We have developed 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 Ti$_{1-x}$Al$_x$N 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 anharmonic contribution and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti$_{1-x}$Al$_x$N alloy, lowering the maximum temperature for the miscibility gap from 6560 K to 2860 K. Our local chemical composition measurements on thermally aged Ti$_{0.5}$Al$_{0.5}$N alloys agree with the calculated phase diagram.
We present an approach to calculate the atomic bulk solubility in binary alloys based on the statistical-thermodynamic theory of dilute lattice gas. The model considers all the appropriate ground states of the alloy and results in a simple Arrhenius-type temperature dependence determined by a {\it "low-solubility formation enthalpy"}. This quantity, directly obtainable from first-principle calculations, is defined as the composition derivative of the compound formation enthalpy with respect to nearby ground states. We apply the framework and calculate the solubility of the A specie in A-Ti all…
We discuss hydrogen diffusion and solubility in aluminum alloyed Fe-Mn alloys. The systems of interest are subjected to tetragonal and isotropic deformations. Based on ab initio modelling, we calculate solution energies, then employ Oriani's theory which reflects the influence of Al alloying via trap site diffusion. This local equilibrium model is complemented by qualitative considerations of Einstein diffusion. Therefore, we apply the climbing image nudged elastic band method to compute the minimum energy paths and energy barriers for hydrogen diffusion. Both for diffusivity and solubility of…
A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.
We present a novel cluster-expansion (CE) approach for the first-principles modeling of temperature and concentration dependent alloy properties. While the standard CE method includes temperature effects only via the configurational entropy in Monte Carlo simulations, our strategy also covers the first-principles free energies of lattice vibrations. To this end, the effective cluster interactions of the CE have been rendered genuinely temperature dependent, so that they can include the vibrational free energies of the input structures. As a model system we use the phase-separating alloy Fe-Cu …
A method to investigate anharmonicity, vibrational anisotropy and thermal expansion using correlated mean-square relative displacements (MSRD) parallel and perpendicular to the interatomic bonds obtained only from Extended X-ray Absorption Fine Structure (EXAFS) analysis based on cumulant expansion is suggested and applied to an amorphous Ni$_{46}$Ti$_{54}$ alloy produced by mechanical alloying. From EXAFS measurements taken on Ni and Ti K edges at several temperatures, the thermal behavior of $\text{MSRD}_\parallel$, $\text{MSRD}_\perp$ and of the cumulants $C_1^*$, $C_2^*$ and $C_3^*$ of the…
The integrity of irradiated zirconium based nuclear fuel cladding is related to the precipitation of hydrides which is closely connected with the solubility of hydrogen. A review on the development of measurement technologies is given and the resulting terminal solid solubilities are reflected with respect to the established model of hydrogen solubility in zirconium alloys. The results often allow for a different interpretation than the established model. An alternative qualitative approach is proposed in which the fixed TSSp for the precipitation of zirconium hydrides is replaced by a kinetic…
The most energetically favourable accommodation processes for common impurities and alloying elements in Be metal and Be-Fe-Al intermetallics were investigated using atomic scale simulations. Fe additions, combined with suitable heat treatments, may scavange Al and Si through their incorporation into the FeBe5 intermetallic. In the absence of Fe, Al and Si will not be associated with Be metal. Li and Mg are also not soluble, but may react with other impurities if present (such as Al or H). Mg may also form the MgBe13 intermetallic phase under certain conditions. He and H exhibit negligible sol…
The thermodynamic properties of the Zr-Nb alloy are investigated at temperatures below 890 K with ab initio calculations. The solution energies of the bcc Nb-rich and hcp Zr-rich solid solutions obtained within the framework of density functional theory are in good agreement with experimental data, although insufficient for a quantitative description of the miscibility gap, for which non configurational entropy has to be accounted for. Whereas electronic free energies can be neglected, we show, using the harmonic approximation and the density functional perturbation theory, that both solution …
