Showing papers in "Journal of Physics C: Solid State Physics in 1970"

Many-electron singularity in X-ray photoemission and X-ray line spectra from metals

Abstract: It is pointed out that the spectra of X-ray induced fast photoelectrons from metal should have a characteristic skew line shape resulting from Kondo-like many-electron interactions of the metallic conduction electrons with the accompanying deep hole in the final state. The same line shape should also occur for the discrete line spectra of X-rays emitted from metals. This mechanism could account for the well-known asymmetries observed for K alpha lines.

A poor man's derivation of scaling laws for the Kondo problem

Abstract: The scaling laws derived by a complicated space-time approach for the Kondo problem in previous work are rederived by a cutoff renormalization technique used previously in the theory of superconductivity.

The Fitting of Pseudopotentials to Experimental Data and Their Subsequent Application

Abstract: Publisher Summary This chapter summarizes results from the theory of pseudopotentials that relate to choosing suitable mathematical forms forfitting. The procedures used are described. It is reported that it is important to distinguish between what is exact and what is approximate, and to discuss where various approximations might be reasonably appropriate and where not. The chapter reviews all the experimentally fitted pseudopotentials. Primarily they come from Fermi surface studies in the case of metals and analysis of optical properties for semiconductors, but phonon spectra, resistivities of liquid metals, and other data have also been important. It is suggested that by making use of all the theory, all the fitted results by interpolating, extrapolating, cajoling, and cudgeling, one should be able to produce a useful pseudopotential for many elements in many situations.

Pseudopotential Theory of Cohesion and Structure

Abstract: Publisher Summary This chapter discusses the pseudopotential theory of cohesion and structure. The pseudopotential theory of properties related to the total energy of simple (sp-bonded) metals is reviewed with emphasis on the structure dependence of the total energy. Some of the topics covered in addition to the explanation of the observed structures of simple metals are phonon dispersion, stacking faults, ordering in alloys and its relation to electronegativity, structures of liquid metals, and the various interpretations of covalent bonding effects. After an elementary introduction that seeks to put this theory in perspective by expounding its general features and relating it to prevailing ideas on metallic bonding derived from earlier theories, the details of the formalism are explored. The conditions for its validity or breakdown are examined. The results of various calculations of structural properties are quoted element by element and discussed. The theory is used to account for observed trends in structures in the periodic table.

The Pseudopotential Concept

Abstract: Publisher Summary This chapter reviews the basic ideas about pseudopotentials. These ideas have evolved and intersected with other developments, therefore, the concept is developed it both from the point of view of an equivalent operator potential and from scattering theory. It is suggested that a correct pseudopotential is defined as one that gave the same energy levels as the real potential, a t least for a range of states of interest, with the emphasis on transforming the Schroedinger equation from. In the chapter, the augmented plane wave, orthogonalized plane wave, Ziman, and Abarenkov forms are discussed. It is reported that with the perspective of time, it also seems appropriate to review why the whole concept of a pseudopotential is necessary, and the cancellation theorem is treated more satisfactorily than previously.

Theory of Dilute Magnetic Alloys

Abstract: Publisher Summary This chapter discusses the properties of metals containing a small concentration of impurity atoms. It deals exclusively in the properties attributable to metallic electrons. Thus, for a sufficiently small amount of the impurities, the problem reduces to that of the scattering of the conduction electrons by a single atom in a metal. This has been a traditional subject. One sets up the potential due to the addition of the impurity and solves the Schrodinger equation for the one-electron problem. In this way, many properties of dilute alloys such as the electrical resistivity, thermoelectric power, specific heat, magnetic susceptibility, phase diagram, energy of solution, etc., have been explained. In this chapter, the former theory of the so-called s-d model is presented. The condition for the formation of the local moment is discussed here. The resistance minimum and other properties are also explained from higher-order effects based on the s-d model. It is discussed how the logarithmic divergence are removed. In this respect, the problem has not been settled yet, and several approaches to the problem are mentioned.

