Compositional Mapping with the Electron Probe Microanalyzer: Part I

Compositional Mapping with the Electron Probe Microanalyzer: Parti

Dale E. Newbury, Charles E. Fiori, Ryna B. Marinenko, Robert L. Myklebust, Carol R. Swyt1, and David S. Bright Microanalysis Research Group Center for Analytical Chemistry National Institute of Standards and Technology Gaithersburg, MD 20899

Compositional mapping with the elec tron probe microanalyzer is a tech nique for creating digital images, us ing the localized concentration of an element or compound to specify the color scale or intensity for display of the image. All of the steps in conven tional single-location electron probe microanalysis are used in composi tional mapping. In addition, various correction methods are used to remove artifacts that arise during scanning. With all corrections applied, quanti tative mapping to trace levels of 100 ppm has been demonstrated in the most favorable cases and mapping at 1000 ppm can be achieved in most in stances. In this two-part series, Dale New bury and co-workers at the National Institute of Standards and Technol ogy discuss the correction techniques used for both wavelength- and energydispersive spectrometries. Part I in cludes a discussion of the problems 1 Permanent address: Biomedical Engineering Re search Branch, NIH, 9000 Rockville Pike, Bethesda, MD 20892-0001

This article not subject to U.S. Copyright Published 1990 American Chemical Society

that spurred the development of com positional mapping as a quantitative technique, the general procedure in volved, and the correction techniques applied to the mapping of major con stituents. Part II, which will appear in the December 15 issue, discusses the correction techniques applied to the mapping of minor constituents, in strument selection, and applications. The terms microbeam analysis and in strumental microanalysis include a wide range of analytical techniques that have the capability of selectively analyzing condensed matter on a spa tial scale of micrometers or finer. The

aspect of this technique is composi tional mapping, which involves the preparation of images that directly de pict the concentrations of elemental constituents in a specimen (3-7). The electron probe technique in volves the use of energetic electrons, with an energy range of 10-30 keV, to bombard the specimen (2). The elec trons interact with the atoms of a solid specimen and create inner shell ioniza tions that subsequently decay, emit ting characteristic X-rays that provide qualitative identification of all ele ments with the exception of H, He, and Li. The measurement of the intensity of the characteristic X-rays relative to

INSTRUMENTATION development of spatially resolved anal ysis 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 instru ment based on a focused beam of elec trons, called the electron probe mi croanalyzer (ΕΡΜΑ) (1). Since then, electron probe microanalysis has ma tured and is used as a primary analyti cal 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 with matter is sufficiently understood to permit quantitative analysis using a combina tion of physical models for the princi pal interelement effects (elastic scat tering of electrons, electron radiation, X-ray absorption, and secondary X-ray fluorescence) and a simple standard ization procedure based on pure ele ments or binary compounds. The earliest electron probes were de signed with optical systems that per mitted control over beam focusing, but the beam was static and fixed on the

ANALYTICAL CHEMISTRY, VOL. 62, NO. 22, NOVEMBER 15, 1990 · 1159 A

INSTRUMENTATION coincident optic axes of the electron column and the wavelength-dispersive X-ray spectrometer(s). Analytical locations on the specimen were selected by mechanical positioning of the stage using an optical microscope with a focus that coincided with the electron/X-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 (S). 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 at 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 in-

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 wt % 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.

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Trace constituents (< 1 wt %) 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 and/or scanning electron microscopy. Such problems could be avoided if a fully quantitative image containing the composition at 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 digi tization of the signals of interest; be cause the characteristic X-ray signals had long been available as digital out puts from the pulse-counting X-ray circuitry, it was natural to consider us ing 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.

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Compositional mapping

Compositional mapping with the elec tron microprobe can be described as a quantitative electron probe microanal ysis carried out at every beam location in a digitally controlled scan (5). The digital X-ray signals for each constitu ent are collected in individual data ar rays and corrected for instrumental, physical, and matrix effects. The con centration 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 map ping 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 es tablishing accurate quantitative re sults, and failure to follow proper pro cedures can lead to large errors in the final concentrations—even to the point of producing completely false values. False results can actually produce an apparent reversal of the chemical con trast 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 infor mation in the form of an image. Dead time correction for X-ray coincidence losses. Photon detection is performed serially, raising the possi bility 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 artifacts that can arise from local varia tions in the count rate (2). The dead time correction for WDS is less of a problem because the pulse-processing time is at least an order of magnitude shorter than that for EDS. Standard mathematical procedures are available

Figure 1. Focusing circle of the wavelength-dispersive X-ray spectrometer and the effect of defocusing caused by deflecting the electron beam X-ray source off the optic axis of the system. The Bragg angle of diffraction is denoted by θ; ΔΘ is the deviation from the Bragg angle caused by scanning the electron beam off-axis.

