Journal of Minerals & Materials Characterization & Engineering, Vol. 1, No.1, pp31-37, 2002
Printed in the USA. All rights reserved
31
A COMPARISON OF LIBERATION DETERMINATIONS BY PARTICLE AREA PERCENTAGE AND
EXPOSED PARTICLE PERIMETER PERCENTAGE IN A FLOTATION CONCENTRATOR
R. Lastra
Natural Resources Canada, Mining and Mineral Sciences Laboratories,
555 Booth St., Ottawa, ON, K1A 0G1, Canada.
FAX [phone], e-mail: [e-mail]
ABSTRACT
To simplify programming, image analyzers commonly
measure either linear intercepts or the areas of particles and
grains to determine liberation based on polished section
mounts. However, the concentration of minerals by
flotation is based on reagents that interact with the exposed
surfaces of the minerals. Thus, it is often perceived that
image analyzers should measure the perimeter of the
mineral of interest in the ore particles. A comparative
liberation study of thirteen samples collected from a
flotation plant processing a complex base metal sulfide ore
showed that the liberation of the ore minerals determined by
area measurements is very similar to the liberation
determined by the exposed perimeters. The liberation
determined by exposed perimeters is more appropriate only
for those cases where the mineral texture is so complex that
it is retained in the small particles generated in conventional
grinding operations.
INTRODUCTION
The main objective of mineral processing is to
concentrate the valuable minerals and to reject the
unwanted or gangue minerals. Mineral concentration
requires particles in which the mineral species are free
from each other. For this, crushing and grinding steps are
performed before the actual concentration is done.
However, overgrinding is unwanted because it increases
costs and may reduce the efficiency of the selection
mechanisms of concentration.
Liberation studies are aimed at determining the amount
of a mineral of interest (MOI) that is in particles
composed of mostly that mineral (liberated) and in
particles with various other proportions of the MOI. The
first step in a liberation analysis is usually size
fractionation. Preparation of polished sections is done on
size fractions to reduce complications in making
representative cross sections of particles with large size
differences. The standard procedure for measuring
liberation is by the microscopic examination of polished
sections. Liberation analysis is most efficiently
performed by automated image analyzers. Image
analyzers commonly measure either linear intercepts (e.g.,
Rosiwal 1898, Jones & Horton 1978, Jones 1983, 1985,
King & Schneider 1998) or the areas of particles and grains
to determine liberation (e.g., Delesse 1848, Petruk 1988,
Lastra et al. 1998). Measurement of linear intercepts yields
results with a more stereological bias than measurement of
areas (Leigh et al. 1996). Thus, it is generally accepted that
measurement of areas is better than the measurement of
linear intercepts. In contrast, the concentration of minerals
by flotation is based on reagents that interact with the
exposed surfaces of the minerals. Thus, it is often perceived
that image analyzers should measure the proportion of
exposed perimeter of the mineral of interest in the ore
particles.
The objective of the present report is to compare the
liberation determined by particle area percentage against
the liberation determined by exposed particle percentage
to ascertain whether the latter serves as a better liberation
parameter, especially for concentration by flotation.
SAMPLES AND METHODOLOGY
Thirteen samples from a copper flotation circuit in
Ontario were obtained. The concentrator processes ~ 3000
tons/day of a copper-zinc ore. The ore is a volcanogenic
base metal sulfide averaging ~2.7% Cu and ~3.6% Zn. The
ore consists mainly of siliceous gangue, pyrite, sphalerite
and chalcopyrite. The samples were composites of one day
of normal operation. Table 1 lists the sampled streams and
Figure 1 gives the flowsheet of the copper flotation circuit.
The samples were wet screened to produce a +53 µm
fraction and a –53µm product. The –53 µm product was
size fractionated with a cyclosizer. A size fraction
–53+13µm of each sample was prepared by blending the
products from Cones 1 to 5 inclusively. The –12µm
fraction represented the product passing Cone 5. Because of
its substantial volume and wide particle size distribution, the
+53 µm fraction of both the primary cyclone overflow
(PCO) and the primary rougher tail (PRT) were further
sieved to produce a +75 µm fraction.

R. Lastra Vol. 1, No. 1
32
Figure 1. Flowsheet of the copper concentrator circuit
and sampling points.
Table 1. List of studied samples.
