XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2485
CASTEP code. In addition for the hydrated surface the
Forcite code (Rappé et al., 1992) was also utilised to ran-
domly distribute the water molecules to reduce the com-
puting time. The VASP and CASTEP simulation were
performed with the generalized gradient approximation
of Perdew-Burke-Ernzerhof (GGA-PBE) (Perdew, Burke
K and Ernzerhof, 1996) exchange-correlation functional,
along with a plane-wave basis set with the cut-off energy
of 450 eV. This was sufficient to converge the total energy
to within 0.2 meV/atom. The valence electron configura-
tions considered for the atoms were: 5d96s1, 4s24p3, 3s23p4,
2s22p4, 2s22p3, 2s22p2, 1s1and 3s1 for Pt, As, S, O, N, C, H
and Na, respectively. The negative charge on the S– atom/s
of the collector polar site was neutralise by inclusion of
the sodium ions (Na+) in the simulations, which were also
adopted in the surface adsorption system to simulate the
neutral conditions. This was based on the report that there
is greater association of the Na+ with S– of collectors such as
MBT– (Galvao et al., 2016). However, to simulate the acidic
conditions the hydrogen (H+) was used instead of Na+.
VASP Code
The sperrylite and platarsite bulk and dry sperrylite and
platarsite (100) surface adsorption with NBX, NBDTC
and DTBAT under neutral and acidic conditions were
performed with VASP code. The calculations included
the long-range dispersion correction approach by Grimme
(Grimme, Ehrlich and Goerigk, 2011) with Becke-Jonson
damping. The Brillouin zone k-points sampling of 6×6×6
and 4×4×1 for the bulk and surface were generated based
on the Monkhorst-Pack scheme (Monkhorst and Pack,
1976). The projector augmented wave (PAW) pseudopo-
tentials for the electron-electron interaction (Blochl, 1994)
were employed. All structural optimization calculations of
the bulk and surface models were obtained using a con-
jugate gradients technique with an iterative relaxation of
the atomic positions for the surface, while for the bulk the
lattice was allowed to relax as well. The convergence toler-
ances and self-consistent convergence tolerance of the elec-
tron density were 0.02 eVÅ–1 and 1.0×10–7 eV/atom, and
employing integration scheme of Methfessel-Paxton smear-
ing with width of 0.2 eV, respectively. The collectors mol-
ecules were optimized using GGA-PBE within the VASP
code at gamma point (k-points =1×1×1) and employing
the similar parameters as the surface optimization. Prior to
calculating the adsorption energies of the collector on the
surface, the NBX, NBDTC and DTBAT collector models
were optimized in a cubic cell of 40 Å, which was sufficient
to avoid the interactions between collector molecules in
adjacent supercells.
CASTEP Code
The adsorptions on hydrated surface were performed
within the CASTEP code adopting the long-range disper-
sion correction approach to the DFT by Tkatchenko and
Scheffler (TS) (Tkatchenko and Scheffler, 2009). As sug-
gested by Monkhorst-Pack, a k-point grid of 1×1×1 were
employed to reduce the computing time of such large sys-
tems (Monkhorst and Pack, 1976). The ultrasoft pseudo-
potentials were applied for the interactions between valence
electrons and the ionic core. The force, ionic displacement,
and energy for the convergence tolerances were set to
0.05 eV/Å, 0.002 Å and 2.0×10–5 eV/atom, respectively.
Energy Calculations
The relaxed surface energy which is the energy required to
cleave the bulk crystal was computed by using the equation
1 (Nemutudi, Mkhonto and Ngoepe, 2022):
E 2A
E nslabh^Ebulkh@
surface
slab =
-^6 (1)
where A is the area of the surface slab, Eslab is the total
energy of the slab, n is the number of atoms in the slab and
Ebulk is the total energy of the bulk per atom. The stabil-
ity of the surface is indicated by the lowest positive surface
energy.
The strength of the adsorbates (NBX, NBDTC and
DTBAT) adsorptions on the dry (100) surface was deter-
mined from the adsorption energies (Eads.) using the equa-
tion 2, (Mkhonto et al., 2022), (Wei et al., 2019), (Zhang
et al., 2011):
E [E E E
Adsorption System Surface Adsorbate =-+^h (2)
where, ESurface is the energy of the un-adsorbed surface slab,
EAdsorbate is the energy of the isolated adsorbate, and ESystem
is the energy of the adsorbed surface slab.
In the case of hydrated surface, the adsorption energies
were computed from the difference between the adsorbed
surface-water-collector (collector attached on the surface)
and the un-adsorbed surface-water-collector (collector
detached from the surface) in the environment of 80 H2O
molecules using equation 3 (McFadzean, Mkhonto and
Ngoepe, 2023):
E [E E ]
Adsorption W A [S W A ]
Adsorbed Un-adsorbed
=-
++++6S @(4)
In both equations (2) and (3) positive adsorption energy
corresponds to an endothermic process (shows un-favoured
interaction between the adsorbate and the surface) and
negative adsorption energy corresponds to an exothermic
adsorption process (shows a strong interaction between the
adsorbate and the surface).
CASTEP code. In addition for the hydrated surface the
Forcite code (Rappé et al., 1992) was also utilised to ran-
domly distribute the water molecules to reduce the com-
puting time. The VASP and CASTEP simulation were
performed with the generalized gradient approximation
of Perdew-Burke-Ernzerhof (GGA-PBE) (Perdew, Burke
K and Ernzerhof, 1996) exchange-correlation functional,
along with a plane-wave basis set with the cut-off energy
of 450 eV. This was sufficient to converge the total energy
to within 0.2 meV/atom. The valence electron configura-
tions considered for the atoms were: 5d96s1, 4s24p3, 3s23p4,
2s22p4, 2s22p3, 2s22p2, 1s1and 3s1 for Pt, As, S, O, N, C, H
and Na, respectively. The negative charge on the S– atom/s
of the collector polar site was neutralise by inclusion of
the sodium ions (Na+) in the simulations, which were also
adopted in the surface adsorption system to simulate the
neutral conditions. This was based on the report that there
is greater association of the Na+ with S– of collectors such as
MBT– (Galvao et al., 2016). However, to simulate the acidic
conditions the hydrogen (H+) was used instead of Na+.
VASP Code
The sperrylite and platarsite bulk and dry sperrylite and
platarsite (100) surface adsorption with NBX, NBDTC
and DTBAT under neutral and acidic conditions were
performed with VASP code. The calculations included
the long-range dispersion correction approach by Grimme
(Grimme, Ehrlich and Goerigk, 2011) with Becke-Jonson
damping. The Brillouin zone k-points sampling of 6×6×6
and 4×4×1 for the bulk and surface were generated based
on the Monkhorst-Pack scheme (Monkhorst and Pack,
1976). The projector augmented wave (PAW) pseudopo-
tentials for the electron-electron interaction (Blochl, 1994)
were employed. All structural optimization calculations of
the bulk and surface models were obtained using a con-
jugate gradients technique with an iterative relaxation of
the atomic positions for the surface, while for the bulk the
lattice was allowed to relax as well. The convergence toler-
ances and self-consistent convergence tolerance of the elec-
tron density were 0.02 eVÅ–1 and 1.0×10–7 eV/atom, and
employing integration scheme of Methfessel-Paxton smear-
ing with width of 0.2 eV, respectively. The collectors mol-
ecules were optimized using GGA-PBE within the VASP
code at gamma point (k-points =1×1×1) and employing
the similar parameters as the surface optimization. Prior to
calculating the adsorption energies of the collector on the
surface, the NBX, NBDTC and DTBAT collector models
were optimized in a cubic cell of 40 Å, which was sufficient
to avoid the interactions between collector molecules in
adjacent supercells.
CASTEP Code
The adsorptions on hydrated surface were performed
within the CASTEP code adopting the long-range disper-
sion correction approach to the DFT by Tkatchenko and
Scheffler (TS) (Tkatchenko and Scheffler, 2009). As sug-
gested by Monkhorst-Pack, a k-point grid of 1×1×1 were
employed to reduce the computing time of such large sys-
tems (Monkhorst and Pack, 1976). The ultrasoft pseudo-
potentials were applied for the interactions between valence
electrons and the ionic core. The force, ionic displacement,
and energy for the convergence tolerances were set to
0.05 eV/Å, 0.002 Å and 2.0×10–5 eV/atom, respectively.
Energy Calculations
The relaxed surface energy which is the energy required to
cleave the bulk crystal was computed by using the equation
1 (Nemutudi, Mkhonto and Ngoepe, 2022):
E 2A
E nslabh^Ebulkh@
surface
slab =
-^6 (1)
where A is the area of the surface slab, Eslab is the total
energy of the slab, n is the number of atoms in the slab and
Ebulk is the total energy of the bulk per atom. The stabil-
ity of the surface is indicated by the lowest positive surface
energy.
The strength of the adsorbates (NBX, NBDTC and
DTBAT) adsorptions on the dry (100) surface was deter-
mined from the adsorption energies (Eads.) using the equa-
tion 2, (Mkhonto et al., 2022), (Wei et al., 2019), (Zhang
et al., 2011):
E [E E E
Adsorption System Surface Adsorbate =-+^h (2)
where, ESurface is the energy of the un-adsorbed surface slab,
EAdsorbate is the energy of the isolated adsorbate, and ESystem
is the energy of the adsorbed surface slab.
In the case of hydrated surface, the adsorption energies
were computed from the difference between the adsorbed
surface-water-collector (collector attached on the surface)
and the un-adsorbed surface-water-collector (collector
detached from the surface) in the environment of 80 H2O
molecules using equation 3 (McFadzean, Mkhonto and
Ngoepe, 2023):
E [E E ]
Adsorption W A [S W A ]
Adsorbed Un-adsorbed
=-
++++6S @(4)
In both equations (2) and (3) positive adsorption energy
corresponds to an endothermic process (shows un-favoured
interaction between the adsorbate and the surface) and
negative adsorption energy corresponds to an exothermic
adsorption process (shows a strong interaction between the
adsorbate and the surface).