A relation between structure and pair potential for liquid metals

We emphasize the importance of considering the relationship between the structure of a liquid and the interatomic potential directly from the point of view of wave vector space (k space). Although the Ornstein-Zernike equation was not originally derived from this point of view, this equation when transformed into the k-space representation has direct physical content, when coupled with a normal mode representation according to the approaches of Pines and Bohm (1952), and Percus and Yevick (1958). These normal modes are defined isothermally, and the relation to the dynamical modes of the liquid is discussed. The use of a simple k-space relationship between the transform of the Ornstein-Zernike direct correlation function and the transform, V_k , of the interatomic potential is explored. This leads to a correspondingly simple relationship between the structure factor and the interatomic potential. It is equivalent to a generalized Debye-Hückel equation and is expected to be valid only under special circumstances; namely, where the potential is long range in a particular sense and the small k behaviour of V_k is dependent mainly upon this long-range behaviour and relatively insensitive to details of the potential at short distances. It is noted that these conditions appear to be met reasonably well for the liquid alkali metals. The comparison of theory and experiment is somewhat uncertain because of incomplete experimental data on the structure factor as well as unresolved theoretical issues.     

Multiphonon contribution to the structure factor of metals

The structure factor of Na is calculated including two-phonon terms and the Debye-Waller factor. The result is compared with the one-phonon approximation usually employed to evaluate the electronic transport coefficients. This multiphonon contribution can amount to 13 per cent at the melting point and 10 per cent at room temperature in the transport sensitive region of wave vector 1.5 k_F < q < 2 k_F, where k_F is the Fermi wave vector. We conclude that calculations of electronic transport coefficients of metals intended to attain a precision better than 10 per cent above the Debye temperature must take into account the contributions of the Debye-Waller factor and the two phonon terms.     

Molecular dynamics of liquid alkaline-earth metals near the melting point

Results of the studies of the properties like binding energy, the pair distribution function g(r), the structure factor S(q), specific heat at constant volume, velocity autocorrelation function (VACF), radial distribution function, self-diffusion coefficient and coordination number of alkaline-earth metals (Be, Mg, Ca, Sr and Ba) near melting point using molecular dynamics (MD) simulation technique using a pseudopotential proposed by us are presented in this article. Good agreement with the experiment is achieved for the binding energy, pair distribution function and structure factor, and these results compare favourably with the results obtained by other such calculations, showing the transferability of the pseudopotential used from solid to liquid environment in the case of alkaline-earth metals.     

The influence of pair potentials on the structure of polyvalent liquid metals

The structure factors of some polyvalent liquid metals show a shoulder on their first peak. We explain these shoulders on the basis of ionic pair potentials : a shoulder is expected near the wave vector 2k_F, the wave length of the oscillations in the metallic pair potentials. To show this quantitatively, we used the “optimized random phase approximation” of Andersen et al.     

The electron transport properties of pure liquid metals

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 of the perturbation series for ρ _L is discussed, and it is suggested that corrections for higher order terms can be minimized by making the pseudopotential as near as possible to the t-matrix of an ion.

The anomalous properties of Hg are then discussed, in the light of the work of Mott (1966). In this connection it is shown that Edwards' formula (1962) for ρ _L, in which the Fermi velocity, v _F, is taken to be that of a free electron, ?k _F/m, despite deviations from the free-electron curve for ?(k), can be derived by using the expectation value of the current operator in place of e v _F in the Boltzmann equation. This modification of the elementary theory allows the Hall constant of a liquid metal to deviate from 1/nec, as found experimentally.     

The absolute thermoelectric power of polyvalent liquid metals

Results on the measurement of the absolute thermoelectric power of ten polyvalent liquid metals (Al, Bi, Cd, Ga, Hg, In, Pb, Sn, Tl, Zn) from their melting points to about 750°C are reported. The electrical resistivities and the absolute thermoelectric powers of these metals have been calculated using the latest available data on structure factor and Harrison and Animalu form factors. These are compared with the experimental values. It is seen that whereas the predicted and experimental values of the electrical resistivities are in reasonable agreement, those for the absolute thermoelectric power are not. It is suggested that the experimental data on the absolute thermoelectric powers and the resistivities of liquid metals may be used to find the magnitude of the form factor at K = 2k _F.     

Knight shifts of metals in the liquid state

A single orthogonalized plane wave calculation has been made, to zero order in the pseudopotential, of the direct contact Knight shift for 30 liquid metals. The average deviation from experimental values is approximately 15%. Larger unexplained divergences occur for Cu and Hg. In addition it is shown that to zero order in the pseudopotential the factorΩP _F in the Knight shift describing the electron density at the nucleus is almost unaffected by thermal expansion.     

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.     

Quantum-mechanical calculations based on density functional theory

The basic concepts of density functional theory (DFT) together with the local density approximation (LDA) and the recent improvement in form of the generalized gradient approximations (GGA) are discussed. Band structure calculations using the full-potential linearized augmented plane wave (FP-LAPW) method are presented in relation to pseudopotential schemes both corresponding to T=0. For finite temperatures the most advanced technique is the Car-Parrinello (CP) molecular dynamics (MD) approach, e.g. in its projector augmented wave (PAW) implementation. In CP-MD simulations nuclear motion and the electronic degrees of freedom are treated within one formalism. Such DFT calculations are illustrated for selected examples, including the breathing mode of BaBiO₃. the phase transition in SrTiO₃ and VO₂ and the Li diffusion in the superionic conductor Li₃N studied by conventional and CP molecular dynamics.     

