Quantitative Analysis by X-ray Diffraction

Certain minerals in soil clays may be directly estimated from diffraction line intensity and the mass absorption coefficient of the sample to the radiation used. The main advantages of the method described are that no internal standards or calibration charts are required, and any diffraction line of the component to be estimated may be chosen. The results obtained compare favourably with chemical determinations. Orientation of particles during sample preparation makes the estimation of some minerals very difficult. The uncertainty involved in choosing the background level under a diffraction line is the chief source of error in estimating small amounts of very fine-grained minerals. INTRODUCTION Because the intensity of an X-ray diffraction pattern is directly proportional to the concentration of the component producing it, when due allowance is made for absorption effects (Klug and Alexander, 1954), it has been possible to develop methods of quantitative analysis based on diffracted intensities. The diffracted intensity of any hkl reflection from any crystalline compound can be related to the composition of the compound and its matrix, and to the instrumental geometry (Klug and Alexander, 1954; yon Engelhardt, 1961). However, for any particular reflection, many of the parameters can be reduced to a constant. The following derivation of the relationship between diffracted intensity and absorption is reproduced in part from Klug and Alexander (1954). Therein, it is demonstrated that if the incident and diffracted X-ray beam enter and emerge symmetrically on the same side of a 'thick' flat powder specimen, I~ =KV (l) where Ix is the measured intensity of a diffraction line of a crystMline component of the sample, V is the volume fraction of the component, /~ is the linear absorpt on coefficient of the specimen, and K is a constant for any particular line of a particular mineral. This constant depends on the incident X-ray intensity, the diffracting power of the spacing being measured, the geometry of the instrument, etc. The sample has to be sufficiently 'thick' to completely attenuate the incident beam.