arXiv subjects

Andrew M. Rappe

Publications and source records attributed to Andrew M. Rappe.

At least 127 records · Page 7Linked to original sources

arXiv2004

Local Structure and Macroscopic Properties in PMN-PT and PZN-PT solid solutions

We have examined the local structure of PMN-PT and PZN-PT solid solutions using density functional theory. We find that the directions and magnitudes of cation displacement can be explained by an interplay of cation-oxygen bonding, electrostatic dipole-dipole interactions and short-range direct and through oxygen Pb-B-cation repulsive interactions. We find that the Zn ions off-center in the PZN-PT system, which also enables larger Pb and Nb/Ti displacements. The off-centering behavior of Zn lessens Pb-B-cation repulsion, leading to a relaxor to ferroelectric and a rhombohedral to tetragonal phase transition at low PbTiO$_3$ content in the PZN-PT system. We also show that a simple quadratic relationship exists between Pb and B-cation displacements and the temperature maximum of dielectric constant, thus linking the enhanced displacements in PZN-PT systems with the higher transition temperatures.

cond-mat.mtrl-sci↗

arXiv2004

First-principles extrapolation method for accurate CO adsorption energies on metal surfaces

We show that a simple first-principles correction based on the difference between the singlet-triplet CO excitation energy values obtained by DFT and high-level quantum chemistry methods yields accurate CO adsorption properties on a variety of metal surfaces. We demonstrate a linear relationship between the CO adsorption energy and the CO singlet-triplet splitting, similar to the linear dependence of CO adsorption energy on the energy of the CO 2$π$* orbital found recently {[Kresse {\em et al.}, Physical Review B {\bf 68}, 073401 (2003)]}. Converged DFT calculations underestimate the CO singlet-triplet excitation energy $ΔE_{\rm S-T}$, whereas coupled-cluster and CI calculations reproduce the experimental $ΔE_{\rm S-T}$. The dependence of $E_{\rm chem}$ on $ΔE_{\rm S-T}$ is used to extrapolate $E_{\rm chem}$ for the top, bridge and hollow sites for the (100) and (111) surfaces of Pt, Rh, Pd and Cu to the values that correspond to the coupled-cluster and CI $ΔE_{\rm S-T}$ value. The correction reproduces experimental adsorption site preference for all cases and obtains $E_{\rm chem}$ in excellent agreement with experimental results.

cond-mat.mtrl-sci↗

arXiv2001

CO on Pt(111) puzzle; A possible solution

CO adsorption on the Pt(111) surface is studied using first-principles methods. As found in a recent study [Feibelman, et al., J. Phys. Chem. B 105, 4018 (2001)], we find the preferred adsorption site within density functional theory to be the hollow site, whereas experimentally it is found that the top site is preferred. The influence of pseudopotential and exchange-correlation functional error on the CO binding energy and site preference was carefully investigated. We also compare the site preference energy of CO on Pt(111) with the reaction energy of formaldehyde formation from H$_2$ and CO. We show that the discrepancies between the experimental and theoretical results are due to the generalized gradient approximation (GGA) treating different bond orders with varying accuracy. As a result, GGA results will contain significant error whenever bonds of different bond order are broken and formed.

cond-mat.mtrl-sci↗

arXiv2001

A Geometric Formulation of Quantum Stress Fields

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.

cond-mat.mtrl-sci↗

arXiv2001

Unique Quantum Stress Fields

We have recently developed a geometric formulation of the stress field for an interacting quantum system within the local density approximation (LDA) of density functional theory (DFT). We obtain a stress field which is invariant with respect to choice of energy density. In this paper, we explicitly demonstrate this uniqueness by deriving the stress field for different energy densities. We also explain why particular energy densities give expressions for the stress field that are more tractable than others, thereby lending themselves more easily to first-principles calculations.

cond-mat.mtrl-sci↗

arXiv2001

Geometric Formulation of Unique Quantum Stress Fields

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. The resultant expression obtained for the stress field is gauge-invariant with respect to choice of energy density, and therefore provides a unique, well-defined quantity. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen.

