Open AccessTHE ALGORISM AND COMPUTER PROGRAMME FOR INDEXING ORTHORHOMBIC DEBYE-SCHERRER PHOTOGRAPHS
Author(s) -
Lu Xue-Shan,
Luo Shou-Min
Publication year - 1981
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.30.1488
Subject(s) - orthorhombic crystal system , intersection (aeronautics) , physics , diffraction , unit (ring theory) , series (stratigraphy) , crystal (programming language) , line (geometry) , plane (geometry) , crystallography , combinatorics , geometry , mathematical analysis , mathematics , optics , chemistry , paleontology , mathematics education , aerospace engineering , computer science , biology , programming language , engineering
The computer method of indexing Debye-Scherrer photographs has been extended to the case of orthorhombic crystals. Any observed diffraction line may be represented by an equation of a plane hi2A+ki2B+li2C=sin2θi in the A-B-C three dimensional space, where A, B, and C are related to the translational vectors a, b, and c by A = λ2/4a2. B = λ2/4b2, and C = λ2/4c2 respectively. Since the indices (hi, ki, li) are unknown at the outset, these planes are only conditional planes. It is seen that the intersection of three conditional planes, representing respectively three low angle lines with simple indices, will determine a point in the space which might indicate the dimensions of the unit cell. To guard against accidental coincidences, a series of equiatomic curved surfaces is introduced, representing in each case an integral number of configuration units contained in the unit cell. The equation of the equiatomic curved surface is ABC = (pλ3/8Mm0)2 (l/Z2), where p is the density of the crystal, M the formula weight of the configuration unit, m0 the mass of the atom of unit atomic weight, and Z the number of configuraunits contained therein, Z being a parameter. It is seen that if the point determined by the intersection of conditional planes is a physical point, this point must lie on one of the equiatomic surfaces.As a further discrimination, a fourth observed line may be used, to see whether a triplet (h, k, l) of the coefficients may be fitted into the conditional equation to form a plane that will pass through the proposed point.In fact, the whole geometrical problem is reduced to that all planes represented by their respective proper triplets will intersect at one point which passes through an equiatomic surface.The programme is written in Fortran and will be indicated by POWDBX-OR.