用赝势方法计算某些简单金属的状态方程

本文提出了一种确定简化的Heine-Abarenkov模型赝势参数的新方法,使用零温、零压下晶体的体积模量和晶格常数的实验值来确定赝势参数γ_c以及电子-离子平均相互作用能的修正系数H。用这种模型势和二阶微扰理论计算了十一种简单金属的状态方程。在293K计算出的压力-体积关系与实验数据进行了比较。除了Zn在不同实验数据之间本身就偏离较大外,理论与实验的符合都比较好。 关键词：     

A pseudopotential approach to the superconducting state parameters of (Ni33Zr67)1? x M x (M=Ti, V, Co, Cu) ternary metallic glasses

Superconductivity in ternary metallic glasses has been investigated using the model pseudopotential approach, which has been found quite successful in explaining superconductivity in metals, binary alloys and binary glasses. It is observed that this simple methodology successfully explains superconducting behaviour of ternary glasses without requiring the solution of Dirac equation for a many body problem or estimation of various interactions as required in ab-initio pseudopotential theory. In the present work superconducting state parameters of fourteen metallic glasses of (Ni-Zr)-M system (M=Ti, V, Co, Cu) have been determined in the BCS-Eliashberg-McMillan framework. It is observed that addition of V, Co, and Cu as the third element (M) to a binary metallic glass (Ni₃₃ Zr₆₇) causes the parameters λ,T _c, α, andN ₀ V to decrease, and Coulomb pseudopotential (μ*) to increase with concentration of M, showing that the presence of third element (M) causes suppression of superconducting behaviour of the alloy. The decrease inT _c with increasing concentration of third element (M) may be attributed to the modifications in density of states at the Fermi levelN(E _F), and probable changes in the band structure of the alloy due to addition of the third element (M). Slight difference is noticed when Ti is added to the Ni₃₃ Zr₆₇ alloy. In this caseT _c rises initially and then decreases with concentration of M, showing a peak at aboutx=0.05. This indicates that on addition of Ti, 3d states grow near the Fermi level and hence contribute substantially toN(E _F), favouring superconducting behaviour in this case. The present results forT _c show an excellent agreement with the experimental data. QuadraticT _c equations have been proposed, which provide successfully theT _c values of ternary metallic glasses under consideration. Paper presented at National Conference on Current Trends in Condensed Matter Research, Warangal, India, September 20–22, 2004.     

Unified study and transport properties of simple metals

The resistivity, thermoelectric power at the melting points and temperature variation of resistivity of the liquid alkali metals are studied with local Heine-Abarenkov and the modified Ashcroft pseudopotentials. The parameters of the model potentials are obtained from a unified study of the static and dynamic properties of the metals. The effect of different dielectric function and structure factor on the transport properties is discussed. It is shown that the simple modified Ashcroft pseudopotential reproduces the result fairly well except for Li and Cs.     

Binary and multiparticle electron-electron interaction on the surface

It is shown for the first time that electron-electron scattering of slow electrons with an energy of 10–50 eV at the surface of some metals is mainly an event of binary scattering of particles with conserved total momentum and energy, while analogous scattering at the surface of a semiconductor (n-Si) and an insulator (MgO) is a multiparticle event. A model is proposed, in which the electron subsystem of a solid is characterized by short-range order. Each electron is at the center of a spherical cell and surrounded by nearest neighbors (electrons) with a coordination number of 12. The overlap of the fields of charges gives rise to a negative potential U _c (r) ≈ U _c , which is virtually constant along the coordinate and contains spherical cells with a central field U(r) of individual charges. The value of constant negative potential U _c depends on the extent of electron screening, which is high for metals and low for semiconductors and insulators. In metals, scattering governed by the binary mechanism may take place (i.e., scattering of a primary electron in the central field of an electron of the metal); this is ensured by a relatively small value of constant potential U _c . The electron subsystem of the metal behaves as a Fermi gas of weakly interacting quasiparticles. Electron screening in semiconductors and insulators is insignificant, and constant negative potential U _c is an order of magnitude higher than the analogous potential in metals. Slow primary electrons are scattered in the total field of many charges before they reach the central field of an individual electron. The electron subsystem of a semiconductor and an insulator in the excitation range studied here behaves as an ensemble of strongly interacting particles.     

Dependence of lattice constants and bulk moduli on pseudopotential properties

Using a nearly-free-electron model and model pseudopotentials, an analytical relation between the Wigner-Seitz radius for a metal, r_ws, and the core radius of the model pseudopotential, r_c is derived. In addition, a semi-empirical formula for the bulk moduli is obtained.     

