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A parameter-free electronic structure approach is applied to the study of stability and chemical order in the 15 substitutional body-centered cubic (bcc)-based alloys made of the six transition metals of groups 5 (V, Nb, Ta) and 6 (Cr, Mo, W) of the periodic table. The method is based on a Green’s function description of the electronic structure of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with a generalized mean-field approach. In contrast to the results summarized in the assessed phase diagrams, stability and ordering trends are predicted in a broad range of alloy composition for at least seven alloys, and explanation is found in their electronic structure properties. Short-range order results, thermodynamics analysis, and bcc-based phase diagrams are also presented.

Recently discovered AlCe alloys have shown promise in a number of applications, but the propensity of Ce to react with Al and other alloying elements can complicate the phase equilibria and design approach. To solve this, the CALPHAD method is used to explore an alloy within the quinary Al-Ce-Cu-Mg-Si system by developing a thermodynamic database with self-consistent parameters. The database includes a description of all 10 binary systems and 8 ternary systems consisting of: (i) 6 Al-containing ternaries (Al-Ce-Cu, Al-Ce-Mg, Al-Ce-Si, Al-Cu-Mg, Al-Cu-Si and Al-Mg-Si); and (ii) 2 additional ternaries that include Mg and Si (i.e., Ce-Mg-Si and Cu-Mg-Si). The thermodynamic description for the Al-Ce-Mg and Al-Mg-Si systems were reassessed to ensure consistency with the binary systems and the Ce-Mg-Si system is presented for the first time and compared to theoretical data from DFT (Density Functional Theory). In addition to the ternary interactions, the quaternary compound Al3Cu2Mg9Si7 and solid solution extending from the ternary Al2CuMg phase (Al,Si)2CuMg are incorporated. The CALPHAD method is employed and leveraged through the use of a Materials Design Simulator (MDS) to accelerate the design of novel aluminum-cerium-based alloys. The combination of a CALPHAD-based framework with experimental efforts and industrial insight permits the development of three new Al-Ce alloys: Al-3.5Ce-0.4Mg-7Si (Ce-modified A356), Al-5Ce-1Cu-0.5Mg-10Si and Al-19Ce-0.9Mg-1.1Si.

This article presents a review of the phase equilibria of the Pu-Zr system and discusses the contradictory reports on the experimental phase diagram and misinterpretations that have led to confusion over time. In addition, a review of the few Pu-Zr CALculation of PHAse Diagrams (CALPHAD) assessments is presented with emphasis on the heat of formation of the bcc phase, highlighting a disagreement between CALPHAD and ab initio calculations. Based on the information gathered in this study, a critical re-assessment of the Pu-Zr system involving the ζ (Pu28Zr), θ (Pu4Zr), kinetically hindered κ (PuZr2), and once observed ι phases is called for.

First-principles molecular dynamics simulations were used to generate the samples of amorphous a-AlB 2 , a-AlBC and a-AlBN alloys. All alloys exhibit boron clustering. The Al–C network of a-AlBC shows some similarity to the structure of the Al 4 C 3 phase however noticeable segregation of this phase is not identified. In a-AlBN, a small segregation of nanoscale w-AlN-like domains was revealed. The phonon spectra of the amorphous samples consist of one broad band spreading up to 39 THz. Hardness, ideal tensile strength, Debye temperature, and fracture toughness of the alloys are in the range 7.1–9.1 GPa, 9.2–20.1 GPa, 745–789 K and 1.43–1.46 mPa m 1 / 2 , respectively. Crystalline AlB 2 is predicted to be closer to a brittle material, whereas the amorphous alloys will exhibit ductile behavior. All the amorphous samples should exhibit semiconducting properties with a predicted mobility gap in the range of 1.52–3.03 eV.

SmCo5 permanent magnets exhibit enormous uniaxial magnetocrystalline anisotropy energy and have a high Curie temperature. However, their low energy product is a significant deficiency. To increase the energy product in SmCo5, we propose substituting cobalt with iron, that has a much larger magnetic moment, in a SmCoNiFe3 magnet where nickel is used as a thermodynamic stabilizer.

Single-track laser melting experiments were performed on bulk Ti-Nb alloys to explore process parameters and the resultant macroscopic structure and microstructure. The microstructures in Ti-20Nb and Ti-50Nb (at.%) alloys exhibited cellular growth during rapid solidification, with average cell size of approximately 0.5 µm. Solidification velocities during cellular growth were calculated from images of melt tracks. Measurements of the composition in the cellular and intercellular regions revealed nonequilibrium partitioning and its dependence on velocity during rapid solidification. Experimental results were used to benchmark a phase-field model to describe rapid solidification under conditions relevant to additive manufacturing.

