CALCULATIONS OF THE MEAN SQUARE RELATIVE ATOMIC DISPLACEMENTS IN A SIMPLE MODEL OF AN ANHARMONIC CRYSTAL

1995 ◽  
Vol 09 (23) ◽  
pp. 1513-1519
Author(s):  
M. F. PASCUAL ◽  
V. I. ZUBOV
Keyword(s):  
Square Lattice ◽  
Mean Square ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Anharmonic Crystal ◽  
Atomic Displacements ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Mean

We have used the correlative method of unsymmetrized self-consistent field to calculate the mean square relative displacements (MSRD) of atoms in the two-dimensional model of the anharmonic crystal with square lattice. The longitudinal and transversal components of MSRD between the nearest, second, third and next neighbors have been computed. An influence of the anharmonicity on various components as well as peculiarities of the lattice considered are discussed.

ON THE INTERATOMIC CORRELATIONS AND MEAN SQUARE RELATIVE ATOMIC DISPLACEMENTS IN AN ANHARMONIC SIMPLE CUBIC LATTICE

1996 ◽  
Vol 10 (13) ◽  
pp. 599-607 ◽  
Author(s):  
M.F. PASCUAL ◽  
A.L. ROSA ◽  
V.I. ZUBOV
Keyword(s):  
Mean Square ◽  
Cubic Lattice ◽  
Atomic Displacements ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Mean ◽  
Low Dimensional

In order to study the interatomic correlation moments (QCM) and the mean square relative atomic displacements (MSRD), there has been employed the correlative method of unsymmetrized self-consistent field (CUSF). In the second order of CUSF we have calculated the longitudinal and transversal components of QCM and MSRD between the nearest, second and fourth neighbors, in the simple cubic lattice. The results are discussed in relation to those obtained previously for low-dimensional models.

CALCULATIONS OF THE INTERATOMIC CORRELATION MOMENTS IN A SIMPLE MODEL OF AN ANHARMONIC CRYSTAL

1994 ◽  
Vol 08 (08n09) ◽  
pp. 523-534 ◽  
Author(s):  
V. I. ZUBOV ◽  
M. F. PASCUAL
Keyword(s):  
Order Approximation ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zeroth Order ◽  
Anharmonic Crystal ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Anharmonic Crystals ◽  
Second Order Perturbation Theory

To study the interatomic correlations in anharmonic crystals we have used the correlative method of unsymmetrized self-consistent field (CUSF). The zeroth-order approximation of this method takes into account the main anharmonic terms but disregards the dynamical interatomic correlations at intermediate and long distances. With the aid of the first- and second-order perturbation theory we have derived the general expressions for quadratic correlations in two-dimensional models of crystals taking into account anharmonic terms up to the fourth order. Herewith we have constructed the corresponding diagrams. Correlations between the nearest, second, and third neighbors in square lattice have been calculated.

ON THE INTERATOMIC CORRELATIONS AND MEAN SQUARE RELATIVE ATOMIC DISPLACEMENTS IN AN ANHARMONIC MODEL OF THE CLOSE-PACKED CRYSTAL

1995 ◽  
Vol 09 (14) ◽  
pp. 839-847 ◽  
Author(s):  
V. I. ZUBOV ◽  
M. F. PASCUAL ◽  
C. G. RODRIGUES
Keyword(s):  
Hexagonal Lattice ◽  
Mean Square Displacement ◽  
Square Lattice ◽  
Mean Square ◽  
Anharmonic Crystal ◽  
First Order ◽  
Atomic Displacements ◽  
Self Consistent Field ◽  
Line Passing ◽  
Anharmonic Crystals

The correlative method of unsymmetrized self-consistent field (CUSF) is used to study the interatomic correlations and mean square displacements in anharmonic crystals. In the first order of CUSF we have derived the formula for the atomic mean square displacement and quadratic correlation between displacements of two nearest neighbors along the line passing through their centers [Formula: see text] where n is the dimensionality of a lattice and Z is the coordinational number. In the second order of CUSF we have calculated the quadratic correlation moments and mean square relative displacements in the two-dimensional model of an anharmonic crystal with hexagonal lattice. The results are compared with those for square lattice obtained previously.

