Prediction Of Phase Stability Research Articles

A comparative study of predicting high entropy alloy phase fractions with traditional machine learning and deep neural networks

Predicting phase stability in high entropy alloys (HEAs), such as phase fractions as functions of composition and temperature, is essential for understanding alloy properties and screening desirable materials. Traditional methods like CALPHAD are computationally intensive for exploring high-dimensional compositional spaces. To address such a challenge, this study explored and compared the effectiveness of random forests (RF) and deep neural networks (DNN) for accelerating materials discovery by building surrogate models of phase stability prediction. For interpolation scenarios (testing on the same order of system as trained), RF models generally produce smaller errors than DNN models. However, for extrapolation scenarios (training on lower-order systems and testing on higher order systems), DNNs generalize more effectively than traditional ML models. DNN demonstrate the potential to predict topologically relevant phase composition when data were missing, making it a powerful predictive tool in materials discovery frameworks. The study uses a CALPHAD dataset of 480 million data points generated from a custom database, available for further model development and benchmarking. Experiments show that DNN models are data-efficient, achieving similar performance with a fraction of the dataset. This work highlights the potential of DNNs in materials discovery, providing a powerful tool for predicting phase stability in HEAs, particularly within the Cr-Hf-Mo-Nb-Ta-Ti-V-W-Zr composition space.

Predicting the formation enthalpy and phase stability of (Ti,Al,TM)N (TM = III-VIB group transition metals) by high-throughput ab initio calculations and machine learning

The development of transition-metal-alloyed (Ti,Al)N thin films has become a common strategy to achieve optimized mechanical and thermal properties. Selection of a suitable alloying element, however, should consider the effect on Al solubility, directly influencing phase stability during the deposition. Here we use high-throughput ab initio formation enthalpy calculations to assess stability of the cubic (c) vs. hexagonal wurtzite-type (w-) phase of TM-alloyed (Ti,Al,TM)N. This compositionally-limited ab initio dataset serves to fit several machine-learning (ML) models enabling phase stability predictions over the entire compositional range. Of all the models, the linear regression using Magpie feature descriptor pre-processed by a genetic algorithm has the highest accuracy. For Ta, Nb, Mo, and W addition below ∼10 at.%, our ML model predicts enhanced stability of c-(Ti,Al,TM)N due to increased solubility of Al. Other alloying elements, especially Sc and Y from IIIB group and Hf and Zr from IVB group, decrease the cubic metastable solubility limit. In agreement with available experimental data, all transition metals except for Cr and V increase the volume of c-(Ti,Al,TM)N and w-(Ti,Al,TM)N.

Predicting Phase Stability at Interfaces.

We present the RAFFLE methodology for structural prediction of the interface between two materials and demonstrate its effectiveness by applying it to MgO encapsulated by two layers of graphene. To address the challenge of interface structure prediction, our methodology combines physical insights derived from morphological features observed in related systems with an iterative machine learning technique. This employs physical-based methods, including void-filling and n-body distribution functions to predict interface structures. For the carbon-MgO encapsulated system, we have shown the rocksalt and hexagonal phases of MgO to be the two most energetically stable in the few-layer regime. We demonstrate that monolayer rocksalt is heavily stabilized by interfacing with graphene, becoming more energetically favorable than the graphenelike monolayer hexagonal MgO. The RAFFLE methodology provides valuable insights into interface behavior, and a route to finding new materials at interfaces.

Phase Selection Rules of Multi-Principal Element Alloys.

Computational prediction of phase stability of multi-principal element alloys (MPEAs) holds a lot of promise for rapid exploration of the enormous design space and autonomous discovery of superior structural and functional properties. Regardless of many plausible works that rely on phenomenological theory and machine learning, precise prediction is still limited by insufficient data and the lack of interpretability of some machine learning algorithms, e.g., convolutional neural network. In this work, a comprehensive approach is presented, encompassing the development of a complete dataset that contains 72387 density functional theory calculations, as well as a predictive global phenomenological descriptor. The phase selection descriptor, based on atomic electronegativity and valence electron concentration, significantly outperforms the widely used valence electron concentration, excelling in both accuracy (with an f1 score of 63% compared to 47%) and its ability to predict the HCP phase (0.48 recall compared to 0). The comprehensive data mining on the global design space of 61425 quaternary MPEAs made from 28 possible metals, together with the phenomenological theory and physical interpretation, will set up a solid computational science foundation for data-driven exploration of MPEAs.

Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides

Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides

DFT aided prediction of phase stability, optoelectronic and thermoelectric properties of A2AuScX6 (A= Cs, Rb; X= Cl, Br, I) double perovskites for energy harvesting technology

In this work, the density functional theory (DFT) was used to predict the physical properties of A2AuScX6 (A = Cs, Rb; X = Cl, Br, I) double perovskites (DPs). The stability was confirmed by computing the formation energy, binding energy, phonon dispersion curve, stiffness constants, tolerance, and octahedral factors. The nature of electronic conductivity and chemical bonding were explored. The band gap values using TB-mBJ are 1.88, 1.68, and 1.30 eV for Cs2AuScX6 [X = Cl, Br, I] and 1.93, 1.71, and 1.32 eV for Rb2AuScX6 [X = Cl, Br, I], respectively. The dielectric function, absorption coefficient, refractive index, energy loss function, photoconductivity, and reflectivity were also calculated and analyzed. The absorption coefficients in the visible range are 0.333 × 106 cm−1, 0.27 × 106 cm−1, and 0.213 × 106 cm−1 for Cs2AuScX6 [X = Cl, Br, I] and 0.345 × 106 cm−1, 0.281 × 106 cm−1, and 0.218 × 106 cm−1 for Rb2AuScX6 [X = Cl, Br, I], respectively. We also investigated the thermoelectric properties and found the figure of merit (ZT) values of 0.44, 0.47, and 0.62 for Cs2AuScX6 (X = Cl, Br, I) and 0.47, 0.53, and 0.54 for Rb2AuScX6 (X = Cl, Br, I) at 300 K. The results revealed that the studied compounds are potential candidates for solar cells and thermoelectric devices.

MAX phases – Past, present, and future

The MAX phases are a class of nanolaminated materials composed of an early transition-metal (M), an A-group element (A) and C, N, B and/or P (X). Progress in MAX phase research in recent years has increased their number from the original 50 or so, to more than 300 phases. Since half of the 342 MAX phases have been discovered after 2018, an overview of the progress made in the field is timely. Currently, 28 M elements, 28 A elements, and 6 X elements have been incorporated in the MAX phases, alloys included. We further categorize MAX phases based on the synthesis route used to make them; if made via a one-step approach in bottom-up synthesis or formed through elemental replacement reactions in top-down synthesis. This classification is also correlated to theoretical phase stability predictions, that in turn, can be used to identify novel synthesizable MAX phase compositions as well as to suggest suitable synthesis routes. Furthermore, using phase stability predictions we identify 182 new theoretically stable MAX phases awaiting experimental confirmation. Notably, as MAX phases are precursors for MXenes, the dramatically increased interest in the latter for a large host of potential applications renders the former even more valuable.

Rapid discovery of high hardness multi-principal-element alloys using a generative adversarial network model

Multi-principal element alloys (MPEAs) continue to gain research prominence due to their promising high-temperature microstructural and mechanical properties. Recently, machine learning (ML) and materials informatics have been used extensively for screening MPEAs, however, most of these efforts were focused on constructing classification and regression models for predicting phase stability and mechanical properties of known compositions. These approaches may accelerate the screening process but optimizing new compositions with desirable properties within a practical time frame from an infinitely large design space of MPEA systems remains a grand challenge. To tackle this composition optimization challenge, a generative adversarial network coupled with a neural-network ML model was utilized to design MPEAs by filtering compositions that have high hardness. Even in a high-dimensional space with 18 elements as descriptors, the ML model was able to generate optimized compositions from which one composition was found to have 10% higher hardness (941 HV) than the maximum in the training data (857 HV). Density-functional theory was used to provide thermodynamic and electronic insights to higher hardness of the new MPEA found. The present work can optimize compositions from a wide design space of 18 elements (including W, Ta and Nb) that presents an opportunity to synthesize new compositions for applications ranging from corrosion-resistant alloys to nuclear materials. The findings suggest that generative ML can greatly accelerate materials discovery by identifying novel compositions, which can serve as a data-informed tool to guide experiments.