Up to date, the electronic structure properties of amorphous lanthanum hexaboride, a-LaB6, were not yet investigated, and the thermodynamic and mechanical properties of crystalline lanthanum hexaboride (c-LaB6) were studied incompletely. The goal of this work was to fill these gaps in the study of lanthanum hexaborides. The electronic and phonon structures, thermodynamic and mechanical properties of both crystalline and amorphous lanthanum hexaborides (c-LaB6, a-LaB6, respectively) were investigated within the density functional theory. An amorphyzation of c-LaB6 gives rise to the metal – semiconductor transition. The thermal conductivity decreases on going from c-LaB6 to a-LaB6. The elastic moduli, hardness, ideal tensile and shear strengths of a-LaB6 are significantly lower compared to those of the crystalline counterpart, despite the formation of the icosahedron-like boron network in the amorphous phase. For c-LaB6, the stable boron octahedrons are preserved after the failure under tensile and shear strains. The peculiarity in the temperature dependence of heat capacity, Cp(T), at 50 K is explained by the availability of a sharp peak at 100 cm−1 in the phonon density of states of c-LaB6. An analysis of the Fermi surface indicates that this peak is not related to the shape of the Fermi surface, and is caused by the vibration of lanthanum atoms. In the phonon spectrum of a-LaB6, the peak at 100 cm−1 is significantly broader than in the spectrum of c-LaB6, for which reason the anomaly in the Cp(T) dependence of a-LaB6 does not appear. The calculated characteristics are in good agreement with the available experimental data.

First-principles calculations were carried out to study the hypothetical MoC, Mo2C, Mo3C2 and random MoCx, x = 1.0, 0.875, 0.75 and 0.5 phases, and those that were experimentally verified, as well as the random cubic and hexagonal TiC–MoC and cubic and orthorhombic Ti2C–Mo2C solid solutions (alloys). The electronic and phonon structures, formation energy, elastic constants and moduli, hardness, Debye temperature, fracture toughness and stress-strain relation for these structures were calculated in order to understand the differences in phase stability; to explain their properties; and to predict possible new stable phases. The phase diagrams of the Mo–C system for three compositions, 67 at.% Mo + 33 at.% C, 60 at.% Mo + 40 at.% C and 50 at.% Mo + 50 at.% C, were built in the temperature range of 0–4000 K. First-principles molecular dynamics simulations and the group-theoretical analysis are used to identify the plausible mechanisms of the temperature-induced structural transformations in the α-, γ- and γ’-phases of MoC. The composition dependence of the mechanical characteristics of the solid solutions was found to have an extremal character, and in particular a maximum hardness for the cubic Ti0.75Mo0.25C (27.2 GPa) and orthorhombic Ti0.5Mo1.5C (14.6 GPa) alloys. The theoretical phase stability diagrams for the Mo–C system and Ti–Mo–C alloys contain not only the structures experimentally observed but also hypothetical phases, and the available experimental properties were reproduced and explained.

First-principles calculations based on density functional theory and ultra-soft pseudo-potentials were carried out to investigate electronic, mechanical, and thermodynamic properties of Ti-Nb-B2 solid solutions. The mixing energy is found to be negative for all compositions indicating that formation of the solid solutions is energetically favorable. An analysis of the electronic structure shows that the Ti-Nb interactions are responsible for the stabilization of the solid solutions. A non-monotonic change of the density of states at the Fermi level was revealed. Despite the fact that the bulk modulus of TiB2 is lower compared to that of NbB2, calculated elastic constants, hardness and ideal shear strength gradually decrease on going from TiB2 to NbB2. The correlation between these values and the mixing energy is not observed. The calculated phonon spectra and the thermodynamic characteristics indicate that the thermodynamical properties of the solid solutions will change gradually between TiB2 and NbB2. The results obtained are compared with available experimental data.

