Oxygen K-edge electron energy loss spectra of hydrous and anhydrous compounds

First-principles calculations have been employed to examine the possible use of electron energy loss spectroscopy (EELS) as a tool for determining the presence of OH groups and hence hydrogen content in compounds. Our density functional theory (DFT) based calculations describe accurately the experimental EELS results for forsterite (Mg2SiO4), hambergite (Be2BO3(OH)), brucite (Mg(OH)2) and diaspore (α-AlOOH). DFT calculations were complemented by an experimental time resolved study of the oxygen K-edge in diaspore. The results show unambiguously that there is no connection between a pre-edge feature in the oxygen K-edge spectrum of diaspore and the presence of OH groups in the structure. Instead, the experimental study shows that the pre-edge feature in diaspore is transient. It can be explained by the presence of molecular O2, which is produced as a result of the electron irradiation.


Introduction
It was first claimed by Wirth (1997) that the presence of hydrogen bound to oxygen could be detected in compounds by electron energy loss spectroscopy (EELS) through the observation of a pre-edge feature at energies of ≈528 eV. This interpretation of the electron energy loss (EEL) spectra was immediately challenged ( van Aken et al 1998, Wirth 1998. While numerous applications of this approach have been presented (see references in Garvie (2010)), alternative explanations of the origin of the 'pre-peak' feature have been brought forward (e.g. van Aken et al 1998, Jiang 2006 On leave at: IPICyT, División de Materiales Avanzados, San Luis Potosí, S.L.P., Mexico. Garvie 2010). Specifically, time resolved EELS studies seem to indicate that under electron irradiation in the TEM, a transient peak near 530 eV may be observed in H-bearing as well as anhydrous minerals. This peak has been associated with an electron transition in molecular O 2 , which is thought to be liberated due to damage induced by the incident electron beam (Jiang 2006, Garvie 2010. Early theoretical approaches (van Aken et al 1999) did not support the claim by Wirth (1997), but the agreement of the spectra from the model calculations with experiment was only moderate. More recently, however, based on the work by Pickard and Payne (1997), the computation of EEL spectra in the framework of density functional theory models has become feasible, where the flexibility of mature plane wave/pseudopotential based approaches, which allow complex geometries to be optimized, is combined with the capability to include the effect of core holes. In fact, an example of a computed EEL spectrum addressing the question of whether a pre-peak feature is characteristic for hydroxy-apatite has been presented by Gao et al (2009). However, in that study the experimental spectrum was not well reproduced and it was necessary to perform the calculations using a supercell approximating the disordered structure.
The present study proceeds by demonstrating the accuracy of DFT based calculations of electron energy loss spectra for the oxygen K-edge. The first compound chosen for this benchmark is hambergite, Be 2 BO 3 (OH), because it has four symmetrically independent oxygen atoms, three of which participate in the coordination of boron in planar BO 3 groups, while one is part of an OH group. There is no disorder or partial occupation of Wyckoff positions and the EELS shows a very distinct oxygen K-edge spectrum with two well separated main maxima (Garvie 2010). We also compute the EEL spectrum of forsterite, Mg 2 SiO 4 , which has three symmetrically independent oxygen positions, but no OH groups, and where the EEL spectrum shows a distinct double maximum (Garvie 2010). In contrast, in brucite, Mg(OH) 2 , there are only two symmetrically equivalent OH groups and two spectra have been presented (Wirth 1997, van Aken et al 1999) which differ from each other significantly. After discussing the reliability of our approach, we then compute the oxygen K-edge spectrum of diaspore, α-AlOOH, and complement the modeling study by the experimental determination of time resolved EEL spectra of diaspore.

