Initial Wave Vector Research Articles

Effect of hydrostatic pressure on the incommensurate phase ofK2SeO4

A neutron scattering study of the effect of hydrostatic pressure on the incommensurate phase transformation in ${\mathrm{K}}_{2}$Se${\mathrm{O}}_{4}$ was performed in order to obtain information concerning the nature of the competing forces that give rise to a structural instability at a general wave vector. It was found that an increase in pressure lowers the transition temperature ($\frac{d{T}_{i}}{d{P}_{i}}=\ensuremath{-}6.5$ K/kbar) and results in a smaller value of the initial incommensurate wave vector. The pressure dependence of the incommensurate to ferroelectric phase transition was also investigated ($\frac{d{T}_{c}}{d{P}_{c}}\ensuremath{\simeq}\ensuremath{-}9$ K/kbar). The latter transition displays a distinct pressure hysteresis.

Temperature shift of the maximum of neutron critical scattering in the second born approximation

AbstractTwo approximate forms of the cross‐section obtained in the second Born approximation are discussed with respect to the temperature shift of the main maximum of critically scattered neutrons in ferromagnets. The disscusion is given for the correlation of the Ornstein‐Zernike type and the correlation function reflecting the lattice symmetry of a simple cubic crystal. It is shown that the temperature shift depends on the momentum transfer vector q, the diffusion coefficient D, and the initial wave vector k0.

Surface roughness scattering of electrons in semiconductors and semimetals

Surface roughness scattering is calculated for carriers in ellipsoidal energy bands. The purpose is to identify which dimension of the Fermi surface determines the degree of roughness which is required to produce diffuse reflection. It is concluded that the surface corrugations must be deep enough so that (kperpendicular to -kRperpendicular to ) xi 0 is comparable to unity, where xi 0 is the RMS bump height and kperpendicular to and kRperpendicular to are the initial wavevector and reflected wavevector in the sense defined by Price (1969).

Wave propagation in a stratified shear flow

The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J > ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J > ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J [gsim ] ¼ conclusions of an earlier treatment by Booker & Bretherton.

Electron-Phonon Interaction for Indirect Interband Transitions in Germanium

Calculation of the interaction of electrons with short-wavelength phonons becomes tractable when the initial and final electronic wave vectors have high symmetry and a local-pseudopotential representation is used. After discussion of the general Bloch formulation for the electron-phonon interaction and of the pseudopotential method in band theory, we calculate as a specific example all allowed transitions in germanium between wave vectors $\ensuremath{\Gamma}$ and $L$ for electron states at the edge of the gap. Our result for the matrix element ${\ensuremath{\Gamma}}_{{2}^{\ensuremath{'}}}+\mathrm{LA}\ensuremath{\rightarrow}{L}_{1}$ is nearly twice that deduced from optical absorption by McLean. The sensitivity of the results to the short-wavelength behavior of the pseudopotential is tested by use of two sets of pseudopotential parameters. Approximations are given for the case of wave vectors not exactly at the symmetry points. In the principal calculation, it is assumed that each nucleus rigidly carries a spherical pseudopotential. Since this is questionable in covalently bonded Ge, we also attempt, with partial success, to calculate by the deformable-ion method. This traditional alternative is ambiguous and unjustifiable, but it indicates the effect of using a different prescription in perturbing the crystal pseudopotential by a phonon. Resulting matrix elements are generally smaller.

Anomalous Hall Effect and Magnetoresistance of Ferromagnetic Metals

The anomalous Hall effect and the magnetoresistance of ferromagnetic metals are in· vestigated on the basis of the localized d·electron (or f-electron) model. First the Hamil· tonian of the interaction between conduction electrons and localized electrons is given, which is valid when the orbital angular momenta of localized electrons are not quenched. Then we find that the scattering matrix of a conduction electron depends in a complicated way on the directions of the initial and final wave vectors and of the magnetization. The transition probability calculated to the first Born approximation by using the above matrix elements leads to the electrical resistivity of the form expressed by Eq. (1. 1) in the text. To the second Born approximation we find that the transition probability from a state k to another state k 1 is not equal to that from k 1 to k and leads to the anomalous Hall effect. The magnitude and the temperature dependence of both effects are reasonable for iron and nickel when compared with experiment. In rare-earth metals, both effects can also be obtained and, besides, the electric quadrupole moments which are associated with the orbital angular momenta cause an additional scat· tering. When we calculate the normal resistivity by adding the exchange and quadrupole scatterings, we obtain a good agreement with experiment on the magnetic contribution to the resistivity of rare-earth metals with more than half-filled 4f shells

Exchange and Correlation Corrections to the Electron-Phonon Interaction

The method of Bardeen and Pines for treating electron-phonon interactions in normal metals is extended to include exchange and correlation effects. The interaction matrix element is found to depend not only on electron momentum transfer but also on the initial electron wave vector. An average over initial wave vector direction is therefore made; the average taken is discussed as being more reasonable than that of Bailyn in a previous treatment. Shielding is also introduced in a more physical manner than in Bailyn's paper---via the dielectric constant as it arises in the random phase approximation. An alternate method of treating the problem in the long wavelength limit---employing deformation potential techniques---verifies the results of the above method in this limit.

Exchange and Correlation Effects in Electron-Phonon Scattering in Normal Metals

The theory of Bardeen for the electron shielding of the perturbation potential arising from lattice vibrations is extended to cover exchange and correlation effects. The method is to set up a self-consistent set of one-electron equations, and calculate the effect of the perturbation in the charge densities. The exchange term is corrected to conform to the results of the Bohm-Pines theory, but the plasma wave function is assumed not to be disturbed by the lattice. With this approximate model, a solution to the problem can be obtained. For small-angle scattering, the results do not return to the original Bardeen values. The interaction potential matrix element depends on the initial electron wave vector k as well as on the difference between initial and final state wave vectors. Hence, to use the results an average over k must be made, and we make an average over the Fermi surface. The general effect of the exchange hole is to increase the scattering.