Ultramicroscopy 140 (2014) 51–56
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First-principle calculations analysis of ELNES splitting for Mn3O4 spinels related to atomic local symmetry Po-Tuan Chen a, Chuan-Ming Tseng a,b, Tung-Yuan Yung c, Ming-Wen Chu a, Cheng-Hsuan Chen a, Michitoshi Hayashi a,n a
Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan Institute of Physics, Academia Sinica, Taipei 115, Taiwan c Institute of Nuclear Energy Research, Atomic Energy Council, Executive Yuan, Longtan, Taoyuan 32546, Taiwan b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 October 2013 Received in revised form 14 January 2014 Accepted 18 February 2014 Available online 6 March 2014
By using a real space multiple scattering method (FEFF code) with a 2 2 2 cluster model, we investigated the effects of characteristic Jahn–Teller distortion on the electron energy loss near-edge structure (ELNES) of Mn3O4 spinel. In particular, we examined a correlation between the characteristics of the density of state and the ELNES spectral feature as a function of Jahn–Teller distortion. To this end, we introduced a geometrical variation approach to an Mn3O4 cluster model containing both Mn3 þ and Mn2 þ sites. Upon a prominent Jahn–Teller distortion of the Mn3 þ -octahedral site, we resolved the associated spectral features of Mn, comprising three peaks that merged upon increasing the symmetry of octahedral site from tetragonal (D4h) to cubic (Oh). We have also investigated the interplay between the Mn L-edge and corresponding O K-edge spectra. & 2014 Elsevier B.V. All rights reserved.
Keywords: ELNES Mn3O4 Jahn–Teller effect FEFF
1. Introduction Manganese oxide spinels are used in many industrial applications, including photodecomposition [1], ion exchange [2], molecular absorption [3], supercapacitors [4], magnetic utilization [5], and batteries [6]. A spinel has the general formula AB2O4, where A and B are metal cations in the nominal oxidation states of þ 2 and þ3, respectively. In a normal spinel (Fig. 1), the octahedral sites are occupied by B3 þ ions while the tetrahedral sites are occupied by A2 þ ions. The so-called Jahn–Teller effect explains the relationship between a spinel's geometric symmetry and its electronic configuration in various oxidation states. Several spectral investigations have been undertaken to experimentally probe the Jahn–Teller splitting energy in Mn-containing spinels [7,8]. Manganese atoms at B3 þ sites can induce Jahn–Teller distortion, decreasing the local symmetry of the octahedron from Oh to D4h. This distortion may give rise to splitting of the signals in the spectra of the spinel. Electron energy loss spectroscopy (EELS) is used widely to investigate the electronic structures of materials; in particular, their electron energy loss near-edge structures (ELNESs; i.e., the
n
Corresponding author. Tel.: þ 886 2 33665250. E-mail address: [email protected] (M. Hayashi).
http://dx.doi.org/10.1016/j.ultramic.2014.02.002 0304-3991 & 2014 Elsevier B.V. All rights reserved.
intensity variations within approximately 10 eV of the edge threshold) that arise as a result of electronic perturbations of the energy level distribution and environment of the atom being excited. Characteristic features of ELNES, such as the oxygen K-edge and the transition metal L-edge, are commonly used as fingerprints of the oxidation state [9], the coordination of specific ions in 3d metal oxides structures [10], and the local structural environments for atoms in a crystal [11]. The spectral features are practically equivalent to the near-edge fine structures observed in X-ray absorption spectroscopy (XANES); they are of appreciable academic interest because of the rich chemical and physical information contained. As an industrially significant example, mixed-valence Mn3O4 is constituted by Mn2 þ species at the A sites (thus, Mn2Aþ ) and Mn3 þ species at the B sites (Mn3B þ ) [12]. The site-specific model has been used to interpret ELNES spectra of Mn3O4; it can be employed to demonstrate how these two sites contribute to ELNES spectra. Tatsumi et al. [13] have proposed that MnB contributes to the higher energy region than MnA due to the more ionic character of the octahedral site. In addition, using electron energy loss spectroscopy in conjunction with scanning transmission electron microscopy (STEM-EELS), Tan et al. [14] have proposed that the Mn L3-edge in the ELNES spectrum comprises two peaks from different A and B sites, respectively. Several comparisons of the experimentally measured Mn L2,3- edges of the respective Mn2Aþ and Mn3B þ
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2. Method 2.1. Calculation methods Calculations of the densities of states (DOS) and ELNES of Mn3O4 are performed with the real-space, full multiple scattering FEFF8 [21,22]. ELNES spectra are originated from the excitation of electrons in the inner shells or valence bands to unoccupied states in the conduction bands. The spectral data contain a general feature: above the edges, a series of wiggles or oscillatory structures appear that are related directly to the transition from the initial states jψ i 〉 to final states jψ f 〉 of the material. According to the review paper of Moreno et al. [22], the corelevel ELNES spectra can be given by Fermi's golden rule and the formula can be numerically simulated using real-space multiple scattering Green function approach. The Core-level ELNES spectra can be given, in terms of double-differential scattering cross2 section d s=dΩdω with respect to scattering angle Ω and energy loss ω, by d s k' ¼ 4γ 2 a0 2 q 4 Sðq; ωÞ k dΩdω 2
Fig. 1. Schematic representation of the local geometry of AB2O4 spinel (herein, Mn3O4). The central oxygen atom is surrounded by one divalent cation (denoted by A) at a tetrahedral site and three trivalent cations (denoted by B) at octahedral sites. MnA–O, MnB–O(a), and MnB–O(e) bond lengths are useful geometrical parameters for this discussion.
sites of Mn3O4 with the Mn3 þ sites in Mn2O3 and the Mn2 þ sites in MnO have revealed remarkable similarities despite fundamental differences in crystal structures [15–18]. Ahmad et al. [19], on the other hand, have suggested that contributions from differences in coordination—octahedral (Mn3B þ ) or tetrahedral (Mn2Aþ )sites— should be non-negligible for interpretation of ELNES features. Moreover, experimentally observed XANES [20] and ELNES measurements of Mn3O4 at higher resolution (0.1 eV) are identical exhibiting further distinctive three peaks at the Mn L-edge. These measured splitting results may be interpreted due to the fact that Jahn–Teller distortion effect can be associated with Mn at B site [7,8]. Hence the effect of Jahn–Teller distortion on the contribution from B site should be investigated. As far as we are concerned, Tatsumi et al.'s study [13] adopted the Mn3 þ and Mn2 þ sites in the individual clusters MnO6 and MnO4, respectively. Their sophisticated quantum chemistry simulation shows two peaks: one at the lower energy is due to Mn2 þ at A site and the other at the higher energy is due to Mn3 þ at B site. However, the further splitting feature appearing in the experimentally observed high resolution XANES and ELNES spectra is absent. In order to discuss how these two sites, especially the B site, contribute to ELNES spectra as a function of geometrical distortion in a more direct and systematic manner, both Mn3 þ and Mn2 þ sites should be taken into account in one proper cluster. To this end, we will propose a multiple-site cluster model and adopt the real-space, multiple-scattering approach FEFF8 code [21,22] for its ELNES simulations. Detailed assignment of the origin of peaks may require a consideration of the ground state spin and the energies of spin multiplets [23], which would create a number of final states that would continue to make both ELNES and XANES calculations challenging tasks for us. Therefore, in this study we will focus on how structural distortion affects the contributions from different ion sites and how these contributions appear as qualitative features in the calculated ELNES spectra. While using FEFF with the multiplesite cluster model to address the Mn L-edge and O K-edge features, we will take the Jahn–Teller distortion effect into account by monitoring the changes of the near-edge fine structures in the simulations through systematic variation of the lattice constant of Mn3O4.
ð1Þ
and Sðq; ωÞ ¼ ∑ j〈ψ f jexp ðiq UrÞjψ i 〉j2 δðω þ Ei Ef Þ;
ð2Þ
f
where Ei and Ef are the initial and final state energies, respectively, q the momentum transfer and S(q,ω) is the dynamic structure factor. Practical calculations of Eq. (2) are usually based on the independent-particle approximation. We assume that the electron scattering cross-section is dominated by low-q excitations and the dipole approximation can be used for exp(iq r) 1 þ q r. The sum of final states in Eq. (2) can be performed implicitly using Green's function, which leads to S(q,ω) in the dipole limit can be rewritten as Sðq; ωÞ ¼ jψ i 〉q U r ρðr'; r'Þq U rjψ i 〉 ¼ ∑ M L ðEÞρLL' ðEÞM L' ðEÞ; L;L'
ð3Þ
where ML(E) are the dipole matrix elements, and ρLL'(E) ¼ 1/π Im GLL' is the one-electron density matrix. In specific, the final states are given by the eigenstates within the quasi-particle theory based on Green's function. The final state Hamiltonian is given by h' ¼ p2 =2m þV Coul' þ Σ ðEÞ:
ð4Þ
Eq. (4) includes a core-hole in the Coulomb potential V'coul and an energy-dependent self-energy Σ(E). FEFF codes use the Hedin–Lundqvist model based on the plasmon-pole model for an electron gas for the self-energy Σ(E) [24], which is based on a dynamically screened exchange operator in an electron gas. Regarding core-hole effect, we have also simulated an EELS spectrum of each site without core-hole. The core-hole effect leads to an apparent red-shift and to vary the intensity of peaks, which are general trends examined by using FEFF code [26]. However, the internals between splitting peaks in the spectra of MnB L3-edge and O K-edge do not significantly change. Thus, in this study we only presented the calculated results with the consideration of core-hole. Moreover, the atomic coordinates are generated using crystallographic parameters from the Inorganic Crystal Structure Database (ICSD) [25]. Mn3O4 has a tetragonally distorted spinel geometry (space group I41/amd) with lattice parameters a and c of 5.763 and 9.4696 Å, respectively. Practical calculations are performed with the 2 2 2 cluster as shown in Fig. 2, rather than the Mn4O16 cluster in Fig. 1. The cluster containing 299 atoms is close to the limitations of the FEFF code. The self-consistent potential and full multiple scattering is calculated in 6.0 Å radius. Some bands of the inner-box atoms are found to differ from those of the outer-box atoms by approximately 0.5 eV (Fig. 2). The EELS
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Fig. 2. 2 2 2 cluster model is used for practical calculations; the spectra of only the atoms in the middle box are considered for the calculations reported herein.
features resulting only from the atoms in the middle box are of concern in this study because these atoms are better representations of atoms in real environments. To compare the experimental and calculated spectra, the ELNES spectra are calculated with an energy step of 0.05 eV corresponding to the experimental resolution and a rigid shift of 2 eV to lower energy is applied to each calculated spectrum. Thus, all calculated spectra are aligned roughly to the first edge of the signal in the experimental data. To distinguish between the contributions of the structural parameters for the ELNES (e.g., local symmetry), a geometrical variation method is introduced in which the geometry is modified through slight changes in the geometrical parameters, consisting of the lattice constant x and all atom positions in the unit cell. The changes in the ELNES spectra are, therefore, qualitatively generated by the changes of these specific geometrical parameters. A method of varying one bond length or one bond angle while maintaining the others constant is not employed herein, because all geometrical parameters in a solid are correlated. 2.2. Experimental details The EELS spectra of Mn3O4 were acquired using a FEI Tecnai F20 transmission electron microscope, operated at 200 kV and equipped with an electron monochromator that achieved an energy resolution of approximately 0.24 eV. The Mn3O4 powders were commercially available (Aldrich); the powder specimens for the EELS studies were prepared through ultrasonic dispersion of the powders in EtOH and then the crystals were collected using TEM lacey Cu grids. An EELS collection angle of approximately 14 mrad and an acquisition time of 5 s were applied systematically. The carbon edge of approximately 284 eV from the lacey-carbon support was used as an internal reference for spectral alignment.
3. Results and discussion 3.1. Splitting features in O K-edge Panel (a) in Fig. 3 displays an O K-edge EELS spectrum obtained after removal of the background and that obtained through FEFF calculations. The spectroscopic edge in the experiment appeared near 530.1 eV. The O K-edge exhibits four distinct features, labeled as a group of peaks oa and peaks ob, oc, and od. The group of peaks oa in the ELNES spectrum consists of three peaks, denoted oa1, oa2, and oa3, with the difference between oa1 and oa2 being
Fig. 3. Experimental and calculated EELS of (a) O K-edge and (b) Mn L-edge of Mn3O4. The splits and peaks ma, for the signals of Mn atoms correspond to the peaks oa of O atoms. In particular, the signal for the Mn L-edge resulted from two distinct structures from A and B sites.
approximately 1 eV and that between oa1 and oa3 being approximately 3 eV. In addition, the peak ob features a shoulder, marked as peak obn. In Fig. 3(a), the number of peaks are the same in both experimental and calculated spectra. The experimental and calculated spectra are comparable in the shapes of their peaks ob, oc, and od. A comparison of the energy loss in the near-edge part (the group of peaks oa and that of the peak obn) suggests, however, that there are discrepancies, especially for the prominent peak oa3. The ELNES phenomenon is related to a core electron being excited to an unoccupied band. The O K-edge calculation reflects directly the unoccupied states of the density of states (DOS) of the O atoms (Fig. 4). The DOS calculation in Fig. 4 is a useful tool to explain the experimental peaks in Fig. 3(a). The far-edge region peaks oc and od, extending to approximately 30 eV above the threshold in the ELNES, can be interpreted in terms of multiple scattering of an excited electron with low kinetic energy. The peak ob, located approximately 10 eV above the threshold, is related to the projected sp-hybridized orbitals of unoccupied O atoms. The group of peaks oa, in the region 530–533 eV, is mainly attributable to transitions from the O atoms' 1s core states to 2sp-hybridized orbitals mixing with the band for the d states of the transition metal cations with energy above the Fermi level. As abovementioned, the calculated spectra of the oxygen K-edge do not match with the experimental data because there is the possibility of the DOS oa3 being significantly overestimated. We have assumed two possible causes for this: (1) The calculations of the electronic structures are very sensitive to the self-energy of Σ. A more sophisticated self-energy approximation and/or nonspheric symmetry potential should be taken into account. (2) Because of neglecting spin multiplet effects, the occupations of the O sp orbitals overlapped with the Mn d band predicted by FEFF may be barely sufficient. We have admitted that a quantitative calculation of the O K-edge is still a challenging task. In this study, since we focused on the local symmetry of the spinel related to the spectra splitting, we did not pursue more quantitatively accurate calculations.
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Fig. 4. DOS of Mn3O4. The DOS is associated directly with ELNES. Two arrows in the spectrum of MnB indicate that the doubly degenerate eg orbital had split into orbitals a1g (d3z2 r2) and b1g (dx2 y2).
