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A STANDARD MATERIAL FOR STEREOLOGICAL CORRECTION

D. LIN1 and J.A. FINCH2

1Cominco Ltd., P.O. Box 2000, Trail, B.C., Canada, V1R 4S42 McGill University, Department of Metallurgical Engineering, 3610 University St. Montreal, Quebec,

Canada, H3A 2B2

(Received March 1999; in revised form September 1999)

Abstract — The determination of mineral liberation by microscopic examination of ore particle sectionsis stereologically biased. Procedures have been developed to correct this bias, but most have not beenthoroughly tested. A standard material, a material of known particle composition and locking character-istics, would allow the proper testing of these procedures. In this work, a method was developed for thecreation of a standard material consisting of two phases: glass and lead borate. Simple-locked particlesand particles with granular and layered textures can be created. The standard material is versatile andeasy to use.

Résumé — La détermination de la libération de minéraux par examen microscopique de sections departicule de minerai est biaisée stéréologiquement. Des procédures on été développées afin de corrigerce biais, mais la plupart n'ont pas été entièrement évaluées. Un matériel étalon, un matériel decomposition de particules et de caractéristiques d'emprisonnement connues, permettrait une évaluationappropriée de ces procédures. Dans ce travail, on a développé une méthode pour la création d'un matérielétalon consistant de deux phases: verre et borate de plomb. Des particules à emprisonnement simple etdes particules avec des textures granulaires et avec couches peuvent être créées. Le matériel étalon estversatile et facile à utiliser.

INTRODUCTION

Mineral liberation represents the ultimate limit in the separa-bility of mineral phases. The measurement of mineral libera-tion is usually accomplished by mounting the particles in aresin matrix, polishing a surface and examining the surfacewith an optical or electron microscope. Images of the surfaceare digitised and processed with an image analyser. The imageanalyser measures the liberation by determining the mineralcomposition of the individual particle sections. This method ofmeasuring liberation is stereologically biased. Liberated parti-cles will always yield liberated sections whereas locked parti-cles can yield liberated or locked sections. As a result, miner-al liberation will always be over-estimated.

Methods have been developed to correct the stereologicalbias [1, 2, 3, 4, 5, 6, 7], but the effectiveness of these methodsis difficult to test since the true liberation is not known.Standard materials, that is, materials of known particle libera-tion and locking characteristics, have been developed in anattempt to allow the assessment of these correction proce-dures. The present work describes a method of producing aversatile standard material that can be used to test the robust-ness of stereological correction procedures.

For the standard material, a two-phase (binary) systemis all that is required because liberation is measured onephase at a time: while the liberation of one mineral phase isbeing measured, the rest of the mineral phases in the sam-ple can simply be grouped together as the second phase. Atrue, two-phase material is essential if density fractionationof the particles is performed to provide the independent andtrue measure of particle composition. If there are more thantwo phases, there will not be a direct correlation betweenparticle density and particle composition. Obviously, a sig-nificant density difference between the two phases is nec-essary to provide good resolution to the density splits. Anear-perfect separation such as that obtained using heavyliquids is desired to ensure the precision of the splits.

For the standard material, there must be a method ofdistinguishing the two phases. If optical microscopy isused, the two phases must be different colours or havesome other differentiating feature. If electron microscopy isused, the two phases must have different grey levels whenviewed with backscattered electron imaging. The backscat-tered grey level of a phase is directly related to its averageatomic number such that a low atomic number material willappear dark and a high atomic number material will appear

Canadian Metallurgical Quarterly, Vol 39, No 2, pp 121-128, 2000© Canadian Institute of Mining, Metallurgy and Petroleum

Published by Canadian Institute of Mining, Metallurgy and PetroleumPrinted in Canada. All rights reserved

D. LIN and J.A. FINCH

bright. In this work, the standard material was designed foruse with electron microscopy.

It is desirable that the standard material be able toexhibit simple locking (i.e., only one interface between thephases in the particle). Simple locking is probably the mostimportant of all locking types in mineral processing fol-lowing the argument that since comminution is aimed atcreating free particles, the mineral which fails to be liberat-ed is most likely concentrated in the next simplest class -the simple-locked particle class. Simple locking also cre-ates the most severe stereological bias and is, therefore, asevere test of any stereological correction procedure [1,2].