Thermoelastic Theory of Stressed Crystals and Higher-Order Elastic Constants

Abstract: Publisher Summary This chapter presents the general theory of thermoelasticity of stressed solids to apply the theory to the interpretation of experiments, which measure nonlinear thermoelastic properties of solids, and to illustrate this application by working out some examples. Experimental work has been motivated by the development in recent years of the measurement of ultrasonic wave velocities as functions of stresses applied to the sample, and the measurement of the amplitude of the first harmonic generated by the passage of an ultrasonic fundamental wave through the sample. These experiments, and others such as the generation of sum- and difference-frequency waves by the interaction of two ultrasonic waves, are all interpreted from the same theoretical basis, namely nonlinear thermoelasticity of anisotropic solids. As thermoelasticity is characterized by a rather cumbersome notation, and indeed throughout the years by many different sets of such notation, corresponding to different theoretical and experimental situations, it is worthwhile to set out the general theory in a unified notation, suitable for application to all experiments on nonlinear thermoelasticity.

Lattice dynamics of magnesium oxide

Abstract: Measurements of the inelastic neutron scattering by longitudinal optic phonons in MgO are reported. These results and those previously obtained for other branches are used in an investigation of various lattice dynamical models, including shell and breathing shell models. It is shown that the agreement with the measured data is improved by the inclusion of breathing effects.

The spontaneous resistivity anisotropy in Ni-based alloys

Abstract: From experiments on a number of Ni based alloys, it is shown that the difference in resistivity for currents perpendicular to and parallel to the magnetization direction is due to spin-orbit induced resistivity transfer from the spin down electron current to the spin up electron current

Antiferromagnetic model with known ground state

Abstract: The ground state of the one-dimensional antiferromagnetic model, with the Hamiltonian H=1/2 j Sigma i=1n sigma i. sigma i+1+1/4j Sigma i=1n sigma i. sigma 1+2 n sigma i. sigma 1+2 (j>O, N even, N+1 identical to 1, N+2 identical to 2) can be given explicitly in terms of spin eigen-functions. Various properties of the ground state are studied. An approximate determination of the low-lying excited states shows the usual linear frequency-wave-vector relationship.

Localization of normal modes in vitreous silica, germania and beryllium fluoride

Abstract: The authors previously (1968) presented vibrational spectra for vitreous silica, germania and beryllium fluoride, calculated from atomic arrangements in physical models based on the random network theory. The present work describes the localization properties of the normal modes of vibration. It is shown that the vibrations are, on the whole, less extended in space than the plane wave-like modes which characterize regular crystals. Localization tends to be greatest at high frequencies and, especially, near band edges. If nonbridging oxygen atoms are present in the structure, the spectra of vitreous silica and germania exhibit an additional band of very intense localization; atomic motions associated with modes in this band are effectively restricted to no more than a few atoms.

Theory of the crystal structures of transition metals

Abstract: The structure trend that is observed across the transition metal series as the number of valence electrons N increases 3 to 11 is explained quantitatively. The difference in the total one-electron band structure energy between the close-packed structures face-centred cubic and hexagonal close-packed is shown to determine completely which structure is favoured, whereas an additional hard-core repulsive contribution is necessary when comparing the body-centred cubic and close-packed structures at the noble metal end of the series. The calculations were performed assuming a model transition metal characterized by only the two d-resonance parameters epsilon d and Gamma , from which the densities of states for the three structures were obtained using energy levels calculated by the hybrid nearly- free-electron tight-binding scheme of Pettifor.

Localized Moments and Nonmoments in Metals: The Kondo Effect

Abstract: Publisher Summary This chapter summarizes the experimental situation in the magnetic impurity problem, particularly with respect to the questions of moment formation and the Kondo effect. The discussion given here is not directly applicable to the rare earths except for cases where because of a near instability of a particular valence state an antiferromagnetic covalent s-f exchange dominates and a Kondo effect is observed. The implications of the Kondo effect on the scattering from magnetic impurities in superconductors constitute an area of considerable current activity. There is considerable evidence that simple magnetic ordering and the Kondo effect are competitors. The competition arises simply from the fact that just as large external fields remove the divergence, the indirect RKKY fields responsible for short range order in dilute alloys wipe out the dynamic effects which arise beyond the first Born approximation. Silverstein and Harrison and Klein considered this effect and showed how these internal RKKY fields can quench the logarithmic term and lead to a maximum in R (T) as observed experimentally.

