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We have performed sound velocity measurements in (V$_{1-x}$Cr$_x$)$_2$O$_3$in the vicinity of the critical point of the first order Mott transition line.The pressure sweeps at constant temperature reveal a large dip in the $c_{33}$compression modulus, this dip sharpens as the critical point is approached. Wedo not observe signs of criticality on the shear modulus $c_{44}$ which isconsistent with a transition governed by a scalar order parameter, inaccordance with the DMFT description of the transition. However, the amplitudeof the effect is an order of magnitude smaller than the one obtained from DMFTcalculations for a single band Hubbard model. We analyze our results using asimple model with the electronic response function obtained from the scalingrelations for the conductivity.

Lattice softening effects at the Mott critical point of Cr-doped V$_2$O$_3$