The Thermodynamics of Advanced Fuels – International Database (TAF-ID) was developed using the Calphad method to provide a computational tool to perform thermodynamic calculations on nuclear fuel materials under normal and off-normal conditions. Different kinds of fuels are considered: oxide, metallic, carbide and nitride fuels. Many fission products are introduced as well as structural materials (e.g., zirconium, steel, concrete, SiC) and absorbers (e.g., B4C), in order to investigate the thermochemistry of irradiated fuels and to predict their chemical interaction with the surrounding materials. The approach to develop the database and the models implemented in the database are described. Examples of models for key chemical systems are presented. Finally, a few examples of application calculations on severe accidents with UO2 fuels, irradiated fuel chemistry of MOX and metallic fuels and metallic fuel/cladding interaction show how this tool can be used. To validate the database, the calculations are compared to the available experimental data. A good agreement is obtained which gives confidence in the maturity degree and quality of the TAF-ID database. The working version is only accessible to the participants of the TAF-ID project (Canada, France, Japan, the Netherlands, Republic of Korea, United Kingdom, USA). A public version is accessible by all the NEA countries. The current version contains models on the Am–Fe, Am–Np, Am-O-Pu, Am–U, Am–Zr, C–O–U-Pu, Cr–U, Np–U, Np–Zr, O–U–Zr, Re–U, Ru–U, Si–U, Ti–U, U-Pu-Zr, U–W systems. It is progressively extended with our published assessments. Information on how to join the project is available on the website: https://www.oecd-nea.org/science/taf-id/.

The interaction of actinides and actinide alloys such as the &delta, stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is presented which covers the elements: Pu, U, Fe, Ga across their whole composition and temperature ranges. The phase diagram and thermodynamic properties of plutonium-iron (Pu-Fe) and uranium-iron (U-Fe) systems are successfully reassessed, with emphasis on the actinide rich side. Density functional theory (DFT) calculations are performed to validate the stability of the stoichiometric (Pu,U)6Fe and (Pu,U)Fe2 compounds by computing their formation enthalpies. These data are combined to construct the Pu-U-Fe ternary phase diagram. The thermodynamic assessment of Fe-Ga is presented for the first time and application to the quaternary Pu-U-Fe-Ga system is discussed.

The stability, electronic and phonon structures, mechanical and thermodynamic properties as well optical spectra of the Ti1−xZrxB2 solid solutions were investigated in the framework of a first-principles approach. The miscibility gap was predicted with the consolute temperature TC = 1973 K and composition xC = 0.4. The negative deviation of the calculated bulk, shear, Young moduli, Debye temperature, Vickers hardness and fracture toughness from the mixing rule is observed. The ideal shear stress of 41.1 GPa for Ti0.5Zr0.5B2 was found to be lower compared to that for TiB2 (43.5 GPa) and ZrB2 (43.1 GPa). The calculated elastic moduli and Poisson ratio exhibit the spatial anisotropy inherent to hexagonal structures. It was shown that the thermodynamic characteristics of the Zr-rich solid solutions could be well reproduced in a temperature range up to 1000–1400 K using the harmonic approximation. The calculated dielectric constants e R ( ω ) and e I ( ω ) , and optical reflectivity spectra R ( ω ) for Ti1−xZrxB2 were analyzed in comparison with available optical spectra of parent diborides from other authors.

In this work, thermodynamic and kinetic diffusivities of uranium–niobium (U–Nb) are re-assessed by means of the CALPHAD (CALculation of PHAse Diagram) methodology. In order to improve the consistency and reliability of the assessments, first-principles calculations are coupled with CALPHAD. In particular, heats of formation of γ-U–Nb are estimated and verified using various density-functional theory (DFT) approaches. These thermochemistry data are then used as constraints to guide the thermodynamic optimization process in such a way that the mutual-consistency between first-principles calculations and CALPHAD assessment is satisfactory. In addition, long-term aging experiments are conducted in order to generate new phase equilibria data at the γ 2 / α + γ 2 boundary. These data are meant to verify the thermodynamic model. Assessment results are generally in good agreement with experiments and previous calculations, without showing the artifacts that were observed in previous modeling. The mutual-consistent thermodynamic description is then used to evaluate atomic mobility and diffusivity of γ-U–Nb. Finally, Bayesian analysis is conducted to evaluate the uncertainty of the thermodynamic model and its impact on the system's phase stability.

A newly developed self-consistent CALPHAD thermodynamic database involving Al, Am, Ga, Pu, and U is presented. A first optimization of the slightly characterized Am-Al and completely unknown Am-Ga phase diagrams is proposed. To this end, phase diagram features as crystal structures, stoichiometric compounds, solubility limits, and melting temperatures have been studied along the U-Al → Pu-Al → Am-Al, and U-Ga → Pu-Ga → Am-Ga series, and the thermodynamic assessments involving Al and Ga alloying are compared. In addition, two distinct optimizations of the Pu-Al phase diagram are proposed to account for the low temperature and Pu-rich region controversy. The previously assessed thermodynamics of the other binary systems (Am-Pu, Am-U, Pu-U, and Al-Ga) is also included in the database and is briefly described in the present work. Finally, predictions on phase stability of ternary and quaternary systems of interest are reported to check the consistency of the database.

