Accession Number : AD0258611

Title :   THEORETICAL INVESTIGATION OF THE ELECTRONIC ENERGY BANDS FOR THE ZIRCONIUM-OXYGEN CRYSTAL. PART II. SYMMETRY-ADAPTED ORBITALS AND SECULAR ELEMENTS

Corporate Author : STOCKHOLM UNIV (SWEDEN)

Personal Author(s) : FLODMARK,STIG ; ROOS,BJORN

Report Date : MAR 1961

Pagination or Media Count : 1

Abstract : Explicit formulae for the elements of the split secular equations which yield the electronic energy bands in the close-packed hexagonal Zr-O system are presented. The methods used to split the secular equations in the present report are based on the theoretical development outlined previously (AD-257 432). Certain singular idempotent projection matrices, labelled by the diagonal elements of the irreducible representations of the different little groups of the crystal symmetry group, are very useful for the determination of the split secular matrices. These matrices are given for the case where the screw symmetry of the crystal is not considered; they are unique except for similarity transformations. A systematic method of further transforming the singular secular matrices into reduced form and, finally into real form is outlined. Some relations for the elements of the secular equations and a discussion of the influence of the screw symmetry are given. (Author)

Descriptors :   *CRYSTALS, *OXIDES, *SOLID STATE PHYSICS, *ZIRCONIUM COMPOUNDS, ALGEBRA, ATOMIC ORBITALS, CRYSTAL LATTICES, ELECTRONICS, ENERGY, MATHEMATICAL ANALYSIS, MATRICES(MATHEMATICS), OXYGEN, ZIRCONIUM

Distribution Statement : APPROVED FOR PUBLIC RELEASE