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Results are presented for the density of states of binary alloys from a calculation using the matrix coherent potential approximation. A form of the density of states with realistic features was obtained even though the quasicrystalline assumption for the off-diagonal elements was not employed. These features arise solely from the local information about small clusters of atoms. However, it is felt from these results that a proper density of state can only be calculated from information of larger clusters.

Using a generalized version of the single-site coherent potential approximation (CPA) the electronic density of states is calculated for the Anderson model of cellular disorder with random diagonal and random off-diagonal elements. An elliptical probability distribution for the site energies is assumed. The off-diagonal matrix elements are assumed to be linearly dependent on the site energy. In dependence on the fluctuation widths the electronic density of states in this model can have an appreciably different shape compared to models with non-fluctuating off-diagonal elements. Unter Verwendung einer verallgemeinerten Version der single-site Coherent-Potential- Approximation (CPA) wird die Elektronenzustandsdichte fur das Andersonmodell berechnet bei zellularer Unordnung mit stochastischen Diagonal- und stochastischen Nichtdiagonal- elementen. Fur die Energien am herausgegriffenen Platz wird eine elliptische Wahrschein- lichkeitsverteilung und fur die Nichtdiagonalelemente lineare Abhangigkeit von den Diagonalenergien angenommen. In Abhangigkeit von der Schwankungsbreite der Nichtdiagonalelemente in diesem Modell konnen wesentliche Un. erschiede in der Kurvengestalt fur die Zustandsdichte im Vergleich zu dem Modell mit nichtschwankenden Nichtdiagonal-elementen festgestellt werden.

The authors present a method which improves the results of the coherent potential approximation (CPA) generally used to study the electronic properties of disordered alloys. They replace the disordered medium by an effective one characterized by a local coherent potential which varies from place to place and depends on the particular alloy configuration. The local electronic density of states is determined by equations similar to that found in the CPA, and then conveniently averaged over all the possible configurations in order to obtain the alloy density of states. As opposed to the CPA, this method yields tails in the allowed energy bands. As an illustration for the method, the authors calculate the electronic density of states of a simple one-dimensional model and compare it to the exact density of states and to the results of CPA calculation.

The tight binding approximation for d electrons in liquid metals first studied by Roth (1972) using multiple scattering theory is re-examined by a diagrammatic analysis and is rederived by a new method and also extended to liquid metal alloys. The diagrammatic analysis permits a simple physical interpretation of the multiple scattering theory discussed by Schwartz and Ehrenreich (1971). Using a selfconsistent approximation the authors derive expressions for the electronic density of states N(E) using various approximations for the atomic correlation functions. In particular, it is shown that for a correlated liquid treated within SCA the electronic self energy Sigma (E) can be decomposed quite generally into a local and a non local part and that only the local part of Sigma (E) contributes to N(E).

We present a theoretical model that enables us to discuss the combined effects of fluctuations and interchain coupling on the Peierls transition in a quasi-one-dimensional metal. A significant result is that fluctuations lead to the appearance of a pseudo-gap in the electronic density of states above Tp.

I discuss the effect of sharp structure in the electronic density of states on the temperature dependence of the interband-$s\ensuremath{-}d$-phonon-scattering resistivity. The a priori density of states of Pd is used to calculate the resistivity, which is found to be in excellent agreement with experimental high-temperature results.

A theory is presented explaining the recently observed superconductivity at 9 °K in Pd-H and at 11 °K in Pd-D as due to the quenching of the spin-fluctuations and as due to the decrease of the Coulomb pseudo-potential μ present in Pd. That one observes for PdD a larger superconducting transition temperatureT c than for PdH is explained by the larger lattice expansion resulting for adding H to Pd. The observed non-monotonic dependence ofT c on the Hydrogen concentration is explained by the fact that approximately λ ∝N(0) for smallN(0), whereN(0) is the electronic density of states at the Fermi-energy and where λ denotes the electron-phonon coupling constant. Superconducting transition temperatures are estimated for PtH and RhH.

A short-range disorder model is used to predict the predominant features of the density of states of amorphous III–V semiconductors. Confirmation of this model would help establish the existence of III-III and V-V bonds in these materials.

A method is presented to calculate the electronic density of states of liquid metals and alloys in the one orbital tight-binding approximation. We derive expressions for the density of states using a self-consistent single-site approximation.

