Table of contents

The low-temperature frequency-dependent conductivity for the Kondo system obtained by applying linear response formalism has been derived through a simple expansion of a small parameter in the Nagaoka model.

From the most reasonable assumption of a nonbonding property for the 4f electrons in the rare earths, thermodynamical principles can be utilized to account for their photoemission spectra.

The equations are calculated using the model pseudopotential of Wallace. In calculating the vibrational contribution to the total pressure, the volume variation of the Gruneisen parameter is taken into account. The calculated isotherms at 300K and 100K are compared with the experimental measurements of other researchers. The agreement between theory and experiment at 300K is extremely good up to a pressure of 45 kilobars. The agreement at 100K is fairly good up to a pressure of 20 kbar. Using the same potential the temperature variation of the second order elastic constants are calculated making the approximation of replacing the normal mode frequency by the square root of the second moment mu ₂. The calculated results indicate that in the case of C₁₁ and C₁₂ the temperature dependence has the right behaviour, whereas C₄₄ almost comes out independent of temperature as against the experiment which shows a rapid decrease.

For f.c.c. and h.c.p. crystals structural phase transitions involving soft acoustic modes are discussed. A simple nearest neighbour force model is used. Two extreme types of transition are distinguished; one of these entails a softening of all modes whereas in the second type there is only appreciable softening of a single mode.

The phase transitions from close packed to distorted structures occurring in Cd-Mg and In-Tl alloys are discussed. The authors document and apply the nearest neighbour theory derived in a previous paper by Finnis and Heine (see ibid., vol.4, no.7, 960, 1974) to explain the nature of the distorted phases and the behaviour of the elastic constants at the transitions. They identify these as examples of the R and F types of transition respectively, defined previously.

Comprehensive measurements of the orbitally averaged scattering rate characterized by the Dingle temperature have been carried out for a number of orbits in dilute alloys of copper containing nickel, germanium or gold as solute. By combining the data for orbits traversing different regions of the Fermi surface and using a Fourier series inversion scheme, characteristic maps depicting the anisotropy of the local electron-impurity scattering rate 1/ tau *(k) over the Fermi surface have been deduced for each type of impurity scattering centre. The maps show a pronounced anisotropy which is different for each of the three solutes. The results may be understood in terms of the partial wave scattering model of Coleridge, and enable the differences Delta eta ₁ between the phase shifts characterizing the host and impurity potentials to be determined.

Specimen size dependences of the dielectric constant and of its variations with temperature have been investigated by measuring the optical plasma resonance absorption of small silver particles embedded in glass. The following relations hold at the wavelength 405 nm: epsilon ₂ (imaginary part at 300K)=0.23+2.64/R, and epsilon ₂(300K)- epsilon ₂(1.5K) approximately=0.07-0.08/R where R is the particle radius in nm. Agreement has been found with the free path effect but not with the quantum size effect theories of Kawabata and Kubo (1966) and of Glauberman and Adamyan (1969). The behaviour of the temperature dependence can partly be explained by thermal lattice contraction. The ratio of electron density to the optical effective mass shows no distinct changes as R varies from 10.5 nm to 1.1 nm. It may hence be concluded that normal metallic properties are present in silver particles embedded in glass which contain more than about 400 atoms.

The temperature dependence of the electrical and thermal resistivities of the alkali metals sodium, potassium and rubidium is determined within the free electron approximation and using Behari and Tripathi's model (1969) for the phonon spectrum. The normal and Umklapp contributions are considered separately from the conservation laws of wave-vectors and the geometry of the reciprocal space. The results are compared with available experimental data. The nature of the theoretical and the experimental curves is found to be similar, though the agreement is not detailed.

Based on the variational method for solving the Boltzmann equation, the anisotropy of the relaxation time of an electron for the electrical conductivity arising from the electron-phonon Umklapp processes in potassium is evaluated in the temperature region between 4K and 60K, and its effect on the low field Hall coefficient is investigated. The Bardeen matrix element and observed phonon spectrum are taken into account in the calculation. It is found that at 6K the relaxation time varies on the Fermi surface by a factor of three. The effective number of conduction electrons per atom in the Hall effect, eta *, is almost unity at 60K and decreases as temperature decreases, in qualitative agreement with experiment eta * has a minimum at 6K and the minimum value is 0.92.

