arXiv subjects

R. C. Albers

Publications and source records attributed to R. C. Albers.

36 records · Page 2Linked to original sources

arXiv2005

Systematic pathway generation and sorting in martensitic transformations: Titanium alpha to omega

Structural phase transitions are governed by the underlying atomic transformation mechanism; martensitic transformations can be separated into strain and shuffle components. A systematic pathway generation and sorting algorithm is presented and applied to the problem of the titanium alpha to omega transformation under pressure. In this algorithm, all pathways are constructed within a few geometric limits, and efficiently sorted by their energy barriers. The geometry and symmetry details of the seven lowest energy barrier pathways are given. The lack of a single simple geometric criterion for determining the lowest energy pathway shows the necessity of atomistic studies for pathway determination.

cond-mat.mtrl-sci↗

arXiv2004

Equation-of-Motion Approach to Dynamical Mean Field Theory

We propose using an equation-of-motion approach as an impurity solver for dynamical mean field theory. As an illustration of this technique, we consider a finite-$U$ Hubbard model defined on the Bethe lattice with infinite connectivity at arbitrary filling. Depending on the filling, the spectra that is obtained exhibits a quasiparticle peak, and lower and upper Hubbard bands as typical features of strongly correlated materials. The results are also compared and in good agreement with exact diagonalization. We also find a different picture of the spectral weight transfer than the iterative perturbation theory.

cond-mat.str-el↗

arXiv2003

Impurities block the alpha to omega martensitic transformation in titanium

The onset and kinetics of martensitic transformations are controlled by impurities trapped during the transformation. For the alpha to omega transformation in Ti, ab initio methods yield the changes in both the relative stability of and energy barrier between the phases. Using the recently discovered transformation pathway, we study interstitial O, N, C; substitutional Al and V; and Ti interstitials and vacancies. The resulting microscopic picture explains the observations, specifically the suppression of the transformation in A-70 and Ti-6Al-4V titanium alloys.

cond-mat.mtrl-sci↗

arXiv2003

Unscreened Hartree-Fock calculations for metallic Fe, Co, Ni, and Cu from ab-initio Hamiltonians

Unscreened Hartree-Fock approximation (HFA) calculations for metallic Fe, Co, Ni, and Cu are presented, by using a quantum-chemical approach. We believe that these are the first HFA results to have been done for crystalline 3d transition metals. Our approach uses a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtains maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized multi-band Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, self-consistent HFA, which takes into account exact exchange and is free of self-interactions. Although the d-bands sit considerably lower within HFA than within the local (spin) density approximation L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained either experimentally or within LSDA. The HFA total energies are lower than the corresponding LSDA calculations. We believe that this same approach can be easily extended to include more sophisticated ab-initio many-body treatments of the electronic structure of solids.

cond-mat.str-el↗

arXiv2003

Thermal Stabilization of the HCP Phase in Titanium

We have used a tight-binding model that is fit to first-principles electronic-structure calculations for titanium to calculate quasi-harmonic phonons and the Gibbs free energy of the hexagonal close-packed (hcp) and omega crystal structures. We show that the true zero-temperature ground-state is the omega structure, although this has never been observed experimentally at normal pressure, and that it is the entropy from the thermal population of phonon states which stabilizes the hcp structure at room temperature. We present the first completely theoretical prediction of the temperature- and pressure-dependence of the hcp-omega phase transformation and show that it is in good agreement with experiment. The quasi-harmonic approximation fails to adequately treat the bcc phase because the zero-temperature phonons of this structure are not all stable.

cond-mat.mtrl-sci↗

arXiv2003

New Pseudo-Phase Structure for $α$-Pu

In this paper we propose a new pseudo-phase crystal structure, based on an orthorhombic distortion of the diamond structure, for the ground-state $α$-phase of plutonium. Electronic-structure calculations in the generalized-gradient approximation give approximately the same total energy for the two structures. Interestingly, our new pseudo-phase structure is the same as the Pu $γ$-phase structure except with very different b/a and c/a ratios. We show how the contraction relative to the $γ$ phase, principally in the $z$ direction, leads to an $α$-like structure in the [0,1,1] plane. This is an important link between two complex structures of plutonium and opens new possibilities for exploring the very rich phase diagram of Pu through theoretical calculations.

