Compositional Mapping with the Electron Probe Microanalyzer: Part I .
Dale E. Newbury, Charles E. Fiori, Ryna B. Marlnenko, R o M L. Myklebust, Carol R. Swyt’, and David S. BrigM Microanalysis Research Group Center for Analytical Chemistry National Institute of Stangards and Technology Gaithersburg, MD 20809
.
Compositional mapping with the electron probe microanalyzer is a technique for creating digital images, using the localized concentration of a n element or compound to specify the color scale or intensity for display of the image. All of the steps in conuentional single-location electron probe microanalysis are used in compositional mapping. In addition, various correction methods are used to remoue artifacts that arise during scanning. With all corrections applied, quantitatiue mapping to trace leuels of 100 ppm has been demonstrated in the most fauorable cases and mapping a t 1000 ppm can be achieved in most instances. I n this two-part series, Dale Newbury and co-workers a t the National Institute of Standards and Technology discuss the correction techniques used for both wavelength- and energydispersiue spectrometries. Part I includes a discussion of the problems I Permanent address:Biomedical Engineering Research Branch, NIH, 9MM Rockville Pike, Beth-da, MD 20892-0001
This article rot subject to US. Copyright ~ n Sociely Published IS90 A m l ~ Chemical
that spurred the development of compositional mapping as a quantitatiue technique, the general procedure inuolued, and the correction techniques applied to the mapping of major constituents. Part II, which will appear in the December 15 issue, discusses the correction techniques applied to the mapping of minor constituents, instrument selection, and applications. The terms microbeam analysis and instrumental microanalysis include a wide range of analytical techniques that have the capability of selectively analyzing condensed matter on a spatial scale of micrometers or finer. The
aspect of this technique is compositional mapping, which involves the preparation of images that directly depict the concentrations of elemental constituenta in a specimen (3-7). The electron probe technique involves the use of energetic electrons, with an energy range of 10-30 keV, to bombard the specimen (2). The electrons interact with the atoms of a solid specimen and create inner shell ionizations that subsequently decay, emitting characteristic X-rays that provide qualitative identification of all elements with the exception of H, He, and Li. The measurement of the intensity of the characteristic X-rays relative to
development of spatially resolved analysis on a microscopic scale can be traced back to chemical microscopy performed with the optical microscope. The modern era of microanalysis began with Castaing’s development in 1951 of the first practical microbeam instrument based on a focused beam of electrons, called the electron prohe microanalyzer (EPMA) (I). Since then, electron probe microanalysis has matured and is used as a primary analytical tool in many disciplines, including materials science, geology, electronics, biology, and medical research (2). One relatively new and rapidly progressing
a known standard forms the basis for quantitative analysis. The interaction of electrons and X-rays mith matter is sufficiently understood to permit quantitative analysis using a combination of physical models for the principal interelement effects (elastic scattering of electrons, electron radiation, X-ray absorption, and secondary X-ray fluorescence) and a simple standardization procedure based on pure elementa or binary compounds. The earliest electron probes were designed with optical systems that permitted control over beam focusing, but the beam was static and fixed on the
ANALYTICAL CHEMISTRY, VOL. 62, NO. 22. NOVEMBER 15, 1990
-
1159A
