Diffractometer Noise Characteristics: Experimental Determination and Application to Statistical Rocking-Curve Analysis

• Published in: Journal of applied crystallography Vol. 31; no. 2; pp. 185 - 197
• Main Authors: Staley, T. W., Matyi, R. J.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.04.1998; Blackwell
• Subjects: Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Physics; Single-crystal and powder diffraction; Structure of solids and liquids; crystallography; X-ray diffraction and scattering; Noise; Weight function; Intensity; Rocking curve; Theoretical study; Binomial distribution; Diffraction pattern; Models; XRD
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S0021889897009643

This paper examines the dependence of experimental noise in the X‐ray rocking‐curve experiment on the measured intensity, and develops a procedure for the use of this noise characteristic as a weight function for the optimization and analysis of calculated fits to the rocking‐curve pattern. The width of the noise distribution at a given experimental condition is shown to provide a measurement of the reliability of the individual data points, which can be used to attain a statistically unbiased fit to the data. A theoretical model of the dependence of the noise on measured intensity is developed, based on the well known binomial distribution, and the conditions for applicability of this model are discussed. This theoretical noise characteristic is compared to several empirical models and is shown to provide both an excellent estimate of the measured noise and enhanced fits to experimental rocking curves.