John Ziman

A theory of the electrical properties of liquid metals

Abstract The simple theory of resistivity originally applied to pure liquid metals (Ziman 1961, Bradley et al. 1962) is formally extended to liquid alloys. In dilute solutions, size difference between solute and solvent ions can be allowed for, approximately, by a modification of the pseudo-potential of the solute, in a manner reminiscent of the modification of solute valency suggested by Harrison and Blatt (1957) in dealing with the resistance of solid alloys. The theory explains qualitatively a number of interesting features of the behaviour of liquid binary alloys, e.g. the failure of liquid solutions in polyvalent metals to obey the familiar rules of Nordheim and Linde. Some speculations on the anomalous behaviour of mercury amalgams are included. A bibliography of experimental results for both resistivity and density in liquid alloys is collected in Appendix II.

Prometheus Bound: Science in a dynamic steady state

Foreword 1. What is happening to science? 2. Scientific and technological progress 3. Sophistication and collectivization 4. Transition to a new regime 5. Allocation of resources 6. Institutional responses to change 7. Scientific careers 8. Science without frontiers 9. Steering through the buzzword blizzard Further reading.

The Electron-Phonon Interaction

Publisher Summary The interaction of the conduction electrons with the lattice vibrations is at the center of the whole theory of the transport properties of solids. It determines the electrical and thermal conductivity at ordinary temperatures and is the source of thermoelectric effects at high and low temperatures. It is also the cause of the superconducting transition that occurs in many metals at low temperatures. In semiconductors, the mobility of the carriers is often dominated by the same phenomenon. Because the electron–phonon interaction is ubiquitous in solids, it would be impossible to survey the whole experimental field in a short review. The most direct effect of ultrasonic attenuation is complex both in theory and experiment, while the more familiar phenomena such as electrical resistivity give only very rough averages of the scattering probability over the Fermi surface.

The ordinary transport properties of the noble metals

Abstract The Fermi Surfaces in Cu, Ag and Au are now known to be greatly distorted, with thick ‘necks’ passing through the zone boundaries. In this paper we enquire whether such an electronic structure is quantitatively consistent with the observed transport coefficients. The mathematical model is quite simple; the shape of the Fermi surface is made to depend on a single parameter which can be interpreted as the pseudo-potential of the {111} atomic planes acting on an orthogonalized plane wave, giving rise to an energy gap of 5–10 ev at the zone boundaries. Various integrals over the Fermi surface can then be evaluated by elementary methods, and compared with the corresponding experimental quantities. The electronic specific heat and optical mass in the pure metals are consistent with the model. The galvanomagnetic effects are shown to depend a great deal on the anisotropy of the electron relaxation time, whose variation with energy is also probably the electron relaxation time, whose variation with energ...

The electron transport properties of pure liquid metals

Abstract Progress in the theory of the electrical conductivity and other ordinary transport properties of liquid metals since 1961 is reviewed. After a brief account of the basic nearly-free-electron diffraction formula, the quantitative comparison of this formula with experiment is discussed. For the alkali metals, the agreement is adequate, given the uncertainty of the pseudopotentials, although there is controversy about the calculation of the temperature coefficient of ρ L. To explain the observed volume dependence of ρ L, and the thermoelectric power, it also seems necessary to allow for the variation of the pseudopotential with the positions of the Fermi level and the core levels relative to the bottom of the conduction band. Quantitative results for the noble and polyvalent metals are meagre, and although calculations of ρ L for Al and Zn are in excellent agreement with experiment there may be other cases where the basic formula is not adequate. The general question of the structure and convergence...

Thermal conduction in artificial sapphire crystals at low temperatures I. Nearly perfect crystals

In order to obtain a detailed verification of the theory of thermal conduction in dielectric crystals, measurements have been made on a number of artificial sapphire crystals between 2° and 100° K. In the region of the maximum there are variations in conductivity between crystals from different sources. The highest conductivities measured are about 140 W/cm deg., which suggests that estimates of several hundred watts for the maxima of ideal sapphire crystals are not unreasonable. At sufficiently low temperatures the conductivity of a very perfect, long crystal with rough surfaces is observed, in agreement with Casimir’s theory of boundary scattering, to be proportional to T3 and to the radius; the phonon mean free path is then nearly equal to the crystal diameter. Imperfect crystals show some anomalous effects. The extension of Casimir’s theory to apply to short specimens has been verified. Perfect crystals with smooth surfaces exhibit some specular reflexion of phonons; a statistical description of the surface is proposed which leads to the observed variation of this effect with temperature and is compatible with the results of interferometric examination of the surface.

The Calculation of Bloch Functions

Publisher Summary A dozen years ago, a review of the theory of electronic band structure could consist of little more than a summary of the rationale of each of the various methods that had been proposed, and a somewhat skeptical catalog of the numerical results that had been obtained for particular materials. The “methods” themselves seemed to have little in common, except their supposed efficiency in solving the same mathematical problem, and very little had been done to establish the mathematical connections between them. Each small research group had its own favorite method and there had been practically no systematic study of the relative efficiencies of two such methods by comparing their predictions for the same material. Considering the limited computational facilities then available, there was a surprising lack of simplified model calculations that might have demonstrated the significant features of the band structure in typical materials. The technical revolution of the past decade has already been mentioned in this chapter. Some would attribute this to the enormous enlargement of computing power, which now permits a complete self-consistent calculation for any given material within the uncertainties of hypothetical atomic potentials and approximate many-body corrections. Others would point to the fresh air of realism that blew in with the new experimental data on Fermi surfaces, encouraging a practical, empirical attitude among band-structure theorists. This chapter tries to emphasize the intellectual evolution implicit in the improved understanding of the interconnection of the various mathematical techniques and of their relation to the physical features of atoms and crystals that really govern electronic structure.

The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes

Measurements of the thermal conductivity of TiO2, KCl, LiF and of three types of diamond below room temperature are reported. Although the first three crystals were very pure there are great deviations from the form of conductivity curve predicted by Peierls for perfect crystals. A consideration of these and other results suggests that the conductivity of many crystals which have been measured is limited by the existence of more than one isotopic species of the chemical elements involved. These give rise to irregularities in the arrangement of atomic mass in the crystals and are a source of phonon scattering. A theory of this effect is given and is compared with the experimental results for the nine substances for which there are sufficient data. The agreement is satisfactory; only for diamond does it appear necessary to invoke impurities as well as isotopes to explain the observed conductivity.

The theory of the electronic structure of liquid metals

Abstract The [Green function] method of Korringa and of Kohn and Rostoker is generalized to the case of a disordered assembly of atoms. If it can be assumed that the wave-function of an electron has a [wave-vector] k, then its energy can be calculated. The equations depend only on the radial distribution function of the atoms in the liquid and on their phase shifts for electron scattering. But the wave-vector k is not real, as for a Bloch function in a solid. It has an imaginary part, which corresponds to the scattering of the electron by the irregular atomic arrangement. It is shown that the assumption that k exists is equivalent to assuming that the liquid is microscopically homogeneous. The method can be generalized to take account of inhomogeneities; a [local] value of k can be calculated for each configuration of the atoms in a finite cluster immersed in the fluid. No actual numerical calculations are reported in this paper, but the procedure is evidently capable of giving practical results without u...

Low-Temperature Transport Properties of the Alkali Metals. II. The Transport Coefficients

The theory of part I (Collins 1961) is applied to the direct calculation of the ‘ideal’ electrical and thermal resistivities and ‘phonon drag’ thermo-electric power, of the alkali metals. All three coefficients depend, in magnitude and as functions of temperature, on the shape of the Fermi surface and on the lattice spectrum. If it is assumed that the latter is identical in form for all metals in the group, the observed transport coefficients are consistent with a Fermi surface which is quite distorted in lithium, becomes nearly spherical in sodium and potassium, and is again distorted in rubidium and caesium. The argument is not sufficiently accurate to discriminate between s-like and p-like symmetry in each case, nor to decide whether the Fermi surface actually touches the zone boundary; the phonon drag effect is also very sensitive to the purity of the specimen.