Sample description Abbreviation
Primary Cyclone Overflow PCO
Primary Rougher Concentrate PRC
Primary Rougher Tail PRT
Secondary Rougher Concentrate SRC
Secondary Scavenger Concentrate –
Pans On
SSC ON
Secondary Scavenger Concentrate –
Pans Off
SSC OFF
Secondary Scavenger Tail SST
Copper Cleaner 1 Feed CCF
Copper Cleaner 1 Tail CCT1
Copper Cleaner 3 Concentrate CCC
Combined Copper Middlings CCM
Copper Cleaner 2 Tail CCT2
Secondary Cyclone Overflow SCO
One polished section of each size fraction was prepared
making a total of 41 polished sections. The polished
sections were briefly studied by reflected light optical
microscopy and scanning electron microscopy. It was
found that the minerals in these samples are quartz, chlorite,
amphibole, pyrite, pyrrhotite, sphalerite, chalcopyrite and
galena, together with traces of arsenopyrite, cassiterite,
enargite, zircon, monazite, albite, epidote, muscovite,
sphene, calcite, ankerite, siderite, magnetite and an unnamed
Ag-Se-Bi mineral. In addition, there are secondary copper
minerals, such as bornite, covellite and digenite. However,
these secondary copper minerals occur in very low
proportions in comparison to chalcopyrite, which is the
dominant copper mineral. The most bornite-rich sample is
the copper cleaner concentrate (CCC), and even in this
sample, bornite occurs in a very low proportion with respect
to chalcopyrite.
The polished sections were studied using a Kontron
IBAS image analyzer interfaced to a JEOL 733 electron
microprobe (Petruk 1988). The image analysis was done
using backscattered electron (BSE) images. With polished
sections, the grey level of BSE images is a function of the
average atomic number of the mineral grains. The electron
microprobe is equipped with a beam stabilizer that, every
second, checks and maintains a constant beam current.
Thus, during all the run, the grey level range of each mineral
is maintained constant. The operating conditions for the
electron microprobe were 20kV of accelerating voltage and
15nA of beam current. Under those conditions it was
possible to use the grey levels of the BSE image to classify
the main ore minerals of interest:
• Chalcopyrite (cp) group: Mainly chalcopyrite plus
traces of covellite and digenite.
• Sphalerite (sp) group: Mainly sphalerite plus traces
of bornite and enargite.
• Pyrite (py) group: Mainly pyrite plus lower
proportions of pyrrhotite.
The image analysis study of the other minerals was
limited to two general groups:
• Gangue: Mainly quartz. Minor proportions of
chlorite and amphibole. Lesser proportions of
epidote, muscovite, sphene, calcite, and ankerite.
Traces of siderite and magnetite.
• Heavy minerals: Mainly galena. Minor proportions
of aresnopyrite. Lesser proportions of cassiterite.
Trace amounts of enargite, zircon, monazite and an
unnamed Ag-Se-Bi mineral.
A special image analysis program was made to
determine mineral quantities, liberation based on area
measurements and liberation based on perimeter
measurements. The liberation measurements were done for
the three groups of the MOI; i.e., mainly chalcopyrite,
sphalerite and pyrite. At this point some definitions are
introduced to simplify differentiation between the
measurements based on areas and measurements based on
perimeters.
• Liberated MOI: Mineral that occupies at least 95%
of the cross sectional area of a host particle.
• Exposed MOI: Mineral that occupies at least 95%
of a host particle perimeter in cross section.
• Locked MOI: Mineral that occupies less than 95%
of the cross sectional area of a host particle.
• Partly exposed MOI: Mineral that occupies less
than 95% of a host particle perimeter in cross
section.
S. BALL MILL
PRIMARYPCO
PRT
SCO
SSC OFFSSC ON
CCFCCT1
CCC
CCM
CCT2
SST
SRCPRC
SCAV(-)SCAV(+)2NDARY
Cu CL # 1
Cu CL # 2
Cu CL # 3

Vol. 1, No. 1 Comparison Of Liberation Determinations by Particle Area and Perimeter Percentage 33
The image analysis program consisted mainly of two
sub-routines.
Sub-routine Based on Area
• Measurement of the cross sectional area of the
particle and the cross sectional area of the MOI in
the particle.
• Determination of the area percent of the MOI in the
particle area.