Dynamics of Liquid Lithium Atoms. Pseudopotential and EAM-Type Potentials

It is generally accepted that the complicated character of the interparticle interaction in liquid metals is reproduced most correctly by many-particle potentials of the EAM-type (embedded atom model) interparticle interaction. It is shown that in the case of liquid lithium near the melting temperature (T_m = 453.65 K), the spherical pseudopotential provides a better agreement with experimental data on elastic and inelastic X-ray scattering as compared to the known EAM potentials. The calculations of the dynamic structural factor and spectral densities of the longitudinal and transverse atomic currents lead to the conclusion that although the pseudopotential and EAM potentials generate a certain qualitative correspondence in the features of collective dynamics, the interparticle interaction of the spherical type reproduces correctly the general form of the dynamic structure factor in a certain wavenumber range, as well as the dispersion relation for collective excitations.     

Longitudinal Wave Propagation in Dielectric Waveguide Array

Based on the established rigorous theory for two-dimensionally periodic (2DP) medium, Longitudinal propagation in Dielectric Waveguide Array (DWA) was analyzed in detail. Firstly, given longitudinal wave vector (k _z), Brillouin dispersion relations between transversal wave vectors were analyzed. Interactions between space harmonics were also studied. Secondly, on condition that transversal wave vector k _x equaled k _y, dispersion relations between longitudinal and transversal wave vectors were analyzed in detail. Because of interactions between space harmonics increasingly getting stronger with k _z or modulation coefficients increasing, stop-bands could be distinctly displayed and thus longitudinal propagation in DWA could be comprehensively analyzed. The applications about longitudinal propagation in DWA were also discussed.     

Analysis of the liquid structure of 3d transition metals from the Wills-Harrison model

Calculations of the liquid structure of 3d transition metals from the effective pair interactions of Wills and Harrison are performed by using the optimized random phase approximation in order to point out the influence of thes-electron pseudopotential on the repulsive and attractive forces governing the liquid structure. Our results are compared to those obtained in the Weeks, Chandler Andersen approximation and in the thermodynamic variational method.     

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.     

A modified Ashcroft pseudopotential: application to aluminium

Unified study of the different properties of metals clearly reveals the inadequacy of the empty-core Ashcroft pseudopotential even in the case of simple metals. In the present paper we propose a modification of the one-parameter Ashcroft pseudopotential by assuming the parameterr _c to be wave vector-dependent. This introduces a simple modification of the electron-ion pseudopotential in the reciprocal space. The corresponding potential in the configuration space shows that the abrupt change in the Coulomb potential atr=r _c is replaced by a continuous change spread over a small region near the core boundary. The present model has been used to make a unified study of Al and is found to be a significant improvement over the simple Ashcroft model. The agreement between the calculated and experimental values is found to be quite satisfactory.     

Magnetic structure of Ce<Subscript>2</Subscript>Fe<Subscript>17 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> intermetallic compounds

The magnetic structure of intermetallic compounds Ce₂Fe_{17 − x} Mn _x (0 ≤ x ≤ 3) was studied using neutron diffraction. The neutron diffraction patterns measured at 4.2 K contain satellites indicating a modulated structure with the wave vector k = [0, 0, τ]. As the concentration x increases, the value of τ increases, while the average magnetic moment of Fe/Mn atoms decreases. A change in the magnitudes of the average magnetic moment and wave vector k is explained by competition between exchange interactions at distances of nearest neighbor transition element atoms.     

On the structural stability of metallic glasses

We discuss the various possibilities advanced to account for the structural stability of metallic glasses. Using a formalism based on the pseudopotential theory and the Gibbs-Bogoliubov inequality we calculate the free energies and free energies of formation for the glassy phase of MgCa at various concentrations and compare these results with those for the corresponding solid and liquid phases of the same system. Subsequently, we attempt to explain the stability of the metallic glasses by noting a matching between the positions of the first peakq _m in the relevant structure factor and the maximumq _s in the relevant screened pseudopotential.The major part of this work was done in the H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, England     

TiN多型体高压相变的第一性原理计算

基于密度泛函理论框架下的赝势平面波方法,计算了B1(氯化钠结构)、B2(氯化铯结构)、B3(闪锌矿结构)、B_k(六方氮化硼结构)、B_h(碳化钨结构)和B8₁(砷化镍结构)6种TiN多型体的晶体结构、体积弹性模量和相对稳定性.计算指出,不存在B4(纤锌矿)结构的TiN.通过不同外压下的晶格弛豫得到每种结构的焓,发现外压 关键词： 氮化钛 赝势 高压相变 密度泛函理论     

Effect of an electric field on the surface tension of a liquid at low temperatures

An external electric field changes the dispersion law of waves on the surface of a liquid. Besides the usual capillary term (∝k ³, k is the wave number) and gravitational term (∝k), a term quadratic in the wave vector appears in the expression for the square of the frequency in a homogeneous field. These excitations are associated with the variation of the coefficient of surface tension of the liquid at low temperatures. In the case of a large field tangent to the surface, the correction is proportional to T ^8/3, unlike the T ^7/3 correction in the absence of a field. Zh. éksp. Teor. Fiz. 111, 1369–1372 (April 1997)     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

Volume change,lattice strain and non-linear screening in dilute heterovalent alloys: study of A1Li

The electron - liquid pseudopotential theory is used together with the lattice statics method to calculate the lattice distortion around a solute atom in a simple metal host. It is found that for a heterovalent solute not only the third, but also the fourth order non-linear screening contributions to the displacing forces have to be retained in determining the long range displacement field. Our diffuse elastic neutron scattering data for $\text{Al}$Li single crystals show a particular structure near the (110) point in wave-number space, and also confirm the slight contraction of the average lattice spacing on dissolving Li atoms. By using local ion-electron model potentials, calculated for pure Al and Li metals, the origine of this peculiar contraction could be clarified and the structure in the cross section curve is reproduced.