Fundamental and Experimental Calibration

Depending on the type of relationships between the measured quantity and the measurand (analytical quantity) it can be distinguished (Danzer and Currie [1998]) between calibrations based on absolute measurements (one calibration is valid for all1 on the basis of the simple proportion y = b x, where the sensitivity factor b is a fundamental quantity see Sect. 2.4 Hula-nicki [1995] IUPAC Orange Book [1997, 2000]), definitive measurements (b is given either by a fundamental quantity complemented by an empirical factor or a well-known empirical (transferable) constant like molar absorption coefficient and Nernst factor), and experimental calibration. 

In the simplest case, experimental calibration can be carried out by direct reference measurements where the sensitivity factor b is given by the relation of measured value to concentration of a reference material (RM), b = yRvi/xRv,. Direct reference calibration is frequently used in NAA and X-ray analytical techniques (XRF, EPMA, TXRF). 

On the other hand, indirect reference measurements which result in an empirical calibration function, frequently based on a linear model, y = a + b - x + ey see Sect. 2.4, Eq. (2.22), where the intercept a corresponds to 

Apart from the fact that both the fundamental constants b and the conditions under which they are valid (e.g. under which a reaction proceeds quantitatively) sometime were determined and have to be updated from time to time (e.g., on the basis of IUPAC documents). 

In analytical practice, some methods using definitive measurements, in principle, are also calibrated by indirect reference measurements using least squares estimating to provide reliable estimates of b (spectrophotometry, potentiometry, ISE, polarography). 

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