The role of carbon for superconductivity in MgC$_{x}$Ni$_{3}$ from   specific heat
  The influence of carbon deficiency on superconductivity of MgCNi$_{3}$ is investigated by specific heat measurements in the normal and superconducting state. In order to perform a detailed analysis of the normal state specific heat, a computer code is developed which allows for an instantaneous estimate of the main features of the lattice dynamics. By analyzing the evolution of the lattice vibrations within the series and simultaneously considering the visible mass enhancement, the loss in the electron-phonon coupling can be attributed to significant changes of the prominent Ni vibrations. The present data well supports the recently established picture of strong electron-phonon coupling and ferromagnetic spin fluctuations in this compound. 
A. W\"alte, G. Fuchs, K.-H. M\"uller, S.-L. Drechsler, K. Nenkov, L.   Schultz