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Enthalpy of mixing is among the key materials parameters to determine phase stability and phase transformations in solid solutions. The possibility to predict it from first principles in the framework of the density functional theory is one of the corner stones of the modern materials modeling and the future data-driven materials design. Here we have considered body-centered cubic (bcc) Ti-V alloys, a system with high potential for aerospace, automotive biomedical and energy applications, which is known to exhibit the dynamical instability of the crystal lattice for Ti-rich alloys at low temperature. We have calculated the mixing enthalpies ΔH of bcc Ti-V alloys in the whole interval of concentration at high temperature using ab initio molecular dynamics (AIMD) simulations. A comparison with state-of-the-art static calculations at temperature 0 K shows drastic difference between the two methods: while AIMD predicts positive values of ΔH in the whole range of concentrations, the static zero-temperature simulations result in negative values of ΔH for Ti-rich alloys. We have measured the mixing enthalpy of bcc Ti-V alloys experimentally at 1073 K using an isoperibol high temperature Tian-Calvet calorimeter and found that the enthalpies are positive, in agreement with our finite temperature AIMD calculations. We attribute the failure of the standard static calculations of ΔH to lattice distortions associated with the dynamical instability of bcc Ti-V alloys at zero temperature and argue that the effect should be generally important in theoretical predictions of thermodynamic properties, especially for systems with dynamical instability.

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... Jain et al. [47] have reported the activity of V-4Ti alloy. Skripnyak et al. [48] have measured the mixing enthalpy of bcc Ti-V alloys experimentally at 1073 K and found enthalpies to be positive. DFT-based FP methods based were used to calculate thermodynamic data for this system by various researchers. ...

... DFT-based FP methods based were used to calculate thermodynamic data for this system by various researchers. [39,40,42,48] The Ti-V system was optimized by Murray, [43] Saunders, [49] and Ghosh. [50] ...

... Enthalpy of mixing for the Ti-V bcc solutions calculated using SQS is shown in Fig. 2. Results are comparable with the relaxed SQS results from [48] and. [40] The Ti-V system shows the dynamical instability of the crystal lattice for Tirich alloys at low temperatures. ...

Experimental evidence for short-range order (SRO) has been discovered for many alloys, and it affects several physical and mechanical properties of the alloys. Hence, treatment of SRO in the thermodynamic modeling of the phases is required for reliable description of alloy systems. In addition, the availability of first-principles-based thermochemical data has created the possibility for further improving existing thermodynamic descriptions. The present work uses the cluster expansion and cluster variation methods (CE-CVM) for the bcc solid phase to address these issues. Three binary Ti-X (X = Nb, V, Zr) alloys were thermodynamically accessed using existing experimental and calculated first-principles-based thermochemical data. Density functional theory (DFT), along with techniques, such as CE and special quasirandom structures (SQS), were used to calculate thermochemical data. Thermodynamic descriptions of binary Ti-X systems were obtained by optimizing all the available experimental, first-principles-based thermochemical, and phase diagram data. The phase diagram and thermodynamic properties calculated using model parameters agree well with the experimental data. The SRO of the bcc solid phase at various compositions and temperatures were determined using optimized model parameters. While the experimental determination of SRO remains a challenge, a CE-CVM based modeling approach offers a viable option for determining the SRO states of the alloys.

... Titanium and its alloys are widely used in high-temperature heating building materials. The Ti-V alloy with a BCC structure has been widely used in the development of high-temperature structural components in nuclear reactors and automotive industries and aerospace [1]. In principle, pure BCC titanium may be a good choice for high temperature applications, but it only exists at high temperatures above 1155 K, and it is dynamically unstable at low temperatures. ...

... The reported experimental Ti-V phase diagrams can be divided into two groups: with and without the isostructural phase separation line for the BCC solid solutions, respectively. Murray et al and Nakano et al pointed out that there is a reaction at 948 K: β-Ti,V=α-Ti+V [1]. However, Wei and Fowler [3] believed that this reaction was caused by oxygen impurities and pointed out that there is no stable monotectoid reaction was likely to exist in this system. ...

... powerful tool for generation of reliable data on thermodynamic properties [1,[5][6][7]. However, quantum mechanics cannot be used in isolation because it needs to consider the effect of electrons' behavior [8]. ...

In this paper, molecular dynamics (MD) simulation software LAMMPS is used to simulate the elastic properties and stability of Ti-V single-crystal alloys. The relationship between the elastic constant and the mechanical stability of Ti-V alloy with a body-centered cubic (BCC) structure is studied. The energy relationship between TiV alloys with hexagonal close-packed (HCP) structure and BCC structure are compared, respectively. The effects of temperature, crystal orientations, and V content on the mechanical properties of TiV alloys are calculated under uniaxial tensile test. The results show that both ultimate tensile strength and plasticity of the Ti-V alloy with BCC structure decrease with the increase of temperature and V content, due to the phase transition from the BCC structure to the face-centered cubic (FCC) structure. Finally, it is identified that the modes of the transformation from BCC structure to FCC structure during the tensile process are BCC(100)//FCC(110), BCC(010)//FCC(1 $\bar{1}$ 0).

