Systematics in the superconducting and normal state properties in chemically substituted MgB$_{2}$

The superconducting transition temperature, T$_{C}$, the residual resistivity $\rho_{0}$ and the slope of resistivity curve at high temperature, d$\rho$/dT, have been measured in a series of MgB$_{2}$ samples that have been chemically substituted to varying degree with Li or Cu at the Mg-site and by Li or Cu at the Mg-site along with C substitution at the B-site. DC resistivity and ac susceptibility measurements were employed to extract the above parameters. T$_{C}$ versus the electron count (estimated from simple chemical valence count arguments) shows a universal behaviour, with T$_{C}$ being constant at the MgB$_{2}$ value for electron counts lower than in MgB$_{2}$ but rapidly decreasing for larger electron counts. The temperature dependence of resistivity in the normal state fits to the Bloch- Gruneisen formula, from which the Debye temperature, $\theta_{D}$, and the $\rho_{0}$ are extracted. $\theta_{D}$ variation with T$_{C}$ is not systematic, whereas $\rho_{0}$ versus T$_{C}$ shows a systematic variation that depends on the type of the chemical substituent. This dependence has a signature of the nature of the intraband/interband scattering affected by the chemical substitutions. d$\rho$/dT increases with C substitution, but decreases with Li and Cu substitution, implying that C substitution leads to the domination of conductivity by the $\sigma$ band, while in the Li/Cu substituted samples the $\pi$ band dominates conduction.