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Measurement in section of particles of known composition
Minerals Engineering, Vol. l, No. 4, pp. 317-326, 1988
0892-6875/88 $3.00 + 0.00 © 1988 Pergamon Press pie
Printed in Great Britain
MEASUREMENT
IN SECTION OF PARTICLES OF KNOWN C O M P O S I T I O N
D. S U T H E R L A N D %, P. G O T T L I E B %, R. J A C K S O N T, G. WILKIE % and P. STEWART § %
CSIRO, Div. of Mineral & Process Engng., Clayton, Victoria, A u s t r a l i a § M i n e r a l C o m m o d i t i e s Ltd, Brisbane, Queensland, A u s t r a l i a
(Received 19 July 1988)
ABSTRACT Measurement of the exposed fraction of components of composite particles randomly oriented in a polished section leads to an unbiased estimate of their mean volumetric composition. By contrast, the distribution of particle compositions measured in a similar way contains a significant stereological bias. A number of theories have been proposed to account for this, some based on assumed models of the particle structure and others based on the measured texture of the phases present in the particle. The correction of this bias is important in the mining industry, yet few reports are available which give any experimental data. In the present work, three samples of particle composites of known composition were measured in polished section using QEM*SEM, an automated scanning electron microscope. Both linear scans and area scans were made. The results confirmed that a bias is associated with the measurements of the distribution of particle composition. They also confirmed that an area scan is a better estimator than a linear scan. A comparison was made between the measurements and some predictions based on geometrical modelling of the particles and components as simple shapes.
Ke~words Stereology; locked particles; automated mineralogy
INTRODUCTION M e a s u r e m e n t of the mineral p r o p o r t i o n s in c o m p o s i t e particles is a p r o b l e m of c o n s i d e r a b l e i n t e r e s t to the m i n i n g industry. The c o m p o s i t i o n of a separated m i n e r a l product is limited by the u n w a n t e d m i n e r a l s either as free p a r t i c l e s or l o c k e d particles. If the p a r t i c l e s are free it is the e f f i c i e n c y of the s e p a r a t i o n w h i c h is at fault and, if this process can be improved, the product q u a l i t y can be raised. W i t h locked particles, w h i c h will p r o b a b l y be present in both c o n c e n t r a t e and t a i l i n g s t r e a m s , f u r t h e r g r i n d i n g of the o r e is g e n e r a l l y needed. These important p r o c e s s i n g q u e s t i o n s can only be answered if there is a reliable way of m e a s u r i n g p a r t i c l e composition. Two m a i n a p p r o a c h e s have been taken for the e s t i m a t i o n of p a r t i c l e c o m p o s i t i o n and liberation. These are d e n s i t y f r a c t i o n a t i o n and m i c r o s c o p i c observation. T h e first m e t h o d can be used for q u a n t i t a t i v e m e a s u r e m e n t of binary locking but is d i f f i c u l t for high d e n s i t y m i n e r a l s and g e n e r a l l y i n a p p l i c a b l e to more c o m p l e x systems. M i c r o s c o p y is f r e q u e n t l y used in a q u a l i t a t i v e way to give indications of the p r e s e n c e and type of locked p a r t i c l e s b u t e x t e n s i o n of t h e t e c h n i q u e for quantitative w o r k is n o t s i m p l e . M e a s u r e m e n t is done in s e c t i o n and this introduces a stereological b i a s w h i c h is the s u b j e c t of t h i s p a p e r . In addition, the mineral discrimination of o p t i c a l i m a g e s is n o t a l w a y s satisfactory, w h i c h has lead to the use of e l e c t r o n m i c r o s c o p e s y s t e m s . To a c h i e v e r e l i a b l e s t a t i s t i c a l a c c u r a c y m a n y o b s e r v a t i o n s are required, hence
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D. SUTHERLAND et ~[.
the recent interest in automatic scanning instruments to remove the reliance on a human operator. The measurement and interpretation of particle section images can be done by using a random line in the section or the entire random section. Studies have b e e n c a r r i e d out analyzing the theoretical implications of sectioning, both from s t u d i e s of g e o m e t r i c a l l y r e g u l a r p a r t i c l e s [I] or s i m u l a t e d r a n d o m p a r t i c l e s [2]. M o r e g e n e r a l r e s u l t s h a v e a l s o b e e n a c h i e v e d w i t h fewer restrictions on the shape and texture of the particles [3,4,5]. In general it is f o u n d t h a t t h e r e is an o v e r e s t i m a t e of l i b e r a t e d p a r t i c l e s due to measurement in the section and that the bias is more pronounced for estimates based on the line rather than the area. The details of the bias depend on the shape, composition and structure of the particles. Despite the considerable amount of theoretical work done on the stereology of particle composites there are only limited e x p e r i m e n t a l d a t a a v a i l a b l e for comparison. This is due to the difficulty of obtaining sectional measurements and also to the problem of obtaining independent measurements of the particle composition. The current work was aimed at providing experimental data which could be used for comparison with the theoretical predictions.
EXPERIMENTAL METHODS Particle preparation The particles used in this work were essentially simple binaries containing iron oxide and silica in a narrow size range (-595 + 417 micron). They were carefully separated into a series of narrow density ranges using heavy liquids and liquid fluidized bed elutriation [6]. Three fractions were selected having compositions of approximately 20%, 60% and 80% by volume of iron oxide. Particle Measurement The s e c t i o n a l m e a s u r e m e n t s w e r e m a d e u s i n g the Q E M * S E M s y s t e m [7]. The equipment is based on a scanning electron microscope (SEM) equipped to measure b a c k s c a t t e r e l e c t r o n (BSE) intensity and energy dispersive X-ray spectra. This unit is coupled to a high performance mini-computer which controls the movement of the sample stage and electron beam, and collects and analyses data from the various measurement devices. Special purpose electronics h a v e b e e n designed by CSIRO to provide a high speed interface between the computer and the instruments. Samples were presented for measurement as polished sections following careful sample p r e p a r a t i o n and p o l i s h i n g [8]. N i n e s a m p l e blocks, t h r e e of e a c h sample, were loaded into the chamber at one time. Interactive software then automatically controlled the analysis of a l l s a m p l e s w i t h o u t manual i n t e r v e n t i o n . QEM*SEM can operate in either a line scan mode or a particle mode. In this case both modes were used so that results were generated area scans and line scans. These were presented as apparent particle composition histograms for the samples of known volumetric composition. Also the apparent m e a n s a m p l e c o m p o s i t i o n was calculated for comparison with the composition expected for the density fraction. RESULTS Locking Type Particle images of the samples are shown in Figure I. The mineral grain size is generally large so that, e v e n for t h e s e c o a r s e p a r t i c l e s , the l o c k i n g structure is very simple. Most particles contain only a grain or two of each phase leading to the simplest form of binary particles. S u c h particles are interesting from two standpoints. Firstly they will show maximum bias in liberation measurements. The f i n e r the m i n e r a l g r a i n s are which constitute a binary particle of a given size, the closer the sectional measurement approaches the true volumetric value. S e c o n d l y , as c o m m i n u t i o n proceeds and the particle size approaches the mineral grain size, the final stages of locking will be similar to those shown in Figure I.