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 reso lution, although mathematical meth ods 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 stan dards, 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

calculated corrections for each of the major matrix-dependent physical in fluences 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 correc tion, A), and secondary fluorescence (the fluorescence correction, F). The empirical method uses calibration curves expressed as interelement inter action coefficients. The empirical/ physical method is based on experi mentally measured X-ray depth distri bution (e.g., the φ(ρζ) method). Background, defocusing, and col limation corrections. These steps re quire special consideration in quantita tive 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 effects of spectrometer defocusing and collimation can be so severe that they can even dominate the apparent con trast from major constituents. Correc tion is particularly important when mi nor or trace levels are to be mapped.


INSTRUMENTATION Compositional mapping of major constituents

To perform quantitative compositional mapping of major constituents (mass fractions of 0.1 wt % or greater), correc tions must be made for instrumental artifacts associated with the defocusing of the wavelength-dispersive X-ray spectrometer and collimation effects of the energy-dispersive X-ray spectrom eter, which can occur during the image formation process. Defocusing in WDS mapping. The wavelength-dispersive X-ray spec trometers used in electron probe mi croanalysis are focusing devices in which the diffracting crystal is bent to the spectrometer radius (Rowland cir cle), as shown in Figure 1. When the electron beam is located on the com mon optic axis of the electron column and the wavelength spectrometer, radi ation of a particular wavelength λ, which is emitted into the solid angle of collection of the spectrometer, is dif fracted 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 conse quence of this focusing arrangement occurs if the beam is scanned off the point of optimum focus. If no adjust ment to the spectrometer position is made, the effective spectrometer trans mission 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 in tensity 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 bands exist because the diffraction crystal has a substantial width (~1 cm) in the direction perpen dicular to the plane of the drawing shown in Figure 1. The diffraction con dition is satisfied across the full width of the crystal, producing the bands ob served in Figure 2. The magnitude of this instrumental artifact is obviously so severe at low magnifications (< 500 diameters, or field widths > 200 μτα) that it can obscure the real composi tional contrast of the unknown. An ex ample of this effect on the map of a multiphase specimen is shown in Fig ure 3, where the modulation of the X-ray intensity caused by defocusing overwhelms the strong compositional contrast over most of the image. To solve the defocusing problems of the wavelength-dispersive spectrome ter, the analyst can use specimen stage

scanning, spectrometer scanning (more commonly known as crystal rocking), defocus mapping, and defocus model ing. The first two methods are mechan ical and the latter two mathematical in nature. Each has advantages and dis advantages; the best choice depends on available instrumentation. Specimen stage scanning. Me chanical scanning of the specimen is the most obvious solution to the defo cusing problem (15). Instead of scan ning 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 spec trometer focus position. Although simple in concept, imple menting the stage scanning method is hindered in practice by the mechanical backlash of the specimen stage. The backlash can usually be eliminated when the stage travels consistently in the same direction to generate a single line scan; however, to create an image, a scan along orthogonal axes is needed. The scan along a line may be highly accurate, but any backlash will be man ifest in errors that arise when attempt ing to return to the starting position along the axis that is orthogonal to the scan line. Such misregistration will be come increasingly evident at high mag nifications. The latest generation of stages makes use of optical encoding or piezo electric displacement to establish a positive reference position that can be located repeatedly regardless of back lash. This type of stage control pro vides sufficient positional accuracy and precision (±1 /tm) to generate maps for magnifications up to 500 X (field width

Figure 2. Effects of defocusing the wavelength spectrometer caused by scanning the specimen with the elec tron beam. X-ray intensity map is measured from a fiat, pure Cr standard at a field width of 250 μην Parallel bands of constant intensity (spectrometer trans mission) are observed. The bottom scale indi cates intensity wedges used to enhance the band contrast.


Figure 3. Severe spectrometer defo cusing overwhelms the compositional contrast. Map of the intensity distribution of Mg in a Mg-VCo-0 ceramic at a field width of 500 μιη. Large dark area in upper right is a V-rich inclusion. Specimen courtesy of C. Handwerker and J. Blendell. NIST. (Adapted from Reference 14.)