3.2. Mn L-edge attributing to specific sites Panel (b) in Fig. 3 presents the experimental Mn L2,3-edge ELNES spectrum. The energy region below 645 eV is the L3-edge; above 650 eV is the L2-edge. The intensity ratio, I(L3)/I(L2)¼ 0.4, is roughly characteristic of the oxidation state of the Mn atoms [27]. Because the structures are sensitive to the nature of the chemical bonds, the Mn L3-edge exhibits obvious structural splits, which influence each other with the group of peaks oa in the O K-edge ELNES; we will discuss the details in Sections 3.4 and 3.5. Above in the experimental L3-edge we observed three peaks: one located at 639.8 eV and two others, finely split, at 641.3 and 642.1 eV, denoted by ma1, ma2, and ma3, respectively. Such triple splitting is consistent with the experimental observations made with a spectral resolution of 0.1 eV. Moreover, our calculations clearly elucidate the contributions from the different A and B sites. As presented in panel (b) in Fig. 3, the peak ma1 is mainly dominated by the Mn2A þ species, which have in their L3-edge only one major peak. We attribute the splitting structures, the peaks ma1, ma2, and ma3, to the Mn3B þ species. Our three calculated peaks for the Mn3B þ L3-edge are within intervals of about 0.8 and 1.0 eV. Similarly, the Mn L2-edge also displays a splitting structure that is due to both Mn2A þ and Mn3B þ species; they are sufficiently distinguishable in both our experimental and calculated data. Since ELNES is site-specific to the differently coordinated cationic sites, the spectra can be obtained separately and summed [13,14] with a proper weighting ratio such as the ratio of the concentrations of the sites. Therefore by combining the calculated spectra of the Mn2A þ and Mn3B þ species, we obtain a spectrum that agrees well with the experimental data. We explicitly take into account the contribution from the Mn2A þ site in the presence of the Mn3B þ site in which at the scattering center of the Mn2A þ site, the multiple scattering involving Mn3B þ site is included, and vice versa. 3.3. Calculated splitting of d orbitals of Mn atoms We observe in Fig. 4 an unoccupied DOS in which 2p orbitals of O atoms are highly hybridized with 3d orbitals of both MnA and
MnB species. Here, both MnB and MnA atoms contribute to the peak oa1, whereas peaks oa2 and oa3 can be attributed to the MnB atom. Our conclusions from the DOS data are, therefore, consistent with those of the ELNES spectra. Here let us examine how Jahn–Teller distortions arising from Mn3B þ ions contribute to the appearance of split peaks in the fine structure in ELNES spectra. In a local octahedral environment, the Mn3B þ ion has four 3d electrons in a t2geg ground state; this octahedral field can be subjected to a strong Jahn–Teller distortion, reflected as an elongated pair of MnB–O(a) bonds through electron–phonon coupling (see labels in Fig. 1) with slight difference in the lengths of the other four MnB–O(e) bonds. Thus, a decrease in octahedral symmetry, i.e., from Oh to D4h, occurs with t2g and eg orbitals in the Oh crystal-field becoming further split. The triply degenerate t2g orbitals of the MnB atom therein are generally suggested [28] to split into doubly degenerate eg orbitals (dxz and dyz) and a b2g orbital (dxy); this splitting is, however, poorly resolved in Fig. 4. The two arrows on the MnB atom in Fig. 4 shows that the doubly degenerate eg orbital splits into an a1g orbital (d3z2 -r2) and a b1g orbital (dx2 y2). Such splitting of t2g orbitals does not contribute to the energy gain in the d4 configuration because the center of gravity in conserved. For D4h symmetry with Mn3B þ ion having d4 orbital, we suspect that the triple features in the DOS reflect the unoccupied t2g, a1g, and b1g orbitals. The Mn2A þ ions in the tetragonal complexes without Jahn– Teller splitting exhibit two degenerate states: namely, e2 and t32 orbitals. For tetragonal Mn2A þ sites, the main peak of the DOS (Fig. 4) represents the contribution of the e2 orbital; we anticipate that the shoulder located approximately 1 eV above the main peak is related to the t32 orbital [19]. 3.4. Geometrical variation approach The origin of crystal distortion, the so-called Jahn–Teller distortion, has been investigated previously [7,8]. In some spinels containing transition metal ions, such as manganites located at octahedral sites, a distortion arises and the cubic symmetry changes to tetragonal symmetry. In actual cases, the geometrical distortion can be controlled by substitution of A or B site cations in certain ratios [7]. In this study, we focus on the splitting of the group peaks oa and ma in ELNES spectra; we anticipate that it arises due to local symmetry variation at the octahedral sites. In simulation, we control the distortion by varying the lattice constant of the tetragonal (space group I41/amd) single phase. Increasing the plane lattice constant x enhances its D4h symmetry, as operated within FEFF calculations. Panel (a) in Fig. 5 displays the O K-edge ELNES spectra calculated using planar lattice constants of x, x þ0.1, x þ0.2, xþ 0.3, x þ0.4, and xþ0.5 Å. The edge shifts toward the lower energy region in accordance with the artificial increase in cell volume. Since we are interested mainly in the splitting of the peaks, all of the features in the spectra in the Figures below will be aligned to the first peak in the original spectrum of Mn3O4; this position is defined as relative zero. As the lattice constant x increases, the peak oa2 shifts slightly toward the peak oa3 and, coincidently, the peak oa3 also shifts to the lower energy side. The intensity of the peak oa3 is oscillatory while expanding. When the lattice constant reaches x þ0.3 Å, both peaks oa2 and oa3 merge. Under these conditions, the merged peak appears as a shorter and broader band; with further expansion, the merged peak sharpens. The splitting of the signal of the Mn L3-edge can be traced to the electronic configurations of Mn2Aþ and Mn3B þ species. Panel (b) in Fig. 5 shows the contribution from Mn2Aþ species to the Mn L3-edge. As the lattice constant x increased, the intensity increased, the width sharpened, and a shoulder gradually appeared at 1 eV.
P.-T. Chen et al. / Ultramicroscopy 140 (2014) 51–56
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Table 1 Geometrical parameters obtained upon increasing the lattice constant x.
Mn3O4a x þ0.1 x þ0.2 x þ0.3 x þ0.4 x þ0.5 a
x (Å)
z (Å)
Ratio (z/x)
MnB–O(a) (Å)
MnB–O(e) (Å)
MnA–O (Å)
ratio (a)/ (e)
5.763 5.863 5.963 6.063 6.163 6.263
9.456 9.456 9.456 9.456 9.456 9.456
1.64 1.61 1.59 1.56 1.53 1.51
2.225 2.225 2.225 2.225 2.225 2.225
1.963 1.997 2.031 2.065 2.098 2.132
2.043 2.064 2.084 2.105 2.126 2.148
1.13 1.11 1.10 1.08 1.06 1.04
Taken from experimental data in Ref. [25].
three Mn3B þ atoms and one Mn2þ atom through two short equatorial A MnB–O(e) bonds, one long apical MnB–O(a) octahedral bond, and one MnA–O tetrahedral bond. The increase in the lattice constant x results in a decrease in the ratio z/x. For Mn3O4, the ratio z/x is 1.64; in our calculations, the ratio z/x finally reaches 1.51. The more significant parameter, however, is the octahedral environment of the MnBO6 unit, the symmetry of which is related to the ratio of the lengths of MnB– O(a) and MnB–O(e) bonds. We denote this ratio as (a)/(e); as it approaches 1, the symmetry of the MnBO6 unit becomes Oh. The ratio (a)/(e) of Mn3O4 is 1.13 when this ratio is 1.08, the second and third peaks merge. The simple energy splitting in the O K-edge spectra and the three resolved peaks observed for the Mn L3-edge are related to the ratio (a)/(e). Furthermore, two partially resolved peaks with energy splitting in the higher energy region merge into a broad peak and shift to lower energy as the lattice constant x increases. This feature implies that octahedral Mn sites adopt higher symmetry. In simulation, the geometrical variation could also be controlled by decreasing the lattice constant z; this approach, however, involves shortening bond lengths—a practical impossibility in real cases. The energy resolution in the calculations is relative whether the splitting merges or not. Our purpose is to reveal the merging tendency with the geometry variation. Thus, we do not pursue calculations with a finer resolution. 3.5. Correlation between O p-orbital and Mn d-orbital
Fig. 5. ELNES spectra of (a) O K-edge, (b) Mn2A þ L3-edge, and (c) Mn3B þ L3-edge for an artificially controlled Jahn–Teller effect using the geometrical variation method, upon increasing the lattice constant x.
