Directional Monte Carlo Lattice Search Algorithm for the Structure Search of Alumina Clusters (Al₂O₃)_n (n=1~50)

Abstract

Alumina nanoclusters have attracted increasing attention in many technical applications due to their excellent properties in optics, electricity, thermodynamics, chemical reactions and other aspects. Therefore, it is very important to find the optimal structure for further research. In this paper, we use the directional Monte Carlo lattice search algorithm combined with Woodley's potential function to investigate the stable structures of different sizes of alumina nanoclusters in different crystal forms (α, θ and δ). In our algorithm, the lattice was chosen from supercells which the primitive lattice cell from the inorganic crystal structure database (ICSD) was duplicated to generate large supercells of α, θ and δ phases. The initial random structure generated in the lattice, then the selective probability for all chosen and empty atoms is calculated based on the Boltzmann distribution of energy. In the directional Monte Carlo exchange, at elevated temperatures, the system has enough energy to cross energy barriers and find the basins, and at low temperatures, it converges to around the global minimum. After structure searching, we analyze and compare the stable structures of different crystal forms. The results show that the α-alumina clusters consist of multiple (Al2O3)1 and form a multilayer structure, as the size increased, hexagonal aluminum began to form inside the cluster. The θ and δ alumina clusters form a stable monolayer thin film structure, with the increase of size, the monolayer film structure can still be maintained. To further study the relative stability of the cluster structure, we introduced a second-order energy difference. The second-order energy difference of θ and δ alumina clusters has obvious odd-even oscillation, and the even size alumina clusters have relatively higher stability due to better symmetry. α-Alumina is the most stable crystalline phase in the bulk phase, so we take the α-alumina clusters as the benchmark to compare the relative energy of alumina clusters with different crystal types. Through the comparison of relative energy, we found that the thin film structure of θ and δ alumina clusters under the same size is more stable than that of the α-alumina clusters. Therefore, we further carried out first-principles calculations on this film structure, and we found that this film structure has good kinetic and thermodynamic stability and good oxidation resistance.