Improved Spatial Resolution Microanalysis in a Scanning Transmission Electron Microscope

R.G. Faulkner and T.C. Hopkins Department of Materials Technology, University of Technology, Loughborough, England

K. Norrgird A B Atomenergi, Studsvik, Sweden

The attachment of energy-dispersive analysers to scanning transmission electron microscopes makes possible accurate high spatial resolution microanalysis. This paper quantifies the X-ray spatial resolution obtainable for good sensitivity microanalysis as a function of microscope lens settings and primary electron beam accelerating voltage in a 200 kV scanning transmission electron microscope. It is shown that at 200 kV a resolution of approximately 500 A is possible with a 1500 A thick nickel-iron-chromium alloy specimen. At 100 kV the resolution drops to nearer 1000 A These figures are supported by Monte Carlo calculations of electron trajectories in thin films. Comparisons of experimentally measured and theoretically predicted X-ray intensities suggest a severe loss of signal intensity within the microscope; this loss becomes greater at higher accelerating voltages. The influence on microanalysis of angle of specimen inclination to beam and to the detector is considered and precautions necessary to limit beam drift during 1000 s analyses are discussed. The application of high sensitivity, high resolution microanalysis methods to a grain boundary segregation effect in an austenitic creep resistant steel is described. It is shown that titanium segregates in a zone 1000-1 500 di thick on either side of the grain boundary to a level of approximately three times the matrix concentration.

INTRODUCTION

The first attempt at combining a transmission electron microscope with an electron microprobe analyser was made by Duncumb.' Subsequently a commercial instrument, EMMA-4 was produced *, which consisted of a conventional transmission electron microscope fitted with a minilens to condense the beam to a fine spot on the specimen and also with wavelength-dispersive spect ro- meters. The limitations of early EMMA-4 instruments can be listed as follows.

( 1 ) The minimum attainable spot size was only -0.13vm. ( 2 ) Crystal spectrometers are not the most efficient devices

for detecting small quantities of X-rays produced in such an instrument.

(3) There were no Fdcilities for scanning the electron beam across the specimen surface.

Recently machines have been introduced which overcome to some extent the above limitations. They are based on the scanning transmission electron microscope principle (STEM). The minimum beam size is about 40 A in such an instrument and an energy-dispersive X-ray analyser is used to detect the X-rays. Also advances in methods of assessing the data produced from such machines to give accurate chemical analyses have recently been made.4

This paper will discuss the calibration, operation and theoretical capabilities of such a system, JEOL 200C, from the viewpoint of obtaining maximum analysis sensitivity with a high spatial X-ray resolution. It will be shown that factors affecting the performance include the elcctron

0 Heyden & Son Ltd, 1977

accelerating voltage, specimen dimensions and inclination to the beam, beam positional stability and microscope lens settings. A practical application of the technique to yield a quantitative picture of grain boundary segregation in an austenitic steel on a finer scale than has hitherto been possible will be discussed.

THEORETICAL PREDICTION OF MAXIMUM X-RAY RESOLUTION

To achieve maximum X-ray spatial resolution the following factors need to be optimized.

(1) Beam size at the specimen must be minimized. (2) Specimen thickness must be minimized. ( 3 ) Electron accelerating voltage must be maximized. (4) Beam positional stability must be maximized.

The effect of altering electron accelerating potential on the X-ray source size can be theoretically predicted by plotting electron trajectories within thin films (Fig. 1). A Monte Carlo technique is employed to produce this figure. This method predicts the electron trajectories resulting from the interaction of an infinitely narrow and stable beam with a thin film specimen whose atomic number and thickness can be varied. Details of the technique are given in Appendix 1.

and 200 kV) and thin film targets characteristic X-rays from the target matter can be formed along the whole length of the electron trajectory. This is because little of the electron energy is lost in the actual specimen and the

When considering high energy electron beams (i.e. 100

X-RAY SPECTROMETRY, VOL. 6 , NO. 2,1977 73

R.G. FAULKNER, T.C. HOPKINS AND K. NORRGARD

Effect of lens settings

Figure 1. Monte Carlo plot showing 100 electron trajectories in a 1500 A thick iron specimen at an accelerating potential of 100 kV (top) and 200 kV (bottom).

electron energy is nearly always greater than the critical excitation potential, Ec, of the characteristic radiation (E, for Fe = 7.1 11 kev). Hence for thin films and high energy electron beams electron spread size is approxi- mately equal to the X-ray source size.

