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Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: Ab initio method
Journal Pre-proof Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: Ab initio method O.M. Sousa, R.S. Araujo, G.J.B. Junior PII:
S0022-3697(19)31311-3
DOI:
https://doi.org/10.1016/j.jpcs.2019.109298
Reference:
PCS 109298
To appear in:
Journal of Physics and Chemistry of Solids
Received Date: 6 June 2019 Revised Date:
3 December 2019
Accepted Date: 4 December 2019
Please cite this article as: O.M. Sousa, R.S. Araujo, G.J.B. Junior, Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: Ab initio method, Journal of Physics and Chemistry of Solids (2020), doi: https://doi.org/10.1016/j.jpcs.2019.109298. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Author Statement Osmar Machado de Sousa Raiane Sodré de Araújo Gilberto José Barbosa Junior
Osmar Machado de Sousa: Computational calculations, Software WIEN2k, Writing- Reviewing and Editing. Raiane Sodré de Araújo: Bader analysis, Reviewing and Editing. Gilberto josé Barbosa Junior: defect formation energy, Reviewing and Editing.
Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: ab initio method O.M. Sousa1*, R. S. Araujo1, G. J. B. Junior1 1
Physics Department, Federal University of Sergipe, São Cristóvão, Sergipe, 49100-000, Brazil
Abstract: Ab initio calculations based on density functional theory are used to study the structural, energetic, electronic, and magnetic properties of lithium aluminate (LiAl5O8) spinel doped with Fe and Cr. Two possible schemes are considered: (1) doping with Fe or Cr at the Al3+ 8c site and (2) doping with Fe or Cr at the Al3+ 12d site. Exchange and correlation effects are described via the generalized gradient approximation PBEsol functional (structural properties) and the modified BeckeJohnson potential (defect formation energy, electronic structure, and magnetic properties). For each scheme, the local structure around the defect is predicted. Our calculations show that Fe and Cr prefer the octahedral site of Al. A Bader analysis shows that the defect charge is 3+ for both Fe and Cr. Calculation of the electronic structure shows that the 3d states of Cr3+ and Fe3+ are below the Fermi energy and within the band gap of LiAl5O8. For replacement of Al by Fe, the state density calculation shows that Fe3+ has a valence electron configuration of 4s03d5 (8c and 12d sites). For replacement of Al by Cr, it is found that Cr3+ has a valence electron configuration of 4s03d3 (8c and 12d sites). There is a magnetic moment in the unit cell due to the presence of Cr and Fe in the LiAl5O8 lattice.
Keywords: LiAl5O8, Structural properties, Energetic properties, Electronic properties, Magnetic properties.
*Corresponding author. E-mail address: [email protected] (O.M. Sousa). Tel.: +55-79-991476680
1.
Introduction
Spinel structures belong to a crystal group that is used as phosphorous or magnetic materials. The lithium aluminate LiAl5O8 (LAO) spinel host lattice has become a widely used material for the doping of transition metal (TM) ions and rare earth ions [1–5]. The great potential of this compound arises from its complex phase transition and interesting magnetic, optical, chemical, mechanical, and morphological properties, meaning that this material has been well studied in recent years [1–13]. The triplet state of Cr3+ is the stablest, as after dividing the crystalline field, all eight low-spin terms of the 3d3 electronic configuration give rise to several energy levels, making Cr3+ a suitable dopant material for applications in various optoelectronic devices and solidstate laser crystals. Cr-doped LAO exhibits unusual magnetic properties that open the way for possible important applications in microwave, holography, and cathode battery techniques. LAO doped with Fe ions has excellent fluorescent and magnetic properties, and has been extensively studied over the years [6,7]. Figure 1 shows the cubic spinel structure of LAO (under ambient conditions). The crystal symmetry of LAO is described by the P4332 space group (no. 212), with lattice parameters a = b = c = 7.908 Å, and the unit cell contains 56 atoms, with four formula units per cell. There is one tetrahedral site (8c) and two octahedral sites (4b and 12d). There are five nonequivalent atoms: O2-1, O2-2, Al3+1, Al3+2, and Li+. The Al ions occupy the tetrahedral site (Al1, 8c) and an octahedral site (Al2, 12d), whereas the Li+ ion occupies only an octahedral site (4b). The tetrahedral site is surrounded by four oxygens with bond lengths of 1.782 Å for Al–O1 and 1.827 Å for Al–O2. The octahedral site is surrounded by six oxygens with bond lengths of 2.044 Å and 1.850 Å for Al–O1 and 1.944 Å for Al–O2. Both sites are distorted within the structure of LAO. It is known from the literature that the Cr ion has a preference for replacing the Al3+ ion at the octahedral site with C2 local symmetry [14]. However, by electron paramagnetic resonance (EPR) studies, Singh et al. [9] found indications of Cr ions in different environments, and suggested that they may be occupying both sites. On the basis of EPR measurements, Kutty and Nayak [15] determined that the Fe ion can occupy the tetrahedral and octahedral sites. Theoretical calculations of the structural, electronic, and optical properties of LAO using density functional theory (DFT) [16,17] were reported in [13], although this
material not was doped with TM and rare earth ions. In the current work, we perform a theoretical study using DFT in LAO doped with Fe and Cr. The aim of this study is to investigate the structural, energetic, electronic, and magnetic properties of LAO doped with Fe and Cr ions. To the best of our knowledge, the present study is the first theoretical work to examine these properties of LAO. Through this work, we hope to make a theoretical contribution to the present understanding of questions such as: 1. Which Al sites (tetrahedral or octahedral) do the Fe and Cr dopants prefer to occupy, and why? 2. What are the changes in the local structure around defects? 3. What is the charge of the dopants when they are inserted into the host matrix? 4. How are defect states distributed over and around the band gap? 5. What are the magnetic characteristics that defects can produce in the compound? This study is part of a series of theoretical studies using DFT [18–32] on the structural, electronic, magnetic, and optical properties of various pure and doped compounds. The study of these properties through DFT shows that this theory is quite satisfactory. These studies contribute to the reliability of the results presented in this article. The results of the theoretical calculations are compared with experimental ones whenever possible.
2.
