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 This changes the µ* of the mixture and the cancellation of the µ* is no longer valid.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
to that of the strongest line for a reference phase in a 1:1
The reference phase
of choice is α-Al2O3
(corundum), but other phases can work just as well, such as 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
In this case, the strongest line intensity of the phase of
interest is ratioed to the corundum (113) intensity. The I/Ic
value assumes CuKα1
radiation. I/Ic values are published in the
ICDD-PDF data base. Notice that the
matrix effect gets "flushed" from the equations. In the equation
and a 1:1 mixture, WJ/WK
= 1 and all the other factors become a new constant, which
is the RIR. If the ICDD-PDF values are used, then you as
best should consider the analysis semi-quantitative. In other
words your precision may be good, but your accuracy may be in
error up to +/- 20%.
Other internal standards can be used (and in fact, may be preferable because of conflict between overlapping lines). Your best practice is to develop your own I/Ic values for your own experimental set-up. Just remember that when you buy 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 and for the specifc experimental conditions you are using (i.e., radiation, tube type and current, slit sizes, take-off angles, goniometer radius, etc...).
A 1:1 mixture dilutes the original sample intensity, therefore a
amount of internal standard will allow for better quantification
phases. In this case it is best to develop a calibration
mixing known amounts of
analyte. By adding an internal standard you change the relative
fraction of the phases of interest. If WJ is the
weight without standard
added, then W'J
the weight fraction with standard added. In the equations below,
subscript c is for
as it is a common internal standard.
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: