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 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.     

The application of radiation diffuse scattering to the calculation of phase diagrams of F.C.C. substitutional alloys

By using quantitative information about the radiation diffuse-scattering intensity of the disordered f.c.c. substitutional alloy Me′_1-cMe″_c (c—concentration) the Fourier component, , of mixing energies of Me′ and Me″ atoms may be estimated. We have to use the measurement data of the diffuse-scattering intensities at the corresponding reciprocal-space points k of the disordered phase and then determine the parameter (k). The statistical thermodynamics of the non-ideal solid solution is determined by these energy parameters { (k)}. Therefore, one can obtain the configuration free energy of an alloy, F=U-TS (U—internal energy, S—entropy), and then determine its fundamental thermodynamic characteristics, including not only its phase diagram, but also the concentration-dependent order–disorder transformation temperature, temperature and concentration long-range order parameter dependences, chemical activity, heat capacity etc. Some thermodynamic properties are calculated within the framework of the statistical-thermodynamic approach for f.c.c.-Ni–Fe alloy. The diffuse-scattering intensity values are taken from data in the literature.     

Glass formability of W-based alloys through thermodynamic modeling: W–Fe–Hf–Pd–Ta and W–Fe–Si–C

Computational thermodynamics, based on the CALculation of PHAse Diagram (CALPHAD) method, can be an efficient way to predict phase stabilities in multi-component engineering materials. By calculating the stability of the liquid phase at low temperatures, this method could be a useful and cost-effective tool for the design of bulk metallic glasses. Based on the thermodynamic modeling of the constituent binary and ternary systems of W with Fe, Hf, Pd, Ta, Si, or C, thermodynamic databases are built to search for W-based metallic glasses in these alloying systems. Modeling of intermetallic phases combines input from first-principles total energy calculations and predictions of finite temperature properties from the Debye–Grüneisen model. Several plausible W-rich glass-forming alloys are identified in the W–Fe–Si–C quaternary system.     

Effects of replacing Ni by Co on the crystallization behaviors of Al–Ni–La amorphous alloys

Effects of replacing Ni by Co on the crystallization behaviors of three Al–Ni–La amorphous alloys, i.e. Al₈₅Ni₉La₆, Al₈₆Ni₉La₅ and Al₈₇Ni₈La₅ were investigated by X-ray diffraction and differential scanning calorimeter. The results show that the glass-forming ability decreases when Ni is replaced by excessive Co. Meanwhile replacing Ni by Co improves the thermal stability, enlarges the supercooled liquid region ΔT_x and promotes the precipitation of the metastable phase(s) as the primary phase. The apparent activation energy E_a1 of the first reaction changes complicatedly during the replacement and is strongly dependent on the type of the primary phase, i.e. diffusion of atoms.     

The ternary system Al–Ni–Ti Part II: thermodynamic assessment and experimental investigation of polythermal phase equilibria

The Al–Ni–Ti phase diagram has been thermodynamically assessed and a consistent set of thermodynamic functions has been developed. The thermodynamic modeling is based on an experimental investigation of the phase equilibria in the composition range of 0.1x_Al0.7. Alloys were prepared by argon-arc or vacuum-electron beam melting of elemental powder blends. X-ray powder diffraction, metallography, SEM and EMPA-techniques were employed to analyze the samples in the as-cast state as well as after annealing at 800, 900 and 1000°C. The existence of the four ternary compounds, τ₁ to τ₄, has been confirmed, although homogeneity regions differ significantly from reports in the literature. The homogeneous phase, previously claimed at “Al₂₃Ni₂₆Ti₅₁”, is shown by high resolution microprobe and X-ray diffraction measurements to be an extremely fine-grained eutectic structure. The congruent melting behavior of τ₄=AlNi₂Ti is confirmed, but, in contrast to earlier reports, primary crystallization and congruent melting have been observed for τ₁=Al₁₃Ni₂Ti₅ and τ₃=Al₃NiTi₂. In contrast to earlier assessments, τ₁,τ₂ and τ₃ are experimentally found to be stable at 800, 900 and 1000°C. The thermodynamic modeling of the ternary phases τ₂ and τ₃ is done with simplified sublattice models, considering their crystal structure and homogeneity ranges. The sublattice model for τ₄ is taken from an earlier asessment of the nickel-rich ternary phase equilibria. The present assessment covers the entire composition range. An application to the solidification behavior of ternary alloys is also exemplified.     

Thermodynamic assessment of the Nd–Zn binary system

On the basis of available experimental information, the Nd–Zn binary system has been thermodynamically optimized using the CALPHAD method. The solution phases, liquid, bcc and dhcp, were treated as substitutional solutions, while the intermediate compounds, NdZn, NdZn₂, NdZn₃, Nd₃Zn₁₁, Nd₁₃Zn₅₈, Nd₃Zn₂₂, Nd₂Zn₁₇ and NdZn₁₁, were described as stoichiometric phases. A set of self-consistent parameters formulating the Gibbs energies of various phases in this binary system was obtained. Most of experimental data on thermochemistry and phase diagram reported in the literatures were satisfactorily reproduced.     

