Local Field Correction Functions Research Articles

Study of collective dynamics of a non-crystalline aluminum–nickel binary alloy using pseudopotential theory

The phonon dynamics of a transition metal–aluminum alloy, i.e. the Al0.75Ni0.25 binary non-crystalline system, has been studied in terms of the eigenfrequencies of the localized collective excitations using model potential formalism. The self-consistent phonon scheme given by Takeno and Goda, involving multiple scattering and phonon eigenfrequencies that are 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 non-crystalline Al0.75Ni0.25 alloy. The pair potential is obtained in Wills Harrison (WH) form from the well-recognized model potential of Ashcroft as a test case. The local field correlation functions due to Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Sarkar et al (S) and Farid (F) are used to investigate the influence of the screening effects on the vibrational properties. Results for the bulk modulus BT are obtained using the aforesaid local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio (σ), Young modulus (Y), propagation velocity of elastic waves and phonon dispersion curves using model potential are reported here and good agreement with available experimental results was achieved.

Phonon dispersion in binary metallic glasses

The theoretical computation of the phonon dynamics of two binary metallic glasses Zr67Ni33 and Co67Zr33 have been studied from the model potential formalism using three different theoretical models proposed by Hubbard-Beeby, Takeno-Goda, and Bhatia-Singh. Five local field correction functions, viz., Hartree, Taylor, Ichimaru-Utsumi, Farid et al., and Sarkar et al., are used for the first time in the present investigation to study the screening influence on the aforesaid properties. The pair potential is computed in the Wills-Harrison form and used to study the eigenfrequencies of longitudinal and transverse phonon modes. The present data on phonon dispersion curves of the Zr67Ni33 glass are compared with the available MD results at different temperatures. To explain the electron-ion interaction, the pseudo-alloy-atom model is applied for the first time instead of the Vegard’s law. Further, thermodynamic and elastic properties have also been calculated from the elastic part of the phonon dispersion curves. Computed yielding of the Zr67Ni33 glass is found in fair agreement with the available data.

Pressure dependence of the superconducting state parameters of a binary Ca70Mg30 metallic glass superconductor

Theoretical computation of the pressure dependence of superconducting state parameters of a binary Ca70Mg30 metallic glass has been performed using the model potential formalism. Explicit expressions have been derived for the volume dependence of the electron-phonon coupling strength λ and the Coulomb pseudopotential μ*, considering the variation of the Fermi momentum kF and Debye temperature θD with volume. Well-known Ashcroft’s empty core model pseudopotential and five different types of the local-field correction functions, namely, Hartree, Taylor, Ichimaru-Utsumi, Farid et al. and Sarkar et al. have been used for obtaining pressure dependence of transition temperature TC and the logarithmic volume derivative Φ of the effective interaction strength N0V for the metallic glass superconductor. It has been obtained that TC of Ca70Mg30 metallic glass decreases rapidly with increasing pressure up to 60% decrease in the volume, for which the μ* and Φ curves show a linear nature. The superconducting phase disappears at about 60% decrease in the volume.

Superconducting state parameters of ternary amorphous superconductors

The theoretical investigations 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 five Nb x Ta y Mo z ( x = 0.15, 0.30, 0.30, 0.40, 0.45; y = 0.15, 0.30, 0.30, 0.40, 0.45 and z = 0.10, 0.30, 0.30, 0.40, 0.70) ternary amorphous superconductors viz. Nb 0.45Ta 0.45Mo 0.10, Nb 0.30Ta 0.40Mo 0.30, Nb 0.40Ta 0.30Mo 0.30, Nb 0.30Ta 0.30Mo 0.40 and Nb 0.15Ta 0.15Mo 0.70 have been reported for the first time using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. The T C obtained from Hartree (H) local field correction function are found an excellent agreement with available theoretical data. Quadratic T C equation has been proposed, which provide successfully the T C values of ternary amorphous alloys under consideration. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the superconductors.

