▁This ▁has ▁been ▁account ed ▁for ▁using ▁a ▁two - be am ▁correction ▁following ▁the ▁form ▁of ▁the ▁Black man ▁correction ▁originally ▁developed ▁for ▁pow der ▁x - ray ▁diff raction . ▁Com bin ing ▁this ▁with ▁the ▁a for ement ioned ▁Lor ent z ▁correction ▁yields : ▁ ▁where ▁, ▁ ▁is ▁the ▁sample ▁thick ness , ▁and ▁ ▁is ▁the ▁wave - vector ▁of ▁the ▁electron ▁beam . ▁ ▁is ▁the ▁B essel ▁function ▁of ▁zero eth ▁order . ▁ ▁This ▁form ▁see ks ▁to ▁correct ▁for ▁both ▁geometric ▁and ▁dynam ical ▁effects , ▁but ▁is ▁still ▁only ▁an ▁approximation ▁that ▁often ▁fails ▁to ▁significantly ▁improve ▁the ▁kin ematic ▁quality ▁of ▁the ▁diff raction ▁pattern ▁( s ometimes ▁even ▁w ors ening ▁it ). ▁More ▁complete ▁and ▁accurate ▁treat ments ▁of ▁these ▁theoretical ▁correction ▁factors ▁have ▁been ▁shown ▁to ▁adjust ▁measured ▁intens ities ▁into ▁better ▁agreement ▁with ▁kin emat ical ▁patterns . ▁For ▁details , ▁see ▁Chapter ▁ 4 ▁of ▁reference . ▁ ▁Only ▁by ▁considering ▁the ▁full ▁dynam ical ▁model ▁through ▁mult is lice ▁calculations ▁can ▁the ▁diff raction ▁patterns ▁generated ▁by ▁P ED ▁be ▁sim ulated . ▁However , ▁this ▁requires ▁the ▁cry stal ▁potential ▁to ▁be ▁known , ▁and ▁thus ▁is ▁most ▁valuable ▁in ▁ref ining ▁the ▁cry stal ▁potential s ▁suggested ▁through ▁direct ▁methods ▁approaches . ▁The ▁theory ▁of ▁pre cess ion ▁electron ▁diff raction ▁is ▁still ▁an ▁active ▁area ▁of ▁research , ▁and ▁efforts ▁to ▁improve ▁on ▁the ▁ability ▁to ▁correct ▁measured ▁intens ities ▁without ▁a