Fitting of full X-ray diffraction patterns is an
effective method for quantifying abundances during X-ray diffraction (XRD)
analyses. The method is based on the principal that the observed diffraction
pattern is the sum of the individual phases that compose the sample. By adding
an internal standard (usually corundum) to both the observed patterns and to
those for individual pure phases (standards), all patterns can all be
normalized to an equivalent intensity based on the internal standard intensity.
Using least-squares refinement, the individual phase proportions are varied
until an optimal match is reached. As the fitting of full patterns uses the
entire pattern, including background, disordered and amorphous phases are
explicitly considered as individual phases, with their individual intensity
profiles or “amorphous humps” included in the refinement. The method can be
applied not only to samples that contain well-ordered materials, but it is
particularly well suited for samples containing amorphous and/or disordered
materials. In cases with extremely disordered materials
where no crystal structure is available for Rietveld refinement or there is no
unique intensity area that can be measured for a traditional RIR analysis,
full-pattern fitting may be the best or only way to readily obtain quantitative
results. This approach is also applicable in cases where there are several
coexisting highly disordered phases. As all phases are considered as discrete
individual components, abundances are not constrained to sum to 100%.
[1] M. Eckert, “Disputed Discovery: The Beginnings of X- Ray Diffraction in Crystals in 1912 and Its Repercussions,” Acta Crystallographica Section A, Vol. 68, 2012, pp. 30-39. doi:10.1107/S0108767311039985
F. H. Chung, “Quantitative Interpretation of X-Ray Diffraction Patterns of Mixtures. I. Matrix-Flushing Method for Quantitative Multicomponent Analysis,” Journal of Applied Crystallography, Vol. 7, 1974, pp. 519-525.
doi:10.1107/S0021889874010375
F. H. Chung, “Quantitative Interpretation of X-Ray Diffraction Patterns of Mixtures. II. Adiabatic Principle of X- Ray Diffraction Analysis of Mixtures,” Journal of Applied Crystallography, Vol. 7, 1974, pp. 526-531.
doi:10.1107/S0021889874010387
C. R. Hubbard, E. H. Evans and D. K. Smith, “The Reference Intensity Ratio, I/Ic, for Computer Simulated Powder Patterns,” Journal of Applied Crystallography, Vol. 9, 1976, pp. 169-174. doi:10.1107/S0021889876010807
B. L. Davis, “Reference Intensity Quantitative Analysis Using Thin-Layer Aerosol Samples,” Advances in X-Ray Analysis, Vol. 27, 1984, pp. 339-348.
doi:10.1007/978-1-4613-2775-2_38
G. A. Pawloski, “Quantitative Determination of Mineral Content of Geological Samples by X-Ray Diffraction,” American Mineralogist, Vol. 70, No. 7-8, 1985, pp. 663- 667.
D. L. Bish and S. J. Chipera, “Problems and Solutions in Quantitative Analysis of Complex Mixtures by X-Ray Powder Diffraction,” Advances in X-Ray Analysis, Vol. 31, 1988, pp. 295-308.
doi:10.1007/978-1-4613-1035-8_32
D. L. Bish and S. J. Chipera, “Accuracy in Quantitative X-Ray Powder Diffraction Analyses,” Advances in X-Ray Analysis, Vol. 38, 1995, pp. 47-57.
doi:10.1007/978-1-4615-1797-9_5
S. J. Chipera and D. L. Bish, “Multireflection RIR and Intensity Normalizations for Quantitative Analyses: Applications to Feldspars and Zeolites,” Powder Diffraction, Vol. 10, No. 1, 1995, pp. 47-55.
doi:10.1017/S0885715600014305
H. M. Rietveld, “A Profile Refinement Method for Nuclear and Magnetic Structures,” Journal of Applied Crystallography, Vol. 2, 1969, pp. 65-71.
doi:10.1107/S0021889869006558
R. J. Hill and C. J. Howard, “Quantitative Phase Analysis from Neutron Powder Diffraction Data Using the Rietveld Method,” Journal of Applied Crystallography, Vol. 20, 1987, pp. 467-474. doi:10.1107/S0021889887086199
D. L. Bish and S. A. Howard, “Quantitative Phase Analysis Using the Rietveld Method,” Journal of Applied Crystallography, Vol. 21, 1988, pp. 86-91.
