Quantitative X-ray analysis—ratio correction
A method of X-ray analysis measures X-ray diffraction in transmission. In order to carry out quantitative measurements, a background measurement is taken slightly away from the diffraction peak and the ratio of measured intensities used to correct for variations in sample composition.
1. A method of X-ray analysis comprising:
making an X-ray diffraction measurement in transmission by directing X-rays from an X-ray source at an energy E onto a sample at an incident angle ψ 1 to the surface of the sample and measuring a diffraction intensity I d (θ d ) of the diffracted X-rays at the energy E with a X-ray detector at an exit angle ψ 2 to the surface of the sample, a difference 2θ d between the incident angle and the exit angle corresponding to an X-ray diffraction peak of a predetermined component; and
making a correction measurement of X-rays by measuring a background intensity of X-rays I d (θ bg ) at the energy E, with the difference 2θ bg between the incident angle and the exit angle deviating by 0.2 to 5° from the difference 2θ d corresponding to the X-ray diffraction peak; and
calculating the quantity of the predetermined component from the intensity ratio I d (θ fl )/ I d (θ bg ) of the diffraction intensity and the background intensity.
2. The method according to claim 1 , wherein the step of making a correction measurement of X-rays uses incident X-rays directed onto the sample at the same incident angle ψ 1 to the angle used in the step of making an X-ray diffraction measurement and measures the background intensity of X-rays at an exit angle ψ 3 to the surface of the sample, where ψ 3 =ψ 2 ±Δψ and Δψ is in the range 0.2 to 5°.
3. The method according to claim 1 , wherein calculating the quantity of the predetermined component comprises obtaining the quantity of the predetermined component from a calibration curve linking the intensity ratio to the quantity of the predetermined component.
4. The method according to claim 1 wherein the predetermined component is free lime.
5. A method comprising
obtaining a calibration curve relating the intensity ratio to concentration of the predetermined component by carrying out a method according to claim 1 for a plurality of samples each having a known concentration of the predetermined component; and
measuring the quantity of a predetermined component in an unknown sample by carrying out a method according to claim 1 for the unknown sample.
6. An X-ray apparatus, comprising:
a sample stage for supporting a sample extending substantially horizontally;
an X-ray source located to direct X-rays to the sample stage;
an X-ray detector located on the other side of the sample stage for measuring X-ray intensity of diffracted X-rays in a transmission geometry; and
a controller;
wherein the controller is arranged to cause the X-ray apparatus to carry out a method according to claim 1 on a sample mounted on the sample stage.
7. The method according to claim 2 , wherein calculating the quantity of the predetermined component comprises using a linear relation between the intensity ratio and a calculated
W
=
w
fl
1
-
w
fl
where w fl is the weight fraction of the component of interest.
8. The method according to claim 5 further comprising fitting a straight line to the intensity ratio as a function of the concentration of the plurality of samples having a known concentration of the predetermined component.
9. The X-ray apparatus according to claim 6 , further comprising a further X-ray detector located on the same side of the sample stage as the X-ray source for making X-ray fluorescence measurements of the sample.