Exchange and correlation in the theory of simple metals

Abstract: A unified approach for including the effects of exchange and correlation in the theory of simple metals is presented. It is first demonstrated that the indirect potential acting on a conduction electron can be described approximately by a function of the scattering momentum G(q), and that this result follows directly from general theoretical results. Exchange and correlation corrections to the Hartree expressions for model (or pseudo) potential form factors and energy-wavenumber characteristics are derived and these corrections are shown to have a simple dependence on G(q). The selfconsistent theory of Singwi et al. (1968) is used to obtain a pair of transform relations between G(q) and the pair correlation function g(r) which permit G(q) to be calculated directly from g(r). The pair correlation function for a tenuous electron gas is used to compute a G(q) which is found to be selfconsistent. A simple approximate form of G(q), which is also selfconsistent, is suggested.

Impurity conduction in synthetic semiconducting diamond

Abstract: Electrical conductivity and Hall effect measurements have been made on a series of synthetic p-type semiconducting diamonds in the temperature range 80 to 450K. The dominant conductivity mechanism at low temperatures is shown to be impurity conduction, and effects have been isolated due both to impurity-band conduction and to hopping transport between neutral and ionized acceptor centres. The activation energies associated with the latter processes are much lower than the acceptor ionization energy, and the variation with temperature of the onset of impurity conduction as a function of the neutral acceptor concentration accounts for the wide range of activation energies reported for synthetic diamonds by previous authors.

The lattice dynamics of calcium fluoride

Abstract: The phonon dispersion curves of calcium fluoride in the (001), (110) and (111) directions were observed by inelastic neutron scattering on a triple-axis spectrometer. These observations, and all other data relevant to the vibrational properties, were fitted by the 'shell' model for lattice dynamics. Some harmonic vibrational properties were calculated.

Spin diffusion and spin echoes in liquid 3He at low temperature

Abstract: Spin diffusion in a degenerate Fermi liquid is studied, taking into account the effects of the 'molecular field' resulting from the interactions between quasiparticles. It is shown that even in the hydrodynamic limit no equation of the conventional form delta M/ delta t=Dgrad2M exists in general; the true equation is nonlinear and depends on the strength of the interactions. Substantial new effects are therefore predicted when lambda Omega 0 tau D> approximately 1, where Omega 0 is the Larmor frequency, tau D the spin diffusion lifetime and lambda a dimensionless parameter which measures the strength of the molecular field. Specifically, it is predicted that the spin-echo attenuation in a ' phi -180-180' experiment will in general not be exponential and will depend on the external field and the initial pulse angle phi . The new effects should lie in the experimentally accessible region both for pure 3He and for mixtures.

Anderson's theory of localized states

Abstract: Anderson's (1958) theory of localized electron states in an irregular solid is discussed critically. The statistical and analytical properties of the Green function, when states are localized, are analyzed and it is pointed out that these are not incompatible with Lloyd's (1969) exact results. Anderson's argument is repeated in outline, but it has been found possible to make a major simplification in the statistical analysis. Attention is drawn to two doubtful points in the argument and it is suggested that delocalization occurs less easily than Anderson supposed. The argument is applied to a model of a dilute binary alloy. It is proved for a model of the binary alloy that the energy levels do not extend outside the energy bands of the pure metals.

Recombination luminescence in alkali halides

Abstract: Results are presented of a study of x-ray and electron excited luminescence in all alkali halides in the temperature range 4K to 300K. Details are given of the spectral distribution and lifetimes associated with the luminescence bands at about 5K. The lifetime and peak intensities of some bands have been measured as a function of temperature giving parameters characterizing quenching processes. These parameters confirm that many luminescence transitions are nearly forbidden and that the quenching process involves internal radiationless transitions.

