  The nature of quantum criticality in CeCoIn$_5$ is studied by low-temperature
thermal expansion $\alpha(T)$. At the field-induced quantum critical point at
H=5 T a crossover scale $T^\star\approx 0.3$ K is observed, separating
$\alpha(T)/T\propto T^{-1}$ from a weaker $T^{-1/2}$ divergence. We ascribe
this change to a crossover in the dimensionality of the critical fluctuations
which may be coupled to a change from unconventional to conventional quantum
criticality. Disorder, whose effect on quantum criticality is studied in
CeCoIn$_{5-x}$Sn$_x$ ($0\leq x\leq 0.18$), shifts $T^\star$ towards higher
temperatures.
