Table of contents

An expression has been derived for the voltage correlations on a random Bethe resistor lattice. From this expression, the critical exponent for the correlation length is found to be 1.

Relativistic corrections to the muffin-tin potential are shown to produce a significant improvement in the agreement between the measured and calculated LEED intensity profiles for normal incidence and low primary beam energies on W(001).

The recursion method, used so far for the tight-binding Hamiltonian, implicitly requires the representation to be hermitian. Non-hermitian representations arise in (chemical) pseudopotential theory and the authors indicate how to obtain the local density of states in such a more general case. Results are given for the electronic structure of crystalline arsenic.

It is shown that for any dynamical quantity phi associated with an impurity system the variance, var ( phi )_p calculated after averaging the partition function, is greater than or equal to the corresponding variance var ( phi )_q calculated according to the usual quenched prescription in which the free energy is averaged. In particular, if chi ^p, chi ^q denote the respective isothermal susceptibilities subject to the same conditions, then chi ^p>or= chi ^q. This is a general result valid for classical and quantum systems in which the susceptibility is proportional to a variance, and it implies that if a quenched spin system displays a phase transition at a temperature of T_c^q at which a certain variance, say the susceptibility chi ^q diverges, then chi ^p must also be infinite at the same temperature. It is also shown that for a large class of spin S ferromagnetic Ising systems which satisfy the conditions of Griffiths' correlation inequalities and other specified conditions, the covariance between any two spins s_i and s_j is similarly ordered, i.e. cov (s_i,s_j)_p>or=cov (s_i,s_j)_q.

For spin ¹/₂ Ising models with ferromagnetic pair interactions J_ij which are taken to be statistically independent, non-negative, random variables, the authors show that the averaged two-spin correlation function ( sigma _p sigma _q) is less than or equal to the value ( sigma _p sigma _q)_J for the corresponding non-random system in which each J_ij is replaced by its average value J_ij. The inequality implies for sufficiently high temperatures that the averaged isothermal susceptibility chi <or= chi _j. With additional assumptions about the existence and nature of the phase transitions for the systems, one concludes that the critical temperature tau _c for the averaged system is not greater than the corresponding critical temperature tau (J) for the nonrandom system. In the process of obtaining the results it is noticed that Griffiths' inequalities ( sigma _p sigma _q)>or=0 and delta ( sigma _p sigma _q)/ delta J_rs>or=0 imply that delta ²( sigma _p sigma _q)/ delta J_rs²<or=0.

High resolution L₃M_4,5M_4,5 Auger spectra of copper are compared with multiplet structure and transition rate calculations. The comparison reveals unexplained structure to lower energies which is attributed to Auger vacancy satellite lines.

The fundamental equations for the dynamical neutron diffraction including magnetic interaction are developed. Using the close analogy to dynamical X-ray diffraction, the expression for the ratio of reflected-to-incident intensity in the symmetrical Bragg case is derived. Explicit results for a Gd crystal are presented.

The triplet correlation function for liquid rubidium is determined by molecular dynamics. Calculations were based on a realistic pair potential for a density rho =0.0107 AA^-3 and a temperature T=319K. The results are compared with various models.

The Raman-active modes of thiourea, SC(NH₂)₂, and deuterated thiourea, SC(ND₂)₂, have been studied as a function of temperature and comparison is made with previous work. Neutron scattering results, obtained from a single crystal of SC(ND₂)₂ using a triple-axis spectrometer, include dispersion curves for acoustic modes propagating along the a*, b* and c* directions together with parts of optic branches. The measurements have been made mainly in phase V, with some results in phase I. The elastic constants obtained from the acoustic mode dispersion curves are compared with values obtained by Brillouin scattering.

Coherent inelastic neutron scattering was used to measure high-symmetry dispersion curves in deuterated urea. A twelve-parameter force constant model, allowing for atom-atom interactions between neighbouring molecules as well as long-range dipolar forces, is presented in the rigid molecule, harmonic approximation. The model accounts for the measured external-mode Raman frequencies, diagonal elastic constants and neutron results. On the basis of the model, LO-TO splittings for the polar external modes are calculated.

Phonon frequencies of indium phosphide have been determined along the principal symmetry directions (by inelastic neutron scattering). The shapes of the dispersion curves are discussed. The phonon frequencies at the critical points are: Gamma point, 10.3 and 9.2; X point, 9.95, 9.70, 5.8, 2.05; L point, 10.2, 9.5, 5.00, 1.65 THz. In all cases the longitudinal vibrations have a higher frequency than the transverse vibrations, i.e. the surfaces do not cross.