Figure 1 shows that the spread of the electron trajectories and hence the X-ray source size in an iron specimen of 1500 A thickness is several hundred A. It is reasonable to assume that this picture is representative of the situation for any element with atomic number between 20 and 30. Figure 1 shows that it is clearly unnecessary to condense the beam to sizes of much less than 100 A diameter unless foils with thicknesses of less than 500 A are being examined. Since this thickness represents a minimal figure for most electron microscopy work the minimum spot size of 40 A claimed by the manufacturers for the instrument concerned in this study is adequate. Figure 1 also shows that high electron accelerating voltages reduce the X-ray source size by a factor of about 50% for 200 kV compared to 100 kV. The lateral spread of the electrons at 100 kV is considerable: of the 100 incident electron trajectories shown 75% of the electrons are within a diameter of 1000 A. Several of the laterally spread electrons travelled many thousand A before leaving the target. In the case of the 200 kV electron trajectories few scattering acts take place and the number of back- scattered and laterally spread electrons is reduced. In this case 75% of the electrons are within a diameter of 500 A.

PRACTICAL ESTIMATES OF MAXIMUM X-RAY RESOLUTION

Having established a working accelerating voltage in a preselected area of foil of known thickness, the practical variables controlling resolution are lens setting and beam positional stability.

The spot size at the specimen in the instrument used in this work is controlled by a combination of the second condenser lens and objective lens settings. The spatial X-ray resolution as a function of lens setting can be determined. This is done by measuring the X-ray output from a foil of known thickness containing particles of known diameter as shown in Fig. 2. If the composition of the particles and the

e l e c t r o n I beam .L

A

part ic le radius r, (element A >

1 A \\&, I

+ 2 r2 --+ ' element B

Figure 2. Method for determining X-ray spatial resolution.

matrix are known, then the beam radius, r2, can be calcu- lated from the following formula

4r: 3112

r:=-(l+x)

where rl is the radius of the particle, Az is the foil thickness and x can be measured from X-ray intensity ratios using the relation

V,

where V1 and V, are the shaded volumes marked in Fig. 2. An example of a particle from which X-ray source size measurements were made is marked at A in Fig. 3. Details of the derivation of the above equations are given in Avvendix 2.

Figure 3. Scanning transmission electron micrograph of spherical Tic precipitates in 12R72 steel. X-ray source size determinations were made on these particles.

74 X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977

IMPROVED SPATIAL RESOLUTION MICROANALYSIS IN A SCANNING TRANSMISSION ELECTRON MICROSCOPE

A list of values of x, rl, and the resulting calculated values of r2 are given as a function of different lens settings in Table 1 for Tic particles in an austenitic alloy (e.g. A in Fig. 3). The foil thickness in the region from which the

~~ ~~ ~~ ~

Table 1. Beam size determinations at 200 kV

14.5 65 6.7 65 2.8 65 1.3 65 4.3 65 2.3 65 1.0 65 2.9 65 1.8 65 2.8 65 3.5 65 4.3 65 8.8a 45

a 100kV.

40 50 50 55 60 60 60 65 65 70 81 89 40

450 450 700 700 450 600 700 700 700 600 600 600 600

792

558 ) Av660 760 592 463 562 1 526 554

77' ) Av713 653 604 657 713 970

measurements were made was 1500 f 200 A. This determination was made using stereo techniques. The electron beam accelerating voltage was 200 kV. X-ray spatial resolution as a function of lens setting is plotted graphically in Fig. 4. Errors in the estimates of source size are assumed to be ? 50 A. The lens settings necessary to achieve maximum resolution at 100 kV, together with the actual resolution obtained, are also given in Table 1.

X-roy source

diameter, 2 r 1 ( X )

I 1 I I d

500 -

45040 50 60 ro 80 90 C L ~ setting ( m b )

Figure 4. Effect of CL2 lens settings on X-ray source size as deter- mined by sma!l particle analysis in a 200 kV STEM. Foil thickness is 1500+200A.

Effect of beam positional stability

The beam positional stability depends on several features; some of which are listed below. (1) Position of the beam in relation to the hole in the foil. (2) Contamination of the specimen. (3) Stabilization of operating conditions. (4) Heating of the specimen.