Based on first-principles calculations, we show that the maximum reachable concentration $x$ in the (Ga$_{1-x}$In$_x$)$_2$O$_3$ alloy in the low-$x$ regime (i.e. In solubility in $β$-Ga$_2$O$_3$) is around 10%. We then calculate the band alignment at the (100) interface between $β$-Ga$_2$O$_3$ and (Ga$_{1-x}$In$_x$)$_2$O$_3$ at 12%, the nearest computationally treatable concentration. The alignment is strongly strain-dependent: it is of type-B staggered when the alloy is epitaxial on Ga$_2$O$_3$, and type-A straddling in a free-standing superlattice. Our results suggest a limited range of appl…
The solubility and diffusivity of hydrogen in disordered Pd1-xCux alloys are investigated using a combination of first-principles calculations, a composition-dependent local cluster expansion (CDLCE) technique, and kinetic Monte Carlo simulations. We demonstrate that a linear CDCLE model can already accurately describe interstitial H in Pd1-xCux alloys over the entire composition range (0\leqx\leq1) with accuracy comparable to that of direct first-principles calculations. Our predicted H solubility and permeability results are in reasonable agreement with experimental measurements. The propose…
Solid solubility (SS) is one of the most important features of alloys, which is usually difficult to be largely tuned in the entire alloy concentrations by external approaches. Some alloys that were supposed to have promising physical properties could turn out to be much less useful because of their poor SS, e.g., the case for monolayer BNC [(BN)1-x(C2)x] alloys. Until now, an effective approach on significantly enhancing SS of (BN)1-x(C2)x in the entire x is still lacking. In this article, a novel mechanism of selective orbital coupling between high energy wrong-bond states and surface states…
Due to their high strength and advantageous high-temperature properties, tungsten-based alloys are being considered as plasma-facing candidate materials in fusion devices. Under neutron irradiation, rhenium, which is produced by nuclear transmutation, has been found to precipitate in elongated precipitates forming thermodynamic intermetallic phases at concentrations well below the solubility limit. Recent measurements have shown that Re precipitation can lead to substantial hardening, which may have a detrimental effect on the fracture toughness of W alloys. This puzzle of sub-solubility preci…
By means of low-temperature expansions (LTEs), the nucleation free energy and the precipitate interface free energy are expressed as functions of the solubility limit for alloys which lead to the precipitation of a stoichiometric L12 compound such as Al-Sc or Al-Zr alloys. Classical nucleation theory is then used to obtain a simple expression of the nucleation rate whose validity is demonstrated by a comparison with atomic simulations. LTEs also explain why simple mean-field approximation like the Bragg-Williams approximation fails to predict correct nucleation rates in such an ordering alloy.
By devising a novel framework, we present a comprehensive theoretical study of solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline earth (Be, Ca, Sr, Ba) metals in the he boron-rich Mg-B system. The study is based on first-principle calculations of solutes formation energies in MgB$_2$, MgB$_4$, MgB$_7$ alloys and subsequent statistical-thermodynamical evaluation of solubilities. The advantage of the approach consists in considering all the known phase boundaries in the ternary phase diagram. Substitutional Na, Ca, and Li demonstrate the largest solubilities, and Na has the highest (0.5-1 …
In functional materials like thermoelectric materials and superconductors, the interplay between functionality, electronic structure, and phonon characteristics is one of the key factors to improve functionality and to understand the mechanisms. In the first part of this article, we briefly review investigations on lattice anharmonicity in functional materials by Grüneisen parameter (γG). One can find that the γG can be a good scale for large lattice anharmonicity and for detecting a change in anharmonicity amplitude in functional materials. Then, we show original results on estimation of γG f…
Using a first-principles cluster expansion, we shed light on the solid-state phase diagram and structure of the recently discovered high-performance thermoelectrics, Pb-Ag-Sb-Te alloys. The observed nanoscale inhomogeneities are shown to be coherent precipitates of ordered (Ag)m(Sb)n(Te)m+n phases, such as AgSbTe2, all immiscible with rocksalt PbTe. The solubility is high for PbTe in AgSbTe2 and low for (Ag,Sb)Te in PbTe (8% vs. 0.6% at 850 K). The differences in the phonon spectra of PbTe and AgSbTe2 confirm that the inhomogeneities enhance the thermoelectric performance.
