The specific edge effects of 2D core/shell model for spin-crossover nanoparticles

We analyzed the size effect of spin-crossover nanoparticles at the edges of the 2D square lattices core/shell model, where the edge atoms are constrained to the high spin (HS) state. We performed MC simulations using the Ising-like Hamiltonian, \[ H=-J\sum\limits_{(i,j)} {\sum\limits_{\begin{array}{l} i'=\pm 1; \\ j'=\pm 1 \\ \end{array}} {S\left( {i,j} \right)S\left( {i+i',j+j'} \right)} +\left( {\frac{\Delta }{2}-\frac{k_B T}{2}\ln g} \right)\sum\limits_{(i,j)} {S\left( {i,j} \right)} } \mbox{ } \] The molar entropy change is $\Delta $S$\approx $50J/K/mol, ln$g=\Delta $S/R$\approx $6 (R is the perfect gas constant), energy gap is $\Delta $=1300K. The HS fixed edges were based on the observation of an increasing residual HS fraction at low temperature upon particle size reduction. This specific boundary condition acts as a negative pressure which shifts downwards the equilibrium temperature. The interplay between the equilibrium temperature (=$\Delta $/k$_{B}$ln$g)$ variation and the expected variation of the effective interactions in the system leads to a non-monotonous dependence of the hysteresis loop width upon the particle size. We described how the occurrence condition of the first-order transition has to be adapted to the nanoscale.