On b.c.c. 3He, a Highly Anharmonic Crystal

1971 ◽  
Vol 49 (6) ◽  
pp. 761-775 ◽  
Author(s):  
H. R. Glyde
Keyword(s):  
Elastic Constants ◽  
Lattice Dynamics ◽  
Phonon Frequency ◽  
Frequency Dispersion ◽  
Anharmonic Crystal ◽  
Self Consistent ◽  
Anharmonic Term ◽  
Single Method ◽  
The One ◽  
Anharmonic Crystals

The self consistent (SC) theory of lattice dynamics for highly anharmonic crystals is derived via expansion and selected re-summation of the one phonon Green function. Since perturbation treatments of weakly anharmonic crystals use the same expansion, the two cases can then be viewed as variations in a single method. The SC theory to lowest (SCH) and second (SC2) order and a re-order potential power series in which each coefficient appears averaged over the vibrational motion is derived.The SCH theory with the leading correction in the new series, the cubic anharmonic term, is applied to b.c.c. 3He. Phonon frequency dispersion curves, lifetimes, sound velocities, and elastic constants are computed. The phonons are well defined and the elastic constants and isotropy agree quite well with experiment. Although the cubic correction is significant, it suggests that the re-ordered series converges.

ON THE SELF-CONSISTENT STATISTICAL THEORY OF STRUCTURAL, DYNAMICAL, AND THERMODYNAMIC SURFACE PROPERTIES OF ANHARMONIC CRYSTALS I: General Consideration and Properties of the Singular Surfaces of the Two-Dimensional Models

1990 ◽  
Vol 04 (02) ◽  
pp. 317-345 ◽  
Author(s):  
V. I. ZUBOV ◽  
F. BANYERETSE ◽  
N. P. TRETYAKOV ◽  
I. V. MAMONTOV
Keyword(s):  
Surface Properties ◽  
Lattice Relaxation ◽  
Field Method ◽  
The Self ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
Anharmonic Crystal ◽  
Self Consistent ◽  
Dimensional Models ◽  
Anharmonic Crystals

The correlative, or improved, unsymmetrized self-consistent field method (CUSF) is developed to study surface properties of anharmonic crystals. The equations for moments of the one-particle functions of atoms are obtained. Their solution determines the lattice relaxation near the surface, the amplitudes of anharmonic vibrations of atoms and the self-consistent potentials. A calculation method of the Helmholtz free energy of anharmonic crystal — vapour interface is developed. As an application, the properties of the singular surfaces of two-dimensional models with square and hexagonal lattices are calculated.

scholarly journals SHORT PULSE ELECTRON LINAC WITH FULL BEAM LOADING COMPENSATION

2020 ◽  
pp. 78-85
Author(s):  
V.V. Mytrochenko ◽  
S.O. Perezhogin ◽  
V.Ph. Zhyglo ◽  
А.M. Opanasenko
Keyword(s):  
Beam Energy ◽  
Short Pulse ◽  
Frequency Dispersion ◽  
Energy Spread ◽  
Actual Problem ◽  
Electron Injector ◽  
Beam Loading ◽  
Self Consistent ◽  
Accelerating Structure ◽  
The One

Acceleration of intense short-pulsed electron beams in transient mode with energy spread about a few tenths of a percent is the actual problem for RF linacs, in an instance, for an electron injector of a storage ring. In this work we study both analytically and numerically unsteady self-consistent beam dynamics in the one section RF linac fed from SLED. For compensation of the transient beam loading, resulting in beam energy spread, a method of a beam delay with respect to RF pulse is consider. In order to increase efficiency of this method we choose a homogenous dick-loaded waveguide with π/2 phase advance as an accelerating structure that characterized by the minimal frequency dispersion of group velocity. The preliminary results show that the full beam loading compensation is possible for the 1.2 A beam at its acceleration up to 60 MeV during 50 ns.

Anharmonic Phonons in B.C.C. 4He

1972 ◽  
Vol 50 (11) ◽  
pp. 1152-1155 ◽  
Author(s):  
H. R. Glyde ◽  
F. C. Khanna
Keyword(s):  
Lattice Dynamics ◽  
Reasonable Agreement ◽  
Phonon Frequency ◽  
Frequency Dispersion ◽  
Dispersion Curves ◽  
Experimental Results ◽  
Matrix Approach ◽  
T Matrix

A T-matrix approach is used to calculate lattice dynamics of b.c.c. 4He. The phonon frequency dispersion curves and phonon group widths are in reasonable agreement with the experimental results of Osgood et al.

