Quantitative macroscopic treatment of the spatiotemporal properties of spin crossover solids based on a reaction diffusion equation

We propose here a new theoretical treatment of the spatiotemporal properties in spin-crosser solids, based on the expansion of the free energy taking into account the spatial fluctuations of the high-spin (HS) fraction. This leads to an equation of motion on the HS fraction following a reaction diffusion equation (RDE), in which most of the parameters can be derived from the experiments. This equation involves the true temporal and spatial scales at variance from the previous stochastic microscopic models, which were based on a homogeneous treatment of the crystal's properties. We have illustrated this new treatment for a two-dimensional rectangularly shaped system with a square symmetry and we could reproduce quantitatively the process of nucleation, growth, and propagation of the HS fraction inside the thermal hysteresis loop, accompanying a first-order transition. The computed spatiotemporal evolution of the system allowed one to follow the propagation of a well-defined macroscopic HS:LS interface, which was found in excellent quantitative agreement with the experimental observations of optical microscopy on the switchable spin crossover crystal [{Fe(NCSe)(py)(2)}(2)(m-bpypz)]. The RDE treatment should generate predictive models for novel spatiotemporal effects in spin crossover solids and more generally for all kinds of switchable molecular solids.