• Sort the data into liberation classes. Percent of the
MOI in the sample in particles with discrete MOI
compositions: -5, +5-25, +25-35, +35-45, +45-55,
+55-65, +65-75, +75-85, +85-95 and +95%.
Sub-routine Based on Perimeter
• Measurement of the particle perimeter and the
perimeter of the MOI:
• Determination of the coincidence perimeter of the MOI
and the particle perimeter.
• Determination of the perimeter percent of the MOI in
the particle perimeter.
• Measurement of the cross section area of the MOI in
the particle.
• Sort the data into exposure classes. Percent of the MOI
in the sample in particles with discrete perimeter
exposure of MOI: -5, +5-25, +25-35, +35-45, +45-55,
+55-65, +65-75, +75-85, +85-95 and +95%.
Several thousands of particles in each polished section
were analyzed. The image analysis of a polished section
required an average of 30 minutes.
A report of the data for each size fraction of each of the
thirteen samples would be very lengthy. For simplification
purposes, therefore, the data obtained for each size fraction
were combined into data for the original sample, on the
basis of the mineral quantity in each size fraction and the
relative weight percentage of the sieved fractions. In
addition, several liberation classes were combined to make
broader classes: +95%, +75-95% and +0.1-75%. The +95%
class corresponds to liberated MOI particles. Particles with
decreasing area percent of the MOI will be simply referred
to as the locked class +75-95% and the locked class +0.1-
75%. Similarly, several exposure classes were combined to
make broader classes. The +95% class of host particle
perimeter corresponds to an exposed MOI. Particles with
decreasing perimeter percent of the MOI will be simply
referred to as the partly exposed class +75-95% and the
partly exposed class +0.1-75%.
RESULTS
Table 2 gives the weight percentage of each size fraction
of the samples and the Cu and Zn assays. Table 3 gives the
determined mineral quantities [wt. %] in each of the
samples.
Table 2. Weight % retained in each size fraction and Cu
and Zn assays.
Sample Size
fraction
[µm]
wt % Assay
%Cu %Zn
PCO +75 40.7 1.7 2.5
-75+53 5.6 1.9 2.6
-53+12 25.8 4.8 6.1
-12 27.9 2.4 3.2
PRC +53 5.8 25.5 1.3
-53+13 40.4 28.2 2.4
-13 53.8 21.0 3.7
PRT +75 44.6 1.6 2.5
-75+53 4.9 1.9 2.8
-53+12 24.3 2.3 6.3
-12 26.2 0.6 3.1
SRC +53 5.8 29.1 1.2
-53+14 48.7 25.4 3.7
-14 45.5 17.4 5.8
SSC ON +53 12.0 17.5 4.9
-53+13 43.6 4.9 15.1
-13 44.4 3.9 24.0
SSC OFF +53 15.0 7.2 4.7
-53+14 53.3 2.7 14.8
-13.8 31.7 2.5 16.9
SST +53 22.1 0.2 1.6
-53+12 36.5 0.1 5.7
-12 41.4 0.2 3.1
CCF +53 10.7 26.5 1.7
-53+13 46.5 22.1 4.9
-13 42.8 17.9 7.0
CCT1 +53 10 18.6 3.1
-53+11 47 8.1 12.9
-11 43 5.2 11.9
CCC +53 3.0 32.3 1.0
-53+13 49.2 28.0 2.5
-13 47.8 24.5 4.7
CCM +53 9.7 17.1 3.3
-53+13 39.1 5.3 13.7
-13 51.2 4.5 12.5
CCT2 +53 14.2 28.1 1.9
-53+13 52.1 19.2 5.6
-13 33.7 13.9 8.6
SCO +53 23.0 1.2 1.9
-53+12 38.6 2.7 6.1
-12 38.4 1.5 4.1

R. Lastra Vol. 1, No. 1
34
Table 3. Mineral quantities [wt %] in the samples.
