Deformation potentials

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. 

The role of two-phonon processes in the relaxation of tunneling systems has been analyzed by Silbey and Trommsdorf [1990]. Unlike the model of TLS coupled linearly to a harmonic bath (2.39), bilinear coupling to phonons of the form Cijqiqja was considered. In the deformation potential approximation the coupling constant Cij is proportional to (y.cUj. There are two leading two-phonon processes with different dependence of the relaxation rate on temperature and energy gap, A = (A Two-phonon emission prevails at low temperatures, and it is... 

Hydrostatic deformation potential Paul, Paul and Brooks [63P01, 63P03]... 

Once values for R , Rp, and AEg are calculated at a given strain, the np product is extracted and individual values for n and p are determined from Eq. (4.19). The conductivity can then be calculated from eq. (4.18) after the mobilities are calculated. The hole mobility is the principal uncertainty since it has only been measured at small strains. In order to fit data obtained from elastic shock-loading experiments, a hole-mobility cutoff ratio is used as a parameter along with an unknown shear deformation potential. A best fit is then determined from the data for the cutoff ratio and the deformation potential. 

Fig. 4.10. The conductivity of uniaxially compressed (111) and (100) high purity germanium crystals leads to a determination of the shear deformation potential for the designated valley minima in the energy band (after Davison and Graham [79D01]).

The shear deformation potential for the (111) and (100) valley minima determined by fits to the data of Fig. 4.10 are shown in Table 4.5 and compared to prior theoretical calculations and experimental observations. The deformation potential of the (111) valley has been extensively investigated and the present value compares favorably to prior work. The error assigned recognizes the uncertainty in final resistivity due to observed time dependence. The distinguishing characteristic of the present value is that it is measured at a considerably larger strain than has heretofore been possible. Unfortunately, the present data are too limited to address the question of nonlinearities in the deformation potentials [77T02]. 

Although the [100] data are quite limited, the shear deformation potential determined is the only measurement for this valley in germanium. At atmospheric pressure and small strains the (100) valley minimum is well above the (111) valley minima and not accessible for measurement. In the present... 

Chapter 4. Physical Properties Under Elastic Shock Compression Table 4.5. Shear deformation potentials. (See Davison and Graham [79D01].)... 

The data indicate that elastic shock-compression resistance measurements can provide data on the effects of strain on energy gaps and deformation potentials in semiconductors. Drift mobility measurements on holes in germanium and resistivity measurements on samples with different dopings would appear to be of considerable interest. 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

Neglecting the tunneling splitting we can assume the eigenstates Oct) to be localized in the wells of the deformation potential so that... 

Tunnel relaxation of orientational states in the phonon field of a substrate is considered in Appendix 2). When a molecule has a single equilibrium orientation (p = 1) the deformation potential is also characterized by a well-defined barrier AU which separates the equivalent minima. That is why, the subsystem Hamiltonian (4.2.12) used in the exchange dephasing model147,148 with... 

With the atom C strongly bound not only to B but also to the other atoms of a solid-state matrix (i.e., when C fB) the above ratio is small in the parameter mc/mB 1, so that the dominant contribution to the interaction with phonons is provided by the deformation potential. Reorientation probabilities were calculated, with the deformation term only taken into consideration, in Refs. 209, 210. For a diatomic group BC, c A Uv 0.1 eV, whereas eb 10 eV (a typical bond energy for ionic and covalent crystals). A strong binding of the atom C only to the atom B results in the dominant contribution from inertial forces.211 For OH groups, as an example, the second term in Eq. (A2.13) is more than 6 times as large as the first one. 

The broad field of nucleic acid structure and dynamics has undergone remarkable development during the past decade. Especially in regard to dynamics, modem fluorescence methods have yielded some of the most important advances. This chapter concerns primarily the application of time-resolved fluorescence techniques to study the dynamics of nucleic acid/dye complexes, and the inferences regarding rotational mobilities, deformation potentials, and alternate structures of nucleic acids that follow from such experiments. Emphasis is mainly on the use of time-resolved fluorescence polarization anisotropy (FPA), although results obtained using other techniques are also noted. This chapter is devoted mainly to free DNAs and tRNAs, but DNAs in nucleosomes, chromatin, viruses, and sperm are also briefly discussed. 

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 density dependence of Vg in Kr was determined by field ionization of CH3I [62] and (0113)28 [63]. Whereas previous studies found a minimum in Vg at a density of 12 X 10 cm [66], the new study indicates that the minimum is at 14.4 x 10 cm (see Fig. 3). This is very close to the density of 14.1 x 10 cm at which the electron mobility reaches a maximum in krypton [67], a result that is consistent with the deformation potential model [68] which predicts the mobility maximum to occur at a density where Vg is a minimum. The use of (0113)28 permitted similar measurements of Vg in Xe because of its lower ionization potential. The results for Xe are also shown in Fig. 3 by the lower line. 

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 ... 

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. 

Chen and Sladek (1978) investigated the piezoresistance of Ti203, deduced deformation potentials for the holes and came to the conclusion that the overlap between the valence and conduction bands is never large. 

For lattice acoustic-mode deformation potential scattering, s =, giving r = /8 = 1.18. For ionized-impurity scattering, s = —f, giving rn0 = 315 /512 = 1.93. For a mixture of independent scattering processes we must... 

Process ability Surface area, surface free energy, crystal defects, and deformation potential affect compressibility and machineability on high-speed tableting machines with reduced compression dwell times Particle size distribution and shape affect flow properties, efficiency of dry mixing process, and segregation potential Compressibility, flow ability, and dilution potential affect the choice of direct compression as a manufacturing process... 

Figure 6.18 Energy of a single nucleon in a deformed potential as a function of deformation s. The is diagram pertains to either Z < 20 or IV < 20. Each state can accept two nucleons.

The repulsion increases exponentially, and it is steeper than the bond length deformation potential. The attractive force is usually modeled by a 1/r6 term, while various possibilities exist for the repulsion. The functions used in modem programs include, apart from the Morse potential (Eq. 2.13), the Lennard-Jones potential (Eq. 2.25)[401 (e.g., AMBER1411), the Buckingham potential (Eq. 2.26)[421 (e.g., MOMEC[81), or a modification thereof, the Hill potential (Eq. 2.27) (e.g., MM2, MM3[1,2,231). 

Figure 1 2 10. The reduced Lifshitz parameter"z" - (ET - EF)/(EA- ET), where (EA- Er) is the full energy band dispersion in the c-axis direction, as a function of the number of holes in the G subband in A1 doped MgB2. The quantum uncertainty in the z value is indicated by the error bars that are given by D (

---