Persistent Octahedral Coordination in Amorphous GeO 2 Up to 100 GPa by K β 00 X-Ray Emission Spectroscopy

We measure valence-to-core x-ray emission spectra of compressed crystalline GeO 2 up to 56 GPa and of amorphous GeO 2 up to 100 GPa. In a novel approach, we extract the Ge coordination number and mean Ge-O distances from the emission energy and the intensity of the K β 00 emission line. The spectra of high-pressure polymorphs are calculated using the Bethe-Salpeter equation. Trends observed in the experimental and calculated spectra are found to match only when utilizing an octahedral model. The results reveal persistent octahedral Ge coordination with increasing distortion, similar to the compaction mechanism in the sequence of octahedrally coordinated crystalline GeO 2 high-pressure polymorphs.


I. INTRODUCTION
The structure of amorphous and crystalline GeO 2 at high pressure is of interest due to its use in technical glasses and due to fundamental questions related to the compaction mechanism on the atomic scale in this archetypal network forming system [1][2][3][4][5][6][7][8][9][10][11][12][13]. The compaction mechanism in the amorphous phase has important geophysical and geochemical implications, as GeO 2 is a structural analog of SiO 2 , the main component in silicate melts present in Earth's mantle. If amorphous GeO 2 and SiO 2 would reach or even exceed the density of crystalline polymorphs by atomic scale compaction, this could help to explain geophysical observations that point towards buoyantly stable silicate melts at various depths in Earth's mantle [14,15]. It is therefore important to understand the compaction mechanism in an experimentally accessible analog material like amorphous GeO 2 in order to assess the differences from and similarities to the mechanisms in crystalline polymorphs.
The most important parameter to describe the structure of compressed amorphous GeO 2 and its crystalline polymorphs is the average number of nearest oxygen neighbors to germanium, i.e., its average coordination number (CN). There is a well-known pressure lag in the average CN between compressed amorphous GeO 2 and stable crystalline GeO 2 polymorphs: The CN in GeO 2 polymorphs stable at pressures above 5 GPa is six, while the CN of the amorphous state gradually increases from four to six in an extended pressure range up to 20 GPa [1, [3][4][5]8,[10][11][12]16]. In the similar case of SiO 2 , the first stable polymorph with CN of six appears at 7 GPa, whereas compressed amorphous SiO 2 reaches an average CN of six only between 40 and 60 GPa [15,17]. Can the lag in CN between the amorphous and the crystalline state be reversed at higher pressures, as two groups showed in their recent x-ray diffraction studies on GeO 2 [1] and SiO 2 [18]? In amorphous GeO 2 , an increase of the CN from six to seven has been reported between 40 and 60 GPa by XRD [1]. This CN evolution beyond 6-fold does not match the one observed for crystalline GeO 2 polymorphs, which have a CN of six up to at least 110 GPa [19,20]. Moreover, the recent ab initio molecular dynamics (AIMD) study of Du and Tse on amorphous GeO 2 has found that the average germanium CN has a dominant fraction above six only for pressures larger than 80 GPa [21]. In the case of amorphous SiO 2 , the conclusions of different studies concerning the CN at high pressure diverge in a similar fashion, with recent XRD data showing a CN beyond six [18], contradicting previous XRD data [22], ab initio molecular dynamics calculations [23], spectroscopic measurements at the Si L-edge [15], and density measurement [24]. Thus, there is fundamental ambiguity in the compressional behavior of these network-forming systems at extreme pressure in general.
In this study, we address the ambiguity in the average germanium CN in compressed amorphous GeO 2 by a new approach on the basis of measured and computed valenceto-core x-ray emission spectroscopy (VTC XES) spectra of compressed GeO 2 . VTC XES has been mostly applied to 3d transition metal molecular complexes, where it is known to provide insight into the spin state and the type of the bonding ligand [25][26][27][28][29][30][31][32][33][34]. There have been only a few studies on nonmolecular crystalline compounds [35][36][37][38][39]. Here, we demonstrate the potential of this technique for structural characterization of the amorphous state. We find that compressed amorphous GeO 2 remains in persistent sixfold coordination up to 100 GPa, with the GeO 6 octahedra being increasingly distorted with pressure.

