Computerized image processing for evaluation of sampling error in ion microprobe analysis

Arzalytica Chimica Acta, (1978) 15-22 0 Elsevier Scientific Publishing Company,Amsterdam- Printedin The Netherlands

COMPUTERIZED RUAGE PROCESSIXG FOR EVXLUATIQN SAMPLING ERROR IN ION MICROPROBE ANALYSIS

OF

D. M. DRUMiUER, J. D. FASSETCT, and G. H. MORRISON* Department

of Chemistry,

Cornell University, Ithaca, N. Y. 14853

(LT.S.A.)

(Received 3rd March 1978)

SUXMARY

A method is described for the microscale evaluation of samp!e heterogeneity as applied to in-situ ion microprobe analysis. Computer feature analysis of digitized ion images. is utilized to generate sampling constants, which can be related to the degree of heterogeneity present for a particular constituent in the sample. The expected precision for a series of analyses, or the number of analyses required for a desired precision can also be determined. ‘Ibis approach, which is experimentally verified for NRS SRM-664 low-alloy steel, can be used both to minimize sampling error and to assess the applicability of specific reference materials to microprobe analysis. A major difficulty in quantitative microprobe chemical analysis is the availability of suitable standard reference materials. Most available standards have been certified for bulk concentrations by methods that are insensitive to concentration gradients on a microscale. Since microprobe analysis does not allow homogenization of large amounts of material to eliminate sampling problems, as is common practice in bulk techniques, sampling error may constitute a large fraction of the to”d measurement error if these standards are indiscriminately applied to microprobe measurements. Previously, the evaluation of homogeneity of standards has been accomplished by the application of statistical methods to a series of random point analyses. This evaluation results in an estimate of sample heterogeneity on

a microscale. In this approach, the signal variance can be related to a confidence level for analysis with a given probe size. This type of method has been applied to electron probe data [l, 21 and ion microprobe data [ 33 . While the previous method yields all the information necessary to give an indication of sample heterogeneity, an ion micrograph, which contains information equal to that of many separate point analyses, can provide a more direct estimation of the sampling situation. Images can be utilized to show the effect of inclusions or secondary phases on sample heterogeneity. Furthermore, the relationship between probe size and expected sampling error can be directly determined down to the size of a resolution element in the image. This type of approach has been demonstrated by Scilla and Morrison [ 31.

16

it is our purpose to show how the heterogeneity of a material may be estimated by the application of computer image analysis methods to ion microscope images. The method of Scilla and Morrison is modified to exploit the power of the computer to handle quantitatively the large amount of information present in an ion image. In contrast to the method of Scilla and Morrison, in which the evaluation of the image consisted of visual counting of inclusions assuming equal sizes and intensities, computer image processing facilitates measurement of inclusion intensity and area. This information allows a more precise evaluation of heterogeneity. The irrformation generated enables the analyst to appraise the reliability of an analysis of a given size area on the sample, or conversely, the analysis area necessary to achieve a desired precision. The present study applies this approach to the evaluation of the microsampling situation for the ion microprobe using NBS SRM-664 low-alloy steel, but the same concepts should be easily applied to other sample materials and other microprobe techniques with a minimum of modification. EXPERIMENTAL

The CAMECA IMS-300 Ion Microscope used in this study has been previously described in detail [d] . For all samples, the primary ion beam was 02’ at an energy of 5.5 keV. The ion current was 1.0 PA rastered over a sample area 300 pm X 300 pm. The samples were polished by a series of silicon carbide abrasive papers to BOOgrit, followed by wet polishing by alumina (1 pm and 0.3 pm). All samples were presputtered for at least 5 min prior to analysis to remove possible contamination from polishing and handling. Images were recorded on electron-sensitive film and digitized with a microphotodensitometer interfaced to a PDP 11/20 computer_ A PDP 11/20 ccmputer system was also used to process the digitized ion images for generation of sampling information. A description of these computer facilities, as well as a general outline of the software involved, has been previously published [5]. Further details concerning the operating system and the structure of the software are available from the authors. RESULTS

AND

DISCUSSION

The concept of a sampling constant to represent the level of heterogeneity in microanalysis has been developed by Scilla and Morrison [3], and extended for use with digital image analysis by Fassett et al. [5] . The basic assumption is that the element of interest is located in the sample as randomly dispersed inclusions. A determination of the sampling constant for a given element utilizes size, distribution, and intensity information from the ion image to calculate the sampling constant: KS =(1/I,)

(AT

E i=l

ii')' (I--AI/A,)', (1)

