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that the energy gap E and the cyclotron mass m^ at the bottom of the band are the same as those in pure bismuth, a Fermi energy in Bi 95 Sb 5 is calculated to be Eg =0.007 eV. The values for the Fermi energy and Eg in pure bismuth are taken to be those measured by Brown, Mavroides, and Lax in magnetoreflection measurements. 9 They are E e = 0.025 eV and E g = 0.015 eV. The number of electrons per ellipsoid is derived from Eq. (2) to bewhere m^detajy)" 113 is the density-of-states effective mass at the bottom of the band. In pure bismuth, N e is calculated to be N e -0.8 xl0 17 /cm 3 and in Bi 95 Sb 5 , iVg = 0.05xl0 17 /cm 3 . A three-ellipsoid model for the electrons in Bi 95 Sb 5 gives the total number of electrons AT=0.15xl0 17 /cm 3 quoted earlier.The occurrence of a long relaxation time in such a nondilute alloy is somewhat surprising. This is plausible, however, since the electron wavelengths Many superconductors, including niobium, maintain zero resistance when exposed to magnetic fields substantially higher than their thermodynamic or bulk critical fields, H c^. In this sense niobium is a high-field superconductor, and explanations of its behavior may be applicable to more complex materials such as alloys or compounds. Present explanations of high-field superconductivity invoke, directly or indirectly, the thermodynamic argument 1 that if a superconducting region is thin enough to permit substantial field penetration, it will remain superconducting for H>H c fy These theories fall into two classes:(A) Inhomogeneities such as fine filaments exist which have a higher H c i) than the surrounding material. In a strong field the current flows along these filaments, which may be dislocations. 2 As the applied field is increased these filaments are of the order of 1000 A and will not be strongly scattered by individual solute atoms.