doi:10.1107/S0021889887009415
D. K. Smith, G. G. Johnson Jr., A. Scheible, A. M. Wims, J. L. Johnson and G. Ullmann, “Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern,” Powder Diffraction, Vol. 2, No. 2, 1987, pp. 73-77.
doi:10.1017/S0885715600012409
G. Cressey and P. F. Schofield, “Rapid Whole-Pattern Profile-Stripping Method for the Quantification of Multiphase Samples,” Powder Diffraction, Vol. 11, No. 1, 1996, pp. 35-39. doi:10.1017/S0885715600008885
M. Batchelder and G. Cressey, “Rapid, Accurate Phase Quantification of Clay-Bearing Samples Using a Position- Sensitive X-Ray Detector,” Clays and Clay Minerals, Vol. 46, No. 2, 1998, pp. 183-194.
doi:10.1346/CCMN.1998.0460209
S. J. Chipera and D. L. Bish, “FULLPAT: An Improved Full-Pattern Quantitative X-Ray Diffraction Method,” Proceedings of the 38th Annual Clay Minerals Society Meeting, Madison, 16-20 June 2001, p. 105.
S. J. Chipera and D. L. Bish, “FULLPAT: A Full-Pattern Quantitative Analysis Program for X-Ray Powder Diffraction Using Measured and Calculated Patterns,” Journal of Applied Crystallography, Vol. 35, 2002, pp. 744- 749. doi:10.1107/S0021889802017405
S. J. Chipera and D. L. Bish, “FULLPAT: A Full-Pattern Quantitative Analysis Program for X-Ray Powder Diffraction,” International Union of Crystallography, Commission on Powder Diffraction Newsletter, No. 27, 2002, pp. 27-28.
D. L. Bish and R. C. Reynolds Jr., “Sample Preparation for X-Ray Diffraction,” In: D. L. Bish and J. E. Post, Eds., Modern Powder Diffraction, Mineralogical Society of America Reviews in Mineralogy, Washington DC, Vol. 20, 1989, pp. 73-99.
S. Hillier, “Use of an Air Brush to Spray Dry Samples for X-Ray Powder Diffraction,” Clay Minerals, Vol. 34, No. 1, 1999, pp. 127-135. doi:10.1180/000985599545984
P. Sarrazin, S. Chipera, D. Bish, D. Blake and D. Vaniman, “Vibrating Sample Holder for XRD Analysis with Minimal Sample Preparation,” Proceedings of the 53rd Annual Denver X-Ray Conference, Steamboat Springs, 2- 6 August 2004, p. 89.
D. K. Smith, M. C. Nichols and M. E. Zolensky, “POWD 10, a FORTRAN IV Program for Calculating X-Ray Powder Diffraction Patterns, Version 10,” Pennsylvania State University, College of Earth and Mineral Sciences report, University Park, Pennsylvania, 1983.
P. Sarrazin, D. Blake, S. Feldman, S. Chipera, D. Vaniman and D. Bish, “Field Deployment of a Portable XRD/ XRF Instrument on Mars Analog Terrain,” Advances in X-Ray Analysis, Vol. 48, 2005, pp. 194-203.
S. J. Chipera, P. Sarrazin, L. Alcantar-Lopez, D. T. Vaniman, D. L. Bish, D. Blake and G. Chiari, “Real-Time XRD-XRF at a Mars-Analog Sulfate Site in Leadville, Colorado, Using a CHEMIN-Heritage Instrument,” 40th Lunar and Planetary Science Conference, 23-27 March 2009, Houston, No. 1328.
I. C. Madsen, N. V. Y. Scarlett, I. M. D. Cranswick and L. Thaung, “Outcomes of the International Union of Crystallography Commission on Powder Diffraction Round Robin on Quantitative Phase Analysis: Samples 1a to 1h,” Journal of Applied Crystallography, Vol. 34, 2001, pp. 409-426. doi:10.1107/S0021889801007476
O. Omotoso, D. K. McCarty, R. Kleeberg and S. Hillier, “Some Successful Approaches to Quantitative Mineral Analysis as Revealed by the 3rd Reynolds Cup Contest,” Clays and Clay Minerals, Vol. 54, No. 6, 2006, pp. 748- 760. doi:10.1346/CCMN.2006.0540609
