A Method for the Determination of Real-Space Interatomic Force-Constants
- PDF / 346,563 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 95 Downloads / 156 Views
A METHOD FOR THE DETERMINATION OF REAL-SPACE INTERATOMIC FORCE-CONSTANTS. Andrew A. Quong*, Amy Y. Liu* and Barry M. Klein** *Complex Systems Theory Branch, Naval Research Laboratory, Washington DC 20375 *'Physics Department, University of California, Davis CA 95616
ABSTRACT We present a method for the self-consistent determination of inter-atomic force-constants. Using non-local ab-initio pseudopotentials to represent the ion-electron interaction and linear response theory to calculate the self-consistent change in the electron density, we are able to calculate the dynamical matrices at arbitrary points in the Brillouin zone. Diagonalization of the dynamical matrix yields phonon eigenvectors and eigenvalues, and fourier inversion yields the real-space interatomic force-constants. We present numerical results for the phonon-dispersion of a variety of metals.
INTRODUCTION Density-functional theory[i] has given us the ability to calculate from first principles many properties of solids. In particular, by calculating the energy dependence on lattice constant for a particular structure we can obtain equilibrium lattice constants and bulk moduli. Moreover, by comparing energies of different structures, we can predict the relative stability of one phase to another. By distorting of the crystal appropriately, and calculating the change in energy, elastic moduli and high-symmetry phonon frequencies can be determined. Although the determination of the ground state properties for structures containing many atoms per unit cell is possible, the calculation of phonons at arbitrary points in the Brillouin zone and real-space inter-atomic force-constants is beyond the limit of present computers using the total energy method. In this paper, we present a computationally efficient method that allows for the direct computation of the dynamical matrix at arbitrary points in the Brillouin zone. Diagonalization of the dynamical matrix yields phonon frequencies and by taking the inverse fourier transform of the dynamical matrix, the real-space inter-atomic force-constants are obtained.
THEORY Calculation of the phonon dispersion relations in a solid requires the forces of interaction between atoms, which may be determined by expanding the total energy of the solid in a series of the atomic displacements. The energy change to second order is written as
E2 = E E u~%,~~K1Wn),(1 lka P1k'f3
where l't') is the force that couples atoms at sites 1r and I'W', ulK is the displacement of 1'p(rK, the corresponding ion, and a labels the cartesian coordinates. The system of interacting ions and electrons may be transformed into an equivalent single particle system. The single particle wavefunctions 0,(r) and the single particle eigenvalues c, are determined by solving the Kohn-Sham equation of density functional theory[1]. The effective potential for a. single electron contains contributions from the electron-ion interaction V5j(r), written as a sum of ab-initio pseudopotentials, the electron-electron interaction Vee(r), and the exchange-correlat
Data Loading...