The results of thermal expansion measurements using a three-terminal capacitance dilatometer on Ge, GaAs, ZnS, ZnSe and CdTe below 30K and on ZnSe and CdTe between 57 and 90K are reported. Respective values of 0.49, 0.32, -0.14, 0.0 and -0.85 derived for gamma ₀^th, the zero temperature limit of the Gruneisen parameter gamma =3 alpha VB_s/C_p are given. These are in good agreement with the values of gamma ₀^el calculated from the pressure dependence of the elastic constants. gamma (T) as a function of reduced temperature, T/ theta ₀, where theta ₀ is the Debye temperature determined at the zero temperature limit, is found to have an essentially universal form and passes through a negative minimum at T approximately 0.06 theta ₀. The implications of this observation and the importance of the degree of ionicity in dictating gamma ₀ are discussed.

Heat capacities have been measured from 2 to 12K for ZnS and up to 25K for ZnSe and CdTE. Limiting values of the Debye temperature are theta ₀=339K for ZnS, 271K for ZnSe and 161K for CdTe which agree, within experimental error, with those calculated from elastic moduli.

A step by step procedure is suggested for solving electron scattering problems in crystals. First scattering for a single atom is calculated, then for a chain of atoms next for a layer of chains and finally for the entire crystal. The new method has great speed and flexibility. It is applicable to band structure and LEED calculations and is especially useful in the theory of RHEED.

The electrical properties of La_1-xSr_xVO₃ change from those of a semiconductor to those of a metal as x is increased, with a metal-nonmetal transition occurring at x approximately=0.2. This has been studied using AC and DC conductivity and thermopower measurements over a temperature range from 4 to 400K. Evidence for localization is found in AC conductivity and a temperature dependent activation energy at temperatures below 100K. A temperature dependence sigma = sigma ₀exp(-B/T¹n/), where n approximately 4, is interpreted in terms of a model in which the Fermi level occurs within a tail of states at the edge of the valence band. No evidence is found for polaron formation, but the frequency dependence of AC conductivity suggests that multiple site hopping and possible cluster formation is of importance.

Coexisting metallic and semiconducting phases have been obtained by passing DC currents through VO₂ single crystals. The mixed state was studied by optical microscopy. Narrow semiconducting strips that nucleate at the positive edge of a metallic domain and propagate towards its negative edge have been observed under constant currents.

Proper symmetry wavefunctions for positrons in alkali halide crystals are calculated through a plane wave expansion. The band contributions to the effective masses are given. The anisotropies in the momentum distribution due to annihilations in the band states are examined, and the relative importance of anions and cations to annihilation events is assessed. The diffusion of positrons is discussed within a polaron picture, and some previously proposed models for the origin of the longer-lived lifetime component are dealt with.

The thermodynamics of the 1D Ising model with arbitrarily varying exchange integrals is investigated. Using the 'levelling-exponential' method and a simple diagrammatic technique, the asymptotically exact expansion of the free energy with respect to the parameter tanh( beta H) (where H is the external magnetic field) is obtained. General results are specified and discussed for the case of the so-called exclusive double-bond model when one of the exchange integrals is ferro- and the other antiferromagnetic.

The first terms of the high-temperature expansion of the susceptibility are calculated for the degenerate Hubbard model and the magnetic interaction in the strong correlation limit is deduced for any electron concentration. By comparison with the non-degenerate case, it is shown that two mechanisms favour ferromagnetism in the degenerate case: the ordering of the orbital states and the double exchange coupling.

A magnetic spiral structure with propagation vector Q parallel to a hexagonal crystal axis (as exhibited by holmium metal) is perturbed by the hexagonal crystal field anisotropy, introducing modulations Q+or-6Q. By calculating spin deviations from the modulated spiral, the spin Hamiltonian is generated. The Hamiltonian exhibits interactions between the modes omega (q) and omega (q+or-6Q), but is shown to be diagonalized in terms of a new set of independent modes by a novel, non-unitary transformation. Numerical results, which are obtained by using exchange coupling parameters determined at higher temperature (where the hexagonal field is negligible) predict the change in the shape of the spin wave spectrum of holmium at lower temperatures where the field effect is appreciable. From the spin wave spectrum the magnetic zero-point motion is evaluated, and this is found to be larger along the hard directions of the hexagonal plane than along the easy directions. The corresponding modulation of the effective magnetic moments has been calculated numerically for holmium, and found to be consistent with recent experimental observations.

Techniques developed by previous authors to describe the effects of a random distribution of impurity spins on the excitations of a magnetically ordered system are extended to the case of long-range oscillatory types of order which are not necessarily commensurate with the lattice. For non-magnetic impurities, a spin-wave stability condition is used to determine a critical concentration for the onset of such long-range order. For long-range oscillatory exchange the critical concentration can be reduced significantly from the nearest-neighbour result. The results are in good agreement with recent experiments on dilute rare-earth-yttrium alloys.

