Thermodynamic modeling of Ru–Zr and Hf–Ru systems

In this paper, an assessment of the binary Ru–Zr and Hf–Ru systems is presented. The thermodynamic evaluation is based on diagrammatic investigations and high-temperature calorimetric measurements for the formation of the three intermediate compounds. The present work proposes thermodynamic modeling of the binaries calculated according to the CALPHAD method and carried out using the PARROT module in the Thermo-Calc software. The liquid phase and the solution phases (Ru)-HCP-A3, (Zr)-HCP-A3, (βZr)-BCC-A2, (Hf)-HCP-A3 and (βHf)-BCC-A2 are treated as substitutional solutions. The intermetallic Laves phase Ru₂Zr-C14 is modeled with the sublattice formalism. The RuZr-B2 and HfRu-B2 phases are treated as ordered phases originating, respectively, from (βZr)-BCC-A2 and (βHf)-BCC-A2 disordered phases. Considering the relative uncertainty of experimental data due to high temperatures, a good agreement is obtained between calculated and experimental phase diagrams. The optimized set of coefficients and the calculated isothermal section are provided.     

Thermodynamic properties of the ternary system InSb–NiSb–Sb in the temperature range 640–860 K

The ternary InSb–NiSb–Sb system has been studied by X-ray diffraction and by potentiometry. The electromotive forces (EMF) have been measured in the temperature range 640<T/K<860 by using the following galvanic cell:

with x (0.075<x<0.498) and y (0<y<0.359). The investigated samples are located on the following lines of the Gibbs triangle: InSb–Ni_0.33Sb_0.66, InSb–Ni_0.48Sb_0.52, InSb–NiSb, Sb–(InSb)_0.75(NiSb)_0.25, Sb–(InSb)_{0. 5}(NiSb)_0.5, Sb–(InSb)_0.25(NiSb)_0.75. From these measurements, the values of the partial molar thermodynamic functions (Δμ°_m,In, ΔH°_m,In, ΔS°_m,In) (data at reference pressure p⁰=10⁵ Pa), for the liquid InSb alloy, for the three solid heterogeneous regions InSb–NiSb₂–Sb, InSb–NiSb_1±δ?–NiSb₂, InSb–NiSb_1±δ, for six ternary liquid–solid alloys, have been calculated.     

Thermodynamic analysis of the Re–Si system

The Re–Si system is assessed thermodynamically, using the CALPHAD method. The calculated phase diagram and thermodynamic properties are in good agreement with available experimental data. Calculated enthalpies and entropies of fusion are compared with available data for other transition metal silicides, against melting points, showing good agreement with the general trends. This is a useful approach for thermodynamic assessment of alloy systems, where experimentally measured thermodynamic data are limited. The stability of the amorphous phase in this system has also been discussed.     

Thermodynamic analysis and assessment of the Ce–Ni system

An optimised set of thermodynamic parameters for the Ce–Ni system has been obtained using the CALPHAD approach. A thorough thermodynamic analysis of the system has been carried out using different calorimetric techniques and the data have been used in the assessment. The free energy of the liquid phase has been described as a function of temperature and composition using a Redlich–Kister polynomial. Solid compounds have been considered as stoichiometric with the exception of the Laves phases. The phase diagram and thermodynamic quantities calculated from assessed parameters agree well with experimental data.     

Activity measurement of gallium in the B2 phase of the CoGa–Sb system by the EMF method with zirconia-based solid electrolyte

Gallium activity in the B2 phase regions of both binary Co–Ga and ternary Co–Ga–Sb systems was measured by EMF method with stabilized zirconia solid electrolyte The temperature range was 1073–1273 K and Sb concentrations were 1, 2 and 3 mol fractions. Ga activity at 1173 and 1273 K increases sharply in Ga rich region and the addition of Sb to the CoGa phase increases Ga activity. Activity change corresponds to the lattice parameter change with Sb addition to the CoGa phase.     

