A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material

Published

July 1, 2004

Author(s)

N G. Armstrong, W Kalceff, James Cline, John E. Bonevich

Abstract

A Bayesian/Maximum Entropy (MaxEnt) method for determining crystallite size distribution and morphology from size-broadened x-ray line profiles is presented. This method will be used in certifying a nanocrystallite-size standard reference material (SRM) being developed at the National Institute of Standards and Technology (NIST). The proposed SRM will assist in ensuring that uniform procedures in quantifying the microstructure of nanocrystallites from x-ray line profile data are developed. This will become increasingly important as emerging nanotechnology applications begin to call for crystallites designed to have particular morphology and size distributions. The Bayesian/MaxEnt method is presented as a way of overcoming the inherent difficulties in determining the size distribution from the experimental x-ray line profile data. These difficulties pertain to solving the inverse problem of the governing integral equation for crystallite size-broadening. It is proposed that the principles of inductive reason be used to determine the most plausible or probable size distribution, given our knowledge of the experimental data and equipment, while employing any suitable a priori information. These principles are embodied in Bayesian theory, with the entropy function used to assign values to the size distribution constrained by the experimental data, and resulting in a size distribution (or solution) with minimal assumptions.

Proceedings Title

Analysis of Microstructure and Residual Stress by Diffraction Methods, International Conference | 3rd| Diffraction Analysis of the Microstructure of Materials | Springer

Volume

68

Conference Dates

December 2-5, 2001

Conference Location

Trento, 1, IT

Conference Title

Springer Series in Materials Science

Pub Type

Conferences

Keywords

bayesian inference, deconvolution, maximum entropy, nano-technology, size broadening, x-ray powder diffraction

Citation

Armstrong, N. , Kalceff, W. , Cline, J. and Bonevich, J. (2004), A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material, Analysis of Microstructure and Residual Stress by Diffraction Methods, International Conference | 3rd| Diffraction Analysis of the Microstructure of Materials | Springer, Trento, 1, IT (Accessed April 16, 2024)