Table of contents

The motion of positive ions in ³He-⁴He mixtures is investigated in the region where the mobility is limited by ion-³He scattering. The inclusion of a residual polarization interaction has a large effect, and, together with hard-core scattering, is sufficient to bring theory and experiment into qualitative agreement in the nondegenerate region.

The binding energy of an electron to a Coulomb potential is evaluated in the limit of weak coupling to optic modes. The results are compared with bounds given by other workers.

The energy levels of the F centre have been discussed using the Koster-Slater (1954) approach. It has been shown that a simple two-band model reproduces the deep states of the F centre. The ground state is pulled up from the valence band while the excited states are pulled down from the conduction band.

It is shown that in a recent paper by Chaudhuri and Ganguly entitled Absorption and Fluorescence Spectra of Crystalline trans- stilbene (see ibid., 1969, 1560), the crystalline samples were not sufficiently thin to obtain accurate absorption spectra. Direct absorption and specular reflection spectra are presented and the large deviation from the oriented gas model cited by Chaudhuri and Ganguly is shown to be primarily a manifestation of experimental difficulties.

Preliminary results showing the effect of externally applied electric fields up to 50 kV cm^-1 on the apr spectra from X- irradiated ruby crystals are reported. A brief discussion of the results obtained is given.

X-ray measurements of the interference function made on molten alloys of the Hg-In system show little change with composition. A strong change of resistivity with composition, which may be interpreted as evidence of a change in structure, is reported. If this occurs, it is outside the range of the present X-ray measurements.

The one-dimensional X-Y model in a z axis magnetic field with random coupling constants is studied. The free energy is calculated for the case in which the squares of the coupling constants have a generalized Poisson distribution. The effect of randomness in the coupling constants on the low-temperature thermodynamics is studied. In particular, it is found that a phase transition which occurs at zero temperature in the non-random system disappears in the random system. The thermodynamic quantities which are singular in the non- random system have derivatives of all orders in the random system.

The compressible Ising ferromagnet is defined in terms of an exchange integral between the z component of spins on two sites of a lattice which is a function of the distance between the two sites. To the first order, the total Hamiltonian can be shown to contain an interaction term linear in phonon variables and quadratic in spin variables. It is shown that the partition function can be expressed in terms of an effective spin Hamiltonian in which the effects of the phonons have been summed to infinite order. The spin-phonon interaction is shown not to renormalize the phonon frequencies. The results allow the free energy to be expressed as the sum of two separable components for the spins and the phonons, plus an interaction component.

The function h(x) appearing in the magnetic equation of state near the critical point, namely H=M^delta h(x) has been constructed for the two- and three-dimensional Ising model. (h(x) is denoted by h_I(x) in this case.) This has been achieved by first estimating the leading coefficients in the series expansions of h_I(x) about x= infinity (critical 'isochore'), x=0 (critical isotherm) and x=-x₀ (phase boundary), and then extrapolating these series with the aid of Pade approximants. h_J(x) is used to test various approximate forms for h(x), and is compared with experimental results for real ferromagnets and fluids. Finally h_I(x) is used to compute the function m_I( theta ) appearing in Schofield's parametric representation of the equation of state.

An approximate method of solution of the equation of motion chain for double time retarded Green functions is set up for systems with small particle density, that is systems in which the occurrence of more than two or three particles interacting simultaneously is negligible. The method is applicable to both Bose operators and spin operators. Considering only spin systems, already known results obtained via a perturbation theory approach in the limit of low temperature are recovered, showing in this way that the recourse to the Dyson-Maleev transformation is unnecessary. At the same time it is pointed out how, by taking into account the kinematical interaction, the description of the short range order above the Curie temperature may be obtained.

Starting from the integral equation form of Schrodinger's equation, some expressions describing the reflection of electrons from the surface of a perfect crystal in which the atomic scattering is described by a pseudopotential are derived. The obvious application is to low-energy electron diffraction, but surface states and planar defect states can also be treated. The author also indicates how the scattering of Bloch waves by surfaces could be treated.

