Pseudopotential in metals and alloys

In this communication, the pseudopotential investigation of, the various properties of non-transition metals and alloys, is discussed. Various one parametric model pseudopotentials, derived from well known spherical functions s_l(x), are employed in the calculations. Many recurrence relations of the s_l(x) function have been described. The effects of exchange and correlation on conduction electrons are also considered separately by using different dielectric screenings in various properties. The ion-ion interaction, force constants, phonon spectrum, temperature coefficient of Knight shift and electronic transport coefficients of certain metals and alloys are evaluated. The results are compared with available experimental values. Generally good agreement is achieved. The screening charge density of certain metals in low and high density region are also determined.     

Order-disorder transformation in the binary MPt3 and ternary CuMPt6 (M=3d metals) alloys

The order-disorder(O-D) transformation in the binary MPt₃ and the ternary CuMPt₆ (M=3d transition metals) alloys were studied. The O-D transformation temperatures (T_c) were calculated by combining the method of pseudopotentials with the static concentration waves. The method originally proposed by Khachaturyan [Progress in Materials Science, vol. 22, Pergamon Press Ltd., Oxford, 1978, pp. 47-49; Phys. Met. Metallography 13 (1962) 493; Sov. Phys. Solid State 5 (1963) 16; Sov. Phys. Solid State 5 (1963) 548] was applied to the case of ternary CuMPt₆ alloys by using the concept of a pseudoatom. It is found that this model predicts results that are consistent with the experimental data.     

Structure of the (0001) surface of α-Al2O3 from first principles calculations

Fully self-consistent ab initio calculations based on pseudopotentials are used to study the structure and energetics of the basal-plane surface of α-Al₂O₃. The calculated forces on the atoms are used to relax the atomic positions to equilibrium. It is shown that surface relaxations are very large and lead to a reduction of the surface energy by over a factor of two. The results support the validity of earlier work based on pair-interaction models.     

Thermoelastic parameter αKT of sodium chloride at high pressure and high temperature

Two different potential models to the molecular dynamics (MD) simulations have been applied to investigate the thermoelastic parameter αK_T of sodium chloride (NaCl) under high pressure and high temperature. The first one is the shell model (SM) potential that due to the short-range interaction when pairs of ions are moved together as is the case in that polarization of a crystal due to the motion of the positive and negative ions, and the second one is the two-body rigid-ion Born–Mayer–Huggins–Fumi–Tosi (BMHFT) potential with full treatment of long-range Coulomb forces. Particular attention is paid to the comparison of the SM- and BMHFT-MD simulations with the Debye model for the first time, and this model combines with ab initio calculations within local density approximation (LDA) and generalized gradient approximation (GGA) using ultrasoft pseudopotentials and a plane-wave basis in the framework of density functional theory (DFT), and it takes into account the phononic effects within the quasi-harmonic approximation. Note that the MD calculated volumes using SM model is somewhat larger than both the DFT and experimental volumes despite not considering the temperature effect. Compared with SM potential, the MD simulated 300 K isotherm of NaCl with BMHFT potential is very successful in reproducing accurately the measured volumes and the GGA calculated volumes. Generally, it is found that there exist minor differences between the LDA and GGA computed the thermoelastic parameter αK_T of NaCl, with both average results giving good agreement with SM-MD simulations. At an extended pressure and temperature ranges, the variation of thermoelastic parameter αK_T which play a central role in the formulation of approximate equations of state has also been predicted. The properties of NaCl are summarized in the pressure range of 0–300 kbar and the temperature up to 2000 K.     

A one parameter model potential for noble metals

A phenomenological one parameter model potential which includes s-d hybridization and core-core exchange contributions is proposed for noble metals. A number of interesting properties like liquid metal resistivities, band gaps, thermoeletric powers and ion-ion interaction potentials are calculated for Cu, Ag and Au. The results obtained are in better agreement with experiment than the ones predicted by the other model potentials in the literature.     

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.     