We present the first resonant x-ray reflectivity measurements from a liquid surface. The surface structure of the liquid Hg-Au alloy system just beyond the solubility limit of 0.14at% Au in Hg had previously been shown to exhibit a unique surface phase characterized by a low-density surface region with a complicated temperature dependence. In this paper we present reflectivity measurements near the Au LIII edge, for 0.2at% Au in Hg at room temperature. The data are consistent with a concentration of Au in the surface region that can be no larger than about 30at%. These results rule out previou…
The high entropy alloy containing refractory metals Mo-Nb-Ta-W has a body centered cubic structure, which is not surprising given the complete mutual solubility in BCC solid solutions of all pairs of the constituent elements. However, first principles total energy calculations for the binaries reveal a set of distinct energy minimizing structures implying the likelihood of chemically ordered low temperature phases. We apply a hybrid Monte Carlo and molecular dynamics method to evaluate the temperature-dependent chemical order. At 300K a cesium-chloride ordering emerges between mixed (Nb,Ta) si…
To understand the mechanisms by which Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, a combination of experimental (atom probe tomography, x-ray diffraction and thermoelectric power measurements) and modelling (density functional theory) techniques are employed to investigate the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys. Cr occupies both interstitial and substitutional sites in the α-Zr lattice, Fe favours interstitial sites, and a low-symmetry site that was not previously modelled is found to be the most favourable for Fe. Lattice ex…
Carbon solubility in face-centered cubic Ni-W alloys and the phase diagram of C-Ni-W are investigated by means of first principle calculations and semi-grand canonical Monte Carlo simulations. With density functional theory (DFT) total energies as fitting data, we build a superatom model for efficient simulation. Multi-histogram analysis is utilized to predict free energies for different compositions and temperatures. By comparing free energies of competing phases, we are able to predict carbon solubility and phase diagrams of C-Ni-W at different temperatures. A simple ideal mixing approximati…
We present the results of ab initio modeling of structure of dilute Ti-Fe, a typical representative of quenched Ti-based transition-metal alloys. We have demonstrated that beyond the solubility limit this alloy cannot be described in common terms of substitutional and interstitial alloys. Instead, very stable local clusters are formed in both low-temperature hcp and high-temperature bcc phases of alloys, with almost identical local structures. This gives an example of geometrically frustrated state and explains unusual concentration behavior of Mössbauer spectra discovered long ago for this sy…
The thermodynamics properties of the wurtzite and zinc-blende \InGaN alloys are calculated using first-principles density-functional calculations. Special quasi-random structures are used to describe the disordered alloys, for $x= 1/4, 1/2$, and 3/4. The effect of lattice vibrations on the phase diagram, commonly omitted from semiconductor alloy phase diagram calculations, are included through first-principles calculations of phonon spectra. Inclusion of lattice vibrations leads to a large reduction in the order-disorder critical temperature ($\sim 29$% and $\sim 26$% for the wurtzite and zinc…
The Y33.33Ni66.67-xAlx system has been investigated in the region 0 <= x <= 33.3. The alloys were synthesized by induction melting. Phase occurrence and structural properties were studied by X-Ray powder Diffraction (XRD). The Al solubility in each phase has been investigated by XRD and Electron Probe Micro-Analysis (EPMA). The hydrogenation properties were characterized by pressure-composition isotherm measurements and kinetic curves at 473 K. For x = 0, the binary Y33.33Ni66.67 alloy crystallizes in the cubic superstructure with F4-3m space group and ordered Y vacancies. For 1.67 <= x <= 8.3…
Ti50 Pd50-xCrx is a high temperature shape memory alloy with a martensitic transformation temperature strongly dependent on the Cr composition. Prior to the transformation a premartensitic phase is present with an incommensurate modulated cubic lattice with wave vector of q0=(0.22, 0.22, 0). The temperature dependence of the diffuse scattering in the cubic phase is measured as a function temperature for x=6.5, 8.5, and 10 at. %. The lattice dynamics has been studied and reveals anomalous temperature and q-dependence of the [110]-TA2 transverse phonon branch. The phonon linewidth is broad over …
Traditional metallic alloys are mixtures of elements where the atoms of minority species tend to distribute randomly if they are below their solubility limit, or lead to the formation of secondary phases if they are above it. Recently, the concept of medium/high entropy alloys (MEA/HEA) has expanded this view, as these materials are single-phase solid solutions of generally equiatomic mixtures of metallic elements that have been shown to display enhanced mechanical properties. However, the question has remained as to how random these solid solutions actually are, with the influence of chemical…
