Table of contents

It has been conjectured that statistical variations in the density of a random system of weak scatterers can localize electrons below the percolation threshold. The approach taken by Eggarter and Cohen to sustain this conjecture is shown to be internally inconsistent.

By using the condition of perfect screening in a liquid metal the ion-ion-electron correlation function is related to diffraction under pressure and all the electronic triplet correlations in the thermodynamic limit are related to the equation of state. The relations are illustrated for liquid rubidium, and their extension to higher correlations and to ionic melts is indicated.

Within the framework of the Heine-Jones model, the matching at (111) faces of diamond lattices is carefully analysed and shown to be feasible at every point of the boundary plane. The resulting secular equation for surface states allows one to generalize the existence theorems of Shockley and Forstmann and gives two nondegenerate surface states at the point J, in sharp contrast with previous calculations.

A low-temperature series expansion of the surface magnetization for an Ising model on a face-centered-cubic lattice with a free (100) surface is obtained and analysed. The exponent beta ₁ is estimated to be 0.69<or= beta ₁<or=0.74, in good agreement with recent scaling predictions. The relevance of this result to experimental measurements on real magnetic surfaces is briefly discussed.

The thermal magnetoresistance of iron-doped Al₂O₃ shows sharp minima when the frequency of the Delta M_J'=2 transition of Fe²⁺ crosses the frequencies of the two Delta M_J'=1 transitions. From the positions of these minima, a value for the trigonal splitting of the ground state of D=3.75+or-0.05 cm^-1 is obtained. Measurements made at 1.15K, when only the population of the lower levels is significant, show that D is positive; that is, the singlet is lowest in zero field.

Spectroscopic data for gadolinium-hydride and gadolinium-fluoride pairs in calcium fluoride provide direct confirmation of several conclusions about the nature of gadolinium ground-state splittings obtained in a recent paper.

A phonon side-band occurs at about 490 cm^-1 in the vibronic structure of 4f-5d transitions of Ce³⁺ in CaF₂. This frequency is greater than the highest vibrational frequency of the CaF₂ lattice. It is suggested that the side-band is due to a local mode arising from vibration of the eight nearest fluorine neighbours of the Ce³⁺ ion, and that the high frequency is a consequence of increased force constants at the impurity site.

Two two-dimensional Ising models with two- and four-spin interactions are studied. Evidence from high temperature series expansions suggests that the susceptibility exponent gamma remains constant at 1.75, independent of J₄, the strength of the four- spin interaction. This is in agreement with the general 'universality' hypothesis. Mean field theory predicts that for J₄ large enough the transition becomes first-order, but we find no evidence for this from the series expansions.

An approximate, easily generated relationship is suggested between the spin-¹2/ Ising model Curie temperature and the critical site or bond percolation probability (p_sc or p_bc). Quantitatively, it is shown to compare excellently with other simple closed-form theories for the Ising problem in variety of 2- and 3-dimensional lattices and pseudo-lattices. The relationship is exact for a Bethe lattice and, using p_sc, for the triangular lattice, or using p_bc, for the honeycomb lattice.

The ultra-violet and infra-red spectra of U centres formed by proton irradiation of alkali halides have been used to measure their concentration in a study of the factors affecting the fate of the implanted protons. The efficiency of U centre formation varies from one material to another in a way which suggests that the creation of anion vacancies of sufficient size is necessary before U centres can be formed. The effect of temperature shows that the rate of U centre formation is limited by the diffusion of hydrogen species from the end of the proton tracks, and this is confirmed by depth distribution measurements.

The adiabatic elastic constants of GaAs (n type carrier density 1.3*10¹⁶ cm^-3) have been obtained between 2 K and 320 K from measurements of ultrasonic wave velocities by the pulse superposition technique. One aim has been to compare the results with the somewhat scattered data obtained at room temperature by previous workers: particular attention has been paid to estimation of the overall uncertainty in the elastic constants. At 298 K, C₁₁=1.1841+or-0.0037, C₁₂=0.537+or-0.016 and C₄₄=0.5912+or-0.0018 in units of 10¹² dynes cm^-2. The Debye temperature (346.8 K) computed from the data extrapolated to 0 K is in excellent agreement with that (346.7 K) derived from low temperature specific heat measurements. The temperature dependence of the elastic constants have been fitted by an anharmonic oscillator model. The force constants and effective charge have been calculated on the basis of a rigid-ion model. The Gruneisen parameter, particle displacement and energy-flux vectors and cross-sections of the Young's modulus and wave velocity surfaces have been compiled.

