Quantifying Spectra

No one will contest that the most accurate way to quantify a electron probe microanalysis x-ray spectrum uses similar standards collected under the identical conditions as the unknown. By comparing an unknown spectrum to other spectra collected on the same instrument at the same working distance and with the same beam energy, many of the poorly known fundamental parameters cancel out of the quantification equations. If the unknown is compared to pure elemental spectra or other dissimilar spectra then it is also necessary to apply significant corrections for differences in backscatter coefficient, electron stopping power, x-ray absorption and secondary fluorescence. If it is possible to compare the unknown to a spectrum of similar composition then the correction factors are typically similar in the unknown and standard and the correction factors tend to cancel regardless of magnitude. The results are estimates of the material composition with predictable estimates of the associated errors. No technique not based on standards can promise this.

Standards-based analysis is so powerful because of what stays constant in microanalytical spectra. One of the most important characteristics of x-ray generation and emission is that the processes are to a very large extent only properties of the constituent atoms and not the chemistry that binds the atoms together. As a result the overall shape of x-ray line families (K, L or M) does not depend much on whether an element is in pure form or in the presence of other elements. To first estimate all else remaining constant, the intensity of x-rays emitted by an element A in a material M is linearly proportional to the amount of element A (in weight percent). The simplest thing to do is therefore to determine the intensity of element A's x-rays generated by a pure block of element A and compare this to the intensity of element A's x-rays generated in the unknown. This ratio Iunknown/Ipure is known as the k-ratio and is known as Castaing's first estimate of the composition.

Unfortunately, the amount of element A is not exactly equal to the k-ratio. There are corrections that need to applied to account for a handful of uncontrollable factors. These factors are typically identified by the acronym ZAF where Z refers to corrections for the backscatter efficiency and electron stopping power, Arefers to corrections for x-ray absorption and F refers to corrections for secondary fluorescence. The backscatter correction compensates for x-ray generation lost because higher mean atomic number materials backscatter more electrons than low mean atomic number materials. The electron stopping power is a measure of how fast electrons are slowed through interaction with the valence electrons in a material. The absorption correction compensates for the fact that x-rays are typically poorly absorbed by the element that emitted them but may be strongly absorbed by other elements in the material. Once an x-ray has been absorbed it will not be measured by the x-ray detector. However it may be re-emitted as a characteristic x-ray of a lower energy. These re-emitted x-rays are referred to as secondary emission and in some materials they may represent as much as a percent or two of the measured x-ray signal for some elements. This extra x-ray emission is compensated for in the F term.

Standards and References

There are two different types of spectra which are used in the quantification process - standards and references. The difference is subtle but important complicated by the fact that often a single spectrum can serve as both a standard and a reference. A standard spectrum is collected on a material of known composition which provides intensity scale information against which an unknown spectrum will be compared. In the optimal case, a standard is of similar composition to the unknown but strictly speaking it need not be. Often a set of pure element materials or simple binary materials are used as a universal set of standards. When the standard material is of similar composition, the ZAF correction is typically similar in standard and unknown and any errors in the ZAF correction model or the parameters that go into the model cancel. A reference spectrum is a spectrum collected to provide line shape information but not necessarily intensity magnitude information. The characteristic peaks in a standard may interfere but the characteristic peaks must be well separated in a reference. A reference is necessary when the characteristic peaks in a standard are not well separated but a standard may also serve as a reference when the required lines are well separated in standard.

There is no doubt that quantifying against standards is more time consuming than standardless analysis. In addition to collecting the unknown spectrum, it is also necessary to collect standard spectra and possibly also reference spectra for each element in the unknown. Historically the tools for performing standards-based quantification have required far more user intervention than the "press-a-button" standardless approach. While some of these differences are fundamental and can not be eliminated, DTSA-II attempts to make standards-based analysis as easy-as-possible.

DTSA-II provides a alien assistant to step you through the process of performing a quantification. Fortunately, this process is both simple for a novice and efficient for an expert. DTSA-II eliminates many of the "judgement required here" steps in DTSA and replaces them with computer algorithms.

