Measurement of particle absorption by X‐ray fluorescence

The intensi ty, P , of secondary X-rays (either scattered or fluorescent) from a powder specimen will depend on particle size on account of absorpt iont . Wi th vanishing particle size (chemical composition, geometry etc. being kep t equal) a l imit P0 is approached, and PIPe is a convenien t measure of this 'particle absorption' effect (Wilchinsky, 1951). I t should be no ted tha t this definit ion is unambiguous only in the case of a sample wi th a flat surface used in reflection (that is, wi th the pr imary beam impinging on this surface at an angle c~ smaller than the deviation angle 2~0, so t ha t the secondary beam emerges from the same surface). In the transmission case, for instance, one has to define exact ly what 'constant thickness ' means wi th varying particle size. In the following, only the dimension-free reflection case is t reated. I t is possible to measure PIPe in the way indicated by the definition. Wilchinsky (1951) has actually performed diffraction experiments using graded fractions of iron and tungs ten powder, in order to test his theory of the effect. Such experiments are extremely delicate, so tha t the description presently to be given of a less direct but much easier me thod was thought wor th while. This me thod brings out a new aspect of particle absorption, namely its angular dependence, which has not been measured before nor predicted from theory (except by Wilchinsky, in so far as his theory presents a singularity for ~ = 90 ° whereas ~ does not otherwise enter in his formulas for PIPe). An ordinary diffractometer of the Bragg-Bren tano type can be used wi thout essential modifications. The sample is moun ted as usual, but filters, electronic discriminators etc. are so adjus ted tha t only fluorescent radiat ion is registered. A run taken under these condi t ions -bu t with the usual 2:1 sample drive---should yield a constant intensi ty level for a sample free from particle absorption, such as a single-phase solid metal . I n other words, the function P0(¢) is a constant. This is because fluorescence is isotropic, and because the geometrical in tensi ty factor for fluorescence, like tha t for scattering, does not contain the goniometer angle ¢. Therefore, any angular dependance of particle absorption in a powder sample will show up, wi thout any distortion, in the record of a similar run wi th this sample. F rom P(¢) as a funct ion of the goniometer angle ~, the particle absorption factor P(~)/Po can then be derived, provided it has been de te rmined for a single value of ~. This can be achieved in two ways: