Cohesive Energy: The Intrinsic Dominant of Thermal Stability and Structural Evolution in Sn from Size Scales of Bulk to Dimer

Abstract

Size-dependent cohesive energy, Ec(n), is the intrinsic dominant for thermal stability and structural evolution of materials, where n denotes the number of atoms in the material of a particular size. In this work, the Ec(n) of Snn from the size scales of bulk (n = ∞) to dimer (n = 2) is investigated using nanothermodynamic models and ab initio density-functional theory (DFT) with the generalized gradient approximation. With the classification of material structural evolution caused by decreasing n, Ec(n) could be divided into four regimes: (1) For nanoparticles with bulk crystallographic structures (n ≥ 1000), Ec(n) increases nonlinearly with the decrease of n. (2) For large-sized clusters with spherical-like structures (35 < n < 1000), Ec(n) is proportional to n−1/3. (3) For medium-sized clusters with prolate structures (10 ≤ n ≤ 35), Ec(n) is size-independent. (4) For small-sized clusters with specific structures (2 ≤ n < 10), Ec(n) increases with decreasing n rapidly. In addition, the ground-state structures and size dependence of the highest-occupied and lowest-unoccupied molecular orbital gap in Snn (n = 2−20) clusters are also studied with DFT. The calculated and simulated results are in good agreement with experimental and other simulation results. The findings in this work may provide new insight into the fundamental understanding of the thermal stability in nanostructured and cluster-assembled materials.