Panel (c) in Fig. 5 shows the contribution from Mn3B þ species to the Mn L3-edge as a function of the lattice constant x. With an increase in the lattice constant x, the second and third peaks arising from Mn3B þ species move closer together and their intensities increase; these two peaks eventually merge when the lattice constant reaches a value of xþ0.3 Å. The originally split peaks may merge as a result of the absence of a Jahn–Teller effect at the octahedral B sites. In the original case, the lengthened MnB–O(a) bond leads to energy splitting of d3z2 r2 and dx2 y2 orbitals. A gradual change in symmetry to an ideal octahedron Oh bring d3z2 r2 and dx2 y2 orbitals closer together. Finally, the eg orbital (d3z2 r2 and dx2 y2) should appear as a degenerate pair. Table 1 shows the detailed geometrical parameters associated with the planar expansion. Each oxygen atom is fourfold coordinated to
Let us examine how the simulated ELNES spectrum of Mn and that of O are correlated. Blue line in Fig. 6 shows a linear regression line that indicates a correlation of the interval of the 2nd–3rd peaks of the Mn L3-edge and that of the O K-edge in the ELNES spectra as a function of geometrical variation (x) introduced in Section 3.4. The numbers (0, 1, 2, 3, 4, and 5) in Fig. 6 denote lattice expansion of xþ 0.0, x þ0.1, x þ0.2, xþ 0.3, x þ0.4, and xþ 0.5 Å, respectively. Within the original structure (x þ0 Å), the local coordination at B site is D4h symmetry. The calculated ELNES presents that the interval of 2nd–3rd peak of Mn3B þ is 0.98 eV, while that of O is 1.14 eV. With the lattice expansion, we anticipate that the local coordination of B site will approach to a higher symmetry, and the intervals will merge to 0.00 eV. In xþ 0.2 Å case, the intervals of Mn L3-edge and O K-edge of ELNES merge but not completely. Thus, we can still resolve a shoulder; the interval of the main peak and the shoulder of Mn3B þ is 0.60 eV and that of O is 0.62 eV. With the present resolution, there is no interval at xþ 0.3 Å, x þ0.4 Å or xþ 0.5 Å case. Next, we investigate how the interval of the 2nd–3rd peaks of Mn3B þ and that of O in the DOS are correlated. Red line in Fig. 6 exhibits a correlation diagram of these intervals as a function of the geometrical variation. For the original structure (x þ0 Å), the interval of Mn3B þ in the DOS is 0.83 eV and that of O is 1.05 eV. These values are different from those obtained for the correlation
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Reference
Fig. 6. Correlation diagram for the interval of 2nd and 3rd peak of Mn L3-edge and O K-edge associated with their DOS with the geometry variation. The numbers belong to points (0, 1, 2, 3, 4, and 5) denote the lattice expansion of x þ 0.0, xþ 0.1, xþ 0.2, x þ0.3, x þ0.4, and x þ 0.5 Å, respectively.
of the ELNES spectra (0.98 eV for Mn3B þ and 1.14 eV for O), although two linear regression lines (blue and red) show a similar tendency as a function of x. In other words, the different intervals of 2nd–3rd peaks of Mn3B þ and those of O suggest that there exists an important effect due to the coupling of the initial and final states. We should emphasize that with D4h symmetry, the DOS does not completely represent the ELNES. If we take a look at x þ0.5 Å case (approximately to Oh), the intervals of the 2nd–3rd peak of O in the ELNES and the DOS are zero while those of Mn3B þ shows a difference of 0.15 eV. Thus, we think it is quite important to take into account the coupling between the initial and final states in ELNES spectra calculations.
4. Conclusions We have simulated the splitting features in ELNES spectra arising from Jahn–Teller distortions due to the elongated shapes of the octahedra in which Mn3B þ ions are located. In this model, the split peaks in the O K-edge and Mn L-edge can be attributed to specific A and B sites in the spinel. The Mn2A þ ions dominate the first peak, while Mn3B þ ions are associated with the three peaks in the L-edge. In addition, the partially resolved peaks for the O K-edge and Mn L3-edge in the ELNES spectra changed very systematically with the removal of the Jahn–Teller-active Mn3B þ octahedron. The simulation results show that the second and third peaks gradually merge as the local MnO6 octahedron approaches Oh symmetry (i.e., higher symmetry). Resolving the contributions of individual orbitals to the absorption spectra would necessarily require an unambiguous linear dichroism setup, which is, however, not easy to achieve using EELS. Here, we demonstrate that the combination of theoretical calculations and EELS experiments can circumvent this technical difficulty and, thereby, reveal intriguing physical details. In addition, this approach may be useful for local structural analyses of unknown Mn-containing materials from their ELNES spectra.
Acknowledgments The research at National Taiwan University was supported by the National Science Council of Taiwan, Academia Sinica, and the National Taiwan University Excellence Project. MH thanks NTU and NSC for financial support under contract NSC 102–2113-M002–006. PT thanks Dr. Hung-Chung Hsueh of the National Center for Theoretical Sciences of Taiwan for participating in useful discussions. PT and CM contributed equally to this paper.
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Rulis, Ab initio calculation of the O–K, N–K, Si–K, Si–L3, Y–K, Y–L3 edges in the Y–Si–O–N system: a strategy for ELNES/XANES spectral modeling in complex materials, Phys. Rev. B 77 (2008) 035125. [12] V. Baron, J. Gutzmer, H. Rundlof, R. Tellgren, The influence of iron substitution in the magnetic properties of hausmannite, Mn (super 2þ ) (Fe, Mn) (super 3þ )2O4, Am. Mineral. 83 (1998) 786–793. [13] K. Tatsumi, S. Muto, Y. Yamamoto, H. Ikeno, S. Yoshioka, I. Tanaka, Site-specific electronic structure analysis by channeling EELS and first-principles calculations, Ultramicroscopy 106 (2006) 1019–1023. [14] H. Tan, S. Turner, E. Yucelen, J. Verbeeck, G. Van Tendeloo, 2D atomic mapping of oxidation states in transition metal oxides by scanning transmission electron microscopy and electron energy-loss spectroscopy, Phys. Rev. Lett. 107 (2011) 107602. [15] J. Lee, B. Kim, B.H. Kim, B.I. Min, Valence-state transition in SrMn1 xMoxO3 (0 rx r 0.5) investigated by soft x-ray absorption spectroscopy, Phys. Rev. B 80 (2009) 205112. [16] J.H. Hwang, D.H. Kim, J.S. Kang, S. Kolesnik, O. Chmaissem, J. Mais, B. Dabrowski, J. Baik, H.J. Shin, J. Lee, B. Kim, B.I. Min, Soft x-ray absorption spectroscopy study of Mo-rich SrMn1-xMoxO3 (xZ 0.5), Phys. Rev. B 83 (2011) 073103. [17] J.H. Paterson, O.L. Krivanek, Elnes of 3d transition-metal oxides: II. variations with oxidation state and crystal structure, Ultramicroscopy 32 (1990) 319–325. [18] L.A.J. Garvie, A.J. Craven, High-resolution parallel electron energy-loss spectroscopy of Mn L2,3-edges in inorganic manganese compounds, Phys. Chem. Miner. 21 (1994) 191–206. [19] E.A. Ahmad, G. Mallia, D. Kramer, V. Tileli, A.R. Kucernak, N.M. Harrison, Comment on 2D Atomic Mapping of Oxidation States in Transition Metal Oxides by Scanning Transmission Electron Microscopy and Electron EnergyLoss Spectroscopy, Phys. Rev. Lett. 108 (2012) 259701. [20] B. Gilbert, B.H. Frazer, A. Belz, P.G. Conrad, K.H. Nealson, D. Haskel, J.C. Lang, G. Srajer, G. De Stasio, Multiple scattering calculations of bonding and X-ray absorption spectroscopy of manganese oxides, J. Phys. Chem. A 107 (2003) 2839–2847. [21] J.J. Rehr, R.C. Albers, Theoretical approaches to x-ray absorption fine structure, Rev. Modern Phys. 72 (2000) 621–654. [22] M.S. Moreno, K. Jorissen, J.J. Rehr, Practical aspects of electron energy-loss spectroscopy (EELS) calculations using FEFF8, Micron 38 (2007) 1–11. [23] F.M.F. de Groot, X-ray absorption and dichroism of transition metals and their compounds, J. Electron Spectrosc. Relat. Phenom. 67 (1994) 529–622. [24] L. Hedin, S. Lundqvist, Effects of electron-electron and electron-phonon interactions on the one-electron states of solids, in: H. Ehrenreich, F. Seitz, D. Turnbull (Eds.), Solid State Physics, vol. 23, Academic, New York, 1969, p. 1. [25] B. Boucher, R. Buhl, M. Perrin, Propriétés et structure magnétique de Mn3O4, J. Phys. Chem. Solids 32 (1971) 2429–2437 (The crystallographic parameters of Mn3O4 are also collected in the Inorganic Crystal Structure Database, collection code: 76088). [26] V. Mauchamp, M. Jaouen, Core-hole effect in the one-particle approximation revisited from density functional theory, Phys. Rev. B 79 (2009) 235106. [27] H. Kurata, C. Colliex, Electron-energy-loss core-edge structures in manganese oxides, Phys. Rev. B 48 (1993) 2102–2108. [28] J.E. Huheey, E.A. Keiter, R.L. Keiter, Inorganic Chemistry:Principles of structures and reactivity, HarperCollins, New York (1993) 404.