Items (l), (3) and (4), are interrelated because contamination appears to worsen as the hole nears the graphite specimen support block. This contamination causes heating and charging up under the beam with the result that the beam becomes unstable. These effects were minimized to a very low value in our work by use of a coldfinger and ultimately the largest factor became item (3). After running the filament for at least two hours the effect was eliminated to the extent that beam wander over 1000 s was limited to no more than f 50 A. This is an additional error which is considered in the X-ray source size determinations.

Thus, with appropriate lens settings and with beam positional stability maximized, it is possible to achieve a 525 * 100 i% X-ray resolution at 200 kV and a 970 f 100 A X-ray resolution at 100 kV in a foil of 1500 f 200 A thickness. It is significant that the Monte Carlo plots shown in Fig. 1 also indicate similar average source diameters for the same conditions.

THEORETICAL FACTORS AFFECTING X-RAY DETECTION SENSITIVITY

Clearly, there comes a time when the X-ray source diameter and the foil thickness are minimized to such an extent that insufficient X-rays are produced to give high sensitivity microanalysis. The point at which this occurs can be estimated theoretically for the STEM thin foil situation. High sensitivity X-ray analysis depends on a high peak intensity and a high peak-to-background ratio. A guide to sensitivity is given by the ratio of peak intensity to the square root of background intensity.

The arrangement of the specimen with respect to the detector is shown in Fig. 5. Under these circumstances the Iron Ka X-ray peak intensity, R,, in a 1500 A thick foil is given by:

In (Eo/E,) 1, x 10'' WNp Eo/E, 1.602 AE:

R, =7.92 x 10-l4 - AZY

photons s-'

Where W = Fluorescent yield for the element concerned (0.323); N = Avogadro's number (6 x loz3); A = Atomic weight (56); p = Density in g cm-3 (7.9); A z = Foil thickness in cm (1500 x 1O-');E0= Accelerating voltage in eV (1 00 000 or 200 000); E, = Critical excitation voltage in eV (71 11); y = Detector collection efficiency (1.148 x

density in the electron source, electron accelerating voltage, electron beam diameter and lens spherical aberration coeff- cients. 1, values as a function of accelerating voltage for a minimum beam size (40-50 A specified) are available from

1, is the beam current in amps. This is affected by current

Electron beam

3 m m d i a m e t e r

D e t e c t o r ,Eff iciency 6. lid 4 . (701'

= 1 . 1 4 e x l b '

Specimen

Figure 5. Specimen detector geometry.

X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977 75

RG. FAULKNER, T.C. HOPKINS AND K. NORRGARD

the microscope manufacturers and are -1 x 10-"A at 100 kV and 2 x 10-IoA at 200 kV. There is no facility for measuring beam current on the design of microscope used here. The background intensity is composed of noise from the analyser amplifier electronics and from the continuum. The former can be neglected and the latter can be quantified in the following way to give Rb .'

1~x1019 z p 7 a Rb =4.2 X lo2 . - . -* Az photons s-'

1.602 EoE

where E = Emission energy' of the Ka line for the element concerned in eV;Z=Atomic Number; dE=Detector resolution in eV. In this case E=6398.

Calculated values of R,, Rb, R,/& and R p & , at 100 and 200 kV are given in Table 2. The detector resolution is assumed to be 160 eV and its efficiency at converting photons into electronic pulses is assumed to be 100%. The table shows that higher accelerating voltages theoretically give higher values of R,IdRb and hence better X-ray sensitivity.

Table 2. Effect of kV on measured and calculated X-ray sensitivity for iron Ka

k V IA(A) R p R b RpIRb RpIdRb (M=measured) (counts s-' (countss-' 1 (C=calculated)

100 (M) l X I O - ' o 10.4 0.35 29.7 17.6 100 (C) 1 X lo-'' 8.7 0.023 375.7 57.4 200 (M) 2x10-'0 0.99 0.28 3.54 1.87 200 (C) 2x10-1° 11.0 0.023 474.2 72.6

PRACTICAL FACTORS DETERMINING X-RAY SENSITIVITY

Accelerating voltage

In Table 2 measured values of R,, Rb, R,/& and R , & , are also given for accelerating voltages of 100 and 200 kV under the same conditions as those listed in the previous section. There is likely to be a considerable background component arising from primary back-scattered electrons interacting with specimen chamber components. This explains the high measured background values. The fit between experiment and theory for peak values at 100 kV is reasonable. However the experimental peak values at 200 kV are very low. The subsequent analysis work was aU completed at 100 kV on the basis of these results. Nevertheless it should be remembered that 200 kV may well be a better voltage to use.