... Вид концентрационных зависимостей энергии смешения позволяет прогнозировать составы и размеры биметаллических наночастиц, которые могут проявлять нестабильность. В частности, нестабильность характерна для биметаллических наночастиц Ti V с высоким содержанием титана, что подтверждается данными для макроскопических сплавов [19][20][21]. Кроме того, для биметаллических наносистем с размерным несоответствием компонентов характерна асимметричность отдельных концентрационных зависимостей энергии In this work, of the structure formation was investigated using ,, Au Ag Ti Al Ti V bimetallic nanoparticles as the patterns. These bimetallic nanoparticles have different atomic size mismatches and different crystallization temperatures. ...

В данной работе исследуются закономерности структурообразования на примере биметаллических наночастиц Au - Ag, Ti - Al, Ti - V. Данные биметаллические наночастицы обладают различным размерным несоответствием и различной температурой кристаллизации. Проведены серии молекулярно-динамических экспериментов, по результатам которых проанализированы конечные конфигурации с наименьшей энергией и получены концентрационные зависимости энергии смешения. Анализ концентрационных зависимостей энергии смешения позволяет прогнозировать составы и размеры биметаллических наночастиц, которые могут проявлять нестабильность, как например для биметаллических наночастиц Ti - V. Асимметричность отдельных концентрационных зависимостей энергии смешения свидетельствуют о специфических структурных превращениях, характерных именно для данного состава и размера. Установлено, что для биметаллических наночастиц Au - Ag, Ti - Al характерна структурная сегрегация, и она активно проявляется при малых концентрациях более легкоплавкого компонента. Конкурирующими фазами в данном случае выступают ГЦК и ГПУ фазы. Кроме того, для средних из рассматриваемых в статье размеров исследована зависимость температуры кристаллизации от состава биметаллических наночастиц.
In this work, of the structure formation was investigated using Au - Ag, Ti - Al, Ti - V bimetallic nanoparticles as the patterns. These bimetallic nanoparticles have different atomic size mismatches and different crystallization temperatures. A series of molecular dynamics experiments was carried out. Based on their results, the final configurations with the lowest energy were analyzed and the concentration dependences of the mixing energy were obtained. An analysis of the concentration dependences of the mixing energy makes it possible to predict the compositions and sizes of bimetallic nanoparticles, which can exhibit instability, such as for Ti - V bimetallic nanoparticles. The asymmetry of individual concentration dependences of the mixing energy is evidence of specific structural transformations characteristic for the given composition and size. It has been established that structural segregation is characteristic for Au - Ag,Ti - Al bimetallic nanoparticles and it is actively manifested at low concentrations of a more low-melting component. The competing phases in this case are fcc and hcp phases. In addition, for the average sizes considered in the article, the dependence of the crystallization temperature on the composition of bimetallic nanoparticles was investigated.

... Note that the experimental elastic constants for V 15 Ti-bcc alloys were extrapolated from pure V and V-27%Ti [90] alloys by linear interpolation method. For the V 15 Ti-bcc alloy, the LS potential [91] overestimated the elastic constant C 44 (69 GPa) compared with the experimental values (43 GPa) [90] by 60%. While the predicted results of the current potential and the IFS Table 5 Calculated the elastic constants ( C 11 , C 12 and C 44 ) and the bulk modulus ( B ) of V 15 Ti and VTa 2 alloys by the present potential, and as compared to the DFT, experiments and other potential predicted results. ...

Vanadium (V)-based alloys are potential candidates for structural materials of fusion reactors because of their excellent properties; recently, the V–Ti–Ta alloy has received considerable attention. The irradiation-resistant performance is significant for the development and application of fusion reactor materials. In this study, combining with our previously developed potentials of V and Ta, we developed the V-Ti-Ta interatomic potential based on the Finnis–Sinclair (FS) formalism, which is an important step towards an atomic-scale investigation of V-based alloys. The potential parameters were determined by fitting to a large database of experimental data and density functional theory (DFT) calculations. The formation energies of vacancy and self-interstitial atoms, as well as the pressure-volume relation obtained from the present Ti potential, were well reproduced. The typical defect energies of solute atoms Ti and Ta in the V matrix and Ti and V in the Ta matrix, such as the formation energies of substitutional solute atoms, binding energies between solute atoms and point defects, agree well with DFT results. Thus, the developed potentials are expected to be suitable for atomistic simulations of point defects evolution in the V-Ti-Ta ternary system.

