Assessment of the temperature and pressure dependence of molar volume and phase diagrams of Cu and Zn

This study reports the thermodynamic assessment of the temperature and pressure dependence of molar volume of Cu and Zn, as well as their P–T phase diagrams based on the CALPHAD approach. The molar volume of fcc-Cu, hcp-Zn, and liquid phases as a function of both temperature and pressure was directly assessed from the data reported in the literature by implementing the CALPHAD-compatible equation of state (EOS). This EOS incorporates the quasi-harmonic model to eliminate the spurious predictions of negative heat capacity and thermal expansion at high pressure. Furthermore, the P–T phase diagram of each element was determined on the basis of the experimental results and calculated parameters. The experimentally estimated thermodynamic values are in good agreement with the calculated results.     

GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model

Given the energy of a solid (E) as a function of the molecular volume (V), the gibbs program uses a quasi-harmonic Debye model to generate the Debye temperature Θ(V), obtains the non-equilibrium Gibbs function G(V;p,T), and minimizes G to derive the thermal equation of state (EOS) V(p,T) and the chemical potential G(p,T) of the corresponding phase. Other macroscopic properties are also derived as a function of p and T from standard thermodynamic relations. The program focuses in obtaining as much thermodynamical information as possible from a minimum set of (E,V) data, making it suitable to analyse the output of costly electronic structure calculations, adding thermal effects at a low computational cost. Any of three analytical EOS widely used in the literature can be fitted to the p−V(p,T) data, giving an alternative set of isothermal bulk moduli and their pressure derivatives that can be fed to the Debye model machinery.

Program summary

Title of the program:gibbsCatalogue number: ADSYProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSYProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: Persons requesting the program must sign the standard CPC non-profit use licenseComputers on which the program has been tested: Intel Pentium, Alpha, Sun Sparc/Ultra/BladeOperating system under which the program has been tested: Unix, GNU/LinuxProgramming language used: Fortran 77Memory required to execute with typical data: 700 KBNo. of bits in a word: 32No. of processors used: 1No. of bytes in distributed program, including test data, etc.: 277 497No. of lines in distributed program, including test data, etc.: 7390Distribution format: tar gzip fileKeywords: Quasi-harmonic Debye model, equation of stateNature of physical problem: Derivation of the static and thermal equation of state, chemical potential, and thermodynamic properties of a crystal from energy-volume data only.Method of solution: A quasi-harmonic Debye model is used to obtain the vibrational Helmholtz free energy as a function of temperature at the molecular volumes of input. The non-equilibrium Gibbs energy is then minimized at any temperature T and pressure p to obtain the EOS and the chemical potential. Several standard EOS parameters can be derived by fitting analytical forms to the pressure-volume data. Finally, some thermodynamic properties are computed for each (p,T).Restrictions on the complexity of the problem: Thermal effects are assumed to be well represented by a quasi-harmonic Debye model, in which the temperature dependence of the internal parameters is embedded into the temperature dependence of the volume.Typical running time: less than 1 s (Pentium III, 800 MHz) for 25 (E,V) pairs, 10 pressure and 10 temperature values.     

Thermodynamic modeling of selected ternary systems containing Y and CALPHAD simulation of CoNiCrAlY metallic coatings

Metallic coatings can improve the high temperature resistance of superalloys serving in the gas turbines. In general they are Al–Co–Cr–Ni alloys with small Y additions to improve oxide scale adherence.In order to complete the construction of a thermodynamic database for coatings, thermodynamic assessments of four ternary systems have been performed by means of the CALPHAD method, namely Al–Co–Y, Al–Ni–Y, Al–Cr–Y and Co–Ni–Y. All of the experimental phase diagrams and thermodynamic data available in the literature were critically reviewed. The liquid, fcc, bcc and hcp phases were modeled as substitutional solutions. The order-disorder model has been adopted to describe the A1/L1₂ and A2/B2 phase relations. A series of ternary compounds have been modeled during the present work according to the crystal structure or composition. As a result a satisfactory agreement was obtained between our calculations and the experimental data used in the assessment.Finally, interaction parameters calculated in this work have been merged in the thermodynamic database for the simulation of Al–Co–Cr–Ni–Y alloys. This has been validated by comparing our calculations with experimental data regarding selected Ni-based and Co-based alloy coatings.     

