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The elimination of an approximation in the Warren–Averbach analysis
Author(s) -
Delhez R.,
Mittemeijer E. J.
Publication year - 1976
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/s0021889876011035
Subject(s) - logarithm , trigonometric functions , series (stratigraphy) , fourier series , mathematics , power series , series expansion , power function , taylor series , mathematical analysis , geometry , paleontology , biology
The Warren–Averbach analysis for the separation of particle size and strain involves a cosine and a logarithmic power series expansion. It is shown that the neglect of higher‐order terms in the logarithmic series expansion introduces larger errors at small values of the strain than the cosine series while at larger values the dominance is less pronounced. Furthermore it is shown that the power series expansion for the logarithm is superfluous and as a result the Warren–Averbach analysis can be improved. In common practice the differences between the improved method and the original one can easily be 10% for particle‐size Fourier coefficients and 30% for mean square strain values.