The standard material should also be flexible enough tosimulate different types of locking textures. Although astereological correction procedure may be effective withone type of locking texture, it may not be as effective withothers. In addition, it would be instructive to examine theeffect of locking texture on the predictive abilities of dif-ferent liberation models.

There are two categories of standard materials: natural-ly-occurring and artificial. A short review of previousattempts to create standard materials follows.

STANDARD MATERIAL PREPARATION A SHORT REVIEW

Naturally-occurring standard materials

Naturally-occurring standard materials are created fromnaturally-occurring two-phase ores. The ore is broken,screened and the composition of the particles measured bydensity fractionation. There have been several efforts todevelop a standard material from natural sources, but thereare difficulties in finding a two-phase ore whose phases arefree from porosity and impurities. If there are significantquantities of either of these in the particles then the deter-mination of particle composition from density measure-ments is not accurate. Similarly, this would be a problem ifthere were variations in the density of either of the twophases. The use of a naturally-occurring standard materialis limited because the locking texture cannot be controlled.Work performed in this area is described below.

1. Stewart and Jones [8] used a siliceous iron ore whichconsisted of grains of iron oxides (hematite with magnetiteand minor amounts of goethite and limonite) in a siliceousmatrix (quartz with minor amounts of other silicates). Theore was crushed to 90% -1.0 mm and screened. The parti-cles were separated based on density using heavy liquids(for densities below 3.32 g/ml) and a fluidised bed (for den-sities above 3.32 g/ml). The siliceous material was estimat-ed to have a density of 2.65 g/ml and the iron oxides tohave a density of 5.06 g/ml. There were two problems withthis standard material: there may have been significant

porosity in the ore [6(p.118)] and there was some variationin the density of the iron minerals.

2. Bole et al. [9] examined two binary ores: an iron-oxide/silicate sample and a sphalerite/dolomite sample.Both ores were crushed and screened to 417-595 µm andthe iron-oxide/silicate particles fractionated using heavyliquids. The densities of the silicate and iron oxide phaseswere 2.72 and 5.10 g/ml, respectively. The sphalerite/dolomiteparticles were density fractionated using the Magstreamseparator (a centrifugal magnetogravimetric separator).The density of the dolomite was 2.85 g/ml and that of thesphalerite, 4.00 g/ml.

3. Miller and Lin [10] used a unique approach to deter-mining the true liberation of mineral particles. They usedserial sectioning to determine the liberation of an iron oreand a copper ore. Particles were screened to 74-105 µm andmounted in resin. By polishing this pellet down by intervalsof 18 µm, a series of parallel sections was gathered for eachparticle. The composition of each particle was reconstruct-ed based on these sections. Although serial sectioning doesprovide an unbiased measure of the true liberation distrib-ution, it is too tedious and expensive to use in regular lib-eration analyses.

Artificial standard materials

The general procedure to create an artificial standard mate-rial is summarised in Figure 1. Monosize grains of onephase are embedded into a matrix which acts as the secondphase. The matrix phase is usually a plastic or resin in liq-uid form. When the plastic hardens, a two-phase block isformed. The block is then crushed producing free andlocked particles. These particles are screened into differentsize classes and a density fractionation is performed. Thisprocedure allows the manipulation of parameters such asthe grain and particle size so that there is some control overthe locking texture.

Work that has been done in this area is described below:

1. Bagga [11] created a standard material using 600-710µm pyrite particles as the grain material and polystyrene asthe matrix. The locked blocks were crushed after treatmentwith liquid nitrogen to make the polystyrene more brittle.Several particle sizes were separated by screening and adensity fractionation was performed using CaCl2 and ZnCl2solutions. A complete density fractionation could not beperformed since the highest density that could be reachedusing these liquids is about 2 g/ml and the density of pyriteis about 5 g/ml.

