Ti 3 O 5 and Al 2 TiO 5 Crystals Flotation Characteristics from Ti-bearing Blast Furnace Slag: A Density Functional Theory and Experimental Study

: Anosovite crystalline is an ideal mineral for ﬂotation from the Ti-bearing blast furnace (TBBF) slag. Ti 3 O 5 crystal and Al 2 TiO 5 crystal are two kinds of anosovites, and the Al element signiﬁcantly a ﬀ ects the electronic structure and ﬂotation performance of anosovite. The ﬂoatability of Ti 3 O 5 and Al 2 TiO 5 crystals were studied by Mulliken populations, energy bands, and density of states (DOS). In addition, the ﬂotation experiment of the two kinds of anosovite crystals (Ti 3 O 5 and Al 2 TiO 5 ) was conducted and proved that the density functional theory (DFT) calculation results were accurate. Compared with Ti 3 O 5 crystal, the Fermi energy level of Al 2 TiO 5 crystal shifts around 2 eV in a negative direction by DOS analysis, which is beneﬁcial to ﬂotation. And Al 2 TiO 5 crystal possesses a larger value of bond population, which is 0.41, for Ti-O bonds than Ti 3 O 5 crystal and the bond length of Ti-O in Al 2 TiO 5 crystal is shorter, therefore Al 2 TiO 5 crystal shows a stronger covalency. The changes of the Fermi energy level and the covalency bonds in Al 2 TiO 5 crystal both demonstrated that doping the Al component into the Ti 3 O 5 crystal was beneﬁcial to improve the ﬂotation e ﬀ ect. Moreover, the Al 2 TiO 5 crystal had a higher ﬂotation e ﬃ ciency compared to the Ti 3 O 5 crystal when the dosages of salicylhydroxamic acid (SHA) and sodium oleate were the same. Therefore, both DFT calculation and experiment show that the ﬂotation e ﬀ ect of the Al 2 TiO 5 crystal is better than that of the Ti 3 O 5 crystal.


Introduction
In southwest of China, there is a large amount of high Ti-bearing vanadium-titanomagnetite and most of which is used for ironmaking process in blast furnace. Therefore, Ti-bearing blast furnace (TBBF) slag is becoming one of the most important secondary resources of titanium, which contains approximately 20-26% TiO 2 [1][2][3][4]. However, titanium is difficult to separate and utilize due to its dispersity in different fine minerals (about 10 µm). Some researchers [5,6] chose perovskite (CaTiO 3 ) as a Ti enrichment phase for the separation of titanium element. In theory, the amount of TiO 2 in perovskite is about 59%, with a density similar to the glassy phase in the slag, so separating and extracting Ti is difficult from perovskite phase in TBBF slag [7,8]. Compared with perovskite, anosovite crystal contains more than 70% TiO 2 (M x Ti 3−x O 5 and 0 ≤ x ≤ 2, where M represents the divalent Mg, Fe, Ti or trivalent Ti, Fe, Al, etc.) with a density (4.20 g/cm −3 ) significantly higher than that of glass phase (2.81 g/cm −3 ) [7]. Therefore, anosovite crystal may be a better alternative for recovering titanium from TBBF slag.
In our previous research [9][10][11][12][13][14][15][16], Ti-bearing ore sintering and Ti-bearing slag characteristics were studied systematically. B 2 O 3 was chosen as the modifier for obtaining the Ti-rich phases, and the results showed that the rise of the (Mg + Al)/(Ca + Si) ratio and B 2 O 3 in slag were beneficial to form [TiO 6 ] 8− octahedral units and thus beneficial to the precipitation of anosovite from the TBBF slag [14,15]. In addition, Anosovite was successfully obtained from TBBF slag, and the lower cooling temperature and extension of the holding time promoted the coarsening of anosovite crystals [16].
Floatation technology has been applied maturely for mineral separation, and its cost is low. The separation of anosovite crystal from the gangue minerals by flotation is influenced by the electronic structures of mineral crystals [17,18], and the floatability of each mineral is closely related to their electronic structure. Mg and Al had positive effects on the stability of Ti 3 O 5 crystal structure [15], whereas experimental methods were challenging to explain the microscopic mechanisms of this phenomenon [19]. Density functional theory (DFT) [20,21], widely and successfully applied in simulations throughout engineering and sciences, a supplement of modern experimental methods, can be used to analyze mineral crystal structures from atom and electron aspects [22]. Related research was conducted on magnesium-bearing anosovite floatation from Ti-bearing electric slag, and the results showed that Mg entering the Ti 3 O 5 lattice changed the crystal and electronic structures of Ti 3 O 5 . Changes in the electronic structures of minerals are bound to affect the adsorption of reagents on the surfaces, which caused the appearance of defects in the crystalline Ti 3 O 5 and change the flotability of minerals, which was beneficial to floatation [23]. However, besides the magnesium element, there was a certain content of aluminum in the TBBF slag [14][15][16], which may affect the crystalline structure of Ti 3 O 5 crystal. Still, the flotation of anosovite crystals from Ti-bearing blast furnace slag is still not reported in the literature.
Therefore, the electronic structures of Ti 3 O 5 and Al 2 TiO 5 crystals were calculated by DFT, and the influence of Al element on crystal structures of Ti 3 O 5 was studied. In addition, the calculation results were compared with flotation experiment results. and the DFT calculation results provide clarification of the experimental results. It is expected that theoretical support for the separation process of TBBF slag through flotation aluminum-bearing anosovite crystal can be established.