Computational methods
The calculations were performed by DFT, with use of the full-potential linearized augmented plane wave method [33], and were implemented with the WIEN2k computer code [34]. The electronic wave functions and crystalline potentials were expanded into spherical harmonics based on nonoverlapping spheres centered at each nuclear position (the atomic spheres) and plane waves in the rest of the space (the interstitial region). The expansion of the wave functions within the atomic spheres was equal to lmax = 10, and the number of plane waves in the interstitial region was limited to KmaxRMT = 7/RMT(O). The charge density was expanded by a Fourier series up to Gmax = 20. The number of
points used in the calculations was divided into two parts: (1)
the structural and electronic properties used 20 properties used 57
points (7 x 7 x 7) and (2) the optical
points (12 x 12 x 12) in the first Brillouin zone. The valence
electron states considered for the LAO atoms and dopants and their respective muffintin beam radii are shown in Table 1. The effects of exchange and electronic correlation used for relaxation of the atomic positions of LAO doped with Fe or Cr were the generalized gradient approximation (GGA) PBEsol [35], which is an energy functional. We used a modified Becke-Johnson (mBJ) potential [36] to calculate the energy and the electronic, magnetic, and optical properties because the GGA PBEsol potential underestimates the band gaps of semiconductors and insulators. All self-consistent calculations were successfully converged with an energy precision of 10-5 Ry.
3.
Results
3.1.
Defect formation energy
The energetic cost for Fe and Cr doping at the Al3+ (8c and 12d) sites was obtained by our calculating the defect formation energy (EFd), which is given by EFd = (Epure LAO + EFe or Cr ion) − (EFe- or -Cr-doped LAO + EAl ion), where the first term represents the sum of the total energies of the pure unit cell of LAO and the free Fe or Cr atom, while the second represents the total energy of the unit cell of Fe- or Cr-doped LAO plus the energy of the free Al3+ atom (at the 8c or 12d site), which is removed from the unit cell to introduce the impurity. The lattice energies of pure and doped LAO were obtained with the same parameters (lmax, Kmax.RMT, Gmax, number of points k, atomic sphere radii, etc.) for each type of calculation performed. The free atom energies (for Fe, Cr, and Al) were obtained for their stablest structures by DFT plus linearized augmented plane wave plus mBJ calculations. The energy of the free atom was approximated by the total energy of atoms in the primitive unit cell. The calculations for the Fe- and Cr-doped LAO and the free atoms were performed on the basis of polarized spin. The high energies associated with the formation of defects suggest that these defects are not significant in this material, since it is necessary to expend a lot of energy in their formation [37]. From this, and on the basis of its charge state, it is
possible to evaluate which impurity (Fe or Cr) is stabler when it replaces Al3+ at the tetrahedral (8c) or octahedral (12d) site of LAO. The stablest charge state is that with the lowest formation energy for a given Fermi level. Table 2 shows the defect formation energies with two possible accommodations for Fe or Cr ions at the tetrahedral and octahedral Al3+ sites in the LAO lattice. The energy calculations for the defect were performed with the mBJ potential. According to Table 2, there is a small preference for Fe or Cr to replace Al at the octahedral site. However, we can see that the formation energy for incorporation at the Al3+ 8c site is very close to the formation energy for incorporation at the Al3+ 12d site. On the basis of this, we can conclude that both mechanisms are likely to occur. Results from experimental studies of Fe- and Cr-doped LAO agree with our results for the defect formation energy. Kutty and Nayak [15] determined that the Fe3+ ion can occupy both the tetrahedral site and the octahedral site. Our results show that there is a small preference for the Cr3+ ion to occupy the octahedral site, and this agrees with experimental results [38]; however, there is a difference in the formation energy of only 1.01 eV, which shows that the Cr ion can also occupy the tetrahedral site. This result is also in agreement with experimental work by Singh et al. [9], who found that the Cr ion can occupy both sites. On the basis of this, our results are presented assuming that the Fe or Cr ions can replace the Al3+ ion at both the tetrahedral site and the octahedral site.
3.2.
Local structure around defects
For the calculation of the structural properties, the (optimized) theoretical lattice parameter used was that of the pure structure and was taken from [13]. We performed a relaxation of the atomic positions of LAO containing Fe or Cr impurities. To prove that the optimized lattice parameter of the pure structure [13] does not change significantly, the lattice parameter of LAO doped with Fe (8c site) was optimized as an example and was compared with that of the pure structure (Figure 2). The same computational data used for the optimization of the lattice parameter of the pure structure [13] were used in optimizing the lattice parameter of LAO doped with Fe (8c site). Figure 2 shows the optimization of the lattice parameter of Fe-doped
LAO. The lattice parameter that corresponds to the volume optimized for Fe-doped LAO is practically the same as that of pure LAO, with a difference of only 0.1%. This is as expected, since only one Al3+ ion is replaced in the unit cell, corresponding to 1/56 (i.e., a small increase in the optimized unit cell volume), which is the result of the greater ionic radius of Fe compared with Al. We therefore conclude that we can use the optimized lattice parameters of pure LAO [13] to relax the atomic positions of LAO doped with Fe or Cr, leading to a computational gain and reliable results. After the relaxation of the atomic positions, we can analyze the local structures around the Fe and Cr impurities inserted in the LAO network. Knowledge of the local structure around the defects is very important, since this information can be useful in the interpretation of optical spectroscopy and EPR data. The substitution of an Al3+ ion by an Fe or Cr ion causes changes in the distances between the atoms around the defect (tetrahedral and octahedral structure), resulting in a decrease in the crystalline symmetry, and as a consequence, the number of nonequivalent atoms is also changed. Table 3 shows the Fe–O and Cr–O bond lengths at the tetrahedral and octahedral sites. It can be seen from Table 3 that the Fe–O and Cr–O bond lengths at both sites (8c and 12d) are greater than the Al–O bond length (see [39]). This is because the ionic radii of the Fe and Cr impurities are greater than the ionic radius of Al. All calculations of the local structure around the defects were performed with the GGA PBEsol functional. Table 4 shows the atomic coordinates of the Fe and Cr impurities and all of the nearest neighbors connected to them. An Fe or Cr ion replaces Al3+, which previously occupied the position X = 0.2471, Y = 0.7471, Z = 0.7528 (tetrahedral site) or X = 0.3750, Y = 0.6315, Z = 0.3815 (octahedral site). It can be seen from Table 4 that the positions of the Fe and Cr ions when inserted into the tetrahedral or octahedral site to replace Al3+ remain almost the same. This effect is related to the stablest charge configuration of the defect, since, as can be seen from Table 5, all Fe or Cr ions are incorporated in the host lattice with charge 3+ (i.e., the same as Al3+). We conclude that the small differences in both the bond lengths (TM–O) and the atomic coordinates of Fe and Cr when they are inserted at the Al3+ site are entirely related to the differences in the ionic radii.
3.3.