cond-mat↗

arXiv2003

An ab-initio many-body method for electronic structure calculations of solids. I. Description of the method

We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.

cond-mat↗

arXiv2003

An ab-initio many-body method for electronic structure calculations of solids. II. Unscreened Hartree-Fock treatment for the 3d systems Fe, Co, Ni and Cu

The ab-initio many-body method suggested in the preceding paper is applied to the 3d transition metals Fe, Co, Ni, and Cu. We use a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtain maximally localized Wannier functions. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized many-body Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, selfconsistent, Hartree-Fock approximation (HFA). We present these HFA results, which we believe are the first to have been done for crystalline 3d transition metals, and compare them with those obtained from the standard local (spin) density approximation (LSDA) within density functional theory (DFT). Although the d-bands sit considerably lower within HFA than within L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained experimentally or within LSDA. The HFA total energies are lower than the corresponding L(S)DA calculations.

cond-mat↗

arXiv2003

A New Mechanism for the Alpha to Omega Martensitic Transformation in Pure Titanium

We propose a new direct mechanism for the pressure driven alpha to omega martensitic transformation in pure titanium. A systematic algorithm enumerates all possible mechanisms whose energy barriers are evaluated. A new, homogeneous mechanism emerges with a barrier at least four times lower than other mechanisms. This mechanism remains favorable in a simple nucleation model.

cond-mat.mtrl-sci↗

arXiv2002

Mechanism for BCC to HCP Transformation: Generalization of the Burgers Model

Many structural transformations involve a group-nonsubgroup relationship between the initial and transformed phases, and hence are beyond the purview of conventional Landau theory. We utilize a systematic and robust methodology to describe such reconstructive martensitic transformations by coupling group-theoretical arguments to first-principles calculations. In this context we (i) use a symmetry-based algorithm to enumerate transformation paths, (ii) evaluate the energy barriers along these transformation paths using all-electron first principles calculations, (iii) deduce the full set of primary and secondary order parameters for each path to establish the appropriate Ginzburg-Landau free-energy functionals, and (iv) for each path, identify special points of the primary order parameter, as a function of local distortions, corresponding to the end product phase. We apply this method to the study of a pressure driven body-centered cubic (bcc) to hexagonal close-packed (hcp) transformation in titanium. We find a generalization of the Burgers mechanism, and also find that there is no energy barrier to this transformation. In fact, surprisingly, we also find a region of volumes in which the intermediate path becomes more stable than either of the end-points (bcc or hcp). We therefore predict a new orthorhombic phase for Ti between 51 and 62 GPa.

cond-mat.mtrl-sci↗

arXiv2002

Block-Diagonalization and f-electron Effects in Tight-Binding Theory

We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and transferable for f-electron systems as they are for d-electron systems. In both cases we have found it essential to take great care in constraining the fitting procedure by using a block-diagonalization procedure, which we describe in detail.

cond-mat.mtrl-sci↗

arXiv2002

First-Principles-Based Thermodynamic Description of Solid Copper Using the Tight-Binding Approach

A tight-binding model is fit to first-principles calculations for copper that include structures distorted according to elastic constants and high-symmetry phonon modes. With the resulting model the first-principles-based phonon dispersion and the free energy are calculated in the quasi-harmonic approximation. The resulting thermal expansion, the temperature- and volume-dependence of the elastic constants, the Debye temperature, and the Gruneisen parameter are compared with available experimental data.