cond-mat.mtrl-sci↗

arXiv2001

Accurate construction of transition metal pseudopotentials

We generate a series of pseudopotentials to examine the relationship between pseudoatomic properties and solid-state results. We find that lattice constants and bulk moduli are quite sensitive to eigenvalue, total-energy difference and tail norm errors, and clear correlations emerge. These trends motivate our identification of two criteria for accurate transition metal pseudopotentials. We find that both the preservation of all-electron derivative of tail norm with respect to occupation and the preservation of all-electron derivative of eigenvalue with respect to occupation {[Phys. Rev. B {\bf 48}, 5031 (1993)]} are necessary to give accurate bulk metal lattice constants and bulk moduli. We also show how the fairly wide range of lattice constant and bulk modulus results found in the literature can be easily explained by pseudopotential effects.

cond-mat.mtrl-sci↗

arXiv2000

Adsorbate aggregation and relaxation of low-frequency vibrations

We present a study of resonant vibrational coupling between adsorbates and an elastic substrate at low macroscopic coverages. In the first part of the paper we consider the situation when adsorbates form aggregates with high local coverage. Based upon our previously published theory, we derive formulas describing the damping rate of adsorbate vibrations for two cases of such aggregation: (i) adsorbates attached to step edges and (ii) adsorbates forming two-dimensional islands. We have shown that damping is governed by local coverage. Particularly, for a wide range of resonant frequencies, the damping rate of adsorbates forming well separated islands is described by the damping rate formula for a periodic overlayer with the coverage equal to the local coverage in the island. The second part of the paper is devoted to facilitating the evaluation of damping rates for a disordered overlayer. The formula describing the damping rate involves the parameter $β$ which is related to the local density of phonon states at the substrate surface and does not allow a closed-form representation. For substrates of isotropic and cubic symmetries, we have developed a good analytical approximation to this parameter. For a vast majority of cubic substrates the difference between the analytical approximation and numerical calculation does not exceed 4%.

cond-mat.mtrl-sci↗

arXiv2000

Controlling adsorbate vibrational lifetimes using superlattices

We propose using short-period superlattices as substrates to control the vibrational relaxation dynamics of adsorbate overlayers. The mass modulation of superlattices creates both band gaps and large spectral enhancements in the phonon density of states. These modifications can dramatically alter the coupling between vibrational modes of the adsorbate overlayer and the substrate lattice, thereby significantly affecting the lifetime of adsorbate modes.

cond-mat.mtrl-sci↗

arXiv2000

Virtual-crystal approximation that works: Locating a composition phase boundary in Pb(Zr_{1-x}Ti_3)O_3

We present a new method for modeling disordered solid solutions, based on the virtual crystal approximation (VCA). The VCA is a tractable way of studying configurationally disordered systems; traditionally, the potentials which represent atoms of two or more elements are averaged into a composite atomic potential. We have overcome significant shortcomings of the standard VCA by developing a potential which yields averaged atomic properties. We perform the VCA on a ferroelectric oxide, determining the energy differences between the high-temperature rhombohedral, low-temperature rhombohedral and tetragonal phases of Pb(Zr_{1-x}Ti_x)O_3 at x=0.5 and comparing these results to superlattice calculations and experiment. We then use our new method to determine the preferred structural phase at x=0.4. We find that the low-temperature rhombohedral phase becomes the ground state at x=0.4, in agreement with experimental findings.

cond-mat.mtrl-sci↗

arXiv2000

Determination of ferroelectric compositional phase transition using novel virtual crystal approach

We employ a new method for studying compositionally disordered ferroelectric oxides. This method is based on the virtual crystal approximation (VCA), in which two or more component potentials are averaged into a composite atomic potential. In our method, we construct a virtual atom with the correctly averaged atomic size and atomic eigenvalues. We have used our new method to study the composition dependent phase transition in Pb(Zr_{1-x}Ti_x)O_3 lying between x=0.5 and x=0.4. We correctly predict the experimentally determined phase transition from the tetragonal phase to a low-temperature rhombohedral phase between these two compositions.

cond-mat.mtrl-sci↗

arXiv1999

First Principles Study of Carbon Monoxide Adsorption on Zirconia-Supported Copper

