Effects of the surface energy and surface stress on the phase stability of spin crossover nano-objects: a thermodynamic approach

Size-induced phase transformation at the nanoscale is a common phenomenon whose understanding is essential for potential applications. Here we investigate phase equilibria in thin films and nanoparticles of molecular spin crossover (SCO) materials. To calculate the size-temperature phase diagrams we have developed a new nano-thermodynamic core-shell model in which intermolecular interactions are described through the volume misfit between molecules of different spin states, while the contributions of surface energy and surface stress are explicitly included. Based on this model, we rationalize the emergence of previously-reported incomplete spin transitions and the shift of the transition temperature in finite size objects due to their large surface-to-volume ratio. The results reveal a competition between the elastic intermolecular interaction and the internal pressure induced by the surface stress. The predicted transition temperature of thin films of the SCO compound [Fe(pyrazine)][Ni(CN)4] follows a clear reciprocal relationship with respect to the film thickness and the transition behavior matches the available experimental data. Importantly, all input parameters of the present model are experimentally accessible physical quantities, thus providing a simple, yet powerful tool to analyze SCO properties in nano-scale objects. Calculated temperature dependence of the high spin fraction for spin crossover thin films. All input parameters are measurable physical quantities.