CALCULATIONS OF PHONON DISPERSION CURVES

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dc.contributor.authorLawan, Sani Taura
dc.date.accessioned2014-02-04T11:34:55Z
dc.date.available2014-02-04T11:34:55Z
dc.date.issued1999-06
dc.descriptionA 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.en_US
dc.description.abstractThe 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 ien_US
dc.identifier.urihttp://hdl.handle.net/123456789/187
dc.language.isoenen_US
dc.subjectCALCULATIONSen_US
dc.subjectPHONONen_US
dc.subjectDISPERSION CURVESen_US
dc.subjectDENSITY OF STATESen_US
dc.titleCALCULATIONS OF PHONON DISPERSION CURVESen_US
dc.typeThesisen_US
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