American Mineralogist, Volume 67, pages 521-533, 1982

Elemental mapping of minerals by electron microprobe

W. hNsnu

P erkin-Elmerl Phy sic al EIe ctronic s Divisionll6l-C San Antonio Road

Mountain View. California 94043

eNo M. SreucntBn

Department of Chemistry and GeochemistryColorado School of MinesGolden. Colorado 80401

Abstract

The electron microprobe produces two-dimensional images of elemental distributions bydisplaying X-ray photon-caused pulses on a cathode ray tube as the electron beam scansthe sample. The usefulness of the microprobe in mineralogy, diminished by this inaccuratequalitative elemental recording method, increases significantly with quantification of two-dimensionally collected X-ray intensities. A simple intemrpt circuit added to the micro-probe's electron beam scanner defines the raster rate for a data collection computer. Thecomputer, monitoring the X-ray spectrometers through counters, collects X-ray intensitiesat peak and background spectrometer positions from a rectangular grid of2,0fi) points fromsingle or multiple rasters. Standards, scanned in the same manner as analytes, give a grid ofX-ray intensities defining a least-squares fitted surface to compensate for areal defocusingof the spectrometers, and to quantify sample composition. Smoothing eliminates spuriousintensities caused by counting statistics and sample surface irregularities. Measurement ofup to eight elements per sample permits first-principles matrix corrections with mass-absorption coefficients, etc. The computer groups the 2000 data points into compositionalfamilies to make matrix correction calculations practical. The computer plots contour mapsof elemental distributions or ratios with or without matrix correction and quantification.Compositional mapping enhances the probe's areal sensitivity and utility.

IntroductionThe electron microprobe determines in-situ ele-

mental composition and distribution for minerals ona microscopic scale, presenting quantitative X-rayinformation about elemental concentrations on thesurface of polished specimens. An electron beamscans the surface of the sample, three differentways: spot, line, or rectangular area. The spot andline modes produce quantifiable elemental concen-trations but recording techniques usually limit thepresentation of areal elemental distribution to dotson a photograph.

The inadequacy of the standard microprobe as aquantitative areal elemental analyser is illustratedthrough an example. Figure I shows a typicalelemental distribution X-ray dot picture. Each dotrepresents a detected X-ray photon characteristic ofcalcium. The relative density of the dots shows them03-004)V82l0506-452 l $02.00

distribution of the calcium concentration in thelarge triangular zoned plagioclase crystal located inthe lower half of Figure 2. Although the dots inFigure I give a reasonable outline for the crystal,the plagioclase zoning is barely discernible. Super-imposed dots are not distinguished so that smallareas of high calcium concentration are not identi-fied. The low density of the dots, even within thearea covered by the crystal, makes the resulting dotimage statistically unreliable. Increasing the num-ber of dots by slowing the frame rate or by increas-ing the electron beam current exacerbates the prob-lem of superimposed dots. The dot photographsgive inaccurate elemental concentrations becausethe need to produce enough dots to be statisticallysatisfactory conflicts with the necessity to reducethe number of dots to avoid dot overlap.

Should quantitative areal analysis be possible,

521

522

Fig. I . Beam scanner dot photograph of calcium distribution ina zoned plagioclase feldspar.

the increased sensitivity, ease of interpretation, andquantitative results would make such a techniqueuseful in a variety of mineralogical and petrologicalapplications. Also, contour maps of elemental con-centration ratios would indicate important mineral-ogical zoning and microchemistry of geologicalsamples.

The purpose of this research was to investigatethe problems and requirements of areally analyzingrock and mineral samples with the electron micro-probe and the collection and modification of X-rayintensities to give quantitative elemental concentra-tions in rock or mineral specimens.

Several previous attempts have been made toquantify areal elemental concentrations with theelectron microprobe. The collection of location-specific X-ray intensities has been introduced butno methods to convert X-ray intensities to elemen-tal concentrations resulted. Research emphasis hasbeen on the improvement of the display on thebeamscanner oscilloscope. Birks (1971) showedhow X-ray intensities collected from a grid of pointsusing a multi-channel analyzer produce a perspec-tive dot topograph on an oscilloscope when thevertical displacement of each dot is determined bythe intensity of the X-rays at the corresponding gridposition of each counting channel. A related meth-od displays iso-intensity contours drawn manuallyon a grid of X-ray intensities printed by a teletypefrom multichannel analyzer data. Combining lineand raster modes, Heinrich (1964) produced deflec-tion and intensity modulated lines, starting atobliquely displaced points, suggesting a topograph-ic image. Tomura et al. (1968) introduced a tech-

./ANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

nique called "content mapping" which groupedcounts from a 50 x 50 grid of points into intensityranges. A pulser used the ranges to modulate thebrightness of a cathode ray tube on a logarithmicscale. Other methods, usually applying photograph-ic techniques, produce dot photographs to givemultiple exposure and color-coded images to showelemental distribution (Ingersoll, 1969; Hitchings,re76).