200 Mm). 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 be as much as several centimeters. A significant advantage of stage scanning is derived from the counting statistics of the X-ray intensity mea surement. Because the specimen is al ways moved to the position of maxi mum transmission of the spectrometer, intensity measurements are made at constant variance for the same concen tration of the analyzed element. More over, in the standardization step to convert the intensity map to a fc-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 at 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 be rocked along the Rowland circle in syn chronism with the scan on the speci men 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 spectro meters 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 com puter control of crystal rocking for multiple spectrometers. To compen sate for the beam deflection, the speci men-to-crystal distance is varied by movement of the crystal on the Row land circle. In general, the required spectrometer position, Xreq, is a func tion of the x,y position of the beam and the nominal wavelength, λ„ Xreq = f[(x,y),Xn]

(1)

Because the deflections on the speci men plane are small relative to the specimen-to-crystal distance, the small angle approximation (given by θ = sin θ = tan Θ) can be used to develop an empirical correction function. For refocusing of a vertical spectrometer, the change in spectrometer position, Xreq, to compensate for the beam deflection is given by the equation Keq = \ i + (CM/WM)(àK*Xi + AXyAy,-) (2) where CM and WM are the calibration image and the working image magnification values, respectively; Δλ, and Δλ^ are the experimentally determined values of the change in wavelength per unit of beam deflection on the speci men; and Δχ, and Δ>Ί are the deflec tions of the beam at a given location relative to a reference point. The peak λ„ values are first determined for each spectrometer at the extremes of the scan at the lowest magnification in a calibration image by stepping over the peak of a standard. The coordinates and λ„ value for each position are stored in a calibration file for the wave length. From these stored values, the peak Xreq values for any other position in the scanned field, at that magnifica tion or any higher magnification, can

be calculated from Equation 2. Be cause the digital scan is discrete rather than continuous, the control system is designed to complete the action of crys tal rocking prior to the collection of any X-ray counts at a given pixel location. Results obtained on a pure element standard are illustrated in Figure 4. The intensity trace demonstrates ef fective removal of the defocus effect. Like stage scanning, crystal rocking has the advantage of achieving a uni form spectrometer transmission throughout the image scan and uni form counting statistics across the field. However, at magnifications be low 100 diameters, with scan fields ex ceeding 1 mm on edge, the physical size of the crystal restricts the extent of rocking. Nonlinearity may also be ob served because of imperfections in the diffraction crystal at its extremities. Defocus mapping. The experimen tally measured intensity map of the standard in Figure 2 illustrates the spectrometer defocus as a function of position. The information in this stan dard map allows corrections to be made for the defocus effect when determin ing a compositional map of an un known (4,5). When the intensity maps for the unknown and the standard are recorded under nominally identical conditions, afe-valuemap 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 tak en for data from the equivalent pixel in the standard and the specimen intensi ty maps, eliminating the defocus effect in the resultingfc-valuemap. An exam ple of the standard map correction ap plied to a Au-Ag alloy is shown in Fig ure 5. The standard map method is the

Figure 4. Correction of wavelength-dispersive spectrometer defocusing by the crystal rocking method. The (left) uncorrected and (right) corrected intensity maps for Ti are compared for a field width of 1 mm. Straight line is the scan locus. Band of light (left) is the maximum spectrometer transmission. (Adapted from Reference 16.)

Figure 5. Correction of wavelength-dis persive spectrometer defocusing by the standard map method. The intensity map of the unknown is ratioed to the intensity map from a homogeneous standard prior to quantitative matrix correction calculation, (a) Ag standard intensity map and (b)-(d) concentra tion maps for NIST SRM 481. (b) Au-20 Ag, (c) Au 60 Ag, (d) Au-80 Ag. (Adapted from Refer ence 5.)

simplest defocus correction to use; it involves the collection of X-ray intensi ty data matrices on the unknowns and the standards followed by simple arith metic operations to generate the Α-val ue maps. The advantages of defocus mapping are the direct applicability to any number and configuration of wave length spectrometers and the elimina tion of any requirement for mechanical scanning of the stage or the spectro meters. 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 integra tion 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 to accumulate the stan dard map with adequate counting sta tistics. Typically, several standards must be mapped to analyze an un known, and the time penalty incurred in the standard mapping step is consid erable. Second, because the spectrometer transmission is not a constant, the in tensity is not collected at constant vari ance across the defocus axis. The poor statistics of the measurement are exag gerated at the limits of a low-magnifi cation, 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 magnifi cation—are changed, making the tech nique less time efficient.


