Table of contents

Energy loss measurements were made for 12.5-130 keV per nucleon H⁺ and H₂⁺ on carbon and aluminium foils. For incident H₂⁺, both H⁺ and H₂⁺ are transmitted; the energy per nucleon of the latter being lower than that of transmitted H⁺, at low energies. The theory shows this is due to interference effects in the binary excitation of target electrons by the spatially correlated protons and suggests that transmitted H₂⁺ results from di-protons travelling inside the solid with the internuclear axis aligned close to the direction of motion.

Tsai and MacDonald (1973, 1978) published a critical analysis of the authors' molecular dynamic simulation of shockwave propagation. Most of their criticism was directed to the authors' definition of temperature and kinetic energy. It is shown that their analysis is incorrect and that the authors' calculation of kinetic energy is correct and the definition of temperature is reasonable. Most of the misunderstanding arose from the other not understanding that all the authors' calculations were performed in a stationary frame of reference. It is further shown that, when there is a variation in the planar velocity, the Tsai-MacDonald local kinetic temperature is neither equal to the local kinetic energy (expressed as temperature) nor does it have the characteristics of temperature.

The one-parameter renormalisation group transformation of Reynolds et al. (1977) for the site percolation problem in d dimensions is studied. Upper and lower bounds for the transformation are derived. It is shown that in the limit b to 1 (b is the scaling factor) Reynold's et al. transformation is identical to Kirkpatrick's transformation (1977) for the bond percolation problem.

An effective medium theory, which includes the overlap of adjacent removed sites, is formulated for a percolating, two-dimensional triangular lattice. The critical concentration x_c=0.531 is compared with Yuge's value (1977) x_c=0.333, and the exact value x_c=0.500.

The Sherrington-Kirkpatrick model (1978) of an Ising spin glass is generalised to the case of m-component spins. The authors have studied the stability of the solution which preserves the symmetry between replica systems and found that although the solution is stable at high temperatures, it presents an instability in the spin glass phase for any finite m. It is found that in the limit m to infinity the m-component system yields the same free energy as that obtaining for the Berlin and Kac spherical model (1952) of a spin glass and this solution turns out to be the only stable one in the m to infinity limit.

The critical exponents for a zero-temperature phase transition in some rigorously solvable models can be expressed by one parameter only, namely the multiplicity of the dispersion function zero, that changes in the phase transition point. The scaling laws are obeyed.

LEED crystallography is reviewed by describing the four stages of a typical surface-structure analysis by LEED, namely (i) the experimental procedure, (ii) the identification of structural model, (iii) the calculation of LEED intensities expected from the chosen models, (iv) the evaluation of the agreement between calculated and observed intensities. The surface structures determined by means of LEED are listed and briefly discussed.

A comprehensive model is given for the lattice instability in Pb_1-xSn_xTe which explains preceding data, especially those in a previous paper (pt.I). The carrier concentration dependence and the composition dependence are included. Some new data from I which exhibit a large and strongly temperature-dependent TO-phonon width are studied. A single perturbative model is given which explains these data and preceding data. In this model the newly observed width is a lifetime effect due to nearest-neighbour anharmonic perturbations in the lattice Hamiltonian. Another more speculative model is given in which the observed width is a modulation effect arising from the presence of intrinsically non-linear solitary waves in the lattice. Possible layering as evidence for solitary waves is discussed. Some future experiments to distinguish among competing models are also proposed.

Coherent inelastic neutron has been used to measure the high-symmetry dispersion curves in deuterated adamantane (C₁₀D₁₆) at room temperature. The single crystal was grown by slow sublimation. The essential points for a dynamical study of a plastic crystal are briefly summarised and a group-theoretical analysis of the normal modes is given. The existence of librations in adamantane is established. They are found to be severely damped at all wavevectors. A force constant model, allowing for atom-atom interactions between disordered molecules, is then presented in the rigid molecule quasi-harmonic approximation. It accounts quite well for neutron results even for the broad librations and gives interesting information about the interaction mechanism between neighbouring molecules in this orientationally disordered crystal.

The author develops a model treatment of the spectral distribution of phonons emitted by a metal heater film into an insulating substrate where the phonons encounter a strong frequency-dependent elastic scattering. The phonon distribution in both the film and the substrate does not reach a steady state and the spectral distortions are similar to those seen in recent experiments at high input power. The basic physical mechanism lies in the frequency-dependent transition from ballistic to diffusive flow for the phonons in the substrate.

The basic assumptions which go into the arguments which identify localisation and absence of diffusion with a discrete spectrum are critically reviewed. It is shown that localisation does not follow simply from a demonstration that a Green function is a real function of the energy for almost every energy. The possibility of a singular continuous spectrum means that the Green function may be real even though diffusion occurs.