None of these older methods relate sample X-rayintensities to standard X-ray intensities; noneacount for X-ray fluorescence, absorption, or atom-ic number effects; none consider spectrometer defo-cusing at image edges nor allow subtraction ofbackground X-ray intensities.

This paper describes the conception, develop-ment, and examples of contoured areal electronbeam microanalysis.

Experimental

Instrumentation

We used a Philips PH 4500 electron microprobemicroanalyzer referred to subsequently as the EM.The EM has four focusing curved crystal X-rayspectrometers and a beam scanner to record X-rayspectra. All functions of the EM are standard andnon-automated. There were no modifications to theEM except to add a small electronic circuit to thebeam scanner to send some of its timing pulses to acomputer.

To collect X-ray data and to perform the othertasks necessary for areal mapping, we used a Hon-

Fig. 2. Photomicrograph of the plagioclase crystal of Figure l,showing zones. Crossed Nicols.

"/ANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

sowlooth in

. l t rF

pulse lo

compuler

+6.8V

horizonlol 4.7K

sowtoolh in compuler

ICI - LM339 ComoorolorFig. 3. Electronic circuit to transmit timing signals from an EM beam scanner to a computer.

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eywell H316 minicomputer, designed for real-timeon-line data aquisition. The computer, with a smallplotter attached, accumulated X-ray intensities us-ing four 24-bit binary counters, one for each spec-trometer.

The modification to the EM to permit it tocommunicate its status to the computer is shown inFigure 3. This small circuit, or a variation of it, willallow any older EM to do areal mapping. NewerEM's provide necessary signals as standard op-tions. To produce the pulses sent to the computer,the circuit of Figure 3 differentiates the time-basedsawtooth from the vertical (Y) deflection generator.When the differential becomes negative at the endof the vertical sweep, a pulse goes to an interruptline of the computer. The circuit operates the sameway on the horizontal (X) time-based sawtooth.except that it sends a pulse on another intemrpt lineto the computer. The horizontal sweep pulse tellsthe computer that a new line has begun. By compar-ing the number of horizontal lines since the lastvertical return sweep to the number of horizontallines per image, the computer determines the Yposition of the microanalyzer electron beam. Usingthe elapsed time since the last horizontal retrace,the computer determines the X position of theelectron beam.

Methods

The experimental procedures and problems canbe summarized as follows. Data collection requiresthat an EM spectrometer be positioned on an ele-

mental X-ray line or its background. The EM mustraster the beam while sending beam position infor-mation to the computer. The computer, through thecounters, must collect data on the grid over therastered area. The computer has to accumulate thecounts in an array, one number per element (orspectrometer) for each square of the grid.

The X-ray intensities collected thus are neitherqualitatively correct nor acceptable for mapping.Statistical errors of the X-ray photon counts and thesurface topography of the sample introduce spuri-ous apparent concentration highs and lows from achemically uniform sample, requiring more or lesssmoothing to help remove small-scale, spuriousconcentration highs and lows. At magnifications of500x or below, spectrometers become defocused atextremes of the beam raster, generating a curvedintensity surface over the scanned area. To makeintensities a function of element concentration, thecurved intensity surface must be corrected or nor-malized to a plane of uniform relative intensity overthe whole area. Elemental concentrations from theareally collected X-ray intensities require matrixand other corrections to derive concentration func-tions. Unfortunately, it is impractical to correct theintensities from each grid square individually be-cause the correction computation requires about 10seconds for each square. Practicality demands acorrection strategy to shorten calculations to a fewminutes. Finally, the ability to make areal concen-tration contour maps also allows presentation ofelement ratio maps which for many problems

524 "TANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

FLOW DIAGRAM I

Fig. 4. Calculation flow summaxy of data collection and dataprocessing to produce qualitative or quantitative concentrationcontour maps.

should be the most useful data presentation meth-od.

The following sections detail the problems andprocedures to obtain elemental concentration maps.Figure 4 summarizes the calculation flow.

X-ray intensity collection

To collect areal X-ray intensities the electronbeam must move with respect to the sample. Thisrelative motion can be effected in two ways, elec-tronically or mechanically. Mechanical beam track-ing collects X-ray data while the sample is movedunder a stationary electron beam. Electronic beamtracking collects X-ray data as the electron beamrasters over the surface of a stationary sample. Inthe electronic mode the beamscanner controls thebeam motion, thereby forcing a particular datacollection rate. We investigated both methods butpresent only the electronic tracking method. Eachmethod has advantages.