The electronic structure of PdTe 2 has been determined using the Korringa-Kohn-Rostoker method. Unlike the electronic structure of other metal dichalcogenides with the same crystal structure, the eigenfunctions of PdTe 2 show strong metal and ligand mixing. The de Haas-van Alphen frequencies have been calculated and are in good agreement with experimental results. The calculated electronic density of states is in qualitative agreement with measurements of the specific heat of this material.

The electronic density of states at the interface of two semi-infinite linear chains consisting of atoms with $\mathrm{sp}$ orbitals is investigated using the Green's-function formalism. The effect of the interface coupling on the Shockley surface states and the bulklike densities of states is studied in detail.

The density-matrix approach due to March and his collaborators is used to obtain the electronic density of states of liquid metals. A model potential is used for liquid aluminum, and the density of states is calculated for both completely random and correlated systems. Results are compared with previous calculations, and nearly-free-electron-like behavior is found for liquid aluminum.

The specific heat of a series of high-purity $\ensuremath{\beta}$ brasses has been measured below 4.2\ifmmode^\circ\else\textdegree\fi{}K. Because of the possibility of large contributions to the specific heat from small amounts of ferromagnetic impurities, each specimen was examined spectroscopically and was found to contain less than 1 part per million of Fe, Mn, and Co. The data were fitted by the method of least squares to a curve of the form $\frac{C}{T}=\ensuremath{\gamma}+\ensuremath{\beta}{T}^{2}+\ensuremath{\delta}{T}^{4}$, the $\ensuremath{\delta}{T}^{4}$ term being included to account for the apparently large phonon dispersion. All of the coefficients showed a marked decrease with increasing electron-atom ratio. The variation of electronic density of states as a function of electron-atom ratio is compared to the theoretical relation based on the nearly free electron approximation. For the specimen of approximately 50 at.% copper and zinc, $\ensuremath{\gamma}$ was found to be 0.699 mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}2}$ and the Debye temperature 291\ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}K. This compares favorably with the value of 288\ifmmode\pm\else\textpm\fi{}3\ifmmode^\circ\else\textdegree\fi{}K, obtained from low-temperature elastic-constant measurements on an alloy of similar composition.

Bremsstrahlungs isochromats of polycrystalline Al have been measured at threshold voltages of 1 and 2 kV. In contrast to transition metals where corresponding measurements represent the electronic density of states new effects occur in the case of Al. The obtained results establish the dominant role played by the “nondirect transition” process introduced in this paper. This process explains the measured isochromats in terms of a transition process strongly influenced by characteristic energy losses (CEL) as well as direct interband transitions.

The specific heats of face-centred-cubic manganese-copper alloys at liquid helium temperatures have been measured for copper concentrations between 31 2 and 90 wt. per cent. Analysis of the results shows that the major specific heat component is electronic, and that this exhibits a broad maximum of about 12 × 10−3 J mol deg2 between 10 and 30 wt. per cent Cu. At lower Cu concentration the electronic component dips sharply and it is estimated that for pure Mn (γ-phase) the electronic component should be of the same magnitude or lower than in the other transition elements, in contrast to the anomalously large values found in the α- and β-phases of Mn. Implications of the specific heat data on the electronic density of states curve and on the magnetic properties of MnCu alloys are discussed. The lattice component of the heat capacity appears to vary only moderately with concentration.

Nous calculons la contribution d'une bande s etroite aux modules elastiques (1/2) (C11— C12) et (1/3) (C11 + 2C12) d'un reseau cubique simple. Cette contribution est negative. Le resultat est discute en fonction du remplissage de la bande. Nous trouvons une singularite dans la variation du module de cisaillement (1/2) (C11 - C12) lorsque le niveau de Fermi traverse une singularite de Van Hove de la densite d'etats.

Only for Li and Cs among the liquid alkali metals do the density of states and its energy derivatives show significant departures from the free electron model. In addition, the density of states of liquid Hg numerically calculated has a depression near the Fermi energy. The effect of the electronic density of states on the electronic mean free path has been investigated by introducing Mott's density of states ratio g.