2. Woollacott and Valenta [12] embedded grains of a poly-ester resin which had been doped with lead oxide powderand black dye into a matrix of the same polyester resin inliquid form, doped with white dye. The lead oxide powder

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increased the density of the grain material to allow densityfractionation and the dyes provided optical differentiationbetween the grain and matrix phases; this material wasdesigned for optical microscopy. When the matrix resin hadhardened, the locked blocks were crushed and screened to2.5-4.0 mm. The separations were performed using a heavyliquid (ZnCl2 solution). The densities of the grain andmatrix phases were 1.756 and 1.219 g/ml, respectively.

3. Lin et al. [13,14] created their standard material byembedding grains of silica in a matrix of epoxy resin. Thesilica density was 2.62 g/ml and the resin density was 1.22g/ml. The particles were separated using sodium poly-tungstate, a water-soluble heavy liquid. The particle sizewas 75-106 µm.

4. Gay [6] created a standard material in much thesame manner as Woollacott and Valenta. Grains of apolyester resin doped with zinc oxide powder and acoloured dye were embedded in a polyester resin dopedwith a different concentration of zinc oxide and a dif-ferent coloured dye. The densities of the two phaseswere 1.36 and 1.62 g/ml. Two particles sizes, 2.36-2.80mm and 3.35-4.00 mm, were generated by screeningand separated using a ZnCl2 solution.

Refinement of the standard material

Although artificial standard materials have been estab-lished, there are several parameters that can be changed toenhance the quality and the quantity of the artificial stan-dard material. The standard material could be improved by:

1. strengthening the bond between the grain and matrixmaterial. By producing a strong bond between the twophases, there would be a decrease in breakage along theinterfaces and an increase in the amount of locked particles.The amount of locked particles produced should be sub-stantial enough so that large amounts of grain and matrixmaterial do not have to be processed. In addition, stronginterfacial bonding would allow the standard material toprovide a test of models of liberation by size reduction.

2. changing the grain and/or matrix material. Ideally, thephases for the standard material should be brittle so thatthey are easy to crush and possess good polishing proper-ties so the interfaces are clearly delineated when viewedunder a microscope. Also, the two materials should be sig-nificantly different in density. The greater the difference indensity, the greater the resolution of the density separa-tions. However, the density of the denser of the two phasesshould not exceed the upper limit of the separation method.

3. creating other locking textures. With the current proce-dure for producing locked particles, only granular lockingcan be created. While this may reflect the situation in manyores, this is not necessarily always the case. For instance,particles with a layered locking texture (a texture consist-ing of alternating layers of different phases) may result if anore with a banded structure is crushed.

4. developing a strategy for producing only simple-lockedparticles. With the current procedure for manufacturinglocked particles, simple locking can be produced onlywhen the particle size is significantly smaller than the grainsize, but this may seriously reduce the amount of lockedparticles produced. In any case, it is very difficult to controlthe amount of simple locking due to the granular nature ofthe texture: unless the grains are perfectly dispersed in thematrix, grains that are close to each other will almostinevitably create complex locking (locking such that thereis more than one interface between the phases in the parti-cle). This is complicated by the fact that it is impossible tomeasure the degree of simple locking since stereologicalbias affects the determination of the locking texture.

RESULTS

Selection of the phases for the standard material

Two new materials were selected for the production of thestandard material: lead borate (2PbO•B2O3) as the matrixmaterial and glass particles as the grain material [7]. Leadborate is a leaded glass additive and is more commonly

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Fig. 1 Conceptual procedure for the production of artificial locked particles.

1. Embedding of monosizegrains into matrix.

2. Grinding the grain-matrixblocks.

3. Size classification of theparticles

4. Density classification.

D. LIN and J.A. FINCH

used as a source of lead for glass melts or ceramic glazes, butin this work it was used as one of the phases of the standardmaterial. The melting point of lead borate is approximately500°C while the melting point of glass is approximately800°C. The standard material was created by melting the leadborate and embedding the glass particles. The glass particlessoftened slightly and produced a strong bond with the leadborate. (It was later determined that some glass diffused intothe borate which further strengthened the bond.)