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 as scratches or pits in the un known or the standard will appear as artifacts in both the fe-value map and the final compositional 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 magnifi cation in the range of 100-150 diame ters (field size 1-0.67 mm on edge), de pending on the spectrometer charac teristics.

sional standard map from a one-di mensional peak profile (14,17). A digi tal spectrometer peak profile is first recorded for the peak of interest mea sured on a known standard. This digi tal scan is recorded with a sufficiently long dwell time at each spectrometer position to accumulate adequate counting statistics. The key to con structing the standard map from the peak profile is the symmetry of the de focus parallel to the crystal thickness. As shown in Figure 7, for a pixel located a perpendicular distance AS from the line of best focus, the equivalent spec trometer detuning ΔΘ is an angle of ~1° and can be approximated by ΔΘ = (AS'/S 0 )

(3)

ΔΘ = (AS/S0) sin Φ

(4)

where So is the distance of the beam impact point on the spectrometer to the crystal and Ψ 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 (5) S n = IB. sin ΘΡ We can consider So a 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 ap proximately 1 mm for a low magnificaFigure 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 resolved Κα 1 -Κα 2 pair is depicted in the image. Specimen is Cr with an image field width of 500 Mm. (Adapted from Reference 17.)

Defocus modeling. When the spec trometer 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 detun ing the spectrometer off the diffraction peak. Figure 6 shows an intensity map for pure Cr, with a line trace taken along a locus perpendicular to the defo cus axis. The resulting intensity plot depicts the shape of a Cr Κα peak, which is a composite of the partially resolved Και-Κ«2 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 fa miliar procedure for performing a wavelength scan to profile the peak. This geometric equivalence can be used as the basis of a mathematical method for correcting spectrometer defocusing by calculating a two-dimen

tion (100 X) map. The construction of the standard map from the peak profile data requires that the distance AS from the focus line be calculated for each pixel in the scan matrix. The focus line is determined by specific points (Χι,Υι) and (-X^,^), which are directly measured for each spectrometer in the intensity maps of the unknown. The distance AS of any point (XS,YS) from the focus line is given by the equation AS = (~DX3 + F3 - E)l ± (D2 + 1) 1/2 (6)

where D = (Y2 - Y1)/(X2 E=Y1-

D(XJ

X,)

(7) (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/(MN)

0)

where L is the linear dimension of the scan display, M is the magnification of the image on the CRT, and Ν is the number of points in the scan matrix. The final equation, which relates the amount of defocusing to the pixel loca-

AS'

AS' « AS sin Ψ

Figure 7. Relationship between electron beam deflection on the specimen and the deviation from the Bragg angle on the diffraction crystal using defocus modeling. AS is the deflection of the beam in the specimen plane; ΔΘ is the deviation from the Bragg angle 0 B ; and Ψ is the take-off angle, which is the angle from the specimen plane to the spectrometer axis. (Adapted from Reference 17.)


Figure 8. Demonstration of correction of wavelength-dispersive spectrometer defocusing by defocus modeling. Intensity traces are taken along the indicated lo cus (straight line) from a measured map (jagged trace) and from a calculated map (smooth trace). The traces overlap closely except for excursions because of the poor counting statistics in the measured map. Specimen is Fe with an image field width of 500 μπι. (Adapted from Reference 17.)

tion, is given by Δθ = (AS)(sin *)(SF/S0)

(10)

The standard map is generated on a pixel-by-pixel basis by calculating the value of ΔΘ appropriate to each pixel using Equations 6 and 10. This value of ΔΘ 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 de tuning position, relative to the peak in tensity, is used to calculate the appro priate standard intensity value for that amount of defocusing. By repeating this procedure for each pixel, a com plete standard map is generated for the particular magnification and spec trometer orientation. The accuracy with which a standard map can be calculated from a peak pro file 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 cal culated 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 opti mum 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 Fig ure 9. The intensity map for the un known 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 col lapses 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 intro duce 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 be 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 eliminat ed 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 be cause a single archived spectrometer peak profile can be 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 statis tics in the calculated standard map are greatly improved over those in a direct ly measured map, as seen in the com parison 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 A-value map arises only from the intensity map of the unknown. Finally, artifacts aris ing 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 the same limitations as the direct ly measured standard map. The defo cus modeling procedure can be applied down to magnifications of ~150 diame ters. 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 posi tion, the variance is not constant throughout the map and increases with distance from the best focus line.