cond-mat.mtrl-sci↗

arXiv2001

Hubbard-U calculations for Cu from first-principles Wannier functions

We present first-principles calculations of optimally localized Wannier functions for Cu and use these for an ab-initio determination of Hubbard (Coulomb) matrix elements. We use a standard linearized muffin-tin orbital calculation in the atomic-sphere approximation (LMTO-ASA) to calculate Bloch functions, and from these determine maximally localized Wannier functions using a method proposed by Marzari and Vanderbilt. The resulting functions were highly localized, with greater than 89% of the norm of the function within the central site for the occupied Wannier states. Two methods for calculating Coulomb matrix elements from Wannier functions are presented and applied to fcc Cu. For the unscreened on-site Hubbard $U$ for the Cu 3d-bands we have obtained about 25eV. These results are also compared with results obtained from a constrained local-density approximation (LDA) calculation.

cond-mat.str-el↗

arXiv2000

Three-Dimensional Elastic Compatibility: Twinning in Martensites

We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a "landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of compatibility. Our results are also applicable to structural phase transitions in improper ferroelastics such as ferroelectrics and magnetoelastics, where strain acts as a secondary order parameter.

cond-mat.mtrl-sci↗

arXiv1999

Theoretical Atomic Volumes of fcc Thorium and Plutonium

The zero-presssure zero-temperature equilibrium volume and bulk modulus are calculated for fcc Th and Pu by two independent all-electron, full-potential, electronic-structure methods: the full-potential linear augmented-plane-wave (FLAPW) method and the linear combinations of Gaussian type orbitals-fitting function (LCGTO-FF) method. The results produced by these two distinctly different electronic-structure techniques are in excellent agreement with each other, but differ significantly from a previous calculation using the full-potential linear muffin-tin-orbital (FP-LMTO) method. The theoretically calculated equilibrium volumes are nearly 10% larger than the previous FP-LMTO calculations. While the new theoretical volume for Th is in good agreement with experiment when the generalized gradient approximation is used, the calculated equilibrium volume for fcc Pu remains substantially smaller than experiment in qualitative agreement with previous calculations.

cond-mat.mtrl-sci↗

arXiv1995

Prediction of an undimerized, insulating, antiferromagnetic ground-state in halogen-bridged linear-chain Ni compounds

A parameter-free, mean-field, multi-orbital Hubbard model with nonspherical Coulomb and exchange interactions, implemented around all-electron local-density approximation (LDA) calculations, correctly predicts the band-gap energy, the absence of dimerization, and the antiferromagnetic ground state of halogen-bridged linear-chain Ni compounds. This approach also reproduces the insulating ground state and dimerization in PtX linear-chain compounds in agreement with experiment and previous calculations. Three "ps" figures are included at the end of the RevTex file and compressed using uufiles.

cond-mat↗

arXiv1994

Alouani {\it et al.} Reply to Comment on Tuning of the CDW in MX Chains

This is a reply to J. T. Gammel's Comment (9404047) on Tuning of the CDW in MX Chains. We show that while the harmonic elastic energy can fit a small region around zero dimerization, it is insufficient to treat the large amplitude CDW of the MX systems which was the main physics of our Letter (Phys. Rev. Lett. {\bf 71}, 1415 (1993)). We also stress that \underline{anharmonic} elastic potentials are {\it essential} to explain the charge-density-wave systematics of an entire class of MX material.

cond-mat↗

arXiv1993

Tuning of the CDW in the Halogen-Bridged Transition-Metal Linear-Chain Compounds

Local-density-approximation calculations are used to show that the metal-metal distance along the chains controls the charge-density wave (CDW) in halogen-bridged transition-metal linear-chain (MX) compounds. The strength of the CDW can be understood in terms of a two band Su-Schrieffer-Heeger model if a hard-core ion-ion repulsion potential is also added. We predict a second-order phase transition from an insulating to a semi-metallic ground state and explain trends in dimerization, bond-length ratios, band gaps, and Raman breathing modes in terms of the metal-metal distance. Three "ps" figures are included at the end of the file.

cond-mat↗