Local field corrections and effective electron–electron interaction in a two-dimensional polarized electron gas

Abstract We find approximate expressions for the spin-dependent local field correction functions in a two-dimensional spin polarized electron gas by considering their limiting behavior at small and large wavevectors and sum rules. Using these constructed local field functions, we analyze the effective electron–electron interaction by generalizing the self-consistent linear response method of Kukkonen and Overhauser. We will also investigate how the finite width of the electron layer will affect the local spin susceptibility. It is found that the results for quasi-two-dimensional polarized gas differs considerably from those of two-dimensional polarized gas.

Thermodynamics of liquid d- and f-shell metals: a variational approach

The Gibbs–Bogoliubov variational method is applied to investigate the thermodynamic properties of some d- and f-shell metals in liquid phase namely; Rh, Ir, Cu, Ag, Ni, Pd, Pt, Au, La, Yb, Ce, and Th using pseudopotential theory. For description of the structure, Percus-Yevick hard sphere model is used as a reference system. Ashcroft's well-known empty core model potential is used to describe the electron-ion interaction. The local field correction function proposed by Hartree, Taylor, Ichimaru–Utsumi, Farid et al., and Sarkar et al. are applied to introduce the exchange and correlation effects in the study of thermodynamics of these metals. The comparison with available experimental or theoretical findings is found in qualitative agreement and establishes the use of the local field correction functions in such study.

Superconductivity of amorphous Mg 0.70Zn 0.30−xGa x alloys

The screening dependence theoretical investigations 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 five Mg 0.70Zn 0.30− x Ga x ( x = 0.0, 0.06, 0.10, 0.15 and 0.20) ternary amorphous alloys viz. Mg 0.70Zn 0.30Ga 0.00, Mg 0.70Zn 0.24Ga 0.06, Mg 0.70Zn 0.20Ga 0.10, Mg 0.70Zn 0.15Ga 0.15 and Mg 0.70Zn 0.10Ga 0.20 have been reported for the first time using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present 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 O V show weak dependences on the local field correction functions. The transition temperature T C obtained from H-local field correction function is found in an excellent agreement with available experimental data. Quadratic T C equation has been proposed, which provide successfully the T C values of ternary amorphous alloys under consideration. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the ternary amorphous alloys.

Study of superconducting state parameters of ternary metallic glasses through pseudopotential approach

A theoretical investigation on the screening dependence of the superconducting state parameters (SSPs) viz. the electron-phonon coupling strength λ, the Coulomb pseudopotential μ∗, the transition temperature TC, the isotope effect exponent α and the effective interaction strength N0V of some ternary metallic glasses such as Ti50Be34Zr10, (Mo0.6Ru0.4)78B22, (Mo0.6Ru0.4)80B20, (Mo0.4Ru0.6)80P20, (Mo0.6Ru0.4)70Si30, (Mo0.6Ru0.4)84B16, (Mo0.6Ru0.4)72Si28, (Mo0.6Ru0.4)86B14, (Mo0.6Ru0.4)76Si24, (Mo0.6Ru0.4)78Si22, (Mo0.6Ru0.4)80Si20, (Mo0.6Ru0.4)82Si18 and (Mo0.6Ru0.4)80P20 is reported for the first time using Ashcroft's empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al (F) and Sarkar et al (S) are used in the present investigation to study the effect of screening on the aforesaid properties. It is observed that λ and TC are reasonably sensitive to the selection of the local field correction functions, whereas μ∗, α and N0V show weak dependences on the local field correction functions. The transition temperature TC obtained from the H-local field correction function is found to be in excellent agreement with available experimental data. Also, the present results are found to be in qualitative agreement with other earlier reported data, which confirms the existence of the superconducting phase in the above ternary metallic glasses.

Electrical transport properties of liquid alloys

The electrical transport properties namely the electrical resistivity (ρ), the thermoelectric power (TEP) and the thermal conductivity (σ) of several polyvalent alloys like In1−xBix and Sn1−xBix 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) potential of Ashcroft is used for the first time with seven local field correction functions due to Hartree (H), Hubbard–Sham (HS), Vashista–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 concluded that the comparison of present and experimental findings is highly encouraging.