Angle of specimen inclination to electron beam

The specimen arrangement is as shown in Fig. 6. The orientation adjustments in the series of measurements to be described next were made as shown on the side elevation through an angle of 45'. If the specimen is placed in a graphite block at an already inclined angle (see Fig. 7) the results may be further improved. A graph of angle of inclination to the detector versus recorded intensity under fixed conditions for iron Ka X-rays in an iron alloy at

Detector Foil normal

Graphite block

Foil FRONT ELEVATION

c> :::>-Y::-; 1

PLAN

-7

Ti l t axis

%< SIDE ELEVATION

Figure 6. Front, side and plan view of specimen detector arrange- ment.

\

Figure 7. Thin foil specimen placed in the graphite block at an inclined angle.

l7r T I T

/ 45 925 35 1 Angle of Specimen inclination to beam

Figure 8. Effect of specimen inclination on X-ray detection efficiency in JEOL 200 kV STEM.

200 kV is shown in Fig. 8. It can be seen that the angle of inclination must be greater than 35" for effective X-ray detection. This result fits well with values indicated by other workers.6

the minimum level of detectability achieved. Assuming 95% confidence limits this level is given by the standard deviation (s.d.) multiplied by 3.' The standard deviation can be equated to 4 N where N is the total number of counts detected at the energy level of interest. At 100 kV after 1000 s we obtained with our system, Rb equal to 350. Therefore the minimum number of counts above the background necessary to produce a meaningful peak on the X-ray spectrum was about 50. Under the conditions of our experiment 50 counts corresponded to 0.5% iron. Thus the count rates achieved are sufficient to detect 0.5% of any elements with atomic number between 20 and 40 in counting times of 1000 s at 100 kV. This was the minimum requirement of the application to be discussed in the next section.

The sensitivity of any andysis technique is indicated by

76 X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977

IMPROVED SPATIAL RESOLUTlON MICROANALYSIS IN A SCANNING TRANSMISSION ELECTRON MICROSCOPE

Figure 9. Grain boundary in 12R72 steel showing analysis line (CD) used to plot the segregation profiles.

PRACTICAL APPLICATION: GRAIN BOUNDARY SEGREGATION OT TITANIUM IN AUSTENITIC ALLOYS

Figure 9 shows a STEM micrograph of a grain boundary in 12R72 steel (see Table 3 for composition) which has been solution treated at 1100 "C for 15 min and quenched, followed by ageing at 850 O C for 10 h. In this condition the alloy contains grain boundary precipitates of titanium

Table 3. Composition of alloy (12R72) (Wt %)

C Cr Ni Mo Ti Mn Bi Fe

0.11 15.2 14.8 1.4 0.52 2.0 0.44 bal

carbide. An example of a large carbide is seen in the picture (marked B) but there are probably smaller particles distributed evenly along the grain boundaries.' A series of point analyses was made on the line marked CD across the interface away from the larger particles. The microscope settings were those mentioned in previous sections for

maximum X-ray resolution and sensitivity at 100 kV. The specimen inclination to the beam was 35'. The total intensity of X-ray emission from the region indicated in the figure was very similar to that obtained during the calibration experiments and it was therefore assumed that the foil thickness was 1500 2 200 A. Therefore the beam diameter was approximately 970 *lo0 A.

analysed allowing for effects due to escape peaks and background. The concentration of titanium, CTi, chromium, Cc,, iron, CF,, and nickel CN~, were determined in the following way from the integrated intensities of the Ti, Ni, Cr, and Fe peaks;RTi, R N ~ , Rc,, R F ~ respectively. These intensities were taken from areas under the peaks whose energy spreads were 180 eV. This is approximately equivalent t o the area under the peak at full width and half height.

The energy spectrum produced from the detector was

This is a reasonable assumption since, in a thin foil, fluorescence and absorption corrections are negligible4 and the elements quoted above, except for small quantities of molybdenum and manganese, are the only ones present (see Table 3). Background measurements were taken from a similar energy band width centred at 6.8 keV. The detailed values of R and C for the point analyses across the grain boundary are given in Table 4.

For a counting time of 800 s, a typical count of 70 was recorded above the background for titanium. The 95% confidence limits are given by 2&/ where N is the number of counts above background. Assuming equal detector collection efficiency for Fe K a and Ti Ka X-rays and that the background is isotropic in this region of the spectrum, 80 counts in 800 s is roughly equivalent to 1% titanium. Therefore the errors quoted in the titanium concentration determinations are 20.2%. The limit of detectability under these conditions has already been stated as 0.5%, which is the matrix level of titanium in the alloy (see Table 3 ) .