Measurement in section of particles
319
SAMPLE 2
8AMPLE 1
IMAGE8 OF Bt~IARY PAR'i'K~E8 DARK PHASE i8 IRON OXIDE8
~
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3
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images showing locking
type
M e a n of P a r t i c l e C o m p o s i t i o n The results for the m e a n sample c o m p o s i t i o n of iron oxides are given in T a b l e 1. M o d a l a n a l y s i s m e a s u r e m e n t s made in section give an u n b i a s e d e s t i m a t e of the v o l u m e t r i c composition. A l s o shown are e s t i m a t e s of the c o m p o s i t i o n based on the a s s u m p t i o n that the p a r t i c l e s are a m i x t u r e of two m i n e r a l s of known densities so t h a t t h e d e n s i t y f r a c t i o n a t i o n range defines the particle composition. TABLE I
Sample No.
I 2 3
M e a n of SG range
3.26 4.12 4.63 (Values in b r a c k e t s
Modal analysis
(% Fe Oxide)
E s t i m a t e of Sample C o m p o s i t i o n (Vol.%) F r o m SG Line Scan Area Scan
22.7 58.8 80.0
22.1 60.0 79.3
indicate c o n f i d e n c e
(1 .3) (2.1) (1.7)
21 .I (4.4) 63.0 (6.1) 77.4 (3.0)
limits of +/-2 esd)
The d e n s i t i e s taken for the iron oxide and silica phases were 5.10 and 2.72. T h e " s i m p l e " binary system proved m o r e complex on d e t a i l e d examination. The iron oxides w e r e m a i n l y h e m a t i t e (SG 4.9 - 5.2) and m a g n e t i t e (SG 5.2). The q u a r t z (SG 2 . 6 5 ) was a s s o c i a t e d w i t h some s i l i c a t e s of h i g h e r density. The d e n s i t y values c h o s e n w e r e w i t h i n the p r o b a b l e range of the m i n e r a l s and gave e x c e l l e n t a g r e e m e n t w i t h the c o m p o s i t i o n as m e a s u r e d by line scan. These values are slightly higher than those used by S t e w a r t [6] in h i s o r i g i n a l study (5.06, 2.65). The v a l u e s in b r a c k e t s in T a b l e I r e p r e s e n t the e x p e c t e d c o n f i d e n c e intervals of +/-2 esd. These e s t i m a t e s are based on the number of the m e a s u r e m e n t s made, i.e. number of p a r t i c l e s observed b y l i n e or a r e a s c a n s . S i n c e a r e a m e a s u r e m e n t s take much longer than linear m e a s u r e m e n t s the number of p a r t i c l e s
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observed is t y p i c a l l y s m a l l e r for a r e a m e a s u r e m e n t s . This leads to w i d e r c o n f i d e n c e intervals for the area results as can be seen in Table I. The close a g r e e m e n t b e t w e e n the Q E M * S E M m e a s u r e m e n t s and the c o m p o s i t i o n as c a l c u l a t e d from the d e n s i t y f r a c t i o n a t i o n c o n f i r m s the u n b i a s e d n a t u r e of the m e a s u r e m e n t and indicates that the p a r t i c l e s e p a r a t i o n was done in a s a t i s f a c t o r y manner.
DISTRIBUTION Line
OF P A R T I C L E
COMPOSITION
scan a n a l y s i s
Figures 2, 4, 6 g i v e the d i s t r i b u t i o n of a p p a r e n t p a r t i c l e composition, as m e a s u r e d by line scan, for the three samples. The results are g i v e n in both cumulative and frequency form together with the true mean volumetric c o m p o s i t i o n of the samples. The results are fully t a b u l a t e d in an Appendix. The s e c t i o n i n g bias is very apparent. A wide range of p a r t i c l e c o m p o s i t i o n s is observed, f r o m b a r r e n to f r e e , d e s p i t e the fact that all particles are e s s e n t i a l l y of a fixed c o m p o s i t i o n (22%, 60% or 79% iron oxide). In sample I, F i g u r e 2, for instance, about half the p a r t i c l e s appear as b a r r e n and about 10% as liberated when all are of 22% composition. In c u m u l a t i v e form the plot should be a step function. Area
scan a n a l y s i s
C o r r e s p o n d i n g area results are shown for the samples in Figures 3, 5, 7 and the Appendix. The bias of the analysis, though still apparent, is not as s t r o n g as for the linear results. In all cases there are more p a r t i c l e s of i n t e r m e d i a t e c o n c e n t r a t i o n o b s e r v e d than w i t h the line analysis. T h i s m e a n s that there are fewer free and b a r r e n p a r t i c l e s observed. The c u m u l a t i v e plot is steeper. 100,
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COMPARISON
WITH
MODELS
Line scan A l s o included on the plots are the results to be expected if the particles were binary spheres with the two phases separated by a planar boundary. This is probably the simplest model possible for a binary particle. It was used by Stewart [6] and shown to give reasonable estimates of the degree of complete liberation. Now it can be seen to give reasonable results for the distribution of particle composition, though the quantitative agreement is not c o m p l e t e . F o r s a m p l e I the comparison is close, but the higher concentration samples show significantly more particles of apparently low concentration t h a n does the spherical model. The spherical model was used to see how close an estimate could be made of the particle composition using the apparent liberation results. The m e t h o d u s e d was to a s s u m e that the particles were binary spheres all of the same fixed particle composition C. A search was then made to find at which v a l u e of C there was a minimum squared deviation between the measured apparent particle composition d i s t r i b u t i o n and the p r e d i c t e d a p p a r e n t p a r t i c l e c o m p o s i t i o n distribution. The results are given in Table 2. The estimates for samples I and 3 are satisfactory while that for sample 2 is low.