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First-principle calculations analysis of ELNES splitting for Mn3O4 spinels related to atomic local symmetry Po-Tuan Chen a, Chuan-Ming Tseng a,b, Tung-Yuan Yung c, Ming-Wen Chu a, Cheng-Hsuan Chen a, Michitoshi Hayashi a,n a
Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan Institute of Physics, Academia Sinica, Taipei 115, Taiwan c Institute of Nuclear Energy Research, Atomic Energy Council, Executive Yuan, Longtan, Taoyuan 32546, Taiwan b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 October 2013 Received in revised form 14 January 2014 Accepted 18 February 2014 Available online 6 March 2014
By using a real space multiple scattering method (FEFF code) with a 2 2 2 cluster model, we investigated the effects of characteristic Jahn–Teller distortion on the electron energy loss near-edge structure (ELNES) of Mn3O4 spinel. In particular, we examined a correlation between the characteristics of the density of state and the ELNES spectral feature as a function of Jahn–Teller distortion. To this end, we introduced a geometrical variation approach to an Mn3O4 cluster model containing both Mn3 þ and Mn2 þ sites. Upon a prominent Jahn–Teller distortion of the Mn3 þ -octahedral site, we resolved the associated spectral features of Mn, comprising three peaks that merged upon increasing the symmetry of octahedral site from tetragonal (D4h) to cubic (Oh). We have also investigated the interplay between the Mn L-edge and corresponding O K-edge spectra. & 2014 Elsevier B.V. All rights reserved.
Keywords: ELNES Mn3O4 Jahn–Teller effect FEFF
1. Introduction Manganese oxide spinels are used in many industrial applications, including photodecomposition [1], ion exchange [2], molecular absorption [3], supercapacitors [4], magnetic utilization [5], and batteries [6]. A spinel has the general formula AB2O4, where A and B are metal cations in the nominal oxidation states of þ 2 and þ3, respectively. In a normal spinel (Fig. 1), the octahedral sites are occupied by B3 þ ions while the tetrahedral sites are occupied by A2 þ ions. The so-called Jahn–Teller effect explains the relationship between a spinel's geometric symmetry and its electronic configuration in various oxidation states. Several spectral investigations have been undertaken to experimentally probe the Jahn–Teller splitting energy in Mn-containing spinels [7,8]. Manganese atoms at B3 þ sites can induce Jahn–Teller distortion, decreasing the local symmetry of the octahedron from Oh to D4h. This distortion may give rise to splitting of the signals in the spectra of the spinel. Electron energy loss spectroscopy (EELS) is used widely to investigate the electronic structures of materials; in particular, their electron energy loss near-edge structures (ELNESs; i.e., the
n
Corresponding author. Tel.: þ 886 2 33665250. E-mail address: [email protected] (M. Hayashi).
http://dx.doi.org/10.1016/j.ultramic.2014.02.002 0304-3991 & 2014 Elsevier B.V. All rights reserved.
intensity variations within approximately 10 eV of the edge threshold) that arise as a result of electronic perturbations of the energy level distribution and environment of the atom being excited. Characteristic features of ELNES, such as the oxygen K-edge and the transition metal L-edge, are commonly used as fingerprints of the oxidation state [9], the coordination of specific ions in 3d metal oxides structures [10], and the local structural environments for atoms in a crystal [11]. The spectral features are practically equivalent to the near-edge fine structures observed in X-ray absorption spectroscopy (XANES); they are of appreciable academic interest because of the rich chemical and physical information contained. As an industrially significant example, mixed-valence Mn3O4 is constituted by Mn2 þ species at the A sites (thus, Mn2Aþ ) and Mn3 þ species at the B sites (Mn3B þ ) [12]. The site-specific model has been used to interpret ELNES spectra of Mn3O4; it can be employed to demonstrate how these two sites contribute to ELNES spectra. Tatsumi et al. [13] have proposed that MnB contributes to the higher energy region than MnA due to the more ionic character of the octahedral site. In addition, using electron energy loss spectroscopy in conjunction with scanning transmission electron microscopy (STEM-EELS), Tan et al. [14] have proposed that the Mn L3-edge in the ELNES spectrum comprises two peaks from different A and B sites, respectively. Several comparisons of the experimentally measured Mn L2,3- edges of the respective Mn2Aþ and Mn3B þ
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2. Method 2.1. Calculation methods Calculations of the densities of states (DOS) and ELNES of Mn3O4 are performed with the real-space, full multiple scattering FEFF8 [21,22]. ELNES spectra are originated from the excitation of electrons in the inner shells or valence bands to unoccupied states in the conduction bands. The spectral data contain a general feature: above the edges, a series of wiggles or oscillatory structures appear that are related directly to the transition from the initial states jψ i 〉 to final states jψ f 〉 of the material. According to the review paper of Moreno et al. [22], the corelevel ELNES spectra can be given by Fermi's golden rule and the formula can be numerically simulated using real-space multiple scattering Green function approach. The Core-level ELNES spectra can be given, in terms of double-differential scattering cross2 section d s=dΩdω with respect to scattering angle Ω and energy loss ω, by d s k' ¼ 4γ 2 a0 2 q 4 Sðq; ωÞ k dΩdω 2
Fig. 1. Schematic representation of the local geometry of AB2O4 spinel (herein, Mn3O4). The central oxygen atom is surrounded by one divalent cation (denoted by A) at a tetrahedral site and three trivalent cations (denoted by B) at octahedral sites. MnA–O, MnB–O(a), and MnB–O(e) bond lengths are useful geometrical parameters for this discussion.