Materials
The single mineral sample of anosovite (Ti 3 O 5 ) crystal was obtained from titanium production in Sichuan province in China, and its purity was up to 97.12%, with only small amount of Al 2 O 3 , MgO, Cr, etc. dissolve in it. Tt is therefore marked as Ti 3 O 5 crystal and used for the flotation experiment. Besides, the anosovite crystal was doped with aluminum, and the chemical composition is mainly Al 2 TiO 5 , the purity of which is 92.63%. Ti 3 O 5 and Al 2 TiO 5 crystals (each 4 g) were used as raw materials for the flotation experiments in this study.

Construction Analysis of Ti 3 O 5 and Al 2 TiO 5 Crystalline Models
DFT is a high-precision quantum chemical calculation tool that uses electron density instead of wave function as the research object. The Cambridge Sequential Total Energy Package (CASTEP) module in Materials Studio software [24,25] is on the basis of the theory of plane wave pseudopotential and the number and type of atoms can be used to predict and calculate the crystal lattice parameters, band structure, solid density, charge density and wave function. The interaction between ionic core and valence electrons was described using the Ultra-soft pseudopotentials [26]. The selected valence electron configurations in this study were Ti3s 2 3p 6 3d 2 4s 2 , Al3s 2 3p 1 , and O2s 2 2p 4 . Furthermore, the sampling Crystals 2020, 10, 838 3 of 10 accuracy of the Brillouin zone was defined by a 2 × 2 × 1 k-point set. The Pulay density mixing method (PDMM) is used for self-consistent electronic minimization, in which the convergence tolerance energy and maximum force tolerance on each atom was set to 1.0 × 10 −6 eV/atom and 1.0 × 10 −2 eV/Å for the energy calculation.
The crystal structure diagrams of Ti 3 O 5 [23] and Al 2 TiO 5 formed after the solid solution of Al into Ti 3 O 5 crystals were shown in Figure 1. Relevant research results showed that Al-O bond and Ti-O bond with stronger covalency existed in Al 2 TiO 5 crystal formed after the solid solution of Al into Ti 3 O 5 crystal, which was more stable than Ti 3 O 5 crystal [22]. Both crystal Ti 3 O 5 and Al 2 TiO 5 belong to the orthorhombic with space group Cmcm. The lattice parameters a, b, and c of Ti 3 O 5 are 9.84, 3.76, and 9.86 nm, respectively, which for the Al 2 TiO 5 crystal are 9.84, 3.76, and 9.861 nm, respectively. The lattice parameters α, β, and γ of Ti 3 O 5 and Al 2 TiO 5 are 90 • .
Crystals 2020, 10, x FOR PEER REVIEW 3 of 9 Pulay density mixing method (PDMM) is used for self-consistent electronic minimization, in which the convergence tolerance energy and maximum force tolerance on each atom was set to 1.0 × 10 −6 eV/atom and 1.0 × 10 −2 eV/Å for the energy calculation. Crystal cell models of Ti3O5 [23] and Al2TiO5.
The crystal structure diagrams of Ti3O5 [23] and Al2TiO5 formed after the solid solution of Al into Ti3O5 crystals were shown in Figure 1. Relevant research results showed that Al-O bond and Ti-O bond with stronger covalency existed in Al2TiO5 crystal formed after the solid solution of Al into Ti3O5 crystal, which was more stable than Ti3O5 crystal [22]. Both crystal Ti3O5 and Al2TiO5 belong to the orthorhombic with space group Cmcm. The lattice parameters a, b, and c of Ti3O5 are 9.84, 3.76, and 9.86 nm, respectively, which for the Al2TiO5 crystal are 9.84, 3.76, and 9.861 nm, respectively. The lattice parameters , , and of Ti3O5 and Al2TiO5 are 90°.

