Local Field Correction Functions Research Articles

On the study of electrical transport properties of some liquid metals by pseudopotential method

ABSTRACT Our recently evolved pseudopotential is used to study the electrical transport properties such as electrical resistivity ( ρ ), thermal conductivity ( σ ) and thermoelectric power ( TEP ) of some monovalent (Li, Na, K, Rb, Cs), divalent (Mg, Zn, Ca) and polyvalent (Al, Ga, In, Pb, Sn, Bi, Sb) liquid metals. The model potential theory in conjunction with Ziman, mean free path, t-matrix, and Kubo models are implemented in the above-mentioned work for the first time. The Taylor’s local field correction function (T) is taken for observing the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals with Hartree dielectric function (H). The presently computed findings are extremely comparable with available data, either theoretical or experimental results that exist in the literature.

Structure-induced order – disorder transformation in Cd – Na liquid alloys

Abstract The origins of the S-shaped entropy of mixing and order – disorder transformation in Cd –Na liquid alloys have been investigated within a first-principle approach of a pseudo-potential perturbation scheme with the Gibbs–Bogoliubov variation technique.We find that the deepening of the structure part of the entropy around the stoichiometric composition (c Na ≈ 0.33) is responsible for the S-shaped entropy and suggests the existence of short-range order in the liquid state. The role of the local-field correction function, G(q), of conduction electrons on the entropy of mixing is examined. The impact of G(q) on partial structure factors is more visible towards low q (q → 0) than at higher q.

Investigation of some basic thermodynamic properties of Na-K alloy

Investigation of thermodynamic of liquid binary alloys using pseudopotential theory is reported. The potential suggested by Fiolhais et al. with its individual parameters is used for the entire calculation. A transferability of the potential from the solid to liquid medium is achieved for the presently reported binary alloy. The internal energy components, Helmholtz free energy, entropy, and total energy at various proportions of the participating alkali metals are included in the study. The comparison with the other data has been shown in the present article. Exchange and correlation effect is also tested with the help of various local field correction functions.
 BIBECHANA 18 (2) (2021) 1-8

A unified study of electrical transport properties of some liquid metals by pseudopotential method

A well-recognized local pseudopotential is utilized to study the electrical transport properties such as electrical resistivity (ρ), thermal conductivity (σ) and thermoelectric power (TEP) of some liquid metals. The model potential theory in combination with Ziman, mean free path and Kubo models are implemented in the aforesaid study. The Taylor’s local field correction function is taken for studying the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals. The computed data is found highly appreciated order with available either theoretical or experimental outcomes wherever exits.

A Variational Technique for Thermodynamics of Liquid K(1-x)Rbx Alloys

Liquid K_(1-x) Rb_x binary alloys with various thermodynamical proportions of participating elements are investigated. The properties of thermodynamic interest are included in the study. The internal energy (Fint), Helmholtz free enrgy (FH) and the entropy (S) have been calculated in a concentration range from X=0.0 to X=1.0 increasing in a step of 0.1 in the present work. Apart from the internal energy (Fint), various contributions to this energy are also calculated and separately depicted in the present article. A variational approach has been adopted for the present calculation. A single potential with a set of two parameters is used for the calculation of all properties of the alloys. Static Hartree local field function (H) is used to consider screening effect. Various local field correction functions are used to take into account the exchange and correlation effect. Comparison with experimental data at some concentration shows the good agreement with the presently obtained data. With the help of current results, the applied model potential found very suitable with individual parameters for thermodynamical study. As the present results provide the data even where minimum availability of the experimental findings, it can serve as a data base for the future calculation which deals with thermodynamics of the liquid alloys. Present results allow one to get proportion based tuned properties of the K_(1-x) Rb_x for different requirements.

