arXiv subjects

Paul Tangney

Publications and source records attributed to Paul Tangney.

14 recordsLinked to original sources

arXiv2024

Electricity at the macroscale and its microscopic origins

I define the fields that describe electrical macrostructure, and their rates of change, in terms of the microscopic charge density, electric field, electric potential, and their rates of change. To deduce these definitions, I lay some new foundations of a theory of how observable macroscopic fields are related to spatial averages of their microscopic counterparts. I find that the relationships between macroscopic fields are identical in form to the relationships between their microscopic counterparts, meaning that the $\vec{P}$ and ${\vec{D}}$ fields do not appear in them. Without invoking quantum mechanics, I derive the expressions for polarization current established by the Modern Theory of Polarization. I prove that the bulk-average electric potential, or mean inner potential, vanishes in a macroscopically-uniform charge-neutral material, and I show that when a crystal lattice lacks inversion symmetry, it does not imply the existence of macroscopic $\vec{E}$ or $\vec{P}$ fields in the crystal's bulk. I point out that symmetry is scale-dependent. Therefore, if anisotropy of the microstructure does not manifest as anisotropy of the macrostructure, it cannot be the origin of a macroscopic vector field. The macroscopic charge density vanishes in a material's bulk. Therefore, regardless of the microstructure, a macroscopic $\vec{E}$ field cannot emanate from the bulk. I find that all relationships between observable macroscopic fields can be expressed mathematically without introducing the polarization ($\vec{P}$) and electric displacement ($\vec{D}$) fields, neither of which is observable. I also show that most `quantum mechanical' aspects of the existing microscopic theory of electricity in materials are compatible with, or required features of, a statistical theory of classical particles whose charges and masses are comparable to those of electrons and nuclei.

cond-mat.mtrl-sci↗

arXiv2024

Wave theory of lattice dynamics

I present the mathematical structure of classical phonon theory in a general form, which emphasizes the wave natures of phonons, and which can serve as a robust foundation for further development of the theory of strongly interacting phonons. I also show that the Fourier transform (FT) of the mass-weighted velocity-velocity correlation function (mVVCF) is exactly the distribution of the classical kinetic energy among frequencies and wavevectors. Because this result is classically exact, it is general: It is as valid, theoretically, for a liquid or a molecule in a non-thermal non-stationary state as it is for a crystal at thermal equilibrium at a low temperature. Therefore, as well as being of fundamental importance to physical theory, this result implies that calculating the FT of the mVVCF from atomistic simulations is a much more powerful computational tool than it is believed to be. Existing theory shows only that the FT of the mVVCF is proportional to the vibrational density of states at thermal equilibrium, and under the simplifying assumption that the number of available vibrational states is equal to the number of degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2023

Ultrafast polarization switching in BaTiO$_3$ by photoactivation of its ferroelectric and central modes

We use molecular dynamics simulations with machine-learned atomistic force fields to simulate photoexcitation of BaTiO3 by a femtosecond laser pulse whose photon energy exceeds the optical gap. We demonstrate selective displacive excitation of coherent zone-center ferroelectric mode phonons and of the strongly anharmonic central mode. We show that the direction of P can either be reversed by a pulse in hundreds of femtoseconds or, on a longer time scale and when combined with a weak field, switched to any one of its symmetry-equivalent directions.

cond-mat.mtrl-sci↗

arXiv2023

Derivation of Bose-Einstein statistics from the uncertainty principle

The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. Since infinitely precise measurements are impossible, a measurement can, at best, constrain the location of this point to a region of phase space whose area is finite. This paper explores the implications of assuming that this finite area is bounded from below. I prove that if the same lower bound applied to every degree of freedom of a sufficiently cold classical dynamical system, the distribution of the system's energy among its degrees of freedom would be a Bose-Einstein distribution.

