Table of contents

A theory for elementary excitations in random substitutional alloys with off-diagonal as well as diagonal disorder has been developed using a new technique for configurational averaging introduced by Mookerjee (1975). The mathematical formalism is illustrated for the case of electrons in a binary alloy with a tight-binding Hamiltonian. Typical results for the density of states of a one-dimensional chain are shown to compare well with essentially exact numerical calculations.

Thermodynamic properties of dilute ferromagnetic alloys near the percolation threshold are studied. The scaling hypothesis for the percolation problem can be used to derive the temperature and concentration dependences of the magnetization, the heat capacity and the Curie temperature.

The local single-particle correlation function for the symmetric Wolff model is evaluated at zero temperature in the weak-coupling-long-time limit by a stationary-phase argument. The leading behaviour is given by an asymptotic expansion in the coupling strength. The correlation function furthermore has a weak essential singularity at vanishing coupling strength, corresponding to the exponential decay of transient Fermi surface effects, and is scale invariant under a simultaneous change of time scale and coupling-strength scale. In the intermediate and strong coupling regime the calculation breaks down due to many-body effects. Comments are made on some frequently used operator representations and some work by Mattis.

A new tetragonal centre of U³⁺ in CaF₂ compensated by an Na⁺ ion at a (2, 0, 0) site relative to the U³⁺ ion has been observed by EPR at liquid helium temperature (g/sub ///=2.740+or-0.003 and g_{perpendicular to} =2.029+or-0.005).

Plasmon dispersion and damping along the a and c axes in single-crystal magnesium were measured directly by electron energy-loss spectroscopy. No significant anisotropy in dispersion was observed; however, the damping was found to be anisotropic.

An optical study was made of granular deposits of indium, prepared under static ultra-high vacuum, for the energy range 1.4-6 eV. The structure of these deposits was determined in situ, using the replica technique. It is shown that discontinuous deposits display plasma resonances of conduction electrons for h(cross) omega near 4.8 eV. Interband absorption, theoretically expected near 1.4 eV, does not appear on the granular deposits.

Auger peak shape studies of oxygen on the W(100) surface have shown a lack of sensitivity to the adsorbate chemical environment. A quasi-atomic model is described to account for these effects.

Examines the magnetic scattering of neutrons by an atom or ion possessing both a spin and orbital magnetic moment. The calculation of the matrix elements of the Racah tensors is considerably simplified by selection rules based on the groups Sp(4l+2), R(2l+1), R(3) and in the case of f-electrons, the special group G₂. It is shown that, in the case of elastic scattering by an atom or ion whose state is a single Russell-Saunders state, the magnetic scattering amplitude can be written in the conventional form p(q)q_m.s. General expressions for the amplitude p(q) as well as the elastic magnetic form factor are obtained. The evaluation of the coherent magnetic scattering amplitude by an atom in a magnetic field is discussed, and the small-q approximation to the elastic magnetic scattering is considered. The formalism is illustrated for the important case of d- and f-electrons. The generalization of the formalism to the case of mixed atomic configurations is examined in some detail.

Shows how the reference interaction site model equations of Chandler et al. may be used to calculate the partial structure factors and radial distribution functions for a fluid of heteronuclear diatomic molecules. The theory is applied to the properties of the molecular model for molten CuCl proposed by Powles (1975). It is found that the effect of orientational correlations on the partial structure factors will generally be substantial. For reasonable values of the molecular dimensions a semi-quantitative fit with the experimental data of Page and Mika (1971) can be achieved. The implications for the proposed model of CuCl are discussed.

F-centre wavefunctions, calculated in the point-ion and ion-size approximations, and Lowdin-orthogonalized free-ion wavefunctions are used to derive hyperfine interactions of the ground state and orbital g-factors and spin-orbit coupling constants of the first excited state, for all 20 alkali halides. The ion-size correction leads to improved values of the transition energies (mean deviation from experiment <10%) and spin-orbit constants (15%), but some of the hyperfine constants are in error by factors of up to 2.

A molecular model allowing relaxation up to second-nearest neighbours and polarization of the negative ions is used to calculate equilibrium configurations of Ag⁺ substitutional defects in RbCl and RbBr. Including the quadrupolar deformability of the Ag⁺ ion can lead to an equilibrium configuration of the defect which is off-centre along the (110) axis, with a quadrupolar distortion of the surroundings, in agreement with experiment. Dipole moment and pressure dependence of the defect configuration also agree quite well with experiment. The high-pressure on-centre configuration is predicted to show a quadrupolar distortion.