The microstructures of rapidly solidified U-6wt%Nb powder particles synthesized by centrifugal atomization were characterized using scanning electron microscopy and transmission electron microscopy. Observed variations in microstructure are related to particle sizes. All of the powder particles exhibited a two-zone microstructure. The formation of this two-zone microstructure is described by a transition from solidification controlled by internal heat flow and high solidification rate during recalescence (micro-segregation-free or partitionless growth) to solidification controlled by external heat flow with slower solidification rates (dendritic growth with solute redistribution). The extent of partitionless solidification increased with decreasing particle size due to larger undercoolings in smaller particles prior to solidification. The metastable phases that formed are related to variations in Nb concentration across the particles. The microstructures of the powders were heavily twinned.

U-Nb’s discontinuous precipitation, γ matrix bcc → α cellular orth + γ cellular ′ bcc , is intriguing in the sense that it allows formation and growth of the metastable γ ′ phase during the course of its occurrence. Previous attempts to explain the thermodynamic origin of U-Nb’s discontinuous precipitation hypothesized that the energy of α forms an intermediate common tangent with the first potential of the double-well energy of γ at the γ ′ composition. In this work, we examine different possible mechanisms by which the discontinuous precipitation product in the U-Nb system can be stabilized. We put forward a mechanism by which the bulk free energy of the γ can develop a non-monotonic dependency with composition. Additionally we posit that local contributions due to lattice mismatch between the α and γ phases may be responsible for the generation of metastable states that may stabilized by thermodyna mics as well as by kinetics. Our work suggests that local misfit strain tends to play a crucial role in the growth of the discontinuous precipitation product. Depending on the magnitude of strain developed at the α / γ ′ interfaces, either an increasing γ ′ composition or a random distribution of γ ′ compositions around the equiatomic value with respect to increasing temperature could be expected. Moreover, we show how it is possible to stabilize the discontinuous precipitation front through highly anisotropic and fast interface diffusion.

Phase diagram and thermodynamic properties of the Am–U system, that are experimentally unknown, are calculated using the CALPHAD method with input from ab initio electronic-structure calculations for the fcc and bcc phases. A strong tendency toward phase separation across the whole composition range is predicted. In addition, ab initio informed Pu–U and Am–Pu thermodynamic assessments are combined to build a Pu–U–Am thermodynamic database. Regarding the Pu-rich corner of the ternary system, predictions indicate that Am acts as a powerful δ -Pu (fcc) stabilizer. In the U-rich corner, similar predictions are made but to a lesser extent. In both cases, the bcc phase is destabilized and the fcc phase is enhanced. Finally, results and methodology are discussed and compared with previous assessments and guidelines are provided for further experimental studies.

TiN/SiN x heterostructures with one monolayer of the interfacial SiN x have been investigated in the framework of first-principles molecular dynamics calculations in the temperature range of 0 to 1400 K with subsequent static relaxation. The atomic configurations, thermal stability and stress–strain relations have been calculated. Among the heterostructures studied, only the TiN(111)/SiN/TiN(111) and TiN(111)/Si 2 N 3 /TiN(111) ones are thermally stable. Upon tensile load, decohesion occurs between the Ti N bonds adjacent to the SiN x interfacial layer for TiN(001)/SiN/TiN(001) and TiN(111)/Si 2 N 3 /TiN(111) heterostructures, and inside the TiN slab for TiN(001)/Si 3 N 4 /TiN(001) and TiN(110)/SiN/TiN(110) ones. Upon shear, failure occurs in TiN near the interfaces in all the heterostructures, except for the TiN(001)/Si 3 N 4 /TiN(001) one, for which the plastic flow occurs inside the TiN slab. Based on these results we estimate the maximum achievable hardness of nc-TiN/Si 3 N 4 nanocomposites free of impurities to be about 170 GPa.

We propose a new efficient permanent magnet, ${\mathrm{SmCoNiFe}}_{3}$, which is a development of the well-known ${\mathrm{SmCo}}_{5}$ prototype. More modern neodymium magnets of the Nd-Fe-B type have an advantage over ${\mathrm{SmCo}}_{5}$ because of their greater maximum energy products due to their iron-rich stoichiometry. Our new magnet, however, removes most of this disadvantage of ${\mathrm{SmCo}}_{5}$ while preserving its superior high-temperature efficiency over the neodymium magnets. We show by means of first-principles electronic-structure calculations that ${\mathrm{SmCoNiFe}}_{3}$ has very favorable magnetic properties and could therefore potentially replace ${\mathrm{SmCo}}_{5}$ or Nd-Fe-B types in various applications.

Phase diagram and thermodynamic properties of the Plutonium–Uranium (Pu–U) system have been successfully re-assessed using the CALPHAD method with input from ab initio electronic-structure calculations for the bcc phase ( γ -U, ∊ -Pu). Results and methodology are discussed and compared with previous assessments. In addition, the already assessed Pu–Ga (Gallium) and U–Ga data are combined to build the Pu–U–Ga thermodynamic database. The predictions made using this database indicate that a small amount of U impacts the ( δ -Pu) Pu–Ga phase stability by precipitating the complicated η and ζ phases that exist in the Pu–U system. Finally, the present investigation provides guidelines for further experimental studies.

First-principles molecular dynamics simulations of the Pd(0 0 1)/3C–SiC(0 0 1) nano-layered structure were carried out at different temperatures ranging from 300 to 2100 K. Various PdSi (Pnma, Fm 3 ¯ m, P 6 ¯ m2, Pm 3 ¯ m), Pd2Si (P 6 ¯ 2m, P63/mmc, P 3 ¯ m1, P 3 ¯ 1m) and Pd3Si (Pnma, P6322, Pm 3 ¯ m, I4/mmm) structures under pressure were studied to identify the structure of the Pd/Si and Pd/C interfaces in the Pd/SiC systems at high temperatures. It was found that a large atomic mixing at the Pd/Si interface occurred at 1500–1800 K, whereas the Pd/C interface remained sharp even at the highest temperature of 2100 K. At the Pd/C interface, voids and a graphite-like clustering were detected. Palladium and silicon atoms interact at the Pd/Si interface to mostly form C22-Pd2Si and D011-Pd3Si fragments, in agreement with experiment.

First-principles quantum molecular dynamics investigations of TiN(001)/AlN and ZrN(001)/AlN heterostructures with one and two monolayers (1 ML and 2 ML) of AlN interfacial layers were carried out in the temperature range of 0–1400 K with subsequent static relaxation. It is shown that the epitaxially stabilized cubic B1-AlN interfacial layers are preserved in all TiN(001)/AlN heterostructures over the whole temperature range. In the ZrN(001)/AlN heterostructures, the B1-AlN(001) interfacial layer exists at 0 K, but it transforms into a distorted one at 10 K consisting of tetrahedral AlN 4 , octahedral AlN 6 , and AlN 5 units. The thermal stability of the interfaces was investigated by studying the phonon dynamic stability of the B1-AlN phase with different lattice parameters. The calculations showed that the B1-AlN interface should be unstable in ZrN(001)/AlN heterostructures and nanocomposites, and in those based on transition metal nitrides with lattice parameters larger than 4.4 A. Electronic band structure calculations showed that energy gap forms around the Fermi energy for all interfaces. The formation of the interfacial AlN layer in TiN and ZrN crystals reduces their ideal tensile and shear strengths. Upon tensile load, decohesion occurs between Ti (Zr) and N atoms adjacent to the 1 ML AlN interfacial layer, whereas in the case of 2 ML AlN it occurs inside the TiN and ZrN slabs. The experimentally reported strength enhancement in the TiN/AlN and ZrN/AlN heterostructures is attributed to impeding effect of the interfacial layer on the plastic flow.

156 scientists from 24 countries participated in CALPHAD XLI, which was held in Berkeley, California, USA, June 3–8, 2012, with 74 morning and afternoon presentations, and 72 evening presentations. The topics covered during the conference were gathered in five categories: Modeling – Software; Kinetics – Microstructure; CALPHAD Assessments – Experiments; Ab initio; and Nuclear Fuel Materials. In this brief summary, highlights of the conference are presented with titles and abstracts of all presentations.

The microstructures of U–6 wt%Nb powder particles were investigated to assess their use as a distributed fuel phase in dispersion-type nuclear fuels. The powder was produced by centrifugal atomization, leading to rapid solidification of the molten alloy particles. The microstructure of the solidified particles consisted of a dendritic structure comprising metastable α-phase-related dendrites and interdendritic metastable γ 0 phase formation. The relationship between the observed microstructure and processing conditions are discussed.

In this brief review, we show that thermodynamic modeling of complex multicomponent actinide-based alloys is crucial for fuel development and for predicting the impact of evolving fuel chemistry with time on materials performance. With input from energetics and equilibrium properties of alloys from ab initio electronic-structure calculations, within the framework of density-functional theory, the CALPHAD methodology is a viable approach to thermodynamic assessment for this class of materials. Despite the limited availability of experimental thermodynamic data, this approach can predict important features in the phase diagram and, perhaps more importantly, guide and motivate further experiments for validating the methodology and the data for subsequent modeling of materials performance on a higher level.