coincident optic axes of the electron column and the wavelength-dispersive X-ray spectrometerb). Analytical locations on the specimen were selected by mechanical positioning of the stage using an optical microscope with a focus that coincided with the electronm-ray focus. In 1956 the scanning electron probe microanalyzer was developed by Cosslett and Duncumb to produce qualitative compositional maps that depicted the lateral distribution of elemental constituents (8). A related but independent development led to the scanning electron microscope, which forms images from various electron signals (9). The logical union of these two instruments resulted in a composite instrument, the modern electron probe microanalyzer, also known as the analytical scanning electron microscope (ASEM). This instrument can characterize the microstructure of matter with a wide variety of electron and photon signals (2). The qualitative compositional mapping technique developed by Cosslett and Duncumb has been one of the most popular operational modes of the electron microprobe because it produces a direct depiction of the elemental distributions on a microscopic scale. This technique, known as area scanning or dot mapping, is applied in a manner that is virtually unchanged since it was first described (8, 10). The beam on a cathode ray tube (CRT) is scanned in synchronism with the beam on the specimen. When a characteristic X-ray is detected by the spectrometer, the CRT beam is modulated to produce a full-intensity dot at the position on the CRT that corresponds to the position of the beam on the specimen. The dot is recorded by a camera, and the scan continues until a sufficient number of dots are recorded to depict the lateral distribution of the constituent. Although powerful, conventional dot mapping has suffered from some significant limitations. First, the final dot map is qualitative in nature because the count rate a t each point in the scanned image has been lost in the recording process. The area density of dots provides meager quantitative information, and then only in cases where the structure of interest occupies a significant area fraction of the image. Second, because the dot is adjusted to full brightness, no true gray-scale information is possible. Although X-ray rate meter signals have been used to produce a continuous grayscale X-ray intensity area map, the relative inefficiency of X-ray production and detection results in such a low in116OA
tensity signal that the use of rate meter signals is restricted to very high concentration constituents (usually > 25 wt %) and to those elements for which a low-energy X-ray line is available that can be efficiently excited to produce a high count rate. Third, the recording of the dot map on film reduces the flexibility with which the information can be subsequently processed. Registration of multiple images for color superposition on film, for example, is difficult (11). This registration problem can be overcome in parallel recording systems by using the separate color guns of a color CRT for each signal. In practice, it is difficult to achieve good images with this method because of inevitable large differences in count rates that result from measuring constituents at different concentrations and from excitation conditions that can vary widely. Fourth, the dot-mapping technique has poor sensitivity because background correction is not possible. Characteristic and bremsstrahlung X-rays that occur in the energy acceptance window of the wavelength- or energydispersive spectrometer are counted with equal weight. The detection limit using a wavelength-dispersive spectrometer in the dot-mapping mode is 0.5-1 wt %, whereas the detection limit using an energy-dispersive spectrometer (which has a much poorer peak-tobackground ratio) is 5 wt %. Newer energy-dispersive spectrometers use stored and processed X-ray counts to reduce background artifacts (12). Finally, the dot-mapping technique has poor contrast sensitivity, depending on the concentration level of a constituent. It is possible to image a region containing a constituent at 5 wt % against a background that does not contain that constituent. However, it is practically impossible to visualize that same 5 wt % increase above a general high level of 50 wt % because the dots recorded from the high static level overwhelm the small modulation in dot density caused by the actual change in concentration. The time penalty for recording dot maps is significant and is often a barrier to their use. For a high-quality dot map, 100 000-1 000 000 detected X-ray pulses are needed, depending on the distribution of the constituents, which requires a long accumulation time. Mapping major constituents (10 w t % or higher) typically requires 10 min to 1 h with wavelength-dispersive spectrometry (WDS), which has the most favorable mapping characteristics; mapping minor constituents (1-10 wt %) requires 1-5 h or longer, making direct recording on film quite difficult.