D. SUTHERLAND et al.
322
TABLE 2
Estimates of particle composition based on spherical model (Linear analysis % Fe Oxides) Sample Number
True volumetric composition %
I 2 3
22.1 60.0 79.3
Estimated composition % 20.3 50.5 76.0
(Particles are assumed spherical binaries w i t h p l a n a r b o u n d a r y and c o n s t a n t c o m p o s i t i o n . E s t i m a t e d c o m p o s i t i o n gives least s q u a r e d deviation of model and apparent linear composition)
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Area scan The c o m p a r i s o n of the e x p e r i m e n t a l r e s u l t s w i t h those p r e d i c t e d by the spherical model are, once again, reasonable. The major deviations occur for the free and l i b e r a t e d p a r t i c l e s and it is p r o b a b l e that this is due to i n s t r u m e n t m i s i d e n t i f i c a t i o n s of the phases. In o r d e r to r e g i s t e r as a p a r t i c l e of only one phase, every point identification, or pixel, measured must be of that phase. A s i n g l e odd p i x e l w i l l c a u s e the p a r t i c l e to be r e j e c t e d from the free or b a r r e n classes, and such events can result from small quantities of other materials or machine misidentification errors. The mean number of pixels measured for the area analysis was in the region of 600 700 per particle for these samples. QEM*SEM has been optimised to give fast -
M e a s u r e m e n t in section o f particles
'
323
identification with reasonable accuracy, but even an identification reliability of 99.5% would make it very unlikely in this case that a liberated p a r t i c l e w o u l d be classified as fully free. For the present purpose it was considered advisable to combine the two adjacent classes at each end of the composition range. By this means such problems are minimized. In the case of the linear analysis the mean number of pixels per run length was much lower so that errors of this type were not apparent. T a b l e 3 g i v e s the e s t i m a t e s of c o m p o s i t i o n c a l c u l a t e d as b e f o r e on the a s s u m p t i o n of constant particle composition, but now using the area results and c o m b i n i n g the e x t r e m e c o m p o s i t i o n c l a s s e s as m e n t i o n e d a b o v e . T h e agreement is seen to be approximate. Estimates of particle composition based on spherical model (Area analysis % Fe Oxides}
TABLE 3
Sample Number
True volumetric composition %
I 2 3
Estimated composition %
22.1 60.0 79.3
16.2 63.7 84.3
(Particles are assumed spherical binaries w i t h p l a n a r b o u n d a r y and c o n s t a n t c o m p o s i t i o n . E s t i m a t e d c o m p o s i t i o n g i v e s least s q u a r e d deviation of model and apparent area composition)
ESTIMATION OF UNKNOWN PARTICLE COMPOSITIONS The aim of measurements in section is to estimate an unknown distribution of particle concentrations. We have seen that for the particular case here, where all the particles can be assumed to have the same c o m p o s i t i o n , r e a s o n a b l e v a l u e s can be calculated for the particle composition using a model of the particle structure and the m e a s u r e d a p p a r e n t p a r t i c l e c o m p o s i t i o n s . B o t h linear and area results were satisfactory. This situation is, of course, very unusual and is much better resolved by direct modal analysis. The practlcally u s e f u l c a s e i n v o l v e s the d e t e r m i n a t i o n of some u n k n o w n d i s t r i b u t i o n of particle composition. For measurements to be of value it must be possible to differentiate between particles having the same mean particle composition but different distribution of p a r t i c l e concentration. This proposition can be tested using the present results by combining samples I and 2 in suitable proportions to give a bimodal mixture h a v i n g the s a m e m e a n c o m p o s i t i o n as s a m p l e 2. The a p p r o p r i a t e proportions are 33.7% by volume of sample I and 66.3% of sample 3. By simple calculation t h e a p p a r e n t p a r t i c l e c o m p o s i t i o n for this m i x t u r e can be generated and compared with the results for sample 2. This is shown in Figure 8 for both area and line scans. 100
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Fig.8 Comparison of apparent composition for samples with same mean but different distribution of composition
324
D. SUTHERLANDet al.
The results indicate that it would be very difficult to differentiate between these two samples using linear measurements. With area scans the d i v e r g e n c e b e t w e e n the samples is considerably greater indicating that there is a much greater chance of getting useful results. Very similar results were obtained using simulated results based on the spherical model. It would appear that the added effort required in accumulating area data is well justified. DISCUSSION It has been widely appreciated since Gaudin [9] that the o b s e r v e d p a r t i c l e composition in a section is different from the true value. He recognised that more particles will appear liberated than is actually the case and derived a " l o c k i n g f a c t o r " to p r o v i d e a simple correction. Few reports exist of the measurement of the apparent composition in section and the comparison of this with true volumetric values. Stewart and Jones [10] give such results for the iron oxide and silica system used in the present paper. These were analysed in t h e c l a s s e s of " f r e e " a n d " l o c k e d " r a t h e r t h a n the c o m p l e t e a p p a r e n t composition range as attempted here. The results of Stewart and J o n e s show good agreement with the simple spherical model for a much more complete range of particle compositions than the 3 samples tested here. Barbery et al. [11] have also studied one of Stewart's samples and analysed it using an automated optical image analyzer. They estimated the volumetric c o m p o s i t i o n from the a r e a and l i n e a r grades, but w e r e not satisfied with the agreement between their estimates of the composition and the values quoted by S t e w a r t . T h e i r method was based on more general theories of stereology rather than a simple particle model as used here. Lin et al. [2] have made in situ measurements of the particle composition in a section by measuring the sample, shaving a layer from the polished section and remeasuring the sample. By this method they were able to compare the apparent and true particle compositions for simple systems of c o p p e r and iron ores. T h e y u s e d the r e s u l t s to test t h e i r t r a n s f o r m a t i o n m a t r i x g e n e r a t e d by computer s i m u l a t i o n of r a n d o m m i n e r a l p a r t i c l e s u s i n g P A R G E N [12]. T h i s s i m u l a t i o n p r o g r a m a l l o w e d some f l e x i b i l i t y in the generation of particle shapes and textures so that transformation matrices c o u l d be g e n e r a t e d for more realistic looking model particles. Hill et al. [13] have argued, on the basis of a spherical model, that much of the stereological error associated with measurements in section is removed by assessing areas instead of lines. There is some doubt expressed in that paper concerning the detailed calculations of the area sectioning bias, and our own work does not agree with results reported by Hill et al. for the area bias of a 50% binary sphere. Their general conclusion, nevertheless, is sound. Miller and Lin [14], indicated similar findings using PARGEN, while Davy [4] reached the same results based on a more general theoretical argument. She concluded that the degree of liberation apparent in lower dimensional data is greater t h a n f o r h i g h e r d i m e n s i o n a l data. The p r e s e n t w o r k g i v e s e x p e r i m e n t a l confirmation of these predictions. It can be seen that the area results more c l o s e l y a p p r o x i m a t e the true v a l u e s of k n o w n d i s t r i b u t i o n of p a r t i c l e composition. These results are for actual particles and consequently involve no assumptions of the shape or texture of the particles. Further it has been shown that the area results give much more chance of enabling the estimation of unknown particle volumetric composition distributions from measurements in section. It is still clear, however, that the results, even for area analysis, show a significant bias. Some correction is necessary before accurate statements can be made concerning the volumetric particle composition or the true liberation. The direct measurements may be u s e d in a c o m p a r a t i v e sense, that is, the response of the apparently liberated mineral may be compared under different experimental conditions, but care must be taken when making interpretations of the t r u e v o l u m e t r i c concentration. It must be remembered that the observed liberation consistently exceed the true value. CONCLUSIONS Three samples of closely sized and e s s e n t i a l l y b i n a r y p a r t i c l e s in n a r r o w d e n s i t y (and therefore composition) ranges were analysed in section by both line and area scans. The locking type was very simple.
