Al-27 quadrupolar parameters are determined for the three aluminium sites in beta-Ba3AlF9 from the reconstruction of experimental SATRAS and MQ-MAS NMR spectra. These quadrupolar parameters are then computed using the DFT linearized augmented plane wave method implemented in the WIEN2k code. A fine agreement between experimental and calculated values is obtained only after optimizing the beta-Ba3AlF9 structure. The optimized structure is more satisfactory than the previously published one from a crystallographic point of view (bond lengths and angles). This approach which allows to refine crystallographic structures especially when they lack accuracy may be extendable to other compounds containing quadrupolar nuclei. (c) 2006 Elsevier B.V. All rights reserved.