Effects Of Elastic Strain Energy Research Articles

Mindlin's problem for an anisotropic piezoelectric half–space with general boundary conditions

This paper considers Mindlin's problem in an anisotropic and piezoelectric halfspace with general boundary conditions, including 16 different sets of surface conditions. The Green's function due to...

Numerical experiments for effects of elastic strain energy on decomposition process of binary alloy in a two-dimensional system

This paper is concerned with phase decomposition of a supersaturated solid solution in a two-dimensional system. We have investigated the behavior of numerical solutions to the Cahn equation including an elastic strain energy term in such a way as to follow the time evolution of composition modulation by computer. It is found that in our numerical experiment the introduction of the elastic strain energy gives no anisotropic effect on the crystallographic direction of the composition modulation, but leads to the decrease in the decomposition rate and quantity at the equilibrium state. Again, it is demonstrated that for a high solute alloy system inside the spinodal region a large circular precipitate is formed at the center of the flat matrix through a very complicated process accompanied with the aggregation and annihilation of particles. The results so obtained are discussed from a numerical point of view.

The Lorentz Correction in Barium Titanate

It is assumed, following Devonshire, that the ferroelectric behavior of BaTi${\mathrm{O}}_{3}$ arises because of the Lorentz correction, leading to a vanishing term in the denominator of the expression for dielectric constant. If the polarizability varies slowly with temperature, the temperature variation of dielectric constant follows. This temperature variation is assumed to come from that part of the polarization resulting from the displacement of the Ti ion, in a field whose potential energy has fourth-power as well as second-power terms in the displacement. The main object of this paper is to compute the Lorentz correction exactly, not assuming spherical symmetry, but taking account of the precise crystal structure. When this is done, it is found that the Ti ions, and those oxygen ions which are in the same line with them, the line being parallel to the electric field, exert very strong fields on each other, the resulting local field at the Ti ion being much greater than if computed on the assumption of spherical symmetry. This enhanced field makes it clear that even a relatively small ionic polarizability for the Ti ions will be enough to lead to ferroelectricity. The polarization of the Ti ions is however an essential feature of the theory; if they are not polarized, the Lorentz correction is profoundly modified, leading almost exactly to the value given by the approximate theory assuming spherical symmetry, and not resulting in ferroelectricity. Detailed formulas are given for comparison of the present theory with Devonshire's results, so that the present methods can be incorporated in his treatment of the effect of elastic strain energy on the stability of the various phases below the Curie point.