First-principles calculations were carried out in order to investigate the stability and properties of the random Ti1-xSixC solid solutions (alloys) with both the B1 and B3 structures. Lattice parameter, total energy, formation energy, phonon spectra, and elastic properties were studied as functions of composition. The phase diagram, in particular, binodal and spinodal curves were calculated. It was established that at 0 K the B1 alloys are energetically favorable at 0 ≤ x

The phase transitions in the rock-salt type SiC (B1-SiC) under decompression are studied in the framework of first-principles molecular dynamics simulations up to room temperature. The transformation pathways were determined based on an analysis of the symmetry and phonon spectra of high-symmetry transient structures identified in the simulations. The plausible pathways of the transformation of B1-SiC into the 3C-, 2H-, 4H-, 12R-SiC polytypes were suggested. The transformation paths were found to depend on both the availability of soft phonon modes in an unreconstructed phase and the initial conditions of the simulation. It is shown that an increase in cell volume at decompression leads to the condensation of a certain phonon mode. As a result, an intermediate state forms due to the atomic displacements and to subsequent strains related to this mode. All the decompressed structures were compressed back under pressure of 120-250 GPa depending on the type of the decompressed phase and simulation temperature that was in the range of 300-1200 K. The suggested scheme of structural identification can be used to determine the transition paths for the structural transformations of other similar structures under pressure.

First-principles calculations were carried out to investigate electronic structure, phase stability, elastic properties, Debye temperature, and hardness of the TiC–HfC and TiC–TaC random solid solutions as functions of composition. For TiC–HfC, significant miscibility gaps with consolute temperatures about 1975 K are revealed in the binodal and spinodal curves. The negative deviation of the elastic moduli and hardness from linearity are obtained for TiC–HfC, whereas, for TiC–TaC, these characteristics are above their linear interpolation between the end members. Concentration dependences of the Debye temperature for both systems have a negative curvature. To clarify a possible mechanism of stabilization or destabilization of these solid solutions and other similar carbide systems, mixing energies of the M1 1 − xM2 xC alloys, where M1 and M2 are the transition metals of the IV, V, and partially VI groups, were calculated. It is found that the behavior of mixing energies for the M1C–M2C alloys with M1 and M2 of different groups depending on composition is determined by the difference between cell volumes of the end members, Δ V C, the degree of occupancy of the metal band, and the shape of the density of states in the metal band region. Values of Δ V C mainly are responsible for positive mixing energies of the alloys with valence electron concentrations (VECs) equal to 8 and 9 for which occupancy of the metal band weakly changes with composition. The maximum hardness of the solid solutions for which VECs of the end members are different is predicted to be reached for the compositions with VECs = 8.5–8.75.

A numerical method for the simulation of microstructure evolution during the solidification of an alloy is presented. The approach is based on a phase-field model including a phase variable, an orientation variable given by a quaternion, the alloy composition and a uniform temperature field. Energies and diffusion coefficients used in the model rely on thermodynamic and kinetic databases in the framework of the CALPHAD methodology. The numerical approach is based on a finite volume discretization and an implicit time-stepping algorithm. Numerical results for solidification and accompanying coring effect in a Au–Ni alloy are used to illustrate the methodology.

Progress in materials science through thermodynamic modelling may rest crucially on access to a database, such as that developed by Scientific Group Thermodata Europe (SGTE) around 1990. It gives the Gibbs energy G(T)of the elements in the form of series as a function of temperature, i.e. essentially a curve fitting to experimental data. In the light of progress in theoretical understanding and first-principles calculation methods, the possibility for an improved database description of the thermodynamics of the elements has become evident. It is the purpose of this paper to provide a framework for such work. Lattice vibrations, which usually give the major contribution to G(T), are treated in some detail with a discussion of neutron scattering studies of anharmonicity in aluminium, first-principles calculations including ab initio molecular dynamics (AIMD), and the strength and weakness of analytic model representations of data. Similarly, electronic contributions to G(T) are treated on the basis of the density of states N(E) for metals, with emphasis on effects at high T. Further, we consider G(T) below 300 K, which is not covered by SGTE. Other parts in the paper discuss metastable and dynamically unstable lattices, G(T) in the region of superheated solids and the requirement on a database in the calculation of phase diagrams.

