Construction of Lennard-Jones pair potential and pairwise many-body potential for crystal α-boron

For α-boron, R3m group, Lennard-Jones (L-J) pair potential function is fitted, and a pairwise many-body potential is constructed. For constructing both interatomic potentials, only the atomic average cohesive energy and geometric information are needed. And the cohesive energy and geometry of α-boron crystal are calculated by first-principles code Castep. The fitting procedure for the potentials is as follows. For L-J potential, the minimum of the function is set to be located at the nearest neighbors. For the pairwise many-body potential, L-J potential is minimal, and the form of the function is chosen as a piecewise function, which consists of the L-J function and polynomial function. The minima of L-J potential are located at the distances between the different neighbors of atoms, and the potential barriers are at the midpoints of the distances of the two neighbor minima. L-J potential, L-J pair potential, and Tersoff potential for boron are tested and compared with each other, by energy minimization method in molecular dynamics (MD) simulation. The radial distribution function is used to analyze the structure obtained from the simulation results obtained by using different potentials. The results show that the structure after minimization deviates significantly from the initial crystal of α-boron by L-J potential, and final structure is consistent well with the initial ideal crystal, with L-J potential used. The NVT ensemble is used in MD simulation, where the temperature is set to be 2000 K, and the α-boron crystal experiences the thermodynamic evolutions for 10 fs and 100 fs, to obtain the deviated initial structures. Then the minimization by MD simulation is made to test the three potentials, which also shows that the L-J potential can give the much better result than the other two potentials.