Size Consideration on Shape Factor and Its Determination Role on theThermodynamic Stability of Quantum Dots

Abstract

The size-related shape factor λ is established in this work and further introduced in the unified model for the melting piont Tm(D, λ) of quantum dots, respectively, with tetrahedral, decahedral, octahedral, cuboctahedral, and icosahedral atomic structures, where D means the diameter of quantum dots. For these quantum dots, the key difference is λ, which is defined as the surface area ratio between nonspherical and spherical quantum dots with identical volumes. It is found, when size is given, λ behaves as strong shape dependence with the sequence of λ(icosahedron) < λ(cuboctahedron) < λ(octahedron) < λ(decohedron) < λ(tetrahedron). This inevitably results in the sequence: Tm(icosahedron) > Tm(cuboctahedron) > Tm(octahedron) > Tm(decohedron) > Tm(tetrahedron) since the quantum dots with smaller λ value usually have higher thermodynamic stability. However, except shape dependence,λ also has obvious dependence on size, and decreases with size dropping. In fact, λ and D have reverse contribution to Tm(D, λ), that is to say Tm(D, λ) increases with D increasing, while decreases with λ increasing. However, for a certain atomic structure, the thermodynamic stability of quantum dots still decreases with size dropping, associated with the decrease in λ value. The validity of the model for Tm(D, λ) function is confirmed by the experimental and simulation results of the size- and shape-dependent thermodynamic stability in Au, Ag, Ni, Ar, Si, Pb, and In quantum dots.