Figure 9. Location of the line of best focus in the intensity map of an unknown by the threshold method. A threshold level is defined and a binary image is formed with black defined for all pixels below the threshold and white for all pixels at or above the threshold, (a-c) Three progressively increasing thresh olds and (d) final compositional map for the Mg constituent. Image field width is 500 μπι. This Is the same specimen area shown In Figure 3. where the defocusing artifact dominates the contrast from the true Mg distribution. (Adapted from Reference 14.) ANALYTICAL CHEMISTRY, VOL. 62, NO. 22, NOVEMBER 15, 1990 · 1165 A

INSTRUMENTATION Solid-angle effects in EDS. The energy-dispersive spectrometer oper ates in a line-of-sight mode, such that X-rays emitted into the solid angle of the spectrometer are collected (2). Be cause no focusing is involved, the defocusing artifact encountered with WDS does not exist. However, the energydispersive spectrometer does have a fi nite solid angle of acceptance, defined either by the lateral extent of the de tector crystal or by a collimator. The collimator serves to limit stray X-radiation, which is generated elsewhere on the specimen stage or in the specimen chamber, from reaching the detector. For the beam deflections used in most mapping situations, the solid angle is effectively constant. However, at very low magnifications (< 25 diameters, corresponding to a scan deflection of 4 mm or greater) collimation limita tions on the solid angle may occur. When the beam is scanned sufficiently off the optic axis of the microscope, the solid angle of collection of the energydispersive spectrometer will be re stricted. The reduction in collection angle leads to a reduction in the total spectrum count rate relative to the onaxis count rate.

Correction for solid-angle effects re quires an accurate model of the detec tor acceptance angle as a function of beam position. If mechanical stage scanning is available, the solid-angle effect can be completely eliminated by always bringing t h e measurement point to the center of the collimation field. Alternatively, an experimental approach to developing a correction factor involves measuring the intensity from a pure element standard as a function of scan position to determine a scaling factor as a function of pixel location. By repeating this measure ment at several magnifications, an overall mathematical model appropri ate for any magnification can be devel oped. References (1) Castaing, R. Ph.D. Dissertation, Uni versity of Paris, 1951. (2) Goldstein, J. I.; Newbury, D. E.; Echlin, P.; Joy, D. C; Fiori, C; Lifshin, E. Scan ning Electron Microscopy and X-ray Microanalysis; Plenum: New York, 1981. (3) Fiori, C. E.; Swyt, C. R.; Gorien, Κ. Ε. Microbeam Analysis—1984; San Francis co Press: San Francisco, 1984; pp. 179-84. (4) Marinenko, R. B.; Myklebust, R. L.; Bright, D. S.; Newbury, D. E. Microbeam

Analysis—1985; San Francisco Press: San Francisco, 1985; pp. 159-62. (5) Marinenko, R. B.; Myklebust, R. L.; Bright, D. S.; Newbury, D. E. J. Microsc. 1987,145,207-23. (6) Newbury, D. E. Microbeam Analysis— 1985; San Francisco Press: San Francisco, 1985; pp. 204-08. (7) Fiori, C. E. Anal. Chem. 1988,60,86-90. (8) Cosslett, V. E.; Duncumb, P. Nature 1956,777,1172-73. (9) Oatley, C. W. The Scanning Electron Microscope; University Press: Cam bridge, England, 1972. (10) Heinrich, K.F.J. In Advances in Opti cal and Electron Microscopy; Barer, R.; Cosslett, V. E., Eds.; Academic Press: London, 1975; Chapter 6, p. 275. (11) Yakowitz, H.; Heinrich, K.F.J. J. Res. Nat. Bur. Stand. Sect. A 1969, 73,113. (12) McCarthy, J. J.; Fritz, G. S.; Lee, R. J. Microbeam Analysis—1981; San Francis co Press: San Francisco, 1981; pp. 30-34. (13) Myklebust, R. L.; Newbury, D. E.; Marinenko, R. B. Anal. Chem. 1989, 61, 1612-18. (14) Marinenko, R. B.; Myklebust, R. L.; Bright, D. S.; Newbury, D. E. J. Microsc. 1989.155.183-98. (15) Mayr, M.; Angeli, J. X-ray Spectrosc. 1985,14, 89. (16) Swyt, C. R.; Fiori, C E . Microbeam Analysis—1986; San Francisco Press: San Francisco, 1986; pp. 482-84. (17) Myklebust, R. L.; Newbury, D. E.; Marinenko, R. B.; Bright, D. S. Microbeam Analysis—1986; San Francisco Press: San Francisco, 1986; pp. 495-97.

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Compositional Mapping with the Electron Probe Microanalyzer: Part I

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