A thermodynamic reassessment of the Si-Sr system

The Si-Sr binary system has been thermodynamically reassessed in the present work based on the critically reviewed experimental data available in the literature, especially newly published experimental phase diagram data in the Si-rich side. The liquid phase has been modeled with both the substitutional solution model and the associate model, and two sets of self-consistent thermodynamic parameters that describe the system are thus obtained. The shortcomings of the previous assessment are removed, and a better agreement with experimental data is achieved compared with the previous assessment.     

Thermodynamic optimizations of the Nd-Sn and Sn-Tb systems

The thermodynamic optimizations of the Nd-Sn and Sn-Tb binary systems were carried out by means of the Calculation of Phase Diagram (CALPHAD) method on the basis of the available experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, bct, dhcp and hcp phases were described by the substitutional solution model with the Redlich-Kister equation, while all of the intermetallic compounds (Nd₅Sn₃, Nd₅Sn₄, Nd₁₁Sn₁₀, NdSn, Nd₃Sn₅, NdSn₂, Nd₃Sn₇, Nd₂Sn₅, NdSn_3, Sn₃Tb, βSn₇Tb₃, αSn₇Tb₃, Sn₂Tb, Sn₅Tb₄, SnTb₄, Sn₁₀Tb₁₁, Sn₄Tb₅ and Sn₃Tb₅) were described by the sublattice model. A set of self-consistent thermodynamic parameters of each phase in the Nd-Sn and Sn-Tb binary systems has been obtained, and the calculated results are in good agreement with the available experimental data.     

Experimental investigation and thermodynamic calculation of Ti-Hf-Mn system

The phase relationship of Ti-Hf-Mn system was studied by diffusion triple and equilibrated alloy methods. The isothermal sections at 1373, 1273 and 1173 K for this system were constructed by means of electron probe microanalysis (EPMA) and X-ray diffraction (XRD) for the first time. No ternary phase was found in the system at all these temperatures. Six, seven and seven three-phase equilibria regions have been determined at 1373, 1273 and 1174 K, respectively. In this ternary system, the intermetallic compounds TiMn₂, HfMn₂ and HfMn exhibit wide solid solution range at those three temperatures. In particular, the solution range of Ti in HfMn phase decreases with the increase of temperature, from 30.5 at% at 1173 K to 26.5 at% at 1373 K. Based on all available experimental data, the Ti-Hf-Mn system was evaluated using the CALPHAD method. The calculation results are in excellent agreement with the experimental data.     

单元系T—p相图的数学结构

作者以化学元素的稳定单质为基准,推演出了任意物质M_i(相态Ω)的热力学生成活度{相态Ω)的函数形式:?D_Ω数值的大小体现着相态Ω的热力学相对稳定性.根据集合论原理沿D(稳定性)座标取极大值的方法把物理性质互不连续的各个异相态连结在一起,建立了单元系在T-p面上的优势分布方程(PSDE):■作者以H_2O为实例,计算了T-p相图,与实验相图基本一致.     

Thermodynamic assessment of the RE-B (RE = Ce,Dy, Lu) binary systems

Phase equilibria and thermodynamic properties of Nd-Fe-B-based alloys are fundamental to design novel Nd-Fe-B-based permanent magnets with outstanding magnetic properties and lower costs. In order to develop thermodynamic database of multi-component Nd-Fe-B-based alloys with the rare earth (RE) metals, in this work, the RE-B (RE = Ce, Dy, Lu) binary systems were assessed thermodynamically using the CALPHAD method based on the available phase diagram and thermodynamic data reported in the literature. In the thermodynamic modeling, the solution phases including liquid, bcc, fcc, hcp and rhombohedral, are described as the substitutional solution model and their excess Gibbs energies are described by Redlich-Kister polynomial. The binary intermetallic compounds, CeB₄, CeB₆, DyB₂, DyB₄, DyB₆, DyB₁₂, DyB₆₆, LuB₂, LuB₄, LuB₁₂ and LuB₆₆, are treated as the stoichiometric compounds considering the experimental heat capacities and enthalpy increments of some intermetallic compounds. The calculated results are in good agreement with the reported experimental data.     

Experimental study and thermodynamic modelling of the B-Fe-Mn ternary system

This work is focused on an experimental study of phase equilibria in the B-Fe-Mn ternary system combined with a CALPHAD theoretical analysis with the aim of creating a reliable theoretical thermodynamic dataset for calculation of the phase diagram of the ternary system. Boron is modelled as an interstitial element in all solid solutions of Fe and Mn. In the experimental study, B-Mn-Fe alloys were prepared and heat-treated at 873 K for 90 days/2160 h and at 1223 K for 60 days/1440 h. Following heat treatment, the phase equilibria and composition of the coexisting phases were determined using scanning electron microscopy and X-ray diffraction analysis. The experimental results obtained, together with experimental results collected from the literature, were used in the optimization of the thermodynamic parameters by using the CALPHAD method. The result of this work is an optimized thermodynamic dataset for the B-Fe-Mn ternary system allowing the phase diagram and thermodynamic properties to be calculated.     

