10¹² eV⁻¹ cm⁻² with bias voltage. The Au/SiO₂/n-Si/Al device shows a photovoltaic behavior with a maximum open circuit voltage V_oc of 97.7 mV and short-circuit current I_sc of 17.4 μA under lower illumination intensities. The obtained electronic parameters confirm that the Au/SiO₂/n-Si/Al diode is a MIS type photodiode.     

A thermodynamic reassessment of the La–Sn system

Thermodynamic modelling of the La–Sn binary system was carried out with the help of the CALPHAD (CALculation of PHAse Diagram) method. The liquid phase has been described with the association solution model with a ‘ La₁Sn₁’ associated complex. The intermetallic compounds were treated as stoichiometric phases. The calculated phase diagram and the thermodynamic properties of the system are in satisfactory agreement with the majority of the experimental data.     

Thermodynamic description of the Dy–Ni system

The Dy–Ni binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich–Kister polynomial was used to describe the solution phase, liquid (L). Ten compounds, Dy₃Ni, Dy₃Ni₂, DyNi, DyNi₂, DyNi₃, Dy₂Ni₇, DyNi₄, Dy₄Ni₁₇, DyNi₅ and Dy₂Ni₇, were treated as stoichiometric phases. The parameters of the Gibbs energy expressions were optimized according to all the available experimental information of both the equilibrium data and the thermodynamic results. A set of self-consistent thermodynamic parameters of the Dy–Ni system has been obtained. The calculations agree well with the respective experimental data.     

Atomic mobilities, uphill diffusion and proeutectic ferrite growth in Fe–Mn–C alloys

Following the treatment in CALPHAD, experimental data on diffusivities in Fe–Mn and Fe–C binary systems are critically evaluated with the DICTRA software to derive atomic mobilities. The effect of magnetic ordering on diffusion in bcc phase is taken into account, and the obtained atomic mobilities are expressed as functions of temperature and compositions with the Redlick–Kister polynomials. Based on the mobility parameters obtained in this work for the end-members and the interaction terms, comprehensive comparisons between the calculated and experimentally measured quantities are made. Due to the lack of experimental diffusivities for the ternary system, extrapolation based on binary information is performed, the results of which are used to study uphill diffusion of C in fcc Fe–Mn–C alloys. Such C diffusion against its own concentration gradient is a common occurrence for ternary systems containing one interstitial element, provided that the initial alloy compositions of diffusion couples are well chosen. In addition, the operating tie line evolution for proeutectic ferrite growth is also investigated, where C diffusion-controlled fast and Mn diffusion-controlled slow growths are discussed.     

A new equation of state and Fortran 77 program to calculate vapor–liquid phase equilibria of CH4–H2O system at low temperatures

A new equation of state (EOS) and the corresponding computer program package VLEWM are developed to calculate vapor–liquid phase equilibria and volumetric properties of CH₄–H₂O system at low temperatures. The EOS can predict vapor–liquid equilibria and volumetric properties of CH₄–H₂O system accurately at temperatures 273–383 K, and at pressures 0–1000 bar. The program package VLEWM is written in FORTRAN 77. It provides two main functions: (1) to calculate the composition in vapor phase and liquid phase of CH₄–H₂O system at equilibrium and (2) to judge the phase and to calculate molar volume of CH₄–H₂O mixture.     

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.     

Thermodynamic modeling of the Sn–V binary system

The Sn–V binary system was thermodynamically modeled using the CALPHAD approach combined with first-principles calculations. The predicted Gibbs free energy of the end-members in sublattice models of “ V ₃Sn” phase by the first-principles calculations was used to describe the lattice stabilities. A set of thermodynamic parameters for the Sn–V system was obtained using the PanOptimizer program in Pandat software. The calculated phase diagram and thermodynamic properties agree well with the reported experimental data.     

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.     

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 estimate on the convergence of MKZ–Bézier operators

The pointwise approximation properties of the MKZ–Bézier operators M_n,α(f,x) for α≥1 have been studied in [X.M. Zeng, Rates of approximation of bounded variation functions by two generalized Meyer–König–Zeller type operators, Comput. Math. Appl. 39 (2000) 1–13]. The aim of this paper is to study the pointwise approximation of the operators M_n,α(f,x) for the other case 0<α<1. By means of some new estimate techniques and a result of Guo and Qi [S. Guo, Q. Qi, The moments for the Meyer–König and Zeller operators, Appl. Math. Lett. 20 (2007) 719–722], we establish an estimate formula on the rate of convergence of the operators M_n,α(f,x) for the case 0<α<1.     

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.