Another method to calculate grain size distribution parameters: Using Ising model and particle swarm optimization algorithm. (15th November 2022) - Mo, Jiajun; Zhang, Qinghang; Xia, Puyue; Chen, Haiwen; Lu, Zeyi; Yang, Haoxun; Chen, Yibin; Xiao, Wenhao; Wang, Youhai; Liu, Min
Abstract: The grain size distribution parameters and magnetic parameters(exchange constant J and anisotropy parameter K) of CoFe Prussian blue analogues has been calculated using Ising model and particle swarm optimization algorithm in this work. The lattice with free boundary conditions is constructed to simulate the magnetism of Prussian blue analogues. The temperature dependence of magnetization varies with lattice size. Due to the fact that the grain size of the actual system follows lognormal distribution, we use the particle swarm optimization algorithm to search the two parameters of the lognormal distribution σ and D ¯ and the Co-Fe exchange coupling constant J and the anisotropy parameters K of the system. The results show that the grain size is ∼ 17.8 nm calculated by this method, which is close to the result (186 Å) calculated by Debye Scherrer formula. This method can be used to calculate the grain size of magnetic systems more accurately and can be applied to most small grain systems. Once the grain size distribution has been determined, it is also possible to deduce the magnetic parameters (exchange constant J and anisotropy parameter K). Highlights: A new method for calculating grain size is provided. The particle swarm optimization algorithm is used to fit the experimental data. The essential magnetic law of the experimental data is revealed. Simulate the magnetism PBAs grain by Ising model based on free boundary conditions.