Criteria of predicting phase formation for MSi2-Type High-Entropy refractory metal silicides

MSi2-type high-entropy refractory metal silicides (HERMS) have excellent oxidation resistance at medium and high temperatures due to high entropy effect, which is a promising ultrahigh temperature structural material. HERMS have two phase structures, C11b and C40, due to allotropic transformation. Compared to C40, C11b has better fracture toughness, but it is now difficult to synthesize single-phase C11b. The first-principle was used to systematically study phase formation ability of HERMS. Formation enthalpy (ΔHf), mixing enthalpy (ΔHmix) and mixing enthalpy difference (δmix) were calculated for 504 MSi2-type HERMS structures. δmix, VEC and ΔHmixC11b were identified to characterize and predict phase stability of MSi2-type HERMS, in which δmix is a decisive factor, and has general applicability and important guiding significance for material systems with allotropic transformation. The generalized criteria of predicting phase formation for MSi2-type HERMS were proposed. C11b phase formation criterion is VEC > 4.58, δmix < −0.05 eV/atom, ΔHmixC11b < −0.02 eV/atom. C40 phase formation criterion is VEC ≤ 4.58 and ΔHmixC11b > 0.09 eV/atom. Its accuracy was verified by experimental data to be 100%. This work is of great significance for composition design of HERMS and the further study of C11b-type HERMS.

Predicting properties of high entropy carbides from their respective binaries

Using Density Functional Theory calculations, this paper addresses two questions: (1) to what degree can the properties of high entropy carbides created by equi-molar combinations of five of the set of eight refractory metals Hf, Nb, Mo, Ta, Ti, V, W, and Zr be predicted from their respective binary compounds, and (2) can empirical relationships from properties of the binary compounds be used to predict phase stability for these materials. For the former question, it is found that lattice constant, binding energy and bulk modulus are well approximated by binary carbide averages, but carbon vacancy formation energies are less predictable. To address the second question, correlations are explored between binary properties and the entropy forming ability (EFA) of all 56 possible five-element combinations of the eight refractory elements. Significant correlations are not found between cohesive energies or lattice constants of the binary constituents of each composition and that composition’s EFA, but there is a correlation between EFA and the standard deviation of the distribution of bulk moduli of the constituent binaries.

Phase stability of Fe from first principles: Atomistic spin dynamics coupled with ab initio molecular dynamics simulations and thermodynamic integration

The calculation of free energies from first principles in materials is a formidable task which enables the prediction of phase stability with high accuracy; these calculations are complicated in magnetic materials by the interplay of electronic, magnetic, and vibrational degrees of freedom. In this work, we show the feasibility and accuracy of the calculation of phase stability in magnetic systems with ab initio methods and thermodynamic integration by sampling the magnetic and vibrational phase space with coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations [Stockem et al., PRL 121, 125902 (2018)], where energies and interatomic forces are calculated with density functional theory (DFT). We employ the method to calculate the phase stability of Fe at ambient pressure from 800 K up to 1800 K. The Gibbs free energy difference between fcc and bcc Fe at zero pressure as a function of temperature is calculated carrying out thermodynamic integration over temperature on the energies at the DFT level from ASD-AIMD, using a reference free energy difference calculated in the paramagnetic state at temperatures much higher than the magnetic transition temperatures with thermodynamic integration over stress-strain variables with disordered local moment (DLM)-AIMD simulations. We show the importance of the magnetic ordering temperature of bcc Fe on the $\alpha$ to $\gamma$ structural transition temperature, whereas the $\gamma$ to $\delta$ transition is well reproduced independently of the exchange interactions. The Gibbs free energy difference between the two structures is within 5 meV/atom from the CALPHAD estimate, and both transition temperatures are reproduced within 150 K. The present work paves the way to free energy calculations in magnetic materials from first principles with accuracy in the order of 1 meV/atom.

Pressure prediction of phase stability, anisotropic elasticity, and thermodynamic properties of Ti2AC (A = Cd, In) ternary compound

AbstractIn this study, the effects of high pressure on phase stability, anisotropic elasticity, and thermodynamic properties of Ti2AC (A = Cd, In) were predicted by using first‐principles based on density functional theory. The negative formation enthalpy indicates that Ti2AC (A = Cd, In) is thermodynamically stable at pressures of 0–50 GPa. The elastic constants and polycrystalline moduli of Ti2AC (A = Cd, In) increase with increasing pressure, while its elastic anisotropies decrease with increasing pressure. The density of states demonstrates that no phase transition occurs in the pressure range 0–50 GPa. In addition, the influences of high pressure (up to 50 GPa) and temperature (up to 2000 K) on the thermodynamic properties of Ti2AC (A = Cd, In) were systematically studied based on the quasi‐harmonic Debye model. Finally, the sound velocities and minimum thermal conductivities are also discussed.

