William T. Lee

Intrinsic activation energy for twin-wall motion in the ferroelastic perovskite CaTiO3

Even in a topologically perfect crystal, a moving twin wall will experience forces due to the discrete nature of the lattice. The potential energy landscape can be described in terms of one of two parameters: the Peierls energy, which is the activation energy for domain wall motion in a perfect crystal; and the Peierls stress, the maximum pinning stress that the potential can exert. We investigate these parameters in a one order parameter discrete Landau-Ginzburg model and a classical potential model of the ferroelastic perovskite

Surface relaxations in hydroxyapatite

{\mathrm{CaTiO}}_{3}

Effect of surface relaxations on the equilibrium growth morphology of crystals: platelet formation

. Using the one order parameter model we show that the Peierls energy scales with the barrier height of the Landau double well potential and calculate its dependence on the width of the wall numerically. In

Domain wall diffusion and domain wall softening

{\mathrm{CaTiO}}_{3}

Effect of internal friction on transformation twin dynamics in perovskite SrxBa1-xSnO~3 (x=0.6,0.8)

we calculate the Peierls energy and stress indirectly from the one order parameter model and directly from the interatomic force field. Despite the simplicity of the one order parameter model, its predictions of the activation energy are in good agreement with calculated values.

A neutron diffraction and Rietveld analysis of cooperative Li motion in beta-eucryptite

Relaxation processes due to two opposite surfaces in a slab of hydroxyapatite with two (100) free surfaces are reported. Interatomic potentials for hydroxyapatite, chloroapatite and fluoroapatite were refined using elastic and vibrational data. Systems with two free (100) surfaces were relaxed. It was found that the relaxation processes which occurred at the surface included the polarization of layers close to the surface, distortion of the channels in which the hydroxide ions sit and distortion of the tetrahedral phosphate ions. Some of these relaxations only occur in the unit cells closest to the surface; others persist for a few unit cells distance into the bulk. The implications of these results for the growth morphology of hydroxyapatite in bones are discussed.

Surface structure of domain walls in a ferroelastic system with a domain wall pressure

In this paper we report results showing that surface relaxations may profoundly alter the equilibrium growth morphology of crystals. This may result in growth forms not predicted by the Wulff plot. Surface relaxations and polarization fluctuations produce extra terms in the free energy of a growing crystal nucleus which combine with the surface energy to produce an effective surface energy which depends on the size and shape of the crystal. We consider the case of the growth of nuclei of a crystal with cubic symmetry and show that if the surface relaxations are large enough then small nuclei will grow into platelets, although large nuclei still grow into large three-dimensional crystals. We show by considering materials with the perovskite structure that this effect may occur in real materials.

Domain-wall structure and domain-wall strain

A number of experimental and computational studies of materials have shown that transport rates in domain walls may significantly differ from those in the bulk. One possible explanation for enhanced transport in a domain wall is that the domain wall is elastically soft with respect to the bulk. We investigate the softening of a ferroelastic domain wall in a simple, generic model. We calculate saddle point energies of solute atoms in the bulk and domain wall, using a geometry such that variation in the saddle point energy cannot be attributed to the structural differences of the bulk and the wall, but must instead be attributed to softening of the wall. Our results show a reduction of the saddle point energy in the wall, thus indicating that, in this model at least, domain walls are elastically soft compared with the bulk. A simple analysis based on an Einstein model allows us to explain the observed softening of the wall.

Surface relaxations at mineral surfaces

The dynamics of transformation twins in SrxBa1−xSnO3 (x=0.6,0.8) perovskite has been studied by dynamical mechanical analysis in three-point bend geometry. This material undergoes phase transitions from orthorhombic to tetragonal and cubic structures on heating. The mechanical loss signatures of the transformation twins include relaxation and frequency-independent peaks in the orthorhombic, and tetragonal phases, with no observed energy dissipation in the cubic phase. The macroscopic shape, orientation, and relative displacements of twin walls have been calculated from bending and anisotropy energies. The mechanical loss angle and distribution of relaxation time are discussed in terms of bending modes of domain walls.

Trapping of oxygen vacancies in the twin walls of perovskite

Li + mobility and structural changes in the aluminosilicate beta-eucryptite have been studied by high-resolution powder neutron diffraction as a function of temperature from 573 to 873 K. A Li split-atom model was used to describe the disorder of Li + ions in the structure. Analysis of the data shows two anomalies around 698 and 758 K. The first anomaly is attributed to an Mpoint zone boundary transition reported i nt he literature, which is connected to the appearance of the incommensurate structure. The second anomaly is attributed to a displacive phase transition of the framework and doubling in the a cell parameter.