cond-mat.stat-mech↗

arXiv2023

Breakdown of phonon band theory in MgO

We present a series of detailed images of the distribution of kinetic energy among frequencies and wavevectors in the bulk of an MgO crystal as it is heated slowly until it melts. These spectra, which are Fourier transforms of mass-weighted velocity-velocity correlation functions calculated from accurate molecular dynamics (MD) simulations, provide a valuable perspective on the growth of thermal disorder in ionic crystals. We use them to explain why the most striking and rapidly-progressing departures from a band structure occur among longitudinal optical (LO) modes, which would be the least active modes at low temperature (T) if phonons did not interact. The degradation of the LO band begins, at low T, as an anomalously-large broadening of modes near the center of the Brillouin zone (BZ), which gradually spreads towards the BZ boundary. The LO band all but vanishes before the crystal melts, and transverse optical (TO) modes' spectral peaks become so broad that the TO branches no longer appear band-like. Acoustic bands remain relatively well defined until melting of the crystal manifests in the spectra as their sudden disappearance. We argue that, even at high T, the long wavelength acoustic (LWA) phonons of an ionic crystal can remain partially immune to disorder generated by its LO phonons; whereas, even at low T, its LO phonons can be strongly affected by LWA phonons. This is because LO displacements average out in much less than the period of an LWA phonon; whereas during each period of an LO phonon an LWA phonon appears as a quasistatic perturbation of the crystal, which warps the LO mode's intrinsic electric field. LO phonons are highly sensitive to acoustic warping of their intrinsic fields because their frequencies depend strongly on them: They cause the large frequency difference between LO and TO bands known as LO-TO splitting.

cond-mat.mtrl-sci↗

arXiv2012

Fermi level pinning can determine polarity in semiconductor nanorods

First-principles calculations of polar semiconductor nanorods reveal that their dipole moments are strongly influenced by Fermi level pinning. The Fermi level for an isolated nanorod is found to coincide with a significant density of electronic surface states at the end surfaces, which are either mid-gap states or band-edge states. These states pin the Fermi level, and therefore fix the potential difference across the rod. We provide evidence that this effect can have a determining influence on the polarity of nanorods, and has consequences for the way a rod responds to changes in its surface chemistry, the scaling of its dipole moment with its size, and the dependence of polarity on its composition.

cond-mat.mes-hall↗

arXiv2011

Factors influencing the distribution of charge in polar nanocrystals

We perform first-principles calculations of wurtzite GaAs nanorods to explore the factors determining charge distributions in polar nanostructures. We show that both the direction and magnitude of the dipole moment $\mathbf{d}$ of a nanorod, and its electic field, depend sensitively on how its surfaces are terminated and do not depend strongly on the spontaneous polarization of the underlying lattice. We identify two physical mechanisms by which $\mathbf{d}$ is controlled by the surface termination, and we show that the excess charge on the nanorod ends is not strongly localized. We discuss the implications of these results for tuning nanocrystal properties, and for their growth and assembly.

cond-mat.mes-hall↗

arXiv2009

Melting slope of MgO from molecular dynamics and density functional theory

We combine density functional theory (DFT) with molecular dynamics simulations based on an accurate atomistic force field to calculate the pressure derivative of the melting temperature of magnesium oxide at ambient pressure - a quantity for which a serious disagreement between theory and experiment has existed for almost 15 years. We find reasonable agreement with previous DFT results and with a very recent experimental determination of the slope. We pay particular attention to areas of possible weakness in theoretical calculations and conclude that the long-standing discrepancy with experiment could only be explained by a dramatic failure of existing density functionals or by flaws in the original experiment.

cond-mat.mtrl-sci↗

arXiv2006

Giant Wave-Drag Enhancement of Friction in Sliding Carbon Nanotubes

Molecular dynamics simulations of coaxial carbon nanotubes in relative sliding motion reveal a striking enhancement of friction when phonons whose group velocity is close to the sliding velocity of the nanotubes are resonantly excited. The effect is analogous to the dramatic increase in air drag experienced by aircraft flying close to the speed of sound, but differs in that it can occur in multiple velocity ranges with varying magnitude, depending on the atomic level structures of the nanotubes. The phenomenon is a general one that may occur in other nanoscale mechanical systems.

cond-mat.mtrl-sci↗

arXiv2006

On the theory underlying the Car-Parrinello method and the role of the fictitious mass parameter