Glass was used as the grain material because it has sim-ilar brittleness and breakage properties to lead borate.Silica was considered as the grain material, but the use ofglass rather than silica allows greater control over the lock-ing texture (as seen by the creation of the layered texturediscussed later) and because it has a lower melting point.The density of the lead borate and glass were measuredwith a water displacement technique using a pycnometerbottle [15] to be 6.833 g/ml (±0.006)1 and 2.502 g/ml(±0.001), respectively. Subsequent experimentation showedthat after contact some glass diffused into the lead borate togive a SiO2 content of 5.95% (±1.38%) as determined bymicroprobe analysis. The density of the borate was re-determined as 6.052 g/ml (±0.009) and this was the valueused in the density fractionation.

Due to the high density of the lead borate, convention-al heavy liquids could not be used to fractionate the stan-dard material so a Magstream Model 100, a centrifugalmagnetogravimetric separator, was used. (The principles ofthe Magstream separator have been described by Walker,Devernoe and co-workers [16,17,18,19].) The size rangefor the standard material was selected as 425–600 µm since600 µm particles are the largest that the Magstream Model100 can accommodate and splits on the Magstream aremore precise the larger the particle size.1Standard deviation in parenthesis

Production procedure for standard material with a granu-lar texture

The procedure for the creation of the glass/borate standardmaterial with a granular texture was as follows:

1. Thirty grams of 1180-1700 µm glass grains were placedin a 40 ml porcelain crucible. The glass was three Tyler sizeclasses larger than the target particle size to aid in creatingsimple locking.

2. Sixty grams of powdered borate was placed on top ofthe glass grains. Since the glass has a lower density than theborate, the glass will be wetted by the borate as it rises tothe top.

3. The crucible was placed in an induction furnace pre-heated to 600°C. This temperature was maintained for 30minutes.

4. The power was shut off to the furnace and the cruciblewas allowed to cool to room temperature.

5. The sample was removed from the crucible, crushedand wet-screened to remove the fines.

6. The 425-600 µm fraction was screened out.

A SEM (scanning electron microscope) backscatteredelectron micrograph of this material is shown in Figure 2.A large majority of the sections exhibit locking. There werea few voids, but they were small (<10 µm) and were pre-sent in only approximately 1% of the borate sections. Itappeared that there were slightly more simple-locked sec-tions than complex-locked sections. The complexity of thecomplex-locked sections was low; most of the complex-locked sections contained only two interfaces.

Production procedure for standard material with layeredtexture and simple locking

To create a standard material with a layered texture, alter-nating layers of the two phases were bonded together.Simple-locked particles were created from this texture bycrushing blocks of this material to a size below the thick-ness of the layers as shown in Figure 3. The procedure forthe creation of the glass/borate standard material with sim-ple locking was as follows:

1. Long glass slides (75 mm x 25 mm x 1 mm) alternatedwith short glass slides (25 mm x 25 mm x 1 mm) wereclamped together at one end. This permitted the long glassslides to be parallel to each other and separated by a gap ofexactly 1 mm.

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1 mm

Fig. 2 SEM backscattered electron micrograph of 425-600 µmglass/borate standard material particles taken at 30x magnification (lightphase is lead borate; grey phase is glass; dark phase is mounting medium).

2. The slides were placed in a crucible containing boratepowder so that only the lower portion of the long slides was in contact with the powder; the short slides and the clampitself were clear of the powder.

3. The crucible was placed in an induction furnace pre-heated to 600°C. This temperature was maintained for 45minutes.

4. The power was shut off to the furnace and the cruciblewas allowed to cool to room temperature.

5. The clamp and the short glass slides were removed.

6. The sample was removed from the crucible, crushedand wet-screened to remove the fines.

7. The 425-600 µm fraction was screened out.

A SEM backscattered electron micrograph of these par-ticles is shown in Figure 4. Only simple locking wasobserved; no sections with complex locking were seen.