ANALYTICAL CHEMISTRY, VOL. 62, NO. 22, NOVEMBER 15, 1990
Trace constituents (< 1wt %) are usually not accessible to mapping, except in the most favorable circumstances. Because most analog scanning systems permit the display and recording of only one signal at a time, even when multiple spectrometers tuned to different elements are available, conventional dot mapping is highly inefficient. Mapping several constituents in the same field of view requires repeating the scanning process for each new map, when in fact the signals are available in parallel for the instrument. Despite these shortcomings, dot mapping has remained a popular operational mode of the electron probe microanalyzer because of the power of visual information (10).Many biological, physical, and technological processes are controlled by chemical events and structures that exist on spatial scales ranging from atomic dimensions to millimeters. Visualizing the chemical inhomogeneity of matter is of special value in understanding these processes and structures. Conventional single-point electron probe microanalysis provides only numerical concentration information on a region of the specimen with approximately micrometer dimensions. A comprehensive analysis of a complex specimen typically involves the use of dot maps to gain a sense of the elemental distributions, which are then selectively measured at locations of special interest by fully quantitative “point” analyses. Locations of interest are frequently selected by indirect and nonspecific compositional information that is available in backscattered electron images, where the backscattered electron signal scales with the average atomic number of the specimen. Such images are useful for tracking general, large-scale changes in composition, but dot maps are needed for elementspecific imaging. Three factors led to the development of fully quantitative compositional mapping. First, the limitations of dot mapping precluded its application to many interesting problems. Second, the analyst was often asked to reanalyze a specimen and locate a previously dot-mapped microstructural region to perform additional quantitative analyses at new points of interest. This procedure was often difficult because of the lack of physical features that could be rapidly located by optical andlor scanning electron microscopy. Such problems could be avoided if a fully quantitative image containing the composition a t every location were available. Third, independently developed computer-aided imaging techniques modified the manipulation of
data on electron beam instruments. Computer-aided imaging relies on digitization of the signals of interest; because the characteristic X-ray signals had long been available as digital outputs from the pulse-counting X-ray circuitry, it was natural to consider using the X-ray signals in their digital forms rather than converting the pulses back to analog signals. In the digital domain, the information can be manipulated to enhance the analyst’s interpretation of results. Composithal mapping Compositional mapping with the electron microprobe can he described as a quantitative electron probe microanalysis carried out a t every beam location in a digitally controlled scan (5). The digital X-ray signals for each constituent are collected in individual data arrays and corrected for instrumental, physical, and matrix effects. The concentration values that result for each elemental constituent (not just the raw X-ray intensities) are converted by a digital image processor into images that are useful to the analyst. The steps in the compositional mapping procedure differ in some details, depending on whether WDS or energydispersive X-ray spectrometry (EDS) is used.The key steps are (1) dead time correction for X-ray coincidence losses, (2) X-ray peak overlap correction, (3) background correction, (4) defocusing and collimation effects correction, (5) standardization, (6) matrix correction, and (7) visual display. The first six steps are critical in establishing accurate quantitative results, and failure to follow proper procedures can lead to large errors in the fmal concentrations-ven to the point of producing completely false values. False results can actually produce an apparent reversal of the chemical contrast in an image. Steps 1,2,5,and 6 are carried out by procedures identical to those used in conventional single-point analysis. Step 7 involves the general problem of displaying numerical information in the form of an image. Dead time correction for X-ray coincidence losses. Photon detection is performed serially, raising the possibility of losses caused by coincidence, usually referred to as detector “dead time.” The dead time correction for EDS is accomplished by collecting spectra for a constant live time to avoid artifads that can arise from local variations in the count rate (2). The dead time correction for WDS is less of a problem because the pulse-processing time is a t least an order of magnitude shorter than that for EDS. Standard mathematical procedures are available
I
Specimen
Flgure 1. Focusing circle of the wavelengthdlsperslve X-ray spectrometer and the effect of defocusino caused by deflecting the electron beam X-ray source off the optic axis of the system. The & q g angle of dinranion is denoted by 8;A9 is me devklim hom scanning Uw electron b”dcaxis.
for calculating dead time losses and making an adjustment to the measured count rate (2). X-ray peak overlap correction. For EDS, this correction can be made by any of a variety of peak fitting or influence coefficient methods. Overlap problems generally can be avoided with WDS because of its high spectral resolution, although mathematical methods have been developed for those cases where overlap does occur, such as heavy element L- and M-family X-rays. Standardization. The ratio of the characteristic X-ray intensity of the unknown to the characteristic X-ray intensity of a standard pure element or stoichiometric compound is used for standardization. Multielement standards, such as metal alloys, minerals, or glasses, can also be used if available in microscopically homogeneous forms. Much of the flexibility of electron probe microanalyzer compositional mapping results from the simplicity of the standardization step. Matrix correction. Any of the wellestablished methods can be used (2). The physical (ZAF) method is based on
Bragg angle c a d by
calculated corrections for each of the major matrix-dependent physical influences on the electrons and X-rays, which are electron backscattering and stopping power (the atomic number correction, Z),X-ray self-absorption by the specimen (the absorption correction, A), and secondary fluorescence (the fluorescence correction, F). The empirical method uses calibration CUN- expreased as interelement interaction coefficients. The empirical1 physical method is based on experimentally measured X-ray depth distribution (e&, the @ ( p z )method). Background. defocusing, and collimation corrections. These steps require special consideration in quantitative compositional mapping (5, 13). If not treated properly, these errors can be a source of serious artifacts and may produce sufficient modification of the image to interfere with visualization of the true chemical microstructure. The effeds of spectrometer defocusing and collimation can be so severe that they can even dominate the apparent contrast from major constituents. Correction is particularly important when minor or trace levels are to be mapped.
ANALYTICAL CHEMISTRY, VOL. 62, NO. 22, NOVEMBER 15. 1990
1161 A
compodnhl mpplns 01 maw castnuents To perform quantitative compositional
mapping of major constituents (mass fractions of 0.1 wt 70or greater), corrections must he made for instrumental artifactsassociated with the defocusing of the wavelength-dispersive X-ray spectrometer and collimation effects of the energy-dispersive X-ray spectrometer, which can occur during the image formation process. Defocusing in WDS mapping. The wavelength-dispersive X-ray spectrometers used in electron probe microanalysis are focusing devices in which the diffracting crystal is bent to the spectrometer radius (Rowland circle), as shown in Figure 1. When the electron beam is located on the common optic axis of the electron column and the wavelength spectrometer, radiation of a particular wavelength h, which is emitted into the solid angle of collection of the spectrometer, is diffracted at all points on the crystal. This arrangement has the great advantage in conventional single-point analysis of increasing the radiation collected at the detector slit. A negative consequence of this focusing arrangement occurs if the beam is scanned off the point of optimum focus. If no adjustment to the spectrometer position is made, the effective spectrometer transmission for that wavelength decreases as a function of the deflection. The magnitude of this effect can be readily seen in Figure 2, which is a characteristic X-ray intensity map measured on a pure element standard. Bands that depict a narrow X-ray intensity range are observed, with a drop in intensity of more than 50% for the edge of the map compared with the center at the particular magnification chosen. The hands exist because the diffraction crystal has a substantial width (-1 cm) in the direction perpendicular to the plane of the drawing shown in Figure 1. The diffraction condition is satisfied across the full width of the crystal, producing the hands observed in Figure 2. The magnitude of this instrumental artifact is obviously so severe at low magnifications (< 500 diameters, or field widths > 200 pm) that it can obscure the real compositional contrast of the unknown. An example of this effect on the map of a multiphase specimen is shown in Figure 3, where the modulation of the X-ray intensity caused by defocusing overwhelms the strong compositional contrast over most of the image. T o solve the defocusing problems of the wavelength-dispersive spectrometer, the analyst can use specimen stage 1162A
scanning, spectrometer scanning (more commonly known as crystal rocking), defocus mapping, and defocus modeling. The first two methods are mechanical and the latter two mathematical in nature. Each has advantages and disadvantages; the best choice depends on available instrumentation. Specimen stage scanning. Mechanical scanning of the specimen is the most obvious solution to the defocusing problem (15). Instead of scanning the beam off the Rowland circle of the spectrometer, the beam is fixed and the specimen is mechanically scanned by stage motors, always bringing the analyzed location to the optimum spectrometer focus position. Although simple in concept, implementing the stage scanning method is hindered in practice by the mechanical backlash of the specimen stage. The backlash can usually he eliminated when the stage travels consistently in the same direction to generate a single linescan; however, tocreatean image,a scan along orthogonal axes is needed. The scan along a line may he highly accurate, but any backlash will he manifest in errors that arise when attempting to return to the starting position along the axis that is orthogonal to the scan line. Such misregistration will hecome increasingly evident at high magnifications. The latest generation of stages makes use of optical encoding or piezoelectric displacement to establish a positive reference position that can he located repeatedly regardless of backlash. This type of stage control provides sufficient positional accuracy and precision (ilpm) to generate maps for magnifications up to 500 x (field width
Flgure 2. Effectsof defocusing the wavelength spectrometer caused by scanning the specimen with the electron beam. X-ray intensity map is measured hom a flat. pure Cr standard at a field wldth of 250 pm. Parallel bands of constant intensity (spectrometer t r a w mission1are observed. The bonom $-le indimtes intensity wedges used to enhance the band contrast.