A flexible and scalable scheme for mixing computed formation energies from different levels of theory

Computational materials discovery efforts are enabled by large databases of properties derived from high-throughput density functional theory (DFT), which now contain millions of calculations at the generalized gradient approximation (GGA) level of theory. It is now feasible to carry out high-throughput calculations using more accurate methods, such as meta-GGA DFT; however recomputing an entire database with a higher-fidelity method would not effectively leverage the enormous investment of computational resources embodied in existing (GGA) calculations. Instead, we propose here a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner. We then use legacy PBE(+U) GGA calculations and new r2SCAN meta-GGA calculations from the Materials Project database to demonstrate that our scheme improves solid and aqueous phase stability predictions, and discuss practical considerations for its implementation.

Distilling physical origins of hardness in multi-principal element alloys directly from ensemble neural network models

Despite a plethora of data being generated on the mechanical behavior of multi-principal element alloys, a systematic assessment remains inaccessible via Edisonian approaches. We approach this challenge by considering the specific case of alloy hardness, and present a machine-learning framework that captures the essential physical features contributing to hardness and allows high-throughput exploration of multi-dimensional compositional space. The model, tested on diverse datasets, was used to explore and successfully predict hardness in AlxTiy(CrFeNi)1-x-y, HfxCoy(CrFeNi)1-x-y and Alx(TiZrHf)1-x systems supported by data from density-functional theory predicted phase stability and ordering behavior. The experimental validation of hardness was done on TiZrHfAlx. The selected systems pose diverse challenges due to the presence of ordering and clustering pairs, as well as vacancy-stabilized novel structures. We also present a detailed model analysis that integrates local partial-dependencies with a compositional-stimulus and model-response study to derive material-specific insights from the decision-making process.

Theoretical predictions of phase stability for orthorhombic and hexagonal ternary MAB phases.

In the quest for finding novel thermodynamically stable, layered, MAB phases promising for synthesis, we herein explore the phase stability of ternary MAB phases by considering both orthorhombic and hexagonal crystal symmetries for various compositions (MAB, M2AB2, M3AB4, M4AB4, and M4AB6 where M = Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, and Co, A = Al, Ga, and In, and B is boron). The thermodynamic stability of seven previously synthesized MAB phases is confirmed, three additional phases are predicted to be stable, and 23 phases are found to be close to stable. Furthermore, the crystal symmetry preference for forming orthorhombic or hexagonal crystal structures is investigated where the considered Al-based MAB phases tend to favour orthorhombic structures whereas Ga- and In-based phases in general prefer hexagonal structures. The theoretically predicted stable MAB phases along with the structural preference is intended to both guide experimental efforts and to give an insight into the stability for different crystal symmetries of MAB phases.

Thermodynamic modelling to predict phase stability in BCC + B2 Al–Ti–Co–Ni–Fe–Cr high entropy alloys

This paper examines the potential of thermodynamic modelling as a simple and inexpensive means for assessing phase stability in a series of non-equiatomic high entropy alloys and compares with CALPHAD calculations to demonstrate an appropriate level of simplifying assumptions. The modelling was motivated by alloys from the Al–Ti–Co–Ni–Fe–Cr system, which were produced by iteratively following the natural compositional segregation of the two-phase BCC + B2 microstructure present in a Al2TiCoNiFeCr alloy after casting and heat treatment. This produced a range of multicomponent B2-type alloys with different volume fractions of a BCC secondary phase. The solubility limits and traditional empirical thermodynamic driving forces for phase stability were investigated to explain the formation of the two phases. Limitations of prior semi-empirical models are highlighted, with advancements demonstrated by accounting for contributions from the effect of ordering on configurational entropy, the difference in enthalpy from intermetallic compounds, and thermal influences on both entropy and enthalpy. The new models are compared against the current leading thermodynamic modelling approach, CALPHAD, with excellent correlation. This work outlines a methodology to predict and design phase constitution in future high-performance BCC + B2 alloys and, more generally, it demonstrates the value of models with temperature-dependent thermodynamic quantities for exploring new, complex compositional regions.