The theory underlying the Car-Parrinello extended-lagrangian approach to {\em ab initio} molecular dynamics (CPMD) is reviewed and reexamined using 'heavy' ice as a test system. It is emphasized that the adiabatic decoupling in CPMD is not a decoupling of electronic orbitals from the ions but only a decoupling of a subset of the orbital vibrational modes from the rest of the necessarily-coupled system of orbitals and ions. Recent work (J. Chem. Phys. {\bf 116}, 14 (2002)) has pointed out that, due to the orbital-ion coupling that remains once adiabatic-decoupling has been achieved, a large value of the fictitious mass $μ$ can lead to systematic errors in the computed forces in CPMD. These errors are further investigated in the present work with a focus on those parts of these errors that are not corrected simply by rescaling the masses of the ions. It is suggested that any comparison of the efficiencies of Born-Oppenheimer molecular dynamics (BOMD) and CPMD should be performed at a similar level of accuracy. If accuracy is judged according to the average magnitude of the systematic errors in the computed forces, the efficiency of BOMD compares more favorably to that of CPMD than previous comparisons have suggested.

cond-mat.stat-mech↗

arXiv2004

Temperature Dependence of the Band Gap of Semiconducting Carbon Nanotubes

The temperature dependence of the band gap of semiconducting single-wall carbon nanotubes (SWNTs) is calculated by direct evaluation of electron-phonon couplings within a ``frozen-phonon'' scheme. An interesting diameter and chirality dependence of $E_g(T)$ is obtained, including non-monotonic behavior for certain tubes and distinct ``family'' behavior. These results are traced to a strong and complex coupling between band-edge states and the lowest-energy optical phonon modes in SWNTs. The $E_g(T)$ curves are modeled by an analytic function with diameter and chirality dependent parameters; these provide a valuable guide for systematic estimates of $E_g(T)$ for any given SWNT. Magnitudes of the temperature shifts at 300 K are smaller than 12 meV and should not affect $(n,m)$ assignments based on optical measurements.

cond-mat.mtrl-sci↗

arXiv2004

Hydrostatic Pressure Effects on the Structural and Electronic Properties of Carbon Nanotubes

We study the structural and electronic properties of isolated single-wall carbon nanotubes (SWNTs) under hydrostatic pressure using a combination of theoretical techniques: Continuum elasticity models, classical molecular dynamics simulations, tight-binding electronic structure methods, and first-principles total energy calculations within the density-functional and pseudopotential frameworks. For pressures below a certain critical pressure $P_c$, the SWNTs' structure remains cylindrical and the Kohn-Sham energy gaps of semiconducting SWNTs have either positive or negative pressure coefficients depending on the value of $(n,m)$, with a distinct "family" (of the same $n-m$) behavior. The diameter and chirality dependence of the pressure coefficients can be described by a simple analytical expression. At $P_c$, molecular-dynamics simulations predict that isolated SWNTs undergo a pressure-induced symmetry-breaking transformation from a cylindrical shape to a collapsed geometry. This transition is described by a simple elastic model as arising from the competition between the bond-bending and $PV$ terms in the enthalpy. The good agreement between calculated and experimental values of $P_c$ provides a strong support to the ``collapse'' interpretation of the experimental transitions in bundles.

cond-mat.other↗

arXiv2003

A many-body interatomic potential for ionic systems: application to MgO

An analytic representation of the short-range repulsion energy in ionic systems is described that allows for the fact that ions may change their size and shape depending on their environment. This function is extremely efficient to evaluate relative to previous methods of modeling the same physical effects. Using a well-defined parametrization procedure we have obtained parameter sets for this energy function that reproduce closely the density functional theory potential energy surface of bulk MgO. We show how excellent agreement can be obtained with experimental measurements of phonon frequencies and temperature and pressure dependences of the density by using this effective potential in conjunction with ab initio parametrization.

cond-mat.mtrl-sci↗

arXiv2001

How well do Car-Parrinello simulations reproduce the Born-Oppenheimer surface ? Theory and Examples

We derive an analytic expression for the average difference between the forces on the ions in a Car-Parrinello simulation and the forces obtained at the same ionic positions when the electrons are at their ground state. We show that for common values of the fictitious electron mass, a systematic bias may affect the Car-Parrinello forces in systems where the electron-ion coupling is large. We show that in the limit where the electronic orbitals are rigidly dragged by the ions the difference between the two dynamics amounts to a rescaling of the ionic masses, thereby leaving the thermodynamics intact. We study the examples of crystalline magnesium oxide and crystalline and molten silicon. We find that for crystalline silicon the errors are very small. For crystalline MgO the errors are very large but the dynamics can be quite well corrected within the rigid-ion model. We conclude that it is important to control the effect of the electron mass parameter on the quantities extracted from Car-Parrinello simulations.

cond-mat.mtrl-sci↗