Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session H30: Focus Session: Frontiers in Computational Thermodynamics of Materials |
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Sponsoring Units: FIAP Chair: Stefano Curtarolo, Duke University Room: D139 |
Tuesday, March 16, 2010 8:00AM - 8:12AM |
H30.00001: Chasing Exotic Binary Alloy Compounds: The Necessary Synergy of Cluster Expansion and High-Throughput Methods Stefano Curtarolo, Gus L. W. Hart, Ohad Levy Predicting the stable crystal structures of alloys from their components is a major challenge of current materials research. Ab initio methods explore the phase stability landscape of binary alloys by calculating the formation enthalpies of a large number of structures, and identifying the minima at various component concentrations. Major methods of this type are cluster expansion (CE) and high-throughput ab initio calculations (HT). The CE explores structures on specific types of lattices while the HT method explores experimentally-known structures representing all crystal systems. The CE may find derivative superstructures missed by the HT but is not applicable off-lattice. Combining and reciprocally informing both methods resolve their respective drawbacks. We demonstrate this in a several technologically important Hf, Rh alloy systems. These results emphasize the complementary strengths of the CE and HT methods and the need for using both in searching for new stable compounds in metallic systems. [Preview Abstract] |
Tuesday, March 16, 2010 8:12AM - 8:24AM |
H30.00002: Equilibrium and metastable shapes of platinum nanoparticles from first principles Roman Chepulskyy, Stefano Curtarolo An approach for prediction of stable and metastable shapes of nanoparticles as function of their size is developed. It is based on first principles calculation of high-index surface- energies and nanoparticle surface-tension excess free energies without phenomenological approximations. The approach is applied in the case of platinum nanoparticles as being one of the most used catalysts. The theoretical predictions are verified by comparison with direct first principles calculations for small clusters. [Preview Abstract] |
Tuesday, March 16, 2010 8:24AM - 8:36AM |
H30.00003: Free energy reconstruction from steered dynamics: applications to vacancy migration in Fe, phase coexistence in FeCr and structural transitions in LJ$38$ Manuel Athenes, Mihai-Cosmin Marinica, Gilles Adjanor Various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable to estimate free energy differences and, by maximum-likelihood post-processing, to reconstruct free energy landscapes. Here, based on Bayes theorem, we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states. The method is implemented with two steering schedules. First, using non-autonomous steering, we calculate the migration barrier of the vacancy in Fe-$\alpha$ and the solubility of Cr in Fe-$\alpha$. Secondly, using an autonomous scheduling inspired by metadynamics, we accurately reconstruct the two-dimensional free energy landscape of the 38-atom Lennard-Jones cluster as a function of an orientational bond-order parameter and energy, down to the solid-solid structural transition temperature of the cluster and without maximum-likelihood post-processing. [Preview Abstract] |
Tuesday, March 16, 2010 8:36AM - 9:12AM |
H30.00004: First-principles calculations of free energies of solids Invited Speaker: Vidvuds Ozolins Accurate {\it ab initio\/} calculations of the free energies of high-temperature solid phases present a long-standing problem in thermodynamics of materials. We show how density-functional theory molecular dynamics simulations in conjunction with thermodynamic integration over lattice strains can be used to obtain the free energy differences between the fcc, bcc, and hcp phases of metals. For the prototypical cases of Zr and W, we predict hcp/bcc and fcc/bcc energy and entropy differences that are in excellent agreement with the values derived from CALPHAD analysis of experimental data. The proposed methodology will find applications in first-principles calculations of thermodynamic properties and phase diagrams of metallic alloys, as well as in constructing accurate thermodynamic models of structural phase transformations. [Preview Abstract] |
Tuesday, March 16, 2010 9:12AM - 9:24AM |
H30.00005: Stationary properties of the entropy as a functional of the pair correlation and their application to DFT calculations of free energy D.M. Nicholson, C.Y. Gao, D.J. Keffer We propose that within the class of pair potential Hamiltonians the excess entropy is a universal, temperature-independent functional of the density and pair correlation. This result extends Henderson's Theorem which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and convexity of the excess entropy functional are discussed and related to the Gibbs-Bogoliubov inequality and to the free energy. An approximate functional is given and compared to results from thermodynamic integration. We propose that a functional of this type, that is strictly applicable to pair potentials is also suitable for first principles calculation of free energies from Born-Oppenheimer molecular dynamics performed at a single temperature. [Preview Abstract] |
Tuesday, March 16, 2010 9:24AM - 9:36AM |
H30.00006: Ab initio molecular dynamics simulations of molten Al$_{1-x}$Si$_{x}$ alloys M. Kim, K. H. Khoo, T.-L. Chan, G. Schofield, James R. Chelikowsky First-principles molecular dynamics simulations have been performed to study the structure and dynamics of molten Al$_{1-x}$Si$_{x}$ alloys over a range of alloy compositions and temperatures. Employing an efficient real-space density functional method coupled with a subspace filtering algorithm, we were able to perform simulations on large systems by avoiding explicit eigenvalue calculations. The calculated static structure factors show excellent agreement with data from X-ray diffraction experiments. The composition and temperature dependence of the simulated microstructure and atomic diffusivity will also be discussed. [Preview Abstract] |
Tuesday, March 16, 2010 9:36AM - 9:48AM |
