Recall from the previous notes:
The method of standard additions or the spiking method (adopted from XRF work) is a good/reliable technique if you are interested in a particular component in a mixture (i.e., interested only in the weight fraction of that one phase).
This method relies on the addition of known amounts of the component of interest to the sample.
Any reflection from the other component in the mixture can be selected to be use in the analysis, so long as it provides reasonable intensity (signal to noise) and there is minimal peak overlap from other phases that may be present.
Let J = component of interest and K = any other component in the unknown sample.
Using the above equation and looking at the ratio of intensities (Ii) of J to K we obtain:
Noting that the matrix absorption effect cancels, this equations can be simplified to:
If a known amount (X) of the pure component J is added to the mixture, then the concentration of the component in the mixture becomes:
and the equation becomes:
The intensity ratio can be rewritten:
A plot of the intensity ratio versus the grams of analyte added per gram of sample produces a linear relationship.
Important to remember that not too much of the spike can be added. This changes the µ* of the mixture and the cancellation of the µ* is no longer valid.
Rule of thumb: Do not add more than 20% by weight of the spike. Increments of 5% work well.
The RIR is defined as the intensity of the
strongest line of the
sample
to that of the strongest line for a reference phase in a 1:1 mixture.
The reference phase
choices are often alpha-Al2O3 (corundum) and ZnO.
In the special case
of 1:1 mixtures between the sample and corundum, the RIR value is
referred to as "I over I-corundum" value
(i.e., I/Ic). I/Ic values are published in the
ICDD-PDF data base. Notice that the
matrix effect gets "flushed" from the equations. In the equation below
and a 1:1 mixture, WJ/WK
= 1 and all the other factors become a new constant, which collectively
is the RIR.
Other internal standards can be used (and in fact, may be
preferable because of conflict between overlapping lines).
Just remember that when you by a jar of reagent
or prepare your own internal standard, you need to establish the RIR
for that batch. If you renew your
internal standard supply, the distribution of coherent scattering
domains in that batch may be different from the your previous
supply. So you need to reestablish a new RIR for every batch.
Sometimes a 1:1 mixture dilutes the sample intensity. A lesser
amount of internal standard allows for quantification of minor
phases. In this case it is best to develop a calibration curve by
mixing known amounts of
analyte. By adding an internal standard you change the relative weight
fraction of the phases of interest. WJ is the weight without standard
added and W'J is
weight fraction with standard added.
A calibration curve is plotted:
Note that the weight fraction of W'J is the weight after the corundum has been added. Therefore, the weight of J in the original sample is:
If the XRD procedure calls for a standard routine, for example adding 0.2 g of corundum to 0.8 g of sample, then (1-Wc) and Wc become constant.
The ratio then simple becomes:
Example:
