THEORY OF CALIBRATION:
|Concentration vs Intensity calibration curve|
Calibration comprises measurement of calibration samples and determination of the functional relationship between the intensity ‘I’ of the line of an analyte and its concentration c in these samples. The functional relationship is the calibration function or calibration curve. It includes relationships between vaporisation, excitation, radiation offtake, dispersion and the measured value. Since spectrochemical analysis is a process of analysis is a process of analysis by comparison ( in contrast to absolute methods such as weighing ), it is necessary to carry out calibration with samples of accurately known concentration, the calibration samples.
The calibration function must not be confused with the function inverse to it-the read out or evaluation function. In the case of the calibration function I = f1 (c), the concentrations of the calibration samples are assumed to be free of error, and the errors (deviations from a best fit curve after correction of the intensities for systematic errors) are imputed entirely to the spectrometer method, so that the preconditions for regression calculations showing correlation coefficients as a quality index are useless. With the evaluation function c = f2 = ( I ) the concentration c of an analyte in an analytical sample is determined, which is accordingly subject to error, f2 = 1/f1.
For optical emission spectrometry there is no theory of calibration curves which can be used for practical purposes. There are formulae for which it is assumed that it is possible to represent the relationship between line intensity and concentration as a power function : I = I0 ck. The calibration function can be represented mathematically in various ways :
linear calibration function : I = f(c) = a0 + a1 c
non-linear calibration function : I =f(c) = a0 + a1 c +a2 c2+...+an cn
The extent to which the regression approaches the true course of the calibration
curve can be discerned from the residual scatter, namely at the point when the
addition of further terms to the approximation function does not produce any
further improvement in the residual scatter.
Fundamental role of the calibration samples is attested by international community and by International Standardisation Organization (ISO), which delivered the following definitions :
Reference Materials (RM) : they are Materials or substances whose properties are so well defined that they can be used to calibrate the instrument, verify the measure or assign values to the materials.
|CRM sample with Spark analysis spots|
Certified Reference Materials (CRM) : they are Materials whose values concerning one or more properties are certified by means of a valid technical procedure and equipped by a Certificate or other documents from a qualified technical Body ( public or private Organization or Society., which deliver a certificate for the Reference Material )
Calibration samples present three disadvantages :
1) They are expensive
2) Their dimensions and shapes are not always available for the sample-holder stand of the spectrometer.
3) They are available only for some elements and concentrations
In some cases calibration samples can be synthesised, for example by alloying or diluting part of a charge. Because of this manipulation, the calculated values are rarely reliable and their composition should be confirmed by chemical analysis.
When calibrating spectrometers with calibration samples (reference samples)
Recalibration samples are measured a number of times in order to obtain a reliable nominal value suitable for calibration. The additive and/or multiplicative changes in the sensitivity of the spectrometer bring about displacements of the calibration curves in the linear scale of the co-ordinate system. In order to trace (calculate) the actual intensity values at any later time back to the nominal intensity values submitted at the time of calibration a low (LP) and a high (HP) intensity is required for each analyte channel. In metal analysis with spark discharge the low points of all the analyte channels are usually measured with the pure base (Fe, Al, Cu,...). The high points are usually measured from synthetic samples having as many elements as possible with good homogeneity and precision.
The synthetic composition is given as a guide analysis and the samples often do not lie on the calibration curves. Mathematical procedure of calibration is a automated process.
In emission spectrometry recalibration samples run out, because of the polishing of the surface before recalibration. When recalibration samples are replaced there is no guarantee that, even with the same sample number, the new sample concentrations will correspond exactly to the sample being replaced. For this reason when calibrating a spectrometer for metal analysis, a minimum supply of recalibration samples should be available, for example five recalibration samples for each type.
The frequency of recalibration depends on the instrument and its use.
Interdependence with the instrument means that devices of the same kind, specially because of different phototubes stability, must be recalibrated at different intervals. Interdependence with use means that, even if stability is the same, recalibration frequency depends on the kind of analysis (traces analysis, sorting analysis).
(Note: The above post is written in context to calibration of Spark Optical emission spectrometer for metal and alloy analysis.)