Magnetic moments and Bader charge
All calculations of LAO doped with the muffin-tin scheme were performed by our taking into account the polarized spin system. On the basis of these calculations, we expect the system to converge to the spin configuration that makes it as stable as possible. The total spin magnetic moment in the unit of Bohr magneton (μB) is obtained from the difference between the total number of up spins and down spins in the unit cell. Table 5 presents the magnetic moments obtained for the doped systems. The pure system has no magnetic moment. We used the mBJ exchange and correlation potential for the magnetic moment calculations and also for the calculation of the Bader charges, since these data are better described by the mBJ potential than by the GGA PBEsol functional. On the basis of the reproduced charge density, calculations of the Bader charge were performed for all doped systems. The results were obtained with the CRITIC2 software package [40], which has a very efficient implementation of the quantum theory of atoms in molecules [41,42]. We obtained a value of approximately 1μB for the total spin magnetic moment in the unit cell for replacement of Al by Fe at the tetrahedral site. For replacement of Al by Fe at the octahedral site, we obtained a value of − 1μB in the unit cell. The Fe ion has a magnetic moment of approximately 0.87μB at the 8c site and approximately −0.81μB at the 12d site, and the total moment in the interstitial region plus a magnetic moment transferred to each of its four neighboring oxygens at the tetrahedral site and its six neighboring oxygens at the octahedral site, giving the total magnetic moment of the cell. Thus, we conclude that there is an electron in the Fe ion with an unpaired spin, possibly in the d orbital, with an up configuration at the 8c site and down configuration at the 12d site. These results show that the impurity transfers part of its magnetic moment to its vicinity. Hence, the magnetism present in the compound is located in the region of the defect with ferromagnetic configuration, since for the other distant atoms the magnetic moment is zero. The total magnetic moment in the unit cell is 3.0000μB when the Cr ion replaces the Al3+ ion at the tetrahedral and octahedral sites. Of this value in the total cell, the Cr ion is responsible for approximately −2.4000μB at the octahedral site, which when
added to the total moment in the interstitial region of −0.4874μB plus the magnetic moment transferred to each of its six oxygens makes up the total magnetic moment of the cell. At the tetrahedral site, the Cr ion has a magnetic moment of −2.3381μB, and this added to the moment of the interstitial region of −0.4171μB plus what is transferred to the four oxygens gives the moment of the cell. We therefore conclude that there are approximately three electrons in the d state of Cr with unpaired spin with the down configuration at both sites. Our results show that the impurity transfers part of its magnetic moment to its neighborhood (tetrahedral and octahedral sites), causing its magnetism to be in the region of the defect with ferromagnetic configuration. The Bader charges for replacement of Al3+ by Fe and replacement of Al3+ by Cr (Table 5) were approximately 2.5+ for both sites. Although these values are slightly less than 3+, we can assume that these results correspond to the charge of three electrons in Fe and Cr. This result is confirmed by an electron population analysis as part of a study of the electronic properties (see Section 3.4). In general, the Bader charges obtained by DFT calculations are slightly smaller than those predicted from experiments.
3.4.
Electronic properties
Calculations of the total density of states (TDOS), partial density of states (PDOS), and band structure for the pure system have already been performed [13]. Pure LAO is an insulator with an indirect band gap (Δ → Γ) of 8.4 eV. At the top of the valence band are predominately 2p states of O1 and O2, and the bottom of the conduction band is composed of 3s states of Al1 and Al2 and 3p states of Al1. Figure 3 shows the TDOS and PDOS of pure LAO and the Fe or Cr impurities inserted in the host lattice. The TDOS for pure LAO indicates a nonmagnetic system, as already shown in [13]. For the other cases, the TDOS of the doped LAO indicates a magnetic moment, since states with spin up are not identical to those with spin down. When the TDOS of LAO doped with Fe or Cr are compared with the TDOS of the pure system, it is easy to see that with the addition of the impurity, the energy bands close to the band gap undergo more changes than the more distant energy bands. As can be seen from Figure 3,
defect energy levels are inserted into and around the band gap, more precisely in the d states of Fe or Cr impurities. When the Fe ion is inserted into the LAO host lattice (Figure 3), ferromagnetic properties appear in the unit cell (1μB at the 8c site and −1μB at the 12d site). According to Figure 3 (TDOS and PDOS), the d states of spin-up and spin-down Fe, which are located above the Fermi energy (within the band gap), are empty at both the tetrahedral site and the octahedral site. However, the energy levels of the d states of Fe that are below the Fermi energy are occupied by three electrons with spin up and two electrons with spin down (8c site). At the 12d site, there are two electrons with spin up and three electrons with spin down. The total number of electrons occupying both sites below the Fermi energy is five, indicating that the d orbital of Fe has a 3d5 configuration. In the 4s orbital, no electron with spin up or occupied down (4s0) was obtained. Therefore, for replacement of Al3+ by Fe for the 3+ charge state, the state density calculation indicates that Fe has a valence electron configuration of 4s03d5 (8c and 12d sites). Our results for the density of states are compatible with the existence of a magnetic moment in the Fe ion of 0.8μB at the 8c site and −0.9μB at the 12d site; these values indicate the existence of a d electron with unpaired spin, and reinforce the results of the Bader analysis, which indicate that Fe has a charge of 3+. When the Cr ion is inserted at the tetrahedral and octahedral Al3+ sites, the up and down d states of Cr3+ that are located on the band gap are empty, and the energy levels of Cr3+ d states that are below the Fermi energy are occupied by three electrons with spin down at both sites. The total number of electrons occupied below the Fermi energy is three (tetrahedral and octahedral sites), indicating that the d orbital of Cr has a 3d3 configuration. In the 4s orbital, no electron with spin up or occupied down (4s0) was obtained. Thus, for the case of replacement of Al3+ by Cr, the population analysis of the states shows that Cr has a valence electron configuration of 4s03d3 at both sites. These results are compatible with the existence of a magnetic moment in the Cr3+ ion of −2.5μB, indicating the existence of a 3d electron with unpaired spin. This supports the results of the Bader analysis, which show that Cr has a charge of 3+. The density of states and the analysis of the Bader charges show that the electron configuration of Fe is 4s03d5 (8c and 12d sites) and for Cr the configuration is
4s03d3 (8c and 12d sites), indicating that both the Fe ions and the Cr ions have a charge of 3+ (Fe3+ and Cr3+), in agreement with the experimental results [15,39].
