Negative thermal expansion of MgB$_{2}$ in the superconducting state and   anomalous behavior of the bulk Gr\"uneisen function
  The thermal expansion coefficient $\alpha$ of MgB$_2$ is revealed to change from positive to negative on cooling through the superconducting transition temperature $T_c$. The Gr\"uneisen function also becomes negative at $T_c$ followed by a dramatic increase to large positive values at low temperature. The results suggest anomalous coupling between superconducting electrons and low-energy phonons. 
J. J. Neumeier, T. Tomita, M. Debessai, J. S. Schilling, P. W. Barnes,   D. G. Hinks and J. D. Jorgensen