Magnesium ferrite nanostructures for detection of ethanol vapours-A first-principles study

The adsorption behaviour and electronic properties of ethanol vapour on MgFe2O4 ceramic nanostructures are studied using density functional theory technique. The structural stability of MgFe2O4 nanostructure is determined with the help of formation energy. The adsorption behaviour of ethanol molecules on MgFe2O4 base material is analysed in terms of average energy gap variation, Mulliken charge transfer, band gap and adsorption energy. The most prominent adsorption sites of ethanol vapours on MgFe2O4 nanostructure are investigated at atomistic level. The density of states spectrum reveals the clear picture about the electronic properties of MgFe2O4 nanostructure. The density of states and electronic band gap confirmed the adsorption of ethanol vapours on MgFe2O4 nanostructure. The changes in the energy band gap and density of states are observed upon adsorption of ethanol vapour molecules on MgFe2O4 nanostructure. The density of states spectrum also confirms the changes in peak maxima due to the transfer of electrons between MgFe2O4 nanostructure and ethanol vapours. The adsorption of oxygen atom from ethanol vapour on iron in MgFe2O4 is found to be more prominent rather than other adsorption sites. The findings show that MgFe2O4 nanostructure can be utilized to sense the presence of ethanol vapour in the atmosphere.


I. Introduction
The solid state gas/vapour sensor is in demand to monitor the atmospheric pollutants and the environment.Moreover, rapid response of chemical sensor is required to improve the quality and performance of gas/vapour sensors.Alcohol vapour sensors can be utilized for monitoring fermentation process [1], breath analyser and food packaging test [2].In general, the environment contains small amount of alcohol vapour molecules such as ethanol and methanol, which are highly toxic molecules.Especially, these vapours are hazardous to the human central nervous system, resulting in coma, blindness and death.Furthermore, inhalation of high concentration of alcohol vapour molecules can damage brain and other organs permanently.Thus, there is a need to develop a high performance gas/vapour sensor for alcohol detection.
Magnesium ferrite (MgFe 2 O 4 ) is one of the promi-nent spinel structured n-type semiconductor materials with direct band gap of 1.9 eV [3], which can be effectively used in various fields, including hyperthermia [4], sensor [5], metal ion removal [6], anode materials [7], azo-dye degradation [8] and photocatalysts [9].In addition, MgFe 2 O 4 exhibits high resistivity, low dielectric and magnetic losses, hence it is a significant system in heterogeneous catalysis, sensors and adsorption [10].For any gas/vapour sensor, its sensing properties are highly related to the microstructural characteristics of the system, which directly depend on its synthesis method [11].Doroftei et al. [12] reported that MgFe 2 O 4 material shows a good response towards ethanol molecules at 380 °C using auto-combustion method.Kaur et al. [13] reported the surface areas of magnesium ferrite when prepared by co-precipitation, solution combustion and sol-gel method with the help of urea, oxalyl dihydrazide and polyethylene glycol as fuels, respectively.Evidently, various compositions of spinel ferrite structures as well as their synthesizing methods alter their vapour sensing properties [14,15].
Godbole et al. [16] reported about MgFe 2 O 4 nanoparticles as a rapid gas sensor towards alcohol vapour molecules.Liu et al. [17] synthesized the magnesium ferrite nanoparticles and investigated their gas sensing properties towards H 2 S, CH 4 , ethanol and LPG vapours.Jeseentharani et al. [18] synthesized various metal ferrites including MgFe 2 O 4 material and studied their humidity sensing properties.In our previous work [19], we demonstrated the adsorption of H 2 S gas on α-Fe 2 O 3 nanostructures.Therefore, tailoring the electronic properties of MgFe 2 O 4 ceramics inspired the present study to investigate the adsorption behaviour of ethanol vapour molecules on magnesium ferrite.The adsorption of oxygen and hydrogen atom from the ethanol molecule on spinel structured MgFe 2 O 4 nanostructure is investigated and the obtained results are reported.

