The MATH MENU

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Clear...

The first three items are general purpose "Erase" functions. Each will provide a second chance in case they are inadvertently pressed.

Add Work to Results

Adds the spectrum in WORK to the spectrum in RESULTS, non-destructively. This capability is useful primarily in making up a set of references from a collection of spectra. It is possible to cull through the collection looking for those spectra that have high concentrations of the element of interest. These spectra can then be summed together to give one spectrum with the good counting statistics required when making references.

Add Poissón Noise to Work

Adds true counting noise to the spectrum in WORK and places the resulting spectrum into RESULTS. This item puts the appropriate noise on a spectrum generated from first principles.

Measure Beam Energy

Enter the approximate beam energy and click OK. After the fit is complete, a window with the results is displayed. You may install this as the beam energy.

This feature is primarily useful in the scanning electron microscope or electron probe microanalyzer to give a good measure of the exact beam energy required for quantitative electron probe microanalysis. It occurs in all parts of the ZAF-type matrix correction procedure, as well as in all of the other matrix correction procedures. For a detailed discussion of the underlying physics and mathematics used in this procedure see Appendix VI.

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Convert WDS Scan to Energy Scale

This feature will convert a wavelength dispersive scan of a spectral region from dimensions of length, or angle, to those of energy. It is necessary to know the begin and end channel numbers and their associated values. It will probably be necessary to experiment with the eV/Channel value. Keep in mind that this operation will move the resulting spectral fragment into a very different part of the display and it will probably be necessary to use the full 8192 channel capability until you have the desired result. This dialog requires some planning since just "playing around" here will produce quite unexpected results that often will be outside of the display range. The conversion is exact and maintains the correct intensity across the spectral segment. Data may be entered as wavelength, sin q , or millimeters and the correct crystal must be selected. Also, if the peaks are not first order, the diffraction order must be selected.

The advantages of converting a WDS scan to an energy scale is that many of the mathematical operators in DTSA can then be used directly. It is difficult to obtain a response curve for a WDS spectrometer. For those calculations in DTSA that require a response curve we assume unit efficiency, which is sufficient for most purposes.

Smooth

This dialog permits "smoothing" a spectrum with either a 5, 7, or 9 point Savitzky-Golay polynomial. Smoothing should be used with care. Gaussian Convolve will formally convolve the spectrum with the instrumental response function of the detector electronics. Set the resolution (FWHM at Mn Ka ) using the EXPERIMENT HEADER Dialog. For the numerical weights used in the smooth, see comments for the same operators in the Calculator.

Digital Filter

When the "OK" button is pushed, the digital filter will be applied to the spectrum in Work and the filtered spectrum will be placed in Results. It should be noted that this digital filter is distinct from the digital filters used in the curve fitting operations ( Simplex and LLSQ) that have their own filters without user changeable parameters. For a detailed discussion of the theory of the digital filter see Appendix X.

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Background Subtract

Background subtract is used for a number of purposes. The two most important reasons to remove the background from a spectrum are in the making of "Reference" spectra for the linear least squares curve fitting operation, and as a diagnostic in determining problems in an EDS system. Each of these two reasons require the subtract feature to be run with a different emphasis.

The Background Subtract operation works as follows: Two or more "Background ROI's (regions of interest)" are required to be judiciously Set-up in peak and artifact free regions of the spectrum for which it is desired to remove the background. Alternatively, there is an "Auto ROI" mode that will automatically select background regions and do the fitting to those regions. This spectrum must be in "Work" and the "subtracted" spectrum will be placed in Results. It is then required that the user enter the composition of the specimen from which the spectrum was made and the kilovoltage used for the acquisition. Furthermore, the information concerning the detector parameters such as window thickness' should be currently valid. DTSA will then calculate a spectrum shape and scale it to the spectrum in "Work". The information required for scaling is obtained from the ROI's. The size of the ROI is not used in the scaling operation and each ROI has the same "weight" as any other ROI. DTSA will then subtract this generated and scaled spectrum from the spectrum in "Work". Since the generated spectrum is scaled to the actual spectrum, there is no need to specify quantities such as Faraday current, or acquisition time.

When the spectra originate from thin specimens in an analytical electron microscope, the exact chemical composition of the specimen is not important. Indeed, only a guess at the average atomic number will suffice and it is not even necessary to enter the actual elements in the specimen.

However, when the spectra originate from bulk specimens in a scanning electron microscope or electron probe microanalyzer, the exact composition is important to know. This is true because bulk targets differentially absorb their own radiation and the constituent elements can cause large absorption edges to appear in a spectrum. To calculate these edges, it is required that the composition be known accurately. In the SEM case it is also necessary to know the beam energy accurately, since errors of only a few hundred eV can result in an inadequate fit to the top half (high energy) part of the spectrum. The Composition Database part of this dialog is now operational as is described under the Generate Header.

