1 Introduction
Rapid advancement of the electronic technologies necessitates the development of novel functional materials with cheap, non-hazardous, electronically conductive and tunable characteristics for the enhancement of electronic properties. In recent years, there has been a growing interest in inorganic electride materials because of their promising applications in electronics due to their low work function and good electronic conductivity [
1‐
7]. As there are chemically independent electrons occupied in electrides, it is expected that they can be used as electron emitters, superconductors and catalysts for different reactions including depletion of CO
2 and activation of N
2 [
8‐
12]. Various stable inorganic electrides such as C12A7 [
1,
13] and Ca
2N [
14] have been reported in the literature. Based on the nature of electron localisation they are classified as zero-dimensional (electrons localising in cavities) [
15], one-dimensional (electrons localising in a channel) [
16] and two-dimensional (electrons confining in a layer) [
17]. Due to the potential uses of electrides in solid-state physics, there has been a significant interest to discover new electride materials or tailor the currently available electrides to tune their properties.
12CaO·7Al
2O
3 (C12A7) [
1,
12,
13] is a sub-nanoporous inorganic complex oxide mainly found in aluminous cement. It has a positively charged framework {(Ca
24Al
28O
64)
4+} (consisting of twelve nanocages per unit cell) that is compensated by extra-framework anions. When the framework is compensated by two O
2− ions, the resultant complex takes its stoichiometric form and is represented as [Ca
24Al
28O
64]
4+·(O
2−)
2 {C12A7:O
2−} [
18]. Appropriate reduction treatment replaces those two extra-framework O
2− ions with four electrons and the resultant complex takes its electride form with chemical formula of [Ca
24Al
28O
64]
4+·(e
−)
4 {C12A7:e
−}
1. As these four extra-framework electrons localise in the cages, this electride is classified as zero-dimensional. Extra-framework electrons have been replaced by a number of anions including F
− [
19], NH
2− [
20], Cl
− [
19] , S
2− [
21] and OH
− [
22]. Stabilisation of 12CaO·7Al
2O
3 by incorporating O
2−, F
−, Cl
−, S
2− ions has been discussed by Zhmoidin and Chatterjee [
21]. Thermodynamics and kinetics of hydroxide (OH
−) ions inside the cages of 12CaO·7Al
2O
3 (C12A7) were studied and it was concluded that the rate-determining is inward diffusion of OH
− ions [
22]. Encapsulation of NH
2− and H
−, as well as NH
2− was considered by Hayashi et al. [
20] and it was found that C
12A
7:NH
2− acts as a reactive nitrogen source for nitrogen transfer reactions. Furthermore, a variety of transition metals including Au [
23] have been incorporated into C12A7:e
− to optimise its catalytic activity and use as a storage material.
Cationic doping has been recently considered as an efficient strategy to modify the electronic properties of C12A7:e
− for its use in electro catalysis and oxygen reduction reactions. Khan et al. [
24] recently synthesised Sn-doped C12A7:e
− and concluded that doped composite exhibited a long-time stability and methanol resistance during the oxygen reduction reaction that can be used in fuel cells. Very recently, Hu et al. [
25] synthesised Sn-doped C12A7:e
− using sol-gel method and observed that Sn was in the form of Sn
4+ in the doped composite and the electronic configurations of Al and Ca were unaltered. Nevertheless, there are no theoretical studies that consider the experimental observation and calculate the electronic structures, thermodynamical stability and chemical states of doped-Sn.
In the present study, we employ density functional theory (DFT) simulations on a single Sn atom encapsulated and doped in both stoichiometric and electride forms of C12A7. The aim is to provide insights into thermodynamic stability, relaxed structures of encapsulated and doped C12A7, electron transfer between the Sn and C12A7, magnetic behaviour and electronic structures of resultant complexes.
