Quantitative X-ray Diffractometry on Milligram Samples Prepared on Silver Filters S. Altree-Williams Division of Occupational Health and Radiation Control, Health Commission of New South Wales, P.O. Box 163, Lidcombe, Australia 2 14 1
A x-ray diffractlon method is given for the quantitative determination of crystalline phases in a 0.1-10 mg sample. Sample preparation or collection on a silver membrane filter (or equivalent) is required. Quantitation is achieved by measuring the diffraction intensity of the analyte and the attenuation of a silver diffraction line due to the deposited sample. The weight of sample deposited is not required for the quantitation. The detection limit of the method is around 20 pg dependlng on the phase determined. For well characterized phases under condltions of large variation in sample mass absorption coefficient, the accuracy of the analysis was found to be within 10% relative at the 1-mg level.
The theoretical equation for quantitative analysis by x-ray powder diffractometry (XRD) on flat samples less than “infinitely thick” to the diffraction beam is ( I ) ,
1rJ -
1J
WJ ( 1 - e -2pM cosec S , J ) Y
(1)
where Z L =~ intensity of-diffraction line i of phase J; krJ = constant, dependent on analysis conditions and diffraction line i of phase J; WJ = weight fraction of phase J in the sample; I.L = mass absorption coefficient of the sample; = weight per unit area of the sample; and BLJ = angle of incidence of the x-ray beam to the sample for diffraction line i of phase J. The application of quantitative XRD to analyze thin samples has been of direct interest to workers engaged in environmental monitoring where samples are collected on filters and direct analysis on the filter would be convenient. Such a technique would also provide a quantitative microanalytical method for XRD in general. Initial workers (2-5) limited the weight and composition of the loading on the filter so that the effect of sample mass absorption coefficient would be negligible and a linear relationship exist between the quantity of analyte and its diffraction line intensity. Bumsted (6) applied the internal standard technique to assess for p but significant sample preparation was required. Leroux and co-workers provided the breakthrough for the technique first by introducing the silver membrane filter ( 4 ) and later by using its silver diffraction line intensity to compensate for mass absorption effects in the surmounting powder (7).These workers developed a theory for the technique using their f ( T ) terminology. An alternative theory is presented here which is thought to provide a quantitation equation more convenient for use in practice. The ratio of the diffraction intensity of a silver line after and before sample loading will be equal to the sum attenuation of the incident and diffracted x-ray beam caused by the surmounting powder, giving
z
where w , 2 are as for Equation 1; = diffraction intensity of the silver line after and before loading, respectively;
and 0~~ = angle of incidence of the x-ray beam to the filter a t the silver diffraction line. Consider Equation 1. Substitution can first be made for WJ = M ~ / ( Z to . Agive ) (3)
followed by substitution of 1%using Equation 2 to give
where I ,J , k L J ,B r ~ 0~~ , have been previously defined; M J = weight of phase J on filter; L = In ( I ’ A ~ / Z A and ~ ) ; A = area of deposition on the filter. Equation 4 directly relates the weight of phase J on the filter to its diffraction intensity and is independent of the filter loading in the sense that this parameter is determined from silver diffraction line intensity measurements. Quantitation only. The is achieved from measurements of Z L ~ , and constant h , has ~ to be previously determined from deposits of phase J on filters. A further equation of interest is that relating Z lto~MJ when the filter loading is so light that no significant difference occurs between Z A and ~ Under these conditions substitution of = MJ/A can be made in Equation 3 followed by differentiation to find dILJldMJ. Setting M J = 0 gives the slope of the curve for light filter loadings and thus the equation for use under these conditions as
(5) Equation 5 would be used whenever the deviation from linearity is less than n%;that is, whenever the ratio of the Z‘J given by Equations 4 and 5 for the same filter loading is greater than 1 - (n/100).Considering this ratio, expressing the exponential term as a power series, and taking the first approximation, gives the condition for use of Equation 5 as n sin B ~ J 50 sin 0~~ In this work Equation 5 was used when the deviation from linearity was less than 10% (Le., n = 10 in Equation 6).
L