II. Computational details
The spinel MgFe 2 O 4 structure with space group of Fd 3m (227) was used in the present study.The MgFe 2 O 4 nanostructure is investigated with the help of density functional theory using SIESTA package [20].The local geometry relaxation was performed with generalized gradient approximation (GGA) in combination with exchange-correlation functional Perdew-Burke-Ernzerhof (PBE) level of theory including van der Waals (vdW) dispersion correction implemented by vdW-DF [21].Presently, the vdW-DF function is implemented in SIESTA code [21], which has been utilized for computing metal organic materials [22,23].Furthermore, this vdW-DF function somehow reduces the underestimation of the energy band gap.The Perdew-Burke-Ernzerhof function is more suitable for studying spinel ferrites, which is validated by previous reports in literature [24].For structural optimization of MgFe 2 O 4 , the energy cutoff is adjusted to 400 eV and the geometry relaxation was performed until the force and energy were converged to 0.02 eV/Å and 10 −6 eV, respectively.The Brillouin zones of MgFe 2 O 4 nanostructure are sampled with 5 × 5 × 5 k-point of the Monkhorst-pack.The electronic band structures, density of states, charge density and electron localization function (ELF) of MgFe 2 O 4 nanostructure were computed using SIESTA code.The approximation of transfer of electron is based on Mulliken charge analysis [25].The ethanol adsorption properties on MgFe 2 O 4 nanostructure were also investigated using SIESTA package.In the present study, the double zeta polarization (DZP) basis set is utilized for optimizing MgFe 2 O 4 nanostructures [26,27].

Structure of MgFe 2 O 4
The present study is focused to investigate the structural stability of cubic MgFe 2 O 4 spinel nanostructure and to use MgFe  The structural formula of MgFe 2 O 4 is generally expressed as (Mg 2+  1-x Fe 3+ x )[Mg 2+ x Fe 3+ 2-x ]O 4 , where square and round brackets refer to cation sites of octahedral [B] and tetrahedral (A) coordinates, respectively, and x represents the degree of inversion (which is ascertained as the fraction of A-sites filled by Fe 3+ cations).The tunable chemical and physical properties of spinel ferrites arose from their ability to transfer the cations among the octahedral [B] and tetrahedral (A) sites [28].In the present work, the base material consists of MgFe 2 O 4 nanostructure, which has sixteen Mg atoms, thirty two Fe atoms and sixty four O atoms in order to confirm the stoichiometry in the structure.The adsorption behaviour and electronic properties of ethanol molecule on MgFe 2 O 4 nanostructure are investigated and the results are discussed.
In general, the structural stability of MgFe 2 O 4 nanostructure can be determined using formation energy [29,30] as expressed in equation ( 1): where E(MFO−n) refers to the total energy of MgFe

Electronic properties of MgFe 2 O 4 nanostructure
The inspiration behind the present study is to investigate the adsorption behaviour and electronic properties of ethanol on MgFe 2 O 4 nanostructure.The electronic properties of MgFe 2 O 4 nanostructure material are described in terms of energy band structure.Figure 2 shows the electronic band gap of isolated MgFe 2 O 4 nanostructure.The band gap of MgFe 2 O 4 ceramics is observed to be 1.74 eV near the gamma point (Γ).Furthermore, the observed band gap of MgFe 2 O 4 nanostructure is validated with the reported experimental work (1.90 eV [3]).Benko et al. [31] reported the effect of defects on photoelectrochemical properties of MgFe 2 O 4 semiconductor and estimated the experimental band gap of 2.18 eV.The band gap of MgFe 2 O 4 nanostructure may be underestimated in the present study; since the density functional calculation with GGA/PBE exchange-correlation functional is used to study electron-electron interaction in their respective ground state.Moreover, the electronic and adsorption behaviour of ethanol in MgFe 2 O 4 base material remains unchanged even though the band gap is underestimated.
The density of states (DOS) spectrum [32,33] gives the perception of localization of charges in different energy intervals along MgFe 2 O 4 nanostructure.Figure 3 represents the projected density of states (PDOS) and DOS spectrum of the isolated MgFe 2 O 4 nanostructure.The peak maxima are noticed closer to the Fermi energy level (E F ) for isolated MgFe 2 O 4 nanostructure, which is favourable for the adsorption of target vapour/gas molecules that illustrates the transfer of electrons between MgFe 2 O 4 nanostructure and ethanol vapour molecules.The peak maximum in different energy intervals is observed owing to the overlapping of molecular orbitals among Mg, Fe and O atoms in MgFe 2 O 4 material.
In general, with chemi-resistive type of sensor, the current flowing through the molecular device is directly related to the amount of gas/vapour present in the atmosphere.From the observation of electronic band structure and DOS spectrum of MgFe 2 O 4 nanostructure, it is confirmed that MgFe 2 O 4 material can be utilized as chemi-resistive sensor.