M e a s u r e m e n t in section of particles
•
325
In all cases the mean sample composition agreed well with that expected based on the sample density. The a p p a r e n t p a r t i c l e c o m p o s i t i o n analysis was broad, indicating the bias inherent in measurements in the section. The bias was more marked with line scan t h a n w i t h area scan as is expected from theory. The apparent particle composition distribution was approximately that p r e d i c t e d by m o d e l l i n g the particles as simple binary spheres with a plane separating the phases. The r e s u l t s i n d i c a t e t h a t a r e a m e a s u r e m e n t s are preferred to l i n e a r measurements for estimating unknown distributions of particle compositions.
REFERENCES I.
Jones M.P. & Horton R. in M.J. Jones (ed.), Proceedings XIth Commonwealth Mining and Metallurgy Congress, I.M.M. London, 113 (1979).
2.
Lin C.L., Miller J.D. & Herbst J.A. Powder Technol.,
3.
King R.P. in J.P.R. de Villiers and P.A. Cawthorn Publ. Geol. Soc. S. Africa, 7, 443 (1983).
4.
Davy P . J . J .
5.
B a r b e r y G. in W.C. Park, D.M. H a u s e n Mineralogy , AIME, New York, 171 (1985).
6.
Stewart P.S.B., Univ., (1975).
7.
Reid A.F., Gottlieb P., MacDonald K.J. & Miller P.R. in W.C. Park, D.M. H a u s e n and R.D. H a n g n i (eds.), Applied Mineralogy , AIME, New York, 191 (1984).
8.
J a c k s o n B.R., R e i d A.F. & W i t t e n b e r g Metall., No. 289, 93 (1984).
9.
Gaudin A.M. Principles of Mineral Dressing,
50, 55 (1987). (eds.),
ICAM 81, Spec.
App. Prob., 21, 260 (1984).
M.Sc.
Thesis,
and
R.D.
Hagni
Imperial College of Sci.
J.C.
Proc.
12th
Applied
and Tech.,
Australas.
McGraw-Hill,
10. S t e w a r t P.S.B. & J o n e s M.P. in P r o c e e d i n g s Congress , Sao Paulo, Brasil, (1977).
(eds.),
London
Inst.
Min.
pp70 - 91 (1939).
Inter.
Mineral XIII
Proc.
11. B a r b e r y G., H u y e t G. & G a t e a u G. in P r e p r i n t s of Mineral Proc. Congress , Warszawa, Vol. I, 365 (1979).
Papers
Inter.
12. Sepulveda J.E., Miller J.D. & Lin C.L. in Proceedings Proc. Congress, Cannes Vol. I, 120, (1985).
XVth Inter. Mineral
13. Hill G.S., Rowlands N. & Finch J.A. in A.H. Vassiliou, D.M. Hausen and D.J.T. Carson, (eds.), Process Mineralogy VII, Met. Soc. Inc., 617 (1987). 14. M i l l e r J.D. & Lin C.L. p r e s e n t e d Meeting, Florida (April 1985).
at
16th
Annual
Fine
Particle
Soc.
326
D. SUTHERLANDet al.
APPENDIX Experimental
results Apparent
Apparent composition
(%)
49.5 9.1 7.7 6.8 5.0 4.5 3.3 3 .I I .6 I .9 0.6 6.9
Apparent
(%) 0 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 -I 00 100
Composition
by Line
Scan
Percentage of particles in the composition class Sample I Sample 2 Sample 3 (22.1%) (60.0%) (79.3%)
0 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 1 0 0 100
Apparent composition
Particle
Particle
29.3 3.3 3.4 2.4 3.0 4.1 4.7 4.3 5.2 6.0 6.2 28.0
Composition
17.4 I .I I .3 I .6 I .I 2.4 2.7 3.9 4.7 5.4 10.0 48.3
by Area
Scan
P e r c e n t a g e of p a r t i c l e s in t h e c o m p o s i t i o n c l a s s Sample I Sample 2 Sample 3 (22.1%) (60.0%) (79.3%)
6.7 30.4 22.0 14.5 11 .3 5.5 3.2 I .7
2.0 4.9 5.3 2.8 4.0 12.6 9.7 15.8
I .I 2.9 2.9 2.2 3.6 4.0 5.5 6.9
1 .4 1 .7
10.1 7.7
9.5 15.6
I .4 0.0
25.1 0.0
42.5 3.3
0892-6875/88 $3.00 + 0.00 © 1988 Pergamon Press pie
Printed in Great Britain
MEASUREMENT
IN SECTION OF PARTICLES OF KNOWN C O M P O S I T I O N
D. S U T H E R L A N D %, P. G O T T L I E B %, R. J A C K S O N T, G. WILKIE % and P. STEWART § %
CSIRO, Div. of Mineral & Process Engng., Clayton, Victoria, A u s t r a l i a § M i n e r a l C o m m o d i t i e s Ltd, Brisbane, Queensland, A u s t r a l i a
(Received 19 July 1988)
ABSTRACT Measurement of the exposed fraction of components of composite particles randomly oriented in a polished section leads to an unbiased estimate of their mean volumetric composition. By contrast, the distribution of particle compositions measured in a similar way contains a significant stereological bias. A number of theories have been proposed to account for this, some based on assumed models of the particle structure and others based on the measured texture of the phases present in the particle. The correction of this bias is important in the mining industry, yet few reports are available which give any experimental data. In the present work, three samples of particle composites of known composition were measured in polished section using QEM*SEM, an automated scanning electron microscope. Both linear scans and area scans were made. The results confirmed that a bias is associated with the measurements of the distribution of particle composition. They also confirmed that an area scan is a better estimator than a linear scan. A comparison was made between the measurements and some predictions based on geometrical modelling of the particles and components as simple shapes.
