3170 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
the analysis was GXMAP. The measurement parameters
included an X-ray step size of 6 µm, horizontal field with of
700 µm, image resolution of 700 pixels and BSE grey-scale
calibration on quartz (119 BSE).
Stochastic modeling of particle descriptor vectors for the
computation of bivariate Tromp functions
A particle system, observed by image measurements and
extracted by particle-based segmentation, can be effectively
described using descriptor vectors. Particularly, in this
study, the application of MLA images offers planar sections
of a three-dimensional particle system. Here, each particle
is represented by a 2-dimensional descriptor vector derived
from the particle-wise segmentation of 2D images, contain-
ing the particle’s area-equivalent diameter ()d
A
and aspect
ratio (∆ ).These descriptors are adapted from Wilhelm
et al. (2023). In order to evaluate the separation behav-
ior of particle systems resulting from froth flotation tests,
the entirety of particle descriptor vectors associated with
particles of the feed material (F) and of the complete con-
centrate (C) is modeled by mass-weighted bivariate prob-
ability densities f
m
F and ,f
m
C respectively. In the present
study, image measurements of each of the three concen-
trates (C1, C2 and C3) and tailings (T) are available. Thus,
allowing the computation of the number-weighted prob-
ability density f
n
C and f
n
T of descriptor vectors associated
with particles in the concentrate and tailings, respectively,
before computing f
m
F .More precisely, the probability den-
sities f
n
C1 ,f
n
C2 ,f
n
C3 and f
n
T were computed from image
measurements using kernel density estimators, as out-
lined by Scott (2015). Then, as explained in Wilhelm et
al. (2023), these probability densities were transformed to
mass-weighted probability densities ,,,f f f f
m
C1
m
C2
m
C3
m
T and
the probability density f
m
C was computed. Afterwards, the
probability density f
m
F is determined as a convex combina-
tion of f
m
C and f
m
T ,as discussed in Buchmann et al. (2018)
and Wilhelm et al. (2023). This enables the computation of
the bivariate Tromp function T as the ratio of f
m
C and f
m
F
multiplied with the mass ratio of particles observed in the
concentrate and feed, where the value ,∆h T d
A ^indicates
the probability that a particle with descriptor vector ,∆h d
A ^
is separated into the concentrate, as explained in Wilhelm
et al. (2023). In the present paper, T is determined for
three different froth flotation tests involving slag particles.
RESULTS AND DISCUSSION
Composition and Characteristics of Slag Particles
The slag contains four main phases, which include LiAlO2
as the most prominent phase (7.2%), eucryptite (13.5%),
the gangue phase gehlenite (32.6%) and AlMn-spinel
(29.5%). LiAlO2 contains additionally a minor amount of
silicon and gehlenite traces of manganese. Different spinel
types could be already observed from Wittowski et al in
similar slag samples (Wittkowski et al. 2021). In the pres-
ent slag, the majority the spinel type contains 3–12 wt%
Mn. However, Mn-rich spinels with 27–47 wt% Mn were
also detected. Finely intergrown mixed phases account for
15.6% of the area measured, containing Mn (1728 wt%),
Si (20–28 wt%), Al (13–18 wt%) and Ca (0–3 wt%). Thus,
these phases can include mixing phases of eucryptite, AlMn
spinel-types, LiMnSiO4 as well as inclusions of gehlenite
(Table 1).
The evaluation of the MLA images of slag particles in
the feed material show that grains of LiAlO2 are associated
with the gangue phase gehlenite (Figure 3). In total 1.7 %
of all particles contain fully liberated LiAlO2 with an area of
100 %,although these particles represent in total 26 %of
the entire LiAlO2 area in the sample. When defining a lib-
erated target phase consisting of 80 area% of each particle,
LiAlO2 appears to be 50 %liberated. Roughly 41 %of the
LiAlO2 containing particles are present as middlings, which
is defined at the target phase consisting of 30–80 area% of
each particle. Furthermore, 17 %of LiAlO2 occurs within
the locked class, which is defined as the phase accounting
for only 0–30 area% of each particle. 70 %of the measured
particles don’t contain any LiAlO2. LiAlO2 occurs as idio-
morphic grains and is mainly accompanied in middlings
with gehlenite, which can create challenges for an efficient
separation, as the aim is to separation the valuable LiAlO2
from gehlenite. The second most common accompanying
Table 1. Mineral phase composition of the present slag. Shown is the weight fraction of each phase determined from the
area% from MLA information and the sample weight. Besides the four main phases and a mixed phase, other components
with 1.6 wt% include the phases like glaucochroite (CaMnSiO
4 )and LiMnSiO
4 ,which are also known phases during slag
formation in the present slag system Li
2 O-CaO-SiO
2 -Al
2 O
3 -MnO
x (Wittkowski et al. 2021)
Name
Lithium
Aluminate Eucryptite Gehlenite
AlMn-Spinel
Type Mixed Phases Others
Formula/
consisting elements
LiAlO2 LiAl[SiO4] Ca2Al(AlSiO7) Al,Mn -oxide Si, Mn, Al, Ca
-oxide
varying (Si, Mn,
Al, Ca, Ti, Cr)
Area %7.2 13.5 32.6 29.5 15.6 1.6
the analysis was GXMAP. The measurement parameters
included an X-ray step size of 6 µm, horizontal field with of
700 µm, image resolution of 700 pixels and BSE grey-scale
calibration on quartz (119 BSE).
