There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

/pdf/phonons-and-related-crystal-properties-from-density-3mdybdn8w1.pdf

Phonons and related crystal properties from density-functional perturbation theory

[Liu, Chang; Li, Feng; Ma, Lai-Peng; Cheng, Hui-Ming] Chinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, Shenyang 110016, Peoples R China.;Cheng, HM (reprint author), Chinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, 72 Wenhua Rd, Shenyang 110016, Peoples R China;cheng@imr.ac.cn

Advanced Materials for Energy Storage

Most metallic elements have a crystal structure that is either body-centered cubic (bcc), face-centered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements.

https://perssongroup.lbl.gov/papers/rmp2012-instabilities.pdf

Lattice instabilities in metallic elements

Despite decades of study, several key aspects of the Al-H system remain the subject of considerable debate. In an effort to elucidate some of these unknowns, we perform a systematic study of this system using first-principles density-functional calculations. We show that generalized gradient approximation (GGA) calculations provide an accurate picture of energetics, phase stability and structure, diffusion, and defect binding in the Al-H system. A series of calculations for hydrides in the M-H systems (M=Al, Ba, Ca, K, Mg, La, Li, Na, Ni, Pd, Sc, Sr, Ti, V, and Y) also shows that the GGA calculations are a quantitatively accurate predictor of hydride formation energies. For Al-H, we find: (i) In agreement with experiment, the observed metastable hydride, ${\mathrm{AlH}}_{3}$ is found to have a small, negative formation enthalpy at ambient conditions, but a strongly positive formation free energy. (ii) Linear response calculations of ${\mathrm{AlH}}_{3}$ yield vibrational frequencies, phonon densities of states (DOS), and heat capacities in excellent agreement with experimental measurements, and suggest the need for a reinterpretation of measured phonon DOS. (iii) Atomic relaxation and anharmonic vibrational effects both play an important role in the tetrahedral versus octahedral interstitial site preference of H in Al. (iv) The calculated heat of solution of H in the preferred tetrahedral site is large and positive (+0.71 eV), consistent with experimental solubility data and with Al as an endothermic hydrogen absorber. (v) Interstitial H interacts strongly with Al vacancies $(\ensuremath{\square}),$ with a calculated H-$\ensuremath{\square}$ binding energy of 0.33 eV. (vi) In the absence of vacancies, the calculated migration energy of H between the tetrahedral and octahedral interstitial sites is 0.18 eV, but for H migrating away from an Al vacancy, the migration energy increases to 0.54 eV. Vacancy trapping of H can therefore provide an explanation for observed disparate H migration barriers.

Hydrogen in aluminum: First-principles calculations of structure and thermodynamics

First-principles prediction of lattice thermal conductivity κ(L) of strongly anharmonic crystals is a long-standing challenge in solid-state physics. Making use of recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics. Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Nonintuitively, high accuracy is achieved when the model is trained on first-principles forces in quasirandom atomic configurations. The method is demonstrated for Si, NaCl, and Cu(12)Sb(4)S(13), an earth-abundant thermoelectric with strong phonon-phonon interactions that limit the room-temperature κ(L) to values near the amorphous limit.

/pdf/lattice-anharmonicity-and-thermal-conductivity-from-28ms8azarh.pdf

Lattice anharmonicity and thermal conductivity from compressive sensing of first-principles calculations.

The classic metallurgical systems---noble-metal alloys---that have formed the benchmark for various alloy theories are revisited. First-principles fully relaxed general-potential linearized augmented plane-wave (LAPW) total energies of a few ordered structures are used as input to a mixed-space cluster expansion calculation to study the phase stability, thermodynamic properties, and bond lengths in Cu-Au, Ag-Au, Cu-Ag, and Ni-Au alloys. (i) Our theoretical calculations correctly reproduce the tendencies of Ag-Au and Cu-Au to form compounds and Ni-Au and Cu-Ag to phase separate at $T=0$ K. (ii) Of all possible structures, ${\mathrm{Cu}}_{3}\mathrm{Au}$ ${(L1}_{2})$ and CuAu ${(L1}_{0})$ are found to be the most stable low-temperature phases of ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Au}}_{x}$ with transition temperatures of 530 K and 660 K, respectively, compared to the experimental values 663 K and \ensuremath{\approx}670 K. The significant improvement over previous first-principles studies is attributed to the more accurate treatment of atomic relaxations in the present work. (iii) LAPW formation enthalpies demonstrate that ${L1}_{2}$, the commonly assumed stable phase of ${\mathrm{CuAu}}_{3}$, is not the ground state for Au-rich alloys, but rather that ordered (100) superlattices are stabilized. (iv) We extract the nonconfigurational (e.g., vibrational) entropies of formation and obtain large values for the size-mismatched systems: 0.48 ${k}_{B}$/atom in ${\mathrm{Ni}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=1100$ K), 0.37 ${k}_{B}$/atom in ${\mathrm{Cu}}_{0.141}{\mathrm{Ag}}_{0.859}$ $(T=1052$ K), and 0.16 ${k}_{B}$/atom in ${\mathrm{Cu}}_{0.5}{\mathrm{Au}}_{0.5}$ $(T=800$ K). (v) Using 8 atom/cell special quasirandom structures we study the bond lengths in disordered Cu-Au and Ni-Au alloys and obtain good qualitative agreement with recent extended x-ray-absorption fine-structure measurements.

Vidvuds Ozoliņš

Papers

Lattice instabilities in metallic elements

Hydrogen in aluminum: First-principles calculations of structure and thermodynamics

Lattice anharmonicity and thermal conductivity from compressive sensing of first-principles calculations.

Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures

First‐Principles Determination of Multicomponent Hydride Phase Diagrams: Application to the Li‐Mg‐N‐H System