4. Conclusion A theoretical study of the structural, energetic, magnetic, and electronic properties of the LAO spinel host lattice was performed. For these calculations two possible schemes were considered: (1) doping with Fe or Cr at the Al3+ 8c site and (2) doping with Fe or Cr at the Al3+ 12d site. The exchange and correlation effects were described via the GGA PBEsol functional and the mBJ potential. Initially, we determined the local structure around the defects, whose atomic coordinates and bond lengths had small differences from the pure compound because of the greater ionic radii of Fe and Cr. Our calculations show that Fe and Cr prefer the octahedral site of Al. When Fe and Cr ions were inserted into the LAO lattice, a certain amount of magnetic moment appeared in the unit cell: for replacement of Al3+ by Fe, 1μB at the 8c site and −1μB at the 12d site); for replacement of Al3+ by Cr, −30,000μB at the 8c and 12d sites. The electronic structure revealed that the d states of Cr and Fe are below the Fermi level and within the band gap. The valence electron configuration when Fe replaces Al is 4s03d5 (8c and 12d sites), and when Cr replaces Al it is 4s03d3 (8c and 12d sites). A Bader analysis determined that Fe and Cr defects when inserted into the LAO host lattice have a charge of 3+. These results were verified by an electron population analysis, which gave results that were equivalent to the Bader analysis (i.e., a charge of 3+ for both Fe and Cr). These theoretical results are directly linked to the application of this material, since the magnetic and luminescent properties of Cr- or Fe-doped LAO depend on where the impurity is inserted, the type of magnetic moment that arises in the cell, the valence electron configuration, and the electronic transitions from the valence band to the conduction band. This theoretical study therefore makes a significant contribution to the correct analysis of the experimental data and future applications of this material.
Acknowledgments The authors are grateful to CAPES (Brazilian Federal Agency) and CNPq (Brazilian National Council for Scientific and Technological Development).
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https://doi.org/10.1016/0022-4596(79)90107-5. [40] A.O.-Roza, E.R. Johnson, V. Luana, CRITIC2: a program for real-space analysis of quantum chemical interactions in solids, Comput. Phys. Commun. 185 (2014) 1007– 1018. https://doi.org/10.1016/j.cpc.2013.10.026. [41] R.F.W. Bader, G.A. Jones, The electron density distributions in hydride molecules: I. The water molecule, Can. J. Chem. 41 (1963) 586–606. https://doi.org/10.1139/v63084. [42] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, first ed., Clarendon Press, Oxford, 1994. Fig. 1. Cubic spinel structure of LiAl5O8. The Li+ ion occupies the 4b octahedral site. The Al3+ ion occupies both the 8c tetrahedral site and the 12d octahedral site.
Fig. 2. Structural optimization of doped LiAl5O8 (LAO) with Fe ions in the tetrahedral sites. The LAO lattice parameter was relaxed by our varying the volume of the primitive cell from −11% to 11% (in steps of 1%) in relation to the volume of the experimental unit cell used.
Fig. 3. Total density of states (TDOS) for pure LiAl5O8 (LAO) and TDOS and partial density of states (PDOS) for Fe-doped LAO (LAO:Fe) and Cr-doped LAO (LAO:Cr) at the tetrahedral and octahedral sites.
Table 1. Atomic sphere radius (RMT) and valence states used in the present calculations. Element 13
RMT (au)
Valence state
Al
1.6
3s23p1
3
Li
1.5
2s¹
8
O
1.5
2s22p4
1.6
4s23d6
1.6
4s13d5
26
Fe
24
Cr
Table 2. Formation energies of Fe and Cr defects in the LiAl5O8 lattice calculated with the modified Becke-Johnson potential. EFd
Tetrahedral
Octahedral
EFe→Al3+
−2.810
−2.984
ECr→Al3+
−1.002
−2.012
Table 3. Fe–O and Cr–O bond lengths in Fe- and Cr-doped LiAl5O8 (LAO) at the 8c and 12d sites calculated with the generalized gradient approximation PBEsol functional. Fe-doped LAO
Cr-doped LAO
12d Bond
8c Bond
Bond
12d Bond
Bond
8c Bond
length
length
length
(Å)
(Å)
(Å)
Bond
Bond length (Å)
Fe–O5
1.92
Fe–O16
1.82
Cr–O5
1.97
Cr–O16
1.84
Fe–O6
1.92
Fe–O17
1.82
Cr–O6
1.97
Cr–O17
1.84
Fe–O19
1.91
Fe–O18
1.82
Cr–O19
1.94
Cr–O18
1.84
Fe–O20
1.91
Fe–O32
1.99
Cr–O20
1.94
Cr–O32
2.05
Fe–O29
1.96
Cr–O29
1.99
Fe–O30
1.96
Cr–O30
1.99
Table 4. Atomic coordinates of Fe and Cr impurities and all nearest neighbors. The atomic coordinates X, Y, and Z are expressed in terms of the lattice parameter a. 12d site
8c site
X
Y
Z
X
Y
Z
Fe
0.3750
0.6274
0.3774
Fe
0.2526
0.7526
0.7473
O5
0.1347
0.6157
0.3648
O16
0.1128
0.8888
0.6276
O6
0.6152
0.6148
0.3657
O17
0.3723
0.6128
0.6112
O19
0.3671
0.6140
0.6167
O18
0.3888
0.8723
0.8871
O20
0.3828
0.8667
0.3640
O32
0.1083
0.6083
0.8916
O29
0.3652
0.6374
0.1322
O30
0.3847
0.3822
0.3874
Cr
0.3750
0.6293
0.3793
Cr
0.2533
0.7533
0.7466
O5
0.1281
0.6176
0.3644
O16
0.1125
0.8907
0.6251
O6
0.6218
0.6144
0.3676
O17
0.3741
0.6125
0.6092
O19
0.3671
0.6134
0.6216
O18
0.3907
0.8741
0.8874
O20
0.3828
0.8716
0.3634
O32
0.1049
0.6049
0.8950
O29
0.3640
0.6373
0.1297
O30
0.3860
0.3797
0.3873
Table 5. Magnetic moments (total and per atom) and Bader charges (in electron charge units) for Fe- or Cr-doped LiAl5O8 at the 8c and 12d sites of Al3+. The exchange and correlation potential used was the modified Becke-Johnson potential. 8c site Magnetic
12d site q
Magnetic
moment
moment
(µB)
(µB)
Fe
0.8780
IR
0.0253
-0.0399
Total
1.0000
−1.0000
Cr
−2.3381
IR
-0.4171
-0.4874
Total
−3.0000
−3.0000
IR, interstitial region.
2.4896
2.5149
−0.8176
−2.3915
q
2.4702
2.49119
Highlights •
The structural, energetic, electronic, and magnetic properties of lithium aluminate (LiAl5O8) spinel doped with Fe and Cr are studied.
•
Exchange and correlation effects are described via the generalized gradient approximation PBEsol functional and the modified Becke-Johnson potential.
•
A Bader analysis shows that the defect charge is 3+ for both Fe and Cr.
•
For replacement of Al by Fe, the state density calculation shows that Fe3+ has a valence electron configuration of 4s03d5 (8c and 12d sites).
