Table of contents

Leigh et al. (see abstr. A16215 of 1971) have criticized the parametrization of lattice vibration frequencies by force constants on the grounds that it is always indeterminate. The present author uses examples drawn from a wider range of application of equivalent techniques to show that, when indeterminancy exists, it is apparent in the fitting procedure and can always be eliminated.

The electronic band structure of V₃Ga and V₃Si is approximated in the tight binding method, allowing for interchain coupling. The effective integrals are also determined from Mattheiss' APW calculation. Special attention is paid to the density of states curve which is found to possess sharp peaks in the vicinity of the Fermi energy, as was suggested by Clogston and Jaccarino.

Electronic band structure calculations for TiO, VO, MnO, FeO, CoO, and NiO suggest that the 4s band becomes degenerate with the 3d band at VO and thus helps to destroy the Mott insulator state. The large difference in lattice constant between the metallic and insulating oxides is well accounted for in terms of the Mott transition. Calculated values of the crystal field splitting 10 Dq are about 70% of experimental ones.

The authors consider the excitations of a three dimensional disordered Heisenberg antiferromagnet within the framework of a Green function technique developed elsewhere by the authors. A crude estimate is made of the critical concentration of spins at which the system orders magnetically and this estimate is shown to be in reasonable agreement with the results of some recent experimental work.

A variation of the Lurie-Slichter method of pulsed nuclear double resonance in solids is described which has enabled accurate measurements of the 1.108% abundant ¹³C effective magnetogyric ratio in the solid organic polymer polytetrafluoroethylene. Ways are discussed for increasing the resolution of the technique.

The reflectivity of CaF₂, SrF₂ and BaF₂ has been measured near normal incidence in the range 15-30 eV. Correlations have been made, based on calculated positions of free ion energy levels, between reflectivity peaks and core to conduction band transitions.

Raman scattering measurements in KDA and CsDA are used to show that the soft mode in a piezoelectric ferroelectric may not be described as a classical damped oscillator. The discrepancy arises because of a contribution to the selfenergy of the mode at low frequencies which arise from the coupling of the mode with fluctuations in the phonon density.

The equations of Josephson and Lekner (1969) describing the mobility of an impurity in a Fermi liquid admit three solutions for the mobility over a certain temperature range.

The nature of the polarization catastrophe previously reported in several defect calculations is analysed. For the commonly used polarizable point dipole model it is shown that a necessary condition for the avoidance of such catastrophes is that the separation of all ion pairs, i, j must be greater than r_crit=(4 alpha _i alpha _j)^1/6 where the alpha _i's are the electronic polarizabilities. This requirement is independent of the form of the interionic potential function. This condition is identical with that previously derived by Tosi and Doyama for alkali halide molecules, but it is shown that it applies to all ion pairs in the solid. The effect of these inherent instabilities on the calculated energies of defects and of alkali halide molecules is discussed. It is concluded that the most realistic physical extension of the model which avoids these instabilities is the inclusion of the reduction of polarizability with ionic overlap.

The author reports energy levels of the F⁺ centre in MgO, CaO, SrO and BaO calculated using hydrogenic wavefunctions and the point ion lattice approximation. The transition energies, corrected for polarization and lattice distortion, are in good agreement with the experimental results for MgO, CaO and SrO. However, agreement between experiment and theory is quite poor for BaO.

Debye characteristic temperatures of NaF, KCl, KBr and RbCl have been determined by X-ray diffraction from room temperature up to about 80 K. The plot of reduced thermal expansion alpha / alpha _m/2 against T/A alpha theta ² gives a common curve for all the halides, T_m being the melting point, alpha _m/2 the value of alpha at T=¹/₂T_m, A the mean atomic weight and a the lattice constant. An equation between alpha and theta for the alkali halides is established. The values of the root mean square amplitudes is calculated for all the alkali halides from the equation and is compared with those of other workers. The agreement is satisfactory.

Rigorous bounds are derived for the density of electronic states for Weaire's tight binding model of amorphous germanium. The bounds are the same as found by Weaire, including the energy gap. It is further proved that there are the correct number of states, four per atom, above and below the gap.

