arXiv subjects

Philip B. Allen

Publications and source records attributed to Philip B. Allen.

At least 37 records · Page 2Linked to original sources

arXiv2015

Anharmonic Phonon Quasiparticle Theory of Zero-point and Thermal Shifts in Insulators: Heat Capacity, Bulk Modulus, and Thermal Expansion

The Quasi-harmonic (QH) approximation uses harmonic vibrational frequencies omega(H,Q,V), computed at volumes V near the volume where the Born-Oppenheimer (BO) energy is minimum. When this is used in the harmonic free energy, QH approximation gives a good zeroth order theory of thermal expansion, and first order theory of bulk modulus. Here, n-th order means smaller than the leading term by n powers of epsilon, where epsilon is the ratio hbar omega(Q)/E(el) or kT/E(el), and E(el) is an electronic energy scale, typically 2 to 10 eV. Experiment often shows evidence for next order corrections. When such corrections are needed, anharmonic interactions must be included. The most accessible measure of anhamonicity is the quasiparticle (QP) energy, omega(Q,V,T), seen experimentally by vibrational spectroscopy. However, this cannot just be inserted into the harmonic free energy F(H). In this paper, a free energy formula is found which corrects the double-counting of anharmonic interactions that is made when F is approximated by F(H,omega(Q,V,T)). The term "QP thermodynamics" is used for this way of treating anharmonicity. It enables (n+1)-order corrections, if QH theory is accurate to order n. This procedure is used to give corrections to specific heat and volume thermal expansion. The QH formulas for isothermal and adiabatic bulk moduli are clarified, and the route to higher order corrections is indicated.

cond-mat.mtrl-sci↗

arXiv2015

Size Effects in Thermal Conduction by Phonons

Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated periodically. This is a popular model for simulation of bulk heat transport using classical molecular dynamics (MD), and is related to transient thermal grating experiments. Nanoscale effects are seen in perhaps their simplest form. The model is solved by an extension of standard quasiparticle gas theory of bulk solids. Both structure and heat flow are constrained by periodic boundary conditions. Diffusive transport is fully included, while ballistic transport by phonons of long mean free path is diminished in a specific way. Heat current J(x) and temperature gradient dT(x')/dx' have a non-local relationship, via k(x-x'), over a distance |x-x'| determined by phonon mean free paths. In MD modeling of bulk conductivity, finite computer resources limit system size. Long mean free paths, comparable to the scale of heating and cooling, cause undesired finite-size effects that have to be removed by extrapolation. The present model allows this extrapolation to be quantified. Calculations based on the Peierls-Boltzmann equation, using a generalized Debye model, show that extrapolation involves fractional powers of 1/L. It is also argued that heating and cooling should be distributed sinusoidally (de/dt~cos(2pi x/L)) to improve convergence of numerics.

cond-mat.mes-hall↗

arXiv2013

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)$_{1-x}$(ZnO)$_x$

We present total energy and force calculations on the (GaN)$_{1-x}$(ZnO)$_{x}$ alloy. Site-occupancy configurations are generated by Monte Carlo (MC) simulations, based on a cluster expansion (CE) model proposed in a previous study. Surprisingly large local atomic coordinate relaxations are found by density-functional calculations using a 432-atom periodic supercell, for three representative configurations at $x=0.5$. These are used to generate bond length distributions. The configurationally averaged composition- and temperature-dependent short-range order (SRO) parameters of the alloys are discussed. Entropy is approximated in terms of pair distribution statistics and thus related to SRO parameters. This approximate entropy is compared with accurate numerical values from MC. An empirical model for the dependence of bond length on local chemical environments is proposed.

cond-mat.mtrl-sci↗

arXiv2013

Improved Callaway model for Lattice Thermal Conductivity

In developing the phonon quasiparticle picture, Peierls discovered that, in a perfect crystal, without Umklapp (U) events, a current-carrying distribution can never relax to a zero-current distribution. Callaway introduced a simplified approximate model version of the Peierls-Boltzmann equation, retaining its the ability to deal separately with Normal (N) and U events. This paper clarifies and improves the Callaway model, and shows that Callaway underestimated the suppression of N-processes in relaxing thermal current. The new result should improve computations of thermal conductivity from relaxation-time studies.

cond-mat.other↗

arXiv2013

Heat Conduction by Phonons across a Film

Quasiparticle theory gives a local relation between heat current and temperature gradient, provided the quasiparticle mean free path is smaller than the scale of variation of temperature. When mean free paths are comparable to sample size, the relation becomes non-local. This non-local relation is formulated for phonon carriers; an explicit form is found in the approximation where current relaxation rates are replaced by quasiparticle relaxation rates. A quasiparticle definition of local temperature is offered. To extract the spatial variation of the temperature gradient requires inverting the non-local relation. A variational principle is constructed. The heat current is bounded above when evaluated for a trial temperature gradient. The true temperature gradient is the one which minimizes heat current. The simplest variational approximation (a constant temperature gradient) gives an approximate formula for the thickness dependence of the heat transport across a film whose thickness is comparable to mean free paths of phonons. The formula interpolates between ballistic and diffusive limits.