The rate of growth of F centres and thermoluminescence studies in highly pure additively coloured and then X-irradiated KCl crystals show that the first stage of coloration is considerably suppressed and the second stage is enhanced in these crystals. The value of the parameter a defining the linear rate of growth of F centres in the second stage is also high in additively coloured crystals. The thermoluminescence peak positions and the ratio of the excess concentrations of F centres generated during X-irradiation and the corresponding thermoluminescence areas for the additively coloured and then X-irradiated KCl crystals are the same as observed earlier by Jain and Mehendru (1965) for highly pure KCl crystals which were not additively coloured prior to X-irradiation.

Calculations of the phonon sidebands associated with the ²E_g to ⁴A_2g transition in MgO:V²⁺ and the Gamma _3g to Gamma _5g transition in MgO:Ni²⁺ are presented. The problem can be separated into two parts: (i) the coupling of various symmetry adapted displacements of the crystal ions to the transition; (ii) the response of the lattice to symmetry adapted applied forces. It is shown that the results required from (i) are a limited number of coupling parameters. These are treated here as adjustable constants, as are also the changes in force constants in the vicinity of the defect. The calculation of the second part is made using Green function methods. Satisfactory agreement with experiment is obtained by assuming that only displacements of the impurity ion and its nearest neighbours are coupled to the transitions.

The coherent scattering of X-rays by phonons is considered in the harmonic approximation for processes involving any number of phonons. The total scattering cross section is evaluated using the best eigendata and up to 24000 sample frequencies in the Brillouin zone. Intensities are presented for NaF, NaCl, NaBr and Al, and it is found that the results converge rapidly with increasing sample size. A comparison with independent calculations of the one-phonon and two-phonon cross sections shows that the higher order processes are important for moderate values of K. The contribution from the very small wave vector phonons is treated separately, and this enables the integrated diffuse scatter to be calculated near a Bragg peak.

Absolute measurements have been made of the total thermal diffuse scattering of CuK alpha X-rays from single oriented crystals of caesium iodide. Data have been obtained in the major symmetry directions and compared with the theoretical values of total thermal diffuse scattering calculated using the 'deformation dipole' (d.d.) lattice dynamical data of Karo and Hardy (1968). In particular the results are used to discriminate between two variations of the d.d. model, demonstrating the unsuitability of the d.d. (+) variation and the good overall agreement with the d.d. (-) variation. Where feasible, the experimental thermal diffuse scattering has been analysed to yield acoustic and optic phonon dispersion curves. Finally, the discrepancies between the total experimental thermal diffuse scattering and the d.d. (-) theory predictions have been investigated for any asymmetry.

Using local orbital Hartree-Fock orbitals for the Li⁺ and Cl^- ions and the mixed basis method of energy band calculations, the one-electron energy bands of the LiCl crystal were computed for the points Gamma , X and L in the first Brillouin zone. The p-like valence band is found to be 7.84 eV wide and the s-like valence band is found to be 3.03 eV wide. These bands are primarily formed from the outer 3s and 3p halogen states. The band gap at Gamma is computed to be 10.81 eV. At the point X, the s-like state X₁ and the d-like state X₃ are found to lie lowest and to be essentially degenerate. The use of the Fock exchange is seen to produce significant changes in the band structure when compared with previous calculations using model potentials.

A generalization of Hubbard's (1963 and 1964) narrow energy band theory is given which is applicable to transition metal compounds with multiatomic bases. The only correlations considered are those between electrons on the same atom and the calculation is applied to transition metal oxides in the paramagnetic phase. It is shown that the electron correlations reduce the 3d bandwidth in the oxide and it is further shown that when Roth's (1969) decoupling procedure is used there is an extra narrowing due to the band-shift effect.

Anderson's (1958) theory of localized electron states in an irregular solid is discussed critically. The statistical and analytical properties of the Green function, when states are localized, are analyzed and it is pointed out that these are not incompatible with Lloyd's (1969) exact results. Anderson's argument is repeated in outline, but it has been found possible to make a major simplification in the statistical analysis. Attention is drawn to two doubtful points in the argument and it is suggested that delocalization occurs less easily than Anderson supposed. The argument is applied to a model of a dilute binary alloy. It is proved for a model of the binary alloy that the energy levels do not extend outside the energy bands of the pure metals.

