CALCULATIONS OF PHONON DISPERSION CURVES
CALCULATIONS OF PHONON DISPERSION CURVES
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Date
1999-06
Authors
Lawan, Sani Taura
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Abstract
The phonon density of states and dispersion relations of one and two atoms crystal structures
are studied for SC and BCC lattices with interatomic interaction up to and including second
neighbours. Analytical expression for dispersion relations in the principal symmetry directions are
'derived. The force constants of one and two (CsCl) crystals are determined by an optimization
procedure using the dispersion in the [100], [110], [111] directions. The dispersion curves calculated
with a two- neigbour, six- parameter give a reasonable fit to the dispersion data in the principal
symmetry directions.
The secular equation containing three directional symmetry calculated for the
eigenfrequencies of wave vectors also served to establish a histogram of the frequency of the normal
modes in which the singularities caused by the critical points are explicitly included.
The FORTRAN code which is used in the computation of the density of states and dispersion
curves was obtained from the Boardman Physics Program book, and modified substantially for
adaptation for the Personal Computer (PC). The cited standard subroutine libraries which are not
available were substituted with our own written programs. The output of the program was also
redesigned to produce numbers appropriate for use in a plotting software. To avoid singularities
inherent in the original code we converted it to doubled precision and added numbers whicbj§o not
noticeably affect the result.
The program can be used for any lattice phonon dispersion and density of states calculation
once the relative dynamic matrix has been determined.
v i
Description
A THESIS SUBMITTED TO THE POST GRADUATE SCHOOL OF AHMADU
BELLO UNIVERSITY, ZARIA, IN PARTIAL FULFILMENT FOR THE AWARD
OF THE MASTER OF SCIENCE (M.SC) DEGREE IN PHYSICS.
Keywords
CALCULATIONS, PHONON, DISPERSION CURVES, DENSITY OF STATES