A new form of Algol programme for calculation of the refractive index and optical absorption of semiconductors has revealed an error in a recent paper (see abstr. A44755 of 1970). The correct results are shown to differ only slightly from those previously obtained provided some adjustments are made to the parameters corresponding to zone boundary, line width and normalizing factor. The new programme is also valid within the absorbing region, and the results obtained are consistent with available experimental data.

The full five component spectrum of Rayleigh and Brillouin scattering from superfluid mixtures of ³He and ⁴He has been observed. Recordings are shown at different temperatures and concentrations, and a preliminary assessment is made of the relative intensities.

An analogy is drawn between the mean number of clusters and the free energy of a ferromagnet. The corresponding scaling laws, describing the behaviour near the critical point, are tested using the exact solution for the Bethe lattice. Numerical work on the moments of the cluster size distribution for two and three dimensional lattices is found to be consistent with the scaling hypothesis.

A calculation has been made of the Kapitza conductance between a solid and helium as a result of the interaction between independent helium atoms and the solid. In the low temperature limit the expression for the conductance due to transitions between unbound states is the same as that for phonon radiation into the gas, that is, the Khalatnikov model with appropriate minor modifications. At higher temperatures it increases above this limit suggesting that the neglect of the attractive potential is a significant defect of the Khalatnikov model. The conductance due to transitions between bound and unbound states has also been calculated. Because of the neglect of interactions between helium atoms the model only becomes realistic for this process at the higher temperatures when the conductance is less than that due to transitions between continuum states.

The one phonon coherent inelastic neutron scattering cross section is analysed in terms of the transformation properties of the phonon polarization vectors. An expression involving characters of point group representations is derived which is zero when the scattering conditions are such that a particular branch of the phonon dispersion curve has zero scattering cross section. This expression is related to Elliott and Thorpe's expression for sums of the scattering over branches with polarization vectors transforming as the same irreducible representation. The selection rules for LiNbO₃ are derived as an example.

It is shown that the low energy structure of the K⁺K beta _1,3 line in KF, KCl and KBr is very complex. A possible explanation is given in terms of the simultaneous excitation of an outer shell electron and emission of an X-ray photon.

The Schottky defect formation energies (h_s) of seven CsCl structure crystals have been calculated, following the Mott and Littleton method, considering the second neighbour repulsions and the van der Waals interactions explicitly. The computed h_s values (in eV) for CsCl, CsBr, CsI, TlCl, TlBr, NH₄Cl and NH₄Br are 1.860, 1.744, 1.407, 1.269, 1.204, 1.205 and 1.171 respectively. The results indicate that with a satisfactory model of cohesive parameters, the Mott and Littleton procedure yields reliable estimates of defect energies which are compatible with experiments.

The analysis of contributions to elastic constants is made consistent by introducing a first order term into the contribution to the elastic free energy density. The precise relation between Fuchs elastic constants and Brugger elastic constants is made explicit. New relations between elastic constants of different orders are revealed for central force interactions by extending the method that generates the Cauchy relation. The reduction in computation that these produce is illustrated by reference to the electrostatic contributions to the first, second and third order elastic constants of cubic metals.

The temperature dependence of the attenuation of longitudinal hypersonic waves at 9.4 GHz has been measured in 'perfect' specimens of trigonal crystals: quartz, lithium niobate and corundum. It is found that this attenuation follows a T^6.5-law in the range 0.1<or= alpha (db/cm)<or=5. The results are in good qualitative agreement with the theory of Maris and Silverman, which takes into account the finite lifetime of the thermal phonons that scatter the acoustic wave.