... E form is calculated by comparing the Hf x M 1-x N ground-state energy with those of isostructural (cubic) binary HfN and MN. Crystalline structures before geometrical optimisation (closer to results of ab-initio molecular dynamics and experiments for the solid solution considered in [73] ; upper panels and solid symbols) and after geometrical optimisation (structural relaxation caused mainly by different atomic sizes of Hf and M; lower panels and open symbols) exhibit different E form . Note that the distribution corresponding to the 8-atom cubic simulation cell prevents any relaxation since its symmetry results in zero forces acting on all atoms. ...

Amorphous HfMSiBCN materials (M = Y, Ho, Ta, Mo or an enhanced Hf content instead of any other M) are investigated by ab-initio calculations and magnetron sputtering. We focus on combining the high-temperature stability and oxidation resistance of these materials with optimised mechanical, optical and electrical properties. First, we predict the corresponding trends by calculating the effect of the M choice and fraction on formation energy (Eform) and mechanical properties of MN and HfxM1–xN crystals. We discuss the dependence of Eform(HfxM1–xN) on the crystal structure and the distribution of Hf and M in the metal sublattice. The mechanical properties calculated for MN correlate with those measured for HfMSiBCN. The driving force towards N incorporation, decreasing with the periodic-table group number of M according to the calculated Eform(MN), correlates with the measured increasing electrical conductivity and extinction coefficient of HfMSiBCN. Second, we model the amorphous HfMSiBCN materials themselves by ab-initio molecular dynamics. The calculated band gap, localisation of electronic states and bonding preferences of M also correspond to the increasing metallicity with respect to the periodic-table group number of M and confirm the possibility of predicting the trends in characteristics of HfMSiBCN using those of MN. Third, we study the measured HfMSiBCN properties as functions of each other and identify sputter target compositions leading to hard films with high electrical conductivity at a relatively low extinction coefficient. The results are important for the design of hard, conductive and/or transparent high-temperature coatings.

... This means that bcc-Ti cannot exist at low temperature, but it becomes stable not only dynamically, but also thermodynamically at temperatures above 1155 K (at ambient pressure). Therefore, strictly speaking, any theoretical consideration of bcc Ti and Ti-rich alloys requires finite-temperature simulations [38]. ...

A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et al 2003 Science 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100-1700 K is unique. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft

... This means that bcc-Ti cannot exist at low temperature, but it becomes stable not only dynamically, but also thermodynamically at temperatures above 1155 K (at ambient pressure). Therefore, strictly speaking, any theoretical consideration of bcc Ti and Ti-rich alloys requires finite-temperature simulations [29]. ...

A combination of quantum mechanics calculations with machine learning (ML) techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art {\it ab inito} molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys [T. Sato {\ it et al.}, Science {\bf 300}, 464 (2003)]. Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100--1700 K is unique.

The effects of the dissolution of 3d, 4d, and 5d metals, as well as Al, In, and Sn in the bcc lattice of Zr, were studied within the framework of the electron density functional theory. Using the EMTO-CPA method, we calculated the lattice parameters, enthalpies of mixing, single-crystal elastic constants C11, C12, C44, and C', polycrystalline elastic moduli E, G, and plasticity characteristics of disordered Zr-based bcc alloys over a wide concentration range. The PAW-SQS method was used to study the effects of alloying on the specified properties of bcc Zr-X alloys, where X is a series of 4d elements Nb, Mo, Tc, Ru, Rh and 5d elements Ta, W, Re, Os, Ir for concentration cuts 6.25, 25 and 50 at.%. The analysis of concentration and periodic dependences of properties of alloys, their stability is carried out.

The processes of structure formation in Co-Au and Ti-V metal nanoparticles as well as factors affecting the crystallization process are considered. The objects of the study were Co-Au and Ti-V binary nanoparticles containing N = 400, 800, 1520 and 5000 atoms with the equiatomic composition. The computer experiment was carried out using method of molecular dynamics. The interatomic interaction was described by the tight-binding potential. According to the results of a series of computer experiments, it was found that the main factors influencing the possibility of obtaining crystalline phases are: the cooling rate of binary nanoparticles, their size and the size mismatch of atoms included in the composition, as well as the nature of the interaction of metal atoms. The manifestation of stability/instability in binary nanoparticles may be due to patterns of formation of crystalline phases. Moreover, the tendency to segregate one of the components in a binary system may not be the main factor determining the stability/instability of such a system.

Metal hydride electrodes have been widely used in Ni/MH batteries, but their low-temperature discharge (LTD) performance restricts practical application. Herein, we propose a facile strategy for tuning the La/Ce ratio to prepare metal hydride electrodes for ultra-low-temperature Ni/MH batteries. The enthalpy shifts in the positive direction with a decrease in the La/Ce ratio and the thermodynamic stability decreases. Moreover, the resultant enhanced charge transfer and proton diffusion endows the electrode with impressive kinetics at −40 °C. One novel candidate, namely, La0.55Ce0.37M electrode presents the highest reported capacity of 317.3 mAh g⁻¹ (0.2C) and the highest discharge specific capacity of 27.2 mAh g⁻¹ (1C) even at −40 °C. A commercial-grade AAA nickel-metal hydride battery concomitantly presents the specific capacity of 71 and 456 mAh at a large current of 1000 mA at −40 and −20 °C, respectively. The excellent LTD performance indicates the suitability of this strategy for developing advanced ultra-low-temperature Ni/MH batteries.