cond-mat.mes-hall↗

arXiv2013

Evolutionary Method for Predicting Surface Reconstructions with Variable Stoichiometry

We present a specially designed evolutionary algorithm for the prediction of surface reconstructions. This new technique allows one to automatically explore all the low-energy configurations with variable surface atoms and variable surface unit cells through the whole chemical potential range. The power of evolutionary search is demonstrated by the efficient identification of diamond 2*1 (100) and 2*1 (111) surfaces with a fixed number of surface atom and a fixed cell size. With further variation of surface unit cells, we study the reconstructions of the polar surface MgO (111). Experiment has detected an oxygen trimer (ozone) motif (Plass et al, 1998). We predict a new version of this motif which can be thermodynamically stable at extreme oxygen rich condition. Finally, we perform a variable stoichiometry search for a complex ternary system: semi-polar GaN (101bar1) with and without adsorbed oxygen. The search yields a non-intuitive reconstruction based on N3-trimers. These examples demonstrate that an automated scheme to explore the energy landscape of surfaces will improve our understanding of surface reconstructions. The method presented in this report can be generally applied to binary and multi-component systems.

cond-mat.mtrl-sci↗

arXiv2010

Interpreting the 4-index Notation for Hexagonal Systems

A four index notation (e.g. (10-11) is often used to denote reciprocal lattice vectors or crystal faces of hexagonal crystals. The purposes of this notation have never been fully explained. This note clarifies the underlying mathematics of a symmetric overcomplete basis. This simplifies and improves the usefulness of the notation.

cond-mat.other↗

arXiv2007

What happens to geometric phase when spin-orbit interactions lift band degeneracy?

Spin-orbit interaction lifts accidental band degeneracy. The geometric phase gamma(C)=pi for circuits surrounding a line of such degeneracy cannot survive completely unchanged. The change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, gamma(C) decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and gamma(C)=pi is unchanged.

cond-mat.other↗

arXiv2007

Infrared Optical Properties of Ferropericlase (Mg1-xFexO): Experiment and Theory

The temperature dependence of the reflectance spectra of magnesium oxide (MgO) and ferropericlase (Mg1-xFexO, for x=0.06 and x=0.27) have been measured over a wide frequency range (~50 to 32000 cm-1) at 295 and 6 K. The complex dielectric function has been determined from a Kramers-Kronig analysis of the reflectance. The spectra of the doped materials resembles pure MgO in the infrared region, but with much broader resonances. We use a shell model to calculate the dielectric function of ferropericlase, including both anharmonic phonon-phonon interactions and disorder scattering. These data are relevant to understanding the heat conductivity of ferropericlase in the earth's lower mantle.

cond-mat.mtrl-sci↗

arXiv2006

Electronic Structure of ZnO nanowire

This paper presents two first-principles calculations on the lattice- and electronic- structures of a small-diameter infinite and truncated ZnO nanowire. The two calculations show excellent agreement with each other. For the small diameter nanowire, the lattice and electronic properties are determined by the relaxed surface. We find a similarity between the nanowire surface and the surface of the bulk material, and discuss the assignment of the rotational quantum number m to the bands.

cond-mat.mtrl-sci↗

arXiv2006

Density-functional study of adsorption of isocyanides on the gold (111) surface

Density functional theory within the generalized-gradient approximation is used to study the adsorption of the isocyanides CNH and CNCH3 on the gold (111) surface at several coverages. It is found that these molecules are highly selective in their adsorption site preference. Adsorption is possible only at the top site, although binding is rather weak and dipole-dipole repulsion prevents binding at coverages of 1/3 ML and higher. At all other high symmetry sites considered (hcp, fcc, bridge), the isonitriles are not bound. To reveal the main mechanisms of bonding, the isonitriles are compared to CO and ammonia using Au-X radicals as model systems. The systematic trends are understood in terms of $σ$ donation from the ligand lone pair and $π^*$ back donation. Finally, CNH is found to be more strongly bound to an undercoordinated gold atom (adatom) on the surface.

cond-mat.other↗

arXiv2005

Octahedral Tilt Instability of ReO_3-type Crystals

The octahedron tilt transitions of ABX_3 perovskite-structure materials lead to an anti-polar (or antiferroelectric) arrangement of dipoles, with the low temperature structure having six sublattices polarized along various crystallographic directions. It is shown that an important mechanism driving the transition is long range dipole-dipole forces acting on both displacive and induced parts of the anion dipole. This acts in concert with short range repulsion, allowing a gain of electrostatic (Madelung) energy, both dipole-dipole and charge-charge, because the unit cell shrinks when the hard ionic spheres of the rigid octahedron tilt out of linear alignment.

