Active soft matter frequently shows motility-induced phase separation, where self-propelled particles condensate into clusters with an inner liquidlike structure. Such activity may also result in motility-induced crystallization into clusters with an inner crystalline structure. We derive a higher-order active phase-field-crystal model and employ it to study the interplay of passive (i.e., thermodynamic) and active (i.e., motility-induced) condensation or evaporation and crystallization or melting. Stability and morphological phase diagrams indicate the various occurring phase coexistences and transitions, e.g., the destruction of passive clusters in the case of a density-independent effective velocity and the possible creation of active clusters in the case of a density-dependent effective velocity. Finally, simple and complex rotating crystallites are discussed, including states of time-periodic chirality.
Holl et al. (2025) studied this question.