Table of contents

Linear dichroism is used to investigate the phase transition of DyVO₄ at 13.8K, and it is shown that this is a sensitive technique for observing crystallographic phase transitions. Polarizations of the individual components of the ⁴F_9/2 state are obtained, but the complications of the accidental degeneracy in the ground state prevent a complete analysis.

Elastic after-effect measurements on hydrogen and deuterium in palladium confirm a previously reported 'reversed' isotope effect in the temperature range of approximately 100-500K and show that there is a 'normal' isotope effect at lower temperatures (i.e. hydrogen appears to diffuse faster than deuterium).

The diffractive scattering of nearly monochromatic helium and neon beams from a (001) cleaved LiF surface at low temperatures was experimentally studied. A quantum theory of surface rainbow based on a corrugated hard surface model was developed. The calculated relative intensities of diffraction peaks agree with the measured values.

It is shown how the single-site coherent potential approximation and the averaged T-matrix approximation become exact in the calculation of the averaged single-particle Green function of the electron in the Anderson model when the site energy is distributed randomly with lorentzian distribution. Using these approximations, Lloyd's exact result is reproduced.

Results of inelastic neutron scattering measurements on the dispersion relations of normal vibrations in strontium titanate are presented for the purpose of complementing the recent work of Stirling (1972). New measurements on several branches are included. Comparison is made between two independent measurements.

Experiments on diffuse X-ray scattering by potassium chloride, aluminium and silver single crystals have been performed over the temperature range 4-293K. It is observed that scattering from longitudinal modes at 293K is not as expected from known frequencies. The extra scattering can be interpreted as due to anharmonic processes. At lower temperatures, 4 and 77K, along all the symmetry axes, experimental and harmonic scatterings are practical. For all the studied crystals at any temperature, scattering from the transverse modes is predictable from harmonic theory.

The lattice dynamics theory in the long-wavelength limit in inert gas crystals is presented. Long-range octupole interactions are taken into account and their effect on the dispersion relations to within terms of q⁴ (q is the wavevector) at q to 0 is investigated. A method of direct experimental measurement of the octupole interaction constant is proposed. The octupole interaction constant is evaluated from experimental data for Ne crystals.

The high T_c and lattice instability of some A₃B compounds (e.g. V₃Si, Nb₃Sn) have been considered as resulting from fine structure in the bare density of states (Labbe et al. 1967). An alternative explanation is presented which directly connects their high T_c with the shear mode lattice instability. The electronic structure of the A₃B's is such that there is a significant umklapp coupling of electrons near the Fermi surface to low q TA phonons. This leads to enhanced phonon induced e-e attraction as the TA mode goes soft. Estimates show that for reasonable values of the parameters concerned, one can obtain the observed rise, say from T_c(V₃Ge)=6K to T_c(V₃Si)=17K as the TA mode goes completely soft. With the same parameters, good agreement is obtained with the observed pressure dependence of T_c in V₃Ge and the variation of T_c in the system V₃Ge_xSi_1-x(0<or=x<or=1).

A theoretical study is made of phonons in cellular disordered systems by using an approximate averaged equation which corresponds to a slightly generalized quasi-crystalline approximation. This method allows the correlation between neighbouring particles to be taken into account. It is concluded that the exact solutions are obtained in the limiting cases where the correlation forces the system to be an aggregation of ordered systems. Numerical calculations of the state density and the local state density are made for the one-dimensional case over a wide range of the degree of correlation. These calculations show that the method not only can predict, to a considerable extent, the peak structure which characterizes the cellular disordered systems, but also can predict some local features of phonons in these systems.

Wilson's 'incomplete integration' form of the renormalization group equations is derived entirely within the context of graphical perturbation theory. The addition of a magnetic field term to the hamiltonian is considered, and it is shown that in this case the incomplete integration theory is much more complicated than the corresponding 'complete integration' theory. A modified incomplete integration theory, which does not have this disadvantage, is described.

Numerical results are presented for the second and fourth frequency moments of the spectral functions of both the longitudinal and transverse current correlation functions for liquid aluminium using the interatomic potential and the static pair correlation function obtained by Schiff (1969) from molecular dynamics calculations. A memory function approach is employed to estimate the longitudinal and shear viscosities of aluminium at its melting point. The parameters appearing in the various memory functions are determined from the frequency moments of the correlation functions. The theoretical estimates of the viscosities are in good agreement with the available experimental value.

The moments of the electronic density of states of a disordered system described by a tight binding model can be directly computed as a function of the overlap integrals and the local order of the system. Some of the possible techniques for estimating the density of states from its low order moments are discussed. Two methods are particularly emphasized: one using upper and lower bounds for the integrated density of states, the other using a finite continued fraction expansion of the Hilbert's transform of the density of states. The second method seems to be better due to the fact that the continued fraction coefficients rapidly converge towards their asymptotic values. In particular, their behaviour when internal singularities on a band gap appear is analysed.

A theoretical study is made of the properties of carriers which are photoexcited into one of the bands of a semiconductor with mean energy in excess of the thermal energy. Carrier heating then occurs if the recombination process is faster than the electron-phonon thermalization process. Detailed numerical calculations are made of the carrier distribution functions in germanium and silicon at low temperatures arising from excitation by room temperature black-body radiation and cascade capture into shallow impurities. The calculations employ acoustic deformation and nonpolar optical scattering and show that heating occurs below 30K for ionized impurity densities of order 10¹⁵ cm^-3. The hot phototransport parameters for acoustic deformation and ionized and neutral impurity scattering are derived by a perturbation analysis and Monte Carlo techniques.

