2150 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Computation Approach
All calculations were performed by the CASTEP module
in materials studio software based on Density Functional
Theory (DFT). The exchange–correlation functional
applied was the Generalized Gradient Approach (GGA)
of PBE[28–31]. Only the valence electrons (Cu 3d9 4s1, Zn
3d10 4s2, S 3s2 3p4, O S 2s2 2p4, C 2s2 2p2 and H 1s1)
were considered using ultrasoft pseudo-potentials [32,33]
and a plane wave cut-off energy of 350 eV after testing.
Monkhorst-Pack k-point sampling density for sphalerite
(110) surface and Cu-activated sphalerite (110) surface was
6×6×6. The self-consistent field (SCF) convergence toler-
ance was set to 1.0*10–6 eV ·atom–1.
Sphalerite (cubic symmetry) with the space group Pa3
and cell parameter of 5.415 Å was used in our calcula-
tions[34]. Based on the previous study[35,13], the Sphalerite
(110) was considered their most stable plane. Therefore,
after testing the slab thickness, a (2×4×1) ZnS (110) surface
with 10 atomic layers and a 15 Å vacuum layer was con-
structed. The calculated lattice constant for bulk sphalerite
was 5.441 Å, which was close to the experimental value of
5.414 Å [34].
The Ethyl xanthane was optimized at the gamma point
in a 15×15×15 Å3 cubic box. The equilibrium geometries
of the sphalerite (110) surface and Cu-activated surface
are illustrated in Figure 2(a)–(d), respectively. Considering
periodic boundary conditions and charge species in the cal-
culation, Na+ was used in the adsorption model as a coun-
ter ion [36].
The xanthane was initially put above the metal site on
the sphalerite (110) surface (a), Cu-activated surface for
progressive optimization. The adsorption energy (Eads) was
obtained using the equation (1) below:
E Eadsorbates/surface E Eadsorbates
ads surface =--(1)
where, Eads is the adsorption energy, Eadsorbates/surface is the
computed energy of the Xanthane adsorbed on sphalerite
(1 1 0) surface (a), Cu activat surface, Esurface is the energy
of the Sphalerite (110) surface (a), Cu activat surface, and
Eadsorbates is the energy of the xanthane.
The d-band center in this study was calculated accord-
ing to the following equation.[37]
n
n
d
d fd =
3
3
f
f
-3
-3
^fhfd
^fhd #
#
(2)
where εdv is the d band center and is the energy ε is the
density of states.
Micro-Flotation Experiments
Prepared samples (5.0 g) and 40 mL distilled water were
added into a 40 mL flotation cell (XFG-II, Company
name?). The pH of the flotation pulp was adjusted by
NaOH or HCl solutions. Activator CuSO4 (1×10–4 mol/L)
was added and conditioned for 3 min, then the collector
was added and conditioned for 3 min, followed by adding
frother (MIBC) for a further 2 min before the air was intro-
duced into the pulp. An impeller speed of 1850 rpm was
maintained throughout the flotation test. The froth prod-
uct and tailing samples were collected, dried, and weighed.
Adsorption Experiments
50 mL pulp samples of sphalerite (5.0 g) or Cu-activated
sphalerite (5.0 g )were prepared by mixing the materials
with 0.5 g xanthate solutions and distilled water. Using a
solution of 0.01M NaOH and 0.01M HCl, the pulp was
adjusted to the required pH values. The samples were then
kept at the predetermined temperature for 12 hours in a
shaker bath with constant temperature. After centrifuging,
the remaining concentration of xanthate in the superna-
tant was quantified using an ultraviolet spectrophotometer.
(Cary 100 UV-Vis) By employing the initial concentration
and residual concentration in equation (3), we can ascer-
tain the quantity of xanthate adsorbed onto the surfaces of
sphalerite and Cu-activated sphalerite.
Q
V C0 Ceh
1000ms e =
-^(3)
where Qe is the equilibrium adsorption capacity of xanthate
on sphalerite and Cu-activated sphalerite surfaces (mol/
m2), C0 and Ce are the initial and equilibrium concentra-
tions of xanthate, respectively (mol/L), V is the volume of
the solution (mL), S is the specific surface area of sphalerite
and Cu-activated sphalerite (m2/g), and m is the mass of
sphalerite and Cu-activated sphalerite (g).
RESULTS AND DISCUSSION
The Spatial and Electronic Structure of Surface
Relaxation of Sphalerite (110) and Cu-Activated
Sphalerite (110) Surface
The mineral surface is highly important in the flotation
process because it determines the geometry and strength of
the collector absorbed on the mineral surface. Differences
in the coordination structure of mineral surface active sites
are a key factor in mineral flotation separation. Because
the recovery of sphalerite flotation differs greatly from the
recovery of sphalerite following Cu activation, the sur-
face of sphalerite (110) and the surface of Cu-activated
Computation Approach
All calculations were performed by the CASTEP module
in materials studio software based on Density Functional
Theory (DFT). The exchange–correlation functional
applied was the Generalized Gradient Approach (GGA)
of PBE[28–31]. Only the valence electrons (Cu 3d9 4s1, Zn
3d10 4s2, S 3s2 3p4, O S 2s2 2p4, C 2s2 2p2 and H 1s1)
were considered using ultrasoft pseudo-potentials [32,33]
and a plane wave cut-off energy of 350 eV after testing.