Crystal lattice disordered systems, calculating electronic density of states by overlap integral transformation

Low-temperature measurements of the specific heat are reported for Ce 1−x La x Al 3 and Y 1−x Th x Al 3 . The observed maxima for Ce 1−x La x Al 3 are attributed to crystalline field effects. The marked variations in the electronic density of states for Y 1−x Th x Al 3 are ascribed to influences of Brillouin zones. Results are related to the Kondo sideband model.

The A15 type compounds V3Si and Cr3Si have been investigated by photoemission experiments. The results are in good general agreement with previously reported results from X-ray emission spectroscopy and with APW density of states calculations. The results indicate that the rigid band model is not capable of explaining the differences between the two compounds. We conclude from our measurements that the width of the peak in the electronic density of states near the Fermi level of V3Si is less than 0.3 eV. Les spectres de photoemission ont ete etudies dans le V3Si et le Cr3Si avec des photons d'energie jusqu' a 11,1 eV. Les resultats sont de maniere generale en bon accord avec les mesures de spectres d'emission de rayons X et avec les calculs APW de la densite d'etats. Les resultats indiquent que la difference entre le V3Si et le Cr3Si ne peut pas ětre expliquee par le modele de la bande rigide. On en conclut que, dans la densite d'etats de V3Si, la largeur du pic pres du niveau de Fermi est inferieure a 0,3 eV.

We have measured the energy distribution of the photoemission from europium-oxide and europium-selenide. We conclude from our results that in these compounds the electronic density of states shows a pronounced peak, whose width is of the order of 1 eV, at the top of the valence band.

The electron network model of Coulson and Della Riccia is applied to describe a simple lattice consisting of two families of linear chains, coupled together. It is shown that the model displays resonances, at which the wavefunction is preferentially situated at one or the other family of chains, and that at these resonances, there is a 1/√E divergence in the electronic density of states.

The superconducting transition temperatures of "amorphous" transition-metal alloys have been measured. The variation of ${T}_{c}$ as a function of the electron-to-atom ratio is consistent with the presence of an atomiclike parameter characterizing the systematics of ${T}_{c}$, with, however, an unexplained peak at the half-filled $d$ shell. The data do not support a recent explanation based entirely on a simple averaging or smearing of the crystalline electronic density of states.

Work in Zurich on the difference in size and in expansion coefficient between the normal and the superconducting states is summarized. The volume dependences of the critical temperature and of the electronic density of states at the Fermi surface are discussed.

A scheme for the study of the electronic density of states in disordered alloys with arbitrary composition and clustering correlation is presented. The approach is developed within the framework of the effective medium-multiple scattering formalism, but differs in motivation from the diagrammatical and cluster-hierarchical methods in which the system T-matrix is analyzed at the outset in terms of elementary scattering processes. Instead, the present scheme is rooted in the Butler and Kohn locality principle, which states that the electronic density of states can be usefully approximated by the effects of the constituent occupations in a suitably large, but finite, compact neighbourhood of any site in the lattice. When taken over to the self-consistent multiple-scattering formalism, the principle leads to a spatial decay of the fluctuations of the Wannier matrix elements of the system T-matrix with increasing intersite separation. The required T-matrix elements can then be obtained from a spatially truncated set of equations. Within this context, the development of a systematic approximation scheme based on a range truncation of the system T-matrix is given. It is shown that at a given T-matrix truncation range, the scattering processes associated with lower-order cluster-hierarchical schemes are incorporated in the present approach. The formulation of the scheme in the Wannier model is not restricted by the parametric details of the hamiltonian, making it particularly well-suited to the case of a random-hopping integral.

The electronic densities of states are calculated for a two-sublattice alloy in single-site coherent potential approximation (CPA) and for an alloy with off-diagonal randomness in two-site CPA. In the first part of this paper, we study the compositional dependent energy gap and bound states for a Hubbard-like model. In the second part, we investigate the effect of the off-diagonal randomness on the impurity states.

The heat capacities of Ag 7 O 8 NO 3 and Ag 7 O 8 HF 2 have been measured between 0.3 and, respectively, 20 and 4°K. The measurements show that the previously reported type II superconductivity is a bulk property, and give the values of some of the normal and superconducting-state parameters. There is a surprisingly strong dependence of the electronic density of states and Debye temperature on anion identity, but no convincing evidence for a direct effect of anion identity on T c .

A detailed theoretical investigation has been made of the manner in which the electronic density of states of copper changes with the introduction of dilute nonmagnetic impurities. The formalism used is exact for a single impurity in a system of muffin-tin potentials, and takes into account the detailed character of the host band structure. The impurity potential is calculated through a self-consistent procedure utilizing a generalized Friedel sum rule. The results show a marked difference from the predictions of the rigid-band model. We find that the changes in the single-particle electronic density of states are not sufficient to account for the measured changes in the linear component of the specific heat. But due to the comprehensive nature of the calculations, it is possible to conclude that the discrepancy is due to other physical effects.

The constant pressure specific heats ( C p ) of binary Cr-V alloys containing 5–77 at.% V were measured in an adiabatic calorimeter from about 125–625°K. It was found that C p could be represented as the sum of a lattice contribution, c d , described by the Debye function, a dilatation correction to constant volume conditions, ( C p − C v ), and an electronic contribution c E , equal to γ' T , where γ' is the effective electronic specific heat coefficient, γ' is constant. The γ' values were greater than the low temperature (liquid He range) values (γ 0 ) reported by previous investigators, particularly below 30 at. %V. This is attributed to the temperature dependence of the Fermi function and the sharp minimum in the electronic density of states curve near Cr.

The formalism of the moments and the histogram method are used to describe the electronic density of states of an impurity band for concentrations in the metallic range. By simulating the randomness on a computer, we study the possibility of an erosion >> of the density of states near the impurity level, as foreseen by Lifshitz .

The pressure dependence of the thermodynamic critical field of La has been measured, and calculated the pressure effect on the electronic density of states at the Fermi surface is calculated. The value of dln N (0)/dln v is found to be -4.54±1.67, where N (0) and v are the density of states at the Fermi surface and the volume respectively. From the pressure dependence of N (0) and T c of La–1.0%Ce, dln J /dln v is calculated to be -4.3 ( J is the exchange interaction parameter). From the experimental result, the mechanism of superconductivity of La at high pressure is discussed.

The form of part of the electronic density of states curve for palladium is deduced from the low temperature specific heat coefficients γ of palladium-silver and palladium-rhodium alloys by means of the rigid band model of alloying. The curve, which shows a sharp maximum near the Fermi limit, is used to calculate the electronic contribution to the specific heat of palladium over the temperature range 0 °K to 1500 °K. Values of the electronic contribution in palladium are also deduced from the measured specific heat, and are shown to be in good agreement with the calculated values and to differ widely from the approximation Ce = γT. It is also suggested that the experimental specific heat results for palladium alone, without using the alloy data, indicate the occurrence of a maximum in the density of states curve near the Fermi limit.

The results are presented of calculations, for a model three dimensional system, of the effect of the introduction of various types and amounts of disorder into a crystal on the shape of the electronic density of states curve. It is found that even a small amount of disorder is sufficient to remove the van Hove singularities in the centre of the band, while in general the amount of distortion introduced depends on the amount of irregularity in the density of states curve for the perfect crystal, the amount of disorder, and whether this disorder resembles that appropriate to an amorphous system or that appropriate to an alloy.