The paper deals with the problem of low-frequency instabilities. The investigation is performed on the basis of the kinetic equation of Boltzmann-Vlasov, with the collision integral presented in the generalized model form of Bhatnagar, Gross and Krook (1954). Both the frequency and the parameter of the collisions in the case considered are assumed to depend on the moment velocity of the electronic gas particles. The frequency spectrum and the damping (amplification) coefficient of the low- frequency potential longitudinal collective oscillations and waves are determined. The necessary and sufficient conditions for the existence of nondamping oscillations are found. It is shown that no current-convective instability develops in the case of a nonequilibrium nonhomogeneous electronic solid state plasma.

Measurements have been made of the transitions to superconductivity of quench-condensed aluminium films at various stages of annealing. The films exhibit enhancement of the transition temperature and transition characteristics which are broader than may be accounted for by the theory of mean-field fluctuations alone. A model in which the transition broadening is attributed to a distribution of transition temperatures within the films is proposed, and the analysis is carried through to a calculation of transition characteristics. Despite broadening of the magnetic field induced transitions, it appears that disordered films are nevertheless well described by the Ginzburg-Landau theory.

The effective spin at the impurity site, (S₂)_eff, impurity contribution to the magnetic susceptibility, chi , for dilute magnetic alloys are computed using the Bloomfield- Hamann (1967) t-matrix solution for Nagaoka's (1965, 1967) truncated Green function equations. The computation of (S_z)_eff at various temperatures indicates the quenching of the impurity spin at very low temperature. The calculation for the impurity contribution to the magnetic susceptibility shows that for high temperatures (T>or approximately=T_K) the susceptibility varies as (T+T_K)^-1 In the low-temperature region (T<T_K) the result scales to a T^-0.6 power law for the variation of susceptibility with temperature. This is in good qualitative agreement with recent zero-field low-temperature susceptibility measurements for Cu(Fe) and Cu(Cr) alloys.

Attenuation of an ultrasonic wave near the spin-flop transition point in uniaxial antiferromagnets is studied theoretically. The modulation of the exchange interaction caused by lattice vibrations is considered as the interaction between a sound wave and the spins. An anomalous increase in the attenuation against an external magnetic field at a fixed temperature near the spin-flop transition point is obtained for both longitudinal and transverse sound waves. This removes a discrepancy between recent experiments and previous theories. A sharp dependence of the attenuation on the angle between the easy axis of a crystal and a magnetic field is also obtained in agreement with the experiments.

Spin-wave excitations in antiferromagnetic CoO (T_N=290 K) have been measured in the far infrared (100-300 cm^-1) at temperatures between about 2 K and 300 K. Crystals of different origin have been compared in order to eliminate impurity effects. A new resonance is reported at 296 cm^-1 and the absorption data extend to about 470 cm^-1. The resonance frequencies are strikingly insensitive to temperature and in general agreement with recent predictions by Alben (1969) using a time-dependent molecular field theory.

It has been shown that the Fe³⁺ ions in the distorted perovskite GdFeO₃ become ordered antiferromagnetically at 650 K and the ordering arrangement is G_xF_z in Bertaut's (1963) notation. The canted moment has been measured at temperatures below 77 K, and has been found to produce an effective field of 310 Oe at the gadolinium sites opposing the canted moment. The induced susceptibility of the Gd³⁺ ions in zero applied field is in direct opposition to the resultant Fe moment along the c axis. The specific heat has been measured in the temperature range 0.5 K<or=T<or=12 K and the result is a broad, rounded, Schottky curve with a lambda -type anomaly superposed at 1.5 K the Neel point of the Gd system. Susceptibility measurements below 4.2 K are presented for the orthorhombic a, b c axis.

The g factors of the E" ground state of the Yb³⁺ ion are evaluated in the crystal field model, for the case in which the cubic field is modified by a small rhombic distortion. Cubic (001) axes of quantization are used throughout, all operators being described in the tensor operator notation for the cubic group. The conditions under which the mean E" g factor is unaltered by the distortion are examined, the case of a trigonal distortion being treated in detail. A calculation is made of the Yb³⁺ trigonal eigenstates which would lead to the g factors observed for Yb³⁺ in several II-VI lattices.