II. OCTAHEDRAL DISTORTION
The average Ge-O distance is a second important parameter to describe amorphous GeO 2 , linked to the CN by the principles of bond valence theory and increases with increasing CN [40,41]. At constant CN, increasing pressure causes shortening of the average Ge-O bond, determined by the bulk modulus of the coordinating polyhedron [42]. We consider mean Ge-O distance unless indicated otherwise, defined as the arithmetic mean of all Ge-O distances in the first coordination shell.
The distortion of the GeO 6 octahedron of six oxygen neighbors surrounding the germanium is a third parameter important to evaluate in both amorphous GeO 2 and the crystalline polymorphs sequence of rutilelike GeO 2 (r-GeO 2 ), CaCl 2 -like, α-PbO 2 -like and FeS 2 -like GeO 2 [19,43]. Octahedral distortion is described by the variance of both Ge-O distance and bond angles in the GeO 6 octahedra (see Ref. [44], and references therein). The variance in bond length increases from 1% in rutilelike GeO 2 to 5% in α-PbO 2 -like GeO 2 , but drops to zero in cubic FeS 2 -like GeO 2 . The bond angle variance increases from 25°i n high-pressure rutilelike to 80°in FeS 2 -like GeO 2 , passing through a minimum in CaCl 2 -like GeO 2 at 28 GPa. Overall, there is a trend of increasing octahedral distortion in the high-pressure polymorphs of GeO 2 (Fig. 1) [44].
The increasing octahedral distortion from one polymorph to the next allows the GeO 6 octahedra to maintain a mean Ge-O distance larger than those that would be reached by isostructural compression. For instance, while the bulk modulus of the GeO 6 octahedron in rutilelike GeO 2 is about 300 GPa [42], the increasing GeO 6 distortion in the sequence of crystalline high-pressure GeO 2 polymorphs allows the average Ge-O distance to decrease less, resulting in a much higher effective octahedral bulk modulus. While the octahedral distortion in compressed amorphous GeO 2 is not directly accessible to measurement, it can be inferred from the comparison of the mean Ge-O distance to the one of crystalline high-pressure GeO 2 polymorphs, as we show below. While no crystalline GeO 2 or SiO 2 polymorph with a CN above six has been found experimentally [19,20], GeO 2 in the PbCl 2 -like, cotunnite structure with a CN of nine has been proposed and investigated in an ab initio study as a candidate polymorph beyond FeS 2 -like GeO 2 [13].

III. Kβ 00 EMISSION LINE
The Kβ 00 emission line (EL) is part of the VTC XES spectra of GeO 2 and many other chemical systems that combine 3d transition metals or adjacent elements with ligands from the second or third row of the periodic table. Figure 2 shows measured (top) and calculated (bottom) VTC XES spectra of q-GeO 2 and r-GeO 2 with the Kβ 5 , Kβ 00 , and Kβ 2 emission lines. The Kβ 5 EL originates from the 3d orbitals and the Kβ 2 EL originates from overlapping 4p and 4s to 1s transitions. The Kβ 00 EL reflects the binding energy of the oxygen 2s electrons, which are essentially nonbonding in many systems [25,26,45]. However, a few percent mixing of Ge 4p orbitals with oxygen 2s, as evident from the projected density of states, gives rise to the Kβ 00 EL in germanium K-shell spectra. Because of the predominant oxygen 2s character, the Kβ 00 EL is also commonly referred to as a "crossover transition." It is therefore absent in the VTC XES spectrum of elemental Ge (Fig. 2, top).
The intensity of the Kβ 00 EL is a measure of the cationligand distance due to the increasing extent of hybridization of oxygen 2s electrons with cation p valence electrons, here Ge 4p, with decreasing cation-ligand distance [25][26][27]46]. Accordingly, the Kβ 00 of q-GeO 2 with an average Ge-O distance of 1.74 Å at ambient pressure is more intense than the one of r-GeO 2 with an average bond length of 1.88 Å. The emission energy of the Kβ 00 EL differs by about 0.7 eV at ambient pressure between CN ¼ 4 in q-GeO 2 and CN ¼ 6 in r-GeO 2 (Fig. 2). Measurement of the shift of the Kβ 00 in compressed amorphous GeO 2 allows for tracking the germanium CN by comparison to the shift of crystalline GeO 2 references of different CN at high pressure. The average Ge-O distance is extracted from the intensity change of the Kβ 00 EL, by comparison to measured and computed spectra of crystalline references.

