Session J28: Focus Session: Frontiers in Computational Thermodynamics of Materials

The role of Wang-Landau sampling in materials development

An understanding of the thermodynamic behavior of materials as well as the prediction of the properties of ``materials by design'' often depends upon knowledge of the free energy of the system under study. Computer simulations offer a powerful tool for such investigations, but traditional methods often suffer from long time scales and metastable states due to the roughness of the free energy landscape. Wang-Landau sampling\footnote{F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); F. Wang and D. P. Landau, Phys. Rev. E 64, 05610 (2001).} is a powerful alternative to traditional Monte Carlo algorithms which can alleviate many such problems. We will review the Wang-Landau algorithm and discuss various implementations as well as possible application to materials development.   

Dissolving the Periodic Table in Zirconia: Data Mining for Insight

A standard approach to understanding physical phenomena in materials is to manually search for clear trends or correlations in data (i.e., descriptors) governing those materials. Pettifor maps are a classic example of such empirically constructed models. But what if a data set is too large and/or chemically diverse to explain by straightforward human inspection? We present such a case by calculating from first principles the solubility thermodynamics of 70 dopant cations in cubic zirconia. This data set, spanning three charge states and most non-synthetic metals in the periodic table, defies simple ``manual'' explanation. Instead, we employ data mining algorithms and statistical methods to cluster the dopants into distinct classes, and then to build intuitive models for each class' thermodynamics in zirconia. Thus, we show that formal data mining techniques are a powerful means of elucidating meaningful property relationships in complex data sets.   

High-throughput discovering half-metals from materials magnetic properties database

Half-metal materials have been found by investigating their magnetism data, such as band gap and spin polarization around the Fermi level. An efficient algorithm has been implemented to create a database to aid discovering materials magnetism properties. With this tool, a series of new half-metals has been obtained. We present this magnetism data as well as how the online database is used.   

First Principles Modeling of the Temperature Dependent Ternary Phase Diagram for the Cu-Pd-S System

A method for the prediction of temperature dependent phase diagrams using first principles calculations combined with thermodynamics principles will be discussed. Our method allows us to model the phase diagram without any empirical fitting parameters. Due to the importance of sulfidation when dealing with hydrogen separation using copper palladium membranes, we have chosen as our test case the Cu-Pd-S ternary phase diagram which has been experimentally determined. By applying thermodynamic principles and a simple solid solution model, temperature-dependent features of the Cu-Pd-S system can be explained, specifically solubility ranges for substitutions in select crystalline phases. We have also performed electronic density of states calculations to determine the physical origin of the favorability of select substitutions at T=0K. Work is currently underway to use this method to create phase diagrams where no known experimental results exist, specifically the P-Pd-S system.   

Wang-Landau Without Binning

Results are presented for Wang-Landau calculations on a Heisenberg model of BCC Fe that describe the density of states as function defined for all accessible energies instead of a function tabulated at discrete values of the energy. The density of states function described here is an analytic result valid near the ground state supplemented by a polynomial expansion. The probability density of Wang-Landau random walkers is sampled for a fixed density of states, and that probability density can be used to improve the estimated density of states. Methods for evaluating the convergence of the density of states are discussed along with the diffusion behavior of the random walkers. This work was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725, and sponsored by the Laboratory Directed Research and Development Program (ORNL), by the Mathematical, Information, and Computational Sciences Division; Office of Advanced Scientific Computing Research (US DOE), and by the Division of Materials Sciences and Engineering; Office of Basic Energy Sciences (US DOE). Computer resources provided by Florida State University.   

Thermodynamic Stability of Actinide-Dioxide Solid Solutions and Surface Interactions with Water

Fluorite-structured actinide dioxides are the most common forms of fuel used in nuclear energy production worldwide. This talk will provide an overview of insights into the energetics of these compounds derived through the combination of density-functional-theory-based computational studies (including Hubbard-U corrections) and calorimetric measurements. The talk will focus on two main topics: the mixing energetics of cation solid solutions, and the energetics of water adsorption on the surfaces of these compounds. For the first topic, we present results for ThO$_{\rm 2}$ and UO$_{\rm 2}$ based solid solutions, highlighting the roles of elastic energy arising from cation size mismatch, electrostatic interactions, and charge-transfer reactions, in governing the sign and magnitude of the mixing energetics. For water adsorption, we contrast results for surface and adsorption energies on two fluorite-structured compounds, ThO$_{\rm 2}$ and CeO$_{\rm 2}$, that are relevant for understanding the behavior of water on actinide oxide surfaces more generally. Through a comparison between calorimetric measurements and computational results we assess the level of accuracy achieved in the computational modeling, and suggest areas where further experimental studies would be particularly useful.   

