Table of contents

It is shown that the critical behaviour of the general eight-vertex model is equal to that of an Ising model with only two-spin interactions between first, second and third neighbours. The critical exponents of the latter must therefore, in general, depend on the ratios of coupling constants as those of Baxter's eight-vertex model have been shown to do, in contrast to universality so far assumed to hold for all short-range two-spin interactions.

It is shown in the large-n limit that axial anisotropy can induce a change-over from first-order to tricritical and second-order phase transitions in n-component s⁶ models with isotropic interactions as well as in Wallace's hypercubic s⁴ model (1973) with m=O(1) critical components. For m=O(n) one finds in the limit of large axial anisotropy an m-vector-like discontinuity of the order parameter at T₁.

The selfconsistent equations of Kohn and Sham (1965) are applied to metal surfaces. It is shown that at T=0 the highest energy of an occupied state epsilon _F is equal to the chemical potential, and that the workfunction is equal to the difference between the vacuum level of the electrostatic potential and epsilon _F.

Optical absorption and thermoluminescence (TL) output measurements were made on KBr single crystals treated in a high alternating (50 Hz) electric field and irradiated with X-rays at room temperature. A substantial enhancement of both the F-centre concentration and the thermoluminescence light output was observed in AC field treated samples upon X-irradiation. The effect of AC field treatment on the F-centre growth curves is also reported.

The application of renormalisation group recursion relations to the calculation of critical exponents in d dimensions to second order in epsilon =4-d is discussed. It is shown that in the limit of a large scale factor b, the fixed point value, u* of the four-spin coupling constant is correctly given to second order by a renormalisation group equation in which all irrelevant variables, mass renormalisation graphs, and mass terms in the propagators are ignored. Related approximations in the calculation of the critical exponents are justified. The unexpected equality to order epsilon ² of u* and u_0c, the Feynman graph coupling constant, is discussed.

Measurements of the velocity of sound in three Tl-Te alloys (30, 50 and 66.67 at.% Tl respectively) suggest that the loose three-fold coordination in pure liquid Te at temperatures below 700 degrees C gives place to a typically metallic coordination on the addition of only a small amount of Tl. Some measurements of acoustic attenuation as a function of frequency for the 50 and 66.67 at.% alloys show no clear signs of structural relaxation and give ratios of bulk to shear viscosity typical of those found in covalently bonded liquids, in contrast with the high values usually found in ionic liquids.

An investigation is undertaken of the extent to which the Landau and Rumer procedure (1937) for calculating acoustic absorption in dielectrics is invalidated by its assumption that the thermal phonons are in equilibrium. It is shown that this assumption will break down in pure materials at low temperatures for sufficiently high acoustic intensities and frequencies, and that in several such materials at T approximately 10K a substantial change in the 'low intensity' acoustic relaxation time may be expected for intensities approximately 10^-1-10^-2W cm^-2 at frequencies approximately 1 GHz. It is suggested that measurement of this effect could be of use in distinguishing between energy-conserving and non-conserving acoustic interaction processes, and in providing an independent estimate of thermal-phonon relaxation times.

For pt.I, see ibid., vol.7, no.20, 3692 (1974). The theory developed by the authors in the preceding paper is extended to cover the case of high intensities. A discussion is given of the application of the results to experimentally feasible situations.

An important subset of diagrams, the small watermelons and their elementary derivatives, are found to exhibit a finite clustering property; the subset is summed approximately and provides a long-range tail to the Percus core of the direct correlation. Below a certain density, governed by the range of the small watermelons, fluid-like solutions are obtained, whilst above this density the structure is long-range oscillatory. The rigid sphere isotherm shows distinct fluid and solid branches in essential agreement with the machine simulations. The finite clustering of particles implies a dramatic development of the statistical attraction operating in the fluid, and serves to shift the system from the fluid to the solid branch of the isotherm.

Diamagnetic susceptibility for several ionic crystals was calculated by using the LCAO method in the free-ion approximation of the basic atomic spin orbitals. The density matrix of the crystal was then expressed as a superposition of diamagnetic crystal ion densities. Consequently, the susceptibility could be written in the form of a power series of the overlap matrix; the first term describing the system of the free ions, and the other ones, linear quadratic etc. overlap contributions. Numerical applications show that the linear overlap corrections to the susceptibility are very significant and cannot be neglected in calculations. The results of the present work were compared with the experimental data and good agreement was found for alkali halide crystals, whereas in the case of the MgO crystal there is a clear discrepancy between theoretical and experimental results, specific reasons for which are suggested.

It is established in the present work that the decrease in low-temperature phonon conductivity of III-V semiconductors, caused by an introduction of impurities with concentration >or approximately=10¹⁷cm^-3, may be explained by Kosarev's mechanism for the scattering of phonons by charge carriers in the effective electric field of the impurity centres for q>2k_F, and a more consistent consideration of the screening of the phonon-electron interaction in the region of the long-wavelength phonons for Ziman scattering for q>2k_F, as suggested by Crosby and Grenier (1971).