•
For replacement of Al by Cr, it is found that Cr3+ has a valence electron configuration of 4s03d3 (8c and 12d sites).
•
The formation energy for incorporation at the Al3+ 8c site is very close to the formation energy for incorporation at the Al3+ 12d site.
Declaration of interests The authors Osmar machado de Sousa, Raiane Sodré de Araújo, Gilberto josé Barbosa Junior declare that they have no known competing financialinterestsor personal relationships that could have appeared to influence the work reported in this paper.
S0022-3697(19)31311-3
DOI:
https://doi.org/10.1016/j.jpcs.2019.109298
Reference:
PCS 109298
To appear in:
Journal of Physics and Chemistry of Solids
Received Date: 6 June 2019 Revised Date:
3 December 2019
Accepted Date: 4 December 2019
Please cite this article as: O.M. Sousa, R.S. Araujo, G.J.B. Junior, Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: Ab initio method, Journal of Physics and Chemistry of Solids (2020), doi: https://doi.org/10.1016/j.jpcs.2019.109298. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Author Statement Osmar Machado de Sousa Raiane Sodré de Araújo Gilberto José Barbosa Junior
Osmar Machado de Sousa: Computational calculations, Software WIEN2k, Writing- Reviewing and Editing. Raiane Sodré de Araújo: Bader analysis, Reviewing and Editing. Gilberto josé Barbosa Junior: defect formation energy, Reviewing and Editing.
Calculation of the structural, energetic, electronic, and magnetic properties of LiAl5O8 doped with Fe and Cr: ab initio method O.M. Sousa1*, R. S. Araujo1, G. J. B. Junior1 1
Physics Department, Federal University of Sergipe, São Cristóvão, Sergipe, 49100-000, Brazil
Abstract: Ab initio calculations based on density functional theory are used to study the structural, energetic, electronic, and magnetic properties of lithium aluminate (LiAl5O8) spinel doped with Fe and Cr. Two possible schemes are considered: (1) doping with Fe or Cr at the Al3+ 8c site and (2) doping with Fe or Cr at the Al3+ 12d site. Exchange and correlation effects are described via the generalized gradient approximation PBEsol functional (structural properties) and the modified BeckeJohnson potential (defect formation energy, electronic structure, and magnetic properties). For each scheme, the local structure around the defect is predicted. Our calculations show that Fe and Cr prefer the octahedral site of Al. A Bader analysis shows that the defect charge is 3+ for both Fe and Cr. Calculation of the electronic structure shows that the 3d states of Cr3+ and Fe3+ are below the Fermi energy and within the band gap of LiAl5O8. For replacement of Al by Fe, the state density calculation shows that Fe3+ has a valence electron configuration of 4s03d5 (8c and 12d sites). For replacement of Al by Cr, it is found that Cr3+ has a valence electron configuration of 4s03d3 (8c and 12d sites). There is a magnetic moment in the unit cell due to the presence of Cr and Fe in the LiAl5O8 lattice.
Keywords: LiAl5O8, Structural properties, Energetic properties, Electronic properties, Magnetic properties.
*Corresponding author. E-mail address: [email protected] (O.M. Sousa). Tel.: +55-79-991476680
1.
Introduction
Spinel structures belong to a crystal group that is used as phosphorous or magnetic materials. The lithium aluminate LiAl5O8 (LAO) spinel host lattice has become a widely used material for the doping of transition metal (TM) ions and rare earth ions [1–5]. The great potential of this compound arises from its complex phase transition and interesting magnetic, optical, chemical, mechanical, and morphological properties, meaning that this material has been well studied in recent years [1–13]. The triplet state of Cr3+ is the stablest, as after dividing the crystalline field, all eight low-spin terms of the 3d3 electronic configuration give rise to several energy levels, making Cr3+ a suitable dopant material for applications in various optoelectronic devices and solidstate laser crystals. Cr-doped LAO exhibits unusual magnetic properties that open the way for possible important applications in microwave, holography, and cathode battery techniques. LAO doped with Fe ions has excellent fluorescent and magnetic properties, and has been extensively studied over the years [6,7]. Figure 1 shows the cubic spinel structure of LAO (under ambient conditions). The crystal symmetry of LAO is described by the P4332 space group (no. 212), with lattice parameters a = b = c = 7.908 Å, and the unit cell contains 56 atoms, with four formula units per cell. There is one tetrahedral site (8c) and two octahedral sites (4b and 12d). There are five nonequivalent atoms: O2-1, O2-2, Al3+1, Al3+2, and Li+. The Al ions occupy the tetrahedral site (Al1, 8c) and an octahedral site (Al2, 12d), whereas the Li+ ion occupies only an octahedral site (4b). The tetrahedral site is surrounded by four oxygens with bond lengths of 1.782 Å for Al–O1 and 1.827 Å for Al–O2. The octahedral site is surrounded by six oxygens with bond lengths of 2.044 Å and 1.850 Å for Al–O1 and 1.944 Å for Al–O2. Both sites are distorted within the structure of LAO. It is known from the literature that the Cr ion has a preference for replacing the Al3+ ion at the octahedral site with C2 local symmetry [14]. However, by electron paramagnetic resonance (EPR) studies, Singh et al. [9] found indications of Cr ions in different environments, and suggested that they may be occupying both sites. On the basis of EPR measurements, Kutty and Nayak [15] determined that the Fe ion can occupy the tetrahedral and octahedral sites. Theoretical calculations of the structural, electronic, and optical properties of LAO using density functional theory (DFT) [16,17] were reported in [13], although this
material not was doped with TM and rare earth ions. In the current work, we perform a theoretical study using DFT in LAO doped with Fe and Cr. The aim of this study is to investigate the structural, energetic, electronic, and magnetic properties of LAO doped with Fe and Cr ions. To the best of our knowledge, the present study is the first theoretical work to examine these properties of LAO. Through this work, we hope to make a theoretical contribution to the present understanding of questions such as: 1. Which Al sites (tetrahedral or octahedral) do the Fe and Cr dopants prefer to occupy, and why? 2. What are the changes in the local structure around defects? 3. What is the charge of the dopants when they are inserted into the host matrix? 4. How are defect states distributed over and around the band gap? 5. What are the magnetic characteristics that defects can produce in the compound? This study is part of a series of theoretical studies using DFT [18–32] on the structural, electronic, magnetic, and optical properties of various pure and doped compounds. The study of these properties through DFT shows that this theory is quite satisfactory. These studies contribute to the reliability of the results presented in this article. The results of the theoretical calculations are compared with experimental ones whenever possible.
2.
