The elastic gradient energy in solid solutions

1973 ◽  
Vol 7 (7) ◽  
pp. 761-768
Author(s):  
H.E. Cook
Keyword(s):  
Solid Solutions ◽  
Gradient Energy ◽  
Elastic Gradient

The Role of Phonon Dispersion in Controlling Atomic Rearrangement in Solid Solutions

1982 ◽  
Vol 21 ◽  
Author(s):  
T.B. Wu
Keyword(s):  
Solid Solution ◽  
Dispersion Curve ◽  
Phonon Dispersion ◽  
Relaxation Energy ◽  
Gradient Energy ◽  
Composition Fluctuations ◽  
Average Lattice ◽  
Atomic Rearrangement ◽  
Elastic Gradient

ABSTRACTThe elastic energy of a solid solution of atoms of different sizes can be written as a Fourier sum with coefficients as a function of position in reciprocal space. Each coefficient is made up of three components. The first one is an energy associated with taking atoms of the pure elements and placing them randomly on the average lattice o f the alloy. The second one is an elastic gradient energy associated with composition fluctuations and which is proportional to the second derivative of the dispersion curve. The third is the relaxation energy concerned with the motion of atoms away from the average lattice to more comfortable positions. Because of the contribution of the elastic gradient energy, it is shown that the shape of the phonon dispersion curve can affect precipitation or ordering in a solid solution.

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

Optical vibration modes in Hg1-xZnxTe solid solutions near q=0

1989 ◽  
Vol 50 (21) ◽  
pp. 3223-3232 ◽  
Author(s):  
G. Le Bastard ◽  
R. Granger ◽  
S. Rolland ◽  
Y. Marqueton ◽  
R. Triboulet
Keyword(s):  
Solid Solutions ◽  
Vibration Modes ◽  
Optical Vibration

Valence instabilities of Tm in its compounds and solid solutions

1979 ◽  
Vol 40 (C5) ◽  
pp. C5-314-C5-320 ◽  
Author(s):  
F. Holtzberg ◽  
T. Penney ◽  
R. Tournier
Keyword(s):  
Solid Solutions

E. S. R. OF Gd3+ IN La2O3 AND ITS SOLID SOLUTIONS WITH CeO2

1976 ◽  
Vol 37 (C7) ◽  
pp. C7-204-C7-207
Author(s):  
G. BACQUET ◽  
C. BOUYSSET ◽  
D. HERNANDEZ
Keyword(s):  
Solid Solutions
Sign in / Sign up

Export Citation Format

Share Document