Thermoelektrische Eigenschaften reiner Metalle in der Umgebung der Schmelztemperatur

The thermoelectric power of the face-centered cubic metals copper, silver, gold and aluminium was measured in the vicinity of the melting temperature. For all four metals mentioned a discontinuous change of the absolute Seebeck coefficient towards more positive values was found at the melting point. — Values of the thermoelectric power of liquid metals may be calculated with a model using the correlation function of the ions and their pseudopotentials as proposed byZiman. The results agree, at least qualitatively, with the measured values.     

Surface energies of metals in both liquid and solid states

Although during the last years one has seen a number of systematic studies of the surface energies of metals, the aim and the scientific meaning of this research is to establish a simple and a straightforward theoretical model to calculate accurately the mechanical and the thermodynamic properties of metal surfaces due to their important application in materials processes and in the understanding of a wide range of surface phenomena. Through extensive theoretical calculations of the surface tension of most of the liquid metals, we found that the fraction of broken bonds in liquid metals (f) is constant which is equal to 0.287. Using our estimated f value, the surface tension (γ_m), surface energy (γ_SV), surface excess entropy (−dγ/dT), surface excess enthalpy (H_s), coefficient of thermal expansion (α_m and α_b), sound velocity (c_m) and its temperature coefficient (−dc/dT) have been calculated for more than sixty metals. The results of the calculated quantities agree well with available experimental data.     

Statistical-mechanical perturbation theory for liquid metals

The techniques of statistical mechanical perturbation theory are applied to liquid metals. An ion-ion repulsive pair potential is determined from an experimental structure factor curve at a temperature β₀=1/kT₀. The theory then permits the prediction of radial distribution functions, structure factors, compressibilities, and other properties at all liquid temperatures. As a preliminary test of the theory, it has been used to calculate the isothermal compressibilities of Na, Hg and Ga. The results are in very good agreement with the experimental values, which for the last metals differ from earlier theoretical predictions by almost a factor of five.     

Hyperfine fields in iron-metalloid ferromagnetic metals

A new coordination parameter Z_eff is defined at each inequivalent iron site in the interstitial iron-metalloid ferromagnetic metals which uniquely determines the hyperfine field at that site with considerable accuracy. The dependence of Z_eff upon bonding lenghts is defined and can be directly used to generate hyperfine field distributions for amorphous aggregates. It thereby promises to provide a fairly quantitative bridge between computer models and hyperfine field probes in iron metglasses.     

Validity of model-potential approach for the expanded liquid alkali metals

The liquid density along the saturation line is calculated for Na, K, Rb and Cs. Good results are obtained in sodium in the whole experimental range T ? 0.85 T_c (T_c is the critical temperature). The observed discrepancy in the heavier alkali metals for T ? 0.75 T_c is tentatively related to recent speculations.     

Ab initio calculations on the structural and lattice dynamical properties of TmX (X=As,P) compounds

The structural and lattice dynamical properties of TmX (X=As, P) compounds were investigated using normconserving pseudopotentials within the generalized gradient approximation correction (GGA) of Perdew–Burke–Ernzerhof (PBE) in the framework of density functional theory (DFT). The structural parameters (a₀, B, B′, E_coh) were determined through total energy and interatomic force minimization and the overall agreement was found to be good. The pressure dependence of the ratios of normalized lattice parameters a/a₀, normalized volume V/V₀, bulk modulus, elastic constants, Zener anisotropy factor, Poisson's ratio, Young's modulus, shear modulus, and the brittleness were presented and discussed. The thermodynamical properties such as thermal expansion, heat capacity, Debye temperature, and Grüneisen parameter were calculated employing the quasi-harmonic Debye model at different temperatures (0–1000 K) and pressures (0–30 GPa). The phonon dispersion curves and corresponding density of states (DOS) of TmX (X=As, P) were also obtained, and the salient results were interpreted.     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

Central cell effects on the polarizabilities of shallow donors in silicon

With the Topp and Hopfield form for the ionic pseudopotentials, the screened impurity pseudopotentials of the shallow donors P, As and Sb in silicon are obtained in closed form in the linearized Thomas-Fermi model. The results are compared with the screening using a k-dependent dielectric function. Using these impurity pseudopotentials in the multivalley effective mass equation, the binding energies of these donors in Si are estimated variationally. Adopting the Hasse variational method, the polarizabilities of the P, As and Sb donors in Si are computed and are found to be in excellent agreement with the polarizability values of isolated P and Sb in Si, deduced from recent piezocapacitance measurements.     

Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Orpa calculation of structure factors of liquid alkali metals using CHS as reference system

Calculations of structure factors of liquid alkali metals are presented in the optimized random phase approximation with charged hard spheres as reference. The method avoids the artificial truncation of the electron mediated attractive term after q = 2k_f and produces good temperature dependent structure factors for these liquid metals.     

Theoretical investigations of structural, elastic and thermodynamic properties for PtN2 under high pressure

We have investigated structural and elastic properties of PtN₂ under high pressures using norm-conserving pseudopotentials within the local density approximation (LDA) in the frame of density-functional theory. Calculated results of PtN₂ are in agreement with experimental and available theoretical values. The a/a₀, V/V₀, ductility/brittleness, elastic constants C_ij, shear modulus C′, bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio σ and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study thermodynamic properties of PtN₂. The thermal expansion versus temperature and pressure, thermodynamic parameters X (X=Debye temperature or specific heat) with varying pressure P, and heat capacity of PtN₂ at various pressures and temperatures are estimated.     

On the correlation between droplet volume and irradiation conditions in the laser forward transfer of liquids

The analysis of the morphology of droplets printed through laser-induced forward transfer (LIFT) of liquid films shows that: (i)?the droplet volume is linearly related with the energy of the laser pulse that originated it, (ii)?the liquid ejection process is activated by an energy density threshold?F ₀, and (iii)?the droplet volume can be correlated with a dimensional parameter of the laser beam through an oversimple model that states that the amount of printed liquid equals the liquid contained in the cylindrical portion of an irradiated film whose base corresponds to the cross-sectional area of the beam with energy density higher than?F ₀. Although these issues seem to describe correctly the LIFT process, some problematic instances arise from them. Thus, the linear relation between droplet volume and laser pulse energy seems to be inconsistent with the existence of the threshold?F ₀. On the other hand, the compatibility between the model and the aforementioned linear relation requires to be explained. Finally, the model is based on the idea that transfer takes place in a way analogous to the LIFT of solid films, but time-resolved imaging studies have demonstrated that liquid ejection follows a dynamics which seems quite unsuited with that idea. In this work previous results are re-analyzed and new experiments are performed in an attempt to clarify these questions. It is then shown that the inconsistencies pointed out are only apparent, and that the validity of the model is limited to irradiation conditions where the beam dimensions are significantly larger than the thickness of the liquid film. Furthermore, an explanation is provided for the dependence of the success and failure of the model on those irradiation conditions in terms of the diverse liquid ejection dynamics taking place.     

Coherence effects in low energy Na*(3p)+Na+ scattering: Experiment and semiclassical calculations

Pronounced polarization effects have been observed in inelastic collisions of laser state-prepared Na^*(3p,M _L) with Na⁺ leading to Na^*(3d) for the energy rangeE _CM=20–45 eV. Using linearly polarized light the dependence of the inelastic process on the alignment of the electronic charge cloud of the Na^*(3p) prior to the collision has been measured. In studies with left and right hand circularly polarized light the angular momentum transferred in the collision process has been determined. The results are compared with similar data for the 3p→3s deexitation process studied previously [6]. The density matrix of the Na^*(3p) state has been evaluated with respect to the collisional excitation to Na^*(3d). Semiclassical calculations based on the coupled channel impact parameter approximation using pseudopotentials [7] and nonadiabatic rotational coupling elements for the Na ₂ ^* system [12] have been performed. The agreement with the experimental results is good, in particular for the higher collision energies.