Computational details
The computational approach employed here has been described in detail by Gao et al (2009) and further applications have been given by Milman et al (2010). All calculations in the current study were performed using the CASTEP package (Clark et al 2005). The PBEsol generalized gradient approximation (Perdew et al 2008) and the 'on the fly' pseudopotentials from the CASTEP data base were employed throughout. The kinetic cut-off energy was 610 eV. Distances between k-points for Brillouin zone sampling were <0.03Å −1 . For the EELS calculation, core holes were introduced in subsequent calculations for symmetrically distinct oxygen atoms. As we employed periodic boundary conditions, we used supercells to ensure that the distance between pseudo-atoms with a core hole was at least 6Å. Convergence calculations showed that larger distances, which are computationally very expensive, only lead to small changes in the spectra. The contributions of symmetrically distinct oxygen atoms were summed up according to the method described by Mizoguchi et al (2009). Core hole lifetime effects are included in the spectrum calculation via a Lorentzian broadening with FWHM of 0.19 eV (Fuggle and Inglesfield 1992). The broadening due to the lifetime of an excited state is more complicated. We adopted an empirical linear function that describes broadening width as 0.1E where E is the energy above the adsorption threshold (Hebert 2007) in order to describe this effect. The spectrum of a single molecule was obtained by an EELS calculation for a spin-polarized O 2 molecule placed in a 10 × 10 × 10Å 3 box. The rest of the settings (exchange-correlation functional, energy cut-off, k-point sampling) were the same as for the solid state calculations; instrumental broadening for the single molecule EELS calculation was set at Gaussian FWHM of 0.1 eV.

Experimental details
Thin flakes of sample were obtained from a gem-stone quality natural diaspore by treatment in an ultrasonic bath in isopropyl alcohol, then mounted on lacey carbon coated Cu grids. Observations were made on samples with no carbon underneath. The EEL spectra were acquired with a FEI Tecnai F30 transmission electron microscope equipped with a Gatan image filter (GIF). The voltage used was 300 keV and the EELS energy resolution (FWHM) was about 1.0 eV at the minimum dispersion of 0.05 eV and about 1.3-1.4 eV (FWHM) at the usual acquiring dispersion of 0.3 eV/channel. Care was taken to do all necessary alignments in an area adjacent to the area of interest. The time series spectra were done with the beam continuously impinging on the area of interest and acquiring spectra every 30 s. The background was removed from all EEL spectra by polynomial fitting using standard Digital Micrograph procedures.

Hambergite
The structure of hambergite, Be 2 BO 3 (OH), an orthorhombic beryllium borate, has been determined by Zachariasen et al (1963) and has been refined recently by single crystal neutron diffraction by Gatta et al (2012). Experimentally determined structural parameters are given in table 1. There has been no density functional theory based atomistic modeling study of hambergite and hence the results of the full geometry optimization are given in table 1. They are in good agreement with the experimental data (Zachariasen et al 1963, Gatta et al 2012. Specifically, the computed O-H distance is 0.995Å, while the neutron diffraction study gave distances between 0.971 and 1.0105Å, depending on the details of the model used (Gatta et al 2012).
The computed EEL spectrum (figure 1) is in good agreement with the experimental spectrum (Garvie 2010) close to the K-edge. The theoretical spectrum was simulated with a uniform broadening of 0.25 eV, and does not account for multiple scattering or any kind of background. This leads to an increasing discrepancy between experiment and theory at higher energies. The individual contributions from symmetrically distinct oxygen atoms bound to the boron differ little from each other. The contribution from the oxygen which is bound to the hydrogen dominates the scattering between the theoretical EEL spectra of hambergite. The dashed (red) line representing the total spectrum is the sum of the contributions from the four symmetrically independent oxygen atoms. Three of these oxygen atoms (blue lines) are bound to boron, while one (green line) is part of an OH group. The contribution from the latter dominates the total spectrum between the two main peaks and is distinct from the contributions from the BO 3 -group. two main peaks. It is noteworthy that all oxygen atoms equally contribute to the sharp feature at 535 eV, which is therefore not a pre-peak feature due to the hydrogen.

Forsterite
Forsterite, Mg 2 SiO 4 , has been the subject of numerous DFT based modeling studies (Jochym et al 2004, Winkler et al 1996, Demichelis et al 2010, Ashbrook et al 2007. It is well established that its physical properties are described well by DFT-GGA based calculations and the results of the geometry optimization of forsterite are in similarly good agreement with experiment as those of hambergite. The computed EEL spectrum is compared to the experimental spectrum (Garvie 2010) in figure 2. The most prominent feature in both the experimental and the theoretical data set is the edge with two maxima, separated by ≈2.6 eV. The intensity ratios of these two main maxima are not well reproduced. However, as the experimental spectrum is neither corrected for background or multiple scattering, and it is not clear whether it represents a proper powder average, these differences are not indicative of a failure of the model. Also, the theoretical spectrum reproduces minor features, such as the shoulder at 543.7 eV, and the local maxima at 548.1 and 551.8 eV.