The particle size of the simple-locked particles wasselected to be 425-600 µm because the granular-texturedstandard material was this size. If the simple-locked and thegranular-textured standard materials were to be combinedto form a liberation distribution, the particles would have tobe the same size. Simple-locked and layered-texture parti-cles are a useful supplement to the granular-textured stan-dard material.

Density fractionation

To determine the liberation, the particles were separatedinto different density classes using the Magstream separa-tor. In this work, density fractionation was performed onlyon the granular-textured standard material particles.

In common with all separators, separation on theMagstream is not perfect. Also, Bunge and Fuerstenau[20,21,22] observed that the accuracy of Magstream sepa-rations decreases with particle size. A theoretical study bySvoboda [23] concluded that the performance of theMagstream was dependent upon particle size and he cau-tioned against using the Magstream for fine particles. Toensure separation accuracy, the heavies and lights productsmust be re-processed (cleaned).

The density fractionation on the Magstream assumedthat the particles were non-magnetic. To verify this, themagnetic susceptibility of the two phases of the standardmaterial was measured using a Frantz isodynamic magnet-ic separator [24]. As expected, both the glass and leadborate had very low magnetic susceptibility (κglass < 5.32 x10-5 SI units and κlead borate < 1.95 x 10-5 SI units; for com-parison, κchalcopyrite ≈ 4 x 10-4 SI units). Their diamagneticproperties were also measured. Both materials showed nomeasurable diamagnetism.

The standard material was separated with theMagstream into the following composition fractions: -5, 5-15, 15-25,..., 85-95, +95 vol.% borate. To ensure the accu-racy of the separations, the following measures were taken:

1. The products of the first separation (rougher) werecleaned twice. Therefore, for each composition fraction,three separations were performed at both split-points of thefraction.

2. In the cleaning steps, any particles that did not re-reportto the composition fraction were eliminated.

3. The split-points were set 0.5% closer to the midpoint ofthe fraction. For instance, for the 45-55 vol.% borate frac-tion, the split points were set to 45.5% and 54.5 vol.%

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Fig. 3 Simple-locked particles can be created if a layered-texture blockof material is crushed so that the particle size is smaller than the layer

thickness.

1 mm

Fig. 4 SEM backscattered electron micrograph of 425-600 µm simple-locked, glass/borate standard material particles taken at 30x magnification (light phase is lead borate; grey phase is glass; dark phase is mounting

medium).

D. LIN and J.A. FINCH

borate. This leaves a 1% gap in composition between frac-tions, but helps minimise misplaced particles.

The particles that were -5 vol.% borate or +95 vol.%borate were considered to be free. True free glass particles(i.e., 100% glass) were created simply by crushing glass to425-600 µm. True free borate was created by placing boratepowder alone in porcelain crucibles and heating to 600°Cfor 30 min. After the borate had cooled and solidified, itwas removed from the crucible and crushed to 425-600 µm.

Measurement of the grade of the composition fractions

Following Magstream separation, the grade (i.e., the per-cent borate) of the composition fractions was determined.Two different methods were used to measure the grade:water displacement in a pycnometer bottle and imageanalysis. Henceforth, the grade measured using these meth-ods will be referred to as the pycnometer and IA grades,respectively.

The IA grade is determined by microscopic examina-tion of the particle sections. The total area of the two phas-es is measured with an image analyser. It is known that thearea grade is not stereologically biased and is identical tothe volumetric grade [6(p.22)].

In sample preparation, prevention of preferential set-tling (due to density differences between the particles) andpreferential orientation (due to density differences betweenthe phases in the locked particles) is important since this

affects the IA grade. It is important to generate random sec-tions. In these samples, the particles in each fraction shouldhave very similar densities and consequently, there shouldbe little segregation. But, regardless, precautions weretaken to ensure random mounting of the particles.