To collect data using electronic beam tracking,one must coordinate computer and beam scanneraction. The electron beam can be timed as it movesover the stationary sample under control of thebeam scanner. Because the beam sweep rates arevery stable, timing of the beam is an accuratemethod of locating beam position. Accurate loca-tion of the beam requires determining precisely thepoint at which timing begins in relation to the

position of the electron beam. The horizontal returnsweep initiates the time defining the X position ofthe electron beam and causes an intemrpt pulse tothe computer. The vertical return sweep defines theY position of the electron beam and also generatesan intemrpt pulse to the computer.

After the horizontal interrupt, the X-ray photoncounters must be read consecutively causing thesample squares for each element to be offset slightlywith respect to each other. The greatest relativeshift is less than a width of a line on a contour mapand can be ignored. The computer sums intensitydata from eleven horizontal sweeps to generate onerow of matrix data, giving a representative samplingof the total square area on the sample surface. A 50column by 40 row data matrix was chosen forscanning after experimenting with various matrixsizes ranging from 30 x 24 to 100 x 80. A smallernumber of squares results in insufficient resolutionon the contour map. A larger number of squaresreduces the counting time per square necessitatingmuch longer data accumulation times.

On the oscilloscope the rectangular image width-to-height ratio is five to four, the same as the datamatrix dimensions. At a frame rate of one perminute, chosen for a combination of convenienceand resolution, the electron beam spends approxi-mately one minute on the sample area displayed onthe oscilloscope, or about 0.03 seconds per sam-pling grid square. The X-ray count rates determinethe number of frames necessary to generate enoughcounts per grid square so variations in X-ray inten-sity due to elemental concentration differences arenot masked by poor counting statistics. A largernumber of frames results in reduced statistical er-rors but causes blurring of sharp concentrationedges due to electron beam drift in the EM column,especially at high magnifications. No significantblurring occurs on our EM with 25 frames or less atmagnifications of 2000x.

Smoothing X-ray intensity data

Smoothing the X-ray intensities eliminates mostof the variations due to statistical effors and smallscale sample topography. To remove statistical andtopographic variations but avoid smoothing out realvariations in elemental concentration, the computerchecks the eight immediate neighboring matrixpoints. If all the points fall within two standarddeviations of the value of the central point, Gaus-sian smoothing is applied to the central point. If anyof the surrounding points fall outside the admissible

range, a significant concentration slope is indicatedand no smoothing occurs. Points on the edge of theintensity matrix are not smoothed.

Normalizing X-ray intensitte s

In the scanning mode, detected X-ray intensity isa function of element concentration and beam posi-tion on the sample. A normalizing procedure re-moves the position effect, making the X-ray intensi-ties comparable for all points on the scanned area.During spectrometer alignment on the microana-lyzer, the electron beam operates in the stationaryor spot mode, locating the beam at the center of thevisible rastered area. When a spectrometer is fullyfocused, the bombarded spot on the sample, focus-ing crystal and detector slit are all on the focusingcircle. The plane of the focusing circle is perpendic-ular to the plane of the sample. The finite width ofthe crystal and the detector slit generate a series offocusing circles in parallel planes to give a focusingcylinder. The trace of the focusing cylinder on thesample surface is a line close to the Y deflectionaxis.

When the beamscanner generates an X-ray imageof a homogeneous sample, the focusing cylinder-sample surface trace appears as a ridge of higher X-ray intensity. As the electron beam scans from theleft to the right of the image, it passes through thefocusing cylinder surface. When the electron beamhits the sample at a point on the focusing cylinder-sample surface trace, the spectrometer is in focus.As the beam moves away from the focusing trace,the focus deteriorates and the X-ray intensity mea-sured by the spectrometer decreases. At low magni-fication (<500x) the X-radiation detected may be-come negligible when the electron beam is at theright or left edge of the image.

The radiation drop-off rate depends mostly uponthe degree of perfection of the analyzing crystalused. An imperfect analyzing crystal allows greaterangular divergence of reflection of a particular X-ray wavelength and can detect X-rays from a great-er width of the sample than a spectrometer with amore perfect crystal. Increased imperfection of thecrystal reduces the resolution of the spectrometerwhile increasing the thickness of the focusing cylin-der wall. On our EM one mica crystal is morenearly perfect than the others. This mica crystalresolves close X-ray peaks at the expense of a rapidintensity drop-off towards the right and left edge ofan image.

