Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.Comment: 4 page

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

Dynamics of Ordering in Alloys with Modulated Phases

This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved order parameter and resembles the Swift-Hohenberg model. The early-stage growth kinetics is analyzed and compared to the Cahn-Hilliard theory of continuous ordering. The effects of non-linearities on the growth kinetics are discussed qualitatively and it is shown that the presence of an underlying elastic lattice introduces qualitatively new effects. A lattice Hamiltonian capable of describing these effects and suitable for carrying out simulations of the growth kinetics is also constructed.Comment: 18 pages, 3 figures (postscript files appended), Brandeis-BC9

One Dimensional Oxygen Ordering in YBa2Cu3O(7-delta)

A model consisting of oxygen-occupied and -vacant chains is considered, with repulsive first and second nearest-neighbor interactions V1 and V2, respectively. The statistical mechanics and the diffraction spectrum of the model is solved exactly and analytically with the only assumption V1 >> V2. At temperatures T ~ V1 only a broad maximum at (1/2,0,0) is present, while for ABS(delta - 1/2) > 1/14 at low enough T, the peak splits into two. The simple expression for the diffraction intensity obtained for T << V1 represents in a more compact form previous results of Khachaturyan and Morris[1],extends them to all delta and T/V2 and leads to a good agreement with experiment. [1] A.G.Khachaturyan and J.W.Morris, Jr., Phys.Rev.Lett. 64,76(1990)Comment: 13 pages,Revtex,3 figures available upon request but can be plotted using simple analytical functions,CNEA-CAB 92/04

On the stability of 2 \sqrt{2} x 2 \sqrt{2} oxygen ordered superstructures in YBa2Cu3O6+x

We have compared the ground-state energy of several observed or proposed " 2 \sqrt{2} x 2 \sqrt{2} oxygen (O) ordered superstructures " (from now on HS), with those of "chain superstructures" (CS) (in which the O atoms of the basal plane are ordered in chains), for different compositions x in YBa2Cu3O6+x. The model Hamiltonian contains i) the Madelung energy, ii) a term linear in the difference between Cu and O hole occupancies which controls charge transfer, and iii) covalency effects based on known results for $t-J$ models in one and two dimensions. The optimum distribution of charge is determined minimizing the total energy, and depends on two parameters which are determined from known results for x=1 and x=0.5. We obtain that on the O lean side, only CS are stable, while for x=7/8, a HS with regularly spaced O vacancies added to the x=1 structure is more stable than the corresponding CS for the same x. We find that the detailed positions of the atoms in the structure, and long-range Coulomb interactions, are crucial for the electronic structure, the mechanism of charge transfer, the stability of the different phases, and the possibility of phase separation.Comment: 24 text pages, Latex, one fig. included as ps file, to be publisheb in Phys. Rev.

Progress report on DOE research project [Thermodynamic and kinetic behavior of systems with intermetallic and intermediate phases]

A theoretical investigation was made of the coherent displacive phase transformation between two equilibrium single-phase states producing several orientation variants of the product phase. The research was focused on a behavior of coherent systems (martensitic systems, metal and ceramic, and ferroelectric systems) with defects. The computer simulation demonstrated that randomly distributed static defects may drastically affect the thermodynamics, kinetics, and morphology of the transformation. In particular, the interaction of the transformation mode with the defects may be responsible for appearance of two new fields in the phase diagram: (i) the two-phase field describing the tweed microstructure, which consists of the retain parent phase and the variants of the product phase and (ii) the single-phase field describing the tweed microstructure, which consists of the variants of the product phase. These new fields can be attributed to the pre-transitional states observed in some of th e displacive transformations. The microstructure evolution resulting in formation of the thermoelastic equilibrium is path dependent. This unusual behavior is expected in systems with a sharp dependence of the transition temperature on the defect concentration