Superconducting Transitions in Tin Whiskers

Abstract

LETTERS TO THE EDITORfour atoms in the unit cell and thus assigning two of Wallace's diagonal matrix elements a different value than the other two. The discontinuity of the density of state at the band edge is proportional to the difference (H n -H22) and if this is large enough (greater than 271) the bands need not touch at alL It should be mentioned that asymmetry in the energy contours is a necessary feature to explain the sizeable negative Hall coefficient. 3 The purpose of the present note is to point out that the effect of including next-nearest neighbors (in the basal plane) is to introduce an asymmetry in the density of states in the same qualitative fashion as above. Nextnearest neighbors in the plane are easily taken into consideration and, in fact, Wallace 2 has already done so, although he neglects such terms when calculating the density of states. From reference 2, the energy of a state k, including nearest and next-nearest neighbors in the plane and nearest neighbors out of the plane, is;Here K X y 2 =K x 2 +fCy 2 , where K==k-k(corner), e is measured from the band edge, and 70, 70', and 71 are the resonance integrals involving coplanar nearest and nextnearest and interplanar nearest neighbors, respectively. The only effect of including 7</ is a term in K XV 2 . In the two-dimensional approximation (71=0) the y 0 ' term does not affect the density of states to a first order. However, when 71 is retained, the terms in y 0 f and in 70 are of the same order for small n xy and the density of states curve is altered markedly. The calculation for this case can be readily performed with the assumption that 7O'<3CTO, which is certainly true. The result for the density of states per atom to a second order in the energy is given below, where rjo-yo'/yo and 171=71/70-For0<e<27i, 271 r 7r e N(e)~ 1+-WH (TT+12 W I) v37r 2 7o 2 L 2 271 + (-) (f+ 6^i )l (2) (2) For -27i<e<0, 27i f 7T |e| iV(e)~ 1 T^H (TT-I2770771) VSTTWL 2 2 7 i + Gr) (f~67n?(m) } (3)The effect of 70' is seen in Fig. 1. There is a discontinuity in N(e) at zero and both its value and slope are less for the lower band. This is the same qualitative feature found by Carter and Krumhansl. The nextnearest neighbor effect may be of equal or greater im-FIG. 1. The graphite density of states (the solid line is for 70' = 0).portance than the effect of coordination number, although estimates of relative magnitude are difficult to make. It is, however, significant that these two modifications (dissimilar in nature) have similar effects on the density of states curve. This is probably a general property of the graphite lattice symmetry in that if the correct matrix elements were expanded in a Fourier series the above asymmetry would generally appear. The coefficients in the series would be disposable constants and not directly identifiable with any particular overlap integral by itself. The effects considered above and by Carter and Krumhansl would, however, be a major part of the first order coefficients. This change in the density of states is in the corre...

Superconductor Particles As The Working Media Of A Heat Engine

“…Experimental support for this hypothesis is reported by Lutes and Maxwell [7] who report that the phase transition of tin whiskers is abrupt in a transverse magnetic field, even though the demagnetizing factor is one-half.…”

Second law implications of a magnetocaloric effect adiabatic phase transition of type I superconductor particles

“…Hence, the free energy for a particle where k ( T ) / C ( T ) << 1 is minimized when the particle is all superconducting or all normal in phase, a result first posited by Pippard [lo] in 1952. T h e phase transition of tin whiskers [13] provides experimental support for this view.…”

Second Law Violation By Magneto-Caloric Effect Adiabatic Phase Transition of Type I Superconductive Particles

“…Hence, the free energy for a particle where λ(T)/ξ(T) << 1 is minimized when the particle is all superconducting or all normal in phase, a result first posited by Pippard in 1952 [11]. An experiment conducted on tin whiskers by Lutes and Maxwell [14] Performing an adiabatic magneto-caloric process upon such a particle dimensioned specimen, therefore, cannot proceed in the familiar way of a bulk dimensioned specimen as was detailed above, since a mixture of phase state is not permissible for a particle. The transition, consequently, is characterized by an abrupt variation in magnetization, the time for which is limited by the rate of flux movement out of the particle [2], accompanied by thermal relaxation.…”