Intrinsic photoemission and photoconduction of polyethylene in the photon energy range 7<E<14 eV have been experimentally investigated. Both phenomena are parabolic in E with the same threshold energy E_G=8.8 eV. The main features of a model that accounts for the observations are: (a) E_G is the intrinsic electron-hole band gap. (b) Strong absorption for 7.6<E<8.8 eV is due to exciton creation. (c) The bottom of the conduction band lies an energy A above the vacuum level, where 0<A<1.2 eV. (d) The photocurrents are due to rapid motion of carriers through a short distance approximately=10 nm along individual polyethylene chains. (e) The carriers subsequently travel through the polyethylene with a very low mobility.

The study of the effects of confinement of a high density electron gas to a film of vanishing thickness has been extended. The correlation energy is found to approach a constant rather than ln r_s. This energy is estimated numerically. Plasma oscillations are investigated and the frequency is found to be wavenumber dependent ( omega varies as square root q). This dispersion relation is derived classically and conditions for the existence of such modes are presented.

The variation of magnetization with temperature for amorphous ferro- and ferrimagnets is discussed by using a molecular field model, taking into account exactly the structure fluctuations which could exist in amorphous materials.

An estimate for the amount of singlet, triplet and quintuplet character of the wavefunction of a nearest-neighbour pair of spins in a two-sublattice Heisenberg antiferromagnet of spin-1 molecules has been made. The results are applied to alpha -oxygen.

Neutron scattering has been used to investigate the energy dispersion relation of spin waves in CoCl₂ at temperatures between 4.4 K and 34 K. CoCl₂ orders antiferromagnetically at T_N=24.9 K with the Co²⁺ spins lying within ferromagnetic planes which are antiferromagnetically stacked along the hexagonal c axis. The interplanar exchange interactions are much weaker than those within the planes, giving rise to the 'metamagnetic' property of ferromagnetic saturation in relatively weak magnetic fields, and suggesting that above T_N there could be correlations between spins appropriate to a two-dimensional ferromagnet. The observed spin waves at low temperature indeed only exhibit strong dispersion within the basal plane and measurement of this dispersion enables an accurate value for the nearest-neighbour exchange constant to be determined.

This paper makes two brief points about an earlier paper by Cracknell (abstr. A34131 of 1973). One is to identify the group-theoretical labels for the acoustic-mode phonons along Delta , Sigma , and Lambda in FeF₂ in terms of the more traditional LA (longitudinal acoustic) and TA (transverse acoustic) labels. The second is to correct an error in the labels given previously to the phonon symmetries along Delta ; this resulted from an error that previously was not noticed in one of the tables in a paper by Dimmock and Wheeler (1962).

The spin-lattice relaxation of single crystals of CaCd(Ac)₄.6H₂O containing up to 10% of the isomorphous paramagnetic CaCu(Ac)₄.6H₂O was studied within the temperature range 2K-9K. At low temperatures T all samples showed a relaxation time T₁ varying as T₁=A exp( theta ₀/T) with theta ₀=15 K+or-0.5K. A significant variation of relaxation time across the four hyperfine components of the ESR spectrum was also observed, the lower field components having the shorter relaxation times. A possible interpretation of these results in terms of a local vibrational mode at the Cu²⁺ site is discussed.

An X irradiation at 78 K, of a BaClF crystal containing OH^- ions leads to the formation of hydrogen atoms in interstitial sites (H_i⁰ or U₂ centres) thermally stable below T approximately 100K. The magnetic properties of the U₂ centres are compared with those observed in the case of U₂ centres in NaCl crystal. The thermal stability is studied and compared with those of the U₂ and U₃(H_s⁰) centres in NaCl.

The nuclear spin-lattice relaxation rate 1/T₁ is derived as a function of the angle xi between the axis of reorientation and the principal direction of the relaxation interaction, for a system of threefold symmetry which undergoes hindered molecular reorientation. The relaxation mechanisms considered are the anisotropic chemical shielding the nuclear quadrupole, and the nuclear dipole-dipole interactions. It is observed that 1/T₁ is strongly dependent on xi and on the interaction anisotropy. In addition the motional conditions are derived under which the Overhauser signals due to the dipolar coupling between unlike spins, will change sign and where the usually non-exponential relaxation becomes exponential for all practical purposes, thereby substantially easing the extraction of motional correlation times.

The condition for the position of the nuclear magnetic resonance line observed in a many-body system to shift away from the Larmor value gamma H₀ is studied. It is shown that shifts of the order of magnitude of that recently observed in liquid ³He below 3 mK are possible only if the system possesses a peculiar ordering property, not hitherto seen in any many-body system, which is called 'spontaneously broken spin-orbit symmetry'. Some general aspects of the behaviour of systems with this property are studied, without making any particular assumptions about the microscopic dynamics.

Optical properties of thin antimony films are measured in ultra-high vacuum in the energy range 2.5-14.5 eV. The epsilon ₂E² curve shows a great number of interband transitions between 3.8 and 11 eV which are interpreted with the help of band structure calculations. The volume plasmon is situated at 15.8 eV and the surface plasmon is identified at about 11 eV.