Ke~words Stereology; locked particles; automated mineralogy
INTRODUCTION M e a s u r e m e n t of the mineral p r o p o r t i o n s in c o m p o s i t e particles is a p r o b l e m of c o n s i d e r a b l e i n t e r e s t to the m i n i n g industry. The c o m p o s i t i o n of a separated m i n e r a l product is limited by the u n w a n t e d m i n e r a l s either as free p a r t i c l e s or l o c k e d particles. If the p a r t i c l e s are free it is the e f f i c i e n c y of the s e p a r a t i o n w h i c h is at fault and, if this process can be improved, the product q u a l i t y can be raised. W i t h locked particles, w h i c h will p r o b a b l y be present in both c o n c e n t r a t e and t a i l i n g s t r e a m s , f u r t h e r g r i n d i n g of the o r e is g e n e r a l l y needed. These important p r o c e s s i n g q u e s t i o n s can only be answered if there is a reliable way of m e a s u r i n g p a r t i c l e composition. Two m a i n a p p r o a c h e s have been taken for the e s t i m a t i o n of p a r t i c l e c o m p o s i t i o n and liberation. These are d e n s i t y f r a c t i o n a t i o n and m i c r o s c o p i c observation. T h e first m e t h o d can be used for q u a n t i t a t i v e m e a s u r e m e n t of binary locking but is d i f f i c u l t for high d e n s i t y m i n e r a l s and g e n e r a l l y i n a p p l i c a b l e to more c o m p l e x systems. M i c r o s c o p y is f r e q u e n t l y used in a q u a l i t a t i v e way to give indications of the p r e s e n c e and type of locked p a r t i c l e s b u t e x t e n s i o n of t h e t e c h n i q u e for quantitative w o r k is n o t s i m p l e . M e a s u r e m e n t is done in s e c t i o n and this introduces a stereological b i a s w h i c h is the s u b j e c t of t h i s p a p e r . In addition, the mineral discrimination of o p t i c a l i m a g e s is n o t a l w a y s satisfactory, w h i c h has lead to the use of e l e c t r o n m i c r o s c o p e s y s t e m s . To a c h i e v e r e l i a b l e s t a t i s t i c a l a c c u r a c y m a n y o b s e r v a t i o n s are required, hence
317
.3] 8
D. SUTHERLAND et ~[.
the recent interest in automatic scanning instruments to remove the reliance on a human operator. The measurement and interpretation of particle section images can be done by using a random line in the section or the entire random section. Studies have b e e n c a r r i e d out analyzing the theoretical implications of sectioning, both from s t u d i e s of g e o m e t r i c a l l y r e g u l a r p a r t i c l e s [I] or s i m u l a t e d r a n d o m p a r t i c l e s [2]. M o r e g e n e r a l r e s u l t s h a v e a l s o b e e n a c h i e v e d w i t h fewer restrictions on the shape and texture of the particles [3,4,5]. In general it is f o u n d t h a t t h e r e is an o v e r e s t i m a t e of l i b e r a t e d p a r t i c l e s due to measurement in the section and that the bias is more pronounced for estimates based on the line rather than the area. The details of the bias depend on the shape, composition and structure of the particles. Despite the considerable amount of theoretical work done on the stereology of particle composites there are only limited e x p e r i m e n t a l d a t a a v a i l a b l e for comparison. This is due to the difficulty of obtaining sectional measurements and also to the problem of obtaining independent measurements of the particle composition. The current work was aimed at providing experimental data which could be used for comparison with the theoretical predictions.
EXPERIMENTAL METHODS Particle preparation The particles used in this work were essentially simple binaries containing iron oxide and silica in a narrow size range (-595 + 417 micron). They were carefully separated into a series of narrow density ranges using heavy liquids and liquid fluidized bed elutriation [6]. Three fractions were selected having compositions of approximately 20%, 60% and 80% by volume of iron oxide. Particle Measurement The s e c t i o n a l m e a s u r e m e n t s w e r e m a d e u s i n g the Q E M * S E M s y s t e m [7]. The equipment is based on a scanning electron microscope (SEM) equipped to measure b a c k s c a t t e r e l e c t r o n (BSE) intensity and energy dispersive X-ray spectra. This unit is coupled to a high performance mini-computer which controls the movement of the sample stage and electron beam, and collects and analyses data from the various measurement devices. Special purpose electronics h a v e b e e n designed by CSIRO to provide a high speed interface between the computer and the instruments. Samples were presented for measurement as polished sections following careful sample p r e p a r a t i o n and p o l i s h i n g [8]. N i n e s a m p l e blocks, t h r e e of e a c h sample, were loaded into the chamber at one time. Interactive software then automatically controlled the analysis of a l l s a m p l e s w i t h o u t manual i n t e r v e n t i o n . QEM*SEM can operate in either a line scan mode or a particle mode. In this case both modes were used so that results were generated area scans and line scans. These were presented as apparent particle composition histograms for the samples of known volumetric composition. Also the apparent m e a n s a m p l e c o m p o s i t i o n was calculated for comparison with the composition expected for the density fraction. RESULTS Locking Type Particle images of the samples are shown in Figure I. The mineral grain size is generally large so that, e v e n for t h e s e c o a r s e p a r t i c l e s , the l o c k i n g structure is very simple. Most particles contain only a grain or two of each phase leading to the simplest form of binary particles. S u c h particles are interesting from two standpoints. Firstly they will show maximum bias in liberation measurements. The f i n e r the m i n e r a l g r a i n s are which constitute a binary particle of a given size, the closer the sectional measurement approaches the true volumetric value. S e c o n d l y , as c o m m i n u t i o n proceeds and the particle size approaches the mineral grain size, the final stages of locking will be similar to those shown in Figure I.
Measurement in section of particles
319
SAMPLE 2
8AMPLE 1
IMAGE8 OF Bt~IARY PAR'i'K~E8 DARK PHASE i8 IRON OXIDE8
~
Fig.1
3
Particle
images showing locking
type
M e a n of P a r t i c l e C o m p o s i t i o n The results for the m e a n sample c o m p o s i t i o n of iron oxides are given in T a b l e 1. M o d a l a n a l y s i s m e a s u r e m e n t s made in section give an u n b i a s e d e s t i m a t e of the v o l u m e t r i c composition. A l s o shown are e s t i m a t e s of the c o m p o s i t i o n based on the a s s u m p t i o n that the p a r t i c l e s are a m i x t u r e of two m i n e r a l s of known densities so t h a t t h e d e n s i t y f r a c t i o n a t i o n range defines the particle composition. TABLE I
Sample No.
I 2 3
M e a n of SG range
3.26 4.12 4.63 (Values in b r a c k e t s
Modal analysis
(% Fe Oxide)
E s t i m a t e of Sample C o m p o s i t i o n (Vol.%) F r o m SG Line Scan Area Scan
22.7 58.8 80.0
22.1 60.0 79.3
indicate c o n f i d e n c e
(1 .3) (2.1) (1.7)
21 .I (4.4) 63.0 (6.1) 77.4 (3.0)
limits of +/-2 esd)
The d e n s i t i e s taken for the iron oxide and silica phases were 5.10 and 2.72. T h e " s i m p l e " binary system proved m o r e complex on d e t a i l e d examination. The iron oxides w e r e m a i n l y h e m a t i t e (SG 4.9 - 5.2) and m a g n e t i t e (SG 5.2). The q u a r t z (SG 2 . 6 5 ) was a s s o c i a t e d w i t h some s i l i c a t e s of h i g h e r density. The d e n s i t y values c h o s e n w e r e w i t h i n the p r o b a b l e range of the m i n e r a l s and gave e x c e l l e n t a g r e e m e n t w i t h the c o m p o s i t i o n as m e a s u r e d by line scan. These values are slightly higher than those used by S t e w a r t [6] in h i s o r i g i n a l study (5.06, 2.65). The v a l u e s in b r a c k e t s in T a b l e I r e p r e s e n t the e x p e c t e d c o n f i d e n c e intervals of +/-2 esd. These e s t i m a t e s are based on the number of the m e a s u r e m e n t s made, i.e. number of p a r t i c l e s observed b y l i n e or a r e a s c a n s . S i n c e a r e a m e a s u r e m e n t s take much longer than linear m e a s u r e m e n t s the number of p a r t i c l e s