Figure 10 shows the concentration profdes for titanium, iron and nickel on either side of the grain boundary shown in Fig. 9. A similar curve from another grain boundary situated elsewhere in the specimen is shown in Fig. 1 1. In both these cases the concentration of chromium remains constant up to the boundary. The high values of titanium

Table 4. Data for concentration profiles

Distance from GB (A )

0 One side 1000

(,,00

1100 1500

3000

0

5000

Background N T ~ (counts) (counts)

253 238 267 93 277 63

296 105 304 89 285 66 288 44 282 33

235 362 216 92 254 45 22 1 76 28 1 72 27 1 84

CT i (wt %)

3.2 1.2 0.83

1.3 1 .l 0.82 0.55 0.41

5.35 1.50 0.65 1.27 0.98 1 .14

N F e (counts)

4949 51 58 5200

5462 5624 557 1 5516 5420

4363 41 54 4673 4015 4977 4967

CFe (wt %)

67.2 67.6 68.3

67.8 69.3 69 .O 68.5 68.1

64.4 67.8 67.3 67.1 1 67.8 67.3

N C r (counts)

1223 131 1 1289

1342 1376 1320 1323 1393

1156 1129 1239 1039 1272 1273

CCr (wt %)

16.6 17.2 16.9

16.7 17.0 16.4 16.4 17.5

17.1 18.4 17.9 17.4 17.4 17.2

N N i (counts)

956 1065 1064

1153 1026 1113 1169 1115

890 845 983 853 1017 1061

CN i ( W t %)

