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

Through introducing the size (N-t) and the shape factor (lambda), 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 lambda have reverse contribution to B-a, that is, B-a increases with increase in N-t, while it decreases with increase in lambda. 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 lambda 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 lambda(IH) = lambda(truc-DH) < lambda(CO) < lambda(OT) < lambda(DH) < lambda(TH), however, B-a(IH) > B-a(truc-DH) despite lambda(IH) = lambda(truc-DH). In addition, lambda 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.