Deformation potential method

The last system investigated by the deformation-potential method is a member of the large family of charge-transfer molecular crystals containing as anion the tetracyanoquinodimethane (TCNQ) molecule. The K TCNQ" salt as well as the other TCNQ crystals consist of columns of stacked TCNQ molecules coordinated by similar columns of the cations. The energy band structures of the stack have been calculated earlier with the help of Pariser-Parr-Pople parametrization of the unrestricted Hartree-Fock crystal-orbital method The last two columns of Table 9.10 show that this material behaves again as a normal... 

TABLE 9.10. Transport Properties of Some Wide-Band Polymers Calculated by the Deformation Potential Method... 

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. 

Keywords Adsorbed layer deformation Adsorption Aging Polyelectrolytes Streaming potential method... 

More difficult to calculate are the properties which depend on the response of the solid to an outside influence (stress, electric field, magnetic field, radiation). Elastic constants are obtained by considering the response of the crystal to deformation. Interatomic potential methods often provide good values for these and indeed experimental elastic constants are often used in fitting the potential parameters. Force constants for lattice vibrations (phonons) can be calculated from the energy as a function of atomic coordinates. In the frozen phonon approach, the energy is obtained explicitly as a function of the atom coordinates. Alternatively the deriva-tive, 5 - can be calculated at the equilibrium geometry. 

We can now calculate the superconductive transition temperature through the approximate solution of the Eliashberg equation, given the intra-molccular deformation potentials These, and the vibrational frequencies, were calculated using the quahtum-chemical MNDO semi-empirical technique (IS). This method has been successfully used previously on a wide variety of... 

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. 

W. Richter, Resonant Raman Scattering in Semiconductors Electric Susceptibility. Light Scattering. Experimental Method.s. One-Phonon Deformation Potential Scattering. Infrared Active LO Phonons. Multiphonon Scattering. Conclusions. List of Symbols. References. Subject Index. 

A hybrid atomistie/eontinuum mechanics method is established in the Feng et al. [70] study the deformation and fracture behaviors of CNTs in composites. The unit eell eontaining a CNT embedded in a matrix is divided in three regions, whieh are simulated by the atomic-potential method, the continumn method based on the modified Cauchy-Bom rule, and the classical continuum mechanics, respectively. The effect of CNT interaction is taken into account via the Mori-Tanaka effective field method of micromechanics. This method not only can predict the formation of Stone-Wales (5-7-7-5) defects, but also simulate the subsequent deformation and fracture process of CNTs. It is found that the critical strain of defect nucleation in a CNT is sensitive to its chiral angle but not to its diameter. The critical strain of Stone-Wales defect formation of zigzag CNTs is nearly twice that of armchair CNTs. Due to the constraint effect of matrix, the CNTs embedded in a composite are easier to fracture in comparison with those not embedded. With the increase in the Young s modulus of the matrix, the critical breaking strain of CNTs decreases. 

Lattice parameters of ZnO have been investigated over many decades [22-30]. The lattice parameters of a semiconductor usually depend on the following factors (i) free electron concentration acting via deformation potential of a conduction hand minimum occupied by these electrons, (u) concentration of foreign atoms and defects and their difference of ionic radii with respect to the substituted matrix ion, (iii) external strains (e.g., those induced by substrate), and (iv) temperature. The lattice parameters of any crystalline material are commonly and most accurately measured by high-resolution X-ray diffraction (HRXRD) using the Bond method [31] for a set of symmetrical and asymmetrical reflections. Table 1.2 tabulates measured and calculated lattice parameters, cja ratio, and u parameter reported by several groups for ZnO crystallized in wurtzite, zinc blende, and rocksalt structures for comparison. 

It is possible that the approximation (10.1.9) applies also to solid solutions where the average distances between neighbouring molecules are fixed by the long range order. On the other hand, in liquid mixtures we expect that the differences in sizes give rise to local deformations and therefore introduce differences between the distances And as. We shall first consider the simpler case (10.1.9) and then discuss in 6-8 the more difficult problem of the extension of the average potential method to include lattice deformations. 

In particular, the phonon dispersion relations and polarization vectors can be calculated with reasonable accuracy using force-constant models [59] or the embedded atom method [60-62], In recent calculations of Fe-ph and X for surface states, wave functions obtained from the one-electron model potential [63, 64] have been used. For the description of the deformation potential, the screened electron-ion potential as determined by the static dielectric function and the bare pseudopotential is used, Vq z) = f dz e (z,2/ gy)qy), where (jy is the modulus of the phonon momentum wave vector parallel to the surface, and bare Fourier transform parallel to the surface of the bare electron-ion... 

Piela L, Kostrowicki J and Scheraga H A 1989 The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method J. Phys. Chem. 93 3339... 

Permanent deformation has also been investigated. The rate of flow of gold wires has been found to depend on the electrode potential with a minimum of the rate at E i.c [51Pfu]. The ereep of a lead eleetrode has been studied [69Lik]. (Data obtained with this method are labelled FL). 

The pressure dependence of wavenumbers has been investigated theoretically by LD methods on the basis of a Buckingham 6-exp potential. In the studies of Pawley and Mika [140] and Dows [111] the molecules were treated as rigid bodies in order to obtain the external modes as a function of pressure. Kurittu also studied the external and internal modes [141] using his deformable molecule model [116]. The force constants of the intramolecular potential (modified UBFF) were obtained by fitting to the experimental wavenumbers. The results of these studies are in qualitative agreement with the experimental findings. 

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