Rapid calculation of X-ray absorption correction factors for cylinders to an accuracy of 0.1%

Accurate X-ray absorption correction factors A* for cylindrical samples were calculated in the range of the product of linear absorption coefficient μand cylinder radius R of 0 ≤ μR ≤ 2.5 and in the range of Bragg angle θ of 0° ≤ 0 ≤ 90°. A method of double numerical integration that is different from the method usually used resulted in a maximum error of 0.1% with the typical error being much less. A table of values of A* was prepared, and simple equations were obtained for interpolation between values in the table to an accuracy of 0.1% or better. A full-range curve-fitting procedure that is accurate to 0.1% also was developed for routine use when many values of A* must be calculated for a single sample.