Hard sphere
= Hard sphere
{title2=$U(R)=\infty\ (R<d),\quad U(R)=0\ (R\geq d)$}
A <hard sphere> has an impenetrable core and otherwise no pair interaction. Two identical spheres of diameter $d$ cannot have centre separation below $d$. Even without attractive <potential energy>, crowding can produce fluid–crystal coexistence because available configuration space and <entropy> differ between the phases.