The effect of the size and shape on the bond number of quantum dots and its relationship with thermodynamic properties

Abstract

Through introducing the size (N_t) and the shape factor (λ), the size- and shape-dependent bond number B_a of quantum dots, respectively, with icosahedral, truc-decohedral, cuboctahedral, octahedral, decohedral and tetrahedral structures is established in this work. It is found that N_t and λ have reverse contribution to B_a, that is, B_a increases with increase in N_t, while it decreases with increase in λ. As the basic parameter, the size- and shape-dependent B_a function is extended to predict the cohesive energy E_c(N_t) of quantum dots. Similar to B_a, E_c(N_t) shows strong dependence on both the size and shape. Larger N_t leads to higher E_c(N_t), whereas larger λ results in a smaller E_c(N_t) value. There is a sequence: E_c(IH) > E_c(CO) > E_c(truc-DH) > E_c(OT) > E_c(DH) > E_c(TH) if N_t is certain, which is similar to B_a since B_a(IH) > B_a(CO) > B_a(truc-DH) > B_a(OT) > B_a(DH) > B_a(TH) is tested in the whole size range. To some extent, this is due to λ(IH) = λ(truc-DH) < λ(CO) < λ(OT) < λ(DH) < λ(TH), however, B_a(IH) > B_a(truc-DH) despite λ(IH) = λ(truc-DH). In addition, λ is no longer constant and increases with increase in N_t when the shape is given. The fact that whatever the shape is, B_a or E_c(N_t) increases upon increasing N_t, meaning that the shape is a secondary factor if compared with the size. The validity of the size- and shape-related model for the E_c(N_t) function is also confirmed by the simulation results of the size- and shape-dependent thermodynamic stability of Au, Ag, Cu, Ca, Sr, and Si quantum dots with different atomic structures.