320
D. SUTHERLAND et al.
observed is t y p i c a l l y s m a l l e r for a r e a m e a s u r e m e n t s . This leads to w i d e r c o n f i d e n c e intervals for the area results as can be seen in Table I. The close a g r e e m e n t b e t w e e n the Q E M * S E M m e a s u r e m e n t s and the c o m p o s i t i o n as c a l c u l a t e d from the d e n s i t y f r a c t i o n a t i o n c o n f i r m s the u n b i a s e d n a t u r e of the m e a s u r e m e n t and indicates that the p a r t i c l e s e p a r a t i o n was done in a s a t i s f a c t o r y manner.
DISTRIBUTION Line
OF P A R T I C L E
COMPOSITION
scan a n a l y s i s
Figures 2, 4, 6 g i v e the d i s t r i b u t i o n of a p p a r e n t p a r t i c l e composition, as m e a s u r e d by line scan, for the three samples. The results are g i v e n in both cumulative and frequency form together with the true mean volumetric c o m p o s i t i o n of the samples. The results are fully t a b u l a t e d in an Appendix. The s e c t i o n i n g bias is very apparent. A wide range of p a r t i c l e c o m p o s i t i o n s is observed, f r o m b a r r e n to f r e e , d e s p i t e the fact that all particles are e s s e n t i a l l y of a fixed c o m p o s i t i o n (22%, 60% or 79% iron oxide). In sample I, F i g u r e 2, for instance, about half the p a r t i c l e s appear as b a r r e n and about 10% as liberated when all are of 22% composition. In c u m u l a t i v e form the plot should be a step function. Area
scan a n a l y s i s
C o r r e s p o n d i n g area results are shown for the samples in Figures 3, 5, 7 and the Appendix. The bias of the analysis, though still apparent, is not as s t r o n g as for the linear results. In all cases there are more p a r t i c l e s of i n t e r m e d i a t e c o n c e n t r a t i o n o b s e r v e d than w i t h the line analysis. T h i s m e a n s that there are fewer free and b a r r e n p a r t i c l e s observed. The c u m u l a t i v e plot is steeper. 100,
,
01
,
,
,
,
,
,
1 50%o EXPERIMENTAL
~ 40%~30%.
.~ 40 J
30 0
PARTICLE COMPO81TION 22% LINEAR ANALYSIS
LINEAR
i
20
20%
~ 10%
i
o 0
,
,J
,
,
,
,
1
1
,
10
20
30
40
50
60
70
80
90
. . . . .
0% :
i,,y
APPARENT GRADE (PERCENT IRON OXIDE)"
APPARENT GRADE (PERCENT IRON OXIDE)
Fig.2 100 90
~
8o
S
70
~ o ~
eo
Linear
I!, ,~q, ,~,~-, ~- ,~ ,
100
composition
of p a r t i c l e s
of 22%
iron oxides
50%[ ] EXPERIMENTAL
5o
m ~HERE c:] EXPERIMENTAL
~40%" O
o SPHERE
PARTICLE COMPOSITION 22% AREA ANALYSIS
~30%" AREA
i "° 30
0
20
~ 10%-
lo I O
i 10
20
i 30
i 40
~ 50
i 60
L 70
i 80
J 90
0% .
Area
composition
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A P ~ N T GRADE(PERCENT,.ON O X ~ r
APPARENT GRADE (PERCENT IRON OXIDE)
Fig.3
. . . . .
100
of
particles
of
22%
iron
oxides
Measurement in section of particles '
100
,
,
,
,
,
,
[] EXPERIMENTAL
9O
!.o
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[ 50%
~, ~o
LINEAR
321
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" SPI-F.RE EXI~RIMENTAL PARTICLECOMPOSITION60% LINEARANALYSIS
4O
i
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30%' 20%. i
1
10 0
i
t
i
i
~
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i
i
o,
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10 20 30 40 50 60 70 80 90 100 APPARENTGRADE(PERCENTIRONOXIDE) Fig.4
n.n. . 44rh "O"O'0"0"00vO"O
0~
APPARENTGRADE(PERCENTIRONOXIDES"
Linear composition of particles of 60% iron oxides
100 90 O SPHERE
eo
50%
~ ~o ~ 8o ~ ~o
AREA
/ .~40% 0 30% >-
_~ 4o
30[ O
i,
20
10 0
i
0
II SPHERE OE X ~ A I PARTICLECOMPOSITION60% AREAANALYSIS
L
¢
i
i
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i
i
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10 20 :30 40 50 60 70 80 90 100 APPARENTGRADE(PERCENTIRONOXIDE) Fig.5
.
.
.
.
.
.
.
O"O "O"O'~ O"O ~D On APPARENTGRADE(pERCENT~ OXIDE)-
Area composition of particles of 60% iron oxides
COMPARISON
WITH
MODELS
Line scan A l s o included on the plots are the results to be expected if the particles were binary spheres with the two phases separated by a planar boundary. This is probably the simplest model possible for a binary particle. It was used by Stewart [6] and shown to give reasonable estimates of the degree of complete liberation. Now it can be seen to give reasonable results for the distribution of particle composition, though the quantitative agreement is not c o m p l e t e . F o r s a m p l e I the comparison is close, but the higher concentration samples show significantly more particles of apparently low concentration t h a n does the spherical model. The spherical model was used to see how close an estimate could be made of the particle composition using the apparent liberation results. The m e t h o d u s e d was to a s s u m e that the particles were binary spheres all of the same fixed particle composition C. A search was then made to find at which v a l u e of C there was a minimum squared deviation between the measured apparent particle composition d i s t r i b u t i o n and the p r e d i c t e d a p p a r e n t p a r t i c l e c o m p o s i t i o n distribution. The results are given in Table 2. The estimates for samples I and 3 are satisfactory while that for sample 2 is low.