sites of Mn3O4 with the Mn3 þ sites in Mn2O3 and the Mn2 þ sites in MnO have revealed remarkable similarities despite fundamental differences in crystal structures [15–18]. Ahmad et al. [19], on the other hand, have suggested that contributions from differences in coordination—octahedral (Mn3B þ ) or tetrahedral (Mn2Aþ )sites— should be non-negligible for interpretation of ELNES features. Moreover, experimentally observed XANES [20] and ELNES measurements of Mn3O4 at higher resolution (0.1 eV) are identical exhibiting further distinctive three peaks at the Mn L-edge. These measured splitting results may be interpreted due to the fact that Jahn–Teller distortion effect can be associated with Mn at B site [7,8]. Hence the effect of Jahn–Teller distortion on the contribution from B site should be investigated. As far as we are concerned, Tatsumi et al.'s study [13] adopted the Mn3 þ and Mn2 þ sites in the individual clusters MnO6 and MnO4, respectively. Their sophisticated quantum chemistry simulation shows two peaks: one at the lower energy is due to Mn2 þ at A site and the other at the higher energy is due to Mn3 þ at B site. However, the further splitting feature appearing in the experimentally observed high resolution XANES and ELNES spectra is absent. In order to discuss how these two sites, especially the B site, contribute to ELNES spectra as a function of geometrical distortion in a more direct and systematic manner, both Mn3 þ and Mn2 þ sites should be taken into account in one proper cluster. To this end, we will propose a multiple-site cluster model and adopt the real-space, multiple-scattering approach FEFF8 code [21,22] for its ELNES simulations. Detailed assignment of the origin of peaks may require a consideration of the ground state spin and the energies of spin multiplets [23], which would create a number of final states that would continue to make both ELNES and XANES calculations challenging tasks for us. Therefore, in this study we will focus on how structural distortion affects the contributions from different ion sites and how these contributions appear as qualitative features in the calculated ELNES spectra. While using FEFF with the multiplesite cluster model to address the Mn L-edge and O K-edge features, we will take the Jahn–Teller distortion effect into account by monitoring the changes of the near-edge fine structures in the simulations through systematic variation of the lattice constant of Mn3O4.
ð1Þ
and Sðq; ωÞ ¼ ∑ j〈ψ f jexp ðiq UrÞjψ i 〉j2 δðω þ Ei Ef Þ;
ð2Þ
f
where Ei and Ef are the initial and final state energies, respectively, q the momentum transfer and S(q,ω) is the dynamic structure factor. Practical calculations of Eq. (2) are usually based on the independent-particle approximation. We assume that the electron scattering cross-section is dominated by low-q excitations and the dipole approximation can be used for exp(iq r) 1 þ q r. The sum of final states in Eq. (2) can be performed implicitly using Green's function, which leads to S(q,ω) in the dipole limit can be rewritten as Sðq; ωÞ ¼ jψ i 〉q U r ρðr'; r'Þq U rjψ i 〉 ¼ ∑ M L ðEÞρLL' ðEÞM L' ðEÞ; L;L'
ð3Þ
where ML(E) are the dipole matrix elements, and ρLL'(E) ¼ 1/π Im GLL' is the one-electron density matrix. In specific, the final states are given by the eigenstates within the quasi-particle theory based on Green's function. The final state Hamiltonian is given by h' ¼ p2 =2m þV Coul' þ Σ ðEÞ:
ð4Þ
Eq. (4) includes a core-hole in the Coulomb potential V'coul and an energy-dependent self-energy Σ(E). FEFF codes use the Hedin–Lundqvist model based on the plasmon-pole model for an electron gas for the self-energy Σ(E) [24], which is based on a dynamically screened exchange operator in an electron gas. Regarding core-hole effect, we have also simulated an EELS spectrum of each site without core-hole. The core-hole effect leads to an apparent red-shift and to vary the intensity of peaks, which are general trends examined by using FEFF code [26]. However, the internals between splitting peaks in the spectra of MnB L3-edge and O K-edge do not significantly change. Thus, in this study we only presented the calculated results with the consideration of core-hole. Moreover, the atomic coordinates are generated using crystallographic parameters from the Inorganic Crystal Structure Database (ICSD) [25]. Mn3O4 has a tetragonally distorted spinel geometry (space group I41/amd) with lattice parameters a and c of 5.763 and 9.4696 Å, respectively. Practical calculations are performed with the 2 2 2 cluster as shown in Fig. 2, rather than the Mn4O16 cluster in Fig. 1. The cluster containing 299 atoms is close to the limitations of the FEFF code. The self-consistent potential and full multiple scattering is calculated in 6.0 Å radius. Some bands of the inner-box atoms are found to differ from those of the outer-box atoms by approximately 0.5 eV (Fig. 2). The EELS
P.-T. Chen et al. / Ultramicroscopy 140 (2014) 51–56
53
Fig. 2. 2 2 2 cluster model is used for practical calculations; the spectra of only the atoms in the middle box are considered for the calculations reported herein.
features resulting only from the atoms in the middle box are of concern in this study because these atoms are better representations of atoms in real environments. To compare the experimental and calculated spectra, the ELNES spectra are calculated with an energy step of 0.05 eV corresponding to the experimental resolution and a rigid shift of 2 eV to lower energy is applied to each calculated spectrum. Thus, all calculated spectra are aligned roughly to the first edge of the signal in the experimental data. To distinguish between the contributions of the structural parameters for the ELNES (e.g., local symmetry), a geometrical variation method is introduced in which the geometry is modified through slight changes in the geometrical parameters, consisting of the lattice constant x and all atom positions in the unit cell. The changes in the ELNES spectra are, therefore, qualitatively generated by the changes of these specific geometrical parameters. A method of varying one bond length or one bond angle while maintaining the others constant is not employed herein, because all geometrical parameters in a solid are correlated. 2.2. Experimental details The EELS spectra of Mn3O4 were acquired using a FEI Tecnai F20 transmission electron microscope, operated at 200 kV and equipped with an electron monochromator that achieved an energy resolution of approximately 0.24 eV. The Mn3O4 powders were commercially available (Aldrich); the powder specimens for the EELS studies were prepared through ultrasonic dispersion of the powders in EtOH and then the crystals were collected using TEM lacey Cu grids. An EELS collection angle of approximately 14 mrad and an acquisition time of 5 s were applied systematically. The carbon edge of approximately 284 eV from the lacey-carbon support was used as an internal reference for spectral alignment.
3. Results and discussion 3.1. Splitting features in O K-edge Panel (a) in Fig. 3 displays an O K-edge EELS spectrum obtained after removal of the background and that obtained through FEFF calculations. The spectroscopic edge in the experiment appeared near 530.1 eV. The O K-edge exhibits four distinct features, labeled as a group of peaks oa and peaks ob, oc, and od. The group of peaks oa in the ELNES spectrum consists of three peaks, denoted oa1, oa2, and oa3, with the difference between oa1 and oa2 being
Fig. 3. Experimental and calculated EELS of (a) O K-edge and (b) Mn L-edge of Mn3O4. The splits and peaks ma, for the signals of Mn atoms correspond to the peaks oa of O atoms. In particular, the signal for the Mn L-edge resulted from two distinct structures from A and B sites.