ON THE SELF-CONSISTENT STATISTICAL THEORY OF STRUCTURAL, DYNAMICAL, AND THERMODYNAMIC SURFACE PROPERTIES OF ANHARMONIC CRYSTALS II: The Properties of Arbitrary Oriented Surfaces of the Two-Dimensional Model with Square Lattice

1990 ◽  
Vol 04 (03) ◽  
pp. 479-499
Author(s):  
V. I. ZUBOV ◽  
F. BANYERETSE
Keyword(s):  
Surface Properties ◽  
Lattice Relaxation ◽  
Field Method ◽  
Square Lattice ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Anharmonic Crystal ◽  
Thermodynamic Surface ◽  
Self Consistent ◽  
Two Dimensional Model

The correlative unsymmetrized self-consistent field method is used to study surface properties of the two-dimensional model of an anharmonic crystal with square lattice having various Miller indices. The lattice relaxation, the amplitudes of atomic vibrations and the thermodynamic surface functions are calculated. The typical nonsingular and vicinal surfaces are considered. The dependence of thermodynamic surface functions on the surface orientation is obtained.

INTERATOMIC CORRELATION MOMENTS AND MEAN SQUARE RELATIVE DISPLACEMENTS IN AN ANHARMONIC CRYSTAL WITH THE FACE-CENTERED CUBIC LATTICE

1996 ◽  
Vol 10 (21) ◽  
pp. 1043-1051 ◽  
Author(s):  
V.I. ZUBOV ◽  
M.F. PASCUAL ◽  
C.G. RODRIGUES
Keyword(s):  
Face Centered Cubic ◽  
Mean Square ◽  
Anharmonic Crystal ◽  
Cubic Lattice ◽  
Atomic Displacements ◽  
Consistent Field ◽  
Self Consistent Field ◽  
The Face ◽  
Face Centered ◽  
Anharmonic Crystals

Using the correlative method of unsymmetrized self-consistent field we study the dynamical properties of anharmonic crystals, namely, the quadratic correlations between atomic displacements from the equilibrium positions and their mean square relative displacements in anharmonic crystals. In the present paper we calculate these values for a weakly anharmonic crystals with the face-centered cubic lattice in which the nearest neighbors interact. The second order of the method enables one to calculate for this lattice the correlations between the nearest, second, third and fourth neighbors. The results are compared with those obtained previously for simplified models. The dependence on the coordination number and on the dimensionality of the lattice is discussed.

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.

Determining the Morphology and the Interaction Between Terminally-Anchored Polymer Layers

1996 ◽  
Vol 461 ◽  
Author(s):  
A. C. Balazs ◽  
C. Singh
Keyword(s):  
Field Theory ◽  
Colloidal Particles ◽  
The Other ◽  
Two Dimensional ◽  
Planar Surfaces ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Energy Of Interaction ◽  
Self Consistent Field Theory

ABSTRACTUsing a two dimensional self-consistent field theory, we investigate the interactions between two planar surfaces that are coated with terminally-anchored homopolymers. One surface is coated with A chains and the other is covered with B homopolymers. The chains are grafted at low densities and the B polymers are chosen to be solvophobic, while the A chains are relatively solvophilic. We determine the morphology of the layers and the energy of interaction asthe surfaces are compressed. Our results provide guidelines for controlling the interaction between polymer-coated colloidal particles.

ON THE THERMODYNAMICS OF AN ANHARMONIC CRYSTAL WITH HIGH ANISOTROPY

1995 ◽  
Vol 09 (04n05) ◽  
pp. 585-597 ◽  
Author(s):  
V.I. ZUBOV ◽  
M.P. LOBO ◽  
J.N.T. RABELO
Keyword(s):  
Equations Of State ◽  
Quantum Corrections ◽  
Anharmonic Crystal ◽  
Cubic Crystal ◽  
Specific Heats ◽  
Atomic Displacements ◽  
High Anisotropy ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Strong Anharmonicity

The correlative method of the unsymmetrized self-consistent field is used to study the atomic properties of a simple model of an anharmonic crystal with strong anisotropy, namely, a crystal with primitive hexagonal (PH) lattice. The self-consistent potential, Helmholtz free energy and mean-square atomic displacements are obtained in the case of weak anharmonicity. Equations of state are derived and solved. The internal energy and specific heats are calculated. The first quantum corrections are expressed in terms of the de Boer parameter included. An influence of anharmonicity is analyzed. The thermal expansion of the model considered is very anisotropic but the quantum corrections to the lattice parameters are isotropic. The results of calculations are compared with those for one- and two-dimensional models and for the isotropic crystal with the same coordination number as in the PH lattice, i.e. a body-centered cubic crystal. Other things being equal, the coefficient of volume expansion and specific heats of anisotropic crystals are greater than those of isotropic ones. A possibility of studying the strong anharmonicity in anisotropic crystals is discussed.

Sign in / Sign up

Export Citation Format

Share Document