Thermodynamic assessment on the Pb–Ca–Sn ternary system

Thermodynamic modelling of the Pb–Ca–Sn ternary system was carried out with the help of the CALculation of PHase Diagrams (CALPHAD) method.The binary borders related to the ternary system were investigated. The lead–tin system is already calculated, the calcium–tin and calcium–lead systems can be described with the association model in binary liquid. The establishment of the modelling of the Pb–Ca–Sn phase diagram was done after collecting own experimental information. The introduction of new interaction parameters related to the ternary liquid, leads to an accurate restoration of the experimental data.Calculated isothermal, isoplethal sections and liquidus surfaces are presented. They confirm that the calcium solubility in lead matrix drastically decreases with the introduction of tin as well as with the decreasing of temperature. The industrial process applied to the lead–calcium–tin alloys finds some justifications in the calculated phase diagram.     

Mixed site occupancies in the μ phase

The μ phase has been studied in different systems (Ta–Ni, Mo–Co, Nb–Ni) as a function of the composition. In addition, its stability in the Mn–Si system has been investigated. The atom distribution on the five different sites of the crystal structure has been obtained from Rietveld refinement of X-ray powder diffraction data. These experimental data are compared to the values computed from first principles results and from existing Calphad assessments of the different systems. Conclusions are drawn concerning the model to be chosen for describing this phase.     

Ordering potential in liquid Al–Ge alloys structure and thermodynamics

In this paper we use the concept of ordering potential to calculate the atomic structure and the thermodynamic asymptotic limit of the liquid Al–Ge alloy, for which we previously measured the atomic structure and the electrical resistivity. The sign of the ordering potential in the region of the first nearest neighbours indicates whether the alloy is homo or hetero-coordinated. The aim of this work is to reproduce quantitatively the atomic structure by using the simple phenomenological Silbert-Young effective potential. This model can explain both the shape of the structure factor measured by neutron diffraction and the low-angle limit of the Bhatia–Thornton partial structure S_CC(q) given by thermodynamic measurements.     

第一性原理研究Al-Y合金在压力作用下的晶胞结构、力学性质、热力学性质和电子结构

The influence of structural, elastic properties, thermodynamics and electronic properties Al-Y alloy were investigated by using first-principles. The equilibrium lattice constant, elastic constants, and elastic modulus as calculated here agree with results of previous studies. Calculated results of bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio v and Debye temperature all increase as pressure increase, but the opposite is true for heat capacity cp. In addition, the Debye temperature for the phases reduces gradually as follows: Al2Y > Al3Y> AlY. Additionally, the G/B ratio indicates that AlY and Al3Y are ductile materials, while Al2Y is a brittle material, and that the ductility of AlY and Al3Y can be improved with increased pressure, while the brittleness of Al2Y does not improve with increased pressure. Finally, the paper presents and discusses calculations of density of states and charge populations as they are affected by pressure.     

Enthalpies of formation of selected Pd2YZ Heusler compounds

Standard enthalpies of formation of selected ternary Pd-based Heusler type compositions Pd₂YZ (Y = Cu, Hf, Mn, Ti, Zr; Z = Al, Ga, In, Ge, Sn) were measured using high temperature direct synthesis calorimetry. The measured enthalpies of formation (in kJ/mole of atoms) of the Heusler compounds are, Pd₂HfAl (−81.6 ± 2.4); Pd₂HfGa (−79.9 ± 2.9); Pd₂HfIn (−76.4 ± 1.4); Pd₂HfSn (−77.6 ± 1.6); Pd₂MnSn (−54.6 ± 3.1); Pd₂TiGa (−65.6 ± 3.6); Pd₂TiIn (−69.9 ± 2.1); Pd₂TiSn (−78.6 ± 2.4); Pd₂ZrAl (−85.3 ± 3.0); Pd₂ZrGa (−76.2 ± 1.9); Pd₂ZrIn (−85.1 ± 3.9); Pd₂ZrSn (−92.2 ± 3.1); for the B2 compounds, Pd₂MnAl (−87.1 ± 3.0); Pd₂MnGa (−54.5 ± 1.7); Pd₂MnIn (−41.0 ± 2.5); Pd₂TiAl (−81.4 ± 1.9); for the tetragonal compound Pd₂CuAl (−55.2 ± 3.0) and for the orthorhombic compound Pd₂CuSn (−43.1 ± 2.3). Values were compared with those from published first principles calculation and the Open Quantum Materials Database (OQMD). Lattice parameters of these compounds were determined by X-ray diffraction analysis (XRD). Microstructures were identified using scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). Selected alloys were annealed at various temperatures to investigate phase transformations and phase relationships.     