A simple molecular field theory is derived to describe the effects of both field and stress on TmAsO₄. Below T_D, first-order phase transitions between two distortion modes are predicted, similar to the phase changes in a liquid-vapour system. Optical and spectroscopic measurements on TmAsO₄ confirm these predictions.

The adiabatic approximation and perturbation theory to second order in atomic displacement are used to construct a theory of thermal-electron energy shifts. Both intraband and interband 'self-energy' and 'Debye-Waller' corrections are included. A sum rule based on translational invariance clarified the intimate relation between these two types of correction. Various kinds of cancellation between the terms can be seen explicitly for the two limiting cases of a very narrow band and a small gap in a nearly-free-electron band structure.

Investigates the possibility of using phase shifts calculated for electron-atom scattering in performing a band-structure calculation in the solid. No explicit determination of the atomic potential is needed in the augmented plane wave method, because matrix elements can be directly related to the phase shifts. Conduction bands have been calculated for solid argon, and a comparison with other existing calculations is made.

Calculations of the energy levels of a neutral vacancy and of self-interstitials in silicon are performed using a Green function formalism, in a tight-binding approximation. The results obtained using different parametrizations of the band structure of the perfect crystal are compared with results obtained using the Extended Huckel Theory or the pseudopotential method.

As was shown recently, the continuous-time random-walk model of hopping conduction introduced by Scher and Lax (1973) should give no frequency dependence of the conductivity. This stochastic model is generalized, taking into account the relatively slow polarization response of the charge carriers to the electric field produced by instantaneous hops of a test carrier. This modified stochastic model leads to AC conduction as a result of the polarization response, which is treated as a relaxation process. An exact expression is derived for the AC conductivity in terms of a distribution of waiting times between successive hops of a carrier. In the frequency range of interest, an omega ^v dependence (0<v<1) is found for the real and imaginary parts of the conductivity which satisfy the expected form of the Kramers-Kronig relation. The treatment suggests that v increases towards unity with decreasing temperature, in agreement with experimental findings.

A previous percolation theory for hopping conduction is extended to high fields, and applied specifically to the Mott (1969) model (a constant density of states). The importance of nearest-neighbour pair correlations, the local chemical potential, and certain spatial correlations are discussed. The directional constraints created by the spatial correlations and by the nature of the percolation cluster are included approximately. The effect of the local chemical potential is included in an approximation similar to the mean field approximation. The theory is worked out primarily in the moderate field regime. The conductance is found to be proportional to exp (-A+eFl/kT), where exp(-A) is the low field conductance, F the electric field, and l a fraction of the characteristic low-field hopping distance r_m. For three dimensions, l=0.17 r_m, and for two dimensions, l=0.18 r_m. Expressions are also derived for the high-field limit, and agree functionally with derivations by others.

By carefully studying the theoretical foundations of the semiclassical formula n(x)=N(T) exp(-(eV(x)-E_F)/kT) which relates the free electron concentration n(x) to the potential V(x) (and the corresponding formula for the hole concentration) in non-degenerate semiconductors, it is found that the inequality T(K)>0.084 (m/m*)^1/3( mod e epsilon mod (eV cm^-1))^2/3 (=84K for m/m*=10 and mod epsilon mod =10⁴ V cm^-1) is a necessary condition for it to be valid. A new local formula is presented which is a generalization of the semiclassical formula in that its validity is unrestricted by the above-mentioned inequality. The new formula, which depends explicitly on the magnitude of the electric field mod epsilon mod , coincides with the semiclassical one when I>0.084 (m/m*)^1/3 mod e epsilon mod ^2/3, and differs from it considerably when T<0.084 (m/m*)^1/3 mode epsilon mod ^2/3.

In a thin film, intraband electronic transitions are infrared-active. This is because the electrons exchange momentum with the surfaces. The selection rules for the transitions are given, and the matrix elements calculated using a band model. These matrix elements are shown to be the same as those obtained from the effectively-free-electron model, i.e. the model using free-electron wavefunctions with the band dispersion relation. The matrix elements are also the same for a realistic surface potential step as for an infinite one.

A method based on the WKB approximation is developed for finding the analytic wavefunctions of high-energy states of some dynamic Jahn-Teller systems. The sequence of energy levels can be extended higher than numerical methods can conveniently reach. The wavefunctions can be used for calculating reduction factors.

