Table of contents

It is pointed out that the 'discrepancy' between the electron diffraction intensities calculated by Sturkey (1962) and by Fukuhara (1966) is not due to any inherent inaccuracy of Sturkey's method of calculation, and that the correct explanation of the discrepancy is that Sturkey's calculations refer to positron diffraction while those of Fukuhara refer to electron diffraction. A corrected form of Sturkey's development of the theory is given.

The problem of an impurity ion subject to linear Jahn-Teller coupling with vibrational modes of the crystal is reconsidered. A trial ground-state wavefunction is postulated in which one linear combination of vibrational modes behaves as though subject to a molecular Jahn-Teller effect while the rest are decoupled from the electronic states. The linear combination is selected by a variation of the ground-state energy of the system.

Nitrogen-doped gallium phosphide has been irradiated with fast neutrons or 2 MeV electrons. These treatments lead to the formation of interstitial defects involving nitrogen which give rise to localized vibrational modes at 946.7 cm^-1 (¹⁴N) and 925.2 cm^-1 (¹⁵N). These defects anneal at about 530K.

The dispersion relation for transverse sound in a Fermi liquid has been derived for all omega tau ( omega is the sound frequency, tau is the quasi-particle relaxation time), and using this the shear wave properties of liquid ³He have been calculated. For omega tau <1 the dispersion relation should behave classically, but at low temperatures and high frequencies ( omega tau >>1) transverse zero sound should propagate if the liquid is pressurized. The nature and properties of this zero sound are discussed, and suggestions are offered as to how it could be studied experimentally.

The electrical resistance R(T) of a c axis single crystal of dysprosium has been measured in the vicinity of the Neel point T_N using a high-precision (8-digit resolution) direct current comparator method. Numerical analysis of the data yields a power law of the form R(T)=A+B epsilon +C epsilon psi in the range 2.5<or approximately=T-T_N<or approximately=60 K, where A, B>0, C<0, and psi =0.60. This power law does not extend into the region 0<or approximately=T-T_N<or approximately=2.5 K. The breakdown of the power law is consistent with the view that long-range spin fluctuations fail to dominate scattering processes in the immediate vicinity of the Neel point of helical antiferromagnets.

A critical examination is presented of the available experimental evidence relating to the frequency dependence of the electrical conductivity of a wide range of disordered and amorphous semiconductors and insulators. It is pointed out that there is no justification for regarding these effects as true bulk phenomena, and there are good reasons to expect that contacts and interfaces play a dominant role.

It has been found that in crystals of (NH₄)₂(Cu,Fe,Zn)(SO₄)₂.6H₂O the spin-lattice relaxation of the Cu²⁺ ions is mainly the result of their nonresonant coupling to the rapidly relaxing Fe²⁺. The coupling gives rise to small changes in the observed g-factor of the Cu, and to two possible relaxation processes, of which one has been identified experimentally. The results provide perhaps the clearest evidence yet reported for the cross-spin-lattice relaxation of electronic spins.

Measurements of free-to-bound luminescence and bound-exciton luminescence spectra have enabled the binding energies of C, Si, Ge, Zn and Cd acceptors in GaAs to be established accurately. They are respectively 26.y, 35.2, 41.2, 31.4 and 35.4 meV. Data on the ground state and the first s excited state show a smooth relationship which includes the theoretical data of Lipari and Baldereschi (1970).

A resistivity formula derived by Edwards (1965) is considered here. The form originally proposed by Edwards is confirmed. However, it is shown that the resistivity can be written as R= sigma ^-1 where sigma is the conductivity as given by the usual linear response formula and that the resistivity cannot be evaluated in the way originally suggested by Edwards. The reasons why meaningful results can be obtained in some circumstances is explained.

Recent measurements of the anisotropic conductivity in disordered 'one-dimensional' materials are analysed and it is shown that interchain tunnelling contributes to the longitudinal component only at the lowest temperatures. At somewhat higher temperatures, the transverse component becomes diffusive while the longitudinal conductivity remains a percolation process. Conduction in both directions is diffusive in the high-temperature limit. The 'interrupted-strand model' for these systems is briefly criticized and shown to be inconsistent with the data.

The scattering law S_s(k, omega ) observed in incoherent neutron scattering is studied in terms of the generalized Langevin equation of motion for its temporal Fourier transform. An approximate S_s(k, omega ) is obtained from a continued-fraction representation of the equation of motion which contains no arbitrary parameters, satisfies the first three moment relations, and has the correct small and large wavevector k dependence at zero energy transfer. It is shown to give a good description of the incoherent scattering from liquid argon measured by Skold, Rowe, Ostrowski and Randolph (1972). The corresponding velocity autocorrelation function is identical to that derived by Berne, Boone and Rice (1966).

The nature of the eigenvectors of the phonon-phonon interaction matrix is discussed. It is suggested that half of the eigenvectors can be expressed in terms of states of even and odd parity.