cp sp py hea-
vies
sili-
cates
total
PCO 8.3 6.1 14.1 0.3 71.2 100
PRC 73.8 5.1 8.1 1.7 11.3 100
PRT 5.2 6.7 15.8 0.3 72.0 100
SRC 62.6 7.6 14.8 1.8 13.2 100
SSC
ON
18.3 30.0 35.5 3.1 13.1 100
SSC
OFF
10.0 23.5 34.0 1.0 31.5 100
SST 0.4 6.3 16.9 0.3 76.1 100
CCF 63.0 9.2 17.1 1.2 9.5 100
CCT1 23.9 19.4 37.0 1.7 18.0 100
CCC 79.1 5.9 10.2 0.6 4.2 100
CCM 17.6 20.4 37.0 1.9 23.1 100
CCT2 52.4 10.3 24.5 1.7 11.1 100
SCO 5.6 7.4 24.6 1.5 60.9 100
Figure 2 (top) compares the percentage of the total
chalcopyrite in each sample that is liberated relative to that
which is exposed. Figure 2 (middle) compares the liberated
and exposed sphalerite in each sample. Figure 2 (bottom)
compares the liberated and exposed pyrite. In general, the
difference between the liberated and exposed MOI is small.
There are only two cases where the difference is larger than
5%. For chalcopyrite in the copper cleaner tail 1 (CCT1),
the difference is ~6%. For the sphalerite in the scavenger
rougher concentrate (SRC) the difference is 7%. These
differences are undoubtedly within the total measurement
error of the analysis. Therefore, for essentially mono-
mineral particles, the measurement based on the perimeter
(exposed MOI) gives nearly the same result as the
measurement based on the cross sectional area (liberated
MOI).
Figure 3 gives, in the black bars, the percentage of the
MOI in the sample that is in the locked class +75-95%. The
white bars give the percentage of the MOI in the sample in
the partly exposed class +75-95%. There are only two cases
where the difference between the locked and partly exposed
values is equal to or larger than 3%. The chalcopyrite in the
secondary scavenger tail (SST) exhibits a difference of ~3%
between the locked and partly exposed values. Sphalerite in
the same sample (SST) exhibits a difference of ~4%.
Therefore, measurements based on perimeters or based on
areas also give nearly the same results for particles that have
a substantial proportion of the MOI (class +75-95%).
Figure 4 compares the class +0.1-55% of locked and
partly exposed particles. There is only one instance where
the difference between the locked and partly exposed values
is larger than 5%. For the sample of the secondary rougher
concentrate (SRC), sphalerite exhibits a difference of 6%
between the locked and partly exposed values . Therefore,
measurements based on perimeters or based on areas also
give nearly the same results for particles that have a low
proportion of the MOI (class +0.1-75%).
Figure 2. Top: Comparison of amount of
chalcopyrite in the samples occurring as liberated grains
relative to that which is exposed. Middle: Liberated and
exposed sphalerite. Bottom: Liberated and exposed
pyrite. Black bars: liberated. White bars: exposed.
Liberated vs. exposed chalcopyrite
50
55
60
65
70
75
80
85
90
95
100
PCO PRC
PRT
SRC
SSC ON
SSC OFF
SST CCF
CCT1
CCC
CCM
CCT2
SCO
% chalcopyrite
% liberated
% exposed
Liberated vs. exposed sphalerite
50
55
60
65
70
75
80
85
90
95
100
PCO
PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% sphalerite
Liberated vs. exposed pyrite
50
55
60
65
70
75
80
85
90
95
100
PCO
PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
Sample
% pyrite

Vol. 1, No. 1 Comparison Of Liberation Determinations by Particle Area and Perimeter Percentage 35
Figure 3. Locked (black bars) and partly exposed
(white bars) values for the class +75-95%.
Figure 4. Locked (black bars) and partly exposed
(white bars) values for the class +0.1-75%.
chalcopyrite: class +75-95%
0
2
4
6
8
10
12
14
16
18
PCO PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% chalcopyrite
% locked
% partly liberated
sphalerite: class +75-95%
0
2
4
6
8
10
12
14
16
18
PCO
PRC PRT SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% sphalerite
pyrite: class +75-95%
0
2
4
6
8
10
12
14
16
18
PCO
PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC CCM
CCT2
SCO
% pyrite
chalcopyrite: class +0.1-75%
0
5
10
15
20
25
30
35
PCO
PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% chalcopyrite
locked
partly exposed
sphalerite: class +0.1-75%
0
5
10
15
20
25
30
35
PCO PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% sphalerite
pyrite: class +0.1-75%
0
5
10
15
20
25
30
35
PCO PRC
PRT
SRC
SSC ON
SSC OFF
SST
CCF
CCT1
CCC
CCM
CCT2
SCO
% pyrite

R. Lastra Vol. 1, No. 1
36
DISCUSSION
For hypothetical particles composed of only two phases,
it would be easy to visualize phase textures that would give
different results if they were analyzed with a liberation
routine based on areas or one based on exposed perimeters.