The authors have measured the thermal conductivity of single crystals of HCP ⁴He and have determined their c-axis orientations independently by an optical method. In the Umklapp process dominated region it is found, for a Debye characteristic temperature Theta ₀=28.7K, that the conductivities perpendicular and parallel to the c-axis can be represented by: kappa _{perpendicular to} =5.53*10^-6 exp( Theta ₀/2.53T) W cm^-1 K^-1 k/sub ///=1.35*10^-4 exp( Theta ₀/4.64 T) W cm^-1 K^-1. Simple theories predict that the ratio of the two exponents should be 1.4-1.7, which agrees moderately well with the measured value of 1.8. The results confirm those of Hogan and co-workers. The authors have also investigated the extent to which polycrystalline samples are randomly oriented.

The molecular tight binding method is used to compute the band structure of the HF crystal in the linear chain approximation and in the three-dimensional case. The energy bands are classified according to the symmetry properties of the crystal with the hydrogens fixed in such positions as to give a nonpolar crystal. The results are correlated to the eigen- states of the isolated molecules and display a relevant dependence of the k vector. The 1 sigma and 2 sigma molecular states are little changed in the crystal while the 3 sigma and pi levels produce wide bands, still separated by a gap of about 2 eV. The top of the valence states is Gamma ₁⁺ and the lowest state for the conduction band is Gamma ₄^- corresponding to a 4 sigma Hartree-Fock virtual state. The inter-chain interaction produces effects comparable to those due to the nearest molecules so that a one-dimensional model does not seem to be accurate in this case.

A sum rule is derived for the hopping conductivity ( sigma ( omega )) in the rate equation formalism. It is shown that the pair approximation to ( sigma ( omega )) satisfies the sum rule exactly in the limit of low site densities. Detailed comparison of the exact high-frequency expansion of ( sigma ( omega )) with that derived from the pair approximation shows that the pair approximation becomes exact for all omega in the limit of low site densities. The real and imaginary parts of ( sigma ( omega )) are calculated numerically in this limit on the basis of model assumptions about the site statistics and the intersite transition rates which are appropriate to doped crystalline semiconductors. The magnitude of the ratio of the imaginary to the real part of ( sigma ( omega )) is shown to be 0.293 lg ( omega tau ₀)^-1 in this case where tau ₀ is the minimum pair relaxation time.

A temperature diagrammatic analysis is used to investigate the low-frequency three-site impurity hopping Hall conductivity for doped semiconductors, originally treated semiclassically by Holstein. The result agrees with that of Holstein. Discussions are given on the work of Aldea who recently obtained a different result from the above-cited work.

Photoconduction in liquid xenon has been measured as a function of photon encrgy E. light intensity I, and electric field F . In the transparent region E < 7.7 eV photo-currents exist due to ionization of impurities. In the strongly absorbing region 7.7 < E < 8.9 eV only small photocurrent exist: they arc attributed to ionization of impurities by excitons which are directly created in this region. In the strongly absorbing region E > 8.9 eV large photocurrents exist: they are attributed to direct creation of electrons and holes with a quantum efficiency of at least 25 %, Thus the single particle band gap is directly determined to be 8.9 eV, which is in agreement with the gap expected from current intei-pretations of condensed rare gas spectra. All currents are linear in I. From the dependence nnF it is shown that an unbound electron hole pair created by a photon E > 8.9eV mal subsequently recombine with each other and not contribute to the current. The criteria for such self recombination. which can play a large r61e in the observation of photoconductivity, are discussed.

Optical absorption edges at 300 K and 80 K have been measured for single crystals of the compounds ZnSiP₂, ZnSiP_1.5As_0.5, ZnSiP₁As₁, ZnSiP_0.5As_1.5 and ZnSiAs₂. Exponential absorption edge tails were observed in all cases. The minimum energy gap increases from ZnSiAs₂ through the range to ZnSiP₂; a value of approximately 2.0 eV at 300 K for ZnSiAs₂ agrees with previous results, but the value of approximately 2.5 eV for ZnSiP₂ is significantly higher than previous measurements.