The effects of the dissolution of 3d, 4d and 5d metals and Al, Ga, Ge, In and Sn in the bcc Ti lattice (β-phase) were studied within the framework of first-principles calculations. Lattice parameters, mixing enthalpies, single-crystal elastic constants C11, C12, C44 and C', polycrystalline elastic moduli E, G, and plasticity characteristics of bcc Ti-based solid solutions in a wide concentration range up to 50 at. % were investigated using the EMTO-CPA method. The PAW-SQS method was used to study the effects of alloying and local atomic relaxations on the indicated properties of Ti-X bcc alloys, where X is a series of 4d elements Nb, Mo, Tc, Ru, Rh, and 5d elements Ta, W, Re, Os, Ir for the set of concentrations: 6.25, 25 and 50 at. %. The effect of concentration and periodic dependences on the properties of alloys and the dependence of elastic properties on the electronic structure were analyzed. It is shown that the calculated elastic constant C' is a convenient and useful parameter for ranking chemical elements according to the relative strength of the stabilizing effect on the β-phase, in addition, the concentration dependences of C' demonstrate softening with concentration increasing in the case of late transition metals, thereby reflecting the tendency of these metals to form intermetallic compounds with titanium, while early transition metals show a linear grow in stability with increasing concentration.

First principles calculations based on different substitution models are performed to investigate the structural, elastic, thermodynamic, and electronic properties of body-centered cubic (bcc) Zr-Nb alloy which has great potential in biomedicine and nuclear power in the whole interval of concentration. The results show that the calculated lattice parameters decrease linearly with the increase of Nb concentration which are in good accordance with the experimental and other first principles calculations. The structure of bcc Zr is unstable at 0 K, and Nb additions can improve bcc Zr-Nb solid solution mechanical stability. Bcc Zr-Nb disordered solid solution with the relaxed structure deviate from the perfect bcc lattice position and transform into a more stable non-β phase, however, the atoms of the ordered solid solution occupy maintains the ideal sites of bcc structure. The elastic constants Cij, elastic modulus (B, G, E), Poisson’s ratio and elastic anisotropy also have been calculated. When the structure of bcc Zr-Nb alloy is stable, the Nb addition can increase the elastic modulus, B/G ration and Poisson's ratio which will improve the ductility of alloy. The electronic properties have been investigated based on density of states and charge density difference. The bcc Zr-Nb alloy electronic structure is usually composed of metal bonds and covalent bonds, and metal bonds is dominated. Zr50Nb50 has the highest covalent bond ratio. Finally, the thermodynamic properties are evaluated by quasi-Debye model.

We investigate phase stability in all binary alloys comprised of elements from groups 4 (Ti, Zr, Hf), 5 (V, Nb, Ta) and 6 (Cr, Mo, W) of the periodic table. First-principles calculations of the energy landscapes along crystallographic pathways that connect bcc to hcp and bcc to ω show that group 4 elements are very distinct from group 5 and 6 elements. While group 5 and 6 elements are stable in bcc, group 4 elements favor hcp and ω and are predicted to be dynamically unstable in bcc. A comprehensive first-principles investigation of the 36 refractory binary systems using statistical mechanics techniques reveals six distinct classes of alloys, each with a unique phase diagram topology. The predictions of this study are in excellent agreement with previous experimental work. One exception is a class of refractory alloys with high temperature miscibility gaps that are not predicted with the methods used in this work. Our calculations predict the stability of a low-temperature Laves phase in the Nb-V binary that has yet to be observed experimentally. The relationships between alloy chemistry and high-temperature phase stability revealed in this study provide a basis for the systematic design of multicomponent disordered refractory alloys.

Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorganic materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform ‘‘rapid-prototyping’’ of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design.

The effects of solute X (Mo, Nb, V and W) on the phase stability of beta-Ti alloys were studied from first-principles calculations. The first-principles calculations yielded solution enthalpies for hexagonal close-packed (hcp)-Ti35X1 and hcp-X35Ti1 and body-centered cubic (bcc)-Ti26X1 and bcc-X26Ti1 solid solution alloys. The enthalpy curves for the alpha (hcp)- and beta (bcc)-phases of Ti-X alloys were described as a function of the X concentration by using the calculated solution enthalpies and sub-regular solution model. While the enthalpies of the alpha-phases increased with increasing concentrations of Mo, Nb, V and W, the enthalpies of the beta-phases decreased with increasing concentrations. This is consistent with the experimental results, showing that Mo, Nb, V and W are beta-stabilizers. The beta-stabilizing strength of solute elements in Ti alloys is gauged using the experimental critical concentration. We found a good linear correlation between the experimental critical concentration and the theoretical metastable equilibrium concentration at which the enthalpy of the alpha-phase is equal to that of the beta-phase. The metastable equilibrium concentration decreased with the increasing lattice stability of the bcc structure with reference to hcp structure.