A simple method for calculating the magnetic susceptibilities in disordered alloys described in the coherent potential approximation is given. Special attention is drawn here to the paramagnetic case. The equivalence with Fukuyama's (1972 and 1973) results is shown.

Using a hybridized tight binding and nearly free electron model for the host, the authors compute the density of states of isolated or pairs of transition atoms in noble or transition metals. For such pairs they calculate magnetic susceptibility, the specific heat and the low temperature dependent resistivity due to spin fluctuations in a simple RPA approximation. If one neglects for simplicity, Hund's coupling, the spin fluctuations of both impurities are characterized by two temperatures T_f⁺ and T_f^- and each of the considered physical properties is expressed in terms of these temperatures. The change delta v of impurity potential in the presence of pair interactions is determined through Friedel's sum rule and is shown to be essential in all cases, especially in the asymptotic limit. The results of this numerical study of copper based alloys are in rather good agreement with the experimental data.

From a general two ion spin Hamiltonian, an expression is deduced for the energies of spin waves propagating in a hexagonal solid in which the magnetic moments are ordered in a conical or helical structure. The spin wave dispersion relation in the c direction of Er in its conical magnetic phase at 4.5K, which has been studied by Nicklow et al (1971) is reanalysed. In this analysis an alternative kind of anisotropic coupling between the total angular moments (J_i and J_j) on the sites i and j is introduced which is proportional to the following combination of Racah operators: O_2,-2(J_i), O_2,-2(J_j), expressed with respect to a coordinate system with the z axis along the c direction. The resulting anisotropy (both the constant and the q dependent part) is reduced by an order of magnitude in comparison with that deduced by Nicklow et al (1971). The constant anisotropy is found to be equal to about 20 meV (a rough estimate from magnetization measurements gives 5-10 meV). The anisotropic part of the exchange interaction is found to be of the same order of magnitude as the isotropic part.

The Mossbauer effect has been used in a study of CuFe alloys containing up to 4.6 at% iron over the temperature range 4.2 to 300K. It is found that face centred cubic gamma -Fe is not retained in CuFe alloys quenched sufficiently rapidly from the solid solution region but that the spectra of the solution quenched alloys are consistent with a model in which the iron atoms tend to form clusters. After allowing for the alpha -Fe content in a concentrated alloy a value of 3.1+or-0.2 at% is obtained as the solubility limit for Fe in Cu at 1000 degrees C in agreement with values obtained by other techniques. The precipitation of gamma -Fe and the subsequent development of alpha -Fe has been observed in alloys heat treated at 650 degrees C. At low temperatures gamma -Fe is known to be antiferromagnetic and a value of T_N=63+or-4K is obtained for the Neel temperature of gamma -Fe precipitates in copper and a value of 2.7+or-0.3T for the magnetic hyperfine field at 4.2K. By applying an external magnetic field of 8T at 4.2K the magnetic hyperfine spectrum of theta -Fe has been resolved in a composite spectrum.

Using a 40 cm curved crystal spectrograph of the transmission (Cauchois) type the chemical shifts in the X-ray K absorption edge of copper in a number of copper compounds has been measured. In all the compounds investigated the K absorption discontinuity is found to shift towards the high energy side relative to the pure metal. With the help of available data on binding energies of copper in different oxidation states and these experimentally measured shifts, change on the copper atoms in these compounds has been determined.

The optical absorption spectrum of evaporated beryllium films has been measured using an UHV ellipsometric technique. The beryllium films were formed on sapphire substrates held at RT and about 20K but the observed spectra appear to be largely independent of the substrate temperature. It is believed that the data in both cases are to be associated with disordered microcrystalline or amorphous beryllium. It is therefore surprising that present data are so similar to the spectrum obtained on bulk single crystal beryllium by Weaver et al (1973). The paradox is resolved if it is assumed that the details of the electron band structure of crystalline as well as disordered beryllium are governed by short range order; theoretical arguments by Rousseau et al (1970) support this point of view.