Misfit parameter

Comparative values of the lattice parameter, a, of Pd and surrounding elements, the mixing enthalpy at 300K of Pd alloys, the misfit parameter relative to Pd, the possible phases of Pd alloys [34, 35] and the surface energies [36]. 

The solid solution phase a of Cu, dominating in most Cu materials, is hardened by the solute elements s through solid solution hardening which is proportional to the misfit parameter r/s. given by the relative difference in atomic radius to rcu r s = 2(rs - rcu)/( s+ Cu)- Since rc = 128,... 

Fig. 5.8. Phase diagram for three growth modes layer-by-layer, Volmer-Weber and Stranski-Krastanov, as a function of the interfacial coupling W and the lattice misfit parameter r] between the deposit and the substrate. The phase limits denoted FCC (face centred cubic) and DC (diamond cubic) correspond to the use of Lennard-Jones and Stillinger-Weber potentials, respectively. The layer-by-layer growth mode is restricted to the axis r] = 0 in the region W > I (after Grabow and Gilmer, 1988).

Both sohd-solution hardening and precipitation hardening can be accounted for by internal strains generated by inserting either solute atoms or particles in an elastic matrix (11). The degree of elastic misfit, 5, produced by the difference, Ai , between the lattice parameter, of the pure matrix and a, the lattice parameter of the solute atom is given by... 

When a mismatch is inevitable, as in the combination Gej-Sii j. — Si, it is found that up to a value of jc = 0.4, there is a small mismatch which leads to a strained silicide lattice (known as commensurate epitaxy) and at higher values of jc there are misfit dislocations (incommensurate epitaxy) at the interface (see p. 35). From tlrese and other results, it can be concluded that up to about 10% difference in the lattice parameters can be accommodated by commensurately strained thin films. 

Figure 15. Mass misfit for two sequences of dynamic mode shifted by one mass. It is assumed that coincidence is obtained between Mo for the first sequence and Mo for the second sequence. The parameter SM (exaggerated) represents the misfit one mass down this peak.

If the misfit strain is less than a critical value, the undulations cannot mount cracktips, as demonstrated in Fig. 4, where a periodic length is equal to 100 a and film thickness is 30 ML. With the same physical parameters employed for Fig. 3, no islands are created if the misfit strain is less than 0.006. When the misfit strain is less than but close to the critical value, a permanent wave structure sets in the film as in the case ofs = 0.005. If the misfit strain is further reduced, coherency-induced undulations are swept away by thermal fluctuations. 

Using X-ray spectrometry, De la Fuente et al. (1999) measured the thermal dependence of the a and c lattice parameters in a Er32/Lu 10)40 superlattice. Again, strong single-ion CEF contributions, originating from the Er/Lu interfaces, were observed in the volume and tetragonal distortions. Their analysis reveals also important contributions caused by epitaxial misfit. 

A general interface is not energy-minimized with respect to any of its degrees of freedom, and is far from any singular-interface values of the parameters that set its degrees of freedom. Such an interface cannot reduce its energy by adopting a fit-misfit structure (as in the vicinal case) and therefore cannot support localized dislocations or steps. Two examples serve to clarify these distinctions ... 

Analyses of the plastic strains caused by matrix cracks, combined with calculations of the compliance change, provide a constitutive law for the material. The important parameters are the permanent strain, e0 and the unloading modulus, E. These quantities, in turn, depend on several constituent properties the sliding stress, r, the debond energy, T, and the misfit strain, il. The most important results are summarized below. 

In the layered misfit structures each layer set A and B can be described in terms of three basic translations, i.e. by its own component lattice. [The existence of the third vector is contingent upon a strict sequence in the layer stacking. If this is absent, the two three-dimensional subcells/lattices will, in the following discussion, be replaced by two two-dimensional subcells, i.e. by submeshes (nets) built only on the intralayer vectors.] In normal layered structures the unit cells of A and B are commensurate, i.e. their unit vectors are commensurable and the periodicity of the entire structure may be described in terms of a single unit cell. In contrast, we deal with those less-frequent cases in which this is not so at least one of the basic periodicities of A and of B are incommensurate. Then the component unit cell of set A has at least one intralayer unit cell parameter which is not commensurable with the corresponding parameter of set B. Such structures have two incommensurate, interpenetrating, component lattices and can be defined as composite) layered structures with two incommensurate component unit cells. Intermediate cases, in which the nodes of the two component lattices coincide at relatively large... 

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