Heterophase boundary

Grain boundary is the interface between two grains. When these two grains are of the same material, the boundary is called a homophase boundary when they are of different materials, then it is a heterophase boundary. Often, there are other phases that are only a few nanometers thick and can be present between the grains of two different materials in such case, the grain boundary represents three phases. These phases may be crystalline or amorphous. The presence or absence of a third phase has important ramifications on processing, electrical properties, and creep of the material concerned. 

Heterophase assemblages of mixed ionic/electronic conductors of the type A/AX/AY/A under an electric load are the simplest inhomogeneous electrochemical systems that can serve to exemplify our problem. Let us assume that the transport of cations and electrons across the various boundaries occurs without interface polarization and that the transference of anions is negligible. For the other transference numbers we then have... 

Grain boundaries are the most important type of homophase solid-solid interfaces. An example of crystalline heterophase interfaces with high relevance for technological applications are semiconductor heterostructures. 

The terms incommensurate and semi-commensurate are analogous to incoherent and semi-coherent for interfaces - in grain boundaries, heterophase interfaces and epitaxial layers (cf. also Nabarro - with which layered misfit structures have much in common. In extreme cases noncommensurability may arise by mutual rotation (to varying degrees) of component layers with identical component lattices... 

Diffusion from the surface layer to the crystal bulk plays an important role in heterophase systems. It is the diffusion processes that determine in large part whether or not ZnO layers will grow and whether the ZnO/ZnSe(S,Te) heterojunction will have a sharp interface or the ZnO layer will grow via oxygen diffusion into the crystal bulk and will have a broad boundary. Solving Eqs. (8-11), one can determine, from the relationship between the generation rates of A and B vacancies, the quasi-heteroepitaxy parameters at which particular kinds of heterojunctions, conductivity types, and defect concentrations in ZnO and ZnSe(S, Te) layers can be obtained. 

The second approach or microheterogeneous model [1, 19-22] is based upon the principle, that the kinetics of the reaction in its initial stage are not that of a homophase polymerisation in a liquid monomer-polymeric solution, but a heterophase one. The reaction proceeding at the boundary liquid monomer - solid polymer microgranules surface under gel conditions. 

Role of Crain Boundary Structure and Interface Energy at Homophase and Heterophase Interfaces Differences in structure and energy result from the creation of a solid-state interface... 

Fig. 8.11. (a) Structural force per unit area in a heterophase paranematic (thick lines) and nematic system with molten boundary layers (thin lines). Solid lines correspond to the force in the nematic phase and dashed lines to the force in the isotropic phase. For the thicknesses above the corresponding verticals the isotropic (paranematic) or nematic phase is stable, respectively. The force is short-range and attractive, (b) Structural presure in the hybrid nematic system in a biaxial structure (solid line) and bent-director structure (dashed line). In both cases the interaction is long-range and repulsive. 

The pseudo-Casimir force in a heterophase system wiU be illustrated with the example of a thin nematogenic film with order-inducing wetting layers on both confining surfaces discussed before. The resulting fluctuation force can be interpreted in terms of two contributions (i) the interaction between the substrates and the phase boundaries and (ii) the interaction between the two phase boundaries. 

But the flow heterophasic or even with nonuniform flow (laminar, turbulent, or particulate) one can assume that in z = 0 . The dispersion coefficient is negligible, but not in z = 0+. In that sense, boundary condition will be ... 

The first conception (or microheterogeneous model) is based on the assumption that the main contribution to the kinetics of the process in the initial state does not lead to homophaseous polymerization in the liquid monomer/polymeric solution, but the heterophaseous one, proceeding on the solid polymer-liquid monomer boundary under the gel-effect conditions. 

Processes of the first type include formation of the new phase nuclei in the contact zone as a result of heterophase fluctuations under chemical potential and concentration gradient. The description of solid-state reactions of the second and third types, namely those at the moving boundaries between phases that already exist in the diffusion zone, is reduced to the following consecutive stages ... 

Fig. 39. Micro-EDX analysis of Ndl23 crystals grown by the modified TSSG method in low-Po, atmosphere from contamination-firee Nd Oj crucibles with different post-growth heat treatments. In all the cases final oxygenation at 340°C in oxygen was applied. The picture demonstrates (a) tweed structure formation and (b) nanoscale composition fluctuations in crystals with the anomalous peak effect on a magnetization curve. Note that the composition profile for heavy atoms (Ba/Nd ratio) is similar to wave-like fluctuations typical for demixing behavior or a spinodal homophase decomposition rather than for a heterophase decomposition with the formation of a boundary between the crystal matrix and the precipitated phase (M. Nakamura et al. 1996c).

The position of the equilibrium involving the crystalline phase does not play a major role for the question examined. It directly follows from this phase diagram that the isotropic phase-heterophase region-anisotropic phase boundaries should be shifted toward the region of higher concentrations as the temperature increases, which also coincides with the experimental data described above. 

---