A study of collective modes of Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass and estimation of thermodynamic and elastic properties using pseudopotential theory

The collective modes of Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass (BMG) have been theoretically studied using pseudopotential formalism. Shaw’s optimized model potential is used to describe effective interactions. Five different forms of the local field correction functions, viz. Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) have been exploited with modified Bhatia-Singh (BS) computational approach to examine the relative influence of exchange and correlation effects and to reproduce longitudinal and transverse modes of phonon eigenfrequencies using phonon dispersion curves (PDCs). Important thermodynamic and elastic properties are calculated by long-wavelength limits of phonon modes. The comparisons of such properties with earlier reported data are shown good agreement.

Calculation of electrical resistivity of Na-based liquid binary alkali alloys

Electrical resistivity, ρ, for Na-based liquid alkali binary alloys namely NaxK1−x, NaxRb1−x, NaxCs1−x and NaxLi1−x are calculated using the extended Ziman's formula developed by Faber and Ziman. Form factor, Vij(q), and partial structure factor, Sij(q), are the main ingredients of this calculation. For Vij(q), we have chosen Bretonnet-Silbert (BS) pseudo-potential with Ichimaru-Utsumi (IU), and Vashishta-Singwi (VS) local field correction functions. For Sij(q), we have chosen linearized Weeks-Chandler-Andersen (LWCA) thermodynamic perturbation theory. From the comparison of the calculated results of ρ with available experimental data and other theoretical values, a good qualitative consistency is found except for liquid NaxLi1−x alloys. We observe that VS local field correction function along with LWCA theory provides much better results than those obtained with IU local field correction near melting point at the liquid state. Calculated results at temperatures far from the melting curve are deviated much from experimental data. Explanation behind this discrepancy requires a further study with more sophisticated theory.

Thermodynamical Properties of K1-XRbX Alloys in Liquid State

One of the K-based binary alloys – K1-XRbX has been studied in the present work. Various thermodynamical properties are computed with the help of pseudopotential theory. The combination of successive elements of the alkali group has been selected for the formation of binary alloys. The well-behaved pseudopotential proposed by Fiolhais et al. is used for the whole calculation. Eight various local field correction functions (namely Hartree (H), Hubbard-Shame (HS), Nagy (N), Vashishtha-Singwi (VS), Taylor (T), Sarkar et al. (S) Ichimaru-Utsumi (IU) and Farid et al .(F) are employed to determine the effect of exchange and correlation on bare ion potential. The present thermodynamical study is based on the successful approach suggested by Gibbs-Bogoliubov (GB). The article includes the calculation of different parts of energy (E), entropy(S) and Helmholtz free energy (EH). The good agreement of the present data with the other theoretical data as well as experimental data is found.

Vibrational Dynamics of Pd39Ni10Cu30P21Bulk Metallic Glass

In the present study, we report the vibrational dynamics of Pd39Ni10Cu30P21 bulk metallic glass in terms of the phonon Eigen frequencies of the localized collective excitations using Show’s optimized model pseudopotential at room temperature. While theoretical effective atom model (EAM) with Wills-Harrison (WH) approach are used for the computation of the interatomic pair potential (PP) and pair correlation function (PCF). The phonon dispersion curves are computed through Hubbard-Beeby (HB) approach. Various elastic and thermodynamic properties have been reported from the elastic limit of the phonon dispersion curves. The screening dependency on the aforesaid properties is studied by adopting different kinds of local field correction functions

Elastic Properties of Zr<sub>50</sub>Cu<sub>43</sub>Ag<sub>7</sub> Bulk Metallic Glass Using Pseudopotential Theory

Using Hubbard-Beeby approach for phonon dynamics, in conjunction with our recently proposed model pseudopotential; phonon frequencies for longitudinal and transverse modes are computed and associated elastic properties of technologically important Zr-based Zr50Cu43Ag7 bulk metallic glass (BMG) are evaluated. Five different forms of the static local field correction functions, viz., Hartree etal. (H), Taylor et al. (T), Ichimaru and Utsumi et al. (IU), Farid et al. (F) and Sarkar et al. (S) are employed to investigate the influence of the screening effect on the vibrational dynamics of Zr50Cu43Ag7 BMG. Results for bulk modulus, modulus of rigidity, Poisson's ratio, Young modulus, propagation velocity of elastic waves and dispersion curves are studied. The theoretical computations are found to be in good agreement with the available experimental results, which confirms the use of our model pseudopotential to study elastic properties of such a glassy system.