ANALYTICAL CHEMISTRY. VOL. 62. NO. 22, NOVEMBER 15. 1990
t-.r
3
Flgure 3. Severe spectrometer aelocusing overwhelms the compositional contrast.
Map of the intensity diSnibUtion of h4g in a 4 - V Co-0 ceramic at a field width of 500 um. Large dark area in upper right is a V-rich inCluSiOn. Specimen courtesy of C. Handwerkw and J. Blendell. NIST. (Adapted from Reference 74.1
200 pm). Stage scanning is the best of the four methods for producing images at low magnification (< 50 X) with large fields (field width > 2 mm). In principle, the size of the field to be scanned is only limited by the extent of the stage motion, which can he as much as several centimeters. A significant advantage of stage scanning is derived from the counting statistics of the X-ray intensity measurement. Because the specimen is always moved to the position of maximum transmission of the spectrometer, intensity measurements are made a t constant variance for the same concentration of the analyzed element. Moreover, in the standardization step to convert the intensity map to a k-value map (k is the ratio of the characteristic X-ray intensity of the unknown to the standard), it is only necessary to divide the intensity a t each pixel in the image by the value of the intensity measured on an appropriate standard recorded in a single point mode. Crystal rocking. Figure 1 suggests another mechanical solution involving the crystal. When the beam is scanned in the specimen plane and moves off the Rowland circle, the crystal can he rocked along the Rowland circle in synchronism with the scan on the specimen to bring the effective setting of the spectrometer back to the peak position. In terms of the defocus map shown in Figure 2, the line of focus is moved across the scan field in synchronism with the scan. This technique, called crystal rocking, has been used for more than a decade with an analog control for a single-wavelength spectrometer. When multiple-wavelength spectrometers are placed on the instrument, the line of optimum focus is different for each spectrometer, necessitating
different corrections. Swyt and Fiori (16) have discussed the computational techniques for computer control of crystal rocking for multiple spectrometers. To compensate for the beam deflection, the specimen-to-crystal distance is varied by movement of the crystal on the Rowland circle. In general, the required spectrometer position, A,, is a function of the x y position of the beam and the nominal wavelength, A, A,
= f[(xy),A,]
(1)
Because the deflections on the specimen plane are small relative to the specimen-to-crystal distance, the small angle approximation (given by 0 = sin 8 = tan 8) can be used to develop an empirical correction function. For refocusing of a vertical spectrometer, the change in spectrometer position, &, to compensate for the beam deflection is given by the equation A,eq = A" + (CM/WM)(AAxAxi + AAyAyi) (2)
where CM and WM are the calibration image and the working image magnification values, respectively: AAx and AAy are the experimentally determined values of the change in wavelength per unit of beam deflection on the specimen; and Axi and Ayi are the deflections of the beam a t a given location relative to a reference point. The peak A. values are first determined for each spectrometer a t the extremes of the scan a t the lowest magnification in a calibration image by stepping over the peak of a standard. The coordinates and A. value for each position are stored in a calibration file for the wavelength. From these stored values, the peak A,, values for any other position in the scanned field, at that magnification or any higher magnification, can