The sample preparation involved mixing 0.4 ml of thesample with an equal amount of a diluent material (425-600µm graphite particles) and placing the mixture at the bot-tom of a 32 mm mold. The diluent helps to support the sam-ple particles in space (and thus reduce preferential orienta-tion and the incidence of particles touching) and promotesrandom orientation [25]. Graphite was selected as the dilu-ent since it has a low density and a grey level similar to themounting medium resin when observed by backscatteredelectron imaging. The mounting medium was Epofix resin(Struers Inc.). The resin was prepared by mixing with thehardener and then centrifuging at 1600 rpm for 1 minute toremove any air bubbles. A small quantity of the resin (0.8ml) was added to the particles in the mold and mixed. Thesmall amount of resin helps inhibit preferential settling byrestricting the space in which the particles can move. Themold was then centrifuged at 1600 rpm for 5 minutes toremove any air bubbles that may have resulted from themixing. Afterwards, more resin was added to top off themold.

For the standard material, the pycnometer and IA gradeswere measured for each composition fraction. The twogrades should be close to the midpoint. The results areshown in Table I.

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Table I — Pycnometer and IA grades of the composition fractions of the standard material (density of borate,6.052 g/ml; glass, 2.502 g/ml)

Composition fraction Magstream Pycnometer Pycnometer IA

(vol.% borate) split-points (g/ml) density (g/ml) grade (vol.% borate) grade (vol.% borate)

-5 -2.680 2.522 0.6 0.4

5-15 2.680-3.035 2.805 8.5 9.8

15-25 3.035-3.390 3.176 19.0 20.1

25-35 3.390-3.745 3.517 28.6 31.7

35-45 3.745-4.100 3.850 38.0 40.0

45-55 4.100-4.455 4.232 48.7 49.7

55-65 4.455-4.810 4.532 57.2 58.9

65-75 4.810-5.165 4.865 66.6 68.3

75-85 5.165-5.520 5.257 77.6 78.0

85-95 5.520-5.875 5.647 88.6 87.9

+95 +5.875 6.265 106.0 98.1

For all the fractions, both the pycnometer and IA gradesfall in the composition fraction range and in most cases,they are close to the midpoint of the range and the differ-ences in grades are not significant.

The pycnometer grade of the +95 vol.% borate fractionwas greater than 100 vol.%. This can be explained by con-sidering the creation of the standard material. Although theglass is always in contact with the borate, there is a layer ofborate at the bottom of the crucible (the glass grains float inthe borate due to their lower density) that does not come incontact with the glass. The borate density was calculatedonly for borate that had been in close contact with glassgrains and where limited diffusion had occurred. All thehigh density borate reports to the +95 vol.% borate fractionwhere it belongs.

Use of the standard material

The standard material can be used to produce different lib-eration distributions by combining the different composi-tion fractions. These distributions can be used as a check onthe effectiveness of stereological correction proceduresprovided the other components of liberation analysis - sam-ple preparation and image processing - are performed cor-rectly. The known true liberation distribution can be com-pared with the corrected distribution. We have reported onthis comparison elsewhere [26]. In more general terms, thestandard material would enable the whole procedure (notjust stereological correction) to be tested, although thesource of error may be difficult to isolate. In this regard, astandard material is superior to using computer-simulatedparticles since it involves all the steps of a liberation analy-sis. Since the two phases of the standard material arestrongly bonded to each other, the standard material canalso be used to test liberation models. Most of these mod-els assume negligible breakage along grain boundaries.

CONCLUSIONS

A method was developed for the creation of a standardmaterial consisting of glass and lead borate. This standardmaterial is flexible and easy to use. Particles with granularand layered textures were created along with particlesexhibiting simple locking. The standard material can beused to test the steps in liberation analysis including stere-ological correction procedures.

REFERENCES

1. G.S. Hill. Applications of two-dimensional image analysis tomineral liberation studies. Ph.D. thesis, McGill University(1990).

2. G.S. Hill, N. Rowlands and J.A. Finch. Data correction intwo-dimensional liberation studies. Process Mineralogy VII,A. Vassiliou, D. Hausen and D. Carbon eds. (Warrendale,PA: The Metallurgical Society of AIME), 617-32 (1987).

3. C.L. Lin, J.D. Miller and J.A. Herbst. Solutions to the transformation equation for volumetric grade distribution fromlinear and/or areal grade distributions. Powder Technol., 50,55-63 (1989).