Theoretical Investigations of Some Physical Properties of HgX (X = S, Se and Te) Semiconducting Compounds

In the present work, we have investigated total energy, bulk modulus, elastic constants, pressure derivatives of elastic constants and pressure derivative of bulk modulus of HgX (X=S, Se and Te) semiconducting compounds using higher-order perturbation scheme with the application of our own proposed model potential. To consider exchange and correlation effect to the dielectric function, the local-field correction function proposed by Farid et al is employed in the present study. In most of the cases the experimental and other theoretical results of the aforesaid physical properties of the HgX are not available in the literature and hence this study provides a better set of theoretical results of the physical properties of the materials for future comparison either with theoretical or experimental results.

Electrical Transport Properties of K-Based Alkali Liquid Binary Alloys

The electrical transport properties viz. the electrical resistivity (ρ), the thermoelectric power (TEP) and thermal conductivity (σ) of three K-based alkali liquid binary alloys viz. K1-XNaX, K1-XRbX and K1-XCsX were calculated from the pseudopotential form factors and Percus-Yevic (PY) hard sphere structure factors of Ashcroft and Langreth. The well recognized empty core model (EMC) pseudopotential of Ashcroft is used for the first time with seven local field correction functions due to Hartree (H), Hubbard-Sham (HS), Vashishta-Singwi (VS), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) in the present computation and found suitable for such study. It is conclude that, the comparison of present and experimental findings is highly encouraging.

Electrical Transport Properties of K-Based Alkali Liquid Binary Alloys

The electrical transport properties viz. the electrical resistivity (ρ), the thermoelectric power (TEP) and thermal conductivity (σ) of three K-based alkali liquid binary alloys viz. K1-XNaX, K1-XRbX and K1-XCsX were calculated from the pseudopotential form factors and Percus-Yevic (PY) hard sphere structure factors of Ashcroft and Langreth. The well recognized empty core model (EMC) pseudopotential of Ashcroft is used for the first time with seven local field correction functions due to Hartree (H), Hubbard-Sham (HS), Vashishta-Singwi (VS), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) in the present computation and found suitable for such study. It is conclude that, the comparison of present and experimental findings is highly encouraging.

Effect of pressure on some optical properties of GaxIn1−xP semiconductors

A theoretical procedure is presented for the study of optical properties of ternary alloy GaxIn1−xP. The calculations are based on the pseudopotential formalism in which local potential coupled with the virtual crystal approximation (VCA) is applied to evaluate the effect of pressure on the optical properties like refractive index, electronic polarizability, plasmon energy, dielectric constant and equation of state for gallium concentration x = 0, 0.25, 0.50, 0.75 and 1 of the ternary alloy GaxIn1−xP. To incorporate the screening effect, local field correction functions due to Hartree, Taylor, Ichimaru et al. and Nagy are employed. The refractive index, electronic polarizability and dielectric constant computed for the parent binary compounds GaP and InP are in satisfactory agreement with the experimental report. It is seen that the refractive index of GaxIn1−xP decreases nonlinearly with the increase in pressure. The results obtained using Hartree's screening functions are not very close to the experimental data as it does not include any exchange and correlation effects. Overall good agreement with the experimental and other theoretical findings confirms the application.

Temperature Dependent Surface Properties of Liquid Alkali Metals

Temperature dependent surface properties like surface tension (γ) and surface entropy (SV) of liquid alkali metals are studied in the present paper. Our newly constructed parameter free model potential is used to describe the electron-ion interaction. To see the influence of local field correction function on surface properties of liquid alkali metal, we have used Sarkar et al local field correction function. The present results are found in good agreement with available experimental data as well as other theoretical data. Lastly we conclude that our model potential is capable to explain surface properties of liquid alkali metals.

