1. Introduction
Fluorite (CaF
2) is an important ore of fluorine, and becomes a strategic resource reserve in many countries. Crystalline fluorite has a very low index of refraction and an unusual ability to transmit ultraviolet light. It is widely used in many industries, such as aluminum fluoride manufacturing, glass manufacturing, primary aluminum production, ceramic, enamels, and hydrofluoric acid. China, Mexico, Namibia, Kenya, and South Africa are the major producing and exporting countries [
1].
Fluorite often coexists with other calcium-containing minerals such as calcite, gypsum, and francolite due to the similarity in their formation characteristics [
2,
3,
4]. Separation of fluorite from its associated gangue minerals is commonly carried out by flotation [
5,
6]. The conventional collectors used in the flotation of fluorite ores are fatty acids (oleic acid, for example) and their salts [
7].
Fluorite crystals exist in a variety of colors, ranging from colorless through white, yellow, green, and purple to blue, but purple is the most common [
1]. The various colors of fluorite may be attributable to the different impurities in the fluorite crystal [
8]. It is reported that REE, such as cerium (Ce) and yttrium (Y), can replace the calcium (Ca) in fluorite in a form of isomorphism [
9]. When the amount of substitution reaches a certain value, the replaced fluorite is called yttrofluorite and cerfluorite. In addition, the ion radius of calcium (1.06 Å) in fluorite (CaF
2) crystal is very close to 1.10 Å of thorium (Th) and especially 1.05 Å of tetravalent uranium (U) [
8,
10]. It can be found that U and Th replace Ca in fluorite crystal in some scenarios. Lattice defects may change the Fermi energy, frontier orbital, and electronic structure of minerals which exert a considerable influence on the surface properties of minerals [
11,
12]. It is tenable to infer that, the incorporation of impurities such as Ce, Th, U, and Y in the fluorite crystal may lead to the different floatability of fluorite.
So far, the study about the impact of impurity defects on the flotation performance has been mainly focused on sulfide ores by density functional theory (DFT) calculations. Ye et al. investigated the effect of three typical impurities (iron, copper, and cadmium) on the flotation behavior of sphalerite [
13]. They also studied the electronic structures of bulk sphalerite containing 14 typical kinds of impurities by [
14]. Li et al. calculated the electronic property of pyrite crystals containing As, Se, Te, Co, or Ni atoms. The results showed that pyrite containing As, Co, or Ni was easier to oxidize by oxygen than pyrite containing Se or Te, and pyrite containing Co or Ni had greater interaction with xanthate [
15]. Chen et al. investigated the adsorption of oxygen molecules (O
2) on galena (100) surfaces containing Ag, Cu, Bi, and Mn impurities and found that the impurities could change the semiconductor electronic structure of galena surface and influence the adsorption of oxygen molecules [
16].
However, few theoretical studies concerning the influence of impurities on the surface properties of fluorite crystals have been published. In this study, the electronic structures of fluorite bearing Ce, Th, U, and Y impurities were studied by DFT calculations, and the influence of impurities on the reactivity of fluorite was predicted. The findings in the effect of these impurities on the electronic structure and reactivity of fluorite would help solve some encountered problems in fluorite flotation practice.
2. Computational Details
The lattice parameter of fluorite crystal was obtained from the literature [
17]. The symmetry group of fluorite crystal is FM-3M. The unit cell consists of eight F atoms and four Ca atoms, and the cell parameters are
a =
b =
c = 5.4631 Å and α = β = γ = 90°. By replacing one Ca atom by an impurity REE atom, a crystal structure of impurity-bearing CaF
2 was produced. The models of the fluorite supercells are shown in
Figure 1.
All of calculations in this work were carried out by the Material Studio (MS) 7.0 package. Geometry optimization, a first-principle pseudopotential method based on DFT, was performed using the CASTEP module [
18]. Plane wave (PW) basis sets and ultrasoft pseudopotentials were employed for the DFT calculations [
19,
20]. Based on the test results, GGA-PBESOL [
21,
22] was set as the exchange correlation functional and 330 eV was used as the cut-off energy. The Brillouin zone was sampled with Monkhorst and Pack special k-points of a 4 × 4 × 4 grid for all structure calculations [
23,
24,
25,
26]. Only valence electrons were considered explicitly using ultrasoft pseudopotentials [
27,
28,
29], and pseudo atomic calculations were performed for Ca 3s
23p
64s
2, F 2s
22p
5, Ce 4f
15s
25p
65d
16s
2, Th 6s
26p
66d
27s
2, U 5f
36s
26p
66d
17s
2, Y 4s
24p
64d
15s
2. The convergence tolerances for geometry optimization calculations were set to the maximum displacement of 0.001 Å, the maximum force of 0.03 eV/Å, the maximum energy change of 1.0 × 10
−5 eV/atom, and the maximum stress of 0.05 GP, and the self-consistent field (SCF) convergence tolerance was set to 1.0 × 10
−6 eV/atom. Other parameters were default settings.
After geometry optimization, the density of state and the Mullilken population of fluorite supercells were calculated with a single-point energy method using CASTEP module. The Fermi energy and the frontier orbital were calculated also by a single-point energy method using DMol3 module with the same setting parameters as CASTEP. Both structure optimization and frontier orbital calculations of oleic acid were performed by Dmol3 with GGA-PBESOL functional, DNP basis set, all electron core potentials, basis file of 3.5, multipolar expansion of Hexadecapole, global orbital cutoff of 3.7 Å, occupation of fermi and SCF tolerance of 1.0 × 10−6 eV/atom. Other parameters were default settings.
4. Conclusions
The electronic structures of bulk fluorite bearing Ce, Th, U, and Y impurities were calculated using DFT. The results showed that the impurities changed the structure and electronic properties of fluorite, including the Fermi level, density of states, and the Mulliken population. The presence of impurities increased the lattice parameters of fluorite, and made the Fermi level shift towards the direction of high energy, causing the fluorite to accept electrons more easily. The results of DOS and Mulliken population indicated that the incorporation of impurity atoms made oleic acid more easily adsorb on fluorite. The frontier molecular orbital calculations suggested that the incorporation of impurities of Ce, Th, U, and Y can enhance the reactivity of fluorite with oleic acid.