Monkhorst-Pack k-point sampling density for sphalerite
(110) surface and Cu-activated sphalerite (110) surface was
6×6×6. The self-consistent field (SCF) convergence toler-
ance was set to 1.0*10–6 eV ·atom–1.
Sphalerite (cubic symmetry) with the space group Pa3
and cell parameter of 5.415 Å was used in our calcula-
tions[34]. Based on the previous study[35,13], the Sphalerite
(110) was considered their most stable plane. Therefore,
after testing the slab thickness, a (2×4×1) ZnS (110) surface
with 10 atomic layers and a 15 Å vacuum layer was con-
structed. The calculated lattice constant for bulk sphalerite
was 5.441 Å, which was close to the experimental value of
5.414 Å [34].
The Ethyl xanthane was optimized at the gamma point
in a 15×15×15 Å3 cubic box. The equilibrium geometries
of the sphalerite (110) surface and Cu-activated surface
are illustrated in Figure 2(a)–(d), respectively. Considering
periodic boundary conditions and charge species in the cal-
culation, Na+ was used in the adsorption model as a coun-
ter ion [36].
The xanthane was initially put above the metal site on
the sphalerite (110) surface (a), Cu-activated surface for
progressive optimization. The adsorption energy (Eads) was
obtained using the equation (1) below:
E Eadsorbates/surface E Eadsorbates
ads surface =--(1)
where, Eads is the adsorption energy, Eadsorbates/surface is the
computed energy of the Xanthane adsorbed on sphalerite
(1 1 0) surface (a), Cu activat surface, Esurface is the energy
of the Sphalerite (110) surface (a), Cu activat surface, and
Eadsorbates is the energy of the xanthane.
The d-band center in this study was calculated accord-
ing to the following equation.[37]
n
n
d
d fd =
3
3
f
f
-3
-3
^fhfd
^fhd #
#
(2)
where εdv is the d band center and is the energy ε is the
density of states.
Micro-Flotation Experiments
Prepared samples (5.0 g) and 40 mL distilled water were
added into a 40 mL flotation cell (XFG-II, Company
name?). The pH of the flotation pulp was adjusted by
NaOH or HCl solutions. Activator CuSO4 (1×10–4 mol/L)
was added and conditioned for 3 min, then the collector
was added and conditioned for 3 min, followed by adding
frother (MIBC) for a further 2 min before the air was intro-
duced into the pulp. An impeller speed of 1850 rpm was
maintained throughout the flotation test. The froth prod-
uct and tailing samples were collected, dried, and weighed.
Adsorption Experiments
50 mL pulp samples of sphalerite (5.0 g) or Cu-activated
sphalerite (5.0 g )were prepared by mixing the materials
with 0.5 g xanthate solutions and distilled water. Using a
solution of 0.01M NaOH and 0.01M HCl, the pulp was
adjusted to the required pH values. The samples were then
kept at the predetermined temperature for 12 hours in a
shaker bath with constant temperature. After centrifuging,
the remaining concentration of xanthate in the superna-
tant was quantified using an ultraviolet spectrophotometer.
(Cary 100 UV-Vis) By employing the initial concentration
and residual concentration in equation (3), we can ascer-
tain the quantity of xanthate adsorbed onto the surfaces of
sphalerite and Cu-activated sphalerite.
Q
V C0 Ceh
1000ms e =
-^(3)
where Qe is the equilibrium adsorption capacity of xanthate
on sphalerite and Cu-activated sphalerite surfaces (mol/
m2), C0 and Ce are the initial and equilibrium concentra-
tions of xanthate, respectively (mol/L), V is the volume of
the solution (mL), S is the specific surface area of sphalerite
and Cu-activated sphalerite (m2/g), and m is the mass of
sphalerite and Cu-activated sphalerite (g).
RESULTS AND DISCUSSION
The Spatial and Electronic Structure of Surface
Relaxation of Sphalerite (110) and Cu-Activated
Sphalerite (110) Surface
The mineral surface is highly important in the flotation
process because it determines the geometry and strength of
the collector absorbed on the mineral surface. Differences
in the coordination structure of mineral surface active sites
are a key factor in mineral flotation separation. Because
the recovery of sphalerite flotation differs greatly from the
recovery of sphalerite following Cu activation, the sur-
face of sphalerite (110) and the surface of Cu-activated