Table of contents

Electrical conduction in amorphous solids containing both localized and extended states is examined. It is shown that even where there is a continuous distribution of localized states there need not be a continuous change in the energy at which the dominant part of the current flows, as a function of temperature. This gives rise to the concept of energy regions of limited current flow under equilibrium conditions. Conversely, it is shown that a continuous change in the energy of dominant flow, that is in the activation energy, can be used to characterize the energy distribution of the local product of the state density and mobility.

For Pt.I see abstr. A12758 of 1972. The diffuse scattering of long wavelength (7-8AA) neutrons by fluorite solid solutions of YF₃ in CaF₂ in the composition range Ca(Y)F_2.1 to Ca(Y)F_2.32 has been studied. The local distribution of defects is revealed by the variation of scattering with sin theta / lambda . Earlier inferences (part I) from the Bragg neutron diffraction measurements on the clustering of the two types of fluoride interstitial in this system are supported by the present results.

The interstitial impurities in a crystal are thought of as a system of harmonic oscillators coupled by the vibrations of their host lattice. The response function of an impurity is expressed by a host lattice and many-defect contributions. The interaction of the impurities is renormalized within an infinite order perturbation theory, which provides the concept of 'dressed defects'. The procedure is tested on the problem of localized modes on impurities in a one dimensional lattice.

The phonon dispersion curves of strontium fluoride in the (001), (110) and (111) directions were observed by inelastic neutron scattering on a triple axis spectrometer. These observations, and all other data relevant to the vibrational properties, were fitted by the 'shell' model for lattice dynamics. Some harmonic vibrational properties were calculated.

Extensive neutron inelastic scattering measurements of the frequencies of normal modes in strontium titanate propagating in the crystallographic directions (0, 0, zeta ), ( zeta , zeta , 0), ( zeta , zeta , zeta ), (¹/₂, ¹/₂, zeta ) and ( zeta , zeta , ¹/₂) are reported. The temperature dependence of the 'soft' modes at points Gamma and R have been investigated with particular emphasis on the mode of symmetry Delta ₂, propagating in the direction (¹/₂, ¹/₂, zeta ); quantitative estimates of the isotropy of the dispersion surface at Gamma and R are given. Rigid ion, rigid shell, and deformable shell models of the crystal dynamics have been developed. Based on these, the frequency distribution, specific heat, one-phonon X ray scattering intensity. Debye-Waller factor, and two-phonon Raman spectrum have been calculated; where possible, these are compared with the available experimental measurements.

Linear coefficients of thermal expansion have been measured from 2 to 30 K, 55 to 90 K, and at 283 K for single crystals of As, Sb and Bi inclined at various orientations to the symmetry axis. The principal coefficients alpha /sub /// and alpha _{perpendicular to} and volume coefficient beta are reported, together with the Gruneisen parameters gamma , gamma /sub /// and gamma _{perpendicular to} . The anisotropy of expansion is most marked for As and least for Bi: alpha is negative for As below about 150 K, for Sb below 20 K, but always positive for Bi. beta and hence gamma is positive for each: the limiting value is gamma ₀=4.4+or-0.3 for As, 1.00+or-0.03 (Sb) and 1.9+or-0.1 (Bi). gamma (T) has a minimum at 8 to 10 K, a broad maximum between 20 and 40 K, and at room temperature approaches 1.5 for As and 1.0 for Sb and Bi.

Theoretical current-field curves for p type PbTe at 300 K have been derived taking into account the intervalley transfer of holes between the principal and secondary valence bands. Two models of charge carrier scattering in PbTe extant in the literature have been considered; one in which scattering is by acoustic phonons only, and the other in which polar optical phonon scattering is also present. The predicted high field behaviours of these two models are markedly different, and comparison of these results with measurements on dendritic crystals of p type PbTe lends strong support to the mixed scattering model.

Localized polariton modes of small cubic crystals are studied. The eigenfrequencies of these modes are calculated for small cubic crystals in the continuum approximation, using a variational approach. An attempt was made to observe these modes by measuring the far infrared transmission of small cubic AgBr crystals.