Uranium–zirconium alloys are being investigated for use in ultrahigh burn-up, metallic inert matrix nuclear fuels. Characterization of these alloys in the transmission electron microscope with spatial resolutions that are inaccessible by other techniques shows that the orthorhombic α and hexagonal, intermetallic δ phases coexist in an as-cast uranium-rich U-10 wt.% Zr alloy. Analyses reveal the chemistries of and crystallographic relationship between the two phases.

Density-functional theory, previously used to describe phase equilibria in the γ-U–Mo alloys [A. Landa, P. Soderlind, P.E.A. Turchi, J. Nucl. Mater. 414 (2011) 132], is extended to study ground-state properties of the bcc-based (γ) X–Mo (X = Np, Pu, and Am) solid solutions. We discuss how the heat of formation correlates with the charge transfer between the alloy components, and how magnetism influences the deviation from Vegard’s law for the equilibrium atomic volume.

Input from Density Functional Theory (DFT) calculations is used to understand phase equilibria in a binary metallic alloy fuel system: U–Ti. The CALPHAD approach is employed to calculate a U–Ti phase diagram that is consistent not only with experimental data but also—more importantly—with thermodynamic data from DFT calculations: heat of formation of γ(bcc)-U–Ti alloys as a function of composition, and formation enthalpy of the δ-U2Ti compound. Three DFT-based electronic structure methods are utilized: SR-KKR-ASA-CPA, SR-EMTO-CPA, and FPLMTO-SQS, and the use of derived ab initio data avoids the manifestation of unreasonable or inaccurate phase stabilities that result from an otherwise unconstrained Gibbs energy minimization within the CALPHAD approach. We also investigate phase formation of the δ-U2Ti phase in the U–Ti system, that stabilizes in the same C32 structure as other binary metallic fuel alloys such as U–Zr and Np–Zr.

Based on the CALPHAD approach, thermodynamic properties and phase diagram of the Am–Pu system are assessed with input from results of ab initio electronic-structure calculations within the framework of density-functional theory. Despite the limited availability of experimental data on this binary system, thermodynamic assessment has been performed and two phase diagrams are proposed that make distinction at high temperature between the relative stability of the bcc phase and the liquid state. Our investigation provides guidance and motivates further experimental studies.

Density-functional theory previously used to describe phase equilibria in U-Zr alloys [A. Landa, P. Soederlind, P.E.A. Turchi, J. Alloys Comp. 478 (2009) 103-110] is extended to investigate the ground-state properties of U-Mo solid solutions. We discuss how the heat of formation in both alloys correlates with the charge transfer between the alloy components, and how the specific behavior of the density of states in the vicinity of the Fermi level promotes the stabilization of the U{sub 2}Mo compound. Our calculations prove that, due to the existence of a single {gamma}-phase over the typical fuel operation temperatures, {gamma}-U-Mo alloys should indeed have much lower constituent redistribution than {gamma}-U-Zr alloys for which binodal decomposition causes a high degree of constituent redistribution.

A thermodynamic model of the Np–Zr system is developed using the CALPHAD method, and a review of previous work performed on this system is presented here. In general, results obtained are in good agreement with those proposed from experimental observations. It is found that the nature of reactivity of Np with Zr, is different from that of U and Pu: an expected elevation of melting point of Np–Zr alloys was not seen and a miscibility gap existed between the high-temperature bcc phases of Np and Zr. Formation enthalpy of the bcc phase obtained from the model is compared with results from KKR–ASA–CPA calculations. Lattice stabilities of various phases in the system are compared to values obtained from first-principles LDA and GGA calculations. The δ-NpZr2 phase is modeled as a non-stoichiometric phase with a C32 structure, similar to what has been determined for the δ-phase in the U–Zr system. This phase is analogous to ω-phase in pure Zr, which is stabilized at high pressures. Two different possibilities for stability of the δ and ω phases have been proposed in the present work. Finally, calculated changes in enthalpy versus temperature are plotted for two alloys to guide future experimental work in resolving important issues in this system.

Density-functional theory previously used to describe phase equilibria in the gamma-Pu-U-Zr alloys [A. Landa, P. Soderlind, PEA. Turchi, L. Vitos, A. Ruban, J. Nucl. Mater. 385 (2009) 68; A. Landa, ...

Density-functional theory, previously used to describe phase equilibria in the U–Zr alloys [A. Landa, P. Soderlind, P.E.A. Turchi, L. Vitos, A. Ruban, J. Nucl. Mater. 385 (2009) 68], is applied to study ground-state properties of the bcc U–Pu–Zr solid solutions. Calculated heats of formation of the Pu–U and Pu–Zr alloys are in a good agreement with CALPHAD assessments. We found that account for spin–orbit coupling is important for successful description of Pu-containing alloys.