D. SUTHERLAND et al.
322
TABLE 2
Estimates of particle composition based on spherical model (Linear analysis % Fe Oxides) Sample Number
True volumetric composition %
I 2 3
22.1 60.0 79.3
Estimated composition % 20.3 50.5 76.0
(Particles are assumed spherical binaries w i t h p l a n a r b o u n d a r y and c o n s t a n t c o m p o s i t i o n . E s t i m a t e d c o m p o s i t i o n gives least s q u a r e d deviation of model and apparent linear composition)
100 /
r
~
,
,
,
,
,
ao t o SP.ERE
,,
,
I 50% - - -
I
• SPHERE
[3 EXPERIMENTAL
~
5o I ~^R
I
5oi
i/
40%-
PARTICLE COMPOBITION 79% LINEAR ANALYSIS
~30%>-
~
20%10%' O~
0
10
20
30
40
50
60
70
80
90
100 APPARENT
APPARENT GRADE (PERCENT IRON OXIDE)
Fig.6 100
,
90
,
,
,
,
,
,
O SPHERE 50".. AREA
~o
40%
20
~
|
0
i
i
i
i
i
i
i
10
20
30
40
50
50
70
Fig.7
o,, ~ n . a ~ n . .
i
80
90
APPARENT GRADE (PERCENT IRON OXIDE)
20%
,,o,1
10-
o;
PARTICLE COMPOSITION 79"/, AREA ANALYm
30"/,'t
4o
0
• SPHERE [3 EXPERI ENTAL
/
5o
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Linear composition of particles of 79% iron oxides
70
~
(PERCENT
[ ] EXPERIMENTAL
80
o~.J
,
GRADE
c~ .~ .~ . . . . .
IJ
100
APPARENT GRADE (PERCENT IRON OXIDE)"
Area composition of particles of 79% iron oxides
Area scan The c o m p a r i s o n of the e x p e r i m e n t a l r e s u l t s w i t h those p r e d i c t e d by the spherical model are, once again, reasonable. The major deviations occur for the free and l i b e r a t e d p a r t i c l e s and it is p r o b a b l e that this is due to i n s t r u m e n t m i s i d e n t i f i c a t i o n s of the phases. In o r d e r to r e g i s t e r as a p a r t i c l e of only one phase, every point identification, or pixel, measured must be of that phase. A s i n g l e odd p i x e l w i l l c a u s e the p a r t i c l e to be r e j e c t e d from the free or b a r r e n classes, and such events can result from small quantities of other materials or machine misidentification errors. The mean number of pixels measured for the area analysis was in the region of 600 700 per particle for these samples. QEM*SEM has been optimised to give fast -
M e a s u r e m e n t in section o f particles
'
323
identification with reasonable accuracy, but even an identification reliability of 99.5% would make it very unlikely in this case that a liberated p a r t i c l e w o u l d be classified as fully free. For the present purpose it was considered advisable to combine the two adjacent classes at each end of the composition range. By this means such problems are minimized. In the case of the linear analysis the mean number of pixels per run length was much lower so that errors of this type were not apparent. T a b l e 3 g i v e s the e s t i m a t e s of c o m p o s i t i o n c a l c u l a t e d as b e f o r e on the a s s u m p t i o n of constant particle composition, but now using the area results and c o m b i n i n g the e x t r e m e c o m p o s i t i o n c l a s s e s as m e n t i o n e d a b o v e . T h e agreement is seen to be approximate. Estimates of particle composition based on spherical model (Area analysis % Fe Oxides}
TABLE 3
Sample Number
True volumetric composition %
I 2 3
Estimated composition %
22.1 60.0 79.3
16.2 63.7 84.3
(Particles are assumed spherical binaries w i t h p l a n a r b o u n d a r y and c o n s t a n t c o m p o s i t i o n . E s t i m a t e d c o m p o s i t i o n g i v e s least s q u a r e d deviation of model and apparent area composition)
ESTIMATION OF UNKNOWN PARTICLE COMPOSITIONS The aim of measurements in section is to estimate an unknown distribution of particle concentrations. We have seen that for the particular case here, where all the particles can be assumed to have the same c o m p o s i t i o n , r e a s o n a b l e v a l u e s can be calculated for the particle composition using a model of the particle structure and the m e a s u r e d a p p a r e n t p a r t i c l e c o m p o s i t i o n s . B o t h linear and area results were satisfactory. This situation is, of course, very unusual and is much better resolved by direct modal analysis. The practlcally u s e f u l c a s e i n v o l v e s the d e t e r m i n a t i o n of some u n k n o w n d i s t r i b u t i o n of particle composition. For measurements to be of value it must be possible to differentiate between particles having the same mean particle composition but different distribution of p a r t i c l e concentration. This proposition can be tested using the present results by combining samples I and 2 in suitable proportions to give a bimodal mixture h a v i n g the s a m e m e a n c o m p o s i t i o n as s a m p l e 2. The a p p r o p r i a t e proportions are 33.7% by volume of sample I and 66.3% of sample 3. By simple calculation t h e a p p a r e n t p a r t i c l e c o m p o s i t i o n for this m i x t u r e can be generated and compared with the results for sample 2. This is shown in Figure 8 for both area and line scans. 100
100
,.¢ 9 0
~ 90 LINEAR
..a
70
i
5O
~
~ 8o
!.o
AREA
7O
5O
4O
40
~ 3o
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2
2O
0 8AMPtE 1+3
10 ,
0
J
i
i
,
,
i
,
10 L
10 20 30 40 50 60 70 80 90 100
APPARENT GRADE (PtERCENT IRON OXIDE)
0
10 20 30 40 50 60 70 80 90 APPARENT GRADE (PERCENT IRON OXIDE)
Fig.8 Comparison of apparent composition for samples with same mean but different distribution of composition
