Physico-chemical and thermochemical studies of the hydrolytic conversion of amorphous tricalcium phosphate into apatite

The conversion of amorphous tricalcium phosphate with different hydration ratio into apatite in water at 25 °C has been studied by microcalorimetry and several physical–chemical methods. The hydrolytic transformation was dominated by two strong exothermic events. A fast, relatively weak, wetting process and a very slow but strong heat release assigned to a slow internal rehydration and the crystallization of the amorphous phase into an apatite. The exothermic phenomenon related to the rehydration exceeded the crystalline transformation enthalpy. Rehydration occurred before the conversion of the amorphous phase into apatite and determined the advancement of the hydrolytic reaction. The apatitic phases formed evolved slightly with time after their formation. The crystallinity increased whereas the amount of HPO4 2− ion decreased. These data allow a better understanding of the behavior of biomaterials involving amorphous phases such as hydroxyapatite plasma-sprayed coating

The preparation and properties of a glass-ceramic with an aligned microstructure

The work described in this thesis was performed on glass-ceramics in which a random arrangement of crystals is grown as a dispersed phase. The physical properties of this material are isotropic. The technique of hot extrusion has been used to produce a material with an aligned crystal microstructure in a Li₂O-SiO₂ glass-ceramic. The extruded material consists of a glass matrix and two crystalline phases; one of these phases is aligned morphologically and crystallographically parallel to the extrusion axis. The microstructure of this extruded material was analysed statistically in terms of the volume fraction of crystalline phases, the mean crystal- crystal spacing and the distribution function of the number of crystals N(Ɵ), making an angle Ɵ with a reference direction. Control specimens of the same composition heat-treated at the same temperature and for the same time as the extruded samples were also analysed statistically. The following physical properties were measured on the control and extruded specimens: (i) the coefficient of thermal expansion (ii) Young's modulus, rupture strength and microhardness (iii) Resistivity, dielectric constant and loss tangent. In the case of the extruded samples these measurements were made in directions parallel and perpendicular to the extrusion axis; the coefficient of thermal expansion, the mechanical properties and the resistivity were found to be anisotropic for these specimens

Periodic total variation flow of non-divergence type in Rn

We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data.Comment: 36 pages, 2 figure

Singular diffusivity facets, shocks and more

There is a class of nonlinear evolution equations with singular diffusivity, so that diffusion effect is nonlocal. A simplest one-dimensional example is a diffusion equation of the form u_t = \delta(u_x)u_{xx} for u = u(x; t), where \delta denotes Dirac s delta function. This lecture is intended to provide an overview of analytic aspects of such equations, as well as various applications. Equations with singular diffusivity are applied to describe several phenomena in the applied sciences, and to provide several devices in technology, especially image processing. A typical example is a gradient flow of the total variation of a function, which arises in image processing, as well as in material science to describe the motion of grain boundaries. In the theory of crystal growth the motion of a crystal surface is often described by an anisotropic curvature flow equation with a driving force term. At low temperature the equation includes a singular diffusivity, since the interfacial energy is not smooth. Another example is a crystalline algorithm to calculate curvature flow equations in the plane numerically, which is formally written as an equation with singular diffusivity. Because of singular diffusivity, the notion of solution is not a priori clear, even for the above one-dimensional example. It turns out that there are two systematic approaches. One is variational, and applies to divergence type equations. However, there are many equations like curvature flow equations which are not exactly of divergence type. Fortu-nately, our approach based on comparision principles turns out to be succesful in several interesting problems. It also asserts that a solution can be considered as a limit of solution of an approximate equation. Since the equation has a strong diffusivity at a particular slope of a solution, a flat portion with this slope is formed. In crystal growth ploblems this flat portion is called a facet. The discontinuity of a solution (called a shock) for a scalar conservation law is also considered as a result of singular diffusivity in the vertical direction

On the role of kinetic and interfacial anisotropy in the crystal growth theory

A planar anisotropic curvature flow equation with constant driving force term is considered when the interfacial energy is crystalline. The driving force term is given so that a closed convex set grows if it is sufficiently large. If initial shape is convex, it is shown that a flat part called a facet (with admissible orientation) is instantaneously formed. Moreover, if the initial shape is convex and slightly bigger than the critical size, the shape becomes fully faceted in a finite time provided that the Frank diagram of interfacial energy density is a regular polygon centered at the origin. The proofs of these statements are based on approximation by crystalline algorithm whose foundation was established a decade ago. Our results indicate that the anisotropy of intefacial energy plays a key role when crystal is small in the theory of crystal growth. In particular, our theorems explain a reason why snow crystal forms a hexagonal prism when it is very small

Thermal analysis of submicron nanocrystalline diamond films

The thermal properties of sub-μm nanocrystalline diamond films in the range of 0.37–1.1 μm grown by hot filament CVD, initiated by bias enhanced nucleation on a nm-thin Si-nucleation layer on various substrates, have been characterized by scanning thermal microscopy. After coalescence, the films have been outgrown with a columnar grain structure. The results indicate that even in the sub-μm range, the average thermal conductivity of these NCD films approaches 400 W m− 1 K− 1. By patterning the films into membranes and step-like mesas, the lateral component and the vertical component of the thermal conductivity, k<sub>lateral</sub> and k<sub>vertical</sub>, have been isolated showing an anisotropy between vertical conduction along the columns, with k<sub>vertical</sub> ≈ 1000 W m− 1 K− 1, and a weaker lateral conduction across the columns, with k<sub>lateral</sub> ≈ 300 W m− 1 K− 1

Mini-Workshop: Anisotropic Motion Laws

Anisotropic motion laws play a key role in many applications ranging from materials science, biophysics to image processing. All these highly diversified disciplines have made it necessary to develop common mathematical foundations and framworks to deal with anisotropy in geometric motion. The workshop brings together leading experts from various fields to address well-posedness, accuracy, and computational efficiency of the mathematical models and algorithms