A simulated array of particle profiles for use in microscope methods of particle size analysis

A Simulated Microscope

Array

of Particle Profiles for Use in Methods of Particle Size Analysis B. H_ KAYE

Insrirute for Fm Partick (Received

Resenrch.

Laurentian

Unitmtits.

SW.

May 11, 1970; in revised form February

SUMMARY

GEX~l-IOX PRODUCIXG

A technique is suggestedfor

8. 1971)

OF

PARTICLE SIhlULA

TED

PROFILES

TO

PARTICLE

DISPERSIOSS

BE USED

IX

building a simulated array

of profiles which can be used to train operators in the microscope method of analysis and to test automatic microscopes.

Ont_ (w)

It has been shown that the use of insensi-

tire graph papers to plot particle size distribution functions can lead to acceptance of a complex distribution finction which is not cn adequate description of the system_ It is also shown that any insensitivity in the analytical procedure can completely submerge important features of the size distribution function_

INTRODUCTION

Discussion of the various problems associated with microscope methods of analysis often runs into trouble when one attempts to clarify such concepts as “random array of particles”, “a good dispersion”7 “agg,lomerate”, “size of a particle” and “particle shapen. Again, when attempting to isolate the influence of various elements such as “sample error”, “orientation averaging”, “edge effects- and “subjcctive operator bias” on the accuracy and precision of the ultimate size distribution function deduced from the raw data, the situation isoften hopelessly complicated by the lack of a suitable set of standard particle profiles which has completely specified parameters Inter-instrument comparison, especially in the area of automated microscope systems is also complicated by the lack of such a standard set of profiles The set of test profiles described in this communicationwasevolved toprovideasetofstandardparticles for ausein the training of Iine particle analysts and in the comparative testing of automatic microscopes

The first decision which has to be taken with respect to the properties one wishes to build into a set of reference particle profiles is whether or not to select a standard type of distribution function to describe the range and frequency of the various particles placed in the array_ Since it was decided that one of the points of analytical procedure for which the simulated array should be useful was the illustration of the difficulty ofcharacterizing the frequency distributionat t.heextremesofthesizerangepresent,it was decided to have an arbitrary type size distribution function_ Another desirable feature of a standard array is that the particles should have an arbitrary shape. After various possibilities had been explored, the strate_gy illustrated in Fig. 1 was adopted. Starting from a point on the perimeter a wandering line was drawn across the circle, the line having no intended direction or curvature. After several cz~olutions it was taken to the perimeter of the circle. Entry was made to the circle at a second point on the perimeter and a similar random line drawn across the profile The final jigsaw of profiles generated in this manner is shown in Fig l_ A copy of this array was made on stiff cardboard ; the individual profiles generated by the meandering lines were then cut out and weighed to determine their area to within one per cent The profiles of this set provide many interesting features for a test array_ Thus, some of the particles have as many as five sidq others have re-entrant profiles, and there is a 40 to 1 six range in the arcas of the individual profiles. Not all the profiles of the interlocking systems

B.

H. KAYE

GENERATION

OF A RAhTDOM ARRAY OF PROFILES

In the British standard on microscope methods of analysis it is recommended that the density of coverage of particles to be evaluated on the microscope slide should not exceed 5 per cent. One of the intended uses of the test array was to see how easily an operator could recognize a 5 per cent covered field, and how an automatic microscope performed at this recommended level A test array was therefore constructed having a 5 o/ocoverage, theposition and orientation of each particle being randomly selected using random number tales to select _X and y coordinates for the centroid of each particle_ The resulting array is shown in Fig 3. In Fig 4 the crunulative bution of this set of pro&s

percentage

oversize

distri-

is presented. It should be

Fi_e 1. Set of interlocking profiles generated by the process de-

scribed in the text

Fig 3. Array with 5% eoverag;(For ref. I.)

Fi_e 2 Key to enable indiiridual pro&s

to be evaluated

were eventuaIIy used in the array_ In Fig. 2 the particles used in the array are identified by a serial number_ Those not used are shown in cross hatching_ The reason for not using them was that we wished to limit the number of profiles to 71, because of restrictions on the experiment in our original requirements which anz not relevant to this more general presentation of the properties of the array_

40

a key to the dia_fqamsee

1

Fig 4. Area size dislribution of random array of profik

Powder TedutoL, 4 (19X3/71)275-279

!3b¶ULATEL3 ARRAY

OF PARTICLE

ZEISS-

5

ENDTER

TEST-

OF

10

PERCENTAGE THIH

5

IO

20

PERCENTAGE

30-=0506070 OF STATED

Fif

5. Cumulatire

80

PROFILES

95

98

20

ANALYSIS

SHEET

A

so

30505,60x)

NUWER STATED

CF

PARTICLES SlZE

so

4s 43 99 SMALLER

LlW7

99

I-HAN

AREA

area diitribu:ion mph

so LESS

27?

