On the high temperature coalescence of metallic nanocrystals

The high temperature properties of metallic particles with a size of a few nanometers are very important in modern materials science. In the present work we report in situ transmission electron microscope studies of coalescence behavior of nanoparticles at high temperatures. At T > 700 K a new mechanism for coalescence was found. This phenomenon occurs on a time scale 3 to 20 times faster than the classical liquid-like coalescence reported by Pashley [Adv. Phys. 14 (1965) 327]. Before the coalescence the particles undergo shape convulsions of the type described by Iijima and Ichihashi [Phys. Rev. Lett. 56 (1986) 616] which has been termed “quasimelting”, then fast coalescence occurs. The newly formed particles also undergo convulsions until stabilized by the substrate. It is also shown that the electron beam plays a significant role on this process.     

On some recent results concerning the superconducting transition temperature

The Eliashberg gap equations relate the transition temperature T_c of an isotropic superconductor to its electron-phonon spectral function α²F(ω) and Coulomb pseudopotential parameter $\text{μ}{}^1$. Recently the Eliashberg theory has been used to derive some supposedly rigorous results bearing on the problem of attaining higher superconducting transition temperatures: Bergmann and Rainer derived an expression for the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{F(ω)}$; Allen and Dynes showed that in the asymptotic limit of very large $\text{λ(λ?10)k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{=f(μ}{}^1\text{)(λ〈ω}{}^2\text{〉)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and Leavens proved that for any isotropic superconductor k_BT_c ?0.2309A, where A is the area under its electron-phonon spectral function. In this letter we show that the result of Allen and Dynes is not compatible with the other results and is, in fact, incorrect.     

Causes for the variable superconducting transition temperature in uranium metal

The variable superconducting transition temperature of uranium metal appears to depend upon the variability of a low-temperature martensitic transformation. Local structural fluctuations and phase instabilities are suggested as resulting when the transformation is incomplete. The thermodynamic stability of a two-phase modulated structure involving domain formation is discussed along with possible consequences of a domain configuration. Factors affecting T_c are used to explain the anamalous thermal property behavior of α-phase uranium.     

A simple and accurate equation for the superconducting transition temperature

Reasonable and consistent approximations are used to reduce the simplified form of the integral equations for the superconducting transition temperature used by Allender, Bray and Bardeen to a very simple, and remarkably accurate, equation for T_c. This equation is compared with the McMillan equation and found to give just as good agreement with experiment for intermediate-coupling materials and considerably better agreement for strong-coupling materials.     

Ab initio calculation of the superconducting transition temperature

The superconducting transition temperature is calculated for a series of representative metals from a selfconsistent LMTO-bandstructure calculation. We carefully avoid any uncontrolled approximations apart from the use of a local exchange-correlation potential and the rigid-ion approximation for the electron-phonon interaction, Our results for V, Nb, Ta, Mo, W, Pd, Pt, Pb clearly indicate that these popular approximations are incapable of reproducing the observed transition temperatures.     

The superconducting transition temperature for very large electron-phonon coupling

A rigorous derivation of the range of validity of the asymptotic relation $\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{?0.1827[λ<ω}{}^2\text{>]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is presented.     

On the pressure dependence of martensitic and superconducting transition temperature in intermetallic compounds

In order to explain the large pressure dependence of the cubic to tetragonal transition temperature T_M in LaAg an expression has been derived from ?T_M/?P for a two-fold degenerate electronic band interacting with the tetragonal strain mode. Analogy with the pressure dependence of the ferromagnetic transition temperature T_c in an itinerant system is pointed out. The nature of variation of the superconducting transition temperature with pressure is also discussed.     

Calculation of the superconducting transition temperature Tc for metals with phonon-anomalies

It is shown that the electron-phonon coupling constant λ and T_c of the refractory transition-metals VC, VN, NbC, etc. can be obtained from λ and T_c of the corresponding transition-metals V, Nb, etc. The results obtained suggest that superconductivity in the refractory metals involves mainly d-electron transitions between the transition-metal atoms.     

Oscillations of the superconducting transition temperature in aluminum films

Oscillations of the superconducting transition temperature of thin Al-films have been observed during deposition of siliconmonoxide SiO. Friedel oscillations as well as the quantum size effect may account for the observations.     

Influence of correlated spins on the superconducting transition temperature

Using a variational procedure, the depression of the superconducting transition temperature by a system of correlated moving spins is calculated. In particular, corrections to the Abrikosov-Gorkov theory in the neighbourhood of a magnetic phase transition are examined. Characteristic differences in the concentration dependence of the superconducting transition temperature are found in the cases of ferromagnetic and antiferromagnetic spin correlations.     

A least upper bound on the superconducting transition temperature

It is rigorously shown that the superconducting transition temperature of any material for which the Eliashberg theory is valid must satisfy k_BT_c ? 0.2309 A, where A is the area under its electron-phonon spectral function α²F(ω). This relation is a least upper bound, not just an upper bound, in the sense that there is an optimal situation in which the equality holds. This occurs when the Coulomb pseudopotential parameter $\text{μ}{}^1$ is zero and the spectral function is the Einstein spectrum Aδ(ω ? 1.750 A). These results are generalized in an approximate, but sufficiently accurate, way to the case $\text{μ}{}^1\text{≠ 0}$ to obtain the more useful least upper bound $\text{k}{}_{\mathrm{<mtext>B</mtext>}}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{? c(μ}{}^1\text{) A}$ and the corresponding optimal spectrum $\text{Aδ[ω ? d(μ}{}^1\text{)A]}$. Numerical results for the functions $\text{c(μ}{}^1\text{)}$ and d(μ¹) are presented for $\text{0 ? μ}{}^1\text{? 0.20}$. It is shown that the T_c's of many materials (including Nb₃Sn), for which experimental values of A and $\text{μ}{}^1$ are available, do not lie very far below the upper bound.     

Enhancements of the superconducting transition temperature within the two-band model

The two-band model as introduced by Suhl, Matthias and Walker [Phys. Rev. Lett. 3, 552 (1959)] accounts for multiple energy bands in the vicinity of the Fermi energy which could contribute to electron pairing in superconducting systems. Here, extensions of this model are investigated wherein the effects of coupled superconducting order parameters with different symmetries and the presence of strong electron-lattice coupling on the superconducting transition temperature T_c are studied . Substantial enhancements of T_c are obtained from both effects.Received: 2 July 2003, Published online: 2 April 2004PACS: 74.20.-z Theories and models of superconducting state     

Theory of the superconducting proximity effect below the transition temperature

The form of the low-temperature theory of the superconducting proximity effect depends on whether the non-linear terms are assumed to depend only on the local value of the gap or on its average value over some finite range. The local assumption leads to smaller values of the gap and to unphysical results at low temperatures. The effect of non-locality is significant even in the Ginsburg-Landau regime.     

A model for dimensional crossover temperature above the superconducting transition for high-temperature superconductors

We have developed a theoretical model for the calculation of dimensional crossover temperature above the mean-field transition temperature using paraconductivity approach. We have numerically estimated the dimensional crossover (2D–3D and 2D–1D) temperature for the recently reported polycrystalline sample of the type Hg, Tl-1223. Our numerical results indicate that the dimensional crossover temperature is a variable quantity and it depends on the parameter related to superconductivity and the range of temperature where the fluctuation effect is significant.     

Calculated Nb superconducting transition temperature under hydrostatic pressure

Abstract

A full-potential linear muffin-tin orbital method (FP-LMTO) based linear-response approach is used to calculate the electron-phonon coupling in Nb under hydrostatic pressure. The superconducting transition temperature T_c is calculated using the Eliashberg equation. The calculated T_c agrees nicely with the experimental result at ambient pressure, but the agreement is only fair at high pressures. The T_c measured anomaly at 60–70GPa is understood in terms of the 2.5 order Lifshitz transition and its origin is traced back to the qualitative changes in the Fermi surface topology.     

Correlation between superconducting transition temperature and the cauchy discrepancy in body-centered-cubic transition metals

For body-centered-cubic transition metals, an empirical relationship exists between the superconducting transition temperature and the Cauchy discrepancy. This correlation may arise from many-atom effects.     

Doping dependence of the superconducting transition temperature in high-Tc systems

Using a self consistent diagrammatic theory of the one band Hubbard model, a suppression of the superfluid density due to spin fluctuation induced scattering rates is found. This is most pronounced for underdoped systems and enforces fluctuations of the superconducting order parameter and a suppression of the superconducting mean field transition temperature for low doping. Consequently, an optimal doping concentration around χ_opt: = 0:14 occurs within the spin fluctuation mechanism.     

Effect of interlayer single-particle hoppings on the superconducting transition temperature

It is well known that the superconducting transition temperature of high-T _c cuprates depends on the number of CuO₂ planes in the unit cell. The multilayer structure implies the possibility of interlayer hopping. Under the assumption that the interlayer hopping can be specified by the parameter t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))², the quasiparticle excitation spectrum for the bilayer cuprate in the superconducting state has been determined in the framework of the t − t′ − t″ − t _⊥ − J* model using the generalized mean-field approximation. It turns out that the interlayer hoppings does not create any additional mechanism of the Cooper paring and does not lead to an increase in T _c . The splitting of the upper Hubbard quasiparticle band attributed to the interlayer hoppings is manifested as two peaks in the doping dependence of the superconducting transition temperature at temperatures below the maximum T _c value for a single-layer cuprate. It has been found that antiferromagnetic interlayer correlations suppress the interlayer splitting. This probably leads to the common doping dependence of T _c for both single-layer and bilayer cuprates.