be calculated from Equation 2. Because the digital scan is discrete rather than continuous, the control system is designed to complete the action of crystal rocking prior to the collection of any X-ray counts a t a given pixel location. Results obtained on a pure element standard are illustrated in Figure 4. The intensity trace demonstrates effective removal of the defocus effect. Like stage scanning, crystal rocking has the advantage of achieving a uniform spectrometer transmission throughout the image scan and uniform counting statistics across the field. However, a t magnifications below 100 diameters, with scan fields exceeding 1mm on edge, the physical size of the crystal restricts the extent of rocking. Nonlinearity may also be observed because of imperfections in the diffraction crystal at ita extremities. Defocus mapping. The experimentally measured intensity map of the standard in Figure 2 illustrates the spectrometer defocus as a function of position. The information in this standard map allows corrections to be made for the defocus effect when determining a compositional map of an unknown ( 4 , 5 ) .When the intensity maps for the unknown and the standard are recorded under nominally identical conditions, a k-value map can be made by taking the ratio of the unknown to that of the standard on the basis of corresponding pixels. Because the spectrometer transmission depends only on the beam position, this effect cancels when the intensity ratio is taken for data from the equivalent pixel in the standard and the specimen intensity maps, eliminating the defocus effect in the resulting k-value map. An example of the standard map correction applied to a Au-Ag alloy is shown in Figure 5. The standard map method is the
. ,
.
i
Flgure 4. Correction of wavelengthdispersive spectrometer defocusing by the
crystal rocking method. The (len) uncorrected and (rlgM) MBCMinlensny maps Iu TI are mmpared 101 a field wldm of 1 mm. Straight line Is me scan locus. Band 01 llghl (lefi) I s h maximum spschometn bansmisston.(Adapted from Reference 16.)
Flgure 5. Correction of wavelengthdispersive spectrometer defocusing by the
standard map method. The inlensily map of lhe unknown is ralloed to h intensity map from a homogeneous standarc w l a Io qUantllalive matrix cwre~llonCBIcuialion. (a) Ag standard inlensily map and IbHd) COnCenlralion maps lor NlST SRM 481. (b) AY-20 Ag. IC) Au-60 Ag. id) Au-80 Ag. (Adapted ham Relerewe 5.)
simplest defocus correction to use; it involves the collection of X-ray intensity data matrices on the unknowns and the standards followed by simple arithmetic operations to generate the k-value maps. The advantages of defocus mapping are the direct applicability to any number and configuration of wavelength spectrometers and the elimination of any requirement for mechanical scanning of the stage or the spectrometers. However, the disadvantages of defocus mapping are significant. First, because of time constraints, mapping generally uses relatively short dwell times per pixel, compared with normal single-point analysis integration times. Thus the counting statistics measured at a single pixel may be poor when the concentration is low. Even with high concentration standards, it may take hours toaccumulate the standard map with adequate counting statistics. Typically, several standards must be mapped to analyze an unknown, and the time penalty incurred in the standard mapping step is considerable. Second, because the spectrometer transmission is not a constant, the intensity is not collected a t constant variance across the defocus axis. The poor statistics of the measurement are exaggerated a t the limits of a low-magnification, large-deflection scan where the maximum defocus occurs. Third, although defocus maps for standards can be archived and used for other unknowns, a new standard map must be generated whenever the scan conditions-particularly the magnification-are changed, making the technique less time efficient.
ANALYTICAL CHEMISTRY. VOL. 62, NO. 22, NOVEMBER 15, 1990
1163,.
