The Phonon Ceiling on Conventional Superconducting Tc: A Recount with the Allen-Dynes Formula

Published lambda and omega_log values for Al, Nb, Pb, Nb3Sn, MgB2 and H3S are recomputed end-to-end with the Allen-Dynes formula at a single mu* = 0.10. Five of six materials are reproduced within 20% (median absolute error 9.7%). The McMillan exponential saturates at 0.275 omega_log, the Allen-Dynes factors replace saturation with square-root growth, phonon softening largely cancels coupling gains, and a lattice-stability bound lambda < 3.69 gives ceilings of 83 K at omega_log = 300 K and 299 K at 1078 K. A Tc of 293 K requires omega_log of at least 1056 K at maximal stable coupling, or lambda = 31.6 at a typical metallic frequency scale.