Electron-phonon Enhancement Research Articles

Gruneisen parameters, electron-phonon enhancement and superconductivity for Pd-H alloys

Measurements of the low-temperature (1.5-30K) and room temperature thermal expansion have been made for palladium-hydrogen alloys with H/Pd<or approximately=0.7. The low-temperature data have been resolved into the individual electronic and lattice components and values for the corresponding Gruneisen parameters in the zero-temperature limit have been calculated. The influence of the optic modes on the volume dependence of the electron-phonon interaction parameter and its relationship to the contribution to gamma e from the electron-phonon enhancement and the magnitude of the pressure dependence of the superconducting transition temperature of PdH is discussed.

Electronic band structure of h. c. p. electron phases based on the noble metals

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for several close-packed hexagonal intermediate phases in the systems Cu-Ge, Ag-Sn and Ag-Cd. The obtained results, together with previous similar work, conform to a general pattern which suggests that the electronic structure of all h. c. p. phases based on the noble metals can be described in terms of a common nearly rigid band for the conduction electrons. The details of the trend in the density of states are similar to the calculated density of states trends for the h. c. p. metals Zn and Be. The main feature is a large peak in the range of electron concentration between 1.4 and 1.8 which is most likely the result of Fermi surface contacts with the {10.1} Brillouin zone planes, and overlaps across the {10.0} zone planes. A secondary feature is the onset of overlaps across the {00.2} zone planes. A model of an inscribed Fermi sphere into the Brillouin zone is sufficient to indicate the expected behaviour of the trend in the electronic heat capacities in individual phases. Electron-phonon enhancement in the h. c. p. phases appears to be a nearly constant factor, amounting to about 30% of the measured electronic heat capacity values.

Heat capacity of technetium

The heat capacity of technetium has been measured in zero field between 3 and 15 K. A superconducting transition temperature T/subc/ = 7.86 K is found. The electronic heat-capacity coefficient and zero-degree Debye temperature are 4.30 mJ/mole K$sup 2$ and 454 K, respectively. An electron-phonon enhancement factor of 0.65 is found from the McMillan equation. The thermodynamic properties of the superconducting state also indicate that technetium is an intermediate- coupling superconductor. (AIP)

Specific heats of alpha phase and zeta phase Ag-Al alloys in the range 1.5-4.2K

Specific heats have been measured in three alpha phase alloys having the FCC structure, and eight zeta phase alloys having the HCP structure. Electron-phonon enhancement factors for the zeta phase alloys have been estimated from the McMillan formula, using the Debye temperature and the superconducting temperature. It is suggested that the behaviour of the electronic specific heat in the zeta phase, near electron concentration of 1.6, is consistent with the existence of contacts between the Fermi surface and the (10.1) Brillouin zone planes, and with overlaps into the next zone across the (00.2) zone planes.

Experimental study of the anisotropic electron-phonon interaction in A1

From analysis of surface-Landau-level resonance in the (110) sample plane of A1, we have determined the Fermi velocity and electron-phonon scattering rate at three characteristic locations on the Fermi surface. Using the measured velocities and calculated band velocities we extract local values of the electron-phonon enhancement factor λ. A γ T 3 temperature dependence is found for the scattering rate with γ varying by a factor 8 for the three Fermi surface locations. The experimental results are compared with recent theoretical calculations.

Experimental evidence for the Fermi surface overlap effect in ε-phase Ag—Zn alloys, obtained from low temperature specific heats

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for ten Ag-Zn alloys in the range of the h.e.p. ε-phase. After a correction for the electron-phonon enhancement, the trend of the electronic specific heat coefficient is consistent with a nearly rigid band behaviour, showing a general decrease of the density of states at the Fermi level when the corners of the Brillouin zone are filled. A slight deviation from this trend occurs at electron concentration values exceeding approximately 1.85 5 , in agreement with other measured properties and confirming a theoretical model involving overlaps of electrons across the {00.2} planes of the Brillouin zone. The estimated band gaps are of the order of 2 eV. I t appears that whereas in the dilute rj-phase alloys of zinc with silver the rigid band condition is not valid the opposite is true in the concentrated ε-phase alloys.

Low temperature specific heats of zinc alloyed with silver

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for pure zinc and for two n-phase alloys containing 2 at. % and 4 at. % silver in zinc, respectively. After a correction for electron-phonon enhancement the electronic specific heat coefficient for pure zinc differs by only a small percentage from the calculated value reported in the literature on the basis of a band calculation. The results for the alloys show a decreasing trend of the density of states at the Fermi level when silver is added to zinc. This is contrary to a prediction based on a rigid band approach. Hence, the results indicate a complete breakdown of the rigid band condition on alloying. The reasons for this are most likely associated with the influence of the d band electrons or with charge distribution effects between solute and solvent atoms.

Temperature independence of the Hall-constant of the strong coupling amorphous metals Bi, Ga and Pb

The amorphous metals Bi, Ga and Pb have a strong electron-phonon interaction which enhances the bare density of states by a factor of about 3. The enhancement decreases between zero and 20 K by about 30 per cent. The temperature dependence of the Hall-constant in this temperature region is measured with an accuracy of about 10 −3. The Hall-constant is temperature independent within this accuracy. Therefore the temperature dependence of the electron-phonon enhancement does not affect the Hall-constant.

Electron-phonon enhancement of the thermal electron mass in impure systems

It is shown that finite electron life time effects due to impurity scattering in concentrated alloys have no influence on the form of the electron-phonon enhancement of the thermal electron mass.

Nuclear-Spin Relaxation and Knight Shift in Transition Metals

The electron-phonon enhancement of electronic specific heat and the effective Coulomb enhancement of spin susceptibility are taken into account, the former through the Eliashberg-McMillan theory of superconductivity for transition metals and the latter through gyromagnetic effect experiment, in calculating the nuclear-spin relaxation rates in transition metals. The nuclear-spin relaxation rate of vanadium determined experimentally is found to be consistent with the conjecture that the observed Knight shift is almost entirely due to orbital paramagnetism. Inclusion of the above corrections gives better qualitative agreement with observed relaxation rates for V, Nb, and Pt.

Upper Critical Field and the Density of States in Amorphous Strong-Coupling Superconductors

The upper critical field of the amorphous superconductors ${\mathrm{Bi}}_{0.85}$${\mathrm{Tl}}_{0.15}$, Ga, ${\mathrm{Sn}}_{0.86}$${\mathrm{Cu}}_{0.14}$, and ${\mathrm{Pb}}_{0.75}$${\mathrm{Bi}}_{0.25}$ is measured in the temperature range from 1.5 \ifmmode^\circ\else\textdegree\fi{}K to the zero-field transition temperature. Films of the amorphous metals about 1500 \AA{} thick are obtained by quenched condensation onto a substrate at He temperature. The initial slopes of the ${B}_{c2}(T)$ curves are used to determine the electronic density of states at the Fermi surface. For all the investigated materials these values were enhanced compared with the density of states which one obtains from the free electron model. For Ga, ${\mathrm{Sn}}_{0.86}$${\mathrm{Cu}}_{0.14}$, and ${\mathrm{Pb}}_{0.75}$${\mathrm{Bi}}_{0.25}$ the experimental enhancement factor agrees well with the electron-phonon enhancement factor $1+\ensuremath{\lambda}$, where $\ensuremath{\lambda}$ is taken from superconducting-tunneling experiments. The temperature dependence of ${B}_{c2}$ deviates from that predicted by Werthamer, Helfand, and Hohenberg, showing ${B}_{c2}$ values too large in the low-temperature region. It is suggested that the strong-coupling behavior of the amorphous superconductors is responsible for the deviation at low temperature.

Determination of the Electron-Phonon Enhancement Factor from Specific-Heat Data

The electron-phonon enhancement factor is determined for scandium, yttrium, vanadium, platinum, and palladium solely from specific-heat data. The key to the method is that at high temperatures the electron-phonon enhancement factor is zero. Therefore, if the electronic specific-heat coefficient at high temperatures is calculated and compared with the low-temperature value, both the band-structure density of states and the electron-phonon enhancement factor can be determined.

On rigid bands and mass enhancements in noble metal alloys

The rigid band model assumes that the electronic density of states of an alloy can be inferred from that of the host. Band calculations are usually inconsistent with this model when compared with the measured electronic specific heat of alloys. It has been suggested that the apparent discrepancy for alloys with noble metal hosts is due to the neglect of changes in the electron-phonon enhancement of the density of states at the Fermi level. A semi-empirical calculation, based on measurements of the high temperature electrical resistivity, shows that changes in the enhancement factor are much too small to account for the failure of the rigid band model.

Specific Heat of Gold-Zinc Alloys below 3 °K

The electronic specific heat is found to initially increase on adding zinc to gold, in agreement with recent work of Clune and Green who relate this behavior to changes in the electron-phonon enhancement factor superimposed on a rigid-band model. The results for a 7.5-at.%-Zn alloy were stable against drastic changes in heat treatment, whereas those for a 10-at.% alloy were very dependent on heat treatment. It is therefore postulated that the $\ensuremath{\alpha}$-phase region extends only to \ensuremath{\sim} 9 at.% at room temperature, contrary to recent phase diagrams. The results at 10 at.% Zn also suggest that very slow cooling retains a large part of the $\ensuremath{\alpha}$ phase, but quenching produces the ordered phase. A possible explanation is that the high lattice-vacancy concentration immediately after quenching facilitates atomic movement.

Specific heats of LaIn 3, CeIn 3 and PrIn 3 at temperatures between 1·5 and 4·2°K

The specific heats of LaIn 3, CeIn 3 and PrIn 3 have been measured at temperatures between 1·5–4·2°K. In LaIn 3 and PrIn 3 they showed the usual temperature dependence expressed in the formula C=γT+βT 3 , where γ=6·28±0·10 mj°K −2 mole −1, β=1·06±0·01 mj°K −4 mole −1 (Debye temperature θ=194·4°K) for LaIn 3 and γ=11·42±0·09 mj°K −2 mole −1, β=0·94±0·01 mj°K −4 mole −1 ( θ=202·3°K) for PrIn 3. The specific heat of CeIn 3 is an order of magnitude higher. Because of the complex behavior of C p/T vs. T 2 in this compound γ and β were not determined. The electronphonon enhancement factors for LaIn 3 and PrIn 3 as determined from experiment, were found to be 0·59 and 0·54, respectively.

Upper limit on electron-phonon interaction in vanadium carbide

Single crystals of VC χ (χ = 0.87, 0.84, 0.81, 0.76) were not superconducting above 30 mK. indicating that the electron-phonon enhancement of the densities of states determined from electronic specific heats is less than 30 %.

Rigid-Band Behavior in the Specific Heats of PbTl and PbBi Alloys: Electron-Phonon Enhancement Effects

The normal-state specific heats of pure lead and four dilute PbTl and PbBi alloys have been measured in the temperature range 1.0-2.3 K. The fractional rate of change of the electronic specific-heat coefficient $\ensuremath{\gamma}$ with respect to the number of conduction electrons per atom was found to be 0.25\ifmmode\pm\else\textpm\fi{}0.06 for PbTl alloys and 0.51\ifmmode\pm\else\textpm\fi{}0.04 for PbBi alloys. When changes in the electron-phonon enhancement factor as determined from tunneling measurements are included, good agreement is found between the measured changes in $\ensuremath{\gamma}$ and those expected from the rigid-band model. Semiquantitative calculations indicate that changes in the electron-phonon enhancement factor may also account for the apparent discrepancy between previous experimental results and the rigid-band model in noble-metal alloys. The Debye temperature was found to decrease for both lead alloy series.

The fermi surface and optical properties of copper

A Fourier expanded model Hamiltonian is applied to copper. The parameters in this phenomenological Hamiltonian are adjusted to fit the de Haas-van Alphen periods, the cyclotron effective masses, and the position of the lowest direct optical interband absorption. The agreement with experiment suggests that the electron-phonon enhancement of the effective mass is small, and that the optical properties are consistent with direct wave-vector conserving transitions between one-electron states.

Band Structure and Electronic Properties of Silver

A band-structure calculation for silver has been made using Mueller's interpolation scheme. The first-principles calculation by Segall has been adjusted to give better agreement with experiment, and a set of parameters derived to fit these adjusted bands. A density-of-states calculation using these parameters confirms deductions from experimental work using the photoelectric effect which suggest two main peaks in the $d$-band region. However, we find an additional low-energy peak which has not been observed experimentally and no evidence of structure near the Fermi level. The Fermi surface is computed after a recalculation of the Fermi energy which agrees with Segall's results. Reasonable correlation with the experimental dimensions of the Fermi surface is obtained. Finally, various effective masses are calculated. The value obtained for the electronic specific heat suggests that electron-phonon enhancement is somewhat smaller in silver than in copper.

Fermi Surface and Electronic Structure of Indium

The available cyclotron-resonance, size-effect, and de Haas-van Alphen data in indium are compared with the geometry of the Fermi surface defined by secular equations of up to sixth order. The principal Fourier coefficients appearing in the secular equation are found from a simple form factor with a single adjustable parameter. The possible topologies of the Fermi surface are considered systematically in terms of structure plots appropriate to the points of high symmetry in the zone. It is found that a form factor consistent with transport properties, and which accurately reproduces the experimental dimensions on the $\ensuremath{\beta}$-arms, is sufficiently strong to remove all but minute, disconnected remanants of the $\ensuremath{\alpha}$-type arms near the symmetry points $K$. Band structure, density of states, and cyclotron masses are calculated, and the electron-phonon enhancement of these and of the specific-heat mass is estimated from the final form factor.