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  /Tech Notes/Quantitative Analysis

Quantitative analysis is the "bread and butter" of electron microprobe work. It is why the electron microprobes were originally developed. The focused electron beam of the microprobe makes it possible to determine the elemental abundance of a very small area (~ one billionth of a cubic millimeter) in place. A grain only 1-3 microns in diameter can be analyzed without contamination from the surrounding matrix material, and it can be done in a non-destructive manner. Typically the error in this type of analyses is in the one percent range, and the minimum detection limit for most of the periodic table is in the range of 0.01 weight percent.

 Quality of Analyses
 Reasons for Problems


1) Determine what elements are to be analyzed (see Qualitative Analysis).

For good quality analyses it is important that all the elements are either measured or are accounted for in the software. Missing elements can have a significant impact on the measured abundance of the analyzed elements.


2) Check for peak overlaps.

X-ray lines that overlap with an X-ray line of another element are usually avoided by selecting alternative lines. It is equally important to ensure that there are no X-ray lines occurring at the positions where the background is to be measured.


3) Standardize for all the elements being analyzed.

Standardize on good quality, homogeneous standards of known compositions, using the same analytical conditions that will be used during the quantitative analyses process.


4) Make the measurements on the unknowns.

Measure the peak and backgrounds for each element being analyzed.


5) Determine the k-ratios for each element.

The k-ratio is the ratio of the net counts of the unknown versus that of the standard.


6) Correct the k-ratios for the difference in the matrix effects of the unknown relative to the standards.

This correction is a critical part of the analyses, unless the standards and unknowns are nearly identical in composition. If they are not, the number of X-rays being measured from a given element will deviate from the expected. because of a number of factors including:

the total number of beam electrons available to produce the X-rays may be higher or lower, relative to the standard, due to differences in the average atomic number of the two materials,
some of the X-rays may have been absorbed by the surrounding elements, and
some of the X-rays may have been produced not by the beam electrons but by fluorescence from neighboring elements.
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Quality of Analyses:

How do we know if our results are good?

1) Look at the totals.

If all the elements were analyzed, then the total of all the weight percents should add up to approximately 100%. Therefore it is very important not to normalize the results. Normalized results will hide these potential errors.

2) Check the stoichiometry.

If the material being analyzed is a mineral, then there will be a limited range of compositions that are allowed. As an example, below are three feldspar analyses.


weight percent of each oxide

cations per 8 oxygens
calculate values

By just looking at just the totals, all three analyses look like they are good analyses. However some elements could be high, but be hidden by the fact that other elements are low. The stoichiometry given us more information about the quality of the analyses. Since these are feldspar analyses in the ternary system CaAl2Si2O8 - NaAlSi3O8 - KAlSi3O8, the atom abundance Si+Al should always equal 4, and the abundance of Na+Ca+K should always equal 1. Using these rules, one can see that the first analyses is very good, the second one is off a little and the third analyses is off by a significant amount.

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Reasons for Problems:

1) Were all the elements analyzed for?

This will make for low totals and may adversely affect the matrix correction routines.

2) Was the sample in optical focus?

When doing WDS analyses, the point the beam hits the sample must be on the Rowland circle, otherwise the generated X-rays will not enter the detector. The spectrometers are aligned so that when the sample is in optical focus, the sample at the cross hairs will be on the Rowland circle. Moving the stage either up or down will result in a loss of counts. Figure 1 shows how rapidly the counts will drop for a number of different X-ray lines.

3) Is the beam on the cross hairs?

The same problem will occur when the beam is off of the cross-hairs as when the sample is out of optical focus. Specifically the spot generating the X-rays will not be aligned with the spectrometers. As a result there will be a drop in the number of measured X-rays (Fig. 2). This decrease will increase with distance from the cross hairs, and will vary with the X-ray line.

4) Was the standardization done properly?

Did the wrong standard grain get analyzed?
Did bad data get generated by analyzing poor spots? Were some of the spots on pits, cracks or partially off the grain?
Was the standard appropriate for the unknown?

5) Was the beam diameter the same during the analyses as was used during the standardization?

Using a larger beam diameter during the analyses will mean that some of the X-rays will be generated off of the Rowland circle, and therefore fewer will enter the detector. It's important to note that the drop in counts is not uniform from element to element (Fig. 3). This means that the element ratios will change.

6) Was the beam current and accelerating voltage appropriate for the analyses?

Generally an accelerating voltage is used that is at least 2.5 - 3 times the excitation energy of the X-ray line being measured. An accelerating voltage too low will not produced the desired X-rays. A voltage too high will increase the likelihood of volatilizing the sample. Similarly, setting the beam current too high can also cause the sample to volatilize or for elements, such as Na, to migrate away from the beam. In either case, poor analyses will result.

7) Was too little of too much carbon used in the conductive coating?

Non-conductive samples must be coated with a conductive surface before analyses. The coating is usually carbon, because it is a low atomic number element, and therefore will have less of an effect on the analyses. However, it is still important that the same thickness of carbon be used on both the standard and the unknown sample. Using too little or too much carbon can have a very large effect on light element analyses (Fig. 4). For these analyses, it is best to carbon coat the standard and unknown at the same time to ensure the same thickness is obtained.

8) Other sample preparation problems.

Was the sample properly polished? This will have a profound impact on the quality of the analyses.
Was the surface cleaned before carbon coating of any oils or other surface contaminants?
Has the surface oxidized since it was polished last? This can be a big problem with sulfide minerals.

Figure 1. Variation in X-ray counts with distance from the optical focus point (after Taya and Kato, 1983).

Figure 2. Variation in X-ray counts with distance the beam is from the cross hairs (after Taya and Kato, 1983).

Figure 3. Effect of beam diameter
on X-ray counts.

Figure 4. Variation in measured
oxygen as a result of variations
in the carbon coating thickness as measured by carbon abundance.



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Toya, T. and A. Kato, 1983, Practical techniques for microprobe analyses: JEOL part number 270195, 193p.