324
D. SUTHERLANDet al.
The results indicate that it would be very difficult to differentiate between these two samples using linear measurements. With area scans the d i v e r g e n c e b e t w e e n the samples is considerably greater indicating that there is a much greater chance of getting useful results. Very similar results were obtained using simulated results based on the spherical model. It would appear that the added effort required in accumulating area data is well justified. DISCUSSION It has been widely appreciated since Gaudin [9] that the o b s e r v e d p a r t i c l e composition in a section is different from the true value. He recognised that more particles will appear liberated than is actually the case and derived a " l o c k i n g f a c t o r " to p r o v i d e a simple correction. Few reports exist of the measurement of the apparent composition in section and the comparison of this with true volumetric values. Stewart and Jones [10] give such results for the iron oxide and silica system used in the present paper. These were analysed in t h e c l a s s e s of " f r e e " a n d " l o c k e d " r a t h e r t h a n the c o m p l e t e a p p a r e n t composition range as attempted here. The results of Stewart and J o n e s show good agreement with the simple spherical model for a much more complete range of particle compositions than the 3 samples tested here. Barbery et al. [11] have also studied one of Stewart's samples and analysed it using an automated optical image analyzer. They estimated the volumetric c o m p o s i t i o n from the a r e a and l i n e a r grades, but w e r e not satisfied with the agreement between their estimates of the composition and the values quoted by S t e w a r t . T h e i r method was based on more general theories of stereology rather than a simple particle model as used here. Lin et al. [2] have made in situ measurements of the particle composition in a section by measuring the sample, shaving a layer from the polished section and remeasuring the sample. By this method they were able to compare the apparent and true particle compositions for simple systems of c o p p e r and iron ores. T h e y u s e d the r e s u l t s to test t h e i r t r a n s f o r m a t i o n m a t r i x g e n e r a t e d by computer s i m u l a t i o n of r a n d o m m i n e r a l p a r t i c l e s u s i n g P A R G E N [12]. T h i s s i m u l a t i o n p r o g r a m a l l o w e d some f l e x i b i l i t y in the generation of particle shapes and textures so that transformation matrices c o u l d be g e n e r a t e d for more realistic looking model particles. Hill et al. [13] have argued, on the basis of a spherical model, that much of the stereological error associated with measurements in section is removed by assessing areas instead of lines. There is some doubt expressed in that paper concerning the detailed calculations of the area sectioning bias, and our own work does not agree with results reported by Hill et al. for the area bias of a 50% binary sphere. Their general conclusion, nevertheless, is sound. Miller and Lin [14], indicated similar findings using PARGEN, while Davy [4] reached the same results based on a more general theoretical argument. She concluded that the degree of liberation apparent in lower dimensional data is greater t h a n f o r h i g h e r d i m e n s i o n a l data. The p r e s e n t w o r k g i v e s e x p e r i m e n t a l confirmation of these predictions. It can be seen that the area results more c l o s e l y a p p r o x i m a t e the true v a l u e s of k n o w n d i s t r i b u t i o n of p a r t i c l e composition. These results are for actual particles and consequently involve no assumptions of the shape or texture of the particles. Further it has been shown that the area results give much more chance of enabling the estimation of unknown particle volumetric composition distributions from measurements in section. It is still clear, however, that the results, even for area analysis, show a significant bias. Some correction is necessary before accurate statements can be made concerning the volumetric particle composition or the true liberation. The direct measurements may be u s e d in a c o m p a r a t i v e sense, that is, the response of the apparently liberated mineral may be compared under different experimental conditions, but care must be taken when making interpretations of the t r u e v o l u m e t r i c concentration. It must be remembered that the observed liberation consistently exceed the true value. CONCLUSIONS Three samples of closely sized and e s s e n t i a l l y b i n a r y p a r t i c l e s in n a r r o w d e n s i t y (and therefore composition) ranges were analysed in section by both line and area scans. The locking type was very simple.
M e a s u r e m e n t in section of particles
•
325
In all cases the mean sample composition agreed well with that expected based on the sample density. The a p p a r e n t p a r t i c l e c o m p o s i t i o n analysis was broad, indicating the bias inherent in measurements in the section. The bias was more marked with line scan t h a n w i t h area scan as is expected from theory. The apparent particle composition distribution was approximately that p r e d i c t e d by m o d e l l i n g the particles as simple binary spheres with a plane separating the phases. The r e s u l t s i n d i c a t e t h a t a r e a m e a s u r e m e n t s are preferred to l i n e a r measurements for estimating unknown distributions of particle compositions.
REFERENCES I.
Jones M.P. & Horton R. in M.J. Jones (ed.), Proceedings XIth Commonwealth Mining and Metallurgy Congress, I.M.M. London, 113 (1979).
2.
Lin C.L., Miller J.D. & Herbst J.A. Powder Technol.,
3.
King R.P. in J.P.R. de Villiers and P.A. Cawthorn Publ. Geol. Soc. S. Africa, 7, 443 (1983).
4.
Davy P . J . J .
5.
B a r b e r y G. in W.C. Park, D.M. H a u s e n Mineralogy , AIME, New York, 171 (1985).
6.
Stewart P.S.B., Univ., (1975).
7.
Reid A.F., Gottlieb P., MacDonald K.J. & Miller P.R. in W.C. Park, D.M. H a u s e n and R.D. H a n g n i (eds.), Applied Mineralogy , AIME, New York, 191 (1984).
8.
J a c k s o n B.R., R e i d A.F. & W i t t e n b e r g Metall., No. 289, 93 (1984).
9.
Gaudin A.M. Principles of Mineral Dressing,
50, 55 (1987). (eds.),
ICAM 81, Spec.
App. Prob., 21, 260 (1984).
M.Sc.
Thesis,
and
R.D.
Hagni
Imperial College of Sci.
J.C.
Proc.
12th
Applied
and Tech.,
Australas.
McGraw-Hill,
10. S t e w a r t P.S.B. & J o n e s M.P. in P r o c e e d i n g s Congress , Sao Paulo, Brasil, (1977).
(eds.),
London
Inst.
Min.
pp70 - 91 (1939).
Inter.
Mineral XIII
Proc.
11. B a r b e r y G., H u y e t G. & G a t e a u G. in P r e p r i n t s of Mineral Proc. Congress , Warszawa, Vol. I, 365 (1979).
Papers
Inter.
12. Sepulveda J.E., Miller J.D. & Lin C.L. in Proceedings Proc. Congress, Cannes Vol. I, 120, (1985).
XVth Inter. Mineral
13. Hill G.S., Rowlands N. & Finch J.A. in A.H. Vassiliou, D.M. Hausen and D.J.T. Carson, (eds.), Process Mineralogy VII, Met. Soc. Inc., 617 (1987). 14. M i l l e r J.D. & Lin C.L. p r e s e n t e d Meeting, Florida (April 1985).
at
16th
Annual
Fine
Particle
Soc.
326
D. SUTHERLANDet al.
APPENDIX Experimental
results Apparent
Apparent composition
(%)
49.5 9.1 7.7 6.8 5.0 4.5 3.3 3 .I I .6 I .9 0.6 6.9
Apparent
(%) 0 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 -I 00 100
Composition
by Line
Scan
Percentage of particles in the composition class Sample I Sample 2 Sample 3 (22.1%) (60.0%) (79.3%)
0 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 1 0 0 100
Apparent composition
Particle
Particle
29.3 3.3 3.4 2.4 3.0 4.1 4.7 4.3 5.2 6.0 6.2 28.0
Composition
17.4 I .I I .3 I .6 I .I 2.4 2.7 3.9 4.7 5.4 10.0 48.3
by Area
Scan
P e r c e n t a g e of p a r t i c l e s in t h e c o m p o s i t i o n c l a s s Sample I Sample 2 Sample 3 (22.1%) (60.0%) (79.3%)
6.7 30.4 22.0 14.5 11 .3 5.5 3.2 I .7
2.0 4.9 5.3 2.8 4.0 12.6 9.7 15.8
I .I 2.9 2.9 2.2 3.6 4.0 5.5 6.9
1 .4 1 .7
10.1 7.7
9.5 15.6
I .4 0.0
25.1 0.0
42.5 3.3