The Al–R–Mg (R=Gd, Dy, Ho) systems. Part I: experimental investigation

Key experiments were carried out on the three Al–R–Mg (R=Gd,Dy,Ho) systems and the results obtained used for the thermodynamic optimisation reported in a separate paper in this issue [Caccasmani G, De Negri S, Saccone A, Ferro R. Intermetallics this issue.]. The samples were characterized by differential thermal analysis (DTA), X-ray powder diffraction (XRD), light optical microscopy (LOM), scanning electron microscopy (SEM) and quantitative electron probe microanalysis (EPMA). The isothermal sections at 400 °C are all characterized by extended homogeneity regions at a constant rare earth content. The extension of the (Mg,Al)R solid solution, cP2-CsCl type, varies with the R atomic number. Ternary compounds (τ) of Al₂(R,Mg) stoichiometry (hexagonal Laves phases with MgNi₂-type structure) have been found to exist at 400 °C in all the systems. Their temperatures of formation were detected by DTA measurements.     

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.     

The ternary system Al–Ni–Ti Part I: Isothermal section at 900°C; Experimental investigation and thermodynamic calculation

Phase relations in the ternary system Al–Ni–Ti have been experimentally established for the isothermal section at 900°C for concentrations 0.1x_Al0.7. The investigation is based on X-ray powder diffraction, metallography, SEM and EMPA-techniques on about 40 ternary alloys, prepared by argon-arc or vacuum-electron beam melting of proper elemental powder blends. The existence of four ternary compounds, τ₁ to τ₄, is confirmed, however, in contrast to earlier investigations at significantly different compositions and with different shape of the homogeneity regions. This is particularly true for the phase regions of τ₃-Al₃NiTi₂ with the MgZn₂-type structure ranging from Al₃₀Ni₂₈Ti₄₂ (composition lowest in Al) to Al₅₀Ni₁₆Ti₃₄ (composition richest in Al) and for τ₂-Al₂NiTi. The complex atom site substitution mechanism in τ₃ changing from Ti/Al exchange at Al-poor compositions towards Ni/Al replacement for the Al-rich part was monitored in detail by quantitative X-ray powder diffraction techniques (Rietveld analyses). In contrast to earlier reports, claiming a two-phase region Ni{Al_xTi_1-x}₂+τ₃, we observed two closely adjoining three-phase equilibria: ₂-AlTi₃+Ni{Al_xTi_1-x}₂+ τ₄-AlNi₂Ti and ₂-AlTi₃+τ₃-Al₂NiTi₂+τ₄-AlNi₂Ti. The earlier reported “homogeneous phase at Al₂₃Ni₂₆Ti₅₁′” was shown by high resolution microprobe and X-ray diffraction measurements to be an extremely fine-grained eutectic. The experimental results are in fine agreement with the thermodynamic calculation.     

Magnetic ordering and magnetic properties of ErAuxNi1−xIn (0 ≤ x ≤ 1) solid solution

The ErAu_xNi_1−xIn (0 ≤ x ≤ 1) quasiternary compounds crystallize in the hexagonal layered crystal structure of ZrNiAl-type. ErAuIn was reported to be an antiferromagnet with T_N = 3 K and magnetic moments having triangular arrangement within the basal plane (the magnetic order is described by the propagation vector ). On the contrary ErNiIn is a ferromagnet with T_C = 9 K and magnetic moments pointing along the c-axis. The magnetic ordering in ErAu_xNi_1−xIn (0 < x < 1) solid solution, has been investigated by neutron diffractometry in the temperature range between 1.5 and 15 K. Moreover, bulk magnetic measurements have been carried out in the range 1.72–400 K. All alloys of intermediate composition were found to be antiferromagnets with T_N between 4.6 and 7 K. Below 2 K their magnetic order is described by the propagation vector and magnetic moments are aligned along the c-axis. However, for alloys with 0.2 ≤ x ≤ 0.7 the propagation vector was found to turn into with increasing temperature.     

Structural,electronic, elastic,mechanical and thermal behavior of RESn3(RE = Y,La and Ce) compounds: A first principles study

The structural, electronic, elastic, mechanical and thermal properties of the isostructural and isoelectronic nonmagnetic RESn₃ (RE = Y, La and Ce) compounds, which crystallize in AuCu₃-type structure, are studied using first principles density functional theory based on full potential linearized augmented plane wave (FP-LAPW) method. The calculations are carried out within PBE-GGA, WC-GGA and PBE-sol GGA for the exchange correlation potential. Our calculated ground state properties such as lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) are in good agreement with the experimental and other available theoretical results. We first time predict the elastic constants for these compounds using different approximations of GGA. All these RESn₃ compounds are found to be ductile in nature in accordance with Pugh's criteria. The computed electronic band structures and density of states show metallic character of these compounds. The elastic properties including Poisson's ratio (σ), Young's modulus (E), shear modulus (G_H) and anisotropy factor (A) are also determined using the Voigt–Reuss–Hill (VRH) averaging scheme. The average sound velocities (v_m), density (ρ) and Debye temperature (θ_D) of these RESn₃ compounds are also estimated from the elastic constants. We first time report the variation of elastic constants, elastic moduli, Cauchy's pressure, sound velocities and Debye temperatures of these compounds as a function of pressure.     

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.     

Thermodynamic investigations in the solid state of the lanthanum–magnesium–zinc system

The La–Mg–Zn phase diagram is experimentally investigated at 595 K, x_La > 4% and the corresponding isothermal section is partially determined. This section includes 5 substitutional solid solutions based on the binary compounds (LaMg, LaZn, LaMg₃, LaMg_10.3 and La₂Zn₁₇) and three ternary phase (La₈(Mg,Zn)₉₂, La₃(Mg,Zn)₁₁ and La_4.27Mg_2.89Zn₃₀). The enthalpies of mixing in the ternary solid solutions are calculated at 298 K on the basis of tin solution calorimetry experiments.