INSTRUMENTATION Fourth, defocus mapping requires standards that have highly polished areas as large as the area to be mapped on the unknown. Any surface defects such 88 scratches or pits in the unknown or the standard will appear as artifacts in both the k-value map and the fmal comphsitional map. Finally, the limit of the maximum field size (lowest magnification limit) is reached when the scan on the specimen effectively detunes the spectrometer completely off the X-ray peak. For practical work, this limit is a magnification in the range of 100-150 diameters (field size 1-0.67 mm on edge), depending on the spectrometer characteristics.
sional standard map from a one-dimensional peakprofile ( 2 4 , V j . Adigital spectrometer peak profile is first recorded for the peak of interest measured on a known standard. This digital scan is recorded with a sufficiently long dwell time a t each spectrometer position to accumulate adequate counting statistics. The key to constructing the standard map from the peak profile is the symmetry of the defocus parallel to the crystal thickness. As shown in Figure 7, for a pixel located a perpendicular distance A S from the line of best focus, the equivalent spectrometer detuning A 0 is an angle of -1' and can be approximated by
Ae = (AS'/So)
(3)
A'3 = (AS/So)sin Y
(4)
where So is the distance of the beam impact point on the spectrometer to the crystal and Y is the take-off angle of the spectrometer. So depends on the radius R of the Rowland circle and the value of the Bragg angle to which the spectrometer is tuned So = 2R sin BS (5) We can consider SOa constant for all points in the scan, This is a reasonable approximation because So has a value on the order of 15 cm, and AS is approximately 1mm for a low magnifica-
tion (100 X ) map. The construction of thestandardmap from the peakprofile data requires that thedistance A S from the focus line be calculated for each pixel in the scan matrix. The focus line is determined by specific points (XI,YI) and (Xz,Yz), which are directly measured for each spectrometer in the intensity maps of the unknown. The distance A S of any point (XJ,Y3) from the focus line is given by the equation
AS= (-DXJ+Y,-E)li (D2+ 1)" (6)
where
D = (Yz- Y,)/(X, - X I ) (7
E
=
Y,- D(X,)
(8)
The location of the pixel relative to the focus line, above or below the line, is determined by the sign of AS in the denominator of Equation 6. To convert AS from pixel units to distance units, the value must be multiplied by a scale factor (SF)
SF = L / ( M M
(9) where L is the linear dimension of the scan display, M is the magnification of the image on the CRT, and N is the number of points in the scan matrix. The final equation, which relates the amount of defocusing to the pixel loca-
Flgure 6. Wavelength spectrometer defocusing showing an X-ray peak profile when a plot of the intensity is taken along the locus (upper left to lower right) perpendicular to the line of maxi-
mum transmission. A partially resOived KOII-KU~pair 18 depicted In image Specimen 111 Cr with an Image field wldm cd 500 pm (Adapted from Reference 37 )
me
&focus modeling. When the spectrometer is peaked on the Bragg angle for a characteristic X-ray of interest and the electron beam is scanned on the specimen, it is equivalent to detuning the spectrometer off thadiffraction peak. Figure 6 shows an intensity map for pure Cr, with a line trace taken along a locus perpendicular to the defocus axis. The resulting intensity plot depicts the shape of a Cr Ko peak, which is a compsite of the partially resolved Kol-Kaz peaks. There is a geometric equivalence between fixing the spectrometer while scanning the beam on the specimen and fixing the beam on the optic axis while scanning the spectrometer. The latter is the familiar procedure for performing a wavelength scan to profile the peak. This geometric equivalence can be used 88 the basis of a mathematical method for correcting spectrometer defocusing by calculating a two-dimen1164,.
