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Error analysis of 2π powder data for cubic or uniaxial phases
Author(s) -
Frevel L. K.
Publication year - 1978
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889878013096
Subject(s) - combinatorics , quadratic equation , mathematics , lattice (music) , product (mathematics) , error analysis , physics , mathematical analysis , geometry , acoustics
The likely error in the 2 θ measurement of a particular powder reflection can be bracketed by a self‐consistent error analysis. To a specific observed θ m value one assigns arbitrary increments { Δθ m } and calculates iteratively the corresponding increments of any other θ n according to the expression:where q is the product of the square root of the ratio of the quadratic factors for ( h m k m l m ) and ( h n k n l n ) and a correction factor for refraction. By considering special coincidences for which the various Δθ n 's are 0° or nil (0.000 X °), one arrives at a likely bracketing interval for Δθ m . Continuing this process one computes the indicated errors for the remaining reflections. The intent of the error analysis is to induce the experimenter to seek the cause(s) of the indicated errors in the 2 θ determinations, and to delimit more precisely the accuracy of lattice constants of cubic or uniaxial phases.