▁. ▁Cry stal ▁symmetry ▁is ▁described ▁and ▁categor ized ▁by ▁the ▁cry stal ▁system , ▁lattice , ▁and ▁space ▁group ▁of ▁the ▁material . ▁Det erm ination ▁of ▁these ▁attributes ▁is ▁an ▁important ▁aspect ▁of ▁cry stal log raph y . ▁ ▁Pre cess ion ▁electron ▁diff raction ▁enables ▁much ▁more ▁direct ▁determ ination ▁of ▁space ▁group ▁symmet ries ▁over ▁other ▁forms ▁of ▁electron ▁diff raction . ▁Because ▁of ▁the ▁increased ▁number ▁of ▁ref lections ▁in ▁both ▁the ▁zero ▁order ▁La ue ▁zone ▁and ▁higher ▁order ▁La ue ▁zones , ▁the ▁geometric ▁relationship ▁between ▁La ue ▁zones ▁is ▁more ▁readily ▁determined . ▁This ▁provides ▁three - dimensional ▁information ▁about ▁the ▁cry stal ▁structure ▁that ▁can ▁be ▁used ▁to ▁determine ▁its ▁space ▁group . ▁Furthermore , ▁because ▁the ▁P ED ▁technique ▁is ▁ins ens itive ▁to ▁slight ▁mis orientation ▁from ▁the ▁zone ▁axis , ▁it ▁provides ▁the ▁practical ▁benefit ▁of ▁more ▁robust ▁data ▁collection . ▁ ▁Direct ▁methods ▁▁ ▁Direct ▁methods ▁in ▁cry stal log raph y ▁are ▁a ▁collection ▁of ▁mathematical ▁techniques ▁that ▁seek ▁to ▁determine ▁cry stal ▁structure ▁based ▁on ▁measurements ▁of ▁diff raction ▁patterns ▁and ▁potentially ▁other ▁a ▁pri ori ▁knowledge ▁( constraint s ). ▁The ▁central ▁challenge ▁of ▁in ver ting ▁measured ▁diff raction ▁intens ities ▁( i . e . ▁applying ▁an ▁inverse ▁Fourier ▁Trans form ) ▁to ▁determine ▁the ▁original ▁cry stal ▁potential ▁is ▁that ▁phase ▁information ▁is ▁lost ▁in ▁general ▁since ▁intensity ▁is ▁a ▁measurement ▁of ▁the ▁square ▁of ▁the ▁mod ulus ▁of ▁the ▁amplitude ▁of ▁any