Computational methods
The calculations were performed by DFT, with use of the full-potential linearized augmented plane wave method [33], and were implemented with the WIEN2k computer code [34]. The electronic wave functions and crystalline potentials were expanded into spherical harmonics based on nonoverlapping spheres centered at each nuclear position (the atomic spheres) and plane waves in the rest of the space (the interstitial region). The expansion of the wave functions within the atomic spheres was equal to lmax = 10, and the number of plane waves in the interstitial region was limited to KmaxRMT = 7/RMT(O). The charge density was expanded by a Fourier series up to Gmax = 20. The number of
points used in the calculations was divided into two parts: (1)
the structural and electronic properties used 20 properties used 57
points (7 x 7 x 7) and (2) the optical
points (12 x 12 x 12) in the first Brillouin zone. The valence
electron states considered for the LAO atoms and dopants and their respective muffintin beam radii are shown in Table 1. The effects of exchange and electronic correlation used for relaxation of the atomic positions of LAO doped with Fe or Cr were the generalized gradient approximation (GGA) PBEsol [35], which is an energy functional. We used a modified Becke-Johnson (mBJ) potential [36] to calculate the energy and the electronic, magnetic, and optical properties because the GGA PBEsol potential underestimates the band gaps of semiconductors and insulators. All self-consistent calculations were successfully converged with an energy precision of 10-5 Ry.
3.
Results
3.1.
Defect formation energy
The energetic cost for Fe and Cr doping at the Al3+ (8c and 12d) sites was obtained by our calculating the defect formation energy (EFd), which is given by EFd = (Epure LAO + EFe or Cr ion) − (EFe- or -Cr-doped LAO + EAl ion), where the first term represents the sum of the total energies of the pure unit cell of LAO and the free Fe or Cr atom, while the second represents the total energy of the unit cell of Fe- or Cr-doped LAO plus the energy of the free Al3+ atom (at the 8c or 12d site), which is removed from the unit cell to introduce the impurity. The lattice energies of pure and doped LAO were obtained with the same parameters (lmax, Kmax.RMT, Gmax, number of points k, atomic sphere radii, etc.) for each type of calculation performed. The free atom energies (for Fe, Cr, and Al) were obtained for their stablest structures by DFT plus linearized augmented plane wave plus mBJ calculations. The energy of the free atom was approximated by the total energy of atoms in the primitive unit cell. The calculations for the Fe- and Cr-doped LAO and the free atoms were performed on the basis of polarized spin. The high energies associated with the formation of defects suggest that these defects are not significant in this material, since it is necessary to expend a lot of energy in their formation [37]. From this, and on the basis of its charge state, it is
possible to evaluate which impurity (Fe or Cr) is stabler when it replaces Al3+ at the tetrahedral (8c) or octahedral (12d) site of LAO. The stablest charge state is that with the lowest formation energy for a given Fermi level. Table 2 shows the defect formation energies with two possible accommodations for Fe or Cr ions at the tetrahedral and octahedral Al3+ sites in the LAO lattice. The energy calculations for the defect were performed with the mBJ potential. According to Table 2, there is a small preference for Fe or Cr to replace Al at the octahedral site. However, we can see that the formation energy for incorporation at the Al3+ 8c site is very close to the formation energy for incorporation at the Al3+ 12d site. On the basis of this, we can conclude that both mechanisms are likely to occur. Results from experimental studies of Fe- and Cr-doped LAO agree with our results for the defect formation energy. Kutty and Nayak [15] determined that the Fe3+ ion can occupy both the tetrahedral site and the octahedral site. Our results show that there is a small preference for the Cr3+ ion to occupy the octahedral site, and this agrees with experimental results [38]; however, there is a difference in the formation energy of only 1.01 eV, which shows that the Cr ion can also occupy the tetrahedral site. This result is also in agreement with experimental work by Singh et al. [9], who found that the Cr ion can occupy both sites. On the basis of this, our results are presented assuming that the Fe or Cr ions can replace the Al3+ ion at both the tetrahedral site and the octahedral site.
3.2.
Local structure around defects
For the calculation of the structural properties, the (optimized) theoretical lattice parameter used was that of the pure structure and was taken from [13]. We performed a relaxation of the atomic positions of LAO containing Fe or Cr impurities. To prove that the optimized lattice parameter of the pure structure [13] does not change significantly, the lattice parameter of LAO doped with Fe (8c site) was optimized as an example and was compared with that of the pure structure (Figure 2). The same computational data used for the optimization of the lattice parameter of the pure structure [13] were used in optimizing the lattice parameter of LAO doped with Fe (8c site). Figure 2 shows the optimization of the lattice parameter of Fe-doped
LAO. The lattice parameter that corresponds to the volume optimized for Fe-doped LAO is practically the same as that of pure LAO, with a difference of only 0.1%. This is as expected, since only one Al3+ ion is replaced in the unit cell, corresponding to 1/56 (i.e., a small increase in the optimized unit cell volume), which is the result of the greater ionic radius of Fe compared with Al. We therefore conclude that we can use the optimized lattice parameters of pure LAO [13] to relax the atomic positions of LAO doped with Fe or Cr, leading to a computational gain and reliable results. After the relaxation of the atomic positions, we can analyze the local structures around the Fe and Cr impurities inserted in the LAO network. Knowledge of the local structure around the defects is very important, since this information can be useful in the interpretation of optical spectroscopy and EPR data. The substitution of an Al3+ ion by an Fe or Cr ion causes changes in the distances between the atoms around the defect (tetrahedral and octahedral structure), resulting in a decrease in the crystalline symmetry, and as a consequence, the number of nonequivalent atoms is also changed. Table 3 shows the Fe–O and Cr–O bond lengths at the tetrahedral and octahedral sites. It can be seen from Table 3 that the Fe–O and Cr–O bond lengths at both sites (8c and 12d) are greater than the Al–O bond length (see [39]). This is because the ionic radii of the Fe and Cr impurities are greater than the ionic radius of Al. All calculations of the local structure around the defects were performed with the GGA PBEsol functional. Table 4 shows the atomic coordinates of the Fe and Cr impurities and all of the nearest neighbors connected to them. An Fe or Cr ion replaces Al3+, which previously occupied the position X = 0.2471, Y = 0.7471, Z = 0.7528 (tetrahedral site) or X = 0.3750, Y = 0.6315, Z = 0.3815 (octahedral site). It can be seen from Table 4 that the positions of the Fe and Cr ions when inserted into the tetrahedral or octahedral site to replace Al3+ remain almost the same. This effect is related to the stablest charge configuration of the defect, since, as can be seen from Table 5, all Fe or Cr ions are incorporated in the host lattice with charge 3+ (i.e., the same as Al3+). We conclude that the small differences in both the bond lengths (TM–O) and the atomic coordinates of Fe and Cr when they are inserted at the Al3+ site are entirely related to the differences in the ionic radii.
