scholarly journals Pressure and stress tensor of complex anharmonic crystals within the stochastic self-consistent harmonic approximation

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
Lorenzo Monacelli ◽  
Ion Errea ◽  
Matteo Calandra ◽  
Francesco Mauri
Keyword(s):  
Stress Tensor ◽  
Harmonic Approximation ◽  
Self Consistent ◽  
Anharmonic Crystals

SELF-CONSISTENT THEORY OF ELASTIC PROPERTIES OF STRONGLY ANHARMONIC CRYSTALS I: GENERAL TREATMENT AND COMPARISON WITH COMPUTER SIMULATIONS AND EXPERIMENT FOR FCC CRYSTALS

1995 ◽  
Vol 09 (07) ◽  
pp. 803-817 ◽  
Author(s):  
V.I. ZUBOV ◽  
J.F. SANCHEZ ◽  
N.P. TRETIAKOV ◽  
A.E. YUSEF
Keyword(s):  
Elastic Constant ◽  
Characteristic Temperature ◽  
Harmonic Approximation ◽  
Computer Time ◽  
Lattice Points ◽  
Cubic Symmetry ◽  
Atomic Displacements ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Anharmonic Crystals

Based on the correlative method of an unsymmetrized self-consistent field,16–23 we have derived expressions for elastic constant tensors of strongly anharmonic crystals of cubic symmetry. Each isothermal elastic constant consists of four terms. The first one is the zeroth approximation containing the main anharmonicity (up to the fourth order). The second term is the quantum correction. It is important at temperatures below the De-bye characteristic temperature. Finally, the third and fourth terms are the perturbation theory corrections which take into account the influence of the correlations in atomic displacements from the lattice points and that of the high-order anharmonicity respectively. These corrections appear to be small up to the melting temperatures. It is sufficient for a personal computer to perform all our calculations with just a little computer time. A comparison with certain Monte Carlo simulations and with experimental data for Ar and Kr is made. For the most part, our results are between. The quasi-harmonic approximation fails at high temperatures, confirming once again the crucial role of strong anharmonicity.

scholarly journals Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation

2019 ◽  
Vol 3 (7) ◽  
Author(s):  
Ifeanyi John Onuorah ◽  
Pietro Bonfà ◽  
Roberto De Renzi ◽  
Lorenzo Monacelli ◽  
Francesco Mauri ◽  
...  
Keyword(s):  
Muon Spin ◽  
Harmonic Approximation ◽  
Quantum Effects ◽  
Self Consistent ◽  
Muon Spin Spectroscopy

On the Dynamical Propeties of a Strongly Anharmonic Face-Centered Cubic Crystal

1998 ◽  
Vol 12 (27n28) ◽  
pp. 2869-2879 ◽  
Author(s):  
V. I. Zubov ◽  
C. G. Rodrigues ◽  
M. F. Pascual
Keyword(s):  
Crystallographic Direction ◽  
Face Centered Cubic ◽  
Mean Square ◽  
Cubic Crystal ◽  
Cubic Lattice ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Face Centered ◽  
Anharmonic Crystals

We study the interatomic correlations and mean square relative displacements (MSRD) in anharmonic crystals on the basis of the correlative method of unsymmetrized self-consistent field (CUSF). Here we present general formulae for crystals with the anharmonicity, including the strong one, up to the fourth anharmonic terms and perform calculations of the quadratic correlation moments (QCM) in a crystal with face centered cubic lattice, namely in solid Ar. The second order of CUSF allows one to investigate correlations in this lattice between the nearest, second, third and fourth neighbors. The anharmonicity was demonstrated to have strong effect on the interatomic correlations at temperatures above 0.4 of the melting temperature causing a drastic rise near the spinodal point. The dependence of QCM on the distance between atoms and on the crystallographic direction is discussed.

scholarly journals A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

1998 ◽  
Vol 07 (02) ◽  
pp. 243-274 ◽  
Author(s):  
H. Hofmann ◽  
D. Kiderlen
Keyword(s):  
Harmonic Approximation ◽  
Linear Response Theory ◽  
Collective Modes ◽  
Fluctuation Dissipation ◽  
Second Moments ◽  
Fluctuation Dissipation Theorem ◽  
Dissipative Tunneling ◽  
Self Consistent ◽  
Path Approximation ◽  
Consistent Treatment

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients Dμν. The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the Dμν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

Non-linear self-consistent screening applied to metallic hydrogen

1979 ◽  
Vol 57 (8) ◽  
pp. 1185-1195 ◽  
Author(s):  
M. D. Whitmore ◽  
J. P. Carbotte ◽  
R. C. Shukla
Keyword(s):  
Harmonic Approximation ◽  
Spherical Approximation ◽  
Face Centered Cubic ◽  
Superconducting Transition ◽  
Metallic Hydrogen ◽  
Proton Proton ◽  
Effective Electron ◽  
Functional Derivatives ◽  
Self Consistent ◽  
Non Linear

Non-linear self-consistent screening of a proton by a high density electron gas has been used to find effective electron–proton potentials for metallic hydrogen for a number of densities and for both face-centered cubic and body-centered cubic structures. The resulting proton–proton potentials have been employed to calculate the phonons in the self-consistent harmonic approximation, following which the effective distributions α2F(ω) were evaluated in the plane wave, spherical approximation. From these, the superconducting transition temperatures Te and functional derivatives were found.Non-linear effects are seen to be important. For both structures, dynamical instabilities occur for rs ≥ 1.0, indicating densities higher than those predicted by linear theory are required. In addition, for the fcc case, Te is enhanced.Te is found to depend sensitively on the structure assumed; for the bcc case, it is very small.For fcc H. McMillan's equation overestimates Te by about 40%, even when λ = 0.5. Leavens' formula agrees with solutions of the Eliashberg gap equations to within about 10%.

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