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 fundaments 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.Keywords: phase-field-crystal (PFC) models, static and dynamical density functional theory (DFT and DDFT), condensed matter dynamics of liquid crystals and polymers, nucleation and pattern formation, simulations in materials science, colloidal crystal growth and growth anisotropy * Corresponding authors. Emails: heike.emmerich@uni-bayreuth. de, hlowen@thphy.uni-duesseldorf.de, and grana@szfki.hu

Refrigeration is one of the main sinks of the German and European electricity consumption and accordingly contributes to worldwide CO 2 emissions. High reduction potentials are envisaged if caloric effects in solid materials are used. The recent discovery of giant entropy changes associated with ferroelastic phase transformations promises higher efficiency. Ferroic transitions enhance the entropy change of magneto-, elasto-, baro-, and electro-caloric effects. Furthermore, because the refrigerant is in a solid state, this technology completely eliminates the need for halofluorocarbon refrigerants having a high global-warming potential. The smaller footprint for operation and the scalable mechanism open up further applications such as cooling of microsystems. While the principal feasibility of magnetocaloric refrigeration is already evident, it requires large magnetic fields (>2 T) which hampers wide industrial and commercial application. It is expected that this obstacle can be overcome by materials with lower hysteresis and by using stress-or electric fields. In order to accelerate research on ferroic cooling, the Deutsche Forschungsgemeinschaft (DFG) decided to establish the priority program SPP 1599 in April 2011. In this article we will address the major challenges for introducing ferroic materials in practical cooling applications: energy efficiency, effect size, and fatigue behavior. Solid state cooling in this sense can be based on the following ''ferroic-caloric'' classes of materials: ferroelastic shape memory alloys, ferromagnetic shape memory alloys, and ferroelectric materials and their possible combinations in materials with ''multicaloric'' effects. The open questions require the interdisciplinary collaboration of material scientists, engineers, physicists, and mathematicians. 10 wileyonlinelibrary.com ß

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