Computational Study of the Transport Properties of Molten CaO-SiO₂-P₂O₅-FeO System

MSD and self-diffusion coefficients

Figure 1 shows the MSD of Ca, Si, P, Fe and O ions calculated as a function of time in the No. 2 slag system at 1,673 K. The self-diffusion coefficients of each ion can be obtained from the slope of the linear part of the MSD vs. time curve. The self-diffusion coefficients obtained at 1,673 K of Ca, Si, P, Fe and O ions are 0.056 Ų/ps, 0.023 Ų/ps, 0.032 Ų/ps, 0.053 Ų/ps and 0.045 Ų/ps, respectively. The results show that the Ca and Fe ions diffuse more rapidly than other ions in the CaO-SiO₂-P₂O₅-FeO system. The O ion is somewhat less mobile, and the Si and P ions have the lowest mobility. As Table 3 shows, the diffusivity sequence of Ca>O>Si is also reported in molten CaO-SiO₂, CaO-MgO-Al₂O₃-SiO₂ and CaO-CaF₂-SiO₂ slag systems [15, 16, 17, 18]. This suggests the restricted diffusion of the Si ion within a SiO₄ tetrahedron. To our knowledge, there are few experimental or computational diffusion studies for the CaO-SiO₂-P₂O₅-FeO system. Although very limited data are available in the literatures, the Fe ion is more diffusive than O ion, but much less diffusive than Ca ion is confirmed [19, 20]. The self-diffusion coefficient of P is less than O, but larger than Si, which indicating its weaker bonding in tetrahedral coordination. The self-diffusion coefficients in present work are on the same order and magnitude as those reported molten oxide systems.

Figure 1:

Mean squared displacements as a function of time of different ions in the CaO-SiO₂-P₂O₅-FeO system at 1,673 K.

Table 4 shows all the self-diffusion coefficients of Ca, Si, P, Fe and O ions in Nos. 1~10 slags. It can be seen that with the slag basicity increases from 0.6 to 1.5, the self-diffusion coefficients of Ca, Si, P, Fe and O ions increase from 0.04 to 0.065 Ų/ps, 0.017 to 0.027 Ų/ps, 0.023 to 0.038 Ų/ps, 0.037 to 0.057 Ų/ps and 0.033 to 0.053 Ų/ps, respectively. The self-diffusion coefficients of all ions increase with increasing slag basicity. The results represent reasonably well the structural properties of molten CaO-SiO₂ system, which were restricted to the diffusion of Si and O ions by the formation of silica network structure [16]. With the increase of P₂O₅ content from 5 to 14 %, the self-diffusion coefficients of Ca, Si, P, Fe and O ions decrease from 0.097 to 0.043 Ų/ps, 0.04 to 0.018Ų/ps, 0.057 to 0.025 Ų/ps, 0.092 to 0.042 Ų/ps and 0.08 to 0.035 Ų/ps, respectively. As well as Si, increasing the amount of P ions in oxide melts leads to a more close slag structure. Therefore, the polymerization degree of the melts increased and all the self-diffusion coefficients decreased. On the contrary, with the increase of FeO content from 30 to 40 %, the self-diffusion coefficients of Ca, Si, P, Fe and O ions increase from 0.056 to 0.097 Ų/ps, 0.023 to 0.04 Ų/ps, 0.032 to 0.057 Å2/ps, 0.053 to 0.092 Å2/ps and 0.045 to 0.08 Å2/ps, respectively. This is because the Fe ion plays the role of network modifier in the oxide melts. The depolymerization of the slag structure decreases with increasing FeO content, thus, the self-diffusion coefficients increased.

Viscosities

Table 5 shows the viscosities of Nos. 1~10 slags calculated by self-diffusion coefficients. It can be seen that the viscosities decrease from 0.26 to 0.15 Pa·s with the slag basicity increasing from 0.6 to 1.5. Similarly the viscosities decrease from 0.18 to 0.11 Pa·s with the FeO content in slag increasing from 30 to 40 %; and increase from 0.14 to 0.28 Pa·s with the P₂O₅ content in slag increasing from 5 to 14 %. It is apparent that increasing the amount of network formers (e. g., Si and P ions) in molten CaO-SiO₂-P₂O₅-FeO system leads to larger viscosity while adding network modifiers (e. g., Fe and Ca ions) causes viscosity to decrease.

