S. Marais

The theory of fluctuations and texture embryos in structural phase transitions mediated by strain

Structural phase transitions are considered in which the effective ordering interaction J(Rij) arises from local stresses induced by the ordering in cell i and propagated elastically to a distant cell j. The generalized Landau free energy functional is set up and four applications made. Firstly the origin of metastable tweed microstructures is shown to lie in the dense medium of strong embryonic tweed-like microdomains existing as fluctuations at temperatures as high as 2Tc and above. Secondly the tweed-like pattern originates from the very anisotropic interaction associated with domain walls, and four cases are distinguished. Thirdly it is shown that the Landau-Ginzburg theory of the width and shape of a domain wall can be carried over in some cases but not others. Fourthly the magnitude of critical fluctuations is considered together with corresponding corrections to the Landau theory of the phase transition in the four cases.

Theory and computer simulation of tweed texture

Abstract An analytical theory of the ordering interaction J(R ij ) in structural phase transitions mediated by elastic relaxation in the material is outlined. The ordering process in cell i sets up a local stress field due to the sizes, shapes or displacements of atoms or atomic groups, which is propagated elastically to a distant cell j. The atomistic theory for ferro- and antiferro-elastic transitions takes into account two types of singularity, one due to elastic anisotropy and the other to the Zener interaction J z of infinite range in ferroelastic transitions. The form of J k in Fourier space is highly anisotropic with a few “soft” directions coinciding with the orientation of twin boundaries. The asymptoptic J(R) at large R is shown to be very anisotropic as well and decays as R −3 in ferroelastic and R −5 in antiferroelastic systems. Computer simulations for a three-dimensional model of about 29,000 particles show a strong tendency to form tweed texture, as observed experimentally. Well above the s...

Strain coupling as the dominant interaction in structural phase transitions

Abstract A rigorous theory is developed for the ordering interaction J(R ij) in a crystal having a structural phase transition when J(R ij) is mediated by elastic relaxation in the material. The ordering process in cell i sets up a local stress field due to the sizes, shapes or displacements of atoms or atomic groups, which propagates elastically to a distant cell j. The atomistic theory for ferro-and antiferro-elastic transitions takes into account two types of singularity, one due to elastic anisotropy and the other to the Zener interaction Jz of infinite range in ferroelastic transitions, as well as the self-energy of relaxation around each cell. Four types of case are distinguished fora simple cubic model, which between them encompass the phenomena in much more complex situations. The interaction JK in Fourier space is dominated by whether or not domain walls perpendicular to k have a low energy from their strain satisfying Sapriels compatibility relations. Thus embryonic tweed texture in fluctuation...

Strain-related microstructures in materials: A computer simulation study of a simple model

Abstract A simple “atomistic” model based on the strain interaction between local state variables is found to capture the essentials of strain related structural phase transitions in non-martensitic materials. The computer-simulated thermodynamic properties of the order parameter and the related microstructures, e.g. twin boundaries, show the same characteristic features as the experimental observations which are briefly reviewed.

On the origin of kinetic rate equations: Salje-Glauber-Kawasaki

The implicit approximations made in the derivation of the kinetic rate laws proposed by Salje, Glauber and Kawasaki are discussed. The Glauber and Kawasaki rate processes are relevant for discrete Ising systems with non-conserved or conserved order parameters, respectively. The Salje rate equation describes continuous rate processes. Molecular dynamics simulations of the phi 4-Hamiltonians are in close agreement with the predictions of the Salje rate law.

A RATE EQUATION FOR ATOMIC ORDERING IN MEAN FIELD THEORY. II, GENERAL CONSIDERATIONS

For pt.I see ibid., vol.3, p.2963 (1991). The authors study various examples of atomic ordering processes in which it makes sense to analyse the importance of mixed kinetics. The discussion is based on Glauber and Kawasaki types of stochastic processes in a kinetic Ising model with long range interactions, described very well by the mean field approximation. It is found that in the limiting case in which one is not far from the uniform state (i.e. spatially homogeneous) and thermal equilibrium, the rate equation can be cast into the form assumed sometimes in phenomenological rate theories of mixed kinetics. This identification allows for a critical analysis of various length scales, time scales and mixing coefficients that occur in mixed kinetic processes. Finally, the possibilities of observing mixed kinetics are indicated by way of examples borrowed from atomic ordering phenomena in certain minerals, and a few general conclusions are drawn.

A rate equation for atomic ordering in mean field theory. I. Uniform case

A critical discussion is given of the kinetics of (dis)ordering in a simple system of Ising spins with respectively Glauber and Kawasaki types of stochastic processes. The question addressed is whether the rate is governed by the same free energy excess (in equilibrium) as assumed in frequently used rate equations. The authors focus for simplicity on uniform systems with long range interactions whose equilibria are well described by mean field theory. Such situations are realized in systems with effective spin interactions mediated by strain. They find that the rate equation can be expressed in terms of a Glauber or Kawasaki potential. Their analytical forms are found to be quite different from each other and also different from the equilibrium mean field energy. However, the predicted rate equations are not substantially different for most temperatures of interest.

Landau theory revisited

Abstract The Landau free energy GL(T,Q) is an important concept in structural phase transitions because it is often the meeting point of experiment and the development of microscopic models. We review recent work on the real Q and T dependence of GL, the origin of non-classical non-critical exponents for T below Tc, the cross-over from soft mode to O/D behaviour, local bifurcation at T* and relation to ordering kinetics. Framework structures such as many silicates and the perovskite structure allow special geometrical Rigid Unit phonon Modes. The material is then likely to be near to the soft mode limit, resulting in classical behaviour of Q(T) over a very wide T range. Long range correlations result in a very small Ginzburg interval.

The search for periodons

Periodons have been suggested as a mechanism for modulated structures with QIC near one-third of a reciprocal lattice vector, based on a -x2 + x4 anharmonic potential. Molecular dynamic simulation is used to look for periodon-like motion in a crystal in thermal agitation. Such motion was never seen, because periodons are very unstable and their phase space input presumably occupies a negligible portion of the total available phase space. No evidence of a phase transition was found.