High-throughput computational materials design is an emerging area of materials science. By combining advanced thermodynamic and electronic-structure methods with intelligent data mining and database construction, and exploiting the power of current supercomputer architectures, scientists generate, manage and analyse enormous data repositories for the discovery of novel materials. In this Review we provide a current snapshot of this rapidly evolving field, and highlight the challenges and opportunities that lie ahead.

The full-potential Korringa-Kohn-Rostoker Green function method is extended to treat the lattice distortion in the vicinity of a point defect. The method is applied to predict the atomic positions in the neighborhood of d and sp substitutional impurities in Cu. Both the total energy and the Hellmann-Feynman force are used for the calculation of the ground-state configuration, while the semicore states of the impurities are treated as valence states. Our results for the atomic displacements are in very good agreement with the experimental data from extended x-ray-absorption fine-structure and lattice-parameter measurements.

A synergistic approach of thermodynamic and kinetic modeling is applied to the Cr-Ti-V system. To assist the design of (α+β)
and β titanium alloys for structural applications and vanadium alloys for fusion reactor applications, a set of self-consistent
and optimized thermodynamic model parameters is presented to describe the phase equilibria of the Cr-Ti, Cr-V, Ti-V, and Cr-Ti-V
systems. The Laves phases, α-Cr2Ti, β-Cr2Ti, and γ-Cr2Ti, are described by a two-sublattice model assuming antistructure atoms on both sublattices. The calculated thermodynamic
quantities and phase diagrams are in good accord with the corresponding experimental data. To assist the simulation of the
kinetics of diffusional transformations in bodycentered cubic (bcc) alloys, the atomic mobilities of Cr, Ti, and V are modeled.
A set of optimized mobility parameters is given. Very good agreement between the calculated and experimental diffusivities
was found.

We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order N-atoms(3) operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ''metric'' and a special ''preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order N-atoms(2) scaling is found for systems up to 100 electrons. If we take into account that the number of k points can be implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.

Thermodynamic data for the condensed phases of 78 elements as currently used by SGTE (Scientific Group Thermodata Europe) are tabulated. SGTE is a consortium of seven organisations in Western Europe engaged in the compilation of a comprehensive, self consistent and authoritative thermochemical database for inorganic and metallurgical systems. The data are being published here in the hope that they will become widely adopted within the international community as a sound basis for the critical assessment of thermodynamic data, thereby, perhaps, limiting unnecessary duplication of effort. The data for each phase of each element considered aie presented as expressions showing, as a function of temperature, the variation of (a) G-HSER, the Gibbs energy relative to the enthalpy of the “Standard Element Reference” ie the reference phase for the element at 298.15 K and (b) the difference in Gibbs energy between each phase and this reference phase (ie lattice stability). The variation of the heat capacity of the various phases and the Gibbs energy difference between phases are also shown graphically. For certain elements the thermodynamic data have been assessed as a function of pressure as well as temperature. Where appropriate a temperature— pressure phase diagram is also shown.Throughout this paper the thermodynamic data are expressed in terms of J mol−1. The temperatures of transition between phases have been assessed to be consistent with the 1990 International Temperature Scale (ITS90).

An accurate and easily extendable method to deal with lattice dynamics of
solids is offered. It is based on first-principles molecular dynamics
simulations and provides a consistent way to extract the best possible harmonic
- or higher order - potential energy surface at finite temperatures. It is
designed to work even for strongly anharmonic systems where the traditional
quasiharmonic approximation fails. The accuracy and convergence of the method
are controlled in a straightforward way. Excellent agreement of the calculated
phonon dispersion relations at finite temperature with experimental results for
bcc Li and bcc Zr is demonstrated.

Ab initio electronic-structure calculations and the Calphad-type analysis of experimental phase diagrams and other thermodynamic information are known to give conflicting results for the enthalpy of several metastable transition metal phases, e.g., fcc W. We have simultaneously used ab initio total-energy calculations and the cluster expansion as well as Calphad methods in a study of the Pt-W phase diagram. The ab initio calculations show that fcc W is dynamically unstable for all long-wavelength shear modes at T=0 K. Even if fcc W becomes dynamically stable at high temperatures, the enthalpy of fcc W derived from Calphad analyses cannot be compared with the ab initio enthalpy of fcc W without a detailed knowledge of the vibrational entropy. Further, we show that the Calphad method can account for the phase diagram data and ab initio results for fcc and bcc Pt-W alloys provided that a metastable fcc W phase is given an unusually large entropy.

Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born's interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.