Superconducting state parameters of La100-C GaC binary metallic glasses

Abstract The theoretical investigations 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 six binary La100-C GaC (C = 16, 20, 22, 24, 26 and 28 at. %) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present 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 O V show weak dependences on the local field correction functions. The T C obtained from H-local field correction function are found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found to be in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.

RESIDUAL RESISTIVITY OF DILUTE ALLOYS

The residual resistivity for 156 dilute alloys of 19 hosts of different groups of the periodic table has been studied on the basis of the single parametric model potential formalism. Ashcroft's empty core model (EMC) potential is explored for the first time with five different local field correction functions, viz, Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F), and Sarkar et al. (S) to investigate the effect of the exchange and correlation on the aforesaid properties. The comparison of the presently computed outcomes with the available theoretical and experimental data is highly encouraging. The investigation of residual resistivity is found to be quite sensitive to the selection of local field correction function, showing a significant variation with the change in the function.

A pseudopotential approach to the superconducting state properties of CuCZr100-C binary metallic glasses

The theoretical investigation of the superconducting state properties viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature TC, isotope effect exponent α and effective interaction strength N0V of ten binary CuCZr100-C (C = 25–60 at%) metallic glasses is performed, using Ashcroft’s empty core model potential. Five local-field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to study the screening influence on the aforesaid properties. It is shown that the electronphonon coupling strength λ and the transition temperature TC 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 N0V show a weak dependence on the local-field correction functions. The values of TC obtained from the H-local-field correction function are found to be in qualitative agreement with available theoretical or experimental data and show almost linear behavior with respect to the concentration C of Cu. The present results are shown to be in good agreement with other available theoretical or experimental data. The obtained results confirm the existence of the superconducting phase in the metallic glasses.

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 Tc, isotope effect exponent α and effective interaction strength N0V of ten CuCZr100−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 TC 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 N0V show weak dependences on local field correction functions. The Tc 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.

Asphericity in the Fermi surface and Fermi energy of Li 1− xB x (B = Na, K, Rb and Cs) substitutional alloys

A detailed investigation into asphericity in the Fermi surface (FS) and Fermi energy (FE) of Li 1− x B x (B = Na, K, Rb and Cs) substitutional alloys are reported for the first time. The FE computed under pseudo-alloy-atom (PAA) model consideration is found higher than the FE computed under phase mixture (Mix) consideration. The non-linear relation for E F( x) = a 0 + a 1 x + a 2 x 2 is predicted for all the substantial binaries. The exchange and correlation effects are found to suppress the value of FE. The alloying behavior of Na, K, Rb and Cs with Li generates the asphericity in the FS like bcc metals. For Li 1− x B x , the asphericity in the FS of the binary decreases with increase in x, except Li 1− x Cs x . In Li 1− x Cs x , the asphericity in the FS of the binary increases with increase in x. The Li 1− x Cs x solid solution shows maximum Fermi surface distortion (FSD) in comparison to Li 1− x B x (B = Na, K and Rb) systems. Present study also concludes that the impact of local-field correction function on the asphericity in the FS is maximum at [1 0 0] point and minimum at [1 1 1] point. Among the high symmetry directions, the maximum asphericity in the FS is obtained at [1 1 0] point.

Study of Screening Dependence Superconducting State Parameters of Cu C Zr100−C Binary Metallic Glasses by a Pseudopotential

The screening dependence theoretical investigations of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature TC, isotope effect exponent α and effective interaction strength NOV of ten binary CuCZr100−C (C=25, 30, 33, 35, 40, 45, 50, 55, 57 and 60) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F), and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron–phonon coupling strength λ and the transition temperature TC 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 NOV show weak dependences on the local field correction functions. The values of TC obtained from the H-local field correction function are in qualitative agreement with available theoretical or experimental data and show almost linear nature with the concentration C of Cu element. A linear TC equation is proposed by fitting the present outcomes for the H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.