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.

QUASI-CLASSICAL SELF-CONSISTENT THEORY OF ANHARMONIC CRYSTALS

1992 ◽  
Vol 06 (03n04) ◽  
pp. 367-387 ◽  
Author(s):  
V. I. ZUBOV
Keyword(s):  
Particle Density ◽  
Linear Chain ◽  
Field Method ◽  
Anharmonic Crystal ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Probability Densities ◽  
The One ◽  
Strong Anharmonicity ◽  
Infinite Linear

Using the unsymmetrized self-consistent field method the quasi-classical expansion of the one-particle density matrices is considered. The integral equations for the first quantum corrections to the classical one-particle probability densities are derived. The exact solution for the perfect crystals with the strong anharmonicity of the fourth order is found and used to calculate the first quantum correction to the effective amplitudes of the strongly anharmonic vibrations of atoms. The solution is obtained also for the semi-infinite linear chain as the simplest model of the anharmonic crystal with the surface.

scholarly journals Quantum Self-Consistent Ab-Initio Lattice Dynamics

2021 ◽  
pp. 107945
Author(s):  
Ambroise van Roekeghem ◽  
Jesús Carrete ◽  
Natalio Mingo
Keyword(s):  
Ab Initio ◽  
Lattice Dynamics ◽  
Self Consistent

Experimental Determination of the Two-Dimensional State of Stress and the Orthotropic Elasticity Coefficients for Coatings

1990 ◽  
Vol 203 ◽  
Author(s):  
Richard J. Farris ◽  
M. A. Maden ◽  
K. Tong
Keyword(s):  
Elastic Constants ◽  
Physical Property ◽  
The State ◽  
Normal Stresses ◽  
Free Standing ◽  
Vibrationally Excited ◽  
Plane Shear ◽  
Plane Normal ◽  
State Of Stress ◽  
The One

ABSTRACTThe state of stress for a uniform coating away from the edges reduces to that of plane stress, two in-plane normal stresses, and an in-plane shear stress. For this state, the interface between the coating and the substrate is totally stress free. Since the substrate and the coating are not interacting mechanically, an internal section of the substrate can be removed creating a tensioned drum-like membrane without altering the stress state. Holographic interferometry of vibrationally excited membranes is used to evaluate the stress. Using this technique, up to thirty vibrational modes can be obtained. This high degree of redundancy enables one to determine the one shear and two normal stresses that act in the plane of the coating. The only physical property requires is the coating density. The density is obtained from commonly reported literature values. Simple variations on the membrane vibration scheme, e.g., cutting the membrane to create a uniaxially tensioned ribbon, enables one to determine the in-plane Poisson's ratio and shearmodulus.In separate but related experiments on commercially made free-standing films with residual orientation, the above techniques, combined with special free and axially constrainedcompressibility experiments should enable all of the Poisson's ratios and elasticmoduli for an orthotropic material (nine elastic constants) to be determined. Methods for measuring the state of stress and the elastic constants are required to predict the state of stress in complex coating geometries.

scholarly journals The Rules for the Lattice Rotation Accompanying Slip as Derived From a Self-Consistent Model

1999 ◽  
Vol 31 (4) ◽  
pp. 217-230 ◽  
Author(s):  
R. A. Lebensohn ◽  
T. Leffers
Keyword(s):  
Solid Mechanics ◽  
Grain Shape ◽  
Rolling Plane ◽  
Lattice Rotation ◽  
Consistent Model ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
The One ◽  
Equiaxed Grains ◽  
Very High

The rules for the lattice rotation during rolling (plane strain) deformation of fcc polycrystals are studied with a viscoplastic self-consistent model. Very high values of the ratesensitivity exponent are used in order to establish Sachs-type conditions with large local deviations from the macroscopic strain. The lattice rotation depends on the grain shape. For equiaxed grains the lattice rotation follows the MA rule, which is the one normally used in solid mechanics. For elongated and flat grains the lattice rotation follows a different rule, the PSA rule. In the standard version the model performs a transition from MA to PSA with increasing strain. There is avery clear difference between the textures resulting from the two different rules. MA leads to a copper-type texture, and PSA leads to a brass-type texture.

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