The quantification alien

The always helpful alien Trixy is more than willing to step you through the process of quantifying a spectrum. Select zero or more of the spectra in the spectrum list. The selected spectra should have the same beam energy and should have been collected on the same instrument and under the same conditions. Select the Tools - Quantification alien item from the main menu to active the Quantification alien assistant dialog. You will be asked what kind of a quantification you wish to perform.

Select a quantification mode

Select the top option ...fitting to standards and press the Next button to advance to the next page.

Specify the instrument

The next page deals with questions about how the spectra was acquired. You will be asked to specify an instrument. Selecting an instrument will update the list of available detectors to reflect the detectors available on that particular instrument. Select a detector making certain that the detector you select reflects the detector and the resolution of the detector since the algorithms need to know the characteristics of the detector to properly fit the spectrum. Finally specify the beam energy at which the spectrum was collected.

If you had selected one or more spectra when you initiated the quantification alien then these parameters may already be filled in correctly if this information was available in the spectrum.

Specify standard spectra

Select the next button to proceed to select standards. Standards are the spectra which provide the x-ray intensity information for each element in the material. Each element in the material must have an associated standard although one standard can act as a standard for multiple elements. Do not omit any elements. If an element is present in the material it will effect the computed quantities of the other elements.

You may specify standards from disk files, from the database or from a combination of the two. If you have previously added spectra as standards for this particular instrument and detector then the database method is simpler. However you can always specify spectra from disk but be careful that the spectra were collected on the same instrument/detector and under the same conditions.

Specify reference spectra

By default, the standard spectra are evaluated for use as reference spectra. The standards can be good references for a single x-ray transition family if all transitions within the family are not obscured by other elements in the material. A standard can be a reference for one family or sub-family of transitions but not another. If the standards don't include a decent reference for an x-ray transition family, you will be asked to specify a spectrum to serve as a reference. You will need to specify at least one good reference for each element although not for each visible family of transitions.

The references are identified by element and line family. The second column identifies the associated spectrum and the last column displays the signal-to-noise ration of the reference. The signal-to-noise is graded into Good, Ok and Poor depending upon the count statistics in the peaks of interest. You may improve the signal-to-noise by replacing the reference. However ultimately the error bars on the analysis are determined to a large extent by the worst of the reference and the standard. If either the standard or reference has poor signal-to-noise, the results will be of poor precision. Again you may select spectra from file or from the database.

You may also identify spectra for elements you wish to strip but not quantify. Typically, these are elements like carbon when there is a thin carbon contamination layer or oxygen if there is a thin oxide layer. The quality of the analysis will be effected if there are carbon or oxide layers but the quantitative algorithms used don't account for these layers.

Specify other elements

Sometimes an element may be quantified by mechanisms other than fitting a peak. These mechanisms are appropriate for elements that are hard to measure. For example, you may select not to fit oxygen but rather to assume that any missing mass is accounted for by oxygen. This is element by difference. Alternatively, you may assume a stoichiometry for the elements present with respect to an unmeasured element. The unmeasured element is added in later in the proportion specified by the assumed stoichiometry. This is most often the mechanism used for oxygen which can be a difficult element to measure directly but can sometimes be predicted based on a priori chemistry knowledge.

Select the unknown

If you had spectra selected in the spectrum list when you initiated the quantification alien, they will be listed here. You may remove these spectra and/or add new ones. You can load a new spectrum from file. The spectrum should have the same instrument conditions as specified in an earlier page.

The results

Pressing next will initiate the calculation. Each spectrum will be processed independently and the results tabulated. You may select to display the results as "weight percent", "normalized weight percent" or "atomic percent." Pressing "Finish" will transfer the results from the dialog to the report tab as a table summarizing the analysis.

The results are tabulated in the report as "weight percent", "normalized weight percent", "atomic percent" and "k-ratios". In addition, the analytical total (sum) is presented. In addition to the table, two spectra per quantified spectra are added to the spectrum list. The first is the residual spectrum. The residual represents the x-ray events which are unaccounted for by the references. Ideally the residual should look like a smooth Bremsstrahlung background without any characteristics peaks. If characteristic peaks remain, it either means these peaks represent elements which were not included in the quantification (an error) or lines from quantified elements for which references were not provided. It is best of provide references for all peak families since this makes the residual easiest to interpret. The second spectrum is an analytical simulation of the unknown.