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Notes: Abstract Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of “diffuse” scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed ≲0.1λ have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, Δρ d (T)≡ρ d (T)−ρ d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, Δρ d(T) increases logarithmically with ρ d(0); (2) for a cylindrical Fermi surface, Δρ d (T) increases essentially linearly with ρ d (0). [In each case the qualitative dependence of ρ d(0) on λ/d is, for practical purposes, “linear.” However, the correct value of the product ρ∞λ in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of ρ d (0) vs.d −1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.

Notes: Model calculations of line shapes and amplitudes appropriate to radio-frequency size effect resonances on “small” Fermi surface sheets in complex metals have been carried out using a perturbative technique. Detailed results are presented for high-symmetry sheets, with emphasis on the sphere and the circular cylinder; some discussion is also given to suggest what changes may occur in less regular cases. The calculated line shapes are in good agreement with experiment, both for diffuse surface scattering of the resonating electrons and also for specular surface scattering. The behavior of the amplitudes as a function of the mean free path indicates that the expression customarily used in analyzing data for the temperature dependence of the resonance strength should be modified. Except for the field region near onset, where the behavior is more complicated, we find % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWGZbGaeyyhIu% RaamyzamaaCaaaleqabaGaeyOeI0IaamiEaaaakiaac+cacaGGOaGa% aGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacaWG4b% aaaOGaaiykaaaa!3F57!\[s \propto e^{ - x} /(1 - e^{ - 2x} )\] where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWG4bGaaeiiai% abggMi6MaaGnaalaaabaGaaGymaaqaaiaaikdaaaGaaeiuaiaac+ca% cqaH7oaBaaa!3AEC!\[x{\rm{ }} \equiv \frac{1}{2}{\rm{P}}/\lambda \], with P the orbit perimeter and λ the mean free path. This replaces the usually adopted form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaWGZbGaeyyhIu% RaamyzamaaCaaaleqabaGaeyOeI0IaamiEaaaakiaac+cacaGGOaGa% aGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacaWG4b% aaaOGaaiykaaaa!3F57!\[s \propto e^{ - x} /(1 - e^{ - 2x} )\]. Furthermore, the mean free path dependence is found to be essentially independent of the degree of specularity, in contrast to previous theoretical results for “simple” metals. While the difference between the usual and the revised expressions for S(x) is not large at modest mean free paths (that is, for x ≳ 1), it can be quite substantial at larger values of λ. This is of importance when dealing with very pure metals at the lowest temperatures or when trying to assess the residual mean free path in samples of moderate purity.

Notes: Abstract Thermodynamic aspects of the proximity effect have been studied via calorimetric measurements on bulk samples composed of alternating super-conducting (S) and normal (N) layers. Specifically, the thermal properties of lamellar Pb/Sn alloys are reported for samples with periodicities λ in the range 0.6≲λ≲6 µm and for temperatures between 1.5 and 8 K. It is shown that if the thickness of the lead-rich (S) domains is greater than about ten coherence lengths, the proximity effect can be described in terms of a surface free energy whose high-temperature behavior is compatible with the cubic Ginzburg-Landau equation. Values of a parameter related to the extrapolation length are derived from the surface free energies, and are shown to lead to transition temperatures which are in good agreement with the observed values in this regime. At the opposite extreme, where the S-domain thickness is comparable to or less than the coherence length, the results show that the thermal properties are virtually indistinguishable from those expected for a homogeneous superconductor with a very low gap ratio Δ0/kT c. The condition for such “pseudohomogeneous” behavior is estimated to be1/2D S≲2ξ(T), whereD S is the thickness of the lead-rich lamellae and ξ(T) is a temperature-dependent coherence length. The transition temperatures of these alloys agree very well with the theory of Moormann for the large periodicities, and moderately well for the small periodicities if the ratio(NV) S/(NV) N of the theory is regarded as an adjustable parameter. However, if this is taken as the ratio of coupling strengths obtained from tunneling experiments—as suggested by the theory of Silvert for the proximity effect in strong coupling materials—then the agreement is only fair for small lamellar periods. The specific heat jump at the transition temperature is found to be in reasonable accord with calculated values based on the Fulde and Moormann theory, provided that one defines the “jump” suitably and that it is regarded as a function ofT c rather than of lamellar thickness. When the same calculations are extended to the region well belowT c, they give results which agree remarkably well with the data in the neighborhood of the specific heat “jump” associated with the tin-rich lamellae. The effects of lamellar stability, irregularities, strains, and concentration gradients are also discussed.

Notes: Abstract We show that reduced critical fields, entropies, and specific heats of superconductors, regardless of “coupling-strength,” can be fitted essentially within experimental errors by curves appropriate to a system of independent fermion quasiparticles. The analysis proceeds from the formula for the entropy of a system of independent fermionsS=−k B Σ [f lnf+(1−f) ln (1−f)], where we take the quasiparticle spectrum to be the same as in the BCS (weak-coupling) theoryE k 2 =(ε k 2 +Δ2). The temperature dependence of the energy gap is also taken to be the same as in the BCS theory, the only adjustable parameter being the gap ratio Δ(0)/k B T c . The necessary values of this ratio are found to be in reasonable agreement with the experimental values deduced from electron tunneling and infrared absorption. Some speculations are offered for the paradoxical success of this simple model, based on analogies with the effects of strong coupling in the normal state.