Flotation Experimental
The flotation behavior of anosovite crystal was carried out in a small hanging laboratory flotation machine with an effective volume of 60 mL and an impeller speed of 1900 r/min. The water in flotation process was deionized water. The test procedure was as follows: 4 g of anosovite sample with a particle size of about 180 mesh was placed in a 60 mL flotation cell. Then, the collector and frother were introduced in the flotation machine and then stirred for 2 min and 3 min, respectively. Finally, the flotation pulp scraped for 4 min. The pH adjuster was hydrochloric acid and sodium hydroxide, and the test temperature was 20 ± 5 °C. After collecting and drying, the recovery of the product was calculated. Figure 2 and Figure 3 show the band structure of two different anosovites of Ti3O5 and Al2TiO5. The Fermi energy level is uniformly used as the energy zero point in the Figure 2. It can be seen intuitively that the energy band of Ti3O5 is divided into five parts from −60 eV to 10 eV.

Energy Bond Structures of Ti3O5 and Al2TiO5 Crystals
From Figure 3, there are five parts for the valence band of Al2TiO5 crystal, and the band structure of Al2TiO5 is relatively close to that of Ti3O5. This may be due to the same valency of Al 3+ and Ti 3+ , so Al entering into Ti3O5 crystal has relatively little impact on its energy band structure. However, the

Flotation Experimental
The flotation behavior of anosovite crystal was carried out in a small hanging laboratory flotation machine with an effective volume of 60 mL and an impeller speed of 1900 r/min. The water in flotation process was deionized water. The test procedure was as follows: 4 g of anosovite sample with a particle size of about 180 mesh was placed in a 60 mL flotation cell. Then, the collector and frother were introduced in the flotation machine and then stirred for 2 min and 3 min, respectively. Finally, the flotation pulp scraped for 4 min. The pH adjuster was hydrochloric acid and sodium hydroxide, and the test temperature was 20 ± 5 • C. After collecting and drying, the recovery of the product was calculated. Fermi level may result in an increase in the number of holes on the surface of the Al2TiO5, which in turn may increase the adsorption or adsorption rate of the anion collector on the crystal during the flotation process, as well as the adsorption stability, which is conducive to the flotation process [28,29]. Therefore, doping Al component into Ti3O5 should be beneficial to improve the flotation effect.

