Defects, diffusion and dopants in the ceramic mineral “Lime- Feldspar”

ABSTRACT Calcium aluminosilicate, CaAl2Si2O8, is a promising ceramic material that has found applications in several areas, such as glass production and petrology. Atomistic scale simulation techniques are used to study the intrinsic defects, Ca-ion migration paths and doping behavior in CaAl2Si2O8. The most favorable defect is the Al–Si anti-site in agreement with the experimental observation. The O-Frenkel is the second most favorable defect. The Ca-Frenkel is higher in energy only by 0.62 eV than the O-Frenkel. Long-range Ca-ion migration is observed in the ac plane with the activation energy of 2.84 eV suggesting that Ca-ion diffusion in this material is slow. The prominent isovalent dopant on the Ca site is the Sr, which was experimentally substituted on the Ca site to prevent phase transformation. The formation of Ca interstitials and oxygen vacancies is favored by Fe3+ doping on the Si site. The favorable tetravalent dopant on the Si site and the Al site to form Ca vacancies is the Ge.


Introduction
Anorthite (CaAl 2 Si 2 O 8 ), also termed lime-feldspar, is a naturally occurring rock-forming mineral found in many countries including Italy, Japan, USA, India and Srilanka [1][2][3]. It is a potential ceramic material in the industrial preparation of heat exchangers, feldspar glasses, electronic substrates and materials required for biomedicine [4][5][6][7]. As its crystalline phase, it can improve the translucent property of bone china, there is an increasing attention to prepare anorthite-based porcelain to make tableware with high heat stability [8]. Furthermore, calcium-bearing minerals are of interest in the development of electrode materials for rechargeable Ca-ion batteries [9]. Though CaAl 2 Si 2 O 8 was not studied for this purpose yet, theoretical investigation on other Ca-based minerals is available [10][11][12].
There have been extensive research efforts to study its physical and mechanical properties during the past few decades in order to develop this ceramic material for industrial applications [13][14][15]. Anorthite porcelain synthesized by Pal et al. [13] exhibited low thermal expansion coefficient inferring its usage in cooking wares. Le Parc et al. [16] used Raman spectroscopy and neutron scattering experiment to compare the rigidity and disorder behavior of CaAl 2 Si 2 O 8 glass structure with that of the anorthite crystal structure. At high temperatures and pressures, this material undergoes partial Al/Si disorder leading to phase transition [17,18]. The addition of Fe 2 O 3 not only improves its crystalline behavior but also provides color to its glasseous form [18,19]. McGuinn et al. [20] have shown that doping of Sr 2+ or Ba 2+ on the Ca site in CaAl 2 SiO 8 can prevent phase transition and increase its symmetry [21,22]. Though there are many experimental studies available on this material, only a few theoretical works have been reported. Molecular dynamics simulation has been carried by Karki et al. [21] to look at the diffusion and viscosity of molten CaAl 2 Si 2 O 8 at different temperatures and pressures. In a density functional theory (DFT) study by Zhang et al. [23], the surface structure of anorthite was considered for the adsorption of CO 2 molecules and the influence of water on its adsorption predicted.
The fundamental understanding of intrinsic and extrinsic defects in CaAl 2 Si 2 O 8 can be useful to optimize its performance in ceramic and battery industries. Atomistic simulations based on the classical pair potentials can provide valuable information about defect processes including cation disorder, selfdiffusion and promising dopants in CaAl 2 Si 2 O 8 . This simulation technique has been successfully used to model crystalline materials over the last two decades and has provided experiments with unique insight and prediction [24][25][26][27][28]. To the best of our knowledge, there is no simulation study on the defects, diffusion and dopant reported for CaAl 2 Si 2 O 8 in the literature. In this work, we report the results of intrinsic defect processes, Ca-diffusion pathways together with activation energies and solution of MO (M = Co, Mn, Ni, Mg, Zn, Sr and Ba), M 2 O 3 (M = Ga, Fe, In, Sc, Y, Gd and La) and MO 2 (M = Ge, Ti, Sn, Zr and Ce) in CaAl 2 Si 2 O8

Computational methods
All calculations were performed using a classical pair-wise potential simulation code GULP (General Utility Lattice Program) [29]. Interactions between ions were modeled using long-range (Coulombic) and short-range (Pauli repulsion and van der Waals attraction). The Buckingham potentials were used to model short-range repulsive forces (see Table 1) [30,31]. Full geometry relaxations were carried out using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [32]. Forces on all ions in the relaxed configurations were smaller than 0.001 eV/Å. The Mott-Littleton method [33] was used to model point defects. The methodology to calculate migration ion pathway together with activation energy has been well explained in the previous simulation work [34]. The current methodology treats ions as a spherical shape with full charge at the dilute limit. Therefore, it is anticipated that calculated defect energies will be overestimated. However, the trend in relative energies will be consistent [35].

