A structural approach to vibrational properties ranging from crystals to disordered systems

Soft Matter ◽  
2021 ◽  
Author(s):  
Xin Tan ◽  
Ying Guo ◽  
Duan Huang ◽  
Ling Zhang
Keyword(s):  
Disordered Systems ◽  
Structural Disorder ◽  
Structural Approach ◽  
Vibrational Properties ◽  
Disordered Solids ◽  
Intense Debate

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate.

Lie Group Calculation of the Green Function of Disordered Systems

1991 ◽  
Vol 253 ◽  
Author(s):  
Christian Brouder
Keyword(s):  
Green Function ◽  
Lie Group ◽  
Disordered Systems ◽  
Perturbation Expansion ◽  
Structural Disorder ◽  
Dyson Equation ◽  
Interatomic Distances ◽  
The Green Function ◽  
Atomic Centre ◽  
Structural Matrix

ABSTRACTWithin the framework of the muffin-tin multiple-scattering theory, the scattering path operators are given by the inverse of a matrix consisting of atomic t-matrices and a structural matrix. The influence of the displacement of an atomic centre on the structural matrix can be described analytically using Lie group techniques. From this analytical expression and the standard perturbation expansion of the Lippmann-Schwinger equation, it is possible to write the Green function of a disordered system as a series of terms whichare averages over configurations. These averages can be calculated analytically from themoments of the interatomic distances. Special terms of this series are then summed up toinfinity using Dyson equation. This formalism is computationally very effective to calculate electronic properties of systems with thermal or structural disorder. In this paper, the theoretical basis of this approach is briefly described and the convergence properties of the expansions are investigated.

Electron States in Static Disordered Systems and Fluid Systems

1991 ◽  
Vol 02 (01) ◽  
pp. 305-309
Author(s):  
L. CRUZEIRO-HANSSON ◽  
J.O. BAUM ◽  
J.L. FINNEY
Keyword(s):  
Path Integral ◽  
Disordered Systems ◽  
Hard Spheres ◽  
Quantum Statistical Mechanics ◽  
Structural Disorder ◽  
Path Integral Formulation ◽  
Electron States ◽  
Fluid Systems ◽  
Fluid Environment ◽  
Quantum Statistical

The path integral formulation of quantum statistical mechanics is used to study the effect of structural disorder on the electron states at finite temperatures. The following systems are investigated: an excess electron in a) a perfect hard spheres crystal, b) a hard spheres crystal with a vacancy and c) a hard spheres fluid. The localizing effect of a vacancy on the electron equals that of a fluid environment.

scholarly journals Boson-peak-like anomaly caused by transverse phonon softening in strain glass

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shuai Ren ◽  
Hong-Xiang Zong ◽  
Xue-Fei Tao ◽  
Yong-Hao Sun ◽  
Bao-An Sun ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Martensitic Transformation ◽  
Glassy State ◽  
Structural Disorder ◽  
Boson Peak ◽  
Vibrational Properties ◽  
Simulation Studies ◽  
Van Hove Singularity ◽  
Phonon Softening ◽  
Transverse Acoustic

AbstractStrain glass is a glassy state with frozen ferroelastic/martensitic nanodomains in shape memory alloys, yet its nature remains unclear. Here, we report a glassy feature in strain glass that was thought to be only present in structural glasses. An abnormal hump is observed in strain glass around 10 K upon normalizing the specific heat by cubed temperature, similar to the boson peak in metallic glass. The simulation studies show that this boson-peak-like anomaly is caused by the phonon softening of the non-transforming matrix surrounding martensitic domains, which occurs in a transverse acoustic branch not associated with the martensitic transformation displacements. Therefore, this anomaly neither is a relic of van Hove singularity nor can be explained by other theories relying on structural disorder, while it verifies a recent theoretical model without any assumptions of disorder. This work might provide fresh insights in understanding the nature of glassy states and associated vibrational properties.

scholarly journals A RIGOROUS APPROACH TO THE MAGNETIC RESPONSE IN DISORDERED SYSTEMS

2012 ◽  
Vol 24 (08) ◽  
pp. 1250022 ◽  
Author(s):  
PHILIPPE BRIET ◽  
BAPTISTE SAVOIE
Keyword(s):  
Disordered Systems ◽  
Zero Field ◽  
Quantum Gas ◽  
Random Potentials ◽  
3 Dimensional ◽  
Disordered Solids ◽  
Rigorous Approach ◽  
Diamagnetic Behavior ◽  
Thermodynamic Limits ◽  
Grand Canonical

This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence of an almost-sure non-random thermodynamic limit for the grand-canonical pressure, magnetization and zero-field orbital magnetic susceptibility. We also give an explicit formulation of these thermodynamic limits. Our results cover a wide class of physically relevant random potentials which model not only crystalline disordered solids, but also amorphous solids.

scholarly journals Some New Results on Vibrational Properties of Amorphous Group IV Semiconductors

1993 ◽  
Vol 16 (1) ◽  
pp. 65-68
Author(s):  
M. A. Grado Caffaro ◽  
M. Grado Caffaro
Keyword(s):  
Density Of States ◽  
Structure Factor ◽  
Dynamic Structure ◽  
Structural Disorder ◽  
Group Iv ◽  
Dynamic Structure Factor ◽  
Vibrational Properties ◽  
Phonon Density ◽  
Phonon Density Of States ◽  
Group Iv Semiconductors

For neutron scattering, an interesting formula is derived from the coherent one-phonon dynamic structure factor. In this derivation, phonon density of states is involved; this density is related to spectra due to structural disorder, which is investigated. Our considerations refer to amorphous Group IV semiconductors.

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