A theory is developed for indirect two-photon transitions in solids in a magnetic field. Three band models have been introduced, where the electronic transitions are defined by: (a) interband-interband indirect transitions in the case of the four-band model; (b) interband-intraband indirect transitions in the case of the three-band model; and (c) intraband-intraband indirect transitions in the case of the two-band model. The result shows that the contributions from these band models agree with a recent experimental result in InSb. The four-band and two-band models give large contributions only at the limits of low and high magnetic fields, respectively.

The zero-field susceptibility associated with the surface layer of the Heisenberg and the Ising ferromagnets on a semi-infinite simple cubic lattice has been studied by using the Oguchi (1955) method and the constant-coupling approximation. Surface critical temperatures are calculated for general spin and for all values of the bulk exchange constant J and the surface exchange constant J_s=(1+ Delta )J. The minimum values of Delta , denoted Delta _c, which allow surface phase transitions to occur, are determined. It is found that Delta _c decreases as the spin value increases, and Delta _c for the Heisenberg ferromagnet is higher than the corresponding value for the Ising ferromagnet.

A neutron diffraction study was made of the nuclear and the magnetic structure of MnNb₂O₆ single crystals. The thirteen nuclear parameters (space group Pbcn) were determined from 304 reflections at room temperature. The antiferromagnetic structure (Neel temperature=4.4K), determined at 1.2K, is a superposition of G- and A-type structures of the form 0.90 G_x+0.34 G_y+0.28 A_z. The corresponding magnetic space group is P2'₁/c.

The general theory for the non-resonant reduction of the spin-lattice relaxation time T_1m of the one ion by another is presented. Such 'cross-spin-lattice relaxation' can explain the measured reduction of T_1m for Cr³⁺, in zero Zeeman field due to the presence of V³⁺. The temperature dependence of the measurements under such conditions involves the zero-field splitting of the V³⁺ ground states.

Two ZrO₂-CaO single crystals doped with Yb³⁺ coming from the same batch were used in the experiments. One of them was annealed for several weeks at 1000 degrees C. After having examined the purity and crystalline quality of the samples, the spin-lattice relaxation time T₁ of the Yb³⁺ ion in these solid solutions was measured. The experimental results in the temperature range 1.4K<or=T<or=15K can be interpreted according to the general law of variation T₁: T₁^-1=AT+B(exp(W/kT)-1)^-1+CT⁵.

A Mossbauer study of slightly doped magnetite has revealed the occurrence of spin and charge oscillations in the B sublattice of magnetite. The Mossbauer spectra, recorded between 130K and 700K of (Fe) (M_0.05Fe_1.95)O₄ with M=Li⁺, Ni²⁺, Al³⁺, V³⁺, Cr³⁺, Ti⁴⁺, Sn⁴⁺ and Mo⁴⁺ are interpreted in terms of a charge oscillation model, which describes the electron response in narrow bands.

Using extrapolations to 0 eV and 30 eV of experimental data in the energy range 1.5 eV to 14 eV, a Kramers-Kronig analysis of the reflectivity spectra at both room temperature and liquid nitrogen temperature from the basal plane (E perpendicular to c) of single crystals of 3R-WE₂ and 2H-WSe₂ has been performed. The optical data so obtained has been discussed and interpreted in terms of the proposed band model for these materials.

The A exciton series in the liquid-nitrogen-temperature epsilon ₂ spectra of 2H-WSe₂ and 3R-WS₂, derived from Kramers-Kronig analyses of normal-incidence, basal-plane reflectivity spectra, have been fitted to a Lorentzian oscillator model. It has been found that the energy levels and oscillator strengths of the excitons obey a three-dimensional theoretical model for 2H-WSe₂ and a two-dimensional model for 3R-WS₂. The experimental observations are consistent with Toyozawa's (1958) theory for weak exciton-phonon interactions and small exciton effective mass.

Tunable dye laser spectroscopy has been used to study energy transfer processes in CaWO₃:Sm³⁺ crystals. Fluorescence and excitation transitions for samarium ions in different crystal-field sites have been identified and their changes in width and position with temperature studied. This information is used to characterize energy migration among samarium ions as a function of temperature, samarium concentration, time after the laser pulse, and pressure. The interaction mechanism causing energy migration is identified as electric quadrupole-quadrupole. At low temperatures it was found that only single-step transfer between nearby ions takes place, while at high temperatures multi-step diffusion of energy occurs. These results are interpreted in terms of the Anderson (1958) localization concepts for systems with inhomogeneously broadened transitions, and quantitative estimates of the transfer rates and diffusion parameters are obtained.