One example would be for particles like those illustrated in
the top row of Figure 5. It is clear that these particles have a
high percentage their area occupied by the black phase. In
contrast, the exposed perimeter of the black phase is zero for
particle 2 and is low for particles 1 and 3. These
illustrations can be applied to multi-mineral particles by
considering the black phase as the mineral of interest (MOI)
and the white phase as all the other minerals combined.
Nevertheless, for the studied flotation samples, the
results show that there are very small differences between
measurements based on areas and those based on
perimeters. The percentage of the MOI in the sample that is
liberated is similar to the percentage of the MOI in the
sample that is exposed. It could be argued that for near
mono-mineral particles, the possibility of discrepancy
between liberated and exposed particles is very low, because
the particles have a very high proportion of the MOI.
However, the results of this paper also show that the amount
of the MOI in the sample that is locked (class +75-95%) is
very similar to the percentage of the MOI in the sample that
is partly exposed (class +75-95%). In addition, similar
results were also obtained for the class +0.1-75%. Thus,
regardless of the proportion of the MOI in the particles, the
results based on area measurements are similar to those
based on perimeter measurements. This could be explained
by considering particles with simple mineral textures, such
as those illustrated in the lower row of Figure 5. For these
particles, the proportion of the particle area that is made of
the MOI is similar to the proportion of the particle perimeter
that coincides with the perimeter of the MOI.
The studied samples originated from a flotation plant
processing a volcanogenic base metal sulfide ore.
Commonly this kind of ore displays very complex textures
when polished sections of unground fragments are
observed. In spite of that, the particles of the ground ore
display simple textures (e.g., Figure 6).
It is inferred that liberations determined by exposed
perimeters may be more appropriate than liberations based
on areas only if the texture of the ore is so extremely
complex as to be retained in the small particles (~147 to
37µm) generated in the grinding operations. Thus, for most
mineral processing situations, liberation measurements
based on areas are appropriate, although is not completely
impossible to find situations where a complex texture is
retained in the small particles. An example would be ores
with significant proportion of secondary copper minerals
where small particles of chalcopyrite often have rims of
secondary copper minerals, giving a texture similar to that
of particle 1 in Figure 5. A cursory examination of the
polished sections of ground samples would be sufficient to
determine if measurements based on perimeters are better
suited than measurements based on areas. Obviously, the
image analyzer must be versatile enough to allow liberation
measurements to be done based on either areas or
perimeters.
As a closing remark, it is noted that no stereological
corrections were done to adjust the image analysis data. It
was desired to avoid additional data handling that could
obscure the differences between the measurements based on
areas and those based on perimeters. There are several
stereological corrections that can be applied for liberation
measurements based on areas, although it is not certain that
the same stereological corrections would be valid for
determinations based on perimeters.
Figure 5. Example of binary particles with a complex
texture (top row) and a simple texture (bottom row).
Figure 6. Particles with a simple texture in a BSE
image of a typical area from a polished section of the
unsized PCO sample. Abbreviations: cp = chalcopyrite,
sp = sphalerite, py = pyrite, po = pyrrhotite, qtz = quartz.

Vol. 1, No. 1 Comparison Of Liberation Determinations by Particle Area and Perimeter Percentage 37
CONCLUSION
This comparative liberation study of thirteen samples
collected from a flotation plant processing complex base
metal sulfides showed that the liberation of chalcopyrite,
sphalerite and pyrite determined by area measurements is
very similar to the liberation determined by the exposed
perimeters. It is inferred that liberation determined by
exposed perimeters may be more appropriate than liberation
based on areas only for the case where the texture of the ore
is so extremely complex as to be retained in the small
particles (~147 to 37µm) generated in the grinding
operations.
ACKNOWLEDGMENTS
This work was part of a CANMET contract, under the
scientific authority of R. Lastra, awarded to the Research
Productivity Council (RPC), Fredericton, New Brunswick.
The work of Mr. Lech Lewczuk (formerly with RPC) is
gratefully acknowledged.
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