Site symmetry and crystal symmetry: a spherical tensor analysis
نویسندگان
چکیده
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet. Uncomment for PACS numbers title message PACS numbers: 61.72.S-,61.05.cj,02.20.-a,61.50.Ah Site symmetry and crystal symmetry 2
منابع مشابه
Investigation of thermal tunable nano metallic photonic crystal filter with mirror symmetry
Using the transfer matrix method, the effect of temperature on thetransmission spectra of thermal tunable nano metallic photonic crystal filter has beeninvestigated. Three different materials H (high refractive index material), L (lowrefractive index material) and M as a metallic layer, have been used to make thisstructure. M layer is considered to be Silver. The complex refractive index of Sil...
متن کاملEffective calculation of LEED intensities using symmetry - adapted functions
The calculation of LEED intensities in a spherical-wave representation can be substantially simplified by symmetry relations. The wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies. For overlayer systems with more than one atom per unit cell symmetry-adapted functions can be used when the division of the crystal into m...
متن کاملLocal Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure
We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...
متن کاملOrientational Sampling Schemes Based on Four Dimensional Polytopes
The vertices of regular four-dimensional polytopes are used to generate sets of uniformly distributed three-dimensional rotations, which are provided as tables of Euler angles. The spherical moments of these orientational sampling schemes are treated using group theory. The orientational sampling sets may be used in the numerical computation of solid-state nuclear magnetic resonance spectra, an...
متن کاملUltra-Fast All-Optical Symmetry 4×2 Encoder Based on Interface Effect in 2D Photonic Crystal
This paper deals with the design and simulation of all-optical 4×2 encoderusing the wave interference effect in photonic crystals. By producing 4 opticalwaveguides as input and two waveguides as output, the given structure was designed.The size of the designed structure is 133.9 μm2. The given all-optical encoder has acontrast ratio of 13.2 dB, the response time of 0.45 ...
متن کامل