Brucite
Brucite, Mg(OH) 2 , has also been studied extensively by ab initio methods (D'Arco et al 1993, Winkler et al 1995, van Aken et al 1999). An EEL spectrum, obtained by Wirth (1997), is shown in figure 3. It has a very prominent feature at energies lower than the oxygen K-edge. The spectrum by Wirth (1997) differs distinctly from the ELNES spectrum published by van Aken et al (1999), who obtained spectra on samples with a preferential orientation. Even an adjustment of the onset of the energies of the K-edge doesn't lead to a satisfactory agreement between the two spectra. The results of our polarized calculations are compared to the data by van Aken et al (1999) in figure 4. The intensity distributions are, in part, not well reproduced. However, the theoretical spectra are fully polarized, while this has not been the case for the experimental spectra. In addition, the theoretical model has a perfect alignment of the OH groups parallel to the c-axis. This is just a first approximation to the disordered arrangement of the OH groups in the real structure, as neutron diffraction data is best described by models in which the hydrogen atoms are distributed over three sites (Desgranges et al 1996, Chakoumakos et al 1997. However, Figure 3. Experimental EEL spectra of brucite. The continuous (black) line with the prominent pre-edge peak is from Wirth (1997). The two spectra from van Aken et al (1999), shown by dashed (red and blue) lines, were obtained on samples with a different preferential orientation. it is obvious that neither in the theoretical spectra, nor in those shown by van Aken et al (1999) is there a pre-edge feature due to the O-H bonding, and combining these two results we conclude that the spectrum published by Wirth (1997) is not representative of brucite.

Diaspore
Diaspore has been studied extensively by experiment (Mao et al 1994, Friedrich et al 2007a, 2007b, Frost et al 1999, Ruan et al 2001, Winkler et al 2008, San Juan-Farfan et al 2011, Delattre et al 2012 and theory (Winkler et al 1995, Demichelis et al 2007, Delattre et al 2012. It is well established that conventional DFT calculations give a very reasonable description of the interatomic interactions, even though anharmonicity is relevant in this system. A comparison of a computed and an experimentally determined EEL spectrum of diaspore, recorded immediately after the electron beam impinged on the sample, is given in figure 5. Both spectra show no pre-edge feature. However, time resolved EELS (figure 6) showed that for diaspore there is a transient spectral feature at 529.9 eV, which appears after a few tens of seconds of irradiation and then disappears after a further few tens of seconds. This transient feature can be very well modeled with a contribution of molecular O 2 (figure 6).

Conclusion
The current study convincingly demonstrates the accuracy with which EEL spectra can be simulated from DFT based calculations. Specifically, the oxygen K-edge spectra of hydrous and anhydrous minerals are well reproduced. A detailed analysis of the individual contributions of the four symmetrically distinct oxygen atoms in hambergite shows that while there are some differences between the contributions to the EEL spectrum of the oxygen atoms which are part of the BO 3 -groups and those which are part of OH groups, these cannot be readily discerned in the experimental spectrum. Similarly, the individual contributions to the total EEL spectrum from the two symmetrically distinct oxygen atoms in diaspore, one of which is part of an OH group, could only be observed if the experimental resolution would be an order Figure 6. Experimental EEL spectra (continuous black lines) recorded after 30 and 60 s show that, in comparison to a spectrum taken at 0 s (figure 5), a transient feature appears after a few tens of seconds and disappears a few tens of seconds later. This transient feature can be very well modeled by superposing the theoretical EEL spectrum of diaspore on that of molecular O 2 (dashed red lines). of magnitude better than what is currently achievable. Our experiments on diaspore show the same effect that has been observed by Jiang (2006) on CaAl 2 O 4 , namely a pronounced time-dependent pre-edge feature which can best be explained by assigning it to molecular oxygen, which is liberated by beam damage from the sample. The present study therefore confirms the conclusions drawn by Garvie (2010) on the basis of experimental data, leaving little doubt that the hydrogen content of minerals cannot be determined by EELS through a pre-peak feature in the oxygen K-edge spectrum.