A Monte Carlo simulation of Ising chains with competing short-range and infinite-range interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths are generally of higher order and involve changes in the long-range while the short-range order remains unaffected.

The author considers an Ising chain where the random interaction matrix has the symmetrised form J=PV+VP. The matrix elements of V and P are V_ij=exp(- gamma mod i-j mod ) and P_ij=P_i delta _j,i-1+P_i+1 delta _j,i+1, where i, j indicate sites on the chain. The quantities P_i are independent random variables with the same probability distribution. Their mean and variance are fixed to be (P_i)=J₀ gamma /4; (P_i²)-(P_i)²=J² gamma /4, where gamma ^-1 is the range of the interaction. The author then obtains Sigma _j(J_ij)=2J₀, Sigma _j(J_ij²)=J² in the limit gamma to 0, as in a model Hamiltonian that describes a spin-glass transition. The author evaluates exactly in this limit the density of eigenvalues of the random matrix PV. An integral equation for the distribution probability of new local random variables is derived by using the continued fraction method and the asymptotic solution in the limit gamma to 0 is obtained analytically. The largest eigenvalue of PV is found to be J₀ independent of J. However the largest eigenvalue of J=PV+VP is found to be mu _M=J₀+(J₀²+NJ²)¹2/, when gamma =0 and N is the total number of sites. An independent evaluation of the ground state energy shows that E₀<-J square root NN, hence E₀ is not extensive. These results show that the scaling of the variance of the random interactions as J²N^-1 gives highly unphysical results for the present model.

For a Heisenberg paramagnet having both uniaxial anisotropic exchange and single-ion uniaxial anisotropy, two types of dilution are considered: model (a) in which the existence of transverse and longitudinal bonds depends only on a single random variable, and model (b) in which these bonds can fluctuate independently. For both models analytic expressions for the moments up to the fourth are presented that are valid for arbitrary spin and arbitrary range of the magnetic integration. Both the longitudinal and transverse moments are considered. The results are specialised to a number of simple lattices (linear, square, simple cubic, body-centered cubic and face-centred cubic) having nearest-neighbour and second-nearest-neighbour interactions only. Finally, the sixth frequency moment in the case of the isotropic magnet is studied using model (a).

The authors apply the model due to Hubbard and Marshall (1965) to interpret the experimental tetrahedral (A) site Fe³⁺ form factors in Fe₃O₄. A large covalency is inferred for the A-site, and it is shown that approximately 28% of the moment density is transferred away to the oxygen ions. The sigma covalency is seen to predominate. A comparison with the Fe³⁺ tetrahedral form factor in a closely related compound yttrium iron garnet (YIG) has been made and the two are seen to agree well with regard to the main conclusions. The A-site is not a centre of inversion and its form factor has an imaginary part also. The role of the latter in the analysis of experimental data is brought out.

For pt.III see ibid., vol.9, p.4315 (1976). The two-spin systems describe the dipole-dipole interactions between stationary host spins and spins migrating amongst either the tetrahedral or the octahedral interstitial sites. The tetrahedral sites in a FCC crystal form a SC lattice and two models, the symmetric and asymmetric jump models, are considered for third-nearest-neighbour jumps on this lattice. Numerical results for the correlation functions relevant for single crystals and polycrystals are presented over the entire temperature range. It is found that the simpler, but unphysical, symmetric jump model is a good approximation to the more complicated asymmetric jump model. Discrepancies between the numerical results of Barton and Sholl and those of Wolf (1975, 1977) are discussed.

Calculations are presented for the temperature dependence of one-magnon light scattering from two-sublattice ferrimagnets. The scattering Hamiltonians is taken to include linear and quadratic magneto-optical coupling terms. This represents an extension of recent work in which only the linear magneto-optical coupling was considered in calculating the scattered intensities for ferrimagnets. The theory is applied to YIG for which the quadratic magneto-optical coupling is known to be important, and comparison is made with the available light scattering data.

Strong coupling between an electronic transition in the ⁵T_2g(⁵D) manifold of Fe²⁺ ions in FeCl₂ and the E_g optical phonons in this material has been observed by light scattering. The Raman spectrum is temperature dependent and shows a marked change at the antiferromagnetic ordering temperature. Above T_N, the spectrum contains a symmetric band which becomes asymmetric on the high energy shoulder when the temperature is lowered. Just below T_N the band comprises two sharp features accompanied by a third broad band. Well below T_N the sharp features have coalesced. A simple model is presented which successfully accounts for the observed temperature dependence of the band position, width and structure.

A method to obtain the X-ray photoabsorption spectra of a bulk sample based on the specular reflection of continuous radiation on its surface is proposed.