approximately 1 eV and that between oa1 and oa3 being approximately 3 eV. In addition, the peak ob features a shoulder, marked as peak obn. In Fig. 3(a), the number of peaks are the same in both experimental and calculated spectra. The experimental and calculated spectra are comparable in the shapes of their peaks ob, oc, and od. A comparison of the energy loss in the near-edge part (the group of peaks oa and that of the peak obn) suggests, however, that there are discrepancies, especially for the prominent peak oa3. The ELNES phenomenon is related to a core electron being excited to an unoccupied band. The O K-edge calculation reflects directly the unoccupied states of the density of states (DOS) of the O atoms (Fig. 4). The DOS calculation in Fig. 4 is a useful tool to explain the experimental peaks in Fig. 3(a). The far-edge region peaks oc and od, extending to approximately 30 eV above the threshold in the ELNES, can be interpreted in terms of multiple scattering of an excited electron with low kinetic energy. The peak ob, located approximately 10 eV above the threshold, is related to the projected sp-hybridized orbitals of unoccupied O atoms. The group of peaks oa, in the region 530–533 eV, is mainly attributable to transitions from the O atoms' 1s core states to 2sp-hybridized orbitals mixing with the band for the d states of the transition metal cations with energy above the Fermi level. As abovementioned, the calculated spectra of the oxygen K-edge do not match with the experimental data because there is the possibility of the DOS oa3 being significantly overestimated. We have assumed two possible causes for this: (1) The calculations of the electronic structures are very sensitive to the self-energy of Σ. A more sophisticated self-energy approximation and/or nonspheric symmetry potential should be taken into account. (2) Because of neglecting spin multiplet effects, the occupations of the O sp orbitals overlapped with the Mn d band predicted by FEFF may be barely sufficient. We have admitted that a quantitative calculation of the O K-edge is still a challenging task. In this study, since we focused on the local symmetry of the spinel related to the spectra splitting, we did not pursue more quantitatively accurate calculations.
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Fig. 4. DOS of Mn3O4. The DOS is associated directly with ELNES. Two arrows in the spectrum of MnB indicate that the doubly degenerate eg orbital had split into orbitals a1g (d3z2 r2) and b1g (dx2 y2).
3.2. Mn L-edge attributing to specific sites Panel (b) in Fig. 3 presents the experimental Mn L2,3-edge ELNES spectrum. The energy region below 645 eV is the L3-edge; above 650 eV is the L2-edge. The intensity ratio, I(L3)/I(L2)¼ 0.4, is roughly characteristic of the oxidation state of the Mn atoms [27]. Because the structures are sensitive to the nature of the chemical bonds, the Mn L3-edge exhibits obvious structural splits, which influence each other with the group of peaks oa in the O K-edge ELNES; we will discuss the details in Sections 3.4 and 3.5. Above in the experimental L3-edge we observed three peaks: one located at 639.8 eV and two others, finely split, at 641.3 and 642.1 eV, denoted by ma1, ma2, and ma3, respectively. Such triple splitting is consistent with the experimental observations made with a spectral resolution of 0.1 eV. Moreover, our calculations clearly elucidate the contributions from the different A and B sites. As presented in panel (b) in Fig. 3, the peak ma1 is mainly dominated by the Mn2A þ species, which have in their L3-edge only one major peak. We attribute the splitting structures, the peaks ma1, ma2, and ma3, to the Mn3B þ species. Our three calculated peaks for the Mn3B þ L3-edge are within intervals of about 0.8 and 1.0 eV. Similarly, the Mn L2-edge also displays a splitting structure that is due to both Mn2A þ and Mn3B þ species; they are sufficiently distinguishable in both our experimental and calculated data. Since ELNES is site-specific to the differently coordinated cationic sites, the spectra can be obtained separately and summed [13,14] with a proper weighting ratio such as the ratio of the concentrations of the sites. Therefore by combining the calculated spectra of the Mn2A þ and Mn3B þ species, we obtain a spectrum that agrees well with the experimental data. We explicitly take into account the contribution from the Mn2A þ site in the presence of the Mn3B þ site in which at the scattering center of the Mn2A þ site, the multiple scattering involving Mn3B þ site is included, and vice versa. 3.3. Calculated splitting of d orbitals of Mn atoms We observe in Fig. 4 an unoccupied DOS in which 2p orbitals of O atoms are highly hybridized with 3d orbitals of both MnA and
MnB species. Here, both MnB and MnA atoms contribute to the peak oa1, whereas peaks oa2 and oa3 can be attributed to the MnB atom. Our conclusions from the DOS data are, therefore, consistent with those of the ELNES spectra. Here let us examine how Jahn–Teller distortions arising from Mn3B þ ions contribute to the appearance of split peaks in the fine structure in ELNES spectra. In a local octahedral environment, the Mn3B þ ion has four 3d electrons in a t2geg ground state; this octahedral field can be subjected to a strong Jahn–Teller distortion, reflected as an elongated pair of MnB–O(a) bonds through electron–phonon coupling (see labels in Fig. 1) with slight difference in the lengths of the other four MnB–O(e) bonds. Thus, a decrease in octahedral symmetry, i.e., from Oh to D4h, occurs with t2g and eg orbitals in the Oh crystal-field becoming further split. The triply degenerate t2g orbitals of the MnB atom therein are generally suggested [28] to split into doubly degenerate eg orbitals (dxz and dyz) and a b2g orbital (dxy); this splitting is, however, poorly resolved in Fig. 4. The two arrows on the MnB atom in Fig. 4 shows that the doubly degenerate eg orbital splits into an a1g orbital (d3z2 -r2) and a b1g orbital (dx2 y2). Such splitting of t2g orbitals does not contribute to the energy gain in the d4 configuration because the center of gravity in conserved. For D4h symmetry with Mn3B þ ion having d4 orbital, we suspect that the triple features in the DOS reflect the unoccupied t2g, a1g, and b1g orbitals. The Mn2A þ ions in the tetragonal complexes without Jahn– Teller splitting exhibit two degenerate states: namely, e2 and t32 orbitals. For tetragonal Mn2A þ sites, the main peak of the DOS (Fig. 4) represents the contribution of the e2 orbital; we anticipate that the shoulder located approximately 1 eV above the main peak is related to the t32 orbital [19]. 3.4. Geometrical variation approach The origin of crystal distortion, the so-called Jahn–Teller distortion, has been investigated previously [7,8]. In some spinels containing transition metal ions, such as manganites located at octahedral sites, a distortion arises and the cubic symmetry changes to tetragonal symmetry. In actual cases, the geometrical distortion can be controlled by substitution of A or B site cations in certain ratios [7]. In this study, we focus on the splitting of the group peaks oa and ma in ELNES spectra; we anticipate that it arises due to local symmetry variation at the octahedral sites. In simulation, we control the distortion by varying the lattice constant of the tetragonal (space group I41/amd) single phase. Increasing the plane lattice constant x enhances its D4h symmetry, as operated within FEFF calculations. Panel (a) in Fig. 5 displays the O K-edge ELNES spectra calculated using planar lattice constants of x, x þ0.1, x þ0.2, xþ 0.3, x þ0.4, and xþ0.5 Å. The edge shifts toward the lower energy region in accordance with the artificial increase in cell volume. Since we are interested mainly in the splitting of the peaks, all of the features in the spectra in the Figures below will be aligned to the first peak in the original spectrum of Mn3O4; this position is defined as relative zero. As the lattice constant x increases, the peak oa2 shifts slightly toward the peak oa3 and, coincidently, the peak oa3 also shifts to the lower energy side. The intensity of the peak oa3 is oscillatory while expanding. When the lattice constant reaches x þ0.3 Å, both peaks oa2 and oa3 merge. Under these conditions, the merged peak appears as a shorter and broader band; with further expansion, the merged peak sharpens. The splitting of the signal of the Mn L3-edge can be traced to the electronic configurations of Mn2Aþ and Mn3B þ species. Panel (b) in Fig. 5 shows the contribution from Mn2Aþ species to the Mn L3-edge. As the lattice constant x increased, the intensity increased, the width sharpened, and a shoulder gradually appeared at 1 eV.