12.9 14.0 14.0

14.3 12.7 13.8 14.5 14.0

13.1 13.8 14.2 14.3 13.9 14.4

~~~~~~~ ~

X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977 77

R.G. FAULKNER, T.C. HOPKINS AND K. NORRCARD

.I, w t %

CFe c T ~ 70 0

69 0

68 0

67 0

3 0

2 0 I 10

0 3000 2000 1000 0 1000 2000 3000

Distance from grain baundary(8)

Figure 10. Concentration profiles for titanium, iron and nickel in 12R72 steel near to grain boundary.

Region occupied by grain boundary precipitates

0 1000 2000 3000 4000 5000 Distance from groin boundary ( 8 )

Figure 11. As Fig. 10. A set of similar curves from another grain boundary situated elsewhere in the specimen.

concentration actually in the boundary are caused by the presence of grain boundary precipitates of titanium carbide. From Figs 10 and 11 it is clear that there is titanium segregation on a very fine scale to the grain boundary in this alloy. The error limits determined by methods mentioned earlier in the paper are shown in the graphs. The regions likely to be occupied by grain boundary precipitates are also shown. It can be seen that the possibility of the enhanced titanium levels being produced by the carbide present in the boundary is unlikely.

DISCUSSION

Previous results' have indicated theoretically that, in austenitic alloys heat treated in a manner similar to that which the specimen investigated in this work has been heat treated, segregation of titanium on a fine scale was to be expected. Conventional electron microprobe analysis has limited resolution when such fine scale segregation as this is being studied. This is the first time that, to the authors' knowledge, such a high resolution analytical tool has been applied to the problem.

CONCLUSIONS

The operation efficiency of a 200 kV STEM as a high resolution analysis facility has been evaluated. The analytical performance has been assessed practicaiiy and, in some cases theoretically, as a function of the following variables. (1) Accelerating voltage. (2) Lens settings. (3) Foil thickness. (4) Angle of specimen inclination to the beam. (5) Beam positional stability. Resulting from this, determinations of grain boundary titanium, nickel and iron concentration profdes in a heat- treated, iron-based alloy have been measured with the microscope operating under well quantified conditions. Grain boundary segtegation to a level of three times that of the matrix is apparent in a region between 500 and 1500 A on either side of the boundary.

ACKNOWLEDGEMENTS ~~

The authors wish to thank Dr G. Ostberg for the provision of the STEM facilities at AB Atomenergi, Studsvik, Sweden. Also the use of computer and laboratory facilities provided by Professor I. A. Menzies of the Department of Materials Technology, University of Loughborough, is gratefully acknowledged.

REFERENCES

1.

2.

3.

4. 5.

6.

P. Duncumb, Proc. Symp. on X-ray Optics and X-ray Micro- analysis, Stanford, 1963, p. 431. C.J. Cooke and P. Duncumb, Proc. 5th Int. Conf. on X-ray Optics and Microanalysis, Tubingen, 1968, p. 246. C.J. Cooke and I.K. Openshaw, Proc. 4th lnt. Conf on Electron Probe Microanalysis, Pasadena. 1969, p. 64. G. Cliffe and G.W. Lorimer,J. Microsc. 103,203 (1975). S.J.B. Reed, Electron Probe Microanalysis, Cambridge University Press, 1974, p. 327. R.H. Geiss and T.C. Huang, %-Ray Spectrom. 4,196 (1975).

7. S.J.B. Reed, Electron Probe Microanalysis, Cambridge University Press, 1974, p. 197.

8. J. Caisley and R . G . F a k n e r . To be published in the Proc. of Institution of Metallurgists Spring Course on 'Grain Boundaries' April 1976.

9. P. Duncumb and L. Curgenven, T I Research Report No. 303, (1971).

10. M. Green. Proc. Phvs. SOC. 83.435 (1964). Received 26 May 1976; accepted (revised) 1 0 November 1976 0 Heyden & Son Ltd, 1977

78 X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977

IMPROVED SPATIAL RESOLUTION MICROANALYSIS IN A SCANNING TRANSMISSION ELECTRON MICROSCOPE

APPENDIX 1

MONTE CARL0 SIMULATIONS OF ELECTRON TRAJECTORIES IN THIN FILM SPECIMENS

A computer program based on the technique of Curgenven and Duncumb’ was modified and used to simulate electron trajectories in thin film specimens (e.g. Fig. 1). As each electron enters the specimen both elastic and inelastic scattering acts take place. Inelastic collisions take place in large numbers and cause the electrons to lose energy with very little angular deflection. This energy loss can be quantified as a function of distance by the Bethe Law. Elastically scattered electrons are scattered by similarly large numbers of Rutherford interactions.

The program employs the Bethe electron energy loss law to calculate the electron energy as a function of distance travelled in the specimen and the electron range. The range is divided into a number of steps; at each step a random number is generated and, using Rutherford scattering theory, the scattering angle computed. Rutherford scattering theory in its simplest form is described by:

P 2P cot - =

2 1.44 x lo-’ (Z/E) where is the scattering angle; p is the impact parameter

in A. This depends upon the closeness with which the electron approaches the specimen atom during each scatter- ing event; 2 is the atomic number of the target; E is the energy of the electron in keV.

between 0 and 1, generated at each step is used to give a value of p where p = 6 p o . The value of p o used in the above expression is optimized by comparing the number of back- scattered electrons predicted by the Monte Carlo simulation with experimental values of back-scatter coefficients. During scattering the situation is simplified in as much as screening effects and multiple scattering are neglected.

Green” has suggested that in a solid target an electron with an incident energy of 10-100 keV may be scattered 100-1000 times before coming to rest. This implies that in a thin film very few scattering acts take place. In the present work the electron range in the solid specimen was divided in 1000 steps. Because of the high computational times involved with Monte Carlo Type models only 100 electron trajectories are shown plotted. The accuracy of this Monte Carlo model is estimated to be about 20%.

In the computer program the random number, 6 , varying

APPENDIX 2

METHOD OF DETERMINING X-RAY RESOLUTION IN A THIN FOIL

The schematic arrangement of a spherical particle in a thin foil used to make the X-ray spatial resolution determination is shown in Fig. 2 . In the real situation the particle is comprised of 80 wt % titanium and the matrix consists of 65 wt % iron. The method depends on measuring the intensities of emitted iron and titanium X-rays from the specimen, RFe and RTi respectively. These intensities are proportional to the weight fractions of the elements present. If V, is assumed to be the volume of the titanium rich particle and Vz is the volume of the iron rich matrix, then

R Ti

0.8 PTi v, = -

and

RFe

0.65 PFe v, = -

where pTi and p~~ are the densities of titanium and iron respectively. Now if the foil thickness is assumed to be Az, the X-ray emission volume is assumed to be cylindrical with radius r, and the particle is assumed to have a radius r l , then

4r : :. r ; = -(l +x)

3Az where

VZ V1

x = -

This treatment further assumes that there are no fluorescence or absorption interactions with the iron and titanium X-rays, and that X-ray generation efficiencies for the two elements are similar.

X-RAY SPECTROMETRY, VOL. 6, NO. 2,1977 79