First- and second-order perturbation theory is employed to examine the effects of a time-independent perturbation on the dynamical behaviour of the crystal lattice. Shift of frequencies and coupling between long-wavelength optical modes of different symmetries is determined to first- and second-order in the applied force. Specific examples and existing experimental facts are discussed.

It is shown that the exactly solvable three-dimensional model of Lloyd (1969) for disordered electronic systems may be generalized from a one-band tight-binding formulation to potentials used in actual (multi-) band calculations. Therefore, the case of fluctuating overlapping integrals in tight-binding formulations is contained automatically in the generalized model. The ensemble-averaged one-particle Green function and the integrated density of states are calculated. The averaged Green function can be interpreted as the Green function of a system with absorbing potentials. The ensemble-averaged integrated density of states may be written as an average on the integrated density of states of regular systems with different potential parameters.

The density of states of an electron in a tight-binding model of a disordered one-dimensional alloy has been computed with high precision using a development of an exact method due to Schmidt (1957). The 'special energies' at which the density of states vanishes are in accordance with the analytical theory. In the vicinity of a region of infinite density of special energies the envelope of the density of states is found to vary exponentially.

The non-orthogonality problem in the LCAO method for crystals is reviewed and discussed with particular emphasis on the properties of the eigenvalues of certain overlap matrices. A pilot calculation is carried out to demonstrate the numerical behaviour of these eigenvalues and related quantities when the atomic orbitals are of s- or p-type.

For pt. I see abstr. A71897 of 1970. Papers showed how it is possible to renormalize the perturbation expansion for poles caused by strong short range scattering. In this paper, mathematical details of the formalism are presented and a critical test made of the renormalized scheme by calculating the correlation coefficient g_{sigma - sigma} (r=0, t=0). Results are obtained which not only are physically reasonable in that they are positive, but which conform with other estimates of this quantity made by nonperturbative methods.

Starting from the Coulson model for the ground state of H₂, the valence electronic states of ortho-hydrogen crystals are calculated. The maximum value of the Davydov splittings is 1.1 eV at k=0. It is shown that at any point of the Brillouin zone cube edges the Davydov splittings vanish because of time reversal symmetry and all valence bands become degenerate. The effect of isotropic pressure on the valence bands is also calculated.

For pt. I see abstr. A78044 of 1972. A theory for spin waves in a dilute antiferromagnet has been developed which uses the coherent potential approximation (CPA) to treat the randomly varying Ising interactions between nearest antiferromagnet neighbours but treats the off-diagonal parts of the Heisenberg interactions in a more approximate fashion that is consistent with the Goldstone theorem. Although similar to the theory that was found to be successful for K(Co, Mn)F₃ and (Co, Mn)F₂ in paper I, the problem of the magnetic vacancy requires special treatment. A fictitious spin is placed on the Zn atoms but large potentials are introduced there to prevent the spin waves from propagating via these sites. The Green functions, neutron scattering and Raman scattering have been calculated.

Electron spin resonance spectra and electron nuclear double resonance measurements are presented for free radicals with the structure CH₃COHCOO^- formed by gamma irradiation of crystals of lithium lactate. The splitting of the ground state due to the tunnelling rotation of the methyl group is found from the temperature dependence of the populations of the split levels which are reflected in the relative heights of constituent lines of the hyperfine structure. The amplitude of the zero-point torsional oscillation is measured from the relative magnitude of hyperfine coupling tensors and the height of the hindering barrier is deduced from the temperature dependence of the ESR spectrum. All the measurements are consistent with a tunnelling splitting of 22+or-5 GHz.

The intensity of forbidden hyperfine lines ( Delta m=+or-1, Delta M=+or-1), in EPR spectra of the S state ions Mn²⁺ has been measured in the axial field of alpha -Al₂O₃. Calculations of line intensity show the necessity to discriminate between electronic and nuclear quantization axes. An intensity spin operator that leads to a description of experimental results is derived.

The line strength for transitions to or from the J=¹/₂ or J=⁵/₂ level of the neutral acceptor bound exciton in direct-gap semiconductors is shown to be equal to one quarter of the line strength to or from the J=³/₂ level.

For pt. I see abstr. A7013 of 1972. Expressions for the g-values and hyperfine structure parameters of Cu²⁺ ions in tetragonally distorted tetrahedral sites are derived by including the effects of covalency, 4p mixing and the dynamic Jahn-Teller effect. The results are applied to Cu:Cs₂ZnCl₄ where agreement with EPR and optical data is obtained by taking the Jahn-Teller reduction factor K(T₁) approximately 0.65, covalent bonding approximately 18% and 4p mixing approximately 4%.

Infrared absorption measurements have been made on germanium crystals which were irradiated by 2 MeV electrons at 110 K. All samples showed near-edge absorption, while certain crystals also showed an electronic absorption band at 2.40 mu m. These observations are similar to previous measurements made on ion-bombarded germanium. Attempts to modify the strength of the 2.40 mu m band by irradiating crystals containing either oxygen or silicon impurities were unsuccessful. Although the absorption features show similarities to those arising from divacancy centres in silicon, the evidence for divacancies in germanium is still considered to be inconclusive.