Rutherford Backscattering Spectroscopy, Counting Statistics

[Dan Zar]

Homework Statement

I am given a numerical example (to be solved with pen, paper and calculator only) of an RBS spectrum of a AuAgCu-alloy on a glass-substrate. The question is "Can you get the composition? How accurate is the result?

Homework Equations

All the Rutherford Backscattering Spectroscopy equations should be easy for an expert in the field. Z Au= 79, Z Ag = 47, Z Cu = 29. Yield = Area under the peak, Au/Ag=(Yield Au/ Yield Ag)*(charge Ag^2/charge Au^2), etc. Uncertainty of Yield = square root of the area.

The Attempt at a Solution

I am able to get the yields (total areas) by calibrating the areas; I get the following numbers for the relative areas --> Au: 8371, Ag: 1262, Cu: 1427, which end up getting me to the following stoichiometry: Au0.37Ag0.16Cu0.47. Then I believe the square root of the total number of counts (or yield) is the uncertainty of each peak, so how do I know how accurate the result as a whole is? do I add up the total number of counts with the uncertainties (propagate the error) and then whatever percentage of my total number of counts corresponds to the added uncertainties is the accuracy of the result? or, do I have to propagate the error on the ratios even before I get the stoichiometries, which would require a bit of partial differentiation. I am honestly not able to solve problems about counting statistics in Ion Beam Analysis methods, if you can link me to a good text-book like approach of counting statistics in IBA methods I would appreciate it. P.S I am a chemist, be nice :)

 

[mfb]

Did you mark the problem as solved on purpose?

The different mass fractions are not independent. If you want individual uncertainties (let's take Au), you can take the square root of Au counts as uncertainty in the numerator and the uncertainty on the sum of Ag+Cu (added in quadrature, but not including the uncertainty on Au) as uncertainty in the denominator. All multiplied with the masses of the atoms of course, if you want mass fractions.