X-ray photon images collected from an area on a

525

homogeneous smooth sample showed X-ray inten-sity variation with beam position best described bya downward opening hyperbola or parabola with themaximum value at the center of the line. At differ-ent Y positions there is little variation in the hori-zontal distribution curves although the maximumX-ray intensity shifts horizontally as a linear func-tion of Y. A least squares fitted third-order surfacefunction seemed to describe the variation in X-rayintensities over the sample surface without intro-ducing spurious variations:

I"(x,y) : ?r f a2x * a3! I aaxz * a5xY + auy'

r a7x3 + asx2y + a"xy'* aroy3 (1)

where I"(x,y) is the intensity of the standard atcoordinates x,y and a1 is the constant coefficient forith term. The X-ray intensity sutfaces vary in shapewith the element, spectrometer and magnification,requiring a standard surface for each different com-bination of these variables.

Data grouping for ZAF correction

We may compute the concentration of an analytein a sample:

Ca(x,y) : C,(x,y) +9+ + Q)I.(x,y) Fa

where s and A refer to the standard and unknownanalyte respectively, and C, I, and F are respective-ly the analyte or standard element concentration,X-ray intensity, and number of frames (number ofscans over the image area). This first approximateconcentration is adjusted for matrix effects: absorp-tion, secondary fluorescence and atomic numbereffects (ZAF).

Calculation of the matrix or ZAF correctioncould be excessively time consuming. The applica-tion of the X-ray ZAF corrections would take upseveral hours if each point in the data matrix weretreated separately. Results from the ZAF correctionmight be satisfactory when correction factors, cal-culated for one point, are applied to compositional-ly similar points.

To form compositional families, the computergf,oups the points according to the first concentra-tion estimates for each element measured. A com-position identifier is constructed for each of the2000 sample points from the normalized X-rayintensity data. Each composition identifier is a 16bit data word consisting of 8 bit-pairs. The locationof the bit-pair within the data word identifies the

"/ANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

526

element while the values stored in the bit-pairs 00,01, 10 and 1l represent the ranges 0-20, 20-50, 50-80 and 80-I00Vo respectively of the maximum con-centration measured for that element on the ana-lyzed sample surface. Many points will have thesame composition identifier suggesting similarthough not necessarily identical composition. Eachdiferent composition identifier represents a uniquecompositional family of known average composi-tion.

The number, and concentration ranges of thefamilies depend on the maximum concentrationvalue of each element in an analyzed sample. If apoint on the sample indicates a 100% value for anelement, that element will be split into the ranges of0-20, 20-50, 50-80 and 80-100%o. If the maximumfor an element is only 60% at any point on the datamap, that element will be split into the ranges 0-12,20-30, 30-48 and 48-60%. This limiting methodensures that the four-way grouping of an elementcreates smaller, compositionally more accuratelydefined families.

It is also possible to group families assuming non-zero concentration minima for one or more ele_ments, further improving the representation of com-positional families; however, doing so complicatesprogramming.

The ZAF comection

The absorption, secondary fluorescence, andatomic number effects (ZAF) are the matrix effects.We used for the ZAF correction a modified andabbreviated version of the eepeN2 program (Hadi-diacos et a|.,1971). The large size of enneN2, dueto the extensive data matrices, made it impracticalto execute on the H3l6 computer. Since only asmall fraction of the esraN2 data was needed. thedata matrices were replaced by a small routine thatwould use only the necessary information for eachelement. The rest of the program was streamlined.

The program generates a composite correctionfactor for each analyzed element in the sample forthe effects of absorption (FJ, fluorescence (F.) andatomic number (F,). The analyte concentration atany point x,y is given by

ca : R ". .

: {" . (F"F,F,) . (3)l sFA

Correction factors are determined for each compo-sitional family once. The resulting factors are ap-plied to all the points on the sample having the

"IANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

compositional identifier for that compositional fam-ilv.

Elemental ratioing

In many geologic applications the absolute quan-tities of certain elements are not as important as theratios of two or more elements. This ratio can oftenidentify areas composed of a particular mineral orshow zonation by emphasizing fluctuations in con-centrations of alternating replacement elementswithin a mineral. The sum of the concentrations oftwo elements may also be useful.

The resulting map of ratios can be contoured bythe mapping program. The general form of the ratio,R. is

R : kc * d '

where a, b, c, and d represent elements identifiedby their spectrometer number and k is a scalefactor. One or more of the identifiers a, b, c or dmay be equivalent or left blank resulting in thefollowing possible combinations :

a . a a a + b a + b a * bb * c

r ---l-1,

I r ----l-

r - anq -

a + D D a + c a c

If either numerator or denominator goes below 10percent of its maximum value, the ratio is set tozero to avoid unpredictable ratios when counts nearbackground give poor counting statistics. If bothidentifiers in the numerator or the denominator areleft blank, a "l" is substituted as the value used inthe calculation. This results in the additional combi-nations:

a I a * b I-] , -]-, -----:- and - .I I l a * b

Results

In the following presentation of compositionalmaps, quantitative contour specifications have beenremoved from the maps for reproduction. Concen-tration highs are indicated by 'H' and lows by 'L'.