Flgure 7. Relationship betwwn electron beam deflection on the specimen and the deviation from the Bragg angle on the diffraction crystal using defocus modeling. As is me deflection cd me beem in me specomen plans. A B IS me dewation hom me srsgg angie 8.' and IIs takwff angle. whlch Is lhe angle I "me speclmen plane 10 lhe 6peclrm1(1 ax16 (Adapted hom Refaewe 17 I
ANALYTICAL CHEMISTRY, VOL. 62. NO. 22, NOVEMBER 15. 1990
...
c 1501
Ikx loo(
m 51)I
I
.,
r:llwrr R Flgure E. Demonstration of correction of wavelengthdispersive spectrometer defocusingby defocus modeling. Intensity traces are taken along mS indicated IP cus irtraight line1 hom a measured map U a W trace1 and from a U I I C Y I ~ map I ~ (smooth trace). The trace* overlap closely except for BXCUrSIonS W u s e ot the poa coming stmislics in me measured map. Spsclmen is FB with an “age lleld Width Of 500 p m . (AdBPted from ReferenuJ 17.1
tion, is given by A 8 = (AWsin ‘Z”)(SFIS,) (10)
The standard map is generated on a pixel-by-pixel basis by calculating the value of A 0 appropriate to each pixel using Equations 6 and 10.This value of A 0 is used to select the position relative to the peak in the digital peak profile measured on the standard. The value of the intensity measured at this detuning position, relative to the peak intensity, is used to calculate the appropriate standard intensity value for that amount of defocusing. By repeating this procedure for each pixel, a complete standard map is generated for the particular magnification and spectrometer orientation, The accuracy with which a standard map can be calculated from a peak profile is illustrated in Figure 8, where the intensity distribution along the vector AB is plotted for a directly measured standard map (jagged trace) and a calculated standard map (smooth trace). The traces match closely, confirming the accuracy of the procedure. When an unknown is mapped, it is important to locate the line of optimum focus for each spectrometer. The focus line can be readily located even in a complex image field by the following procedure, which is illustrated in Figure 9. The intensity map for the unknown is converted from a 255 graylevel (continuous) image, Figure 3, into a binary image, Figure 9a, where pixels greater than or equal to a defined threshold are arbitrarily set to full white (value = 255 units) and all pixels below the threshold are set to black (value = 0 units). By progressively in-
creasing this threshold, the image collapses to the focus line, as shown in Figures 9b and 9c. The position of the focus line can be accurately found even in complex microstructures that introduce significant discontinuities in the binary images. Although the position of the focus line in the scanned field is reasonably constant, changes in the electronic scan rotation or elevation of the sample can introduce errors that can he eliminated by applying the threshold binary image technique to each unknown. After the focus line is determined, the defocus correction can be calculated and the artifact eliminated in the final map (Figure 9d). The defocus modeling procedure has several advantages. First, it offers greater flexibility and efficiency than the standard mapping procedure because a single archived spectrometer peak profile can he used to calculate standard maps at any magnification, from -150 to 2000 diameters (where defocusing is negligible). Second, the spectrometers are held fixed during the mapping procedure, reducing wear on moving parts. Third, because the peak profile for a particular spectrometer need only be recorded once and then
archived, a peak scan can be measured with a large number of counts at each angular position. The counting statistics in the calculated standard map are greatly improved over those in a directly measured map, as seen in the comparison of the traces in Figure 8. The counting statistics in the calculated standard map are improved to the point that the main contribution to the statistical uncertainty in the k-value map arises only from the intensity map of the unknown. Finally, artifacts arising from surface irregularities in the standard, such as scratches and pits, are eliminated from the calculated standard map. The standard map calculated by the defocus modeling procedure suffers from thesamelimitationsas thedirectly measured standard map. The defoCUB modeling procedure can be applied down to magnifications of -150 diameters. Below this magnification, the spectrometer is detuned so far off the peak that the intensity falls to an unacceptably low value. Also, because the effective transmission varies with position, the variance is not constant throughout the map and increases with distance from the best focus line.
Flgure 9. Location of the line of best focus In t h e intensity map of an unknown by the threshold method. A IhreshoM level Is defined and a binary lmags Is IDmad wlth bladr dsllnad tor a11 plxsls below mS threshold and vhlte lor all pixels at o( SbDW mS ttreshld. (a