3.3.
Magnetic moments and Bader charge
All calculations of LAO doped with the muffin-tin scheme were performed by our taking into account the polarized spin system. On the basis of these calculations, we expect the system to converge to the spin configuration that makes it as stable as possible. The total spin magnetic moment in the unit of Bohr magneton (μB) is obtained from the difference between the total number of up spins and down spins in the unit cell. Table 5 presents the magnetic moments obtained for the doped systems. The pure system has no magnetic moment. We used the mBJ exchange and correlation potential for the magnetic moment calculations and also for the calculation of the Bader charges, since these data are better described by the mBJ potential than by the GGA PBEsol functional. On the basis of the reproduced charge density, calculations of the Bader charge were performed for all doped systems. The results were obtained with the CRITIC2 software package [40], which has a very efficient implementation of the quantum theory of atoms in molecules [41,42]. We obtained a value of approximately 1μB for the total spin magnetic moment in the unit cell for replacement of Al by Fe at the tetrahedral site. For replacement of Al by Fe at the octahedral site, we obtained a value of − 1μB in the unit cell. The Fe ion has a magnetic moment of approximately 0.87μB at the 8c site and approximately −0.81μB at the 12d site, and the total moment in the interstitial region plus a magnetic moment transferred to each of its four neighboring oxygens at the tetrahedral site and its six neighboring oxygens at the octahedral site, giving the total magnetic moment of the cell. Thus, we conclude that there is an electron in the Fe ion with an unpaired spin, possibly in the d orbital, with an up configuration at the 8c site and down configuration at the 12d site. These results show that the impurity transfers part of its magnetic moment to its vicinity. Hence, the magnetism present in the compound is located in the region of the defect with ferromagnetic configuration, since for the other distant atoms the magnetic moment is zero. The total magnetic moment in the unit cell is 3.0000μB when the Cr ion replaces the Al3+ ion at the tetrahedral and octahedral sites. Of this value in the total cell, the Cr ion is responsible for approximately −2.4000μB at the octahedral site, which when
added to the total moment in the interstitial region of −0.4874μB plus the magnetic moment transferred to each of its six oxygens makes up the total magnetic moment of the cell. At the tetrahedral site, the Cr ion has a magnetic moment of −2.3381μB, and this added to the moment of the interstitial region of −0.4171μB plus what is transferred to the four oxygens gives the moment of the cell. We therefore conclude that there are approximately three electrons in the d state of Cr with unpaired spin with the down configuration at both sites. Our results show that the impurity transfers part of its magnetic moment to its neighborhood (tetrahedral and octahedral sites), causing its magnetism to be in the region of the defect with ferromagnetic configuration. The Bader charges for replacement of Al3+ by Fe and replacement of Al3+ by Cr (Table 5) were approximately 2.5+ for both sites. Although these values are slightly less than 3+, we can assume that these results correspond to the charge of three electrons in Fe and Cr. This result is confirmed by an electron population analysis as part of a study of the electronic properties (see Section 3.4). In general, the Bader charges obtained by DFT calculations are slightly smaller than those predicted from experiments.
3.4.
Electronic properties
Calculations of the total density of states (TDOS), partial density of states (PDOS), and band structure for the pure system have already been performed [13]. Pure LAO is an insulator with an indirect band gap (Δ → Γ) of 8.4 eV. At the top of the valence band are predominately 2p states of O1 and O2, and the bottom of the conduction band is composed of 3s states of Al1 and Al2 and 3p states of Al1. Figure 3 shows the TDOS and PDOS of pure LAO and the Fe or Cr impurities inserted in the host lattice. The TDOS for pure LAO indicates a nonmagnetic system, as already shown in [13]. For the other cases, the TDOS of the doped LAO indicates a magnetic moment, since states with spin up are not identical to those with spin down. When the TDOS of LAO doped with Fe or Cr are compared with the TDOS of the pure system, it is easy to see that with the addition of the impurity, the energy bands close to the band gap undergo more changes than the more distant energy bands. As can be seen from Figure 3,
defect energy levels are inserted into and around the band gap, more precisely in the d states of Fe or Cr impurities. When the Fe ion is inserted into the LAO host lattice (Figure 3), ferromagnetic properties appear in the unit cell (1μB at the 8c site and −1μB at the 12d site). According to Figure 3 (TDOS and PDOS), the d states of spin-up and spin-down Fe, which are located above the Fermi energy (within the band gap), are empty at both the tetrahedral site and the octahedral site. However, the energy levels of the d states of Fe that are below the Fermi energy are occupied by three electrons with spin up and two electrons with spin down (8c site). At the 12d site, there are two electrons with spin up and three electrons with spin down. The total number of electrons occupying both sites below the Fermi energy is five, indicating that the d orbital of Fe has a 3d5 configuration. In the 4s orbital, no electron with spin up or occupied down (4s0) was obtained. Therefore, for replacement of Al3+ by Fe for the 3+ charge state, the state density calculation indicates that Fe has a valence electron configuration of 4s03d5 (8c and 12d sites). Our results for the density of states are compatible with the existence of a magnetic moment in the Fe ion of 0.8μB at the 8c site and −0.9μB at the 12d site; these values indicate the existence of a d electron with unpaired spin, and reinforce the results of the Bader analysis, which indicate that Fe has a charge of 3+. When the Cr ion is inserted at the tetrahedral and octahedral Al3+ sites, the up and down d states of Cr3+ that are located on the band gap are empty, and the energy levels of Cr3+ d states that are below the Fermi energy are occupied by three electrons with spin down at both sites. The total number of electrons occupied below the Fermi energy is three (tetrahedral and octahedral sites), indicating that the d orbital of Cr has a 3d3 configuration. In the 4s orbital, no electron with spin up or occupied down (4s0) was obtained. Thus, for the case of replacement of Al3+ by Cr, the population analysis of the states shows that Cr has a valence electron configuration of 4s03d3 at both sites. These results are compatible with the existence of a magnetic moment in the Cr3+ ion of −2.5μB, indicating the existence of a 3d electron with unpaired spin. This supports the results of the Bader analysis, which show that Cr has a charge of 3+. The density of states and the analysis of the Bader charges show that the electron configuration of Fe is 4s03d5 (8c and 12d sites) and for Cr the configuration is
4s03d3 (8c and 12d sites), indicating that both the Fe ions and the Cr ions have a charge of 3+ (Fe3+ and Cr3+), in agreement with the experimental results [15,39].