Ilmenite in magnetite-dots versus contours

Figures 5 through 7 show comparative presenta-tions of X-ray scan data from an ore specimen. Thesample comprises a cluster of ilmenite crystals inmagnetite. Figures 5 and 6 show the iron distribu-tion, while Figures 5 and 7 show the titaniumconcentration in the ilmenite. The variation in X-

JANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

Fig. 5. Beam scanner dot photographs ofiron and titanium ofilmenite crystals in magnetite. Top, iron dot pattern. Bottom,titanium dot pattern defining ilmenite crystals.

ray photon intensity from iron is barely discerniblein the dot photograph of Figure 5. Figure 6 showsthe very close correlation between the low iron andhigh titanium concentrations in Figure 7. The con-tours in Figure 7 occur at intervals often percent ofthe highest titanium concentration, starting at zerotitanium concentration. In Figure 6 a different con-touring method has been applied. Since both ilmen-ite and magnetite contain iron but in differentamounts. the lowest iron concentration serves as abase for the contours which are spaced at tenpercent intervals between the lowest and highestconcentration values of any point on the map. Thislatter technique accentuates the difference in ironconcentration between ilmenite and magnetite areasand shows small variations in iron concentration

not visible using photographic techniques. Linescans across the sample confirmed continuous vari-ation of iron and titanium from the interior to theboundary of the ilmenite crystals shown in both dotphotographs and maps.

N ormalizing int ensity data

Figures 8, 9 and 10 illustrate normalization tocorrect for spectrometer defocusing' Figure 8shows the relative intensity surface from a pure ironstandard. The off-center location of the highestpoint on the standard surface suggests that thespectrometer used to collect the data defocusedasymmetrically and was focused in such a way as tomaximize the minimum count rate on the entiresurface rather than maximizing the count rate of thecenter of the image. Figure 9 shows distribution ofmeasured X-ray intensities from a cross-section ofthe inside edge of a steel tube corroded by geother-mal brines. The lower, blank part of the imageshows no iron within the tube. The upper partshows the X-ray intensity distribution as measuredby the computer. Normalizing produces the surfaceshown in Figure l0 by dividing each point on Figure9 by the corresponding point on Figure 8. On thenormalized surface there is little change in ironconcentration within the section of the map repre-senting the steel tube. The lower concentration ofiron in the central part of the tube in the image isreal and this anomaly may have been the cause forthe increased corrosion of the edge of the tubeimmediately below. The normalization tends to beless reliable at the right and left edges of the imagedue to increased statistical variation as a percentageof measured concentration.

Topographic and compositional effects on X-rayintensity contour maps

Using a more accurate numerical method to por-tray composition in two dimensions accentuatesdetrimental effects such as the focusing effect thatdot photographs subdue. Two effects shown plainlywith contouring are topography and atomic numbereffects.

Figures 11 and 12 illustrate the effect of sampletopography on X-ray intensities recorded by spec-trometers at opposite positions relative to the sam-ple. The sample of Figures 11 and 12 constructedfor this purpose, comprises a cross section of a steeltube containing a steel wire. Polishing caused arelatively soft silica-aluminum gel between the wire

528

and the tube to form asample surface.

The computer-collected

Fig. 6. Contour map of iron content of ilmenite in magnetite asin Figure 5. Low iron content in elongate ilmenite crystals andhigh iron content in magnetite.

Fig. 8. X-ray intensity map of a flat surface of pure iron at500x showing defocusing of spectrometer over the scannedsample surface.

mean count but a small percentage of the constantcontour interval. However, comparing the mapsshows that there is a significant difference betweenthe location of the low contours. The lower con-tours in the lower left part of Figure llb are fartherinto the gel zone than the corresponding contours inFigure 11a. Conversely, in the upper right cornerthe low contours in Figure 1la have moved into thegel zone relative to Figure 1lb. The shifting of theselow contours is due to the shadowing and fluores-cence effects of the raised iron edge. As the electron

Fig. 9. Contour map of iron concentration along the cross-section of a tube wall of a geothermal steam conduit, uncorrectedfor spectrometer defocusing. Uniform iron concentration aboveinterface shows apparent concentration gradient to right and leftof a concentration high to the right of center. Note correspon-dence with gradients of Figure 8.

"TANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

slight depression in the

iron X-ray intensities,using two opposing spectrometers (goniometers),give contour maps showing high iron X-ray photoncounts in the lower left (tube) and upper right (wire)corners. The contours are drawn at ten percentintervals up to the maximum count for each map.

