Volume 99, Issue 6

First-principles calculations of the total energy and elastic properties of the L1 2 -based Al 3 RE (RE = Sc, Y, Lanthanide) at T = 0 K are performed by using the projector augmented-wave method within the generalized gradient approximation. The lattice constants, formation enthalpies, elastic constants and bulk modulus of the L1 2 -based Al 3 RE are obtained. Young's modulus, shear modulus and Poisson's ratios are also estimated in the present work. By using the Debye – Grüneisen model, the Debye temperatures, Grüneisen constants and the sound velocity are obtained for the L1 2 -based Al 3 RE. All the calculated results are in good agreement with experimental values and other theoretical calculations available.

The Calphad method is a very powerful method for dealing with phase equilibria and thermodynamic properties of multicomponent alloy systems. In fact, it is the only method that can do this. However, in order to do this it is necessary to construct multicomponent databases, and the requirements on thermodynamic evaluations, in particular of binary systems, are quite different compared to the case when they are only used as stand-alone evaluations. A number of these issues are discussed in this paper and in particular the influence of changes of the values of binary interaction parameters on the ternary systems Cr–Cu–Ni and Cr–Cu–Fe is investigated. In addition, the Cr–Mo–Ni system is chosen as an example of a system where pure extrapolations (thermodynamic) from its binary subsystems produce a completely incorrect phase diagram. As a conclusion it is found that a massive effort on experimental and computational (Calphad) investigations of ternary systems, supported by ab-initio calculations, is needed in order to make further progress in the field of alloy thermodynamics possible. The quality of a multicomponent database is strongly dependent on the fraction of ternary datasets included in the database.

An extensive thermodynamic investigation of the Al – Ni – Si system is carried out via an integrated approach of calculation of phase diagrams, first-principles calculations, and key experiments. Eighteen decisive alloys are prepared in order to verify the existence of the previously reported ternary compounds and to provide new phase equilibrium data. Phase compositions, microstructure, and phase transition temperatures are determined using the combined techniques of X-ray diffraction, scanning electron microscopy, energy dispersion X-ray analysis, and differential thermal analysis. The order/disorder transition between disordered bcc_A2 and ordered bcc_B2 phases as well as that between disordered fcc_A1 and ordered L1 2 phase are described using a two-sublattice model. A self-consistent parameter set is finally obtained by considering the huge amount of experimental data including 13 vertical sections and 5 isothermal sections from both the literature and the present experiments. Almost all of the reliable phase diagram data can be well described by the present modeling. The reliability of the calculated thermodynamic properties for ternary phases is verified through enthalpy measurement employing drop calorimetry and first-principles calculations. The thermodynamic parameters obtained can also successfully predict most of the thermodynamic properties and describe the solidification path for the selected as-cast alloy Al 6 Ni 55 Si 39 .

A recently developed thermodynamic model for describing the ‘contact conditions’ (concentrations at an interface of the two adjacent phases) is implemented in a kinetic model for liquid/solid phase transformations. The resulting integrated model describes the concentration profiles in the liquid and solid phase during the phase transformation over a large range of solidification front velocities. Examples are shown for steady state solidification in aluminum alloys. The results are in good agreement with experimental data from the literature and the well known continuous growth model by Aziz. In addition to earlier models, transient states can be described. An example is shown for a solidification front that is momentarily disturbed, i. e. set off-equilibrium. One of the results is the time for local re-equilibration at the interface which is of the order of 20 μs for solidification. First results for describing melting are also shown and discussed.

This paper is an extension and improvement of the previous work of the authors. It presents further development of a coupling method between a multiphase Eulerian solidification model and the thermodynamics of multicomponental alloys. The transport equations of the multiphase solidification model are closed by the interphase transfer/exchange terms. The derivation of these terms is based on the diffusion-controlled solidification kinetics and thermodynamics. Direct online coupling of a computational fluid dynamics solver with a thermodynamic software package is time-consuming, therefore a way to access thermodynamic data by means of the tabulation and interpolation technique (In-Situ Adaptive Tabulation) is suggested. The coupling procedure is described and tested with a 0-D solidification benchmark case. Additionally, the suggested coupling method is used to simulate a casting process of a CuSn6P0.5 round strand, which demonstrated the application potential of the coupling idea. The predicted macrosegregations of Sn and P for this casting process shows the same distribution pattern as observed in practice, namely positive segregation in the vicinity of the wall region and negative one in the center of the casting.