Background Subtract Options button will allow the choice of physical models for the generation of the background. In both cases for thin and bulk specimens, one of the models, the "Free Quadratic", is a second degree energy polynomial that has extra freedom to cause a "good" fit over a wide energy range. When making reference peaks for the MLLSQ procedure, the quadratic is the model of choice. The ROI's should be chosen to be near the peak (e.g., one ROI on each side of the peak). If the fit is poor, away from the peak for which a reference is being made, it does not matter, since it is only the peak region with which we are concerned. When choosing the background ROI's, it should be remembered that incomplete charge collection can cause a distortion on the low energy side of a peak, especially in the 3-5 keV range. Consequently, the low energy ROI might need to be placed asymmetrically further from the peak than the high energy ROI (that can be placed quite close to the peak). For the purposes of making MLLSQ reference peaks, we wish to include any left side peak distortion in the reference shape. In many detectors, as an example, the left side distortion on the Ti Ka peak is almost as wide as the peak itself and can be several percent as large. The following figure demonstrates the effect for the chlorine and potassium Ka peaks.

Background subtracted EDS spectrum of a bulk specimen of KCl salt. The background subtraction has removed the absorption jumps. The shaded area represents the deviation caused by incomplete charge collection and should be included in ROI of any reference peak for MLLSQ.

For the situation where we use background subtraction as a diagnostic tool, we will make the following variations on the above theme.

First we define the problem. An Energy Dispersive Spectrometer is capable of responding to radiation other than x-rays originating from the interaction volume of the primary electron beam and the specimen. The detector is also sensitive to backscattered electrons from the specimen or other scattered electrons in the specimen chamber. In fact, scattered beam electrons behave very much like a gas in the specimen chamber. Any electron more energetic than 25 keV will penetrate the usual 7.6 mm Beryllium window (losing some 20-25 keV in energy due to inelastic interaction with the window) and create electron-hole pairs just as efficiently as an x-ray of the same energy as the electron. For the analytical electron microscope it is frequently the case that electrons will scatter onto the support grid (often copper) and cause both characteristic and continuum x-rays to be generated in this semi-bulk material.

The resulting spectrum that we observe is the summation of the spectrum from the specimen volume excited by the primary electron beam (and is the only spectrum we wish to see) and the other "spectra" from scattered electrons and spurious x-rays.

The background subtraction process involves the creation from first principles of an x-ray spectrum that has been tailored to your particular instrumental configuration. If such a spectrum is then scaled to, and subtracted from, a real spectrum from your instrument, then any deviations in the shape of the residual background is a clear indication that either the parameters that you entered into DTSA are not valid, or there is a problem, as just discussed, with stray radiation entering the detector.

Since we desire, in this application of background subtraction, to study deviations of our real background to a theoretically calculated one, we do not want to utilize the quadratic model, discussed above. We instead want to use a model that will impose a "shape" across the entire spectrum with only the amplitude as a fitting variable. Any of the other models in the "Option" sub-menu will accomplish this type of fit. However, it is best for the beginner to use only the "Small" model, for bulk specimens, or the MBH (modified Bethe-Heitler) model for thin specimens in the AEM.

By using some "common sense" physics, it is then possible to pin point the problem exactly, and, hopefully, correct it.

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Strip Escape Peaks

This selection will strip the escape peaks from a spectrum and place the stripped spectrum in RESULTS. The calculation takes into account the tilt of the detector. The fitting procedures automatically do this so it is not necessary to strip escapes before doing peak fitting.

Detector Response into RESULTS

Puts, into results, the current detector response curve used by DTSA. This is useful for a quick determination of the detector efficiency at any given photon energy.

Replace Detector Response by WORK

Copies whatever is in WORK into the detector response. This will now be used as the detector response so be sure you know what is in here.

Calculate Response NOW (from WORK header)

Calculates the detector response immediately from the data stored in the current WORK header. Whatever was in detector response will be replaced by the new calculation.

X Ray Database

Clicking on an element results in the appearance of another dialog that accesses all the characteristic lines, excitation edges, satellite transitions and relative transition probabilities for that element. The data can be presented in energy, for the EDS case, or in any of the standard WDS crystal diffraction cases for several WDS spectrometers from different manufacturers.

You may also enter an energy in eV of an x-ray line and click the "Lookup" button to see a list of all the x-ray lines close to the energy entered. This is useful when searching for interferences. The list may be scrolled up or down with the "Up 10 Lines" and "Down 10 Lines" buttons.

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