The contours in Figures lla and llb differ mostbelow 20 percent and above 80 percent of themaximum count. At low iron concentration thecontours should be little affected by counting statis-tics. The count error is a large percentage of the

Fig. 7. Contour map of titanium content of ilmenite inmagnetite as in Figure 5. High titanium content in elongateilmenite crystals.

i$,ffi

H/\v/, L

. H LL

H H

L L

HL H L

L L I

:"" N

n HQ " u

L

H o L H

:?"d " : "

H, , L , 9 Hd L \

L O

Fig. 10. Contour map of iron concentration of same area asFigure 9, corrected for defocusing. The concentration surface isnearly flat except at extreme left and at reentrant in center due tocorrosion by geothermal solutions.

beam scans over the sample surface, the beam-sample interaction point disappears behind the ironedge depending upon the relative position of thedetecting spectrometer. Figure 12 schematicallyillustrates the effect for the upper right boundary inFigure 11.

An analogous effect occurs and is displayed oncontour maps of topographically smooth samplesnear boundaries of two compositions where onecomposition differs from the adjoining composition

Fig. 11. Iron concentration in areas having two sharp ironinterfaces as measured by two opposing spectrometers(goniometers). Iron surface is topographically higher thanA(OH)3-SiO, gel between. (a) goniometer I measuring fromlower left; (b) goniometer 2 measuring from upper right.

INTEilSITY TEASURED

B Y G O M O S E T e R l - - - -

GOI{IOI{ETER 2 -

PERCEI{T OFMAXTUUX X-R Yrt{TEl{stYY

Fig. 12. Paths of electron beam and X-rays and resulting X-rayintensity for iron interface in upper right ofFigures lla and llb.(a) Paths of electron beam and emitted X-rays relative tomeasuring goniometers. (b) Relative X-ray intensity measuredby each goniometer.

greatly in absorption coemcients and fluorescentyields.

Mapping of a zoned feldspar

An example comparing an elemental contourdiagram with a dot-photograph of a zoned plagio-clase feldspar illustrates the advantages of the con-touring method. Figure 13 shows the calcium con-centration map produced using data from the samearea on the crystal shown in Figures I and 2. Thiscontour map is easily interpreted and shows therelationship between the calcium concentration andthe light and dark zones in the crystal on the

529

TO OON|OTaEIER 2

Fig. 13. Calcium concentration map of part of the zonedplagioclase crystal of Figures I and 2. Two high-calciumconcentrations near crystal edges are calcium silicate inclusionsin ground-mass crystals.

JANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

TO GONIOTETER I

L /

A/ H /

)("' n

JANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

Fig. 14. Compositional families in the ternary system Ti_Co_Cu, allowing 0-100% of each component. The family isdesignated by a three digit number indicating the compositionalrange for Co, Ti and Cu respectively. The lowest compositionrange value is zero, the highest is three. Open circles representcompositions lying outside their families.

photograph in Figure 2. Two peaks, showing veryhigh X-ray intensities to the right and left of thecrystal on the contour map represent two smallinclusions of calcium silicate. These inclusionswere too small to generate enough adjacent dots onthe photo in Figure I to allow them to be identified.The extreme proximity of the contours identifyingeach inclusion indicates that the source of the X-rays lies within the boundaries of only one or twosampling squares. The inclusions are really verymuch smaller than indicated in Figure l3 illustratingone weakness of the method.

ZAF corrections on compositional familiesBefore illustrating the application of ZAF correc-

tion to produce a quantitative map, we present theresults of grouping X-ray data matrix correctionsinto compositional families.

Figure 14 shows the families occurring in a nor-malized three element system which exhibits ab-sorption and fluorescence. Each element occurs inconcentrations ranging up to l00Vo and is split at the20, 50 and,80Vo concentration levels. The numbersidentify 19 families and the range of the elementconcentrations for each family.'The family 210contains 50-80% Co,20-50Vo Ti and 0-20% Cu. Adot identifies the compositional point at which theZAF correction factors are generated for the familv.

The coordinates of the points are determined bynormalizing the average concentration value ofeach element range for the family. Sometimes thismethod generates a point (open circle) outside theactual range of the family, i.e., family 112, Figure14, but usually it is close enough to give reasonablyaccurate elemental correction factors.

Figure 15 shows how the reduction of the maxi-mum concentration affects the number, locationand size of the families. The maximum concentra-tion values for Co, Ti and Cu are 85, 70 and, B}Vorespectively. The number of families in this ternarysystem has increased to 31 and each has a smallercompositional range.

We examined the maximum errors introduced bymatrix correction by family for a Co-Ti-Cu alloy,and they appear to be smaller than systematic andrandom data collection errors. Cobalt absorbsCuKa radiation resulting in enhancement of CoKaradiation intensity. Titanium absorbs both CoKaand CuKa radiation but in differing fractions. Giventhe first approximations of the elemental concentra-tions the ZAF program calculates the compositecorrection factor for each element. When the maxi-mum of each element in the test sample varies, theZAF program generates the composite correctionfactor at avanety of points on the triangular coordi-nate system. Figure 16 shows the values and distri-bution of the composite correction factors for theelement Co over the0-100% compositional range ofthe elements Co, Ti and Cu.

Fig. 15. Compositional families in the temary system Ti-Co-Cu, allowing compositional ranges of 0-85, 0-70 and VB\% forCo, Ti and Cu respectively.

"IANSEN AND SLATJGHTER: ELEMENTAL MAPPING BY MICROPROBE

Fig. 16. ZAF correction factors for cobalt in the ternary system Ti-Co-Cu.

531

o6ao. 0560

For an alloy containing concentrations ranging upto l00Vo for each element, the family ranges andfactor calculation points are distributed as shown inFigure 14. Superimposing Figure 14 on each of theelemental correction factor diagrams, the range offactors within each family, and the factor applied tothat element in that family, can be determined. Thedeviation of the factor applied at a point from the"correct" factor at that point determines the errorin the resulting concentration value. Table 1 liststhe maximum error in the correction factor withineach family represented in Figure 14.

The errors in Table I show that the factor errorsfor Ti and Cu are within acceptable limits for EManalysis. Several ofthe errors for the cobalt correc-tion factor appear unacceptable. However, the co-balt concentration at the points producing the great-est errors is near zero so that the error in the overallsample analysis is not significant. The error in the

cobalt correction factor decreases rapidly for pointsthat contain more significant quantities of cobalt.Although the correction factors for the familiesidentified as l2l,2ll and ll2 are calculated at apoint outside the area covered by the family, themaximum factor errors are not only within but atthe low end of the range of errors for the otherfamilies.

In most samples, 100%o concentrations of each ofthe analyzed elements are unlikely within a smallsample area. Depending upon the sample investigat-ed. the maximum distributions as indicated forFigure 15, 85Vo Co, TOVo Ti and 80% Cu may bemore realistic. When Figure 15 is superimposed onFigures 16 and 17, the maximum effors obtainedfor the families are significantly smaller than theresults from Table 2. In most families the averageerror in the factor applied to the elemental concen-tration is less than half the listed maximum error.

s32 .IANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE

Table 1. Maximum errors in correction factors for compositionalfamilies in Ti-Co-Cu system. Each element occurs in maximum

concentrations of 100 percent.

Table 2. Maximum errors in correction factors for compositionalfamilies in Ti-Co-Cu system. The maximum concentration of

each element is TiJ$%. Co-85%. Cu-8IVo.

FAMI LY FAMILY MAXIMUMT i co

ERRORS, tMAXIMUM ERROR, TCo CuT i c

o020 0 30 1 1o 1 2020o 2 r0 3 0t 0 1r02l r 01 I 1IT2r2012I2 0 020r2I02II3 0 0

Mean Er ror r ? r 2 1 02TI

Quantitative analysis

To illustrate quantitative analysis we synthesizeda control specimen of known composition whichwoulA give appreciableZAF corrections. The speci-men was Stainless Steel 308 welded by Inconel g2.We then analyzed the weld boundary area wherethe steel had dissolved into the inconel and theinconel had diffused a short distance into the steel.Significant compositional values are as follows:

2 1 22 2 02212303 0 03 0 r3 1 03 1 1

Mean Error

o . 71 . 0U . J

0 . 30 . 00 . 80 . 40 . 4

0 . 81 . 3o . '7

u . d0 . 40 . 8u . 51 . 4l ?

0 . 8t ?

u . )0 . 80 . 40 . rr . 2t . 1r . 10 . 8

u . 6 l

1 1

t r . q

7 . O3 , 46 . 82 . 91 0

4 . 4t ?

4 . 92 . 96 . 05 . 6

4 . 32 . 42 . 9

3 . 04 . 02 . 24 . 0t ?

3 . 41 . 62 . 2r . 92 . 32 . 30 . 9

3 . 7 5

1 . 9l q

I 1 81 )

2 . 01 . 1I . 0) i

1 1

I . 9t . 42 . rr . t1 . 3z . u

1 . 5r . 02 i

1 . 61 a

2 . 2u . 51 . 80 . 90 . 8' l a

1 . 91 . 8r . 4

1 . 5 5

inconel-72 .DVo Ni, 3.IVo Fe, 20.0Vo Cr.; stainlesssteel-l0.0Vo Ni, 67.0% Fe,20.7Vo Cr. Figure 17shows the map of nickel concentration at theboundary ofthe weld. Correct percentages ofnickelat the extreme top and extreme bottom of the mapare 37. and 10. respectively. The equivalent per-centages ignoring the ZAF correction are 34. and8.5 respectively.