Superconducting state parameters of Cu C Zr100−C metallic glasses

The theoretical investigation of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _c, isotope effect exponent α and effective interaction strength N ₀ V of ten Cu _C Zr_100?C metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Three local field correction functions proposed by Hartree (H), Taylor (T) and Ichimaru-Utsumi (IU) are used in the current investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N ₀ V show weak dependences on local field correction functions. The T _c obtained from IU-local field correction function are found an excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in metallic glasses.     

A non-local extension of the Gaspari-Gyorffy theory for superconductors

We present a theory which extends the Gaspari-Gyorffy theory to include non-local corrections within the framework of the spherical rigid muffin tin approximation. We thereby construct an on-Fermi-sphere pseudopotential similar to that of the simple free electron metals. We apply our theory to Al and NbC for which ²() andT _c are calculated. It turns out that for NbC the local approximation works well whereas for Al non-local corrections are important.     

A simple model for the quantitative evaluation of the XPS line shape asymmetries in nearly free electron and noble metals

We show that the Born approximation for the scattering by a linearly screened simple model “hole” potential, derived by pseudopotential data, is sufficient to provide an accurate evaluation of the XPS line shape asymmetry parameter α. We get a simple analytical close form expression for α as a function of r_s, which emphasizes the role of electronic screening and evidentiates that α is increasing with increasing r_s.     

Structure of some liquid transition metals using integral equation theory

We present the results of calculations of the structure factorS(q) of some liquid 3d transition metals using the self consistent hybridized mean spherical approximation (HMSA) integral equation. The local pseudopotential used is composed of the empty core model and a part that takes care of s-d mixing through an inverse scattering approach to model the interionic pair potential. The results presented are in very good agreement with experiment for most of the systems investigated near freezing, as well as for the noble metals Cu, Ag and Au, thus, confirming the reliability of the pseudopotential in the present integral equation scheme.     

Elastic Scattering of Electrons by a Cut-Off Coulomb Potential at Low Energies

Elastic scattering of electrons by cut-off Coulomb potential U_c(r) is investigated, where U_c(r) = 0, for r > r_c and U_c(r) = ?1/r + 1/r_c for r ≦ r_c. This is first considered in terms of classical, and later quantum mechanical (partial wave) methods in the low energy range 0 ≦ ? ? 1/r_c, where ? is the energy of the free electron. Scattering in this energy region displays a number of particular characteristics, such as back scattering, at certain energies. It can be concluded that some agreement does exist between the classical and quantum mechanical results.     

Quasi-Classical and Classical Cross Sections for the Scattering of Electrons on the Coulomb Cut-Off Potential

The elastic scattering of electrons on the cut-off Coulomb potential U_c(r) = ?1/r + 1/r_c, for r ≦ r_c and U_c(r) = 0, for r > r_c, has been considered. It has been shown that for ε > 0.5/r_c (ε is the energy of free electrons in atomic units) the analytical quasi-classical expressions describe quite well the behaviour of transport, differential and total cross sections for elastic scattering. It has been shown moreover, that in the energy range considered, transport cross section could be determined with practically the same accuracy already by means of classical, analytical expressions. Born approximations show larger deviations from exact quantum calculations.     

Bestimmung der statischen Strukturfunktion von Natrium bei 102 und 149°C

X-ray measurements of the structure functionS(q) on high purity sodium (99.99%) are reported. Data were taken at 102 and 149 °C. An analysis of that part of the curve, in the regionq≦2k _F shows some deviations from the neutron measurements of Gingrich and Heaton. Better agreement is obtained with the experimental values of Orton, Shaw and Williams and with the theoretical “hard core” curve of Ashcroft and Lekner. Using two temperature-dependent pseudopotentials (Schneider and Stoll, Ashcroft) the electrical resistivity is calculated using the conductivity formula of Ziman. These results are generally about 2/3 of the experimental value. This is attributed either to an incorrect atomic form factor of sodium or to an inaccurately known pseudopotential. The measurements confirm Greenfield's determination of the ratio Γ_{146°c/102°c}(q). As a test of the general form ofS(q) curves the radial distribution function is calculated and discussed.     

High frequency cut-offs in superconductivity theory

The meaning of a high frequency cut-off for the Coulomb interaction at ±iω_max with ω_max ≈ E_f is investigated. It is not difficult to justify such a cut-off for nearly-free-electron metals. The real frequency Coulomb pseudopotential corresponding to the usual imaginary axis (μ¹, iω_c) pseudopotential is rigorously derived. It is markedly different from any assumed in previous work.     

Study of superconducting state parameters of amorphous metals by a pseudopotential theory

The theoretical computation of the superconducting state parameters (SSP) viz; electron-phonon coupling strength λ, Coulomb pseudopotential μ ^*, transition temperature T _c , isotope effect exponent α and effective interaction strength N _O V of some monovalent (Cu and Au), divalent (Ca, Sr, Ba, αHg, βHg and Ra) and polyvalent (Lu, Rh, Sc, Y, La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Ac, Th, Hf, Ru, Os, Ir, V, Ta, Pa, Cr, Mo, U, Re, Np and Pu) amorphous metals based on the different groups of the periodic table have been carried out for the first time using the well known Ashcroft’s empty core (EMC) model pseudopotential. Herein, we have employed five different types of local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) to study the exchange and correlation effects on the present investigations. A very strong influence of all the exchange and correlation functions have been observed in the present study. Our results are in fair agreement with documented theoretical as well as experimental data. A strong dependency of the SSP of amorphous metals on the valency Z was found.      

Thermodynamic properties of rhodium at high temperature and pressure by using mean field potential approach

The thermophysical properties of rhodium are studied up to melting temperature by incorporating anharmonic effects due to lattice ions and thermally excited electrons. In order to account anharmonic effects due to lattice vibrations, we have employed mean field potential (MFP) approach and for thermally excited electrons Mermin functional. The local form of the pseudopotential with only one effective adjustable parameter r_c is used to construct MFP and hence vibrational free energy due to ions – F_ion. We have studied equation of state at 300 K and further, to access the applicability of present conjunction scheme, we have also estimated shock-Hugoniot and temperature along principle Hugoniot. We have carried out the study of temperature variation of several thermophysical properties like thermal expansion (β_P), enthalpy (E_H), specific heats at constant pressure and volume (C_P and C_V), specific heats due to lattice ions and thermally excited electrons (C_V^ion and C_V^el, isothermal and adiabatic bulk moduli (B_T and B_s) and thermodynamic Gruneisen parameter (γ_th) in order to examine the inclusion of anharmonic effects in the present study. The computed results are compared with available experimental results measured by using different methods and previously obtained theoretical results using different theoretical philosophy. Our computed results are in good agreement with experimental findings and for some physical quantities better or comparable with other theoretical results. We conclude that local form of the pseudopotential used accounts s-p-d hybridization properly and found to be transferable at extreme environment without changing the values of the parameter. Thus, even the behavior of transition metals having complexity in electronic structure can be well understood with local pseudopotential without any modification in the potential at extreme environment. Looking to the success of present scheme (MFP + pseudopotential) we would like to extend it further for the study of liquid state properties as well as thermophysical properties of d and f block metals.     

Superconducting state parameters of indium-based binary alloys

Our well-recognized pseudopotential is used to investigate the superconducting state parameters viz: electron-phonon coupling strength λ. Coulomb pseudopotential μ*, transition temperature T _c, isotope effective exponent α and interaction strength N ₀ V for the In_1−x Zn _x and In_1−x Sn _x binary alloys. We have incorporated six different types of local field correction functions, proposed by Hartree, Taylor, Vashistha-Singwi, Ichimaru-Utsumi, Farid et al and Sarkar et al to show the effect of exchange and correlation on the aforesaid properties. Very strong influence of the various exchange and correlation functions is concluded from the present study. The comparison with other such theoretical values is encouraging, which confirms the applicability of our model potential in explaining the superconducting state parameters of binary mixture.     

Application of a structure factor-potential relationship to the electrical resistivity of the liquid alkali metals

In the Ziman formulation for the electrical properties of liquid metals, the resistivity depends on an average of the product of the structure factor and the pseudopotential. Ascarelli, Harrison and Paskin have derived a relationship for small wave vector between the structure factor and the pseudopotential for liquid metals such as the alkali metals. This formulation has been used over the entire range of wave vector (k = 0 to 2k _F). The resistivities of Na, K, Rb and Cs calculated with no adjustable parameters are within 25% of the observed values, while Li is underestimated by about a factor of five. The temperature dependencies of all but Li (which is anomalously non-linear) are in similar agreement with experiments made at constant volume.     

Determining Liquid Structure from the Tail of the Direct Correlation Function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the tail of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the out projection of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.     

Die Sprungtemperatur von Supraleitern

An iteration procedure allows to find an equation for the critical temperatureT _c of superconductors starting from the linearized Eliashberg equations without using any cutoff parameters or a Coulomb pseudopotential. Explicit calculation ofT _c for a simple model leads to Morel, Anderson and McMillan's^1,2 expression thereby allowing for a physical interpretation of the commonly used approximation for the Coulombpseudopotential.     

Surface tension compressibility relation

The generalized van der Waals result for the surface tension of a simple liquid-vapour interface is shown to follow from the exact statistical mechanical expression with the approximation c(r, z ₁, z ₂) = c(r, n(z¯)). Using the statistical mechanical equation for the derivative of the density profile we derive the relation between the surface tension and the isothermal compressibility, to lowest order in T-T_c .