Stochastic modeling of particle descriptor vectors for the
computation of bivariate Tromp functions
A particle system, observed by image measurements and
extracted by particle-based segmentation, can be effectively
described using descriptor vectors. Particularly, in this
study, the application of MLA images offers planar sections
of a three-dimensional particle system. Here, each particle
is represented by a 2-dimensional descriptor vector derived
from the particle-wise segmentation of 2D images, contain-
ing the particle’s area-equivalent diameter ()d
A
and aspect
ratio (∆ ).These descriptors are adapted from Wilhelm
et al. (2023). In order to evaluate the separation behav-
ior of particle systems resulting from froth flotation tests,
the entirety of particle descriptor vectors associated with
particles of the feed material (F) and of the complete con-
centrate (C) is modeled by mass-weighted bivariate prob-
ability densities f
m
F and ,f
m
C respectively. In the present
study, image measurements of each of the three concen-
trates (C1, C2 and C3) and tailings (T) are available. Thus,
allowing the computation of the number-weighted prob-
ability density f
n
C and f
n
T of descriptor vectors associated
with particles in the concentrate and tailings, respectively,
before computing f
m
F .More precisely, the probability den-
sities f
n
C1 ,f
n
C2 ,f
n
C3 and f
n
T were computed from image
measurements using kernel density estimators, as out-
lined by Scott (2015). Then, as explained in Wilhelm et
al. (2023), these probability densities were transformed to
mass-weighted probability densities ,,,f f f f
m
C1
m
C2
m
C3
m
T and
the probability density f
m
C was computed. Afterwards, the
probability density f
m
F is determined as a convex combina-
tion of f
m
C and f
m
T ,as discussed in Buchmann et al. (2018)
and Wilhelm et al. (2023). This enables the computation of
the bivariate Tromp function T as the ratio of f
m
C and f
m
F
multiplied with the mass ratio of particles observed in the
concentrate and feed, where the value ,∆h T d
A ^indicates
the probability that a particle with descriptor vector ,∆h d
A ^
is separated into the concentrate, as explained in Wilhelm
et al. (2023). In the present paper, T is determined for
three different froth flotation tests involving slag particles.
RESULTS AND DISCUSSION
Composition and Characteristics of Slag Particles
The slag contains four main phases, which include LiAlO2
as the most prominent phase (7.2%), eucryptite (13.5%),
the gangue phase gehlenite (32.6%) and AlMn-spinel
(29.5%). LiAlO2 contains additionally a minor amount of
silicon and gehlenite traces of manganese. Different spinel
types could be already observed from Wittowski et al in
similar slag samples (Wittkowski et al. 2021). In the pres-
ent slag, the majority the spinel type contains 3–12 wt%
Mn. However, Mn-rich spinels with 27–47 wt% Mn were
also detected. Finely intergrown mixed phases account for
15.6% of the area measured, containing Mn (1728 wt%),
Si (20–28 wt%), Al (13–18 wt%) and Ca (0–3 wt%). Thus,
these phases can include mixing phases of eucryptite, AlMn
spinel-types, LiMnSiO4 as well as inclusions of gehlenite
(Table 1).
The evaluation of the MLA images of slag particles in
the feed material show that grains of LiAlO2 are associated
with the gangue phase gehlenite (Figure 3). In total 1.7 %
of all particles contain fully liberated LiAlO2 with an area of
100 %,although these particles represent in total 26 %of
the entire LiAlO2 area in the sample. When defining a lib-
erated target phase consisting of 80 area% of each particle,
LiAlO2 appears to be 50 %liberated. Roughly 41 %of the
LiAlO2 containing particles are present as middlings, which
is defined at the target phase consisting of 30–80 area% of
each particle. Furthermore, 17 %of LiAlO2 occurs within
the locked class, which is defined as the phase accounting
for only 0–30 area% of each particle. 70 %of the measured
particles don’t contain any LiAlO2. LiAlO2 occurs as idio-
morphic grains and is mainly accompanied in middlings
with gehlenite, which can create challenges for an efficient
separation, as the aim is to separation the valuable LiAlO2
from gehlenite. The second most common accompanying
Table 1. Mineral phase composition of the present slag. Shown is the weight fraction of each phase determined from the
area% from MLA information and the sample weight. Besides the four main phases and a mixed phase, other components
with 1.6 wt% include the phases like glaucochroite (CaMnSiO
4 )and LiMnSiO
4 ,which are also known phases during slag
formation in the present slag system Li
2 O-CaO-SiO
2 -Al
2 O
3 -MnO
x (Wittkowski et al. 2021)
Name
Lithium
Aluminate Eucryptite Gehlenite
AlMn-Spinel
Type Mixed Phases Others
Formula/
consisting elements
LiAlO2 LiAl[SiO4] Ca2Al(AlSiO7) Al,Mn -oxide Si, Mn, Al, Ca
-oxide
varying (Si, Mn,
Al, Ca, Ti, Cr)
Area %7.2 13.5 32.6 29.5 15.6 1.6