cond-mat.str-el↗

arXiv2005

Quantum Electrical Dipole in Triangular Systems: a Model for Spontaneous Polarity in Metal Clusters

Triangular symmetric molecules with mirror symmetry perpendicular to the 3-fold axis are forbidden to have a fixed electrical dipole moment. However, if the ground state is orbitally degenerate and lacks inversion symmetry, then a ``quantum'' dipole moment does exist. The system of 3 electrons in D_3h symmetry is our example. This system is realized in triatomic molecules like Na_3. Unlike the fixed dipole of a molecule like water, the quantum moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values +/- mu_0 along any direction of measurement in the plane. An electric field F in the plane leads to a linear Stark splitting +/- mu_0 F}. We introduce a toy model to study the effect of Jahn-Teller distortions on the quantum dipole moment. We find that the quantum dipole property survives when the dynamic Jahn-Teller effect is included, if the distortion of the molecule is small. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. Coulomb correlations also give a partial suppression.

cond-mat.str-el↗

arXiv2004

Evolution of Electronic and Vibrational Polarity of NaF Nanocrystals from Diatomic to Bulk: A Density Functional Study

Density functional theory (DFT) is used to study vibrations, electrical dipole moments, and polarizabilities of NaF clusters. Because of prior experimental and theoretical studies, this is a good model system for tracking the evolution of the properties from diatomic molecule to bulk crystal. The ratio of vibrational to electronic contributions to the polarizability increases dramatically with size N in the closed shell clusters (NaF)_N. The open shell system Na_14F_13 has a greatly enhanced electronic polarizability. Contrary to previous studies on this system which treated only the outer electron by quantum mechanics, we find the O_h cubic structure to be stable relative to the polar distorted structures such as C_3v.

cond-mat.other↗

arXiv2004

Density-Functional-Based Determination of Vibrational Polarizabilities in Molecules

We develop a direct derivation for the primary contribution to the vibrational polarizability for molecules, clusters and other finite systems. The vibrational polarizability is then calculated within the generalized gradient approximation to the density functional theory for a variety of molecules and clusters. The agreement between theory and experiment is quite good. The results show that for small ionic molecules and clusters, inclusion of the vibrational polarizability is necessary to achieve quantitative accuracy.

cond-mat.other↗

arXiv2004

Numerical study of resistivity of model disordered three-dimensional metals

We calculate the zero-temperature resistivity of model 3-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal and off-diagonal. The non-equilibrium Green function formalism provides a Landauer-type formula for the conductance of arbitrary mesoscopic systems. We use this formula to calculate the resistance of finite-size disordered samples of different lengths. The resistance averaged over disorder configurations is linear in sample length and resistivity is found from the coefficient of proportionality. Two structures are considered: (1) a simple cubic lattice with one s-orbital per site, (2) a simple cubic lattice with two d-orbitals. For small values of the disorder strength, our results agree with those obtained from the Boltzmann equation. Large off-diagonal disorder causes the resistivity to saturate, whereas increasing diagonal disorder causes the resistivity to increase faster than the Boltzmann result. The crossover toward localization starts when the Boltzmann mean free path relative to the lattice constant has a value between 0.5 and 2.0 and is strongly model dependent.

cond-mat.dis-nn↗

arXiv2003

Dipole Interactions and Electrical Polarity in Nanosystems -- the Clausius-Mossotti and Related Models

Point polarizable molecules at fixed spatial positions have solvable electrostatic properties in classical approximation, the most familiar being the Clausius-Mossotti (CM) formula. This paper generalizes the model and imagines various applications to nanosystems. The behavior is worked out for a sequence of octahedral fragments of simple cubic crystals, and the crossover to the bulk CM law is found. Some relations to fixed moment systems are discussed and exploited. The one-dimensional dipole stack is introduced as an important model system. The energy of interaction of parallel stacks is worked out, and clarifies the diverse behavior found in different crystal structures. It also suggests patterns of self-organization which polar molecules in solution might adopt. A sum rule on the stack interaction is found and tested. Stability of polarized states under thermal fluctuations is discussed, using the one-dimensional domain wall as an example. Possible structures for polar hard ellipsoids are considered. An idea is formulated for enhancing polarity of nanosystems by intentionally adding metallic coatings.

cond-mat.mtrl-sci↗

arXiv2003

Density Functional Study of Cubic to Rhombohedral Transition in $α$-AlF$_3$

Under heating, $α$-AlF$_3$ undergoes a structural phase transition from rhombohedral to cubic at temperature $T$ around 730 K. The density functional method is used to examine the $T$=0 energy surface in the structural parameter space, and finds the minimum in good agreement with the observed rhombohedral structure. The energy surface and electronic wave-functions at the minimum are then used to calculate properties including density of states, $Γ$-point phonon modes, and the dielectric function. The dipole formed at each fluorine ion in the low temperature phase is also calculated, and is used in a classical electrostatic picture to examine possible antiferroelectric aspects of this phase transition.

cond-mat.mtrl-sci↗