Role of Surface Effects in the Vibrational Density of States and the Vibrational Entropy in Spin Crossover Nanomaterials: A Molecular Dynamics Investigation

Abstract

Size reduction effects on the lattice dynamics of spin crossover (SCO) thin films have been investigated through molecular dynamics (MD) simulations of the density of vibrational states. The proposed simple model structure and reduced force field allows us to obtain good orders of magnitude of the sound velocity in both spin states and takes into account the contribution of free surfaces in the vibrational properties of very thin films (below a thickness of 12 nm). The slab method issue from the field of surface physico-chemistry has been employed to extract surface thermodynamic quantities. In combination with the related slab-adapted method, the slab approach provides a powerful numerical tool to separate surface contributions from finite-size effects. Due to the relatively low stiffness of SCO materials, the lattice dynamics seems to be governed by surface instead of confinement effects. The size evolution of thermodynamic quantities is successfully reproduced, especially the increase of the vibrational entropy with the size reduction, in good agreement with experimental observations.

Disentangling Surface Energy and Surface/Interface Stress Effects in Spin Crossover Nanomaterials

“…We note here that the interfacial energy is considered negligible in comparison with the surface energy for a semi‐coherent interface and this term will be thus omitted. In a recent work, [ 50 ] we have shown that the surface entropy difference (per molecule) Δ S s was negligible in the case of this modeled structure. The contribution of solid–solid interface to the entropy is more difficult to estimate, but we can reasonably assume that Δ S int ( L z ) ≈ 0 in this work since a semi‐coherent interface between two phases having similar mechanical and structural properties are considered, so that the production of configurational entropy is limited.…”

“…The investigation of lattice dynamical properties has been carried out in both spin states through the calculation of the total density of vibrational states (vDOS) on a slab having a thickness of ≈13 nm (2500 octahedrons) in the framework of the model I. This thickness has been shown to be sufficiently large to model the vibrational properties of a bulk material, [ 50 ] avoiding the discretization of the vDOS spectrum related to confinement effects. The slab adapted method assures the absence of surface effects.…”

“…(For more details about the assessment of the FF, see the supplementary materials of ref. [50]). It is interesting to compare the strength of intermolecular interactions of this present FF with those employed to simulate the epitaxial strain at a SCO complex‐metallic interface.…”

“…This situation constitutes a reference and is often called slab‐adapted method . [ 50 ] Model I allows to extract thermodynamic and mechanical properties of a system where surface and interface effects are absent. Then, a solid‐vacuum surface is created by increasing the length h = L z + L vacuum of the simulation box in the z ‐direction ( L vacuum ≈ 20 nm).…”

“…Numerical results become independent of L vacuum if this latter is sufficiently large to avoid self‐interactions due to periodic boundary conditions. [ 50 ] This corresponds to the model II (see Figure 1c), from which surface energy can be calculated for the two spin states. Finally, a multi‐layer system surrounded by vacuum and constituted of LS and HS phases, separated by a semi‐coherent solid–solid interface is built.…”