Elastic coherency energy

In crystalline solutions, the developing interfaces are initially coherent—strains are continuous across interfaces. Unless defects such as anticoherency dislocations intervene, the interfaces will remain coherent until a critical stress is attained and the dislocations are nucleated. For small-strain fluctuations, the system can be assumed to remain coherent and the resulting elastic coherency energy can be derived.9... 

Figure 19.9 Effect of elastic inhomogeneity on elastic strain energy of a coherent...

J.K. Lee, D.M. Barnett, and H.I. Aaronson. The elastic strain energy of coherent ellipsoidal precipitates in anisotropic crystalline solids. Metall. Trans. A, 8(6) 963-970, 1977. 

Martensitic transformations involve a shape deformation that is an invariant-plane strain (simple shear plus a strain normal to the plane of shear). The elastic coherency-strain energy associated with the shape change is often minimized if the martensite forms as thin plates lying in the plane of shear. Such a morphology can be approximated by an oblate spheroid with semiaxes (r, r, c), with r c. The volume V and surface area S for an oblate spheroid are given by the relations... 

We note here that gel is a coherent solid because its structure is characterized by a polymer network, and hence, the above theoretical considerations on crystalline alloys should be applicable to gels without essential alteration. It is expected that the curious features of the first-order transition of NIPA gels will be explained within the concept of the coherent phase equilibrium if the proper calculation of the coherent energy and the elastic energy of the gel network is made. This may be one of the most interesting unsolved problems related to the phase transitions of gels. 

NES is an elastic and coherent scattering process, i.e., it takes place without energy transfer to electronic or vibronic states and is delocalized over many nuclei. Owing to the temporal and spatial coherence of the radiation field in the sample. 

The terms elastic and inelastic scattering of electrons describe that which results in no loss of energy and some measureable loss of energy respectively. If the incident electron beam is coherent (i.e. the electrons are in phase) and of a fixed wavelength, then elastically scattered electrons remain coherent and inelastic electrons are usually incoherent. 

Liquefied rare gases(LRGs) are very important both from the fundamental point of view and in application to ionization chambers. In these media, epithermal electrons are characterized by a very large mean free path for momentum transfer -10-15 nm, whereas the mean free path for energy loss by elastic collision is only -0.5 nm. This is caused by coherence in momentum transfer scattering exhibited by a small value of the structure factor at low momentum transfers... 

The Landauer formula assumes elastic processes. If the electrons move coherently (that is without any loss of energy or of phase) they will tunnel if the energy gap through which they must tunnel becomes relatively small, they can tunnel a long way. Generally, the conduction in the tunneling regime is written as... 

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