Interatomic Potentials

The simulations were carried out with a fully ionic model ( La ^{3 +},  F ^-) of unpolarisable ions. The neglect of ionic polarisablity means that some features of the bulk material (for example, high-frequency dielectric constant and optical vibration modes) will not be accurately described, but experience on other ionic systems (Lindan and Gillan 1993; Ferneyhough, Fincham, Price and Gillan 1994) suggests that most thermodynamic properties will be adequately represented in this material (a statement that could not be made with such confidence for a material which contained much more polarizable ions, such as O ^{2 -}). In addition to the Coulomb interactions, short-range potentials of Buckingham type are introduced to describe F-F and F-La interactions. The parameters of the La - F potential were determined by fitting to perfect lattice properties of LaF₃ , the F - F potential was that previously used (Dornford-Smith and Grimes 1995) in studies of nanoclusters of Calcium Fluoride. The forms are

$$\phi_{\rm F-F}^{}$$ (1)

$$\phi_{\rm F-La}^{}$$ (2)

where the separation r is in Å and the energy $\phi$ is in eV. The ability of the potentials to describe the lattice parameters and elastic constants of LaF₃ is demonstrated in Table 1, which reports calculations made using the CASCADE static simulation code (Leslie 1982) with a short-range cut-off radius of 12 Å.

As the La - F potential was fitted to the crystal, it is interesting to ask how well the properties of the LaF₃ molecule are represented. The La - F separation in the isolated molecule is predicted to be 2.05 Å: experimental results are not available, but previous calculations (Krasnov 1966) put the spacing rather larger, at about 2.22 Å. However, the energy for dissociation into ions is 43 eV, in quite good agreement with an earlier theoretical estimate (Krasnov 1966) of 44 eV (if polarization of the Fluoride ion is included, using a shell charge of - 1.3776$\vert$e$\vert$ and a spring constant of 24.36 eV $\mbox{\AA}$^{- 2}, the bond length increases slightly, to 2.15 Å, and the dissociation energy increases to 43.5 eV: in our further calculations we ignore polarization). The symmetric vibration mode of the molecule is predicted to have a frequency of 13.0 THz, which is in fair agreement with the value of 14.7 THz obtained from empirical force constants (Wesley and DeKock 1971). The binding energy of the (LaF₃)₂ dimer is calculated to be 1.8 eV, whereas the experimental result is 2.7 to 3.1 eV (Skinner and Searcy 1971; Roberts and Searcy 1972). In view of the fact that in the model the fluorine is not polarizable, whereas polarization of the fluorine will help to screen the two lanthanum atoms in the dimer, this is reasonable agreement. We may conclude that the interatomic potentials give an adequate representation of the properties of the material over the whole range of the simulations.