IV. MATERIALS AND EXPERIMENTAL METHODS
We loaded amorphous GeO 2 (a-GeO 2 [47]) (three independent loadings), polycrystalline quartzlike GeO 2 (q-GeO 2 ) (two independent loadings), and rutilelike GeO 2 (r-GeO 2 , [48]) (one loading) into diamond anvil cells (DACs). r-GeO 2 was measured at high pressure as a reference material of CN ¼ 6. Panoramic DACs with a pair of anvils of different culet sizes, namely 400 and 300 μm for pressures below 30 GPa and 300 and 200 μm above, were used. The use of different culets is important for the acquisition of the emission signal, as the penetration depths of the different culets into the 200-μm-thick rhenium gasket leads to a lower gasket indentation wall on the side of the larger culet. The sample chambers of 100 and 80 μm diameter, respectively, were completely filled with sample powder. The pressure was determined from the shift of the fluorescence line of ruby chips inside the sample chamber [49]. We estimate the measurement error in pressure to be about AE1 GPa below 20 GPa and about AE2 GPa for pressures above 20 GPa. Elemental germanium was measured at ambient pressure for reference.
Measurements of the XES were performed at beam line P01 at DESY, Germany. The incident beam of 12.5 keV was monochromatized with a Si(111) monochromator and focused by a Kirkpatrick-Baez mirror to 7 × 15 μm 2 FWHM (V × H). It entered the DAC through the diamond with the smaller culet size. We collected the emission signal at near-90°scattering angle with an energy-dispersive von Hamos-type spectrometer [37,50] in such a way that the emitted radiation passed through the side of the larger diamond, a few degrees past the gasket indentation wall. Eight cylindrically bent Si(nn0) crystals with 0.5 m bending radius dispersed the signal onto a Pilatus 100k detector with a pixel size of 172 μm. The detection with Si(660) planes and a mean Bragg angle of 61°resulted in a spectral bandwidth of about 180 eV with an energy resolution of about 1 eV. We used the Si(880) Bragg reflection to determine the dispersion of each analyzer crystal via detecting the elastic scattering at various settings of the monochromator energy. The acquisition time of the VTC XES spectra was 20 min for each pressure step. After summing the signal of the analyzers, we subtracted a second-order polynomial background.

V. COMPUTATION OF SPECTRA
We computed the VTC XES spectra of crystalline GeO 2 polymorphs by numerical solution of the Bethe-Salpeter equation, as implemented in the OCEAN code [51]. The ground state electronic structure was computed within the theoretical framework of density functional theory as implemented in the QUANTUM ESPRESSO package [52], using the local density approximation for the exchangecorrelation functional.
For the crystalline structures of GeO 2 at ambient and high pressure, we used experimentally determined structures of q-GeO 2 (CN ¼ 4) and r-GeO 2 , CaCl 2 -like, α-PbO 2 -like, and FeS 2 -like GeO 2 (all CN ¼ 6) [19,43,53]. q-GeO 2 with CN of four amorphizes above 5 GPa [53]. In order to obtain spectra of CN ¼ 4 above 5 GPa, we stepwise downscaled the volume of the unit cell of highest pressure of 4.6 GPa [53]. The unit cell of cotunnitestructured PbCl 2 -like GeO 2 with CN ¼ 9 [13] was also scaled in volume. In the scaling of the volume of the unit cell all proportions were maintained. At each scaling step, we computed the spectrum and the pressure from the stress tensor. All computed pressures were corrected by subtraction of the linear, pressure-dependent mismatch found for the known crystalline high-pressure GeO 2 polymorphs used in this study. In this way, we achieved agreement between experimental and computed pressure with a deviation below 5 GPa, or in a few cases 8 GPa. The calculated spectra were convoluted and shifted for visualization to match the experimental emission energy of the Kβ 5 EL (Fig. 3, middle). Both emission energy and intensity of the Kβ 00 EL in germanium oxides can be conveniently expressed relative to the Kβ 5 EL, which serves as an internal energy and intensity calibrant. The Kβ 5 EL is almost constant in both emission energy and intensity for germanium oxides, due to the localization and semicore character of the filled 3d shell. The energy of the Kβ 5 EL is equal for the two polymorphs of GeO 2 , and shifted by less than 0.1 eV in elemental germanium (Fig. 2). Energy shifts of the Kβ 00 EL in the VTC XES spectra of GeO 2 are thus described as energy difference ΔE between the Kβ 00 and Kβ 5 ELs, ΔE ¼ EðKβ 00 Þ − EðKβ 5 ). Changes in the intensity of Kβ 00 are expressed as the ratio of the intensities RI ¼ IðKβ 00 Þ=IðKβ 5 ).

