Ichak rentgenografiyasi: natijani ko'rsatadigan tayyorgarlik

Friedel and Bijvoet mates

For every reflection corresponding to a point q in the reciprocal space, there is another reflection of the same intensivlik at the opposite point -q. This opposite reflection is known as the Friedel mate of the original reflection. This symmetry results from the mathematical fact that the density of electrons f(r) at a position r har doim a haqiqiy raqam. Yuqorida ta'kidlab o'tilganidek, f(r) is the inverse transform of its Fourier transform F(q); however, such an inverse transform is a murakkab raqam umuman. Buni ta'minlash uchun f(r) is real, the Fourier transform F(q) must be such that the Friedel mates F(−q) va F(q) bor murakkab konjugatlar bir-birining. Shunday qilib, F(−q) has the same magnitude as F(q) but they have the opposite phase, i.e., φ(q) = −φ(q)
The equality of their magnitudes ensures that the Friedel mates have the same intensity |F|². Ushbu simmetriya to'liq Furye konvertatsiyasini o'zaro fazoning atigi yarmidan o'lchashga imkon beradi, masalan, to'liq 360 ° aylanish o'rniga kristalni 180 ° dan bir oz ko'proq aylantirish orqali. Simmetriyasi sezilarli bo'lgan kristallarda aks ettirishlar bir xil intensivlikka ega bo'lishi mumkin (Bijvoet juftlari); bunday hollarda, hatto o'zaro bo'shliqning kamroq miqdorini o'lchash kerak bo'lishi mumkin. Yuqori simmetriyaning qulay holatlarida, o'zaro ta'sir doirasini to'liq o'rganish uchun ba'zida faqat 90 ° yoki hatto faqat 45 ° ma'lumotlar talab qilinadi.
Fridel-mate cheklovi teskari Furye konvertatsiyasi ta'rifidan kelib chiqishi mumkin
Beri Eyler formulasi e^menx = cos (x) men gunoh qilaman (x), teskari Furye konversiyasini sof real qism va sof xayoliy qism yig'indisiga ajratish mumkin
Funktsiya f(r) agar ikkinchi integral bo'lsa va faqat shu holda haqiqiy bo'ladi Men_gunoh ning barcha qiymatlari uchun nolga teng r. O'z navbatida, bu yuqoridagi cheklov qondirilgan taqdirdagina to'g'ri keladi
beri Men_gunoh = −Men_gunoh shuni anglatadiki Men_gunoh = 0.