Accuracy in Quantitative X-ray Powder Diffraction Analyses

Abstract

Abstract Accuracy, or how well a measurement conforms to the true value of a parameter, is important in XRD analyses in three primary areas, 1) 26 position or d-spacing; 2) peak shape; and 3) intensity. Instrumental factors affecting accuracy include zero-point, axial-divergence, and specimen- displacement errors, step size, and even uncertainty in X-ray wavelength values. Sample factors affecting accuracy include specimen transparency, structural strain, crystallite size, and preferred orientation effects. In addition, a variety of other sample-related factors influence the accuracy of quantitative analyses, including variations in sample composition and order/disorder. The conventional method of assessing accuracy during experimental diffractometry measurements is through the use of certified internal standards. However, it is possible to obtain highly accurate d-spacings without an internal standard using a well-aligned powder diffractometer coupled with data analysis routines that allow analysis of and correction for important systematic errors. The first consideration in such measurements is the use of methods yielding precise peak positions, such as profile fitting. High accuracy can be achieved if specimen-displacement, specimen- transparency, axial-divergence, and possibly zero-point corrections are included in data analysis. It is also important to consider that most common X-ray wavelengths (other than Cu Kα1) have not been measured with high accuracy. Accuracy in peak-shape measurements is important in the separation of instrumental and sample contributions to profile shape, e.g., in crystallite size and strain measurements. The instrumental contribution must be determined accurately using a standard material free from significant sample-related effects, such as NIST SRM 660 (LaB6). Although full-pattern fitting methods for quantitative analysis are available, the presence of numerous systematic errors makes the use of an internal standard, such as a-alumina mandatory to ensure accuracy; accuracy is always suspect when using external-standard, constrained-total quantitative analysis methods. One of the most significant problems in quantitative analysis remains the choice of representative standards. Variations in sample chemistry, order-disorder, and preferred orientation can be accommodated only with a thorough understanding of the coupled effects of all three on intensities. It is important to recognize that sample preparation methods that optimize accuracy for one type of measurement may not be appropriate for another. For example, the very fine crystallite size that is optimum for quantitative analysis is unnecessary and can even be detrimental in d-spacing and peak shape measurements.