Nonstoichiometry and P–T–x diagrams of binary systems

A P–T–x three-dimensional space diagram forms the complete representation between pressure (P), temperature (T) and composition (x) of coexisting phases—solid (S), liquid (L) and vapor (V). It gives the number of nonstoichiometric compounds that may be formed by the components and the stability limits of phases which are in equilibrium. Definitions of stoichiometry and nonstoichiometry are given. Some features of P–T–x diagrams with nonstoichiometric compounds are considered: maximum (T_m^max) and congruent (T_m^c) melting points, difference between the compositions of solid (x^S), liquid (x^L) and vapor (x^V): x^L≠x^S≠x^V at maximum melting point T=T_m^max, the width and position of the homogeneity range, and the nonstoichiometry caused by defects are also discussed. A new technique for the investigation of P–T–x diagrams is presented.     

First-principles investigations on structural,elastic, thermodynamic and electronic properties of Ni3X (X = Al,Ga and Ge) under pressure

The structural, elastic, thermodynamic and electronic properties of L1₂-ordered intermetallic compounds Ni₃X (X = Al, Ga and Ge) under pressure range from 0 to 50 GPa with a step of 10 GPa have been investigated using first-principles method based on density functional theory (DFT). The calculated structural parameters of Ni₃X at zero pressure and zero temperature are consistent with the experimental data. The results of bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio v, anisotropy index A^U and Debye temperature Θ_D increase with the increase of external pressure. In addition, the Debye temperature of these compounds gradually reduce as the order of Ni₃Al > Ni₃Ga > Ni₃Ge. The ratio of shear modulus to bulk modulus G/B shows that the three binary compounds are ductile materials, and the ductility of Ni₃Al and Ni₃Ga can be improved with pressure going up, while Ni₃Ge is opposite. Finally, the pressure-dependent behavior of density of states, Mulliken charge and bond length are analyzed to explore the physical origin of the pressure effect on the structural, elastic and thermodynamic properties of Ni₃X.     

Enthalpies of formation of magnesium compounds from first-principles calculations

An energetics database of binary magnesium compounds has been developed from first-principles calculations. The systems investigated include Mg–X (X = As, Ba, Ca, Cd, Cu, Dy, Ga, Ge, La, Lu, Ni, Pb, Sb, Si, Sn and Y). The calculated lattice parameters and enthalpies of formation of binary compounds in these systems are compared with both experimental data and thermodynamic databases.     

Electrochemical behaviour assessment of novel Mg-rich Mg–Al–RE alloys (RE = Ce, Er)

The electrochemical behaviour of new Mg–Al–RE (RE = Ce, Er) alloys AE91 was investigated in 0.01 M NaCl electrolyte (pH = 12) and compared with that of the most commonly used Mg alloy in the automotive field, the AZ91D. Scanning electron microscopy and quantitative electron probe microanalysis were used to characterize the samples prior to the electrochemical tests. AE91 alloys showed very similar microstructures characterized by a three-phase appearance: a Mg-based solid solution containing only Al and two intermetallic phases γ(Mg₁₇Al₁₂) and (Al_1 − xMg_x)₃Ce or (Al_1 − xMg_x)₂Er. Free corrosion potential measurements, potentiodynamic polarization curves and electrochemical impedance spectroscopy revealed improved passivity behaviour compared to AZ91D alloy. The apparent presence of trace amounts of rare earth oxides in the passive film is presumed to be the reason for the enhanced corrosion resistance of AE91 alloys in the aggressive environment considered.     