4. C.L. Schneider, C.L. Lin, R.P. King and J.D. Miller. Improvedtransformation technique for the prediction of liberation bya random fracture model. Powder Technol., 67, 103-11 (1991).

5. G. Barbery. Mineral liberation: measurements, simulationand practical use in mineral processing (Quebec: Les EditionsGB), 351p. (1991).

6. S.L. Gay. Liberation modelling using particle sections. Ph.D.thesis, University of Queensland (1996).

7. D. Lin. A standard material for liberation analyses and exam-ination of the robustness of stereological correction procedures.Ph.D. thesis, McGill University (1997).

8. P.S.B. Stewart and M.P. Jones. Determining the amounts andthe compositions of composite (middling) particles. Proc.12th Int. Mineral Process. Congress, Sao Paulo, Meeting B,paper 4 (1977).

9. J. Bole, C.L. Lin and J.D. Miller. Experimental verification ofthe PARGEN simulator for liberation analysis. Int. J. MineralProcess., 37, 209-21 (1993).

10. J.D. Miller and C.L. Lin. Treatment of polished section datafor detailed liberation analysis. Int. J. Mineral Process., 22,41-58 (1988).

11. P.S. Bagga. Simulation of the liberation phenomena in mineralsystems. Ph.D. thesis, Pennsylvania State University (1983).

12. L.C. Woollacott and M. Valenta. Use of synthetic ore particlesto test a transformation function in liberation analysis. MineralsEngineering, 9(10), 1017-32 (1996).

13. D. Lin. The production of a standard material for liberationanalysis. M.Eng. thesis, McGill University (1991).

14. D. Lin, J.A. Finch, C.O. Gomez and N. Rowlands. An artificialstandard material for liberation analysis. Powder Technol.,72, 131-8 (1992).

15. M.P. Jones. Applied mineralogy (Oxford: Graham and TrotmanLtd.), 260 p. (1987).

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16. M.S. Walker, A.L. Devernoe, R.W. Stuart, W.S. Urbanskiand U. Andres. A new method for the commercial separationof particles of differing densities using magnetic fluids - theMC process. Proc. XV Int. Mineral Process. Congress, Cannes,307-16 (1985).

17. M.S. Walker, A.L. Devernoe and W.S. Urbanski. Separationof non-magnetic minerals using magnetic fluids in a flow-through MHS rotor. Miner. Metall. Process., 7(4), 209-14(1990).

18. M.S. Walker, A.L. Devernoe, W.S. Urbanski and G.R. Morrow.Mainly "gravity" separations using magnetic fluids underrotation. Proc. XVII Int. Mineral Process. Congress, Dresden,105-16 (1991).

19. M.S. Walker and A.L. Devernoe. Mineral separations usingrotating magnetic fluids. Int. J. Mineral Process., 31, 195-216 (1991).

20. R.C. Bunge and D.W. Fuerstenau. Mineral separations with amagnetogravimetric separator. SME pre-print 90-192, SaltLake City (1990).

21. R.C. Bunge and D.W. Fuerstenau. Separation characteristicsof a magnetogravimetric separator. Proc. XVII Int. MineralProcess. Congress, Dresden, 31-42 (1991).

22. R.C. Bunge and D.W. Fuerstenau. Magnetogravimetric sep-aration in a rotational device. Mag. Electr. Sep., 7(3), 163-84(1996).

23. J. Svoboda. A contribution to the theory of separation in arotating ferrofluid. Minerals Engineering, 9(7), 743-52 (1996).

24. H.H. Hess. Notes on operation of Frantz isodynamic magneticseparator. S.G. Frantz Co.

25. C.O. Gomez, N. Rowlands, J.A. Finch and J.-F. Wilhelmy.A specimen preparation procedure for automated imageanalysis. Process Mineralogy VIII, D. Carson and A. Vassiliou,eds. (TMS-AIME), 359-67 (1988).

26. D. Lin, R. Lastra and J.A. Finch. Comparison of stereologicalcorrection procedures for liberation measurements using astandard material. submitted to Trans. Instn Min. Metall., Jan.1999.

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