Phase transformations interface

Due to the limitations of the test techniques, and the absence of any direct experimental data, the function of HA nanocrystals has rather been presumed on the basis of several deformation models of bone. These include shear transfer between mineral particles via intermediate ductile organic layers, slippage at the collagen-mineral interface, phase transformation of the mineral phase, sacrificial bond disruption between fibrils, microcracking, and uncracked Hgament bridging. 

Penn R L and Banfieid J F 1999 Formation of rutiie nuciei at anatase (112) twin interfaces and the phase transformation mechanism in nanocrystaiiine titania Am. Miner. 84 871... 

Blesa, M.A. Maroto, A.J.G. (1986) Dissolution of metal oxides. J. chim. phys. 83 757—764 Blesa, M.A. Matijevic, E. (1989) Phase transformation of iron oxides, oxyhydroxides, and hydrous oxides in aqueous media. Adv. Colloid Interface Sci. 29 173-221 Blesa, M.A. Borghi, E.B. Maroto, A.J.G. Re-gazzoni, A.E. (1984) Adsorption of EDTA and iron-EDTA complexes on magnetite and the mechanism of dissolution of magnetite by EDTA. J. Colloid Interface Sci. 98 295-305 Blesa, M.A. Larotonda, R.M. Maroto, A.J.G. Regazzoni, A.E. (1982) Behaviour of cobalt(l 1) in aqueous suspensions of magnetite. Colloid Surf. 5 197-208... 

Informations on the vibrational and electron mean free path properties. Such analysis is possible only if the interface phase is very well defined, and if temperature dependent measurements are done and compared. Debye Waller effects can be tangled with ordering transformation of the interface phase as a function of temperature and so on. If a single phase interface with order at least to the second nearest neighbour is recognised, then a temperature dependent Debye Waller, and mean free path analysis can be attempted. 

The second type is simple phase transitions in which one phase transforms into another of identical composition, e.g., diamond graphite, quartz coe-site, and water ice. This type sounds simple, but it involves most steps of heterogeneous reactions, including nucleation, interface reaction, and coarsening. 

Complex phase transformation requires nucleation, interface reaction, and mass transport the interplay of these factors controls the rate of complex phase transformations. Because nucleation, interface reaction, and mass transport are sequential steps for the formation and growth of new phases, the slowest step controls the reaction rate. Table 4-1 shows some examples of phase transformations and the sequential steps. 

In general, a low-temperature polymorph has lower symmetry than a high-temperature polymorph. So, in the phase transformation from high- to low-temperature polymorph, the low-temperature polymorph can have two orientations, which leads to twin formation. This is called the transformation twin. To minimize the interface energy between twinned individuals through transfer-... 

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

Let us remember that Eqns. (12.22) and (12.23) have to be coupled to the diffusion equations in the a and 0 phases in order to complete the total set of kinetic equations for the phase transformation (Le., the advancement of the interface). This set is very complicated and nonlinear and may lead to non-monotonic behavior of vb and the chemical potentials of the components in space and time, as has been observed experimentally (Figs. 10-13 and 12-9). Coherency stresses and other complications such as plastic flow have been neglected in this discussion. 

The conditions and kinetic equations for phase transformations are treated in Chapters 17 and 20 and involve local changes in free-energy density. The quantification of thermodynamic sources for kinetically active interface motion is approximate for at least two reasons. First, the system is out of equilibrium (the transformations are not reversible). Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic case) can exist and because the thermal con-... 

Heterophase Interfaces. In certain cases, sharp heterophase interfaces are able to move in military fashion by the glissile motion of line defects possessing dislocation character. Interfaces of this type occur in martensitic displacive transformations, which are described in Chapter 24. The interface between the parent phase and the newly formed martensitic phase is a semicoherent interface that has no long-range stress field. The array of interfacial dislocations can move in glissile fashion and shuffle atoms across the interface. This advancing interface will transform... 

The conditions for continuous phase transformations (described in Chapter 17) derive from considerations of the molar free energy of a homogeneous, spatially uniform system with no interfaces. For phase transformations involving nonconserved... 

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

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