Chemical and thermodynamic properties of several Al–Ni–R systems

The standard enthalpies of formation at 300 K of the RNiAl phases (R=rare earth) have been obtained by using a high temperature direct reaction drop calorimeter and an aneroid isoperibol calorimeter. State and composition of the samples were checked by X-ray diffraction analysis. Metallographic examination was performed and the phases were further identified by electron microscopy and electron probe microanalysis. The results obtained are discussed and compared with those available for the binary RNi₂ and RAl₂ compounds.     

First-principle calculations of structural,elastic and thermodynamic properties of Fe–B compounds

The structural, elastic and thermodynamic properties of FeB, Fe₂B, orthorhombic and tetrahedral Fe₃B, FeB₂ and FeB₄ iron borides are investigated by first-principle calculations. The elastic constants and polycrystalline elastic moduli of Fe–B compounds are usually large especially for FeB₂ and FeB₄, whose maximum elastic constant exceeds 700 GPa. All of the six compounds are mechanically stable. The Vickers hardness of FeB₂ is estimated to be 31.4 GPa. Fe₂B and FeB₂ are almost isotropic, while the other four compounds have certain degree of anisotropy. Thermodynamic properties of Fe–B compounds can be accurately predicted through quasi-harmonic approximation by taking the vibrational and electronic contributions into account. Orthorhombic Fe₃B is more stable than tetrahedral one and the phase transition pressure is estimated to be 8.3 GPa.     

Thermodynamic activity measurements in the B2 phases of the Fe–Al and Ni–Al systems

The vaporisation of Fe–Al and Ni–Al alloys has been investigated in the temperature range 1140–1600 K and 1178 to 1574 K, respectively, by Knudsen effusion mass spectrometry (KEMS). Eleven different Fe–Al and also eleven Ni–Al compositions have been investigated in the composition ranges 30–51 at.% Al and 38–53 at.% Al, respectively. The Fe–Al samples have been investigated mostly in the B2 region of the phase diagram. The partial pressures and thermodynamic activities were evaluated directly from the measured ion intensities formed from the equilibrium vapour over the alloy and the pure element. From the temperature dependence of the activities the partial and integral molar enthalpies and entropies of mixing have been obtained. These are the most accurate data obtained by mass spectrometry on Fe–Al and Ni–Al systems so far. Nearly temperature independent integral enthalpies and entropies of mixing over the wide temperature range investigated were found, with the mixing entropies being large and negative.     

Formation of AB2-intermetallics by diffusion in the Au–Sb–Bi system

Binary diffusion couples, in which one single-phased product layer is growing between pure elements, were employed to study the diffusion properties of Au₂Bi- and AuSb₂-intermetallics at 230 and 330 °C. The position of the Kirkendall-marker plane inside the reaction zones revealed that in this temperature range the minority element is the faster diffuser in the Laves-phase Au₂Bi as well as in AuSb₂. The concept of integrated diffusion coefficient is used to describe the growth kinetics of the intermetallic compounds. The integrated diffusion coefficient in an intermetallic is related to the tracer diffusivities of the components and the thermodynamic stability of the phases involved in the interaction. The tracer diffusion coefficients were deduced from the interdiffusion experiments. The isothermal cross-section through the ternary phase diagram Au–Sb–Bi at 230 °C was constructed by means of the diffusion couple technique. No ternary phases are found in this system. Both intermetallic compounds Au₂Bi and AuSb₂ are in equilibrium with the (Sb,Bi)-solid solution. The solubility of Sb in the Laves-phase Au₂Bi was found to be negligible. Up to about 10.5 at.% of Bi can be dissolved in the AuSb₂-phase, the Bi-atoms substituting Sb in the cubic lattice of AuSb₂.