THEORY OF CALIBRATION:
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| 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.
CALIBRATION SAMPLES
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.
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| 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.
RECALIBRATION SAMPLES
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.)