Adsorption of ethanol vapour on MgFe 2 O 4
In the beginning stage of adsorption study of ethanol molecules on MgFe 2 O 4 base material, bond lengths of the system must be relaxed.The optimized bond lengths between the Mg & O and Fe & O are found to be 2.001 Å and 2.059 Å, respectively.In addition, we have also carried out the vibrational frequency calculation to verify that all relaxed spinel nanostructures are related to global minima.Moreover, in the present work we mainly focused on five different adsorption sites with global minima position as follows: The changes in the band gap of MgFe 2 O 4 nanostructure for the positions from A to E are noticed to be 0.53, 0.41, 0.64, 0.20 and 0.44 eV, respectively.Therefore, the changes in the energy band gap upon adsorption of ethanol molecules on MgFe 2 O 4 nanostructure and adsorption energy clearly show that MgFe 2 O 4 nanostructure can be efficiently used for the detection of ethanol vapour.Benko et al. [31] reported that magnesium ferrite has the energy band gap value of 2.18 eV.Recently, Fan et al. [3] have also confirmed that the energy band gap of pristine MgFe 2 O 4 material as 1.9 eV, which supports the present work.The validation of the present study with previously reported work is a significant criterion.Zhang et al. [36] proposed the inverse spinel structure MgFe 2 O 4 with Pt catalyst (Pt/MgFe 2 O 4 ), which provides efficient catalytic properties for CO oxidation below the normal humidity and temperature.Jeseentharani et al. [18] synthesized the various metal ferrites including CoFe 2 O 4 , MgFe 2 O 4 , using solid-state reaction.These ferrites nanoparticles have been efficiently used as humidity sensors.Liu et al. [17] synthesized MgFe 2 O 4 using solid-state reaction and demonstrated gas/vapour sensing towards H 2 S, CH 4 , ethanol and LPG.Recently, Godbole et al. [16] experimentally confirmed that MgFe 2 O 4 can be utilized for the alcohol vapour sensor.From the literature, we noticed that there are no computational works reported on MgFe 2 O 4 nanostructure as an ethanol sensor using first-principles studies.Moreover, the most favourable adsorption site of ethanol vapour molecule on MgFe 2 O 4 base material can be found only after investigating the percentage of average energy gap variation compared to its isolated counterpart.The other significant deciding factor to investigate the adsorption of ethanol vapour on MgFe 2 O 4 material is described in terms of transfer of electrons, which is examined by Mulliken charge transfer (Q) [37][38][39]  Mulliken charge with different negative values of adsorption energy are observed along with the changes in average energy gap variation.Thus, we conclude that the adsorption of O atom from ethanol molecules interacting with Fe atom in MgFe 2 O 4 nanostructure is observed to be the most favourable adsorption event.
Figure 6 illustrates the electron density of isolated MgFe 2 O 4 nanostructure upon adsorption of ethanol molecules.From the electron density diagram it is confirmed that the electron density is higher along the hydroxyl group (adsorption site) upon adsorption on MgFe 2 O 4 material.Thus, the transfer of electrons is noticed during the adsorption of ethanol vapour molecules, which strengthens presumption that MgFe 2 O 4 nanostructure act as a chemi-resistor material for the sensing of ethanol vapour molecules.
Figure 7 shows the projected density of states (PDOS) and density of states (DOS) spectrum of MgFe 2 O 4 nanostructure for the positions A to E. From this, it is evident that the more peak maxima are ob-served in LUMO level of MgFe 2 O 4 nanostructure.This implies that the free electrons can easily transfer between MgFe 2 O 4 nanostructure and ethanol molecules, which confirms the use of MgFe 2 O 4 material as chemical sensor.