A generalized Wigner-Seitz method is applied to the band structure of aluminium. The calculation is based on a muffin-tin potential derived from the electronic density of the free atomic states normalized with respect to the volume of the Wigner-Seitz cell. Because of the spherical symmetry of the potential the wave function can be expanded in terms of spherical harmonics. Their number has to be limited to 12 according to the number of central points of the 12 rhombohedrons constituting the Wigner-Seitz surface. The method provides E(k) in any direction of the Brillouin zone (BZ). For reasons of saving computer time E(k) is computed for each band at 300 points of the irreducible wedge of the BZ and properly fitted to a Fourier expansion of 10 terms. By means of this expansion E(k) is easily obtained at 5 × 105k-points. The density of states and its variation under pressure can be computed then by simply ordering those 5 × 105E-values of each band into a sequence of energy intervals of 0.01 Ryd width, by counting their number in each of those and finally summing up the contributions of all bands. Mit Hilfe einer verallgemeinerten Wigner-Seitz-Methode wird die Bandstruktur von Aluminium berechnet. Dabei wird ein muffin-tin-Potential benutzt, das sich aus der Elektronendichte der Zustande des freien Atoms ergibt, wenn diese auf das Volumen der Wigner-Seitz-Zelle umnormiert werden. Wegen der Zentralsymmetrie des Potentials kann die Wellenfunktion nach Kugelflachenfunktionen entwickelt werden. Ihre Anzahl ist auf 12 zu beschranken, entsprechend der Anzahl von Rhomboedermittelpunkten, welche die Wigner-Seitz-Oberflache enthalt. Die Methode liefert E(k) fur jede Richtung der Brillouin-Zone (BZ). Zur Einsparung von Maschinenrechenzeit wird E(k) fur jedes Band in 300 Punkten des Fundamentalbereichs der BZ berechnet und an diesen Stellen mit einer 10 Glieder enthaltenden Fourier-Entwicklung optimal zur Ubereinstimmung gebracht. Mit Hilfe dieser Entwicklung kann E(k) leicht an 5 × 105k-Punkten bestimmt werden. Die Zustandsdichte und deren Anderung unter Druck last sich dann dadurch berechnen, das man diese 5 × 105E-Werte jedes Bandes in ein Raster aufeinanderfolgender Energieintervalle von 0,01 Ryd Breite einordnet, in jedem Intervall auszahlt und schlieslich uber die Beitrage aller Bander aufsummiert.

The coherent potential approximation for the electronic density of states in a disordered substitutional alloy is applied in detail to a system of muffin-tin potentials. All expressions are formulated in terms of the phase shifts of the individual atomic scatterers. A simple example, illustrating a tight-binding system in which the pure constituents have different bandwidths, is discussed.

Morita and Chen's scheme of generalizing the coherent potential approximation, in which the diagonal and off-diagonal randomness are included, is applied to the calculation of the electronic density of states for the linear random binary alloy. The result obtained in the two-site coherent potential approximation is reported.

The atomic arrangement of the ideal amorphous form of germanium or silicon is thought to be a tetrahedrally coordinated random network. Since the diamond structure is only one crystalline limit of such a network with the appropriate short range order, it is instructive to compare the density of states and the optical spectrum of amorphous Ge and Si not only with those quantities calculated for cubic Ge and Si, but also with those for such simple polytypes as 2H and 4H. Our computations indicate that while N ( E ) for these polytypes becomes progressively more like presently available experimental N ( E ) as one continues to add atoms to the unit cell, the gross features of the optical spectra of these polytypes are all very nearly alike, and are consistently different from the amorphous material.

Recent progress in the analysis of the properties of a simple tight binding Hamiltonian, appropriate to the study of the role of topological disorder in determining properties of amorphous semiconductors, is reviewed. The band structure generated by such a Hamiltonian for the diamond cubic structure is compared with a more realistic calculation for Ge.

Measurements of the electronic specific heat and susceptibility of the superconducting intermetallic compound LaIn 3 indicate that the susceptibility is exchange enhanced by a factor of 5.76. This corresponds to an effective electron-electron interaction of 2.91 eV. Using a simple model for the electronic density of states which postulates a peak in the vicinity of the Fermi energy, we obtain a good fit to the experimental temperature-dependent susceptibility.

A theory is presented for superconductivity in amorphous transition metals. It is shown that in contrast to simple metals for transition metals the changes in the phonon spectrum, in the electronic density of states and in the electronic matrix elements which result from strong lattice disorder can enhance as well as decreaseTc. The numerical results for the superconducting transition temperatureTc of amorphous 4d-and 5d-transition metals agree well with the experimental results.

We combine the accurate resonance-parameter approach to transition-metal band structure, in the final version of Pettifor, with a Gilat-Raubenheimer method resorting to a dissection of the irreducible wedge into tetradedra to calculate the electronic density of states of f.c.c. Cu. Such an approach allows avoiding of any interpolation procedure.

The model for the electronic density of states in β-W-compounds proposed by Cohen et al.5 is used the electrical resistivity of such substancies. The parameters which fit the experimental ϱ(T) curve are different from those fitting other experiments.

We derive the density of states of a disordered structure by using the CPA self-consistent method. We assume first the hopping integrals of the one-electron hamiltonian to be randomly distributed according to a Lorentz probability law. The density of states appears to be analogous to that obtained by Lloyd in reference 1. We calculate then the density of states in the case of a probability distribution of finite extent.