In this letter, we present an analysis to understand why the McMillan-like Tc formula: , proposed in a previous paper by the authors, applies to crystalline superconductors satisfactorily but less satisfactorily to non-crystalline ones.

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A Tc formula is derived analytically from the Eliashberg equation by an iterative method. The Karakozov et al. Tc formula is only a weak-coupling limit of it. The values of Tc calculated from this formula are in agreement with the experimental values for both crystalline and amorphous superconducting materials. Certain reasonable approximations are made to render the Tc formula simplified and several useful formulae for Tc containing only a few parameters are obtained, one of which is just the Rowell empirical Tc formula. The Tc formulae obtained in the present paper are compared further with some empirical ones proposed by previous authors and some comments are given.

A formula of the critical temperature for superconductors with small λ is derived from the Eliashberg equation.

The numerical solution of the Eliashberg equation is analysed by a graphic analytic method, and the following conclusions are arrived. The superconducting Tc of a superconductor can be enhanced through the ‘hardening' of its normalized effective phonon spectrum g(ω). And the ‘softening' of g(ω) could enhance the Tc for a superconducting material with small λ, but not for the superconductor whose A is large.