Optical absorption techniques have been used to study the effects of plastic deformation at 80 and 290 K on V centres in KBr and KCl produced by 2 MeV electron irradiation at 290 K. It is suggested that new V centres present in deformed crystals are associated with halogen interstitials trapped at dislocations (V_x band) and at impurities dispersed during dislocation motion (V_s band). The V₃ band in KBr and the 6.4 eV band in KCl present in undeformed material decrease during deformation of irradiated crystals. The V_x band appears in two stages on warming after deformation at 80 K. It is proposed that moving dislocations ionize or dissect interstitial defects in their path. The reaction products become mobile at higher temperatures and can diffuse to dislocations to produce V_x absorption.

The Anderson problem of the localization of electrons in disordered systems is discussed by analysing the residues of the off diagonal propagator. On the assumption that the eigenvalues are statistically independent, Anderson's upper limit is reproduced, while improved conditions are obtained by assuming specific correlations amongst the levels. The form of the wavefunctions and analytical structure of the selfenergy are also discussed. Several types of disorder are analysed and mobility edges are shown to exist in some cases.

The ground state energies of phosphorus, arsenic and antimony in silicon and germanium crystals are calculated. The 'central cell corrections' due to the repulsive core potentials and spatial variations of the effective mass and dielectric function are taken into account and a good agreement with experiment is achieved. The ground state of bismuth impurity is also discussed.

Modifications introduced by the transverse magnetic electron-electron interaction are discussed using a SCF technique. The diamagnetic susceptibility at Q=0 and omega =0 is nearly unchanged from the result in which this interaction is ignored. In the dynamical case, however, the screening action is important and determines the frequencies of the transverse collective modes. It is shown that the excitation spectrum of these modes is directly related to the cross section for magnetic neutron scattering. Detailed information on the dispersion and lifetime of the transverse collective excitations as well as of the single particles in charged systems may be obtained by such experiments.

For pt.I see abstr. A62503 of 1970. An upper bound is found for the free energy of a compressible Ising system with spin-phonon interactions using the Gibbs-Bogolyubov inequality. The results are identified as a molecular field approximation. The thermodynamic behaviour of the system is compared with that of the Bean-Rodbell model. An instability in the magnetization suggestive of a first order transition occurs for sufficiently large values of the spin-phonon coupling parameter. The contribution of the spin-phonon interaction to the thermal expansion anomaly is also discussed.

Measurements of the transport properties of bismuth telluride and its alloys are reported in the literature for single crystal, polycrystalline and hot pressed powder samples. Since these materials are highly anisotropic, the transport properties of these three types of sample are not in general the same under equivalent conditions of temperature and carrier concentration. The author compares theoretically the electrical and thermal conductivities, the Seebeck coefficient and the Hall coefficient of three types of sample so that meaningful comparisons may be made between the various results reported in the literature. The theory presented is applicable, in general, to anisotropic semiconductors having uniaxial symmetry.

It is shown that in a covalent complex the values of the orbit-lattice interaction matrix elements are dominated by electron transfer and overlap effects so that the current crystal field modulation model is inadequate for such complexes. This is demonstrated by means of a sample calculation on a small molecule, and it is shown how the 'exact' dynamic effects should be evaluated within the framework of molecular orbital theory.

Detailed assignments are given for normal modes of vibration in vitreous silica, germania and beryllium fluoride. They have been obtained by calculating the atomic displacement eigenvectors for selected modes throughout the spectrum, and separating the kinetic energy of these modes into contributions from cation motion, bond-stretching, bond- bending and bond-rocking motions of the anions. Bands in the 1050, 500-800 and 400 cm^-1 regions of the silica spectrum can be attributed largely to bond-stretching, bond-bending and bond-rocking vibrations respectively, while a low frequency shoulder below about 350 cm^-1 is found to be mainly acoustic in character. In the vibrational spectrum of vitreous germania, bands which occur at about 850, 500, 370 and 200 cm^-1 are similar in their respective assignments to those listed above for silica. In the case of beryllium fluoride, the highest frequency band, at around 700 cm^-1, is dominated by cation motion.