Crystal structure of CaAl 2 S i2 O 8
The crystal structure of CaAl 2 S i2 O 8 (lattice parameters: a = 8.186 Å, b = 12.876 Å, c = 14.182 Å, α = 93.3°, β = 115.79° and γ = 91.12°) belongs to triclinic phase with P � 1 symmetry as reported by Bruno et al. [36]. Both  ] where A, ρ and C are parameters that were selected carefully to reproduce the experimental data. The values of Y and K represent the shell charges and spring constants. A very large spring constant means there is no shell charge and the atom is treated as the core.  Al and Si form tetrahedral units and they are interlinked by sharing their corners (see Figure 1). Table 2. There is a good agreement between the calculated and experimental lattice parameters indicating the efficacy of the potentials.

Intrinsic defect processes
Defects play a significant role in mechanical and diffusion properties of a material. A series of isolated point defects (vacancies and interstitials) were calculated and then they were combined to calculate Frenkel and Schottky defect formation energies. The anti-site defects were also considered in the form of isolated and cluster. Impurity defects (e.g., Al 0 Si andSi � Al Þ were considered separately and their defect energies were combined to calculate the anti-site (isolated) reaction energy. In the case of cluster form, both defects were considered simultaneously. The difference between the defect energies {E (cluster) -E (isolated)} is defined as binding energy. Defect reaction energies as written using Kröger-Vink notation [37] are shown in equations 1-14.  [17,18]. Exoergic binding energy of -0.47 eV shows that isolated defects (Al 0 Si and Si � Al Þ are not stable and they aggregate to form clusters (Al 0 Si : Si � Al ) X without an energy penalty. In many oxide materials, the anti-site defect has been identified experimentally and theoretically [38][39][40][41]. The O Frenkel is identified as the second most favorable defect energy process. However, this process would require moderate temperature. Other Frenkel and Schottky defect processes exhibit high endothermic energies implying that they are highly unlikely to occur at normal temperatures. The formation of CaO in this material was considered via CaO Schottky-like reaction (equation 6). The formation energy for this process is 4.53 eV per defect suggesting that formation of V 00 Ca and V �� O in this material is only possible at high temperatures.

Calcium ion diffusion
The performance of a material is partly dependent on its diffusion properties. The diffusion of Ca-ions in this material can be of interest in the application of Ca-ion batteries. Materials exhibiting long-range Ca-ion diffusion with low activation energy are one of the essential conditions for constructing a promising Ca-ion battery. However, it is expected that the Ca-ion diffusion in Cabearing oxide materials would be slow due to its ion size with a double positive charge. Previous quantum mechanical simulations [10,42] analyzed the suitability of minerals as electrode materials for Ca-ion batteries and high activation energies of migration confirmed the slow diffusivity ion of Ca-ions. Atomistic simulations based on the classical pair potentials can provide useful information on diffusion pathways and activation energies as this information is generally difficult from the experiment. The present methodology has been successfully applied to various ionic materials to calculate migration pathways together with activation energies [11,12,25,26]. For example, there is an excellent agreement between calculated and experimentally determined Li-ion diffusion pathway in LiFePO 4 [43,44]. Five different local Ca hops (see Figure 2) were identified for the vacancy-mediated Ca-ion migration. Local Ca hops with their separations and corresponding activation energies are reported in Table 4. Activation energies for individual Ca hops are greater than 2.50 eV suggesting that Ca-ion diffusion in this material is very limited. Figure 3 shows the energy profile diagrams calculated for local hops. Local hops were connected in different ways to construct long-range diffusion pathways (see Table 5).
In all cases, the movement of Ca-ions is observed in the ac plane. The pathway with the lowest activation energy of 2.84 eV is noted for D↔E↔D↔B. Other pathways exhibit slightly higher activation energies only by ~0.13 eV than that calculated for the lowest energy pathway. We should add that we have considered a range of other paths with longer Ca-Ca hoping distances of >5.75 Å, but these were all found to have prohibitively high migration barriers (>4 eV).