Crystal Growth Mechanisms: Energetics, Kinetics, and Transport

Abstract: Publisher Summary This chapter reviews a survey and organizes the extremely diverse phenomena coming under the heading of crystallization, and presents a physics framework for understanding their mechanisms. This framework consists of the application of statistical mechanics, thermodynamics, kinetic theory, and especially transport theory to crystallization problems. The chapter emphasizes the quantitative approach on well-defined systems, both for experiment and theory. The subject of the growth of crystals is an interdisciplinary one, in the sense that contributions to this field have been and continue to be made by scientists and engineers from many professional fields: solid-state physicists, mineralogists, crystallographers, physical chemists, mathematicians, chemical engineers, metallurgists, and probably many others. A similar diversity exists in the wide range of media of publication of the research, and in the departments of universities and research organizations in which the work is performed. The chapter discusses crystallization problems by analyzing them from the point of view of a particular discipline of physics. It begins with the more general disciplines—that is, thermodynamics and statistical mechanics and proceeds to more specialized ones—that is, mass transport and fluid flow.

Spin waves in antiferromagnetic FeF2

Abstract: Spin-wave dispersion in antiferromagnetic FeF2 has been investigated by inelastic neutron scattering using a chopper time-of-flight spectrometer. The single mode observed has a relatively flat dispersion curve rising from 53 cm-1 at the zone centre to 79 cm-1 at the zone boundary. A spin Hamiltonian which includes a single-ion anisotropy constant D (Hsi=-DSiz2), three exchange parameters Jl(Hex12=JlS1.S2) and dipolar interactions has been fitted to the measured energies. The authors find D=6.46 (+0.29, -0.10) cm-1, J1 (coupling neighbouring ions along the c axis)=-0.048 (+or-0.060) cm-1, j2 (coupling neighbouring ions at the corner and body centre of the cell)=+3.64(+or-0.10) cm-1, and J3 (coupling neighbouring ions along the a axis)=+0.194 (+0.060) cm-1.

The origin and intensities of low energy satellite lines in X-ray emission spectra: a molecular orbital interpretation

Abstract: The occurrence of low energy satellite peaks in X-ray emission spectroscopy is briefly reviewed and the theories to explain their origin are discussed. A molecular orbital model is presented and the application of this method to the X-ray fluorescence transitions observed in silica, based on the SiO4 unit, is described in detail. The arguments are extended to the compounds of other second row main group elements. It is found that the molecular orbital approach describes the observed trends in satellite main peak energy separation more accurately than the crossover transition theory of O'Brian and Skinner (1970). It is suggested that low energy satellite peaks arise from the perturbation and splitting of atomic orbitals due to bond formation.

The vibrational spectra of lithium niobate, barium sodium niobate and barium sodium tantalate

Abstract: Crystallographic studies of Ba2 NaNb5O15 have shown that the possible space groups are D62, C112v and D192h. The coincidences between the infrared and Raman spectra support the conclusion, based on the ferroelectric properties of the crystal, that the space group is C112v. The anomalous tantalum compound has a spectrum compatible with a similar structure. The vibrations are classified as internal modes of the Mo6 octahedron (M=Nb, Ta) and lattice translations involving motion of the cation. Force constants are calculated for internal modes using the Wilson FG matrix method and for lattice modes using the Born-von Karman theory.

Effect of non-magnetic localized states in superconducting alloys

Abstract: The authors have calculated in detail the excitation spectrum and superconducting critical temperature for dilute non-magnetic alloys containing transition-metal impurities, the host metal being an isotropic Bardeen-Cooper-Schrieffer superconductor. The localized d states at the impurity sites are considered to affect the superconductivity due to the resonance scattering interaction as proposed by Zuckermann, and the model of Ratto and Blandin is used to take account of the Coulomb repulsion between d electrons of opposite spin. It is shown that these alloys are essentially Bardeen-Cooper- Schrieffer superconductors, with an effective coupling constant which decreases approximately linearly with impurity concentration until the superconductivity is quenched.