This work is motivated by the need for large-scale simulations to extract physical information on the iron-chromium system that is a binary model alloy for ferritic steels used or proposed in many nuclear applications. From first-principles calculations and the experimental critical temperature we build a new energetic rigid lattice model based on pair interactions with concentration and temperature dependence. Density functional theory calculations in both norm-conserving and projector augmented-wave approaches have been performed. A thorough comparison of these two different ab initio techni…
Using an ab initio approach, we explore the stability of small vacancy and vacancy-chromium clusters in dilute body-centred cubic Fe-Cr alloys. To explain experimental observations described in C.D. Hardie et al., J. Nucl. Mater. 439, 33 (2013) and showing the occurrence of Cr segregation in low-Cr alloys, we investigate if chromium can form stable bound configurations with vacancies in alloys with chromium concentration below the low-temperature chromium solubility limit of 10-11 at. %. We find that a single vacancy can attract up to four Cr atoms in the most energetically favourable cluster …
Due to the vast compositional space of multi-principal element alloys (MPEAs), the rational design of MPEAs for optimized microstructures is difficult. Therefore, a high-throughput first-principles study of Mo-V-Nb-Ti-Zr, a refractory MPEA, was conducted to gain insights into the underlying microstructures. Using Monte-Carlo simulations powered by cluster expansion, we uncover the principles governing the MPEA's microstructures across a large compositional space that includes non-equiatomic compositions and encompasses the constituent binaries, ternaries, and quaternaries. In the spirit of Hum…
We report the synthesis of tetragonal $\mathrm{FeS}_x\mathrm{Se}_{1-x}$ films ($x \leq 0.78$) by pulsed-laser deposition. To fabricate the tetragonal alloy films with tetragonal FeSe and hexagonal FeS targets, we adopted an alternate deposition technique with FeSe buffer layer on MgO(001). The overall film composition is controlled by the thickness ratio of FeS / FeSe layers. The out-of-plane lattice parameter of the films follows Vegard's law, demonstrating homogeneous alloying by inter-diffusion. The sulfur solid solubility reaches $x = 0.78$ in the $\mathrm{FeS}_x\mathrm{Se}_{1-x}$ films, w…
Hydrogen uptake and hydride formation in Al$_x$CoCrFeNi high-entropy alloys: First-principles, universal-potential, and experimental study
Ruhr-Universität Bochum（波鸿鲁尔大学）；Max-Planck-Institut for Sustainable Materials（马克斯·普朗克可持续材料研究所）；University of Stuttgart（斯图加特大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Goethe University Frankfurt（法兰克福歌德大学）；Federal Institute for Materials Research and Testing (BAM)（联邦材料研究与测试研究所）
InGaN-based visible LEDs find commercial applications for solid-state lighting and displays, but lattice mismatch limits the thickness of InGaN quantum wells that can be grown on GaN with high crystalline quality. Since narrower wells operate at a higher carrier density for a given current density, they increase the fraction of carriers lost to Auger recombination and lower the efficiency. The incorporation of boron, a smaller group-III element, into InGaN alloys is a promising method to eliminate the lattice mismatch and realize high-power, high-efficiency visible LEDs with thick active regio…
Ultrafine-grained aluminum alloys offer interesting multifunctional properties with a combination of high strength, low electrical resistivity, and low density. However, due to thermally induced grain coarsening, they typically suffer from an intrinsic poor thermal stability. To overcome this drawback, an Al-2%Fe alloy has been selected because of the low solubility of Fe in Al and their highly positive enthalpy of mixing leading to the formation of stable intermetallic particles. The two-phase alloy has been processed by severe plastic deformation to achieve simultaneously submicrometer Al gr…
High-temperature, high-dose, neutron irradiation of W results in the formation of Re-rich clusters at concentrations one order of magnitude lower than the thermodynamic solubility limit. These clusters may eventually transform into brittle W-Re intermetallic phases, which can lead to high levels of hardening and thermal conductivity losses. Standard theories of radiation enhanced diffusion and precipitation cannot explain the formation of these precipitates and so understanding the mechanism by which nonequilibrium clusters form under irradiation is crucial to predict materials degradation and…
Short-range order (SRO) in Fe-rich Fe-Cr alloys is investigated by means of atomistic off-lattice Monte Carlo simulations in the semi-grand canonical ensemble using classical interatomic potentials. The SRO parameter defined by Cowley [Phys. Rev. B 77, 669 (1950)] is used to quantify the degree of ordering. In agreement with experiments a strong ordering tendency in the Cr distribution at low Cr concentrations (~< 5%) is observed, as manifested in negative values of the SRO parameters. For intermediate Cr concentrations (5% ~< c_Cr ~< 15%) the SRO parameter for the alpha-phase goes through a m…
While 2D materials attract considerable interests for their exotic electronic and mechanical properties, their phase behaviour is still largely not understood. This work focuses on (Mo:Ti)S$_2$ binary alloys which have captured the interest of the tribology community for their good performance in solid lubrication applications and whose chemistry and crystallography is still debated. Using electronic structures calculations and statistical mechanics we predict a phase-separating behaviour for the system and trace its origin to the energetics of the $d$-band manifold due to crystal field splitt…