In previous papers an account has been given of a new perturbation approach to the many-electron theory of insulators with regular lattices. The discussion was based on Wannier functions. To discuss distorted lattices the analogues of Wannier functions for distorted lattices are required. It is suggested that they be obtained by a unitary transformation of the Wannier functions. A possible form is suggested for the transformation, and an account of how the perturbation theory is affected is then given. By means of a simple example, NaCl it is shown that the elastic but also by the consequences that follow from the requirement that as the nuclei move the electrons must follow, and that the basic wavefunctions must therefore change, to preserve orthogonality. The analogues of the Wannier functions for a distorted lattice are thereby given physical significance. Criteria for the equilibrium conditions of a periodic lattice are also discussed.

Crystal-field and exchange parameters for KNiF₃ are derived from APW band energies calculated by Mattheiss. Comparison with the results of previous molecular orbital calculations and experimental data demonstrates that band structure calculations provide a simple and effective way of determining localized interaction parameters. In this work the band and localized state energies are related using the 'decoupling transformation' method. This provides a complete parametrization of the Ni²⁺ 3d band in this case, for which the Slater-Koster method fails.

Measurements of the magnetic susceptibility, magnetic moment and specific heat of holmium phosphate, HoPO₄, show that there is a magnetic phase transition to an antiferromagnetic state at a Neel temperature of 1.39 K. The measurements indicate that the g value of the Ho³⁺ ion is highly anisotropic with g_c=16.0, g_a=g_a'=0, and the overall behaviour may be well described in terms of the Ising model. At T_N there is a typical lambda anomaly in the specific heat curve whereas at lower temperatures there is a pronounced contribution due to the nuclear hyperfine interaction. It is proposed that the ordered state is a simple two sub-lattice arrangement with the axis of alignment corresponding to the tetragonal c axis. This supposition is confirmed by a measurement of the magneto-electric susceptibility.

Measurements have been made by pulsed NMR of the spin-lattice relaxation times T₁ of ⁶³Cu, ⁶⁵Cu and ⁸¹Br nuclei in three polycrystalline cuprous halides of zinc blende structure from 78 to 300 K. The temperature dependence of T₁ is well described by Van Kranendonk's temperature function and testifies to a two-phonon quadrupolar relaxation mechanism. The ratio of values of T₁ for ⁶³Cu and ⁶⁵Cu is in all cases in good agreement with the inverse square of their quadrupole moments. The fivefold increase in T₁ for copper nuclei on proceeding from CuCl through CuBr to CuI is attributed predominantly to its dependence on the thirteenth power of the lattice parameter. Values of gamma , the parameter characterizing antishielding and other effects, of order 10³ are required to account for absolute values of T₁.

A technique applicable to Mossbauer spectroscopy enables the recoilless gamma -rays to be effectively isolated from other radiation emitted from the source and yields absorption spectra which have improved stability and resolution, at the expense of some loss in signal-to-noise. The technique is particularly suitable for the accurate determination of absolute values of absorber recoilless fractions. Results are presented for the 23.9 keV¹¹⁹Sn gamma -rays emitted by a BaSnO₃ source. The recoilless fraction for a BaSnO₃ absorber at 295 K is found to be 0.57+or-0.02.

The optical spectrum with Zeeman effect of Type I Er³⁺:CaF₂ single crystal shows that the Er³⁺ ions are situated at trigonal, tetragonal, and cubic sites. The lines of the absorption spectrum are identified according to these site symmetries by means of Zeeman effect patterns. Some of their g values are reported. An analysis of the crystal field effect on the Er³⁺ ions at C_3v site symmetry is given. The accuracy of the calculation of the crystal field parameters is discussed.

The position and extended fine structure of X-ray K-absorption edge of niobium in its various compounds has been investigated using 400 mm bent crystal (mica, 100 planes) spectrograph. The observed shifts in the K-absorption edge of niobium in its various compounds have been explained in terms of elementary concepts of molecular orbital theory.