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Here we review the basic concepts and applications of the phase-field-crystal (PFC) method,
which is one of the latest simulation methodologies in materials science for problems, where
atomic- and microscales are tightly coupled. The PFC method operates on atomic length and
diffusive time scales, and thus constitutes a computationally efficient alternative to molecular
simulation methods. Its intense development in materials science started fairly recently following
the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial
studies, dynamical density functional theory and thermodynamic concepts have been linked to
the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we
summarize these methodological development steps as well as the most important applications
of the PFC method with a special focus on the interaction of development steps taken in hard
and soft matter physics, respectively. Doing so, we hope to present today’s state of the art in
PFC modelling as well as the potential, which might still arise from this method in physics and
materials science in the nearby future
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