Self-consistent theory of second order elastic constants for nonionic anharmonic crystals

1972 ◽  
Vol 15 (2) ◽  
pp. 158-170 ◽  
Author(s):  
T. Paszkiewicz
Keyword(s):  
Elastic Constants ◽  
Second Order ◽  
Consistent Theory ◽  
Self Consistent ◽  
Anharmonic Crystals

Self-Consistent Theory of Second-Order Elastic Constants with an Application to Noble-Gas Crystals

1970 ◽  
Vol 2 (12) ◽  
pp. 4995-5002 ◽  
Author(s):  
M. L. Klein ◽  
G. K. Horton ◽  
V. V. Goldman
Keyword(s):  
Elastic Constants ◽  
Noble Gas ◽  
Second Order ◽  
Consistent Theory ◽  
Self Consistent

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.

THE MICROSCOPIC THEORY OF THE SURFACE PROPERTIES OF ANHARMONIC CRYSTALS I: General Method and (001) Surface of BCC Crystal

1992 ◽  
Vol 06 (02) ◽  
pp. 197-219 ◽  
Author(s):  
V. I. ZUBOV ◽  
I. V. MAMONTOV ◽  
N. P. TRETYAKOV
Keyword(s):  
Surface Properties ◽  
Helmholtz Free Energy ◽  
Three Dimensional ◽  
Microscopic Theory ◽  
Lattice Relaxation ◽  
Surface Anisotropy ◽  
Consistent Theory ◽  
Self Consistent ◽  
Anharmonic Crystals ◽  
General Method

The self-consistent theory of the structural, dynamical, and thermodynamic surface properties of anharmonic crystals previously given for one- and two-dimensional models is extended to the surfaces of three-dimensional crystals which take into account the surface anisotropy. After considering the reference system, in the general case, the equations for the properties of the interface cyrstal-vapour to the second order in the temperature are derived. The (001) face of the BCC crystal is investigated. The lattice relaxation and dynamics are calculated. The surface Helmholtz free energy and other thermodynamic properties are obtained. At high temperatures, the surface specific heat increases linearly with temperature due to the anharmonicity.

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