Coherency strain model

After the observation of DIGM and LFM in the 1970s," several models and mechanisms were proposed for the driving force of the phenomena. Among them, the coherency strain model of Hillert is now widely supported by some critical experiments of Yoon and others." " ... 

O Keeffe (1991Z)) has used bond valences to model the coherent interface that occurs between the semiconductors Si and MSi2 with M = Ni or Co (27139). Although these systems contain Si-Si bonds and therefore do not obey the assumptions of the bond valence model (condition 3.2), the mathematical formalism of the model still works because of the high symmetry. As both Si-Si and Si-Ni bonds are found in NiSi2, the cubic structure is strained (cf. BaTiOs in Section 13.3.2) and this strain affects the structure of the interface. Of the six possible interfacial structures examined, the two with the lowest BSI eqn (12.1) are those that are believed to occur in NiSi2 and CoSi2 respectively, and in both cases the strain introduced at the interface is correctly predicted. 

Until the last few decades colloid science stood more or less on its own as an almost entirely descriptive subject which did not appear to fit within the general framework of physics and chemistry. The use of materials of doubtful composition, which put considerable strain on the questions of reproducibility and interpretation, was partly responsible for this state of affairs. Nowadays, the tendency is to work whenever possible with well-defined systems (e.g. monodispersed dispersions, pure surface-active agents, well-defined polymeric material) which act as models, both in their own right and for real life systems under consideration. Despite the large number of variables which are often involved, research of this nature coupled with advances in the understanding of the fundamental principles of physics and chemistry has made it possible to formulate coherent, if not always comprehensive, theories relating to many of the aspects of colloidal behaviour. Since it is important that colloid science be understood at both descriptive and theoretical levels, the study of this subject can range widely from relatively simple descriptive material to extremely complex theory. 

The slab geometry also suffers from other finite-size effects. If the extent of the unit cell parallel to the interface is too small, artificial strain effects axe introduced, because the metal and ceramic axe forced to be coherent by the periodic boundary conditions. Of course, this may be eliminated by enlarging the unit cell, which unfortunately leads to very computerintensive calculations, as is the case with the cluster models. However for the slab model, the oscillations in the electronic density of states are not as dramatic when varying the number of atoms as in the case with clusters. This is because the slab is infinite parallel to the interface. This implies the spectrum is continuous, and the metal slab does not have an artificial band gap, unlike the metal cluster. 

In the microcrystallite model [38,39], the microcrystals (coherent scattering domains) are sufficiently small (15 to 20 A) to prevent the observation of Bragg reflections. In addition, strains ensure amorphous behavior. 

Early observations of elastic strain relaxation during growth of epitaxial layers led to paradoxical results. An attempt to interpret the observations on the basis of the critical thickness theory in its most elementary form suggested that, once the thickness of a film exceeded the critical thickness, the final elastic strain of the film should be determined by the thickness of the film alone, independent of the original, or fuUy coherent, mismatch strain. This is implied by the result in (6.27), which states that that the mean elastic strain predicted by the equilibrium condition G(/if) = 0 is completely determined by hf beyond critical thickness, no matter what the value of Cni- However, it was found that the post-growth elastic strain as measured by x-ray diffraction methods did indeed vary with the initial elastic mismatch strain, and it did so in different ways for different film thicknesses (Bean et al. 1984). As a consequence, the critical thickness theory came under question, and various alternate models were proposed to replace it. However, further study of the problem has revealed the relaxation process to be much richer in physical phenomena than anticipated, with the critical thickness theory revealing only part of the story. 

An almost forgotten issue is the proposed relativistic nature of an electron as elucidated by Lorentz. The electron was seen as a flexible spherical unit of charge which distorts as it contracts in the direction of any motion. To account for the relativistic contraction of macroscopic bodies Lorentz further assumed that the electrical forces which bind atoms together were essentially states of stress and strain in the aether. Countless prominent scientists have expressed similar views without trying to develop a coherent theory of matter. The Lorentz electron model antedates de Broglie s postulate of matter waves and the development... 

In this model process the interface between the two lattices is assumed to be coherent, at least in the neghborbood of that kinetic unit which is transforming, and to be essentially parallel to a low index lattice plane of I. On the interface there are steps (or a step, if it is the periphery of a two-dimensional nucleus) and on the steps there are kinks. In Fig. 14 a section parallel to the interface is shown cutting through a step ABCD with a kink at BC. The two lattices are indicated as being strained in the neighborhood of the kink, the result of a decrease in volume on transformation. Transformation is assumed to occur in the following manner. 

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