Deformation potential theory

The change of the conduction level, Vq, is obtained from measurements of Vq as a function of fluid density. The electrons in the conduction band are scattered by these fluctuations. The scattering potential Vq( r ) is obtained by an expansion of the average value Vq in terms of the density fluctuations. 

The excess electrons are scattered on the potential fluctuations. The mean free path, A, is then given as 

Other adaptations of the deformation potential theory to the problem of electron transport in fluid argon were reviewed by Steinberger (1987). 

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The mobility of quasi-free electrons has recently been explained by the deformation potential theory. Originally from solid-state physics, this theory was applied by Basak and Cohen [68] to liquid argon. The theory assumes that scattering occurs when the electron encounters a change or fluctuation in the local density which results in a potential change. The potential is assumed to be given in terms of dFo/dfV, d Fo/dfV, etc. The formula they derived for the mobility is ... 

Basak S, Cohen MH. (1979) Deformation-potential theory for the mobility of excess electrons in liquid argon. Phys Rev B 20 3404-3414. 

Nishikawa M. (1985) Electron mobility in fluid argon Application of a deformation potential theory. Chem Phys Lett 114 271-273. 

In region (1), the electron can be considered as quasifree. (An electron is regarded as completely free only in the vacuum.) The structure of the fluid is unperturbed by the presence of the excess electron. The wave function is extended. The basic electron/liquid interaction may be treated as single scattering of an electron on a molecule or atom modified by the structure factor of the liquid, S(q) (Lekner, 1967), or it is considered as multiple scattering off density fluctuations in the framework of the deformation potential theory (Basak and Cohen, 1979). 

Note in passing that the common model in the theory of diffusion of impurities in 3D Debye crystals is the so-called deformational potential approximation with C a>)ccco,p co)ccco and J o ) oc co, which, for a strictly symmetric potential, displays weakly damped oscillations and does not have a well defined rate constant. If the system permits definition of the rate constant at T = 0, the latter is proportional to the square of the tunneling matrix element times the Franck-Condon factor, whereas accurate determination of the prefactor requires specifying the particular spectrum of the bath. 

When the electrostatic properties are evaluated by AF summation, the effect of the spherical-atom molecule must be evaluated separately. According to electrostatic theory, on the surface of any spherical charge distribution, the distribution acts as if concentrated at its center. Thus, outside the spherical-atom molecule s density, the potential due to this density is zero. At a point inside the distribution the nuclei are incompletely screened, and the potential will be repulsive, that is, positive. Since the spherical atom potential converges rapidly, it can be evaluated in real space, while the deformation potential A(r) is evaluated in reciprocal space. When the promolecule density, rather than the superposition of rc-modified non-neutral spherical-atom densities advocated by Hansen (1993), is evaluated in direct space, the pertinent expressions are given by (Destro et al. 1989)... 

The deformation potential model seems to provide a suitable framework to understand the quasi-free electron mobility in nonpolar liquids. Already several extensions or modifications on this theory have been proposed, and the dependence on temperature and pressure seems to be adequately explained. However, several authors have taken dilferent approaches to the problem showing that a consensus in our understanding has not yet been reached. 

Molecular tl iy for fracture could be traced ba k to an application of the rate-process theory to fracture teiomena (65) and al the similar line of thou t Beuche (1) developed his theory for fracture in p<%mer. Zhurkov (66,67) derived independently the same equation to the Beuche s one the time to fracture. Based on this equation the activation energies for the fracture were estimated from the experimental results on the time to fracture under the unaxial load (20,68). Change of deformation potential in a stressed chain was discussed by Kausch (J9.20). Fracture developement has been discussed from the a >ects of micromori lr of polymers by Peterlin (J5, 69-71), Kausch (19,20) and DeVries(/7,61, 72). 

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

Fig. 39. Temperature dependences of the transverse (312MHZ and q h, u c) and longitudinal (various frequencies and q, u b) elearonic ultrasound-attenuation coefficients of UPt, (Muller et al. 1986a). The most striking feature is the pronounced longitudinal attenuation peak at about 12 K, which is ascribed to a deformation-potential coupling to the heavy-fermion bands. The inset proves the quadratic frequency dependence of the longitudinal peak height as expected from theory, solid line (Muller and Bartell 1979).

Issues of Material Compressibility. There is a full theory of compressible and nonlinear viscoelastic materials that would be equivalent to the compressible finite deformation elasticity theory described above (eq. 39), but more complicated because of the need to develop an expansion of the time-dependent strain potential function as a series of multiple integrals (108,109). One such formahsm is discussed briefiy under Lustig, Shay and Caruthers Model. Here a simphfied model that is based upon the K-BKZ framework with a VL-like kernel function (98) is examined. 

Just a few years ago there was no theory which could even come close to calculation of the phonon dispersion curves of a crystal like GaAs from first principles. This is indeed a very large improvement in the ability of the theory to make realistic calculations with no input from experiment. There are remaining many problems that go beyond the limited examples given here. These include defects,piezoelectric constants, dielectric properties, electronic deformation potentials, etc. 

A correlation between phonon mode frequencies and strain components in films with different strains can, in principle, allow determination of the isotropic deformation potentials, a and b (see Equations 9 and 8). a-Plane GaN films offer a unique opportunity to obtain the Ai(TO) phonon deformation potentials by GIRSE. This is particularly important in view of the existing discrepancy in the literature between the values of the Ai(TO) phonon deformation potentials determined by Raman scattering [54] and theory [14]. Further, the aEi(io) and fcii(LO) have not been experimentally determined yet. 

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