Structure and stability of Al$_2$Fe and Al$_5$Fe$_2$

We employ first principles total energy and phonon calculations to address the structure and stability of Al$_2$Fe and Al$_5$Fe$_2$. The observed structure of Al$_2$Fe, which is reported as stable in the assessed Al-Fe phase diagram, is distinguished by an unusually low triclinic symmetry. The initial crystallographic structure determination additionally featured an unusual hole large enough to accommodate an additional atom. Our calculations indicate the hole must be filled, but predict the triclinic structure is unstable relative to a simpler tetragonal structure based on the prototype Mo Si$_2$. This tetragonal structure is interesting because it is predicted to be nonmagnetic, electrically insulating and high density, while the triclinic structure is magnetic, metallic and low density. We reconcile this seeming contradiction by demonstrating a high vibrational entropy that explai ns why the triclinic structure is stable at high temperatures. Finally, we note that orthorhombic Al$_5$Fe$_2$ is also destabilized by the tetragonal structure but may be stabilized at high temperatures, again by vibrational entropy and partial occupancy associated with the diffusion of Al atoms along channels.   

Equation of state of paramagnetic CrN from ab initio disordered local moments molecular dynamics

A first-principles method is suggested for the calculation of thermodynamic properties of magnetic materials in their high temperature paramagnetic phase [1]. It is based on ab-initio molecular dynamics and simultaneous redistributions of the disordered but finite local magnetic moments. We apply this disordered local moments molecular dynamics (DLM-MD) method to the case of CrN and simulate its equation of state. In particular the debated [F. Rivadulla et al., Nat Mater 8, 974 (2009); B. Alling et al., Nat Mater 9, 283 (2010)] bulk modulus is calculated in the paramagnetic cubic phase and is shown to be very similar to that of the antiferromagnetic orthorhombic CrN phase for all considered temperatures. \\[4pt] [1] P. Steneteg, B. Alling, I. A. Abrikosov, arXiv:1110.1331v1 [cond-mat.mtrl-sci]   

Lattice dynamics of anharmonic solids from first principles

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. In addition to that the bcc-hcp phase diagram for Zr is calculated with high accuracy. arXiv:1103.5590v3 [cond-mat.mtrl-sci]   

Unified cluster expansion method applied to the configurational thermodynamics of cubic Ti$_{1-x}$Al$_{x}$N

We study the thermodynamics of cubic Ti$_{1-x}$Al$_{x}$N using a unified cluster expansion approach for the alloy problem [1]. The purely configurational part of the alloy Hamiltonian is expanded in terms of concentration and volume-dependent effective cluster interactions. By separate expansions of the chemical fixed lattice, and local lattice relaxation terms of the ordering energies, we demonstrate how the screened generalized perturbation method can be fruitfully combined with a concentration-dependent Connolly-Williams cluster expansion method, getting the best out of both two schemes that are traditionally used separately. Utilizing the obtained Hamiltonian in Monte Carlo simulations we access the free energy of Ti$_{1-x}$Al$_x$N alloys and construct the isostructural phase diagram. The results show striking similarities with the previously obtained mean-field results: The metastable c-TiAlN is subject to coherent spinodal decomposition over a large part of the concentration range, e.g., from x 0.33 at 2000 K. \\[4pt] [1] B. Alling, A. V. Ruban, A. Karimi, L. Hultman, and I. A. Abrikosov, PHYSICAL REVIEW B 83, 104203 (2011)   

Atomistic modeling of thermodynamic equilibrium of plutonium

Plutonium metal has complex thermodynamic properties. Among its six allotropes at ambient pressure, the fcc delta-phase exhibits a wide range of anomalous behavior: extraordinarily high elastic anisotropy, largest atomic volume despite the close-packed structure, negative thermal expansion, strong elastic softening at elevated temperature, and extreme sensitivity to dilute alloying. An accurate description of these thermodynamic properties goes far beyond the current capability of first-principle calculations. An elaborate modeling strategy at the atomic level is hence an urgent need. We propose a novel atomistic scheme to model elemental plutonium, in particular, to reproduce the anomalous characteristics of the delta-phase. A modified embedded atom method potential is fitted to two energy-volume curves that represent the distinct electronic states of plutonium in order to embody the mechanism of the two-state model of Weiss, in line with the insight originally proposed by Lawson et al. [Philos. Mag. 86, 2713 (2006)]. By the use of various techniques in Monte Carlo simulations, we are able to provide a unified perspective of diverse phenomenological aspects among thermal expansion, elasticity, and phase stability.