Data are a crucial raw material of this century. The amount of data that have been created in materials science thus far and that continues to be created every day is immense. Without a proper infrastructure that allows for collecting and sharing data, the envisioned success of big data-driven materials science will be hampered. For the field of computational materials science, the NOMAD (Novel Materials Discovery) Center of Excellence (CoE) has changed the scientific culture toward comprehensive and findable, accessible, interoperable, and reusable (FAIR) data, opening new avenues for mining materials science big data. Novel data-analytics concepts and tools turn data into knowledge and help in the prediction of new materials and in the identification of new properties of already known materials.

Considering Ti-V alloys with the body-centered cubic crystal lattice, a system with mechanical instability for Ti-rich alloys, we calculate their elastic properties using Projector Augmented Wave method and the exact muffin‑tin orbital method in a complete interval of V concentrations. The substitutional disorder is modeled using the special quasi-random structures technique and the coherent potential approximation. The efficiency and accuracy of the simulation techniques is analyzed, and a strategy for efficient high-throughput calculations of elastic properties of disordered alloys is proposed. Dependences of the single crystal elastic moduli on V concentration and a set of mechanical characteristics of polycrystalline alloys are presented and discussed. The effect of V content on the mechanical stabilization of the bcc Ti-V alloys is investigated. In agreement with experiment, we find that titanium-rich alloys are mechanically unstable, however the alloys become mechanically stable with increasing content of V in the system. We observe a nonlinear dependence of the alloys Young's moduli in a vicinity of the mechanical stabilization and suggest that this effect can be used to design alloys with low values of the elastic moduli.

Titanium and vanadium form a complete series of solid solutions at temperatures above 885°C. Below 885°C, vanadium is slightly soluble in α titanium (about 1.5 pet V at 650°C) and a two-phase α plus β region extends to 18.5 pet V at 650°C. The alloys up to 15.0 pet V transform into a supersaturated α solid solution upon rapid cooling from the β phase. Above 15 pet V the β phase may be retained. The temperature at which the β to β martensite-type transformation takes place decreases steadily from 850°C for 0.5 pct V to 325°C for 12.7 pct V.

The phase diagram of numerous materials of technological importance features high-symmetry high-temperature phases that exhibit phonon instabilities. Leading examples include shape-memory alloys, as well as ferroelectric, refractory, and structural materials. The thermodynamics of these phases have proven challenging to handle by atomistic computational thermodynamic techniques due to the occurrence of constant anharmonicity-driven hopping between local low-symmetry distortions, while maintaining a high-symmetry time-averaged structure. To compute the free energy in such phases, we propose to explore the system's potential-energy surface by discrete sampling of local minima by means of a lattice gas Monte Carlo approach and by continuous sampling by means of a lattice dynamics approach in the vicinity of each local minimum. Given the proximity of the local minima, it is necessary to carefully partition phase space by using a Voronoi tessellation to constrain the domain of integration of the partition function in order to avoid double counting artifacts and enable an accurate harmonic treatment near each local minima. We consider the bcc phase of titanium as a prototypical example to illustrate our approach.

Free energy calculations at finite temperature based on ab initio molecular dynamics (AIMD) simulations have become possible, but they are still highly computationally demanding. Besides, achieving simultaneously high accuracy of the calculated results and efficiency of the computational algorithm is still a challenge. In this work we describe an efficient algorithm to determine accurate free energies of solids in simulations using the recently proposed temperature-dependent effective potential method (TDEP). We provide a detailed analysis of numerical approximations employed in the TDEP algorithm. We show that for a model system considered in this work, hcp Fe, the obtained thermal equation of state at 2000 K is in excellent agreement with the results of standard calculations within the quasiharmonic approximation.

We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1−xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1−xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.

The subsolidus equilibrium phase diagrams of Ti–V, Ti–Nb and Ti–Ta alloys have been computed through cluster expansion, lattice dynamics and Monte Carlo modeling methods combined with Density Functional Theory total-energy calculations. Computed phase boundaries in Ti–V alloy are found to be in good agreement with reported CALPHAD assessed experimental boundaries. For Ti–Ta system, the computed phase boundaries agree well with CALPHAD boundaries for Ta-rich alloys. For Ti-rich alloys, the transformation temperatures are overestimated by up to 200 K. In the case of Ti–Nb system, the calculated boundary of the bcc-solid-solution phase decreases rapidly in temperature with increasing Nb concentration compared to CALPHAD boundary, deviating from the latter by up to 600 K at 80% Nb. Our calculation gives qualitatively correct hcp-solid-solution regions for all the three alloy systems (i.e., solubility of V/Nb/Ta in hcp Ti). A key difficulty in modeling these systems is the presence of mechanical instability in the bcc phase at high Ti concentration. In this work, we circumvent this difficulty by excluding structures exhibiting instability in the cluster expansion construction process. We find that, while such a scheme is often appropriate (as in the Ti–V and Ti–Ta systems), it can become unreliable when the result exhibit a too strong sensitivity to the exclusion rule used (as in the Ti–Nb system). In all systems, we find that the inclusion of lattice vibration effects is crucial to obtain even qualitative agreement with experiment.