17

where K, is the sampling con&n> (in pm); ii is the intensity of inclusion i; N is the total number of inclusions; 1, is the total intensity of the ion image; -4, is the total area of the image (in pm*); and A, is the total area of the inclusions. To a first approximation, a greater number of inclusions results in a smaller sampling constant, which.indicates a more homogeneous material. Of somewhat less importance are size and intensity of the inclusions, and the randomness of their dispersion throughout the sample. It should be noted that, although phase distributions in materials are three-dimensional in nature, the ion microscope is essentially a two-dimensional analytical technique, since the depth of analysis is negligible in comparison to the lateral dimensions of the analysis area in the short exposure times used to obtain an image. Thus, a measurement of inclusion density in inclusions per unit area, rather than per unit volume, is more applicable to the ion microscope. The resulting sampling constant of eqn. (1) therefore has units of pm rather than of pm*. The resultant sampling constant can be used to estimate the.precision of a measurement obtained from a particular sampling area, or it can be used to determine the required sampled area to achieve a desired precision. It can also serve as a basis for comparison of the sampling situation of one element to another in a particular sample, or to compare the same element in different sample materials. In addition to the effect of elemental inclusions in the determination of the sampling constant, the presence of a background signal affects the result, reducing the constant by the factor Ii/r,, the fraction of the total signal which is due to the inclusions. The term (1 -AI/AT)+ is a correction for the fraction of the total surface area covered by inclusions, and is effectively eliminated if the area occupied by inclusions is small. As was previously mentioned, an assumption is made that the species of ‘interest is present in the sample predominantly as inclusions, as are the major alloying elements in the NBS Standard Reference Material studied. The ion images in Fig. 1 show spatial distributions for four representative elements in NBS SRM-664 low-alloy steel. These show. the four general types of elemental distributions encountered in the 660 reference series. Figure l(a) is the ion image of s6Fe+. Iron comprises 96.7% of NBS 664, and although the image is not totally uniform from point to point because of slight changes in the sputtering environment, iron does not qualify for this method, since it is essentially homogeneous_ Figure l(b-d) shows the ion images of “Al’, ‘*Ti+, and 51V+. _Aluminum is perhaps the most heterogeneous element in the sample, located primarily in small, widely spaced inclusions. Because of the small density of inclusions, a larger sample area was chosen for analysis in order to ob”tain a more precise value for the sampling constant. The distribution of inclusions shown for titanium is also characteristic of niobium and zirconium. Note that the lnelusion density is much greater than for the previous case, although on a microscale the elements are still quite inhomogeneously dispersed. The ion

18

a

b-

C

d

Fig. 1. Ion images from NBS SFLM-664 steel: (a) “Fe+; (b) “Al+; of view: 115 Km_

(c) 48Ti+; (d) ” ‘J+. Fields

image of vanadium is considerab!y more homogeneous in appearance than those previously described. However, the inclusions are still easily visible above the image background. Other elements with distributions of this type are chromium and manganese_ Although a quick visual inspection of ion images can yield a rough estimate of heterogeneity, the calculated results may vary appreciably, since inclusions are weighted for area and intensity. In addition, the densities recorded on the film must first be converted to ion intensities, and the non-linear nature of this relationship may also alter the result. In the actual calculation of sampling constants, the inclusions must first be separated from the image background. The way in which the eye does this involves many complex decision-making processes not feasibly adapted to computer methods. In most cases, however, choosing a fixed threshold for the image serves adequately to define the inclusions, and the degree of reproducibility afforded by the computer far outstrips any subtleties that may be lost. In this study the average intensity for the image is arbitrarily

19

Fig. 2. Contour plot for titanium in NBS SRM-664 image file 128 X 128.

steel. Field of view: 115 pm. Size of

chosen as the threshold. At this intensity, the partial derivative of integrated intensity is equal to the partial derivative of integrated area. The image is then separated into contiguous areas lying above threshold, and a feature map is produced. A contour map for the titanium image in Fig. l(c) is shown in Fig. 2. The contour lines enclose areas of the image which lie above the threshold chosen. Once the inclusions have been isolated in this manner, it is a simple matter to determine R, as defined in eqn. (l), as all variables are calculable. The results of these calculations for alloying elements in NBS-664 are shown in Table 1. In a straightforward inclusion counting method, considering the Poisson statistics involved [3], the pre,cision of the calculated sampling constant would be proportional to (n)-y, where n is the number of inclusions counted. Since inclusions are size- and Men&$-weighted, however, the precision can be shown to be proportional to (l,‘/iC I ii’)-+, terms defined as in eqn. (1). Even in this more general case, the precision of the determination is still TABLE

1

Calculated sampling constants for alloying elements in NBS SRM-664

low alloy steel

Element

Al

Ti

V

Cr

Mn

Zr

Nb

KS

77.5

25.5

19.4

14.0

7.2

35.1

34.9

20

closely related to the number of inclusions counted. To determine a-precise sampling constant, a precise inclusion density must be determined. A precise inclusion density is calculated by the maximization of the number of inclusions counted. In most cases one image field of view, or one image area, will contain a sufficient number of inclusions to determine a reasonably precise sampling coz&znt. In worse case situations, however, more than one image may be necessary. In this case, the information fiom several independent images may be easily combined to improve the precision of the sampling constant determination. Al uminium is representative of this worse case situation, as previously described. A great advantage of using an image to estimate sample heterogeneity is the copious amount of information present. An ion image with a 250-pm diameter contains the equivalent of over 49,000 analyses of l-pm* points. For the reported sampling constants, except for aluminum, one image area was used for the calculation. Figure 3 shows two line scans of the titanium image in Fig. l(c) chosen at random, but far enough apart on the image to ensure that the information