Molten salt with dissolved uranium is being considered for the Laser Inertial Confinement Fusion Fission Energy (LIFE) fission blanket as a backup in case a solid-fuel version cannot meet the performance objectives, for example because of radiation damage of the solid materials. Molten salt is not damaged by radiation and therefore could likely achieve the desired high burnup (>99%) of heavy atoms of 238 U. A perceived disadvantage is the possibility that the circulating molten salt could lend itself to misuse (proliferation) by making separation of fissile material easier than for the solid-fuel case. The molten salt composition being considered is the eutectic mixture of 73 mol% LiF and 27 mol% UF4, whose melting point is 490°C. The use of 232 Th as a fuel is also being studied. ( 232 Th does not produce Pu under neutron irradiation.) The temperature of the molten salt would be ~550°C at the inlet (60°C above the solidus temperature) and ~650°C at the outlet. Mixtures of U and Th are being considered. To minimize corrosion of structural materials, the molten salt would also contain a small amount (~1 mol%) of UF3. The same beryllium neutron multiplier could be used as in the solid fuel case; alternatively, a liquid lithium or liquid lead multiplier could be used. Insuring that the solubility of Pu 3+ in the melt is not exceeded is a design criterion. To mitigate corrosion of the steel, a refractory coating such as tungsten similar to the first wall facing the fusion source is suggested in the highneutron-flux regions; and in low-neutron-flux regions, including the piping and heat exchangers, a nickel alloy, Hastelloy, would be used. These material choices parallel those made for the Molten Salt Reactor Experiment (MSRE) at ORNL. The nuclear performance is better than the solid fuel case. At the beginning of life, the tritium breeding ratio is unity and the plutonium plus 233 U

Density-functional formalism is applied to study the phase equilibria in the U–Zr system. The obtained ground-state properties of the γ (bcc) and δ (C32) phases are in good agreement with experimental data. The decomposition curve for the γ -based U–Zr solutions is calculated. Our calculations confirm that experimentally observed “partial” ordering of the alloy components in the δ -UZr 2 (AlB 2 ) phase, in which Zr atoms occupy the “Al” position and the two “B” sites are randomly shared by the U and Zr atoms, is the most energetically favorable within the C32 structure. We argue that stabilization of the δ -UZr 2 phase relative to the α -Zr (hcp) structure is due to an increase of the Zr d -band occupancy that occurs when U is alloyed with Zr. A comparison with stabilization of the ω -phase (also C32) in Zr under compression is made.

The thermodynamic quantities of high temperature metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by using the tetrahedron cluster approximation of the cluster variation method (CVM). The energetics of the binary (Ta–W and Mo–Ta) alloys are treated within the framework of the first-principles TB-LMTO (tight-binding linear muffin tin orbital) method coupled to CPA (coherent potential approximation) and GPM (generalized perturbation method). The equilibrium phase diagrams are calculated for the refractory Ta–W and Mo–Ta bcc alloys. In addition, the mechanical properties, i.e., temperature dependence of the elastic moduli C11, C12 and C44 and those of the ideal tensile and shear strengths of the bcc Ta–W and Ta-Mo alloys have been also studied.

The thermodynamic properties and phase transformations of metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The thermodynamic quantities, like thermal lattice expansion coefficients, specific heats, Grüneisen constants, elastic constants calculated by using the SMM are compared with those of other theoretical schemes and the experimental results. The hcp-bcc structural phase transformations observed for IVB elements, Ti, Zr and Hf, are discussed in terms of the anharmonicity of thermal lattice vibrations. The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys. In addition, the temperature dependence of the elastic moduli C11, C12 and C14 and those of the ideal tensile and shear strengths of the bcc elements Mo, Ta and W are studied: We also discuss the melting transitions of metals and alloys within the framework of the SMM and estimate the melting temperatures through the limiting temperature of the crystalline stability.

The thermodynamic properties of high temperature metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by using the tetrahedron cluster approximation of the cluster variation method (CVM). The energetics of the binary (Ta-W and Mo-Ta) alloys are treated within the framework of the first-principles TB-LMTO (tight-binding linear muffin tin orbital) method coupled to CPA (coherent potential approximation) and GPM (generalized perturbation method). The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys.

CALPHAD assessment of the thermodynamic properties of a series of Pu-based alloys is briefly presented together with some results on the kinetics of phase formation and transformations in Pu–Ga alloys.