A rule for chemical shifts of X-ray absorption edges

Abstract: An empirical rule governing the chemical shifts of X-ray absorption edges has been proposed and tested.

The Physics of Quantum Crystals

Abstract: Publisher Summary A quantum crystal is one in which the zero point motion of an atom about its equilibrium position is a large fraction of the near neighbor distance. Both short range correlations and long range correlations (phonons) are of importance and must be treated with care in the description of quantum crystals. Recently, considerable progress has been made along these lines. This chapter discusses this progress. It discusses the gross properties of the rare gas solids (mostly solid helium). Particular attention is given to the interplay of “mass” and “interaction” which leads to an expanded lattice and the large zero point motion. It examines the Hartree approximation to the ground state energy of solid helium in order to illustrate the need for including short range correlations in the description of the system. This chapter describes a number of treatments of the short range correlation problem. The first successful theory of the ground state energy in quantum crystals is due to Nosanow. The “theory of correlated crystals” due to Brueckner and FrohbergZ and the “quasi-crystal approximation” of Maasey and Woo are also discussed in this chapter.

The antiferromagnetic-ferromagnetic transition in iron-rhodium alloys

Abstract: The critical field required to induce this transition in Fe-Rh alloys close to the equiatomic composition has been measured using pulsed magnetic fields up to 280 kOe. Measurements of the thermal expansion and high field magnetization have also been carried out. It is found that application of Kittel's theory of exchange inversion to the results leads to serious numerical discrepancies. A four sublattice model is developed which indicates the importance of the excess entropy of the ferromagnetic over the antiferromagnetic phase in exciting the antiferromagnetic-ferromagnetic transition. The exchange iteration β between iron sublattices is small and negative and, although its lattice parameter dependence is large and positive, there is no suggestion of exchange inversion corresponding to a change in sign of β at the antiferromagnetic-ferromagnetic transition. Thus the ferromagnetic state is stabilized by the excess entropy even in the presence of antiferromagnetic interactions and this stability is maintained right up to the Curie temperature

Measurement of the elastic constants of argon from 3 to 77 degrees K

Abstract: The velocity of sound has been measured in argon single crystals by the pulse-echo technique for both longitudinal and transverse waves from 3 to 77 degrees K. The values of the elastic constants obtained by extrapolation of the results to 0 degrees K are: c11=4.39, c12= 1.83 and C44=1.64, in units of 109N m-2. Comparison with several lattice dynamical models indicates that models incorporating only central two-body forces are inadequate. New values for the adiabatic bulk modulus permit more accurate calculation of the Debye characteristic temperature and the Gruneisen parameter.

Parametrization of the correlation crystal field

Abstract: Quite large discrepancies are found when crystal field splittings are fitted to a one-particle potential V= Sigma Anmynm. It is suggested that the parametrization of the experimental data can be improved by introducing an additional potential which represents the two particle correlation induced by the environment. This separates the problem of describing the discrepancies from the problem of explaining them in terms of specific mechanisms. A formal development of the correlation crystal field concept is given, and suggestions are made regarding the treatment of experimental data. Some possible generalizations of this concept are also discussed.

The temperature dependence of the band-edge effective masses of InSb, InAs and GaAs as deduced from magnetophonon magnetoresistance measurements

Abstract: Magnetophonon peaks are observed in the second derivative of the magnetoresistance of high purity samples of n-type InSb, InAs and GaAs over a wide range of temperatures. The temperature dependence of the band-edge effective mass in each material is deduced and compared with that predicted from the dilatational component of the change in band gap with temperature. In the case of InSb, the agreement is excellent but, with InAs and GaAs, the observed change is greater than that predicted although still less than that obtained by substitution of the change of optical energy gap with temperature.