Methane hydrate thermodynamic phase stability predictions in the presence of salt inhibitors and their mixture for offshore operations

A thermodynamic model is developed and used in this study to predict the phase equilibrium conditions of a methane -aqueous salt inhibitor -water hydrate system. The modified van der Waals-Platteeuw (vdWP) model is used to calculate the equilibrium condition of the hydrate phase. To compute the fugacities of gas and liquid phases, the Peng-Robinson equation of state (PR-EoS) and a previously developed Pitzer-Mayorga-Zavitsas-hydration model are used. The model predictions are compared to experimental results on methane hydrate phase equilibrium in the presence of an aqueous salt inhibitor. The absolute average relative deviation in predicted methane -aqueous salt inhibitor -water hydrate equilibrium pressure (AARD-P%) with the developed Pitzer-Mayorga-Zavitsas-Hydration model is 3.59% for CH4+NaCl, 1.52% for CH4+KCl, and 2.70% for CH4+ CaCl2. Finally, the hydrate suppression temperature caused by aqueous salt inhibitors and their mixtures on methane hydrate phase stability is calculated, and it is CaCl2>KCl>NaCl in that order. This work's phase equilibrium model demonstrates the potential application of determining methane hydrate equilibrium conditions in the presence of aqueous salt inhibitors and their mixtures used in offshore oil field applications.

Ab-initio predictions of phase stability, electronic structure, and optical properties of (0001)-MAX surfaces in M2AC (M = Cr, Zr, Hf; A = Al, Ga)

Here, we report MAX phases' surface properties, which are essential for thin-film technology due to their excellent resistance to high-temperature oxidation, corrosion, and wear. The surface stability, electronic, and optical properties of 0001-surfaces in M2AC (M = Zr, Hf, Cr; A = Al, Ga) are investigated and compared with their bulk counterparts. The interplay between chemical bonding and charge distribution is discussed from electronic structure, including the Fermi surfaces. Four possible (0001)-terminated surfaces are considered by breaking M − C and M-A bonds in which cleavage energy of M − C is higher than M-A. The Cr–Al bond in Cr2AlC is stronger than other M-A bonds. The charge density of valance A-p electrons redistributes in the surface area, distinct from that of the bulk. The A- and M(C)-terminated (0001)-surfaces are the most stable and energetically favorable terminations due to lower surface energies. The optical properties of the most stable (0001)-surfaces were also investigated to understand the dielectric and photoconductive behavior in the (0001)-terminated surfaces of M2AC.

A framework for quantifying uncertainty in DFT energy corrections

In this work, we demonstrate a method to quantify uncertainty in corrections to density functional theory (DFT) energies based on empirical results. Such corrections are commonly used to improve the accuracy of computational enthalpies of formation, phase stability predictions, and other energy-derived properties, for example. We incorporate this method into a new DFT energy correction scheme comprising a mixture of oxidation-state and composition-dependent corrections and show that many chemical systems contain unstable polymorphs that may actually be predicted stable when uncertainty is taken into account. We then illustrate how these uncertainties can be used to estimate the probability that a compound is stable on a compositional phase diagram, thus enabling better-informed assessments of compound stability.

Ruthenium-based half Heusler alloys RuTiX (X = Si, Ge, Sn): An FP-LAPW-based analytical study of structural, electronic, elastic, mechanical and transport properties

An full potential linearized augmented plane wave (FP-LAPW)-based analytical study of structural, electronic, mechanical and thermoelectric properties has been done for the Ruthenium-based half heusler RuTiX (X = Si, Ge and Sn) compounds. An efficient method to develop Half Heusler (HH) alloys is by examining their stability of structure in various phases, by plotting electronic band structures, computing elastic constants and also by studying the presence of magnetic moments. In this study, we have used DFT-based calculations to scrutinise the paramagnetic/ferromagnetic (FM) as well as metallic/semiconducting behavior of these HH compounds. The predicted phase stability using the energy versus volume curves reveals that they are stable in Type C phase. RuTiSi and RuTiGe are found to be stable in the paramagnetic phase whereas RuTiSn is stable in the FM phase with a finite value of magnetic moment. The electronic band structures and density of states (DOS) plots predict that the studied compounds belong to [Formula: see text]-type degenerate semiconductors as the Fermi Level lies within the valence band. Due to the existence of finite DOS at the Fermi level, they show an enhanced metallic behavior. A small value indirect gap is found between valence band maximum (VBM) and conduction band minimum (CBM) in all these studied RuTiX HH alloys depicting their semiconducting nature. The elastic constants of cubic phase are computed for the first time and they obey the mechanical stability criteria. The positive value of [Formula: see text] and value of [Formula: see text]/[Formula: see text] ratio of these HH compounds exhibit their ductile nature. The thermoelectric properties of these compounds are investigated, and a comparatively higher figure of merit reveals their scope of application in thermoelectric devices.