Hydrogen embrittlement (HE) affects all major high-strength structural materials and as such is a major impediment to lightweighting e.g. vehicles and help reduce carbon-emissions and reach net-zero. The high-strength 7xxx series aluminium alloys can fulfil the need for light, high strength materials, and are already extensively used in aerospace for weight reduction purposes. However, depending on the thermomechanical and loading state, these alloys can be sensitive to stress-corrosion cracking (SCC) through anodic dissolution and hydrogen embrittlement. Here, we study at the near-atomic-scal…
Certain alloys of iron and nickel (so-called 'Invar' alloys) exhibit almost no thermal expansion over a wide range of temperature. It is clear that this is the result of an anomalous contraction upon heating which counteracts the normal thermal expansion arising from the anharmonicity of lattice vibrations. This anomalous contraction seems to be related to the alloys' magnetic properties, since the effect vanishes at a temperature close to the Curie temperature. However, despite many years of intensive research, a widely accepted microscopic theory of the Invar effect in face-centered-cubic Fe…
Kinetics of phase decomposition accompanied by precipitation of sigma-phase in a Fe73.7Cr26.3 alloy isothermally annealed at 832 K was studied by means of Mössbauer spectroscopy. Two stage decomposition process has been revealed by three different quantities viz. the average hyperfine field, <H>, the short-range parameter, alpha1, and the probability of atomic configuration with no Cr atoms within the first two coordination shells around the probe Fe atoms, P(0,0). The first stage, that has terminated after ca.300 h of annealing, has been associated with the decomposition into Fe-rich phase in…
Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and b…
The boson peak (BP) is a universal feature in the Raman and inelastic scattering spectra of both disordered and crystalline materials. The current paradigm presents the boson peak as the result of a Ioffe-Regel crossover between ballistic (phonon) and diffusive-type excitations, where the loss of coherence of phonons is described as a purely harmonic process due to structural disorder. This "harmonic disorder" paradigm for the BP has never been challenged or tested at the atomistic level. Here, through a set of atomistically-resolved characterizations of amorphous metallic alloys, we uncover a…
In this work, TiFe-based alloys have been developed according to the stoichiometry Ti1-xAxFe1-yBy (A \equiv Zr; B \equiv Mn, V). The hydrogen solubility properties have been investigated to develop dynamic hydrides of Ti-based alloys for hydrogen storage applications. The hydrogenation behavior of these alloys has been studied, and their hydrogen storage capacities and kinetics have been evaluated. Several activation modes, including activation at high temperatures under hydrogen pressure, have been attempted for the as-milled powders. In order to clarify the structural / microstructural chara…
Non-equilibrium synthesis methods allow to alloy bulk-immiscible elements into multinary nanoparticles, which broadens the design space for new materials. Whereas sputtering onto solid substrates can combine immiscible elements into thin film solid solutions, this is not clear for sputtering of nanoparticles in ionic liquids. Thus, the suitability of sputtering in ionic liquids for producing nanoparticles of immiscible elements is investigated by co-sputtering the systems Au-Cu (miscible), Au-Ru and Cu-Ru (both immiscible), and Au-Cu-Ru on the surface of the ionic liquid 1-butyl-3-methylimidaz…
Patterns and periods of charge density waves (CDW) in transition metal dichalcogenides exhibit complex phase diagrams that depend on pressure, temperature, metal intercalation, or chalcogen alloying. The phase diagrams have been understood in the context of phenomenological Landau free energy model, but the microscopic mechanisms underlying them are still not clear. Here, we present a new microscopic theory based on the interatomic potential, and have explicitly calculated temperature-dependent phase diagrams using the interatomic potential extracted from first-principles calculations. With de…
The random substitutional solid solution between the antiferromagnetic (AFM) full-Heusler alloy Ru$_2$MnSn and the ferromagnetic (FM) full-Heusler alloy Ru$_2$FeSn provides a rare opportunity to study FM-AFM phase competition in a near-lattice-matched, cubic system, with full solubility. At intermediate $x$ in Ru$_2$Mn$_{1-x}$Fe$_x$Sn this system displays suppressed magnetic ordering temperatures, spatially coexisting FM and AFM order, and strong coercivity enhancement, despite rigorous chemical homogeneity. Here, we construct the most detailed temperature- and $x$-dependent understanding of t…
Nanobelts, nanoribbons and other quasi-one-dimensional nanostructures formed from layered, so-called, van der Waals semiconductors have garnered much attention due to their high-performance, tunable optoelectronic properties. For layered alloys made from the gallium monochalcogenides GaS, GaSe, and GaTe, near-continuous tuning of the energy bandgap across the full composition range has been achieved in GaSe1-xSx and GaSe1-xTex alloys. Gold-catalyzed vapor-liquid-solid (VLS) growth of these alloys yields predominantly nanobelts, nanoribbons and other nanostructures for which the fast crystal gr…