PROFILES

on Gaussian

probabilit\

pap=-

noticed that for the purposes of testing equipment and/or operators them is a rather interesting kink at about 12 per cent_ The ability to detect this kink presents a severe test for the precision and accuracy of any instrument andior operator exploring the field of view. The system of profiles is also quite convenient in that it approximates to the Gaussian distribution except for the tails. This factor is illustrated in Fig. 5 where the distribution of Fig. 4 has been plotted on Gaussian probability graph paper. As can be seen from this curve, the Gaussian distribution function could be used to describe the distribution of profiles over approximately 60 per cent of the total range. In our experience many analystswould, in theabsence offurther information, assume that the deviations at the tails were acceptabledeviationsdue to theuncertainty ofdetermining the small population of the extreme sizes. While it is true that normally there is less confidence in the tails of the distributions than in the middle, the curve in Fig. 5 illustrates the danger of assuming that the deviations at the extremities of a curve are due to experimental error- A-great deal of experimental work would be required to define accurately the distribution function describing the tails of the distribution. An interesting example cf how the analytical procedure is not always sensitive to the determination of the tails of the distribution function is shown in Fig 6, in which the data from a student

Fi_e 6. Srudcnr analysis of the simulate 5 :, ana> using a ZcizsEndtcr particle size anal~zcr. (3).

analysis of the profile array Fig. 3 is gil-en. The student used a Zeiss Endter particle size analyzer with linearly distributed increases in diameter bctween size groups There were 9 possible groups and the size ranges were in arbitrary units A magnified image of the particle profile was projected on to the central light spot of the Zeiss Endter. In using this particular equipment no particles larger than size group 7 were detected by the student The measured set of frequencies for the 7 size groups are given in Fig_ 6. It can be seen that there is no sampling error since all the profiles were measured. The student without further guidance from the instructor plotted his measured distribution on Gaussian probability graph paper. The results of this plot are shown in Fig 6. The student’s conclusion was “the results of this analysis seem to indicate a Gaussian distribution”. To permit the resolution of the liner details of the distribution function it would have beenn ecessary to use a much more highly resolved interrogation system attached to the Zeiss. Endter. Graph papers having non-linear axes should bc used with great caution in analytical procedures In Fig 7 the true distribution of the profiles of Fig 3 is shown plotted on Iogarithmic probability -graph paper Some analysts would feel quite justified in drawing a satisfactory ‘best estimate” indicated by the dotted line Again, the argument would probably

B_

H.

KAYJZ

-._

_._T

5

IO

PERCENTAGE

20

?053506070

60

OF PROFILES LESS STATED ARE A

SO

95

THAN

Of2

--

99 EQUAL

TO

Fig 7. Cumulative area distribution on logarithmic probabiliry pph paper-

be that since. for approximately 70 per cent of the size groups, the powder is described by this function, then one is justified in extrapolating into an area where the total population of particles per group is smail and therefore known with less certainty than the population of the groups nearer the median of the distribution Figure 7 illustrates the danger of this type of argument For many purposes the size distribution functions which are represented by the bes? straight lines in Figs. 5 and 7 could perhaps be used in a theoretical analysis of a system; however. this question would have to be expIored in some detail before the technologist could be allowed to use these distribution functions in any treatment of a fine particle system.

FUR-l-HER

EXPF3UMEN-i-S

Fig 8. Array with 10% covcrqc

xvrrHTHEsDIuLATEDRANDo1sI ARRAY

To extend the useNness of the test array it was photogr?phed and reduced in size Since there is no symmetry in the field of view, the negative of the field of view can be placed in eight independent positions By using a second negative of the field of view placed immediately behind the first field there are many possibly ways of creating a simulated 10 per cent co\-ered field of view_ In Fig 8 we show one such set of profiles simulating a 10 per cent coverage. In this picture the overlap of some of the particles can be clearly seen. We have used this simulated array to test the analyst’s reaction to particles which he thinks are clusters In fact the clusters of Fig 8 could

Fig 9. Array with 15% &erase. have been formed purely by a random process of overlap as the particles were deposited on a filter paper. Many analysts regarded the clusters of this diagram as being particles. The test profiles of Fig.

8 can be used to explore the various interpretations operators will give to the concept of a “particle”. The various combinations which can be used to generate various sets adding up to 10 per cent are useful to show the analyst how a certain percentage of area is lost in an 0verlapFIng process Againin Powder TechmL. 4 (1970/71)

275-279

SlMuLAlED

ARRAY

OF PARTICLE

Fig9weshowasimulated lSpercentview_ Ofcourse by this time there is serious loss due to overlap. However, in general terms the set of profiles can be used to discuss the propertiesofa 15 per cent covered fieldof view-Again, these fieldsofview can be used to investigate what operators would feel is a particle. When the photographs of Figs 8 and 9 are printed in a suitablemanner, the obvious overlap disappears and we are left with dense opaque particle profiles_ We are carrying out a series of tests on automatic microscopes using the 5,lO and 15 per cent simulated field of view of Figs 3, 8 and 9 to test purely logic operations in these various machines It is hoped to present a more comprehensive report of this study at a later date_

coscLus10ss

We have suggested a technique for building a simulated array of profiles which can be used to train operators in the microscope method of analysis and which can be used to test automatic microscopes It has been shown that the use of

279

PROFILES

insensitive graph papers to plot particle size distribution functions can lead to acceptance of a complex distribution function which is not an adequate description of the system Again, it is shown that any insensitivity in the analytical procedure can completeIy submerge important features of the size distribution function.

ACKNOWLEOG

EME?m!s

The author is grateful for the assistancegiven by the students of the Physics Department of Laurentian University in the preparation of test arrays. The work described in this communication was supported in part by a grant from the National Research Council of Canada; this support is gratefully acknowledged

REFERENCES

Pow&r

Technol

C (1970,71)

m-c279