Modelling the Structure of Nanoparticle-embedding Matrices: Molecular Dynamics in $\mathrm{Li}_2\mathrm B_4\mathrm O_7$

A new model describing interatomic and angular interactions, taking into account periodic properties in borate-type solid phases, is presented and applied to $\mathrm{Li}_2\mathrm B_4\mathrm O_7$ through simulations at temperatures ranging from 0 K to the melting point and in the pressure range 0 to 10000 MPa. Simulation reproduces quite well cell lengths, atomic positions and distances in boron-oxygen polyhedrons and the polar nature of the crystal structure. An order-disorder type ferro-paraelectric transition of the second kind is found to occur at a Curie point $T_C\approx839$ K, corresponding to jumping of Li atoms between two lattice sites. By increasing or decreasing the pressure, the total energy and the crystal properties for simulations performed at 300 K show a shoulder at $p_t\approx5000$ MPa, implying the existence of a reversible second-order phase transition. The cell volume below $p_t$ follows a Murnaghan law with the bulk modulus $B_0=15.6$ GPa and its first derivative $B'_0=4.31$ (at ambient pressure). In contrast to the low-pressure phase where threefold and fourfold boron atoms coexist, in the high-pressure phase all borons are fourfold-coordinated. The present approach can be directly applied to modelling the structure of nanosized systems.