In a mixture of crystalline substances, the intensities measured by X-ray powder diffractometer are proportional to the quantities of the respective minerals. So it is possible to employ the powder method for quantitative phase analysis. The Rietveld method has become one of the most popular methods in mineralogical analysis based on X-ray powder diffractions. The basis of the Rietveld method was published in the late 1960’s. This method is very well described, but is quite complex and so not easy to use.
However, there are many laboratories that evaluate a large number of similar samples every day and need a simple and easy procedure for quantitative phase analysis. Therefore we have developed an easy program based on full-profile approach. This program minimizes the difference between an experimental and calculated pattern
M = Σwi [yi(obs.) – yi(calc.)]²,
where yi(obs.) is the intensity measured at a point i in the diffraction pattern, wi is its weight and yi(calc.) is the calculated intensity. The summation runs over all measured data points.
The calculated intensity is evaluated using the equation
yi(calc.) = Σ Σ sjk Gijk Ikj ,
where sjk is a scale factor, Gijk is the peak-shape function and Ikj is the tabulated intensity for phase k and peak j . The summation is over all reflections j and all minerals k.
The main measured materials in our laboratory are burnt clay and cordierite grog. The software has been used for almost 25 years with very good results and over 100 000 samples have been evaluated over the years. The reproducibility of measurements for the majority phase with contents above 10% is below 2% (relative) and for minor phases with a phase content below 10% is better than 5% (relative).