Refractive Index of BAs<sub>1-x</sub>P<sub>x</sub> Semiconductors

Ternary alloys of group III-V semiconductors have important applications in fabrication of electro-optical devices. Their refractive index and related optical properties are of attractive interest in theoretical and experimental study. According to the Philips scale of iconicity, BP (fi =0.006) and BAs (fi =0.002) are the most covalent of the III-V semiconductors and there are interesting consequences of this property. We present a theoretical procedure for the study of refractive index of ternary alloy BAs1-xPx. The calculations are based on the pseudopotential formalism in which local potential coupled with the virtual crystal approximation (VCA) is applied to evaluate refractive index for the entire range of the alloy composition x of the ternary alloy BAs1-xPx. To incorporate screening effect, Nagy’s local field correction function has been employed. The screening functions of Hartree, Taylor, Ichimaru et al., Farid et al. and Sarkar et al. are also integrated for comparative study. Our results for parent compounds are compared to experiment and other available such theoretical findings and showed relatively good agreement. During present theoretical study it is concluded that refractive index fairly depends on the selection of the local field correction function.

Study of Collective Modes and Elastic Constants of Zr<sub>57</sub>Ti<sub>5</sub>Cu<sub>20</sub>Ni<sub>8</sub>Al<sub>10</sub> Bulk Metallic Glass

The methodical expressions for the phonon frequencies of Zr57Ti5Cu20Ni8Al10 bulk metallic glass (BMG) both for longitudinal and transverse phonon modes are computed for the first time using Hubbard-Beeby (HB) approach and our well recognized model potential. The self-consistent phonon scheme given by Takeno-Goda, involving multiple scattering and phonon Eigen frequencies expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the Zr57Ti5Cu20Ni8Al10 BMG. In the present paper, the local field correction functions due to Hartree (H), Farid et al (F), Sarkar et al (S) and Hubbard Sham (HS) are used to examine the influence of screening effects on the vibrational properties. Further, from the long wavelength limit of phonon frequencies, various elastic constants have been calculated and are found to be in good agreement with experimental and other available data.

Atomic Transport Properties of 3D Liquid Transition Metals Using Different Reference Systems

Atomic transport properties like self diffusion coefficient (D), viscosity coefficient (η) of 3d liquid transition metals are studied. Here we have applied our own model potential to describe electron ion interaction with different reference system like Percus - Yevick Hard Sphere (PYHS), One Component Plasma (OCP) and Charge Hard Sphere (CHS) systems. We have investigated the effect of different correction function like Hartree (H), Vashishta-Singwi (VS), Hubbard-Sham (HS), Sarkar et al (S), Ichimaru-Utsumi(IU), Taylor (T) and Farid et al (F) on atomic transport properties. The proper choice of the model potential alongwith the local field correction function and reference system plays a vital role in the study of the atomic transport properties of 3d liquid transition metals.

Concentration Dependent Physical Properties of SiSn Solid Solution

In the present investigation, we report theoretical study of total energy, energy band gap in X-direction, bulk modulus, elastic constants and pressure derivative of elastic constants of Si1-xSnxsolid solution using higher-order perturbation theory along with application of our proposed potential, where x is concentration of Sn. The parameter of our potential is determined using zero-pressure equilibrium condition. In the present calculations, The local-field correction function can be employed to consider exchange and correlation effects. The present study showed that the physical quantities under investigation varied with the concentration of the constituent element.

Concentration Depended Thermodynamic Properties of Fe-Co Liquid Binary Alloy

The thermodynamic properties like heat of mixing (ΔE), entropy of mixing (ΔS) and volume of mixing (ΔΩ) of Fe-Co liquid binary alloys are computed using our newly constructed parameter free model potential. We have also attempted to investigate the effect of various forms of exchange and correlation functions, namely, Hartree (H) and Taylor (T) on the thermodynamic properties of Fe-Co liquid binary alloys. It is found that the proper choice of the model potential along with the local field correction function play an important role in investigating the thermodynamic properties of Fe-Co liquid binary alloys.