  This paper shows by computer simulations that some crystalline systems have
curves in their thermodynamic phase diagrams, so-called isomorphs, along which
structure and dynamics in reduced units are invariant to a good approximation.
The crystals are studied in a classical-mechanical framework, which is
generally a good description except significantly below melting. The existence
of isomorphs for crystals is validated by simulations of particles interacting
via the Lennard-Jones pair potential arranged into a face-centered cubic (FCC)
crystalline structure; the slow vacancy-jump dynamics of a defective FCC
crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal
model does not exhibit isomorph invariances. Other systems simulated, though in
less detail, are the Wahnstrom binary Lennard-Jones crystal with the ${\rm
MgZn_2}$ Laves crystal structure, monatomic FCC crystals of particles
interacting via the Buckingham pair potential and via a novel purely repulsive
pair potential diverging at a finite separation, an ortho-terphenyl molecular
model, and SPC/E hexagonal ice. Except for NaCl and ice, the crystals simulated
all have isomorphs. Based on these findings and previous simulations of liquid
models, we conjecture that crystalline solids with isomorphs include most or
all formed by atoms or molecules interacting via metallic or van der Waals
forces, whereas covalently- or hydrogen-bonded crystals are not expected to
have isomorphs. Crystals of ions or dipolar molecules constitute a limiting
case for which isomorphs are only expected when the Coulomb interactions are
relatively weak. We briefly discuss the consequences of the findings for
theories of melting and crystallization.