Discussion

Compositional mapping works well and workswith minimum modification to an EM. All but thedata collection programs can be written in pon-TRAN. The method is easily applicable to old EM'sbut is most suited to the newer EM's. Our labora-tory now uses compositional mapping for about50Vo of our EM work.

For new EM's with integral computers, no hard-ware modifications are necessary to do composi-tional mapping. At least one of the new EM's hasanalyzing crystals that have a rocking motion coor-

2 . r2 . O0 . 50 . 90 . 8r . t2 . 3

l a

0 . 81 . 40 . 9

0 . 31 )

2 . 5' t ?

o . 72 , L

r . 3 5

8 . 8I 7 . O

4 . 21 2 . 0

6 . 65 . 45 . 3? o

3 . r5 . 84 . 66 . 0

4 . 74 . 0 .1 . 62 . 3

5 . 8 s

3 6(3,1.9) L H

. 6 . dL O n t 1

t "

o68)

H ^!H

L - n

* n o * H

Fig. 17. Quantitative analysis of Ni at weld boundary betweenInconel 82 (top) and Steel 308 (botrom). Steel dissolved ininconel. Contour numbers represent weight percent. Numbers inparentheses are weight percent without ZAF correction. Circlednumbers are "true" weight percent.

"' id

. , D

H

L L

LH

H L

H 1

LL 6

L Ht

I H ,

- L

L HL

L

L

- L

\ L \

L H

L

. , L Hn H

LH L

LH H

"a

H

L

H

L^

(9

JANSEN AND SLAUGHTER: ELEMENTAL MAPPING BY MICROPROBE 533

dinated with beam sweep, helping to eliminatedefocusing over the image area, simplifying pro-gramming and allowing mapping at lower magnifica-tions.

Although compositional mapping provides a newway for the study of minerals, it has some disadvan-tages. We have compared mapping with pointcounting along lines across zones of artificial plagio-clase crystals. The point counts along the lineshowed very well the stepwise decrease in calciumoutward from the grain center. However, composi-tional mapping showed zones badly obscured bycalcium highs caused by tiny inclusions of calciumsilicate. The coarseness ofthe 50 x 40 grids accen-tuated the effect of the inclusions. If, as on thenewer EM's, X-ray intensities could have beencollected from only the center of each grid squarethrough digital control of the beam, then only anoccasional inclusion would be in the beam.

Very sharp compositional boundaries of mineralgrains where an element concentration changesfrom a very high value to or near zero "smears" togive a width to the region where none exists. Thesmearing results from several factors: (1) finitebeam diameter;(2) contouring method; (3) samplingof all of each sampling grid square, instead of onepoint of the grid square; (4) smoothing; (5) topogra-phy at boundaries; (6) real smearing of the bound-aries during sample polishing and (7) random statis-tical errors in the X-ray intensities. Sampling onlyone point per grid square coupled with smoothing

could improve the boundary definition significantly.Currently, when looking critically at a boundaryarea, we simply increase the magnification from500x to 1000x or 2000x which almost doubles orquadruples boundary resolution.

Finally, compositional mapping can work onEM's or scanning electron microscopes equippedwith energy dispersive systems. Using energy dis-persive detectors eliminates the spectrometer defo-cusing corrections, but complicates and increasesdata collection timing.

ReferencesBirks, L. S. (1971) Electron Probe Microanalysis, ed. 2, Wiley-

Interscience, New York.Cullity, B. D. (1956) Elements of X-Ray Ditrraction, Addison-

Wesley, Reading, Massachusetts.Hadidiacos, G. G., Finger, L. W., and Boyd, F. R., (1971)

Computer reduction of electron probe data. Carnegie Institu-tion Year Book, 69, (1969-1970), 294.

Hall, C. E. (1966) Introduction to Electron Microscopy, ed' 2,McGraw-Hill, New York.

Heinrich, K. F. J. (1964) Instrumental developments for electronmicroprobe readout. Advances in X-Ray Analysis, 7, 382.

Hitchings, J. R. (1976) Color aids data interpretation. Research./Development, 27, 26.

Ingersoll, R. M., and Derouin, D. H. (1969) Application of colorphotography to electron microbeam probe samples. Review ofScientific Instruments, 40, 637.

Tomura, T., Okano, H., Hara, K. and Watanabe, T. (1968)

Multistep intensity indication in scanning microanalysis. Ad-vances in X-Ray Analysis, ll, 316.

Manuscript received, April 2, 1980;accepted for publication, January 19, 1982.