H30.00007: Theoretical study of the atomic structure and thermodynamics of amorphous hafnia Xuhui Luo, Alex Demkov Hafnium dioxide is now used in Si technology and is considered a possible gate dielectric in III-V channel devices. As deposited, HfO$_{2 }$films are disordered, however, the low temperature of crystallization is an obstacle to further scaling. Thus understanding the thermodynamic properties of amorphous hafnia is of great importance. Owing to extremely high melting temperature there are rather few experimental studies of amorphous hafnia quenched from the melt. This makes a theoretical study rather attractive. We use first principles melt-quench procedure to generate theoretically atomistic models of amorphous hafnia. We find that there are two types of amorphous structures. Type I amorphous structures (related to tetragonal hafnia) have molar volume between that of monoclinic and tetragonal hafnia. The energy is 0.30 eV/(HfO$_{2})$ higher than that of the monoclinic phase. The volume of type II amorphous hafnia (related to monoclinic hafnia) is about 4{\%} larger than that of monoclinic hafnia. This is comparable to that of the disordered films grown by atomic layer deposition (ALD). The energy of type II amorphous structure is 0.60 eV/(HfO$_{2})$ above that of the monoclinic phase. We use the nudged elastic band method to calculate the transition barrier between the monoclinic phase and type II amorphous hafnia. The calculated barrier of 0.15 eV/(HfO$_{2})$ suggests the crystallization temperature of about 900K which is close to experiment. [Preview Abstract] |
Tuesday, March 16, 2010 9:48AM - 10:24AM |
H30.00008: Generating and utilizing derivative structures Invited Speaker: Gus L. W. Hart Derivative superstructures play an important role in different material phenomena such as chemical ordering in alloys, spin ordering in magnets, and vacancy ordering in non-stoichiometric materials. Large sets of derivative superstructures are often used in (practically) exhaustive searches of binary configurations on a lattice to determine ground state properties of intermetallic systems. Other physical observables may also be targeted if an appropriate Hamiltonian is available. We present a group-theoretic approach for generating derivative superstructures. The approach is completely general---it can be applied to any crystal type, non-Bravais lattices, mixed anion/cation double binary systems, and surface systems as well as bulk systems. We give examples of problems that can be addressed with the group-theoretic approach such as optimization of band gaps and effective masses in III-V heterostructures, significant increases of Monte Carlo cell sizes for lattice gas simulations, exhaustive testing of lattice models, and the identification of new crystal structures (and predicting the corresponding systems in which the structure may be observed). [Preview Abstract] |
Tuesday, March 16, 2010 10:24AM - 10:36AM |
H30.00009: Predictions of the $\mathrm{Pt}_{8}\mathrm{Ti}$ phase in unexpected systems Richard Taylor, Stefano Curtarolo, Gus Hart The binary phase with 8:1 stoichiometry (prototype $\mathrm{Pt}_{8}\mathrm{Ti}$) has been observed in 11 systems. In every case, the elemental phase of A is face centered cubic (fcc) and is one of the group 10 (IUPAC nomenclature) elements (Pt, Pd, or Ni). High-throughput quantum mechanical energy calculations indicate, however, that the fcc group 9 elements Rh and Ir may also form the $\mathrm{A}_{8}\mathrm{B}$ phase with W. Extending the high-throughput search to the entire transition metal group (including La) reveals an unexpected wealth of new predictions---36 in total. Furthermore, several predictions occur in common alloy systems (e.g., Cu-Zn, Cu-Ni) which are believed to be well characterized. The results of a finite temperature simulation involving the cluster expansion method are presented for one system predicted to form the $\mathrm{A}_{8}\mathrm{B}$ phase, Rh-W. Computed order-disorder transitions suggests the phase may be experimentally realizable in Rh-W. [Preview Abstract] |
Tuesday, March 16, 2010 10:36AM - 10:48AM |
H30.00010: Calculating Thermodynamic Properties for Classical and DFT Hamiltonians G. Brown, D. M. Nicholson, M. Eisenbach Using a Gibbs-Bogoliubov approach, the thermodynamic density of states (DOS) for a Hamiltonian can be calculated using that previously determined from the DOS for a similar Hamiltonian. We illustrate this approach for a classical Heisenberg model of bcc Fe by starting from a Hamiltonian that includes up to fourth-neighbor exchange [Tao, et al, J.\ Appl.\ Phys.\ {\bf 97}, 10A722 (2005)] and calculating the DOS for a Hamiltonian that includes up to tenth-neighbor exchange. The DOS for this system is calculated using the Wang-Landau method [Wang and Landau, J.\ Appl.\ Phys.\ {\bf 97}, 10A722 (2005)] and then compared to the new formalism. The approach can also be used to efficiently calculate the DOS, and hence the thermodynamic properties, for a density-functional theory Hamiltonian starting from classical Heisenberg model. [Preview Abstract] |
Tuesday, March 16, 2010 10:48AM - 11:00AM |
H30.00011: Geometrical frustration and macroscopic residual entropy in an elemental boron explained by a frustrated Ising model T. Ogitsu, F. Gygi, J. Reed, M. Udagawa, Y. Motome, E. Schwegler, G. Galli An elemental solid, $\beta$-rhombohedral boron, is known to have a macroscopic amount (roughly 4 atomic percent) of intrinsic defects, and recent first principles studies have shown that $\beta$-boron has {\it negative defect formation energy} due to the interplay between electron deficiency and the peculiar bonding properties of boron. Consequently, $\beta$-boron was shown to be the thermodynamically stable phase at all temperature below melting temperature at ambient pressure over all the other allotropes and polymorphs considered so far. In this talk, we will show that boron defects possesses geometrical frustration that is well described by an AF Ising model on an expanded kagome lattice, and that the model has an exactly degenerate and disordered ground state with macroscopic residual entropy. We will discuss how the peculiar transport properties of $\beta$-boron, reported over the past forty years, can be explained by the hopping of boron atoms between the macroscopic amount of degenerate configurations. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. [Preview Abstract] |
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