Screening dependence of superconducting state parameters of Cu–Zr binary metallicglasses

Screening dependence investigations of the superconducting stateparameters (SSP), namely the electron–phonon coupling strengthλ, Coulomb pseudopotentialμ*, transition temperatureTC, isotope effectexponent α and effectiveinteraction strength NOV of ten binary CuCZr100−C (C = 0.25,0.30,0.33,0.35,0.40,0.45,0.50,0.55,0.57 and 0.60) metallic glasses have been reported using Ashcroft’s empty core (EMC)model potential. Five local field correction functions proposed by Hartree(H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al (F) and Sarkar et al (S)are used in the present investigation to study the screening influence on theaforesaid properties. It is observed that the electron–phonon coupling strengthλ and the transitiontemperature TC are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotentialμ*, isotope effectexponent α and effectiveinteraction strength NOV show weak dependences on the local field correction functions. TheTC obtained from the H-local field correction function is found to be in qualitative agreement withavailable theoretical or experimental data and shows an almost linear nature with the concentrationC of the elementCu. A linear TC equation is proposed by fitting the present outcomes for the H-local field correctionfunction, which is in conformity with other results for the experimental data.Also, the present results are found to be in qualitative agreement with other suchdata earlier reported, which confirms the superconducting phase in the metallicglasses.

Superconducting state parameters of Cu xZr 100− x binary metallic glasses

The screening dependence investigations 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 10 binary Cu x Zr 100− x ( x = 0.25, 0.30, 0.33, 0.35, 0.40, 0.45, 0.50, 0.55, 0.57 and 0.60) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present 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 O V show weak dependences on the 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 and show almost linear nature with the concentration ‘ x’ of Cu element. A linear T C equation is proposed by fitting the present outcomes for IU-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.

Study of monovacancy resistivity of some metallic elements and their dilute alloys by pseudopotential

In this article, the monovacancy resistivity of 24 metallic elements and their 156 dilute alloys of the different groups of the periodic table are reported on the basis of model potential formalism. Ashcroft’s well known empty core (EMC) model potential is explored first time with five different types of the local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) to investigate the effect of the exchange and correlation on the aforesaid properties. The comparison of presently computed results with available theoretical and experimental findings is highly encouraging. Present investigation of the monovacancy resistivity is found to be quite sensitive to the selection of local field correction function and showing a significant variation with the change in the function.

Electrical resistivity of K-based liquid binaries

The study of the electrical resistivity of alkali K-based liquid binaries, viz, K1−xNax, K1−xRbx, and K1−xCsx have been made by well recognized model potential. The most recent local field correction functions due to Farid et al. (F) and Sarkar et al. (S) are used for the first time in the study of electrical resistivity of liquid binary mixtures and found suitable for such study. The results due to the inclusion of Sarkar et al.’s local field correction function are found superior to those obtained due to Farid et al.’s local field correction function. The present results compare well the experimental data.

Pseudopotential in the study of phonon dynamics of Pd-based metallic glasses

The phonon dynamics of Pd35Zr65 and Pd80Si20 two non-crystalline systems have been studied in terms of the eigen frequencies of the localized collective excitations using model potential formalism. The pair potential and pair correlation function are obtained in Wills–Harrison (WH) form from the well recognized model potential of Gajjar et al. The phonon dispersion curves are computed from the three approaches proposed by Hubbard–Beeby (HB), Takeno–Goda (TG) and Bhatia–Singh (BS). Various elastic and thermodynamic properties have been studied from the elastic limit of the dispersion relations. The advanced local field correction function due to Sarkar et al. is used for the first time to include the influence of exchange and correlation on the aforesaid properties. The ratio (r2/r1) of the position of the second peak (r2) to that of the first peak (r1) of g(r) for both metallic glasses is close to the c/a ratio in close-packed hexagonal structure. Qualitatively, the phonon dispersion curves (PDC) computed from the BS approach are found to be better than HB and TG approaches.