Application of the maximum entropy method to x-ray profile analysis

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dc.contributor Armstrong, Nicholas Gray Garvin en_AU
dc.date.accessioned 2007-03-14T01:53:28Z
dc.date.accessioned 2012-12-15T03:52:07Z
dc.date.available 2007-03-14T01:53:28Z
dc.date.available 2012-12-15T03:52:07Z
dc.date.issued 1999
dc.identifier.uri http://hdl.handle.net/2100/329
dc.identifier.uri http://hdl.handle.net/10453/20102
dc.description University of Technology, Sydney. Department of Applied Physics.
dc.description.abstract The analysis of broadened x-ray diffraction profiles provides a useful insight into the structural properties of materials, including crystallite size and inhomogenous strain. In this work a general method for analysing broadened x-ray diffraction profiles is developed. The proposed method consists of a two-fold maximum entropy (MaxEnt) approach. Conventional deconvolution/inversion methods presently in common use are analysed and shown not to preserve the positivity of the specimen profile; these methods usually result in ill-conditioning of the solution profile. It is shown that the MaxEnt method preserves the positivity of the specimen profile and the underlying size and strain distributions, while determining the maximally noncommital solution. Moreover, the MaxEnt method incorporates any available a priori information and quantifies the uncertainties of the specimen profile and the size and strain distributions. Numerical simulations are used to demonstrate that the MaxEnt method can be applied at two levels: firstly, to determine the specimen profile, and secondly to calculate the size or strain distribution, as well as their average values. The simulations include both sizeand strain-broadened specimen profiles. The experimental conditions under which the data is recorded are also simulated by introducing instrumental broadening, a background level and statistical noise to produce the observed profile. The integrity of the MaxEnt results is checked by comparing them with the traditional results and examining problems such as deconvolving in the presence of noisy data, using non-ideal instrument profiles, and the effects of truncation and background estimation in the observed profile. The MaxEnt analysis is also applied to alumina x-ray diffraction data. It is found that the problems of determining the specimen profile, column-length and strain distributions can be solved using the MaxEnt method, with superior results compared with traditional methods. Finally, the issues of defining the a priori information in each problem and correctly characterising the instrument profile are shown to be critically important in profile analysis. en_AU
dc.format.extent 215959 bytes
dc.format.extent 3068865 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language en en_AU
dc.language.iso en_AU
dc.rights http://www.lib.uts.edu.au/disclaimer.html en_AU
dc.rights Copyright Nicholas Armstrong en_AU
dc.subject Entropy. en_AU
dc.subject X-rays. en_AU
dc.subject Diffraction. en_AU
dc.title Application of the maximum entropy method to x-ray profile analysis en_AU
dc.type Thesis (PhD) en_AU


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