4. Conclusion A theoretical study of the structural, energetic, magnetic, and electronic properties of the LAO spinel host lattice was performed. For these calculations two possible schemes were considered: (1) doping with Fe or Cr at the Al3+ 8c site and (2) doping with Fe or Cr at the Al3+ 12d site. The exchange and correlation effects were described via the GGA PBEsol functional and the mBJ potential. Initially, we determined the local structure around the defects, whose atomic coordinates and bond lengths had small differences from the pure compound because of the greater ionic radii of Fe and Cr. Our calculations show that Fe and Cr prefer the octahedral site of Al. When Fe and Cr ions were inserted into the LAO lattice, a certain amount of magnetic moment appeared in the unit cell: for replacement of Al3+ by Fe, 1μB at the 8c site and −1μB at the 12d site); for replacement of Al3+ by Cr, −30,000μB at the 8c and 12d sites. The electronic structure revealed that the d states of Cr and Fe are below the Fermi level and within the band gap. The valence electron configuration when Fe replaces Al is 4s03d5 (8c and 12d sites), and when Cr replaces Al it is 4s03d3 (8c and 12d sites). A Bader analysis determined that Fe and Cr defects when inserted into the LAO host lattice have a charge of 3+. These results were verified by an electron population analysis, which gave results that were equivalent to the Bader analysis (i.e., a charge of 3+ for both Fe and Cr). These theoretical results are directly linked to the application of this material, since the magnetic and luminescent properties of Cr- or Fe-doped LAO depend on where the impurity is inserted, the type of magnetic moment that arises in the cell, the valence electron configuration, and the electronic transitions from the valence band to the conduction band. This theoretical study therefore makes a significant contribution to the correct analysis of the experimental data and future applications of this material.
Acknowledgments The authors are grateful to CAPES (Brazilian Federal Agency) and CNPq (Brazilian National Council for Scientific and Technological Development).
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Fig. 2. Structural optimization of doped LiAl5O8 (LAO) with Fe ions in the tetrahedral sites. The LAO lattice parameter was relaxed by our varying the volume of the primitive cell from −11% to 11% (in steps of 1%) in relation to the volume of the experimental unit cell used.
Fig. 3. Total density of states (TDOS) for pure LiAl5O8 (LAO) and TDOS and partial density of states (PDOS) for Fe-doped LAO (LAO:Fe) and Cr-doped LAO (LAO:Cr) at the tetrahedral and octahedral sites.
Table 1. Atomic sphere radius (RMT) and valence states used in the present calculations. Element 13
RMT (au)
Valence state
Al
1.6
3s23p1
3
Li
1.5
2s¹
8
O
1.5
2s22p4
1.6
4s23d6
1.6
4s13d5
26
Fe
24
Cr
Table 2. Formation energies of Fe and Cr defects in the LiAl5O8 lattice calculated with the modified Becke-Johnson potential. EFd
Tetrahedral
Octahedral
EFe→Al3+
−2.810
−2.984
ECr→Al3+
−1.002
−2.012
Table 3. Fe–O and Cr–O bond lengths in Fe- and Cr-doped LiAl5O8 (LAO) at the 8c and 12d sites calculated with the generalized gradient approximation PBEsol functional. Fe-doped LAO
Cr-doped LAO
12d Bond
8c Bond
Bond
12d Bond
Bond
8c Bond
length
length
length
(Å)
(Å)
(Å)
Bond
Bond length (Å)
Fe–O5
1.92
Fe–O16
1.82
Cr–O5
1.97
Cr–O16
1.84
Fe–O6
1.92
Fe–O17
1.82
Cr–O6
1.97
Cr–O17
1.84
Fe–O19
1.91
Fe–O18
1.82
Cr–O19
1.94
Cr–O18
1.84
Fe–O20
1.91
Fe–O32
1.99
Cr–O20
1.94
Cr–O32
2.05
Fe–O29
1.96
Cr–O29
1.99
Fe–O30
1.96
Cr–O30
1.99
Table 4. Atomic coordinates of Fe and Cr impurities and all nearest neighbors. The atomic coordinates X, Y, and Z are expressed in terms of the lattice parameter a. 12d site
8c site
X
Y
Z
X
Y
Z
Fe
0.3750
0.6274
0.3774
Fe
0.2526
0.7526
0.7473
O5
0.1347
0.6157
0.3648
O16
0.1128
0.8888
0.6276
O6
0.6152
0.6148
0.3657
O17
0.3723
0.6128
0.6112
O19
0.3671
0.6140
0.6167
O18
0.3888
0.8723
0.8871
O20
0.3828
0.8667
0.3640
O32
0.1083
0.6083
0.8916
O29
0.3652
0.6374
0.1322
O30
0.3847
0.3822
0.3874
Cr
0.3750
0.6293
0.3793
Cr
0.2533
0.7533
0.7466
O5
0.1281
0.6176
0.3644
O16
0.1125
0.8907
0.6251
O6
0.6218
0.6144
0.3676
O17
0.3741
0.6125
0.6092
O19
0.3671
0.6134
0.6216
O18
0.3907
0.8741
0.8874
O20
0.3828
0.8716
0.3634
O32
0.1049
0.6049
0.8950
O29
0.3640
0.6373
0.1297
O30
0.3860
0.3797
0.3873
Table 5. Magnetic moments (total and per atom) and Bader charges (in electron charge units) for Fe- or Cr-doped LiAl5O8 at the 8c and 12d sites of Al3+. The exchange and correlation potential used was the modified Becke-Johnson potential. 8c site Magnetic
12d site q
Magnetic
moment
moment
(µB)
(µB)
Fe
0.8780
IR
0.0253
-0.0399
Total
1.0000
−1.0000
Cr
−2.3381
IR
-0.4171
-0.4874
Total
−3.0000
−3.0000
IR, interstitial region.
2.4896
2.5149
−0.8176
−2.3915
q
2.4702
2.49119
Highlights •
The structural, energetic, electronic, and magnetic properties of lithium aluminate (LiAl5O8) spinel doped with Fe and Cr are studied.
•
Exchange and correlation effects are described via the generalized gradient approximation PBEsol functional and the modified Becke-Johnson potential.
•
A Bader analysis shows that the defect charge is 3+ for both Fe and Cr.
•
For replacement of Al by Fe, the state density calculation shows that Fe3+ has a valence electron configuration of 4s03d5 (8c and 12d sites).
•
For replacement of Al by Cr, it is found that Cr3+ has a valence electron configuration of 4s03d3 (8c and 12d sites).
•
The formation energy for incorporation at the Al3+ 8c site is very close to the formation energy for incorporation at the Al3+ 12d site.
Declaration of interests The authors Osmar machado de Sousa, Raiane Sodré de Araújo, Gilberto josé Barbosa Junior declare that they have no known competing financialinterestsor personal relationships that could have appeared to influence the work reported in this paper.