Large vibrational effects upon calculated phase boundaries in Al-Sc

An Unexpected Decrease in Vibrational Entropy of Multicomponent Rutile Oxides

High-entropy oxides (HEOs), featuring infinite chemical composition and exceptional physicochemical properties, are attracting much attention. The configurational entropy caused by a component disorder of HEOs is popularly believed to be the main driving force for thermal stability, while the role of vibrational entropy in the thermodynamic landscape has been neglected. In this study, we systematically investigated the vibrational entropy of multicomponent rutile oxides (including Fe0.5Ta0.5O2, Fe0.333Ti0.333Ta0.333O2, Fe0.25Ti0.25Ta0.25Sn0.25O2, and Fe0.21Ti0.21Ta0.21Sn0.21Ge0.16O2) by precise heat capacity measurements. It is found that vibrational entropy gradually decreases with increasing component disorder, beyond what one could expect from an equilibrium thermodynamics perspective. Moreover, all multicomponent rutile oxides exhibit a positive excess vibrational entropy at 298.15 K. Upon examinations of configuration disorder, size mismatch, phase transition, and polyhedral distortions, we demonstrate that the excess vibrational entropy plays a pivotal role in lowering the crystallization temperature of multicomponent rutile oxides. These findings represent the first experimental confirmation of the role of lattice vibrations in the thermodynamic landscape of rutile HEOs. In particular, vibrational entropy could serve as a novel descriptor to guide the predictive design of multicomponent oxide materials.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

A Combined Experimental and First-Principles Based Assessment of Finite-Temperature Thermodynamic Properties of Intermetallic Al3Sc

We present a first-principles assessment of the finite-temperature thermodynamic properties of the intermetallic Al3Sc phase including the complete spectrum of excitations and compare the theoretical findings with our dilatometric and calorimetric measurements. While significant electronic contributions to the heat capacity and thermal expansion are observed near the melting temperature, anharmonic contributions, and electron-phonon coupling effects are found to be relatively small. On the one hand, these accurate methods are used to demonstrate shortcomings of empirical predictions of phase stabilities such as the Neumann-Kopp rule. On the other hand, their combination with elasticity theory was found to provide an upper limit for the size of Al3Sc nanoprecipitates needed to maintain coherency with the host matrix. The chemo-mechanical coupling being responsible for the coherency loss of strengthening precipitates is revealed by a combination of state-of-the-art simulations and dedicated experiments. These findings can be exploited to fine-tune the microstructure of Al-Sc-based alloys to approach optimum mechanical properties.

First-Principles Atomistic Thermodynamics and Configurational Entropy

In most applications, functional materials operate at finite temperatures and are in contact with a reservoir of atoms or molecules (gas, liquid, or solid). In order to understand the properties of materials at realistic conditions, statistical effects associated with configurational sampling and particle exchange at finite temperatures must consequently be taken into account. In this contribution, we discuss the main concepts behind equilibrium statistical mechanics. We demonstrate how these concepts can be used to predict the behavior of materials at realistic temperatures and pressures within the framework of atomistic thermodynamics. We also introduce and discuss methods for calculating phase diagrams of bulk materials and surfaces as well as point defect concentrations. In particular, we describe approaches for calculating the configurational density of states, which requires the evaluation of the energies of a large number of configurations. The cluster expansion method is therefore also discussed as a numerically efficient approach for evaluating these energies.

Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures

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 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 vibrational contribution including anharmonicity 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 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.

Ab initio identified design principles of solid-solution strengthening in Al

Solid-solution strengthening in six Al-X binary systems is investigated using first-principle methods. The volumetric mismatch parameter and the solubility enthalpy per solute were calculated. We derive three rules for designing solid-solution strengthened alloys: (i) the solubility enthalpy per solute is related to the volumetric mismatch by a power law; (ii) for each annealing temperature, there exists an optimal solute-volume mismatch to achieve maximum strength; and (iii) the strengthening potential of high volumetric mismatch solutes is severely limited by their low solubility. Our results thus show that the thermodynamic properties of the system (here Al-X alloys) set clear upper bounds to the achievable strengthening effects owing to the reduced solubility with increasing volume mismatch.

First-principles calculation of self-diffusion coefficients

We demonstrate a first-principles method to compute all factors entering the vacancy-mediated self-diffusion coefficient. Using density functional theory calculations of fcc Al as an illustrative case, we determine the energetic and entropic contributions to vacancy formation and atomic migration. These results yield a quantitative description of the migration energy and vibrational prefactor via transition state theory. The calculated diffusion parameters and coefficients show remarkably good agreement with experiments. We provide a simple physical picture for the positive entropic contributions.

Reliable first-principles alloy thermodynamics via truncated cluster expansions

In alloys cluster expansions (CE) are increasingly used to combine first-principles electronic-structure calculations and Monte Carlo methods to predict thermodynamic properties. As a basis-set expansion in terms of lattice geometrical clusters and effective cluster interactions, the CE is exact if infinite, but is tractable only if truncated. Yet until now a truncation procedure was not well defined and did not guarantee a reliable truncated CE. We present an optimal truncation procedure for CE basis sets that provides reliable thermodynamics. We then exemplify its importance in Ni3V, where the CE has failed unpredictably, and now show agreement to a range of measured values, predict new low-energy structures, and explain the cause of previous failures.

Mg segregation at Al/Al3Sc heterophase interfaces on an atomic scale: experiments and computations

Microscopic factors governing solute partitioning in ternary two-phase Al-Sc-Mg alloys are investigated combining three-dimensional-atom-probe (3DAP) microscopy measurements with first-principles computations. 3DAP is employed to measure composition profiles with subnanometer-scale resolution, leading to the identification of a large enhancement of Mg solute at the coherent alpha-Al/Al(3)Sc (fcc/L1(2)) heterophase interface. First-principles calculations establish an equilibrium driving force for this interfacial segregation reflecting the nature of the interatomic interactions.

Multiscale modeling of precipitate microstructure evolution

We demonstrate how three "state-of-the-art" techniques may be combined to build a bridge between atomistics and microstructure: (1) first-principles calculations, (2) a mixed-space cluster expansion approach, and (3) the diffuse-interface phase-field model. The first two methods are used to construct the driving forces for a phase-field microstructural model of theta'- Al2Cu precipitates in Al: bulk, interfacial, and elastic energies. This multiscale approach allows one to isolate the physical effects responsible for precipitate microstructure evolution.