Measurements are reported of the photoconduction spectra of several electron irradiated type Ia and type IIa diamonds in the neighbourhood of the GR1 and ND1 absorption systems, and the absorption lines which have been labelled GR2 to GR8, R9 and R10. Minima occur in the photoconduction spectra at the positions of maxima in the GR1 absorption system. Sharp peaks which persist at temperatures down to 8 K are observed in the photoconduction spectra at the positions of maxima in the ND1 absorption system and the lines GR2 etc. Mechanisms which might give rise to these sharp photoconduction peaks are discussed.

A strong interaction has been observed between the magnon and phonon excitations in ferrous difluoride which is believed to originate from the phonon modulation of the crystal field, much as in Van Vleck's model for paramagnetic relaxation. A detailed investigation is possible because previous studies of various magnetic properties of FeF₂ give sound values for the crystal field parameters. The spin Hamiltonian is shown to contain a coupling linear in both the nuclear displacements and spin, and it gives a good description of the low temperature neutron scattering measurements for all wave-vectors in the (001) and (100) directions.

The equation of state and the critical amplitudes are calculated for the Ising model in two and three dimensions on the basis of a modified form of the droplet model for critical phenomena proposed by Reatto. A droplet formula for the spin-spin correlation function is proposed. This formula has a homogeneous form but the scaling laws involving the dimensionality do not hold necessarily. The droplet model for the Heisenberg Hamiltonian is considered in detail by taking into account that the magnetization of a droplet can be in any direction.

A variational calculation by Murray (see abstrs. A34684 and A34685 of 1966) on spin waves in a disordered ferromagnet is reviewed, shown to contain two errors and corrected. Murray had reached the conclusion that the critical concentration of magnetic atoms obtained by this method was in disagreement with the results of classical percolation theory. By correcting the errors in Murray's calculation the conclusion is reached that her method cannot given an accurate estimate for the critical concentration.

For Pt. I see Ibid., vol.5, 1830 of 1972. In this article the study of the effects of nonmagnetic impurities on the critical properties of the Ising model is continued. Two separate aspects of the problem are considered. The behaviour of the susceptibility as the impurity concentration changes at constant temperature is investigated using expansions in terms of the concentration variable. The high temperature series expansions for the fourth field derivative of the free energy are also studied in order to determine whether its singularity occurs at the same temperature as that of the susceptibility. The problems of extracting meaningful results from the series analysis are discussed.

The thermoluminescence of X-ray coloured NaCl and NaCl:Cu crystals is studied in the temperature range 300 K-510 K. Five glow peaks centred at 343, 363, 391, 420 and 445 K are recorded for a warming rate of 40 K min^-1 and analysis indicates first order kinetics with activation energies 1.05, 1.12, 1.21, 1.47 and 1.47 eV respectively. The 391 and 420 K peaks can be related to the presence of dissolved copper ions. The first (391 K) is ascribed to hole release from Cu²⁺ centres formed by irradiation while electron release from an F centre neighbouring a Cu²⁺ ion is believed to cause the 420 K peak. It is suggested that the other peaks originate from F centres generated during the initial growth stages.

The dipole-dipole contribution to the energy of a pair of proton spins in an external magnetic field is profoundly altered by the reorientation of the interproton vector, though the Zeeman energy may be unaffected. The study of the relaxation time associated with this transfer of dipole-dipole energy to the lattice is an established way of studying slow classical molecular motions. An extension of this technique is made to the case of methyl groups which at low temperatures are undergoing fast coherent quantum mechanical tunnelling rotations. It is shown that the dipolar relaxation time depends in this case on transitions which effectively randomly modulate the tunnelling motion. Using a strong collision version of spin thermodynamic theory, a relationship between the transition rate p and the dipolar relaxation time T_D is obtained. Experiments are reported on 4-methyl 2,6 ditertiarybutylphenol crystals for which previous magnetic resonance work in the temperature range 10-40 K indicated a value of p of order 1 s^-1 at 4.2 K for the 4-methyl group.