The dimensional dependence of the shape factor on thermodynamics

In this paper, the size-dependent model of the shape factor λ is established and the melting point T _m(D, λ) of quantum dots with tetrahedral, decahedral, octahedral, cuboctahedral and icosahedral atomic structures is further introduced into the model, where D represents the diameter of quantum dots. For these quantum dots, the key difference is λ, which is defined as the surface area ratio between non-spherical and spherical quantum dots with identical volumes. It is found that when the size is given, λ behaves as strongly shape dependent with the sequence of λ. The validity of the model for the T _m(D, λ) function is confirmed by the experimental and simulation results of the size- and shape-dependent thermodynamic stability in silver (Ag) quantum dots.