Application of the self-consistent field method to the theory of surface states of electrons in a crystal

1958 ◽  
Vol 8 (2) ◽  
pp. 148-152 ◽  
Author(s):  
Jaroslav Koutecký
Keyword(s):  
Surface States ◽  
Field Method ◽  
The Self ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

scholarly journals A self-consistent field for methane and its applications

1941 ◽  
Vol 178 (973) ◽  
pp. 119-134 ◽  
Keyword(s):  
Field Method ◽  
The Self ◽  
Angular Distributions ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Distribution Energy ◽  
Slow Electrons ◽  
Total Collision ◽  
Tetrahedral System

An approximate self-consistent field for methane has been obtained by first averaging the proton distribution over all orientations so as to obtain a spherically symmetrical field due to all the nuclei. The eight-electron problem then presented was solved by the usual self-consistent field method without exchange. Rapid convergence to self-consistency was found by using as initial approximations the charge distributions given by Coulson for the two-quantum orbitals of the tetrahedral system, averaged over all orientations. The self-consistent wave functions are used to calculate the charge distribution, energy, diamagnetic susceptibility and polarizability of the molecule and also the van der Waals forces between two molecules. The scattering of slow electrons by the self-consistent field obtained is also investigated in detail and compared with observations of total collision areas and angular distributions for methane. The observed similarity of behaviour between argon and methane in scattering slow electrons is reproduced by the theory provided the same approximation of using the self-consistent field without exchange is employed for each. Comparison of observed and calculated values of the quantities investigated indicate that the methane field is little less satisfactory than the corresponding fields for atoms.

The use of the self-consistent field method to take into account the anisotropy caused by the orientation and shape of the grains of metals

2003 ◽  
Vol 3 ◽  
pp. 82-95
Author(s):  
V.N. Nikonov
Keyword(s):  
Mechanical Properties ◽  
Bauschinger Effect ◽  
Equations Of State ◽  
Field Method ◽  
The Self ◽  
Metallic Material ◽  
Consistent Field ◽  
Self Consistent ◽  
Speed Range ◽  
Self Consistent Field

In the process of manufacturing parts by plastic deformation, the shape and orientation of the grains of the metallic material changes. The emerging mechanical texture causes anisotropy of the mechanical properties of the material. On the basis of the analysis of the interaction of grains at the microlevel, equations of state are obtained that describe the mechanical properties of the material in a wide temperature-speed range under the action of alternating loads, the superplasticity state, and the Bauschinger effect. The knowledge of the anisotropy introduced by the technology of manufacturing the part is necessary for a numerical analysis of the residual mechanical properties of the parts.

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