For pt.I, see abstr. A30634 of 1973. A study of the spin-wave modes of a metallic ferromagnet, carried out in a previous work for the T=0K case, is extended to the finite-temperature case. The two damped spin-wave branches of poles found in the previous work are shown to persist for finite temperatures, as long as the temperature is small compared with the Fermi temperature. At higher temperatures, the two branches mix and only one important branch is obtained. This structure of branches is shown to result from the existence of two Fermi surfaces (one for each spin) and to be closely related to the Kohn-anomaly points. Conditions of measurability are briefly considered.

High precision data for the electrical resistance of dysprosium in the region of the Neel point have been obtained using the direct current comparator method. Results are given for both b- and c-axis samples cut from the same high quality monocrystal. In the immediate vicinity of the Neel point (BT-T_N mod <or=2.5K), the c-axis resistance, R_c, cannot be convincingly described by a power law. Reasons for this are discussed. However, R_c is described by a power law for 2.5<or=T-T_N<or=60K and for -15<or approximately=T-T_N<or approximately=-2.5K with exponents psi ₊=0.60 and psi _- approximately=1.25 respectively. In the case of b-axis data, R_b is linearly dependent on T for T>or=T_N, whereas a power law, of weak amplitude but with psi _- approximately=1.25, is valid below T_N. The results suggest that dR/dT varies as the magnetic specific heat below T_N for both the b- and c-axis resistance.

The theory of the twisted-wall structure of domain walls is adapted for the case of cylindrically symmetric bubble domains. A general formulation of the problem is presented. A special case of a single bubble with a large radius considered in a film with a thickness much larger than the wall width, is solved. The result is qualitatively equivalent to results of the theory in the case of straight walls.

The nonexponentiality in the Zeeman spin-lattice relaxation of nontunnelling methyl groups is shown to be closely related to the fact that the relaxation depends on the experimental method. Experimental results on CF₃COOAg demonstrate that the half-amplitude times by the saturation- tau -90 degrees method can be, provided the saturating 90 degrees pulses are properly spaced, twice as long as those by the 180 degrees - tau -90 degrees method for the magnetic field perpendicular to the fluorine plane above the temperature of the T₁ minimum. The exponentiality of the relaxation below the T₁ minimum temperature, independent of the crystal orientation, implies that the intergroup induced transitions are able to equalize the populations of the degenerate E^a and E^b levels in a time much shorter than any of the time constants describing the Zeeman relaxation. The value 25 kJ mol^-1 is obtained for the activation energy of the CF₃ group reorientations. Experiments on polycrystalline acetone show a similar but somewhat smaller dependence on the experimental method.

By combining the Born theory of pyroelectricity with a microscopic theory of dielectric properties, it is shown how an order-of-magnitude estimate of the pyroelectric coefficientp at low temperatures can be made from phonon theory in certain favourable cases. The ratio omega _M/ omega _D' omega _M being a characteristic optic mode frequency and omega _D the Debye frequency, is an essential dimensionless parameter determining the magnitude of p. The thermodynamics of pyroelectrics is used to calculate upper bounds to the pyroelectric coefficients of a variety of materials at room temperature. The low-temperature bound yields p<DT,D being determined by omega _D and the dielectric constant.

The dependence of magnon-pair excitations upon temperature and dilution of the magnetic ion concentration has been examined by inelastic light scattering in the antiferromagnetic compounds KNi_1-cMg_cF₃. Ten values of c were examined, ranging from pure KNiF₃, which shows a well defined low-temperature magnon pair at 746 cm^-1, up to values above the percolation limit (c=0.68) for the perovskite structure. For increasing values of c between 0 and 0.5, the magnon-pair mode decreases in frequency and increases in linewidth in accordance with expectations based on earlier work in the (MnZn)F₂ system. As the Ni concentration is lowered further the results indicate an increasing departure from expected behaviour. In particular, the pair mode continues to broaden but remains relatively constant in frequency. Quantitative magnetic data at higher values of c are precluded by disorder-induced first-order Raman scattering by phonons. A brief discussion of the phonon spectra is included. Detailed temperature dependence between 25K and 300K is also obtained for magnon pairs at several concentrations of magnesium.

The thermoluminescence response to gamma rays of the most sensitive glow peaks in LiF (II to V) reaches a maximum and then decreases. The decrease in response is attributed to radiation damage. It is observed that even after the considerable reduction in the TL, which results from a heavy dose, the saturation exposure for these peaks remains the same. However, by redistributing the traps amongst the peaks by pre-annealing at 200 degrees C for 23 hours, the saturation exposure can be altered. Since saturation exposure is indicative of the availability of trap centres, it is suggested that radiation damage in LiF is due to a decrease in the luminescence centres. This decrease could be due to the aggregation of simple luminescent centres into complex centres. The possibility of the M-centre being one such centre is discussed.