The authors derive an expression for the force on a classical charge moving with arbitrary velocity v in the neighbourhood of a metal surface. A simple physical argument shows why the parallel component of the velocity-dependent force is half the normal component for a slowly moving charge.

The effects of the random local magnetic fields on the magnetisation and the susceptibility are studied in the Ising model.

A general theory of the exchange averaging of magnetic resonance spectra is presented. This theory is developed in terms of nonperturbational approximations to the equations of motion of the relevant spin correlation functions and is expressed in terms of nonlinear integro-differential equations. Numerical solutions of the equations are presented for the averaging of the fine-structure splittings of S=1 spins on a simple cubic lattice.

Crystals of the scheelite material LiY_0.99Tb_0.01F₄ have been prepared by rather simple and effective hydrofluorinating techniques. The measured Tb³⁺ spectrum consists of four hyperfine lines with a spacing of 253 Oe and a width of 40 Oe(at 4.2K). In terms of the spin-¹/₂ Hamiltonian H=g/sub /// beta H_zS_z+ Delta s_{perpendicular to} +AS_zI_z the spectrum could be fitted with the following values for the constants: g/sub ///=17.7+or-0.2, Delta /h=27.98+or-0.06 GHz and A/h=6.26+or-0.06 GHz. The results are important in estimating single-ion parameters appropriate to a description of the low-temperature ferromagnetism in the isomorphous compound LiTbF₄.

Paramagnetic centres produced by irradiation of Sr(ClO₃)₂ single crystals have been studied by electron spin resonance. The products of x- or delta -irradiation at 298K are ClO₂ and O₃^- centres. ClO₂ is trapped at six magnetically inequivalent sites in the crystal lattice, forming three pairs. The magnetic parameters for two of the pairs, that is, ClO₂(B) and ClO₂(C), are in close agreement with ClO₂ centres reported in other systems; while the third pair, that is ClO₂(A), has slightly different hyperfine parameters. The principal g-values of this centre (A) are g_xx=1.9984, g_yy=2.0170 and g_zz=2.0142 and those of the A tensor are A_xx=90.0 G, A_yy=-8.7 G and A_zz=-5.0 G. The chlorine centres that are trapped at six magnetically inequivalent sites produced by radiation damage reveal hexagonal symmetry among themselves. UV or thermal bleaching (at 90 degrees C) removes all the chlorine centres, giving a single anisotropic line, trapped at two magnetically inequivalent sites with a g_av=2.0092. This new centre is identified as an O₃^- centre.

The frequencies of tunnelling rotation of both methyl groups in the free radical (CH₃)₂CCOOH, formed by gamma -irradiation of crystals of alpha -aminoisobutyric acid, are studied at 4.2K from small shifts of electron nuclear double resonance frequencies. The tunnelling frequencies (splitting of ground state divided by h) are >4 GHz and 1.4+or-0.1 MHz. The latter is of interest as the first case to be studied of a tunnelling frequency much less than the hyperfine interaction, so that the corresponding electron spin resonance hyperfine structure at low temperatures appears superficially to be characteristic of a methyl group whose rotational motion is completely frozen.

The molecular-field treatment by Bean and Rodbell (1962) of a deformable Ising ferromagnet is modified to include piezoelectricity and spin-lattice coupling, so that it may be applied to deuterated KDP. In this case, the pseudo-spin exchange coupling depends linearly on strain mod sigma ₆ mod , and it is seen that this dependence can produce a first-order transition for appropriately chosen values of the coupling parameters. From the condition that the slope of polarisation be infinite at T_c plus a consistency condition on the exchange, it is shown that the mean value (Z) of a pseudo-spin can have a maximum possible value at the Curie point. The value of the spontaneous polarisation ratio P_s(T_c)/P_s(0) which corresponds to maximum (Z) is 0.704. This provides a qualitative understanding of the shape of the polarisation curve to within a fraction of a degree of T_c, where critical fluctuations become important.

The temperature dependence of some of the more important vibronic bands in diamond is investigated. Spectra of the N3, ND1, 640 nm, H3, 3.188 eV and 594 nm bands are given, together with detailed measurements of the intensity, peak energy and width of most of the zero phonon lines over the temperature range of typically 20 to 350K. These data, and published data on the N9 band, are analysed in terms of coupling of the electrons to vibrational modes that are totally symmetric in the point group of the optical centres. It is shown that the shapes of the N3, ND1, 640 nm, 3.188 eV, 594 nm and N9 bands may be closely described by the theory and yield effective densities of coupled phonon states. These densities of states predict, to a high accuracy, the temperature dependence of the respective zero phonon intensities. It is shown that the long-wavelength modes dominate the temperature dependence of the zero phonon energy, and so, after allowing for lattice expansion effects, the peak energy may be fitted using the densities of states.

New data on post-irradiation annealing of LiF TLD phosphor are presented. The results show a new peak at 400 degrees C and increased availability of luminescence centres that are responsible for the radiation-induced sensitisation. A model to explain the observed phenomena is presented. The new peak trap centres and the increase in luminescence centres are attributed to the breakup, on irradiation, of a complex centre. The complex centre itself is formed on annealing at 400 degrees C.