Energy-Band Theory

2021 ◽  
pp. 89-172
Author(s):  
Jürgen Kübler
Keyword(s):  
Linear Combination ◽  
Plane Waves ◽  
Arbitrary Spin ◽  
Historical Background ◽  
Energy Bands ◽  
Band Theory ◽  
Plane Wave Method ◽  
Spherical Waves ◽  
Structure Constants ◽  
Scattering Phase

Various methods to calculate energy bands and the electronic structure of solids are described in detail. Although the emphasis lies on linear methods well known for their transparency and high numerical speed, traditional methods are described to supply historical background and to point the way to modern methods. After introducing Bloch electrons and the reciprocal space, plane waves, orthogonalized plane waves, and pseudopotentials are discussed, followed by the important augmented plane wave method (APW). Multiple scattering theory defines scattering phase shifts encoding atomic properties and the structure constants that describe the crystal lattice. Linear combination of atomic orbitals (LCAO) and linear combination of muffin-tin orbitals (LMTO) result in efficient and fast methods as does the related augmented spherical waves (ASW) method. The treatment of arbitrary spin configurations using the ASW method and the formulation of incommensurate spiral structures on the basis of the unitary SU(2) group are developed in detail.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

scholarly journals Structural Optimization, Electronic Band Structure, Mechanical and Thermodynamics Properties of Fe3Al

2021 ◽  
pp. 1-11
Author(s):  
I. S. Okunzuwa ◽  
E. Aigbekaen Eddy
Keyword(s):  
Density Functional ◽  
Electronic Band Structure ◽  
Plane Waves ◽  
State Density ◽  
Structural Parameter ◽  
Mechanical And Thermal Properties ◽  
Energy Bands ◽  
Electronic Band ◽  
Salt Structure ◽  
Quantum Espresso

We calculated the structural, electronic, mechanical and thermal properties of Fe3Al semiconducting using Quantum ESPRESSO, an open source first principles code based on density-functional theory, plane waves, and pseudopotentials. Structural parameter results (equilibrium lattice parameters, bulk modulus and its derivative pressure) have been reported. The underestimated band gap is obtained along with higher state density and energy bands around the fermi level. Mechanical properties of the rock-salt structure of Fe3Al, such as, shear modulus (G), Young’s modulus (E), and Poisson’s ratio () were investigated. The thermodynamic parameters are also present. The results are in good agreement with the available experimental and other theoretical results.

Band Theory: Origin of Energy Bands

2021 ◽  
Author(s):  
Mathieu Hautefeuille ◽  
Juan Hernández-Cordero
Keyword(s):  
Energy Bands ◽  
Band Theory

scholarly journals A Method for Deriving the Mean Volume Scattering Phase Function for Zodiacal Dust

1985 ◽  
Vol 85 ◽  
pp. 215-218
Author(s):  
S.S. Hong
Keyword(s):  
Linear Combination ◽  
Phase Function ◽  
Dust Particles ◽  
Zodiacal Light ◽  
Volume Scattering ◽  
Zodiacal Dust ◽  
Scattering Phase ◽  
The Mean ◽  
Scattering Phase Function ◽  
Phase Functions

AbstractA linear combination of 3 Henyey-Greenstein phase functions is substituted for the mean volume scattering phase function in the zodiacal light brightness integral. Results of the integral are then compared with the observed brightness to form residuals. Minimization of the residuals provides us with the best combination of Henyey-Greenstein functions for the scattering phase function of zodiacal dust particles.

Electromagnetic diffraction in optical systems - I. An integral representation of the image field

1959 ◽  
Vol 253 (1274) ◽  
pp. 349-357 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Integral Representation ◽  
Optical System ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Optical Systems ◽  
Angular Aperture ◽  
Spherical Waves ◽  
Simple Physical Interpretation ◽  
Electromagnetic Diffraction

An integral representation is obtained for the electromagnetic field in the image space of an optical system . This representation, which is not restricted to systems of low angular aperture, is in the form of an angular spectrum of plane waves, and is closely related to that introduced by Luneberg (1944) as a vector generalization of well-known formulae of Debye (1909) and Picht (1925). It is shown that the representation has a simple physical interpretation in terms of a modified Huygens—Fresnel principle which operates with secondary plane waves rather than with secondary spherical waves.

MOTION OF THE GROUND ON ARRIVAL OF REFLECTED LONGlTUDlNAL AND TRANSVERSE WAVES AT WlDE‐ANGLE REFLECTlON DlSTANCES

Geophysics ◽  
1961 ◽  
Vol 26 (3) ◽  
pp. 277-297 ◽  
Author(s):  
T. C. Richards
Keyword(s):  
Plane Waves ◽  
Field Work ◽  
Phase Changes ◽  
Wide Angle ◽  
Observation Distance ◽  
Transverse Waves ◽  
Additional Tool ◽  
Spherical Waves ◽  
Wide Range ◽  
The Many

The horizontal and vertical motions of the surface of the ground on the arrival of reflected longitudinal and transverse waves from an elastic discontinuity are determined theoretically, with special reference to those parameters encountered in exploring for limestone structures in the foothills of Western Canada by wide‐angle reflection techniques. The results, which cover a wide range of possible overburden velocities, are expressed by means of curves from which the displacement for any practical elastic contrast, depth and observation distance may be readily determined. Properties of these curves are examined empirically. The theory assumes plane waves in determining the amplitude ratios at the structural or free surface discontinuities and spherical waves in deriving spread factors. Corrections to the curves on account of a non‐uniform overburden velocity are considered in the case of a typical central foothills well. The evidence for PP and PS in model, and to a less extent in field work and the significance of phase changes on reflection are discussed. It is concluded that the horizontal geophone should prove to be a useful additional tool in wide‐angle reflection surveys in disturbed foothills zones. Here, it could confirm or refute the arrival of a reflection registered by the vertical geophones in the many cases where doubt exists.

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