We have computed formation energies for all technologically relevant transition metal solutes in the α, β, and ω phases of Ti, employing ab initio simulations. We analyze and explain their periodic-table trends, and from their differences we derive stabilization energies which provide direct insight into phase stabilization effects of the various solutes with respect to α, β, and ω. This allows us to identify strong β stabilizers in the middle of each electronic d shell in consistency with experimental knowledge. Based on an extension of the stabilization energies to free energies we derive a wide range of Ti-transition metal phase diagrams. A detailed comparison to available experimental martensitic transformation temperatures and to measurements performed in this study shows that, despite some quantitative discrepancies, the qualitative trends can be expected to be correct. An important feature that is displayed by a limited range of the computed phase diagrams is a triple point at which the three phases, α, β, and ω, meet. This insight provides a plausible explanation for the complexity observed in gum metals, a class of Ti alloys with very special materials properties.

A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.

Herefore unpublished enthalpy data which were used in the derivation of smooth enthalpy and heat-capacity data for NBS SRM (Standard Reference Material) 720 ( alpha //2O//3, heat capacity and enthalpy standard) are presented along with some details of the high-temperature experiments. Recent NBS low-temperature measurements on SRM 720 are smoothed by a least-squares spline technique and a revised table of certified values for enthalpy and heat capacity of alpha -Al//2O//3 from 10 K to near the melting point (2250 K) is presented.

The dynamical and thermodynamical stability of the bcc and fcc
disordered RexW1-x system is studied within the
density-functional theory. The configurational part of the free energy
is obtained from ab initio electron structure calculations together with
the cluster expansion and the cluster variation formalism. Electronic
excitations are accounted for through the temperature-dependent
Fermi-Dirac distribution. The lattice dynamics of Re and W is studied
using the density-functional linear-response theory. The calculated
dispersion curves show that fcc Re is dynamically stable while bcc Re
exhibits phonon instabilities in large parts of the Brillouin zone,
similar to previous results for fcc W. Interestingly, the phonon
dispersion curves for fcc Re show pronounced phonon anomalies
characteristic of superconductors such as TaC and NbC. Due to the
instabilities in bcc Re and fcc W the vibrational entropy, and therefore
the free energy, is undefined. In order to predict the regions where the
disordered RexW1-x alloy is unstable we calculate
the phonon dispersion curves in the virtual crystal approximation. Then
we apply a concentration-dependent nonlinear interpolation to the force
constants, which are calculated through a Born-von Kármán
fit to the ab initio obtained dynamical matrices. The vibrational free
energy is calculated in the stable regions for the phases as a function
of concentration. The complete analysis gives a region where the bcc
phase would become thermodynamically unstable towards a phase
decomposition into disordered bcc and fcc phases.

To obtain more precise data, we determined the solubility in a broadcr temperature range than used -~arlier, with use of high-purity materials. We used the methods of microstructural and x-ray analysis, and measurements of electrical resistivity and microhardness. Alloys with as much as 5% V were prepared from titanium iodide and VEL-1 electrolytic vanadium. Melting was conducted in the suspended condition in an atmosphere of purified helium. Ingots in the form of rods 10 mm in diameter were homogenized at 1000 ° for 25 h and then cold rolled to a diameter of 3 mm, with 91% reduction. The composition of the alloys was determined by chemical aaalysis. Samples were annealed in double-evacuated quartz ampules at 700, 600, 500, and400 ° for 100, 200, 300, and 500 h, respectively, followed by water quenching from each temperature. Microstructural analysis showed that the solubility of vanadium is ~3.~ at 600 and 500 ° . With decreasing temperature the solubility decreases, not exceeding 2.5% at 400 °. With increasing vanadium concentrations there is gradual refining of the original c~ solid solution (Fig. la and b) and the appearance of fl precipitates and gradual growth of fl phase (Fig. ic). *Atomic percent, here and below.

This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, Fn(r), independent of v(r), such that the expression Ev(r)n(r)dr+Fn(r) has as its minimum value the correct ground-state energy associated with v(r). The functional Fn(r) is then discussed for two situations: (1) n(r)=n0+n(r), n/n01, and (2) n(r)= (r/r0) with arbitrary and r0. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

The locally self-consistent Green’s function (LSGF) method is an order-N method for calculation of the electronic structure of systems with an arbitrary distribution of atoms of different kinds on an underlying crystal lattice. For each atom Dyson’s equation is used to solve the electronic multiple scattering problem in a local interaction zone (LIZ) embedded in an effective medium judiciously chosen to minimize the size of the LIZ. The excellent real-space convergence of the LSGF calculations and the reliability of its results are demonstrated for a broad spectrum of metallic alloys with different degree of order. The relation of the convergence of our method to fundamental properties of the system, that is, the effective cluster interactions, is discussed.

