Solute Size and Valence Effect in Some Superconducting Alloys of Transition Elements

The use of the concept of an effective electron-atom ratio, $N_{\mathrm{eff}}$, which contains a solute size correction (rather than the usual ratio $N$ used in Matthias' rule), introduced earlier in correlating superconducting critical temperatures of some dilute solutions of transition elements of the 4th, 5th, and 6th columns in niobium, has been extended to include some other transition-metal solutes of columns 7, 8, 9, and 10 in niobium. The concept has also been tried on some other transition-metal solid solutions of wider range of composition. For these latter alloys the analysis reveals that peaks in the curve of $T_c$ versus electron-atom ratio occur at $N_{\mathrm{eff}}\sim 4.4$ and ∼6.6, whereas with the uncorrected electron-atom ratio, these peaks tend to occur near $N\sim 4.7$ and ∼6.4. The variation of $H_{c2\mathrm{}}$ with $N_{\mathrm{eff}}$ for alloys of transition metals of columns 4 and 5 suggests that the maximum values of $H_{c2\mathrm{}}$ also occur near $N_{\mathrm{eff}}\approx 4.4$. Both peaks in $T_c$ versus $N_{\mathrm{eff}}$ and $H_{c2\mathrm{}}$ versus $N_{\mathrm{eff}}$ seem to be independent of whether the solvent or solute atom is in the $3d$, $4d$, or $5d$ series.