Experimental investigation and thermodynamic assessment of phase equilibria in the Cr-Re-Ru ternary system

The phase equilibria of the Cr-Re-Ru ternary system at 1100 °C and 1200 °C have been experimentally investigated using electron probe microanalyzer and X-ray diffraction. The σ₁-Cr₂Re₃ and σ₂-Cr₂Ru phases with the same D8_b crystal structure do not form a continuous intermetallic compound phase at 1100 °C and 1200 °C in the Cr-Re-Ru ternary system confirmed by experimental results. According to the experimental results in this work, the Cr-Re-Ru ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The calculated isothermal section at 1400 °C shows that the two independent phases σ₁-Cr₂Re₃ and σ₂-Cr₂Ru are replaced by the continuous intermetallic compound σ. The current established thermodynamic database of the Cr-Re-Ru ternary system may provide the essential information, and support for the thermodynamic assessment of multicomponent system and the development of Ni-based superalloys.     

Experimental reinvestigation and thermodynamic description of Bi-Te binary system

The Bi-Te phase diagram was determined by equilibrium alloy method, combined with electron probe microanalysis (EPMA), X-ray diffraction (XRD) and thermal analysis (DSC). The experimental result shows that there is a β-phase with a large composition range at low temperature, while Bi₂Te and Bi₄Te₃ are relatively stable in the solid-liquid region. A consistent phase diagram that covers the experimental findings has been achieved. Based on the new experimental phase diagram, coupling with the reported thermodynamic data, the thermodynamic optimization of the Bi-Te binary system was carried out with the help of CALPHAD approach. A group of reasonable thermodynamic parameters was obtained.     

Phase equilibria and microstructure development in Mg-rich Mg-Gd-Sr alloys: Experiments and CALPHAD assessment

Mg-Sr alloys are promising to fabricate orthopedic implants. The alloying of rare earth elements such as Gd may improve the comprehensive mechanical properties of Mg-Sr alloys. The information on the phase diagram and the microstructure development are required to design chemical composition and microstructure of Gd alloyed Mg-Sr alloys. The phase equilibria and the microstructure development in Mg-rich Mg-Gd-Sr alloys (Gd, Sr < 30 at. %) are experimentally investigated via phase identification, chemical analysis, and microstructure observation with respect to the annealed ternary alloys. The onset temperatures of liquid formation are measured by differential scanning calorimetry. A thermodynamic database of the Mg-rich Mg–Gd–Sr ternary system is developed for the first time via CALPHAD (CALculation of PHAse Diagram) approach assisted by First-Principles calculations. The thermodynamic calculations with the developed database enable a well reproduction of the experimental findings and the physical-metallurgical understanding of the microstructure formation in solidification and annealing.     

A brief history of CALPHAD

Some 35 years ago, Larry Kaufman and Himo Ansara provided the stimulus to bring together a small number of scientists who were working on the calculation of alloy phase diagrams using as basis the required consistency of experimental thermodynamic and phase boundary data. This group represented the origins of CALPHAD and of subsequent developments concerned with computer coupling of phase diagrams and thermochemistry. From those origins, the “CALPHAD Method” has become a successful and widely applied tool in all areas of materials development.     

Thermodynamic assessment of MCl–YCl3 (M=Na,K, Rb,Cs) systems

Thermodynamic properties and phase diagrams of the MCl–YCl₃ (M=Na, K, Rb, Cs) systems were reassessed by using the CALPHAD method with the latest phase diagram data. A two-sublattice ionic solution model (M⁺)_P(Cl⁻, ${\mathrm{YCL}}_6^{3-}$, YCl₃)_Q reflecting the ionic behavior of the components was adopted to describe the liquid phase in the systems. A new set of optimized model parameters was found, and the calculated phase diagrams and enthalpies of mixing have good agreement with experimental data. The calculated liquidus near to YCl₃ side agrees much better with experimental data compared with previous work. In consideration of high and low temperature modifications as well as stability of intermediate compounds, Gibbs energies of formation of these compounds evaluated in the present work are more reasonable.