Table of contents

The Jahn-Teller effect has been investigated for strong coupling between a triply degenerate electronic state and a triply degenerate vibrational mode (T*t). Analytic expressions have been derived for the lowest energy levels for finite but large coupling constant k, and calculation of the splitting between these levels have been obtained. Splitting between the lowest T and A states agrees well with Caner and Englman's (see abstr. A23249 of 1966) fit of their numerical data.

A recent small-signal, space-charge calculation of Meaudre and Mesnard (see abstr. A44908 of 1974) is discussed and related to other work in the field. The Meaudre-Mesnard results are shown to yield inappropriate high- and low-frequency limiting response. A recombination time constant appearing in the treatment is also a poor approximation. Finally, an approach is discussed which avoids these deficiencies.

Expressions are obtained for the distribution of lifetimes and the mean lifetime of excited Mossbauer nuclei which contribute to gamma -ray emission lines detected by selective modulation. The treatment is restricted to the case of pure natural-broadened line profiles.

It is suggested that the large breadths of X-ray photoelectron peaks in ionic crystals may be due to coupling of the localized hole to lattice vibrations rather than lifetime broadening associated with interatomic Auger processes. Measurement of the temperature dependence of the linewidths could resolve the broadening mechanism.

Starting from a quantized phonon Hamiltonian with N branches and a quartic interaction this model is solved in the limit N to infinity by the Migdal approach of the renormalization group. The well known critical indices are obtained for the spherical model: eta =0, nu =2/(d-2), alpha =(d-4)/(d-2). In a very direct way the self-consistent phonon theory is shown to be equivalent to the spherical model. The purpose of this paper is to show clearly the difficulties and the limitations of the Migdal approach.

The increase in the intensity of the X-rays scattered from high-wavevector TA modes in silicon following a 10^-2 J hot-electron pulse has been measured. It is found that there is evidence for a non-thermal phonon population in these modes resulting from the phonon decay process after electron phonon scattering. The phonon lifetime in these modes is about 10^-6s.

The field of conformational defects in polymers is made accessible to Lifshitz's Green-function method. By introducing local coordinate frames, a fictitious polymer chain is constructed which has the irregular conformation of the real chain but, at the same time, the phonon spectrum of the regular chain, and is described by a dynamical matrix which differs from the real one only in localized regions around the conformational defects. A general and very simple expression for the B-matrix of an isolated polymer skeleton in arbitrary irregular conformation is presented.

Lattice dynamical calculations are presented for the vibrational amplitudes of the constituent atoms in various II-VI and III-V semiconductor compounds as a function of temperature. The calculated results are discussed and compared with the available experimental data. It appears that a lattice theory including anharmonic interactions may provide better insight into the melting criteria.

The authors ascertain the number of linearly independent terms in the most general expression, to fourth power of the order parameter for the Landau free energy of a superfluid having Cooper pairs with nonzero orbital angular momentum l; this then determines how many input parameters must be supplied by any underlying dynamical theory before the free energy can be minimized near the critical temperature. Also solved is the restricted but technically harder problem for triplet pairing with the order parameter, (a spin-space matrix), constrained to be proportional to a unitary matrix.

A model equivalent to the Anderson model is introduced, and an approximation equivalent to a single-site CPA is discussed. On this approximate model averaged two-particle Green functions are calculated. The results are interpreted to show that localized states cannot exist in any CPA for any finite disorder.

A straightforward attempt to estimate the influence of the first vertex correction for a homogeneous electron gas is made. The approximation scheme is also tested on a solvable model of a core electron coupled to an electron gas.

The surface Green-function method is used to calculate the surface band structure of Si(111) faces as described by the conventional abrupt step model. The calculation yields a single narrow band located in the absolute thermal gap, in qualitative agreement with previous tight-binding calculations for this face, but differing from experimental data. An approximation suggested by the above method consists in neglecting the plane waves with wavevector lying outside the Jones zone. This approximation is studied analytically, including a careful description of the wavefunctions near the surface.

The cyclotron resonance of conduction electrons in AgBr has been measured at 136 GHz and at 891 GHz. The apparent effective 'mass' of the electrons is greater by 5.2 per cent at the higher frequency. This increase is compared with the predictions of polaron theory. Good agreement exists with a variational calculation by Larson which assumes the interaction Hamiltonian of Frohlich and a wavefunction based on a modified one-phonon Tamm-Dancoff approximation.

In the hop conduction range, the dependence of the transverse magnetoresistance rho / rho ₀ on the orientation and the magnitude of the magnetic induction beta (of several tesla) was studied in Ga-doped Ge samples with acceptor concentrations, N_A, ranging from approximately=1-6*10¹⁵cm^-3.

For a constant rate G of generation of electron-hole pairs, lg J_ph (J_ph is the photocurrent) increases as T^-1 at high temperatures and reaches a maximum value of J_m at T=T_m. Thereafter, lg J_ph decreases as T^-1 with further decrease in temperature and finally, at low temperatures, J_ph becomes independent of temperature. The lg J_ph against T^-1 characteristics scale to high current and T_m increases with increasing G. At constant temperature, say T₁, J_ph is a linear function of G up to the value of J_m corresponding to T₁, and in this range the curves scale to higher currents levels with decreasing T. For J_ph>J_m, J_ph increases as G¹2/, and in this range the curves scale to high current levels with increasing T. At very high light levels or at low temperatures, corresponding to the case where J_ph is temperature independent, the J_ph against G curves for different constant temperatures all merge and J_ph is found to be linearly proportional to G.