The hcp – bcc phase transformation in nanocrystalline zirconium with an initial grain size of about 7 nm is studied by means of molecular dynamics simulations based on an analytic embedded atom method. The radial distribution function, the fraction of different type atoms differentiated by the common neighbor analysis method and snapshots of a slice through the simulation cell with relaxation time are all used to describe the hcp – bcc phase transformation process in nanocrystalline zirconium. The results indicate that the new phase of bcc structure zirconium first appears in the grain boundary regions, and then the interphase boundary migrates from the bcc to hcp phase, finally the grain of pure bcc phase grows. In addition, the critical temperature of phase transformation for nanocrystalline zirconium is determined as 1225 ± 25 K, which is somewhat higher than the experimental value of 1136 K for conventional zirconium.

Metallic materials in engineering applications are mostly multi-component and multi-phase alloys. The solidification principles of these materials still lack quantitative description. In this work, the solute partition behavior and its influence on the solidification process of multi-component alloys are studied based on CALPHAD. A complete thermodynamic model for the accurate calculation of the partition coefficients in solidification is described. The model is applied to Al – Si – Mg ternary alloys, and the predicted partition coefficients are compared with some former experimental data. Good agreement between the calculation results and the experimental data demonstrates the validity of the present model. The variation of solute partition coefficients of both Si and Mg is studied in dendritic solidification of Al – Si – Mg alloys. It is found that the partition coefficient changes greatly during solidification. By coupling CALPHAD with a micro-scale solidification model, the predicted solidification path for different composition and cooling rates and the off-eutectic fraction of Al – Si – Mg alloys agrees well with the experimental results. The conventional theory of constrained dendrite growth for binary alloys is extended to multi-component alloys based on the CALPHAD method with consideration of the solute interactions, through which the primary dendrite spacing is estimated.

CoSb 3 is a very promising thermoelectric semiconductor with narrow gap and good electrical transport properties. It is also a special compound with an intrinsically caged crystal structure. By taking void filling in the intrinsic cages and impurity substitution for Co in the skutterudites as examples, a few phase-diagram-related problems in thermoelectric materials are discussed. The first topic shows that the filling fraction limit for an impurity in the crystal voids could be taken as a phase-diagram-related issue to be solved by first-principles energetic calculations. But the partial void filling also reveals that the structural integrity of a compound with special structure is very sensitive to electron filling and its influence on chemical bonding, which needs further study. This is assumed to be a general problem linking with the group of compounds with special 2-D layered or 3-D caged structures, a focus of current thermoelectric research. The second topic relates to the solid solution problem when mixing CoSb 3 with IrSb 3 (or RhSb 3 ) to realize new materials with random distribution of Ir or Rh at Co sites. By going through most of the currently state-of-the-art thermoelectric compounds including CoSb 3 /IrSb 3 , PbTe/(Ag,Sb)Te 2 , MgSi 2 /MgSn 2 /MgGe 2 , and ZrNiSn/HfNiSn, it is found that their mixing enthalpies are usually slightly positive, implying the possibility of mixing 2- or 3-similar compounds to realize nanocomposites with low internal strain for promising performance. Related experimental and theoretical issues on nanocomposite thermoelectrics are briefly discussed.

The phase equilibria at 340°C of the Al – Ni – Zn system were investigated by combining the diffusion couple technique with the equilibrated alloys method. The samples were examined by means of optical microscopy, X-ray diffraction, scanning electron microscopy, and electron probe microanalysis. Two ternary compounds ( 1 and 2 ) were found to exist at 340°C. The solubilities of Zn in AlNi, Al 3 Ni 2 and Al 3 Ni were determined to be about 20, 2 and 1 at.% Zn, respectively. The solubilities of Al in β 1 -NiZn and in were measured to be about 11.5 and 1 at.% Al, respectively. The solubilities of Zn in both AlNi 3 and Al 3 Ni 5 are below 1 at.% Zn.

The thermodynamic modeling and optimization of the Ce-Mg, Ce-Y, Mg-Nd, Nd-Y, Ce-Mg-Y and Mg-Nd-Y systems have been carried out by means of the CALPHAD technique. The solution phases, liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed, were described by the substitutional solution model. The isostructural MgCe, MgNd and MgY phases with B2 structure form continuous range of solid solutions in the Ce-Mg-Y and Mg-Nd-Y ternary systems. The order-disorder transition between the solutions with A2 structure and compounds with B2 structure in the systems has been taken into account and thermodynamically modeled. The other compounds Mg 2 Y, Mg 24 Y 5 , Mg 3 R, Mg 41 R 5 , Mg 2 R and Mg 12 Ce (R = Ce and Nd) in the Mg-R-Y system exhibit different solubilities of the third component. A set of self-consistent thermodynamic descriptions of the Ce-Mg-Y and Mg-Nd-Y systems was obtained.

