▁given ▁diff ract ed ▁beam . ▁This ▁is ▁known ▁as ▁the ▁phase ▁problem ▁of ▁cry stal log raph y . ▁ ▁If ▁the ▁diff raction ▁can ▁be ▁considered ▁kin emat ical , ▁constraints ▁may ▁be ▁used ▁to ▁probabil ist ically ▁relate ▁the ▁phases ▁of ▁the ▁ref lections ▁to ▁their ▁amplit udes , ▁and ▁the ▁original ▁structure ▁can ▁be ▁solved ▁via ▁direct ▁methods ▁( see ▁Say re ▁equation ▁as ▁an ▁example ). ▁Kin emat ical ▁diff raction ▁is ▁often ▁the ▁case ▁in ▁x - ray ▁diff raction , ▁and ▁is ▁one ▁of ▁the ▁primary ▁reasons ▁that ▁technique ▁has ▁been ▁so ▁successful ▁at ▁solving ▁cry stal ▁structures . ▁However , ▁in ▁electron ▁diff raction , ▁the ▁prob ing ▁wave ▁interact s ▁much ▁more ▁strongly ▁with ▁the ▁electro static ▁cry stal ▁potential , ▁and ▁complex ▁dynam ical ▁diff raction ▁effects ▁can ▁domin ate ▁the ▁measured ▁diff raction ▁patterns . ▁This ▁makes ▁application ▁of ▁direct ▁methods ▁much ▁more ▁challeng ing ▁without ▁a ▁pri ori ▁knowledge ▁of ▁the ▁structure ▁in ▁question . ▁ ▁Ab ▁Init io ▁structure ▁determ ination ▁ ▁D iff raction ▁patterns ▁collected ▁through ▁P ED ▁often ▁agree ▁well - en ough ▁with ▁the ▁kin emat ical ▁pattern ▁to ▁serve ▁as ▁input ▁data ▁for ▁direct ▁methods ▁calculations . ▁A ▁three - dimensional ▁set ▁of ▁intens ities ▁mapped ▁over ▁the ▁reci pro cal ▁lattice ▁can ▁be ▁generated ▁by ▁collect ing ▁diff raction ▁patterns ▁over ▁multiple ▁zone ▁axes . ▁App lying ▁direct ▁methods ▁to ▁this ▁data ▁set ▁will ▁then ▁yield ▁probable ▁cry stal ▁structures . ▁Cou pling ▁direct