I

Po.sition,pm

-I

I

I

Position. pm

1

I

100

Fig. 3. Line scans of titanium in NBS SPCM-664 of Fig. l(c). Length of scan: 115 JJIXI.

steel:

(a) line 30 of Pig. l(c);

(b) line 90

21

in one is independent from that in the other. The scans show the variation of ion intensity across the image, and each is the equivalent of 115 l-pm2 point analyses, although all the data were collected simultaneously in the imaging mode. The two scans are significantly different, and would result in quite different evaluations of the sample heterogeneity. Since the greater part of the titanium signal for NBS 664 is due to the inclusions, a line scan like that in Fig. 3(a), which does not cross any of the larger inclusions, would result in an incorrect estimate of the microsampling situation. The same could possibly be true of any random scan, which may or may not represent the elemental heterogeneity of the sample as a whole. By using the great amount of information available horn an ion image, however, a more accurate evaluation of sample heterogeneity may be obtained. The sampling constant obtained from the described methods may be used to predict the number of replicate spot analyses necessary to yield a desired precision, assuming sampling to be the major source of error, or to predict the expected sampling error for a given number of analyses. The eqluation to predict expected sampling error follows from those of Scilla and Morrison [S] :

Es = 100

fKJ(a,n)+,

(2)

where E, is the predicted sampling error, in percent of the mean; t is a statistical factor; K, is the calcuiated sampling constant; u. is the analysis area in pm2 ; and n is the number of replicate analyses. The value of t reflects the precision with which the value of K, has been determined. For a sampling constant calculation with n inclusions, t is found in the Student f tables, assuming that the Poisson distribution is approximated by the normal distribution [3]. Table 2 shows the results of 10 replicate analyses for titanium in NBS 664 steel using a sampling area of 3960 pm?. The ratio of 4STi+/54Fe+ was used to eliminate the effect of fluctuations of the primary ion beam intensity during the period of analysis. The previously calculated value of 25.5 pm + 2.9 pm was used to calculate the expected sampling error (relative standard deviation) for the ten analyses. A value of 1.943 was used for t, which represents six degrees of freedom at a 95% confidence level, since seven normalized inclusions were counted in the titanium image used for the sampling constant calculation. TABLE 2 4sTi+/SqFe* ratios from 10 random spots of 3960~pm’

NBS SRM-664

low alloy steel

Area

1

2

3

4

5

6

7

8

9

10

YL’i+/s4Fe+

1.566

0.644

1.699

1.274

0.486

1.681

0.520

1.598

1.457

0.780

E,, predicted= Ekptl. RSD

a%=

25.5.

24.8% 21.5%

22

The actual results are seen to agree, within experimental precision, with those predicted by using the imagederived sampling constant. If a higher precision were desired, either a larger sampling area or a greater number of replicates would be necessary. Kate that the sampled area used for the above comparison is quite large compared to the area sampled in many probe analyses. In fact, an estimate of the sampling error expected for ten replicate analyses with a 100~pm2 beam is 200%. Yet when the actual analysis is performed, a much-higher apparent precision may be observed, because with a constituent located mainly in widely spaced inclusions, the probability of actually striking an inclusion with the beam may be rather small. What results is a set of measurements which reflects the concentration of the constituent in the matrix, with the possibility of what seems an “anomalous” value when the beam strikes an inclusion. If this “anomalous” result is then neglected, both a misleadingly low concentration and unrealistically high precision may result. If this situation arises during calibration of a standard, erroneously high values will then be obtained for subsequent analyses. The above emphasizes the importance of an appreciation of the microsampling situation in probe analysis_ The use of the sampling constant concept as described here would enable the analyst to determine the sampling area required to assure results within a desired confidence interval of the true concentration, and also eliminate the rejection of valid data. A compilation of sampling constants spanning appropriate elements representative of differing matices can be easily accomplished by the application of this method. Such a compilation may provide the key to quantitation for both ion microprobe and ion microscope analysis. The present paucity of standards now limits the range of any compilation. This work was supported by the National Science Foundation under Grant No. CHE77-04405 and through the Cornell Materials Science Center. REFERENCES 1 H. Yat;otitz and J. I. Goldstein (Eds.), Practical Scanning Electron Microscopy, Plenum Press, 1975, p. 445. 2 K. F. J. Heinrich, R. B. Marine&o, and F. C. Reugg, Proceedings of the Twelfth Annual Conference of the Microbeam Analysis Society, 1977, p. 148A. 3 G. J. Scilla and G. H. Morrison, Anal. Chem., 49 (1977) 1529. 4 G. H. Morrison and G. Slodzian, Anal. Chem., 47 (1975) 932A. 5 J. I). Fassett, J. R. Roth, and G. H. Morriion, Anal. Chem., 49 (1977) 2322.