Measurements of photoconductivity in amorphous Si:Te:As are presented and the interpretation of the results has led to a simple trapping model for the amorphous semiconductor which is considerably at variance with the presently accepted model of a localized density of states tail extending into the energy gap from the band edges. A self-consistent, quantitative theory is used to analyse the data and, in contrast to the work on the subject which has been published to date. The authors, have plotted curves to demonstrate the correlation between the present theory and the data. The physical significance of the model is discussed.

The calculations exhibit general features of the Umklapp process in a simple context. It is shown that the Umklapp rate is not limited by any small parameter and that special behaviour (independent of the boundary conditions) occurs at extremal points of the bands. It is also shown that interband surface scattering has only small probability for electrons in small pocket states.

Fisher's rigorous bound chi < chi _saw, where chi _saw is the susceptibility calculated from the self-avoiding walk (SAW) generating function, is applied to (i) the ferromagnetic Ising alloy, (ii) the dilute Ising ferromagnet, (iii) the layer susceptibility of a free surface, (iv) the Ising ferromagnet in a transverse field, and (v) the dilute Ising ferromagnet in a transverse field. The author obtains an upper bound T_UB for the temperature T₀ below which a spontaneous magnetization occurs. The use of a microscopically varying molecule field is analysed. A heuristic argument is given to show that, for the dilute Ising ferromagnet in a transverse field, the critical transverse field at zero temperature jumps from zero to a value at least equal to that of the one-dimensional ground state as x passes through the critical percolation concentration.

Explicit expressions for the longitudinal and transverse spin susceptibilities of an itinerant ferromagnet with many bands are derived by means of diagrammatic techniques within the random phase approximation. The Hamiltonian used is a generalization of the Hubbard one-band Hamiltonian. No approximation is made for the wavevector or band index dependence of the form factors, and both interband and intraband contributions are treated. The expression for the longitudinal component shows features, absent in the one band case, which may account for the discrepancy found by Lowde and Windsor between their experimental values for the longitudinal contribution to the neutron scattering cross section of nickel, and those calculated using (essentially) a one-band theory.

The metamagnetic phase transition of DyVO₄ was investigated spectroscopically at T=1.4K. In the Zeeman pattern with external magnetic field H_ext parallel to the magnetic-moment direction it was found that in an intermediate field range H_c1<or=H_ext<or=H_c2 the positions of the absorption lines are nearly independent of H_ext, the critical field H_c2 depending strongly on the crystal shape. This behaviour is explained by the assumption that in the intermediate field range the sample is divided into antiferromagnetic and paramagnetic regions.

The magnetic properties of the distorted perovskite GdCrO₃ have been investigated by magnetic moment measurements in the temperature range below 100K and specific heat measurements below 10K. Measurements show that the canting of the Cr³⁺ ions from a simple antiferromagnetic alignment is due to antisymmetric exchange coupling between Cr ions. The value of the weak ferromagnetic moment F_z is 400 emu mol^-1. The interaction between the Cr³⁺ and Gd³⁺ ions produces an effective field at the Gd sites of 5.5 kOe, acting in the opposite direction to F_z. At a temperature of approximately 7K the Cr-Gd interaction is sufficient to cause the Cr system to undergo a spontaneous spin reorientation from a G_xF_z to a G_zF_x mod. At 2.3K the interaction between the Gd³⁺ ions is sufficient to bring about a co-operative transition to an antiferromagnetic state.

The structural phase change arising from the cooperative Jahn-Teller effect has been studied by Raman scattering and optical birefringence methods in the mixed crystals Tb_pGd_1-pVO₄ and Dy_pY_1-pVO₄ with p varying from one to zero. The introduction of Gd and Y dilutes the active components causing the phase change, resulting in a reduction of the transition temperature T_D(p). Varying p varies the splitting of E_g phonons below T_p(p) and also the energy of low-lying collective electronic excitations. The Tb system shows unique behaviour with p=0.365; a transition from tetragonal to orthorhombic symmetry occurs at 8.5K but the crystal reverts to tetragonal symmetry below 2.3K. The effect in the Tb system can be explained by mean-field theory. The Dy compounds are explained using series expansion and modified mean-field methods.

The theory relevant to the observation of nuclear magnetic resonance of dilute impurities in solids, by the change in the gamma- and beta-ray emission distributions from oriented nuclei, is discussed for the situation where an electric quadrupole interaction produces a splitting of the nuclear magnetic resonance line comparable with the interaction energy with the applied RF field. The major deviations from conventional adiabatic fast passage expected for a single sweep of the RF frequency through the resonance condition are shown to be well reproduced by recent experimental results, indicating the validity of the theoretical model discussed.

Hot-pressed ceramics of the lead titanate zirconate system with different grain sizes were prepared and some of their electrical properties measured. The values of the dielectric and piezoelectric properties were analysed together with information on barium titanate ceramics already published in the literature. Many similarities were found between both systems. There are two main contributions to the properties; the single-crystal single-domain intrinsic effect and the contribution of the wall motion. The intrinsic effect is analysed considering the grains as monodomains. A model is developed which proposes that each grain has a different transition temperature T_c. The T_c values are taken as following a Gaussian distribution and the behaviour of the dielectric constant against temperature is computed and checked with experimental results. All the results can be explained qualitatively with the model; a connection between findings and the idea of diffuse phase transitions is outlined.