DOS Distributions of Ti3O5 and Al2TiO5 Crystals
The distributions of electronic DOS of Ti3O5 and Al2TiO5 crystals are shown in Figure 4 and Figure 5. From Figure 4, the valence band of Ti3O5 consists of five parts.
From the DOS of each atom, it can be seen that the valence band peak for Ti3O5 crystal at approximately −59.1 eV, which is attributed to orbit Ti4s electrons. Moreover, almost the entire valence band peak at −35.0 and −20.0 eV come from Ti3p orbit and O2s orbit electrons, respectively. The above-mentioned valence bands are all with very sharp peaks and narrow energy bands, which show that the electron is distributed comparatively locally. The electronic peak ranged from −8.0 to -4.0 eV is contributed the O2p and part of Ti3p and Ti3d orbit. The O2p orbit exhibits a very high electronic peak due to the strong localization of electron in the orbit. The overlap of the electronic peaks of the O2p and Ti3d orbit at −8.0 ~ 4.0 eV, and the Fermi energy level indicates that electrons of the Ti3d to O2p orbit have a transition phenomenon and can interact with each other. The results are consistent with Wang et al [23]. There are some changes in the valence band of Ti3O5 after Al entering Ti3O5 lattice. From Figure 5, Al3s and Al3p orbits appear on the peaks of Al2TiO5 valence band at about −18, −6, and −0 eV and the Fermi energy level. Therefore, in addition to the contribution of Ti3d and O2p orbits, the valence band peak at the Fermi energy level of Al2TiO5 crystal also comes from Al3s and Al3p orbits. Moreover, the electronic peaks of the O2p, Ti3d, Al3s, and Al3p orbit overlap at the Fermi energy level, demonstrating that they can interact with each other. Fermi level may result in an increase in the number of holes on the surface of the Al2TiO5, which in turn may increase the adsorption or adsorption rate of the anion collector on the crystal during the flotation process, as well as the adsorption stability, which is conducive to the flotation process [28,29]. Therefore, doping Al component into Ti3O5 should be beneficial to improve the flotation effect.

DOS Distributions of Ti3O5 and Al2TiO5 Crystals
The distributions of electronic DOS of Ti3O5 and Al2TiO5 crystals are shown in Figure 4 and Figure 5. From Figure 4, the valence band of Ti3O5 consists of five parts.
From the DOS of each atom, it can be seen that the valence band peak for Ti3O5 crystal at approximately −59.1 eV, which is attributed to orbit Ti4s electrons. Moreover, almost the entire valence band peak at −35.0 and −20.0 eV come from Ti3p orbit and O2s orbit electrons, respectively. The above-mentioned valence bands are all with very sharp peaks and narrow energy bands, which show that the electron is distributed comparatively locally. The electronic peak ranged from −8.0 to -4.0 eV is contributed the O2p and part of Ti3p and Ti3d orbit. The O2p orbit exhibits a very high electronic peak due to the strong localization of electron in the orbit. The overlap of the electronic peaks of the O2p and Ti3d orbit at −8.0 ~ 4.0 eV, and the Fermi energy level indicates that electrons of the Ti3d to O2p orbit have a transition phenomenon and can interact with each other. The results are consistent with Wang et al [23]. There are some changes in the valence band of Ti3O5 after Al entering Ti3O5 lattice. From Figure 5, Al3s and Al3p orbits appear on the peaks of Al2TiO5 valence band at about −18, −6, and −0 eV and the Fermi energy level. Therefore, in addition to the contribution of Ti3d and O2p orbits, the valence band peak at the Fermi energy level of Al2TiO5 crystal also comes from Al3s and Al3p orbits. Moreover, the electronic peaks of the O2p, Ti3d, Al3s, and Al3p orbit overlap at the Fermi energy level, demonstrating that they can interact with each other. From Figure 3, there are five parts for the valence band of Al 2 TiO 5 crystal, and the band structure of Al 2 TiO 5 is relatively close to that of Ti 3 O 5 . This may be due to the same valency of Al 3+ and Ti 3+ , so Al entering into Ti 3 O 5 crystal has relatively little impact on its energy band structure. However, the energy of all Al 2 TiO 5 band increased about 2 eV compared with that of Ti 3 O 5 , indicating that he valence and conduction bands have increased in energy. Moreover, the anions adsorption on the surface of minerals is promoted by the movement of Fermi energy level and thus the adsorption probability increases [27]. Therefore, the adsorption of anosovite on the mineral surface is affected by the site of the Fermi energy level. Changes in the electronic structures of minerals are bound to affect the adsorption of reagents on the surfaces, which change the flotability of minerals. A decrease in the Fermi level may result in an increase in the number of holes on the surface of the Al 2 TiO 5 , which in turn may increase the adsorption or adsorption rate of the anion collector on the crystal during the flotation process, as well as the adsorption stability, which is conducive to the flotation process [28,29]. Therefore, doping Al component into Ti 3 O 5 should be beneficial to improve the flotation effect.

Distributions of Ti3O5 and Al2TiO5 Atomic Charges
The distributions of electronic states of atoms were from Mulliken population analysis. The valence electrons distributed around atoms are known as atom populations and the overlapped electron charges distributed between two atoms are called bond populations. With the help of Mulliken population analysis [30][31][32][33], the charge distribution, transfer distribution and bonding between atoms can be understood.

Distributions of Ti3O5 and Al2TiO5 Atomic Charges
The distributions of electronic states of atoms were from Mulliken population analysis. The valence electrons distributed around atoms are known as atom populations and the overlapped electron charges distributed between two atoms are called bond populations. With the help of Mulliken population analysis [30][31][32][33], the charge distribution, transfer distribution and bonding between atoms can be understood.  [23]. There are some changes in the valence band of Ti 3 O 5 after Al entering Ti 3 O 5 lattice. From Figure 5, Al3s and Al3p orbits appear on the peaks of Al 2 TiO 5 valence band at about −18, −6, and −0 eV and the Fermi energy level. Therefore, in addition to the contribution of Ti3d and O2p orbits, the valence band peak at the Fermi energy level of Al 2 TiO 5 crystal also comes from Al3s and Al3p orbits. Moreover, the electronic peaks of the O2p, Ti3d, Al3s, and Al3p orbit overlap at the Fermi energy level, demonstrating that they can interact with each other.

Distributions of Ti 3 O 5 and Al 2 TiO 5 Atomic Charges
The distributions of electronic states of atoms were from Mulliken population analysis. The valence electrons distributed around atoms are known as atom populations and the overlapped electron charges distributed between two atoms are called bond populations. With the help of Mulliken population analysis [30][31][32][33], the charge distribution, transfer distribution and bonding between atoms can be understood. Table 1 is the calculation results of the Mulliken population analysis of Ti 3 O 5 crystal, which is similar to Wang et al. [23]. It can be seen from the average charge of the atom that the electrons number in the Ti atom is 10.87e and lost 1.12e, which indicated that the Ti in Ti 3 O 5 crystal is a donor of electrons. Meanwhile, the number of electrons localized on the O atom is 6.67e and obtained 0.67e, indicating that O is acceptor of electrons. Besides, the calculation of Mulliken populations of Ti-O bonds in Ti 3 O 5 crystal shows that the value of bond population for Ti-O is 0.367 and the bond length is 2.038 Å. Therefore, the Ti-O bond inside the Ti 3 O 5 crystal is covalent, which has directionality, saturation and certain hydrophilicity.    Tables 1 and 2

Flotability of Ti 3 O 5 and Al 2 TiO 5 Crystals
The electron structures of anosovite crystalline display obvious difference between Ti 3 O 5 and Al 2 TiO 5 crystal for the doping of aluminum into Ti 3 O 5 crystal. In addition, they have a significant difference on the chemical compositions, so it is reasonable to assume that the flotabilities of Ti 3 O 5 and Al 2 TiO 5 crystal is different. Therefore, the flotation experiments on the Ti 3 O 5 and Al 2 TiO 5 crystals used sodium oleate, SHA were conducted, and the experiment results are given in Figures 6 and 7. When the dosage of sodium oleate was 8.0 × 10 −5 mol/L, the recovery rate of Ti 3 O 5 crystal reaches the highest value of 72.21%, while that of Al 2 TiO 5 crystal reaches the maximum value of 79.24%. When using SHA as collectors, the best recovery rate of Ti 3 O 5 and Al 2 TiO 5 crystals were 80.12% and 84.15%, respectively. For comparison [34], the anosovite of Mg 0.09 Ti 2.9 1O 5 from Ti-bearing electric slag has a higher recovery, which can reach a maximum recovery of 93.26% at an SHA dosage of 4 × 10 −5 mol/L. It can be seen from Figures 6 and 7 that the recovery rate of anosovite crystal is higher when SHA is used as the collector, indicating that sodium oleate had a stronger ability to capture anosovite. More importantly, the recovery rate of Al 2 TiO 5 crystal has a higher recovery rate compared with Ti 3 O 5 crystal when the flotation conditions are the same. Therefore, doping the Al component into the Ti 3 O 5 crystal should be beneficial to improve the flotation effect from TBBF slag. More importantly, the recovery rate of Al2TiO5 crystal has a higher recovery rate compared with Ti3O5 crystal when the flotation conditions are the same. Therefore, doping the Al component into the Ti3O5 crystal should be beneficial to improve the flotation effect from TBBF slag.

Conclusions
In this paper, DFT is used to study the effects of Al on anosovite crystal structure, electronic structure, and flotation behavior. Moreover, the flotation experiment on Ti3O5 and Al2TiO5 crystals are conducted, and DFT calculation results are accurate. The main conclusions are as follows: (1) The energy of all Al2TiO5 band increased about 2 eV compared with that of Ti3O5, indicating that the valence and conduction bands have increased in energy. The energy band shifts to the positive direction promotes the flotation effect.
(2) Compared with Ti3O5 crystal, O atom obtains more electrons in Al2TiO5 crystal because the Ti atom receives electrons more easily than Al atoms in the Al2TiO5 crystal. The Al2TiO5 crystal possesses a larger Ti-O bond population than Ti3O5, and the Ti-O bonds length is shorter; therefore, the covalency of Al2TiO5 crystal is stronger. Moreover, the Al-O bonds covalency in the Al2TiO5 crystal is greater than that in the Ti3O5 crystal.

Conclusions
In this paper, DFT is used to study the effects of Al on anosovite crystal structure, electronic structure, and flotation behavior. Moreover, the flotation experiment on Ti 3 O 5 and Al 2 TiO 5 crystals are conducted, and DFT calculation results are accurate. The main conclusions are as follows: (1) The energy of all Al 2 TiO 5 band increased about 2 eV compared with that of Ti 3 O 5 , indicating that the valence and conduction bands have increased in energy. The energy band shifts to the positive direction promotes the flotation effect.
(2) Compared with Ti 3 O 5 crystal, O atom obtains more electrons in Al 2 TiO 5 crystal because the Ti atom receives electrons more easily than Al atoms in the Al 2 TiO 5 crystal. The Al 2 TiO 5 crystal possesses a larger Ti-O bond population than Ti 3 O 5 , and the Ti-O bonds length is shorter; therefore, the covalency of Al 2 TiO 5 crystal is stronger. Moreover, the Al-O bonds covalency in the Al 2 TiO 5 crystal is greater than that in the Ti 3 O 5 crystal.
(3) The Al 2 TiO 5 crystal has a higher recovery rate compared with the Ti 3 O 5 crystal when the flotation conditions are the same. Therefore, doping an Al component into the Ti 3 O 5 crystal should be beneficial for improving the flotation effect from TBBF slag.

Conflicts of Interest:
The authors declare no conflict of interest.