Cluster evolution in molecular three-dimensional spin-crossover systems

The nucleation and growth properties of domains of molecules of the same state in open boundary three-dimensional (3D) spin-crossover systems of various shapes are discussed within the framework of the mechanoelastic model. The molecules are situated on face-centered-cubic lattices and are linked by springs through which they interact. Monte Carlo simulations imply that clusters nucleate from corners in the case of systems having well-developed faces and from kinks in the case of spherical samples, in accordance with available experimental data. In addition, a method to characterize the cooperativity in these systems is proposed, which by scanning the fluctuations in the 3D samples can be related directly to powder x-ray-diffraction experiments.

Figure 1

HS-LS relaxation curves (left) and hysteresis loops of the thermal spin transition (right) for different shapes and different sizes of the fcc sample with the model parameter values given in the text.

Figure 2

Snapshots of the systems taken during the HS-LS relaxation (top panel) and the HS-LS thermal transition (bottom panel) for the systems discussed in Fig. 1 at $n_{\mathrm{HS}}=0.7$ for small samples of 10 000 molecules (top rows in each panel) and large samples of 200 000 molecules (bottom rows in each panel) with the model parameter values given in the text. (HS: yellow spheres; LS: blue spheres.)

Figure 3

Normalized energy increase as a function of the cluster size relative to the total size [this ratio is actually the LS fraction or $\left(1-n_{\mathrm{HS}}\right)]$ for the large samples presented in Fig. 2.

Figure 4

(Top) Cluster formation for a large sphere $(1.3\times {10}^6$ molecules) from several points on the surface and their evolution towards the central part of the sphere with the model parameter values given in the text during the HS-LS relaxation at low temperatures. The sphere has been represented cut in order to see how the clusters propagate inside the crystallite. (Bottom) Cluster propagation in a similar sample with a higher interaction constant of $k=0.8\mathrm{N}{\mathrm{m}}^{-1}$ (the LS state is represented as smaller semitransparent blue dots to illustrate the single cluster evolution).

Figure 5

Illustration of the data analysis procedure based on scanning different areas of the sample.

Figure 6

Thermal spin-transition curves calculated within the framework of the mechanoelastic model for a cube of $50\times 50\times 50$ molecules with different values of the spring constant corresponding to weak $(k=0.05)$, moderate $(k=0.4)$, and strong $(k=0.8)$ interactions (top) together with snapshots of the systems in the two extreme situations and with the evolution of the corresponding x-ray powder-diffraction peaks during the thermal spin transition in the cooling branch (left panels) and the heating branch (right panels) for weak (top), moderate (middle), and strong interactions (bottom). (HS: yellow spheres; LS: blue spheres.)

Figure 7

(Top) Study of the cooperativity dependence with the size effects using the scanning method for $n_{\mathrm{HS}}=0.1,0.36,0.65,0.9$ for the heating branch of the thermal transition; (bottom) temperature scanning rate dependency of x-ray peaks for two different scanning rates. In the inset: the hysteresis loops for the two scanning rates.