The magnetic properties of a Pt⁺ ion, substituted for the Al³⁺ ion of a ruby lattice, in a uniform constant applied magnetic field H, have been investigated using a Jahn-Teller model and a cluster approximation. The platinum ion is coupled to the E vibrational modes of the cluster. g values measured at a temperature of 4.2 K, when the applied field is along one of the approximate tetrad axes, are consistent with values deduced from the theory when covalency reduction factors have values k₁=0.84, k₂ approximately 1. Consequences of the theory for third transition series ions with s=¹/₂ in Eg orbitals occupying substitutional sites of cubic symmetry are also briefly discussed.

Europium added to silver chloride under a nonoxidizing atmosphere enters the lattice substitutionally in the divalent state. A single silver ion vacancy is associated with each europium ion in a nearest cation position at 93 K and leads to an electron resonance which shows orthorhombic symmetry. At room temperature most of the vacancies are dissociated and the predominant spectrum arises from Eu²⁺ in a field of octahedral symmetry. The temperature variation in the width of lines which constitute the outer fine structure components of the spectrum gives an activation energy of 0.22+or-0.05 eV for the vacancy motion. In heavily doped specimens a single line spectrum is observed from aggregated europium. Eu²⁺ is found to sensitize silver chloride in the bulk. At room temperature irradiation with blue light produces a reduction in the number of Eu²⁺ ions and an optical absorption peak at 550 nm due to silver colloid, Irradiation with red light bleaches the colloid band and restores the original number of Eu²⁺ ions.

Paramagnetic resonance spectra are reported for V²⁺ ions occupying orthorhombic symmetry sites in the cubic lattice of magnesium oxide. The local distortion from O_h symmetry at the vanadium ion site is attributed to a cation vacancy located in a nearest neighbour position along a (110) direction. The spectra are composed of 'forbidden' Delta M_s=+or-2 and Delta M_s=+or-3 transitions in addition to the 'allowed' Delta M_s=+or-1 transitions. The spectra which were recorded at microwave frequencies near 9.5 GHz and 35 GHz may be described by the spin Hamiltonian, H=g beta B.S+D(S_z²-¹/₃ S(S+1))+E(S_x²-S_y²)+AI.S with g=1.9910 (isotropic), mod D mod =0.1819 cm^-1, mod E mod =0.0419 cm^-1 and mod A mod =0.0072 cm^-1 (isotropic). The observed hyperfine structure is complicated by the presence of 'forbidden' lines, which become allowed off axis owing to the breakdown of the Delta M_I=0 selection rule by the second order mixing of the fine structure and hyperfine structure terms. The spectrum from Cr³⁺ in a similarly distorted site has been examined at 35 GHz, a frequency higher than those previously used. In contradistinction to X and K band measurements by other workers, all possible Delta M_s=+or-1 transitions are observed.

The paramagnetic resonance spectrum of VO²⁺, Cr³⁺ and Fe³⁺ in blue zoisite (tanzanite) shows these ions to substitute for Al³⁺ in two sets of very distorted octahedral sites. The spectra can be fitted with spin Hamiltonians of rhombic symmetry. Colour differences correlate with differences in the vanadium spectra.

It is shown that equal intensities of the two ENDOR transitions for ¹⁶⁹Tm²⁺ and ¹⁷¹Yb³⁺ in CaF₂ indicate that the relaxation rates T_x^-1( mod ¹/₂,-¹/₂( to or from mod -¹/₂,-¹/₂)) and T_x'^-1( mod ¹/₂, ¹/₂( to or from mod -¹/₂,-¹/₂)) are approximately equal. The relative simplicity of the wavefunctions for the 4f¹³ configuration in a cubic crystal field, and of the Hamiltonian for the orbit-lattice interaction, enables one to make an explicit calculation of the various relaxation rates in terms of the orbit lattice parameters V( Gamma _i,l). Matrix elements of the hyperfine interaction between ground and excited states of the J=⁷/₂ manifold are found to be important in leading to calculated values for T_x^-1 which are comparable to those for T_x'^-1. Similar magnitudes for T_x^-1 and T_x'^-1 are shown to be expected for systems with large components of unquenched orbital angular momentum, in contrast to systems with little orbital angular momentum where T_x'^-1 approximately=0.