Coarse Graining of Intermolecular Vibrations by a Karhunen-Loève Transformation of Atomic Displacement Vectors

2009 ◽  
Vol 5 (7) ◽  
pp. 1814-1821 ◽  
Author(s):  
Hirohiko Houjou
Keyword(s):  
Coarse Graining ◽  
Atomic Displacement ◽  
Displacement Vectors ◽  
Karhunen Loeve Transformation ◽  
Karhunen Loève Transformation ◽  
Intermolecular Vibrations

scholarly journals Orientation Dependent Mechanical Responses and Plastic Deformation Mechanisms of ZnSe Nano Films under Nanoindentation

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 3014
Author(s):  
Chao Xu ◽  
Futi Liu ◽  
Chunmei Liu ◽  
Pei Wang ◽  
Huaping Liu
Keyword(s):  
Plastic Deformation ◽  
Elastic Recovery ◽  
Structural Evolution ◽  
Atomic Displacement ◽  
Deformation Mechanisms ◽  
Formation Mechanisms ◽  
Plastic Deformations ◽  
Mechanical Responses ◽  
Displacement Vectors ◽  
Dynamics Simulations

Although ZnSe has been widely studied due to its attractive electronic and optoelectronic properties, limited data on its plastic deformations are available. Through molecular dynamics simulations, we have investigated the indentations on the (001), (110), and (111) planes of ZnSe nano films. Our results indicate that the elastic modulus, incipient plasticity, elastic recovery ratio, and the structural evolutions during the indenting process of ZnSe nano films show obvious anisotropy. To analyze the correlation of structural evolution and mechanical responses, the atomic displacement vectors, atomic arrangements, and the dislocations of the indented samples are analyzed. Our simulations revealed that the plastic deformations of the indented ZnSe nano films are dominated by the nucleation and propagation of 1/2<110> type dislocations, and the symmetrically distributed prismatic loops emitted during the indenting process are closely related with the mechanical properties. By studying the evolutions of microstructures, the formation process of the dislocations, as well as the formation mechanisms of the emitted prismatic loops under the indented crystalline planes are discussed. The results presented in this work not only provide an answer for the questions about indentation responses of ZnSe nano films, but also offer insight into its plastic deformation mechanisms.

Die Karhunen-Loève-Transformation

1997 ◽  
pp. 295-307
Author(s):  
Thomas Lehmann ◽  
Walter Oberschelp ◽  
Erich Pelikan ◽  
Rudolf Repges
Keyword(s):  
Karhunen Loeve Transformation ◽  
Karhunen Loève Transformation

Modulated Atomic Displacement Description and Easy Structural Factor Computing

1982 ◽  
Vol 21 ◽  
Author(s):  
P. Wolfers
Keyword(s):  
Wave Vector ◽  
Atomic Displacement ◽  
Crystallographic Structure ◽  
General Description ◽  
Single Wave ◽  
Scattering Center ◽  
Displacement Vectors ◽  
Vector Approximation ◽  
Vector Case ◽  
Modulated Phase

ABSTRACTThe displacement of a particular atom in a modulated crystallographic structure can be described in terms of a Fourier Series. In the harmonic single wave vector approximation, the structure factor can be written as a function of the atomic displacement vectors. Such expressions are however not valid in the multi-wave-vector case. We propose a general description for the modulation of displacement where each scattering center (atom) is distributed on several sites whose population is modulated. In the paper, we will show that approach is well suited for computing. We have developed a general least squares program which has been applied to the modulated phase of αU(T < 43 K) [2].

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