By means of scanning electron microscopy equipped with energy dispersive X-ray spectroscopy and X-ray diffraction, the phase relations in the zinc-rich corner of the Zn – Fe – Cr ternary system at 450°C were determined using heat-treated alloys. The experimental results indicate that a ternary phase named ζ′ is in equilibrium with liquid, ζ-FeZn 13 and θ-CrZn 17 . The solubilities of Cr in the ζ phase and Fe in the θ phase are limited, being 0.6 wt.% and 0.7 wt.%, respectively. Meanwhile, based on the interatomic potentials obtained using the lattice inversion method, atomistic calculation was carried out to determine the site preference and solubilities of Cr in the ζ phase. Good agreement between the experimental results and theoretical calculations was achieved.

Modern high-strength low-alloy steels commonly contain microalloying additions of titanium, niobium or vanadium in different combinations in order to obtain the desired microstructure and mechanical properties. Titanium has a strong tendency to form TiN in the range of the solidus temperature. This has been reported to have a negative effect on the impact toughness of the material. Thermodynamic calculations showed that the titanium and nitrogen content and the titanium to nitrogen ratio determine if the formation of TiN takes place during solidification or in the solid state. These calculations where complemented by simulations of solidification using the Scheil – Gulliver model and DICTRA. The results were compared with microstructure investigations of plate and slab material with titanium contents between 0.003 wt.% and 0.015 wt.% using light-optical microscopy and electron probe microanalysis. While the formation of TiN particles cannot be ruled out even at the lowest Ti levels, the temperature of formation and the volume fraction varied significantly depending on the Ti content. With respect to the first results of this preliminary study, i. e. the comparison of equilibrium, Scheil and DICTRA calculations, it can be assumed that the Scheil model is the most appropriate one at present.

The directional solidification transport behaviors in blade-like castings of Al – Cu and Fe – C alloys were simulated based on a multilength-scale continuum model for solidification transport processes. The simulations were closely coupled with the commercial ThermoCalc package via its TQ-interface codes, for instantaneous determination of the related thermodynamic data at each calculation time step. Comparisons were made between the simulation results obtained by the ThermoCalc-coupled modeling and the model using the regression functions for the solidification thermodynamic data. The present numerical investigations confirm the feasibility of a close linkage of ThermoCalc software/Databases to the solidification simulations, but indicate an urgent need to cut down significantly the CPU-time spent for accessing the ThermoCalc/Databases for an efficient coupled computation.

Cobalt-based amorphous alloy ribbons were prepared by means of melt-spinning. The effect of addition of a rare earth element yttrium on the glass forming ability (GFA) and thermal stability were investigated by X-ray diffraction analysis and differential scanning calorimetry. The results show that a small amount of yttrium is effective in improving the glass forming ability and thermal stability of a Co – Fe – Zr – Nb – B alloy. As-quenched glassy ribbon containing 4 at.% yttrium shows the highest GFA and thermal stability. The glass transition temperature T g , reduced glass transition temperature T rg , supercooled liquid region Δ T x , GFA parameter γ and Vickers hardness are 886 K, 0.618, 96 K, 0.423 and 1158 respectively. Crystallization kinetic studies show that the crystallization activation energies for (Co 45 Fe 21 Zr 4 Nb 10 B 20 ) 96 Y 4 glassy ribbon are as high as 826 kJ mol − 1 for the first crystallization peak. The excellent GFA and thermal stability of Y-containing alloy is mainly attributed to the scavenging of oxygen and large mismatch in atomic size induced by the addition of yttrium.

Physico-chemical analysis techniques, including X-ray powder diffraction, scanning electron microscopy, optical microscopy and differential thermal analysis were employed in constructing the isothermal section of the Y – Ti – Si system at 773 K. The isothermal section consists of 12 single phase regions, 21 binary phase regions and 10 ternary phase regions. No ternary compound is found in the work. None of the phases in this system reveals a remarkable homogeneity range at 773 K.