2 Computational methods
Electronic structure calculations were performed on a single Sn atom encapsulated and doped in C12A7. We used a plane wave based DFT code VASP (Vienna Ab initio Simulation Package) [
26,
27], which solves the standard Kohn–Sham (KS) equations using plane waves as basis sets. The exchange-correlation term was modelled using generalized gradient approximation (GGA) as parameterised by Perdew, Burke, and Ernzerhof, PBE [
28]. Conjugate gradient algorithm [
29] was used to optimise the structures. Forces on the atoms were calculated using the Hellmann–Feynman theorem including Pulay corrections. In all relaxed configurations, forces on the atoms were less than 0.001 eV/Å. A plane-wave basis set with a cut-off value of 500 eV and a 2 × 2 × 2 Monkhorst–Pack [
30]
k-point mesh were used in all calculations. Encapsulation energy for a single Sn atom in C12A7:O
2− was calculated using the following equation:
$${E}_{\text{Enc}}= {E}_{\left({\text{Sn}}@{\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}-{E}_{\left({\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}-{E}_{\left({\text{Sn}}\right)},$$
(1)
where
\({E}_{\left({\text{Sn}}@{\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}\) is the total energy of a single Sn atom encapsulated in C12A7:O
2−,
\({E}_{\left({\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}\) is the total energy of bulk C12A7:O
2− and
\({E}_{\left({\text{Sn}}\right)}\) is the energy of an isolated gas phase Sn atom.
Substitution energy for a single Sn atom to replace a single Al atom in C12A7:O
2− was calculated using the following equation:
$${E}_{\text{Sub}}= {E}_{\left({\text{Sn:C}}12{\text{A}}7{\text{:O}}^{2-}\right)}+{E}_{\left({\text{Al}}\right)}-{E}_{\left(+{\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}-{E}_{\left({\text{Sn}}\right)},$$
(2)
where
\({E}_{\left({\text{Sn:C}}12{\text{A}}7{\text{:O}}^{2-}\right)}\) is the total energy of a single Sn atom substituted on the Al site in C12A7:O
2−,
\({E}_{\left({\text{C}}12{\text{A}}7{\text{:O}}^{2-}\right)}\) is the total energy of bulk C12A7:O
2− and
\({E}_{\left({\text{Sn}}\right)}\) is the energy of an isolated gas phase Sn atom.
Encapsulation and substitution energies with respect to bulk Sn were also calculated and reported. The van der Waals (vdW) interactions were included in all calculations as parameterised by Grimme et al. [
31]
4 Conclusions
In conclusion, we examined the efficacy of encapsulating and doping of a single Sn atom into the stoichiometric and electride forms of C12A7 using spin-polarised DFT together with dispersion. The calculations show that both forms of C12A7 exoergically encapsulate the Sn atom. The electride form exhibits an enhancement (by 2.36 eV) to encapsulate the atom due to the significant electron transfer (1.52 |e|) between extra-framework electrons and the Sn atom. Both encapsulated complexes are magnetic. Whilst there is a significant change (~ 1 eV towards conduction band) in the Fermi energy for C12A7:O2− only a small change (0.26 eV towards valence band) is noted for C12A7:e−.
Doping is endoergic in both forms of C12A7, however, the electride form is more energetically favourable (by 1.80 eV) for the doping process than that of stoichiometric form. In the stoichiometric form, the Sn forms almost + 4 state releasing some electrons to the cage. The electride form reduces the charge on the Sn atom due to the extra-framework electrons. Nevertheless, it is expected that similar charge state is formed for the Sn in the electride form as well. This observation is in agreement with the experiment. Resultant complexes are magnetic in both cases. Doping in C12A7:O2− has increased the Fermi energy by 1.60 eV towards the conduction band. Fermi energy is almost unaltered (~ by 0.04 eV) up on doping in C12A7:e−. Current simulation study provides a detail information regarding the stability, electron transfer, magnetic behaviour and electronic structures of Sn-encapsulated and Sn-doped C12A7. We anticipate that future experimental study can use this information to interpret their experimental data.
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