Solution of dopants
The performance of a material is partially dominated by the substitutional dopants. A range of dopants were considered for screening and predicting promising dopants that can be verified experimentally. Appropriate charge-compensation defects and lattice energies were introduced to calculate solution energies. In the supplementary information, Buckingham potentials used for dopants are provided (see Table S1).

Divalent dopants
First, divalent dopants (M = Co, Mn, Ni, Mg, Zn, Sr and Ba) were considered on the Ca site. The following equation was used to calculate the solution energy.
Exothermic solution energy is calculated for Sr 2+ and Ba 2+ suggesting that they are the most prominent dopants on the Ca site (see Table 6). Possible composition that can be available in nature or from experimental preparation is Ca  [20]. Other   Figure 3).

Trivalent doping
Next, a range of trivalent dopants (M = Ga, Fe, In, Sc, Y, Gd and La) were considered on the Al site. The following equation explains the defect process in which trivalent dopants are substituted on the Al site without introducing charge compensating defects.   Figure 2) of Ca vacancy hopping between two adjacent Ca sites. Table 5. Possible long-range Ca ion diffusion paths and their corresponding activation energies (see Figure 2).  presence of a small amount of Fe 3+ in the feldspar glasses makes them colorful [18]. The Sc 3+ is identified as the second most favorable dopant and its solution energy is 0.71 eV. High positive solution energies (>1 eV) are calculated for the other dopants suggest that this process is possible at high temperatures. Thereafter, the Si site was considered for doping of trivalent dopants. In this case, negative charges are introduced in the lattice and they are compensated by positively charged Ca interstitials. This process will lead to the formation of additional Ca in the lattice. The formation of Ca interstitials can increase the capacity of CaAl 2 Si 2 O 8 and enhance the diffusion of Ca ion. The following equation was used to calculate the solution energy for this process.
Calculated solution enthalpies are shown in Calculations reveal that the Fe 3+ is the most favorable dopant (see Table 8). The trend in solution energy is the same as calculated for Ca interstitial as charge compensating defect.

Tetravalent doping
Finally, tetravalent dopants (M = Ge, Ti, Sn, Zr and Ce) were considered on the Si site. Solution energy was calculated using the following reaction equation.
Favorable dopant for this process is the Ge 4+ (see Table 10). Finally, tetravalent dopants (M = Ge, Ti, Sn, Zr and Ce) were considered on the Si site. Solution energy was calculated using the following reaction equation.
Formation of Ca vacancies is favored by the doping of Ge 4+ though this process is endoergic with the solution energy of 2.50 eV. High solution energies (>3.50 eV) are calculated for other dopants meaning that they are highly unfavorable.

Ca-diffusion in the presence of dopants
\Here we calculate the activation energies for Ca-ion diffusion in the presence of most favorable dopants (Sr 2 + on the Ca site, Fe 3+ on the Al site and Ge 4+ on the Si site). Table 11 shows the activation energies for the local Ca hops and the long-range diffusion pathways. There is a very small reduction (by ~0.10 eV) in the activation energy in all cases. This small perturbation in the activation energies can be due to the ionic radius mismatch between host and guest ions. The current simulation considered the doping at dilute limit. Once the doping concentration increases the further reduction in the activation can be expected.

Conclusions
In this study, atomistic simulation techniques are used to understand the defect energetics, diffusion of Caion and solution of dopants. The Al-Si anti-site is found to be the most dominant defect inferring the cation disorder in this material as observed in the experiment. The second most favorable defect is the O-Frenkel. The Ca-ion diffusion pathway takes place in the ac plane exhibiting low ionic conductivity. The candidate isovalent dopants on the Ca, Al and Si sites are Sr, Fe and Ge respectively. Additional Ca or oxygen vacancies can be introduced by doping Fe 3+ on the Si site. The formation of calcium vacancies is favored by doping of Ge on the Al site. The present study aims to simulate further experimental work on the doped CaAl 2 Si 2 O 8 .