Titanium alloys exhibit three distinct crystal structures: α, β, and ω. For various applications alloying elements can be used to stabilize the desired phase. Extensive data exist to determine the thermodynamic equilibrium phase, typically phase coexistence. However, the normal state of commercial alloys is a quenched solid solution. While alloy designers have well-established rules of thumb, rigorous theory for nonequilibrium single-phase crystal stability is less well established. We develop a theory to predict which phase a particular alloy will adopt, as a function of minor element concentration. We use two different methods based on density functional theory with pseudopotentials and plane waves, with either explicit atoms or the virtual crystal approximation (VCA). The former is highly reliable, while the latter makes a number of drastic assumptions that typically lead to poor results. Surprisingly, the agreement between the methods is good, showing that the approximations in the VCA are not important in determining the phase stability and elastic properties. This allows us to generalize, showing that the single-phase stability can be related linearly to the number of d electrons, independent of the actual alloying elements or details of their atomistic-level arrangement. This leads to a quantitative measure of β stabilization for each alloying transition metal.

The energy differences between the ground state body-centered structure and closed-packed face-centered structure for transition metals in the middle of the series show unusually large disagreements when they are obtained by the thermochemical approach based on the analysis of experimental data or by first-principles electronic structure calculations. Considering a typical example, the lattice stability of Mo, we present a solution to this long-standing problem. We carry out ab initio molecular dynamics simulations for the two phases at high temperature and show that the configurational energy difference approaches the value derived by means of the thermochemical approach. The main contribution to the effect comes from the modification of the canonical band structure due to anharmonic thermal motion at high temperature.

An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

High temperature reaction calorimetry has seen considerable advances over the past twenty years. New and more sensitive calorimeters,
improved sample handling techniques, and better control of the final dissolved state has made solution calorimetry and drop
solution calorimetry, using molten lead borate and other solvents, very versatile and reliable techniques. This paper summarizes
these advances and presents examples of specific applications to problems of transition metal oxide chemistry, high pressure
geophysics, melt and glass energetics, and metastable materials relevant to the earth sciences.

We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N-atoms(2) scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special 'preconditioning' optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package), The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

Typescript. Thesis (Ph. D.)--Iowa State College, 1952. Includes bibliographical references.

Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}

Within the framework of the exact muffin-tin orbitals (EMTO) theory we have developed a new method to calculate the total energy for random substitutional alloys. The problem of disorder is treated within the coherent potential approximation (CPA), and the total energy is obtained using the full charge density (FCD) technique. The FCD-EMTO-CPA method is suitable for determination of energy changes due to anisotropic lattice distortions in random alloys. In particular, we calculate the elastic constants of the Cu-rich face centered cubic Cu-Zn alloys ( alpha-brass) and optimize the c/a ratio for the hexagonal Zn-rich alloys for both the epsilon and eta phases.

The nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core.

Phase separation reactions in Ti–50 V alloys

- Fuming

W. Fuming, H.M. Flower, Phase separation reactions in TiÀ50 V alloys, Mater. Sci.
Technol 5 (1989) 1172-1177, doi: 10.1179/mst.1989.5.12.1172.

A reinvestigation of the systems Ti-Cr and Ti-V

- Ermanis

The constitution of tantalum-titanium alloys

- Summers-Smith

D. Summers-Smith, The constitution of tantalum-titanium alloys, J. Inst. Met. 81
(1952) 73.

- F Ermanis
- P A Farrar
- H Margolin

F. Ermanis, P.A. Farrar, H. Margolin, A reinvestigation of the systems Ti-Cr and Ti-V, Trans. Metall. Soc. AIME 221 (1961) 904-908.

Solubility of vanadium in alpha-titanium

- V M Shushkanov
- L S Moroz
- V V Obukhovskii
- N P Kapitonova
- N V Ivanov

V.M. Shushkanov, L.S. Moroz, V.V. Obukhovskii, N.P. Kapitonova, N.V. Ivanov, Solubility of vanadium in alpha-titanium, Russ. Metall (1973) 156-158.

- S Banerjee
- P Mukhopadhyay

S. Banerjee, P. Mukhopadhyay, Phase Transformations -Examples from Titanium and
Zirconium Alloys, Pergamon, Oxford, 2007, doi: 10.1016/S1470-1804(07)80054-X.

The titanium-vanadium system

- H K Adenstedt
- J R Pequignot
- J M Raymer

H.K. Adenstedt, J.R. Pequignot, J.M. Raymer, The titanium-vanadium system,
Trans. Am. Soc. Met. 44 (1952) 990-1003.

- O Hellman

O. Hellman, Thermal Properties of Materials from First Principles, University Electronic Press, Link€ oping, 2012. http://liu.diva-portal.org/smash/get/diva2:535576/
FULLTEXT01.pdf.