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Non-linear reference lines

Consider a hypothetical series of calibration samples with only three main elements: e1, e2 and e3. Let e2 and e3 vary randomly between 0% and 30%, and e1 is the remainder. The elements could be, for example, Fe, Cr and Ni in a range of high alloy steels.

Let us assume there is no error in the intensities or concentrations and that the intensities of e2 and e3 are linear with concentration but that our reference element e1 is in second order.

If we use the Normal method ratioed to e1, we get something like this:

[Normal calibration]

and it would be tempting to delete one of the upper points to improve the fit. Though this would not be justified since there is no error in our data and we have simply used the wrong calibration function.

If we use the Ratio or Virtual method, we get something like this:

[Ratio or Virtual Calibration]

and it would be tempting to use second order to get a better fit near 0, though this would not completely remove the scatter. The scatter is there simply because of the limitations of the Ratio or Virtual method when the reference intensity is not proportional to its concentration.

This problem is typically encountered when using resonant lines as an internal standard. Examples are: Fe 372nm for steel, Cu 325nm for copper base material, Al 396nm for aluminium alloys etc.


  1. Th.Nelis, M.Aeberhard, R.Payling, J.Michler P.Chapon; Relative calibration mode for compositional depth profling in GD-OES; J. Anal. At . Spectrom., 2004 , 19 , 1354 1360, DOI: 10.1039/b406187j

First published on the web: 15 May 2000

Authors: Richard Payling & Thomas Nelis