In order to verify the validity of the calculated results, we measured the viscosities of above molten slags by the rotating cylinder method [22]. In the viscosity measurement test, both the crucible and spindle are made of pure iron. The comparisons of the measured and the calculated values for the viscosities are shown in Figure 2. The calculated values are in good agreement with the experimental ones.

Figure 2:

Calculated viscosities using MD simulations against experimental data.

Links between transport and structural properties

Each Si and P tetrahedron was classified into five types of structural units, i. e. Q⁰, Q¹, Q², Q³, and Q⁴, where the superscript referred to the number of bridging oxygen atoms in the unit [23]. Figure 3 shows the concentration variation of Qⁿ with changing slag basicity, FeO content and P₂O₅ content, respectively. It is important to note that the Qⁿ(Si+P) in present work includes both Qⁿ(Si) and Qⁿ(P). Seen from Figure 3(a), with the increase of slag basicity, the proportion of Q⁰(Si+P) shows a remarkable uptrend while the proportions of Q²(Si+P), Q³(Si+P) and Q⁴(Si+P) decrease obviously. It suggests that the degree of polymerization of the Si-O and P-O network structures is weakened. This phenomenon is also observed with the increase of FeO content in slag. At the same time, the proportions of Q⁰(Si+P) and Q¹(Si+P) decrease slightly with the increase of P₂O₅ content in slag while the proportions of Q²(Si+P) and Q³(Si+P) increase slightly. It can be concluded that the network of both P and Si ions are more polymerized and tend to form complex anions.

Figure 3:

Effect of (a) basicity, (b) FeO content and (c) P₂O₅ content on Qⁿ(Si+P).

The ratio of non-bridging oxygen/tetragonal oxygen (NBO/T) is a measure of the de-polymerization of the molten system. Mills et al. [24] proposed a relational expression between the polymerization of the molten CaO-Na₂O-Al₂O₃-SiO₂ slag and the mole fractions of different oxides.

Similarly, the parameter Q(Si+P), which is a measure of the polymerization of the molten CaO-SiO₂-P₂O₅-FeO system and which can be calculated by

Figure 4 shows the relationship between the calculated viscosities and the parameter of Q(Si+P) at 1,673 K. It can be intuitively seen that the viscosities vs Q(Si+P) is a linear-related function. However, there is a special point that the deviation between the calculated data and the fitting data is pretty huge. The reason for this may be that the P₂O₅ content is extremely high, which going beyond the application of eq. (7). Without thinking about this special point, the coefficient of determination R² increases from 0.65 to 0.92.

Figure 4:

Relationship between the calculated viscosities and the parameter of Q(Si+P) at 1,673 K.

FT-IR spectra analysis

The structures of the slags were also detected by FT-IR spectroscopy (Nicolet 5DXC). Figure 5(a) shows the effect of slag basicity on the FT-IR spectra of the slags. In general, the spectra was composed of three regions, i. e. 800–1,200 cm^–1 with strong intensity, 600–800 cm^–1 with weak intensity and 400–600 cm^–1 with middle intensity. The band in the 800–1,200 cm^–1 range has been generally assigned to the symmetric stretching vibration of SiO₄ and PO₄ tetrahedra. The bands shift to lower wavenumber region with increasing slag basicities, which suggests that the proportions of Q²(Si+P) and Q³(Si+P) decreased. Therefore, the degree of polymerization of the slags decreased [25]. With the increase of FeO content, this phenomenon also showed in Figure 5(b). However, the bands shift from low wavenumber to high wavenumber in Figure 5(c), which indicates that more polymerized structures were formed with increasing P₂O₅ content. The weak 600–800 cm^–1 bands represent the Si-O symmetry stretching [26, 27]. The characteristic peak near 695 cm^–1 corresponds to the FeO₄ tetrahedra stretching bands [28]. The medium intense band in the 400–600 cm^–1 range represents the bending vibration of T-O-T (T denotes Si or P).

Figure 5:

FT-IR spectra of slag samples with varying (a) basicity, (b) FeO content and (c) P₂O₅ content.