We have calculated the adsorption energy of carbon monoxide on a monolayer of copper adsorbed on the (111) face of cubic zirconia. We investigate the structural parameters of three phases of bulk zirconia (cubic, tetragonal, and monoclinic) and find excellent agreement with experiment. We have also analyzed the structural relaxation of both the stoichiometric and reduced (111) surfaces of cubic zirconia ($c$-ZrO$_2$). For adsorption of copper on $c$-ZrO$_2$, we find that the preferred binding site is atop the terminal oxygen atom, favored by 0.3 eV over other high symmetry sites. We compare CO adsorption on zirconia-supported copper to the results of carbon monoxide on copper (100) (S. P. Lewis and A. M. Rappe, J. Chem. Phys. {\bf 110}, 4619,(1999).) and show that adsorption on oxide-supported copper is over 0.2 eV more stable than adsorption on the bare surface.

cond-mat.mtrl-sci↗

arXiv1999

Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.

physics.chem-ph↗

arXiv1999

Transferable relativistic Dirac-Slater pseudopotentials

We present a method for constructing a scalar-relativistic pseudopotential which provides exact agreement with relativistic Dirac-Slater all-electron eigenvalues at the reference configuration. All-electron wave functions are self-consistently computed in the valence region at the exact all-electron scalar relativistic eigenvalues. This method improves tr ansferability of the resulting pseudopotential and presents a better starting point for th e designed non-local pseudopotential approach {[Phys. Rev. B {\bf 59}, 12471 (1999)]}. We present calculations for the gold atom as an example of the new approach.

cond-mat.mtrl-sci↗

arXiv1997

Structure and Vibrations of the Vicinal Copper (211) Surface

We report a first principles theoretical study of the surface relaxation and lattice dynamics of the Cu(211) surface using the plane wave pseudopotential method. We find large atomic relaxations for the first several atomic layers near the step edges on this surface, and a substantial step-induced renormalization of the surface harmonic force constants. We use the results to study the harmonic fluctuations around the equilibrium structure and find three new step-derived features in the zone center vibrational spectrum. Comparison of these results with previous theoretical work and weith experimental studies using inelastic He scattering are reported.

cond-mat.mtrl-sci↗

arXiv1997

Designed nonlocal pseudopotentials for enhanced transferability

A new pseudopotential generation method is presented which significantly improves transferability. The method exploits the flexibility contained in the separable Kleinman-Bylander form of the nonlocal pseudopotential [Phys. Rev. Lett. 48, 1425 (1982)]. By adjusting the functional form of the local potential, we are able to improve the agreement with all-electron calculations. Results are presented for the Ca atomic pseudopotential. Configuration testing, logarithmic derivatives and chemical hardness all confirm the accuracy of these new pseudopotentials.

cond-mat↗

arXiv1997

Continuum Elastic Theory of Adsorbate Vibrational Relaxation

An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and the adsorbate overlayer modeled as an array of point masses connected to the surface by harmonic springs. The theory provides a simple expression for the relaxation rate in terms of fundamental parameters of the system: $γ= m\barω_0^2/A_c ρc_T$, where $m$ is the adsorbate mass, $\barω_0$ is the measured frequency, $A_c$ is the overlayer unit-cell area, and $ρ$ and $c_T$ are the substrate mass density and transverse speed of sound, respectively. This expression is strongly coverage dependent, and predicts relaxation rates in excellent quantitative agreement with available experiments. For a half-monolayer of carbon monoxide on the copper (100) surface, the predicted damping rate of in-plane frustrated translations is $0.50\times 10^{12}$~s$^{-1}$, as compared to the experimental value of $(0.43\pm0.07)\times 10^{12}$ s$^{-1}$. Furthermore it is shown that, for all coverages presently accessible to experiment, adsorbate motions exhibit collective effects which cannot be treated as stemming from isolated oscillators.

cond-mat.mtrl-sci↗

arXiv1996

Substrate-adsorbate coupling in CO-adsorbed copper

The vibrational properties of carbon monoxide adsorbed to the copper (100) surface are explored within density functional theory. Atoms of the substrate and adsorbate are treated on an equal footing in order to examine the effect of substrate--adsorbate coupling. This coupling is found to have a significant effect on the vibrational modes, particularly the in-plane frustrated translation, which mixes strongly with substrate phonons and broadens into a resonance. The predicted lifetime due to this harmonic decay mechanism is in excellent quantitative agreement with experiment.

mtrl-th↗