Lattice dynamics in gallium using the "6-exp" potential with parameters determined by the "least squares" method

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Wallace Larry Freeman (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Clifton Clark

Abstract: The equations of motion for the dumbbell molecules of gallium are derived using the harmonic approximation. The "6-exp" interaction potential energy function is used to derive analytic expressions for the interatomic coupling constants. The intermolecular coupling constants are then determined numerically. These are used to calculate the elements of the dynamical matrix. The dynamical matrix is solved for the normal mode frequencies. The "Least Squares" method is used with a computer program to select a set of "6-exp" parameters to best fit the frequencies measured by others. Since some imaginary frequencies occurred for all sets of parameters found, the model does not agree with experimental results. There are two possible reasons for this disagreement: (1) The "6-exp" interaction function may not be applicable to gallium or (2) it may be invalid to treat gallium as having a molecular structure.

Additional Information

Language: English
Date: 1971
Gallium $x Analysis
Lattice dynamics
Equations of motion
Dispersion relations
Least squares

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