IV. Conclusions
2 O 4 nanostructure to investigate the adsorption behaviour of ethanol in terms of electronic band gap, Mulliken charge transfer and adsorption energy.Figure 1 refers to the schematic diagram of MgFe 2 O 4 nanostructure with applied periodic boundary condition (PBC).The periodic boundary conditions on proposed cubic MgFe 2 O 4 spinel structure are used to reduce the edge effects.Furthermore, the MgFe 2 O 4 nanostructures are approximate and equivalent in an infinite array.Thus, we have chosen MgFe 2 O 4 spinel type nanostructure with applied PBC along the cubic face, which are utilized in the computation work.

Figure 1 .
Figure 1.Schematic diagram of MgFe 2 O 4 nanostructure 2 O 4 nanostructure, E(Mg), E(Fe) and E(O) are the corresponding energy of isolated Mg, Fe and O atoms and n is the total number of atoms in MgFe 2 O 4 nanostructure.Besides, x, y and z refer to the number of Mg, Fe and O atoms, respectively.In this work, the formation energy of MgFe 2 O 4 nanostructure is found to be −5.89eV, which infers the stability of MgFe 2 O 4 nanostructure.

C 2 HFigure 3 .Figure 4 .
Figures 4a,b represent H and O atoms from ethanol vapour molecules interacting with an Mg atom in MgFe 2 O 4 nanostructure named as positions A and B, respectively.Figures 4c,d illustrate H and O atoms from ethanol adsorbed on Fe atom in MgFe 2 O 4 nanostructure mentioned as position C and position D, respectively.Figure 4e represents the interaction of H atom from

Figure 5 .
Figure 5. Energy band structure of position: a) A, b) B, c) C, d) D and e) E . The positive value of Mulliken charge infers the transfer of free electrons from ethanol vapours to MgFe 2 O 4 nanostructure.In contrast, the negative magnitude of the Mulliken charge transfer confirms that the unbound electrons are transferred from MgFe 2 O 4 material to the ethanol vapour molecules [40-42].The Mulliken charge transfer for various positions A to E are found to be 0.678 e, 0.699 e, 1.630 e, 0.893 e and 0.170 e, respectively.It is evident that positive value of Mulliken charge is observed when ethanol molecules get adsorbed on MgFe 2 O 4 nanostructure.The large variation of the energy band gap is observed for position D with a moderate positive value of Mulliken charge together with a corresponding minimum value of adsorption energy.However, for position C high positive magnitude of Mulliken charge with low value of energy band gap variation is noticed, even though the corresponding adsorption energy values are found to be high.Interestingly, for position A and B almost the same values of

Figure 6 .Figure 7 .
Figure 6.Electron density of: a) isolated MgFe 2 O 4 nanostructure, b) position A, c) position B, d) position C, e) position D and f) position E

Table 1
represents the energy band gap, Mulliken charge transfer, percentage of average energy band gap variation and adsorption energy.As a result, it is clearly revealed that MgFe 2 O 4 nanostructure is a good candidate for ethanol vapour detection.Accordingly, MgFe 2 O 4 nanostructure exhibits good sensing response at all prominent adsorption sites.However, it is noticed that the interaction of O atom from an ethanol molecule with Fe atom in MgFe 2 O 4 material is more prominent than other adsorption sites, which is precisely verified by average energy gap variation.

Table 1 .
Mulliken charge, adsorption energy and average energy gap variation of MgFe 2 O 4 nanostructure