P.-T. Chen et al. / Ultramicroscopy 140 (2014) 51–56
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Table 1 Geometrical parameters obtained upon increasing the lattice constant x.
Mn3O4a x þ0.1 x þ0.2 x þ0.3 x þ0.4 x þ0.5 a
x (Å)
z (Å)
Ratio (z/x)
MnB–O(a) (Å)
MnB–O(e) (Å)
MnA–O (Å)
ratio (a)/ (e)
5.763 5.863 5.963 6.063 6.163 6.263
9.456 9.456 9.456 9.456 9.456 9.456
1.64 1.61 1.59 1.56 1.53 1.51
2.225 2.225 2.225 2.225 2.225 2.225
1.963 1.997 2.031 2.065 2.098 2.132
2.043 2.064 2.084 2.105 2.126 2.148
1.13 1.11 1.10 1.08 1.06 1.04
Taken from experimental data in Ref. [25].
three Mn3B þ atoms and one Mn2þ atom through two short equatorial A MnB–O(e) bonds, one long apical MnB–O(a) octahedral bond, and one MnA–O tetrahedral bond. The increase in the lattice constant x results in a decrease in the ratio z/x. For Mn3O4, the ratio z/x is 1.64; in our calculations, the ratio z/x finally reaches 1.51. The more significant parameter, however, is the octahedral environment of the MnBO6 unit, the symmetry of which is related to the ratio of the lengths of MnB– O(a) and MnB–O(e) bonds. We denote this ratio as (a)/(e); as it approaches 1, the symmetry of the MnBO6 unit becomes Oh. The ratio (a)/(e) of Mn3O4 is 1.13 when this ratio is 1.08, the second and third peaks merge. The simple energy splitting in the O K-edge spectra and the three resolved peaks observed for the Mn L3-edge are related to the ratio (a)/(e). Furthermore, two partially resolved peaks with energy splitting in the higher energy region merge into a broad peak and shift to lower energy as the lattice constant x increases. This feature implies that octahedral Mn sites adopt higher symmetry. In simulation, the geometrical variation could also be controlled by decreasing the lattice constant z; this approach, however, involves shortening bond lengths—a practical impossibility in real cases. The energy resolution in the calculations is relative whether the splitting merges or not. Our purpose is to reveal the merging tendency with the geometry variation. Thus, we do not pursue calculations with a finer resolution. 3.5. Correlation between O p-orbital and Mn d-orbital
Fig. 5. ELNES spectra of (a) O K-edge, (b) Mn2A þ L3-edge, and (c) Mn3B þ L3-edge for an artificially controlled Jahn–Teller effect using the geometrical variation method, upon increasing the lattice constant x.
Panel (c) in Fig. 5 shows the contribution from Mn3B þ species to the Mn L3-edge as a function of the lattice constant x. With an increase in the lattice constant x, the second and third peaks arising from Mn3B þ species move closer together and their intensities increase; these two peaks eventually merge when the lattice constant reaches a value of xþ0.3 Å. The originally split peaks may merge as a result of the absence of a Jahn–Teller effect at the octahedral B sites. In the original case, the lengthened MnB–O(a) bond leads to energy splitting of d3z2 r2 and dx2 y2 orbitals. A gradual change in symmetry to an ideal octahedron Oh bring d3z2 r2 and dx2 y2 orbitals closer together. Finally, the eg orbital (d3z2 r2 and dx2 y2) should appear as a degenerate pair. Table 1 shows the detailed geometrical parameters associated with the planar expansion. Each oxygen atom is fourfold coordinated to
Let us examine how the simulated ELNES spectrum of Mn and that of O are correlated. Blue line in Fig. 6 shows a linear regression line that indicates a correlation of the interval of the 2nd–3rd peaks of the Mn L3-edge and that of the O K-edge in the ELNES spectra as a function of geometrical variation (x) introduced in Section 3.4. The numbers (0, 1, 2, 3, 4, and 5) in Fig. 6 denote lattice expansion of xþ 0.0, x þ0.1, x þ0.2, xþ 0.3, x þ0.4, and xþ 0.5 Å, respectively. Within the original structure (x þ0 Å), the local coordination at B site is D4h symmetry. The calculated ELNES presents that the interval of 2nd–3rd peak of Mn3B þ is 0.98 eV, while that of O is 1.14 eV. With the lattice expansion, we anticipate that the local coordination of B site will approach to a higher symmetry, and the intervals will merge to 0.00 eV. In xþ 0.2 Å case, the intervals of Mn L3-edge and O K-edge of ELNES merge but not completely. Thus, we can still resolve a shoulder; the interval of the main peak and the shoulder of Mn3B þ is 0.60 eV and that of O is 0.62 eV. With the present resolution, there is no interval at xþ 0.3 Å, x þ0.4 Å or xþ 0.5 Å case. Next, we investigate how the interval of the 2nd–3rd peaks of Mn3B þ and that of O in the DOS are correlated. Red line in Fig. 6 exhibits a correlation diagram of these intervals as a function of the geometrical variation. For the original structure (x þ0 Å), the interval of Mn3B þ in the DOS is 0.83 eV and that of O is 1.05 eV. These values are different from those obtained for the correlation
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Reference
Fig. 6. Correlation diagram for the interval of 2nd and 3rd peak of Mn L3-edge and O K-edge associated with their DOS with the geometry variation. The numbers belong to points (0, 1, 2, 3, 4, and 5) denote the lattice expansion of x þ 0.0, xþ 0.1, xþ 0.2, x þ0.3, x þ0.4, and x þ 0.5 Å, respectively.
of the ELNES spectra (0.98 eV for Mn3B þ and 1.14 eV for O), although two linear regression lines (blue and red) show a similar tendency as a function of x. In other words, the different intervals of 2nd–3rd peaks of Mn3B þ and those of O suggest that there exists an important effect due to the coupling of the initial and final states. We should emphasize that with D4h symmetry, the DOS does not completely represent the ELNES. If we take a look at x þ0.5 Å case (approximately to Oh), the intervals of the 2nd–3rd peak of O in the ELNES and the DOS are zero while those of Mn3B þ shows a difference of 0.15 eV. Thus, we think it is quite important to take into account the coupling between the initial and final states in ELNES spectra calculations.
4. Conclusions We have simulated the splitting features in ELNES spectra arising from Jahn–Teller distortions due to the elongated shapes of the octahedra in which Mn3B þ ions are located. In this model, the split peaks in the O K-edge and Mn L-edge can be attributed to specific A and B sites in the spinel. The Mn2A þ ions dominate the first peak, while Mn3B þ ions are associated with the three peaks in the L-edge. In addition, the partially resolved peaks for the O K-edge and Mn L3-edge in the ELNES spectra changed very systematically with the removal of the Jahn–Teller-active Mn3B þ octahedron. The simulation results show that the second and third peaks gradually merge as the local MnO6 octahedron approaches Oh symmetry (i.e., higher symmetry). Resolving the contributions of individual orbitals to the absorption spectra would necessarily require an unambiguous linear dichroism setup, which is, however, not easy to achieve using EELS. Here, we demonstrate that the combination of theoretical calculations and EELS experiments can circumvent this technical difficulty and, thereby, reveal intriguing physical details. In addition, this approach may be useful for local structural analyses of unknown Mn-containing materials from their ELNES spectra.
Acknowledgments The research at National Taiwan University was supported by the National Science Council of Taiwan, Academia Sinica, and the National Taiwan University Excellence Project. MH thanks NTU and NSC for financial support under contract NSC 102–2113-M002–006. PT thanks Dr. Hung-Chung Hsueh of the National Center for Theoretical Sciences of Taiwan for participating in useful discussions. PT and CM contributed equally to this paper.
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