Table of contents

MgCr₂O₄ has been examined by powder neutron diffraction. There is no evidence for an off-centre displacement of the Cr³⁺ ions as recently proposed, though displacements up to about 0.02 AA cannot positively be ruled out.

ESR and ENDOR have been used to investigate the F⁺ centre in MgO crystals enriched in the isotope ¹⁷O. A study has been made of the hyperfine interactions between the trapped electron and ¹⁷O nuclei at the first four anion shells neighbouring the oxygen vacancy. The results are consistent with a wavefunction in which most of the unpaired spin is in 2p orbits on the twelve nearest O^2- ions with smaller admixtures of 3s and 3p orbitals in the six nearest Mg²⁺ ions. There is also evidence for small 2p admixtures at further O^2- sites.

Intense 'shake-up' satellites have been observed at an energy separation of 12-13 eV from the titanium 2s, 2p_1/2 and 2p_3/2 photoemission lines in TiF₃.

The thermoluminescence spectrum of LiF has been observed after heavy gamma irradiation. Unlike the spectra reported in the literature this is found to extend to the red region and contain peaks at 330 nm, 348 nm, 436 nm and 635 nm.

Extensions of Lowdin's LCAO Approximation for the calculation of the cohesive energies and elastic properties of ionic solids have been made. The relevant equations have been generalized and the specific case of ions having closed shells of d orbitals has been detailed. AgF has been chosen as a test case and the cohesive energy has been calculated at the experimental internuclear separation for two orders of nearest neighbours.

The conduction in liquid selenium above 720 degrees C occurs predominantly by the electrons in the extended states. The author investigates the field dependence of the conductivity in the extended states. He has found the relation sigma approximately exp( alpha (E)F¹2/), which is in agreement with a suggested model for the conduction mechanism in liquid selenium at higher temperature. Two kinds of low-frequency oscillations in liquid selenium are observed: oscillation in a transverse magnetic field and oscillation in the negative (differential) resistance region of the I-U characteristic. Build-up of the space-charge domains is assumed to cause the latter oscillation.

The Debye-Waller factor has been calculated for specularly reflected He beams by taking into consideration the normal component of the incident atom velocity in addition to the influence of the attractive potential well. The calculated figures are, in most cases, too small to correspond to the experimental values of the reflected intensities. The apparent low thermal roughness of the surface is discussed.

It is shown that on a plausible approximation the three-phonon contribution to the lattice thermal resistivity can be described in terms of simple exponential decays toward a set of terminal distributions, one for each reciprocal lattice vector. The result of this is to produce an Umklapp-process drift term in the steady-state distribution as well as a Normal-process drift. The Callaway result follows when Umklapp processes are negligible. For a perfect infinite lattice a correction to the single mode relaxation time result of more than a factor of three greater than the Callaway correction is predicted.

Resolvent super-operator techniques are used to establish a formal expression for the exact nonlinear response of nondegenerate semiconductor electrons to an arbitrary high d.c. electric field in the presence of arbitrary phonon and impurity scattering. The theory is based on the Liouville equation and is exact in the thermodynamic limit. Infinite-order perturbation expansions of the field-dependent resolvent lead to a simple kinetic equation for the one-electron density matrix. The steady-state Boltzmann high-field transport equation is derived exactly under the assumptions of weak scattering and point collisions, that is for zero collision broadening and neglecting the influence of the field within the collisions. Collision broadening corrections are derived for arbitrary scattering processes.

The critical region around the true phase transition temperature is estimated for Ising-like models near d=4 and for the same models with long (but finite) range interactions at arbitrary d. The results justify the use of the Ginzburg criterion for the critical region. The rapid and nonanalytic decrease towards zero of the size of the critical region as d to 4 from below is analysed and its consequences for the validity of the epsilon -expansion are discussed.

Critical properties of a lattice model of isotropically interacting 'continuous spins' are studied using high-temperature series expansions. Both the spin-spin and spin-field interactions are different from the planar classical Heisenberg model, yet the ground-state symmetry is the same. The model is found to behave in most respects like the planar classical Heisenberg model, and in three dimensions the following values of critical indices are found: gamma =1.32+or-0.04 and alpha =-0.04+or-0.06. In two dimensions there is flimsy evidence for a divergent susceptibility with an exponent gamma approximately=3'. The results support the belief that for finite-range interaction and fixed dimensionality, unrenormalized critical indices are determined by the underlying symmetry.

The exact high temperature susceptibility series for the spin-1/2 uniaxially anisotropic Heisenberg model is derived through order T^-7 for various lattices and anisotropies. The series is extrapolated by the Pade approximant method to give the critical parameters for a ferromagnet having spontaneous magnetization parallel to the symmetry axis of the system. When the anisotropy changes from the Ising limit to the isotropic Heisenberg limit the critical temperature of the system decreases, slowly in the Ising limit and rapidly in the isotropic limit. Our results are consistent with the hypothesis that the critical index remains constant as the anisotropy varies from the Ising limit toward the isotropic limit, and changes discontinuously when the system becomes isotropic.

Diagrams are used to present an exact high-temperature low-field series expansion for the Gibbs free energy of the classical n-vector model ferromagnet. It is shown, within the framework of the series expansion method, that, to leading order in (small) n, the zero-field Gibbs free energy and the zero-field susceptibility of the ferromagnet are effectively equal to the self-avoiding polygon and self-avoiding chain generating functions, respectively. The critical point and critical exponents determined by the above properties of the ferromagnet to leading order in n are identified with those of the corresponding self-avoiding walk problem.

The M₁ band in KCl shows a weak, temperature independent magnetic circular dichroism which is interpreted as due to a magnetic mixture of the excited state of this band with those of M₂ and M₂' bands. The magnetic circular dichroisms of the R₁, R₂ and R_M bands of R centres in KCl have also been measured at liquid helium temperatures.

For pt.I. see ibid., vol.6, 2733-44 (1973). The zeroth and first moments of the magnetic circular dichroism of the R₁, R₂ and R_M bands of R centres have been calculated in the frame of Silsbee's model. The experimental results of Merle d'Aubigne and Duval (1968) as well as those of the first paper of this series are interpreted, yielding the following values of the involved parameters: Jahn-Teller constant, k²=1.25+or-0.25, effective mean energy of the Gamma ₃ lattice vibration, h(cross) omega _E=(120+or-20) cm^-1; spin-orbit constant of the R₁-band excited state, lambda ₁=(-27+or-4) cm^-1.