VI. RESULTS AND DISCUSSION
The evolution of the Kβ 00 EL of compressed r-GeO 2 up to 56 GPa is shown in Fig. 3 (top). The Kβ 00 EL intensity increases and shifts continuously, reflecting the decreasing mean Ge-O distance and the increasing binding energy of oxygen 2s electrons with pressure. Selected computed spectra of crystalline ambient and high-pressure GeO 2 polymorphs are shown in Fig. 3 (middle). With increasing pressure, both within a given structure and across structural transitions, the Kβ 00 EL shifts to higher binding energies. Its intensity is highest for q-GeO 2 (CN ¼ 4) and lowest for PbCl 2 -like GeO 2 (CN ¼ 9) at 121 GPa, thereby reflecting the increasing mean Ge-O distance with increasing CN. Selected VTC XES spectra of compressed a-GeO 2 are shown in Fig. 3 (bottom). While the Kβ 5 EL is constant in position within the measurement uncertainty, the Kβ 00 EL shifts with pressure by more than 2 eV between 0 and 100 GPa. Its intensity initially decreases to a minimum at 15 GPa and then continuously increases up to 100 GPa. Compression of q-GeO 2 shows a similar behavior (not shown). In the following, we evaluate the measured spectra in terms of ΔE and RI, as defined above, which allows us to determine the average germanium CN and average Ge-O distance.
A. Germanium coordination number  [19], and α-PbO 2 -like GeO 2 [19,54], and for the scaled potential extreme-pressure CN ¼ 9 structure of PbCl 2 -like GeO 2 (violet) [13]. Isostructural compression decreases ΔE, as indicated by the dashed lines of negative slope for each structure. Between ΔE of the fourfold, sixfold, and ninefold coordinated structures lies a decrease of 0.25 eV on average. Thus, the position of the Kβ 00 EL with respect to Kβ 5 reflects the germanium CN. The sequence of the four crystalline octahedral polymorphs results in isostructurally continuous weak decrease and additional stepwise decrease across structural transitions. The solid light red line represents the linear average of this structural evolution toward increasing octahedral distortion.    which is indicated for r-GeO 2 at all pressures but omitted otherwise for clarity. ΔE of both a-GeO 2 and q-GeO 2 decreases steeply from about 9.0 to about 8.1 at 20 GPa, changes slope and continues to decrease linearly, following the trend observed in the spectra of compressed r-GeO 2 (red dashed line), which transforms to the CaCl 2 structure at 25 GPa [43]. The blue and violet dashed lines indicate the expected trends of q-GeO 2 and PbCl 2 -like GeO 2 , scaled from the slope observed in the computed spectra (in Fig. 4, top).
The qualitative agreement between trends observed in computed and in measured spectra of GeO 2 reference structures is excellent and underlines the sensitivity of ΔE with respect to coordination. The quantitative agreement of ΔE and its high-pressure trend of r-GeO 2 is not sufficient to base the quantitative evaluation on computed spectra. We therefore calculated the average germanium CN of compressed a-GeO 2 and q-GeO 2 from measured ΔE, using as references for linear interpolation the measured high-pressure trend of r-GeO 2 from 0 to 56 GPa and the trend of q-GeO 2 (dashed lines in Fig. 4, bottom). The resulting CN and a general fit are shown in Fig. 5.
The rise of the average germanium CN from four at ambient pressure to six at about 20 GPa is in good agreement with other studies (see inset of Fig. 5) [1, 3,6,8]. Above 20 GPa, the data indicate a persistent CN of six up to 100 GPa. This observation contrasts with results obtained from XRD by Kono et al., who reported a steep rise between 40 and 60 GPa from CN ¼ 6 to 7, followed by further increase to 7.4 at 91 GPa (green squares). In contrast, results from ab initio molecular dynamics (blue squares) rather strengthen the predominance of sixfold coordinated germanium up to 100 GPa. In Fig. 5, the data from Du and Tse were recalculated using the integration of the Ge-O gðrÞ with a cutoff of 2.3 Å. In the original paper, a cutoff of 2.5 Å was used, which leads to inclusion of a small amount of second shell oxygen neighbors in the calculation of the CN [21].
The observed trend of ΔE, compared to those predicted for GeO 2 with CN of 4, 6, and 9, leaves little space for doubt about the persistence of sixfold coordination up to 100 GPa. The interpretation of the measured spectra in terms of Ge-O distance allows for an even deeper insight into the compaction mechanisms in amorphous GeO 2 .

B. Ge-O distances
Imposed by the requirements described by bond-valence theory [40,41], the mean Ge-O distance of the structures of coordination numbers CN ¼ 4, 6, and 9 have mean Ge-O distances significantly different from each other: 1.74 Å in fourfold coordinated q-GeO 2 at ambient pressure, between  AIMD data are based on evaluation of the molecular dynamics results from Du and Tse [21]. The inset shows the pressure range up to 25 GPa, with additional literature data from XRD and neutron diffraction (ND) measurements.
1.88 and 1.85 Å in sixfold coordinated r-GeO 2 between ambient pressure and 25 GPa, 1.77 Å in FeS 2 -like GeO 2 at 108 GPa, and 1.96 Å in ninefold coordinated PbCl 2 -like GeO 2 at 120 GPa. This leads to three linear trends in RI as function of mean Ge-O distance, offset from each other by about 10% in computed spectra (Fig. 6, top). Figure 6 (bottom) shows the measured RI of compressed q-GeO 2 and r-GeO 2 . The experimental values of compressed r-GeO 2 up to 56 GPa follow a linear trend. Error bars in the bond length result from the uncertainty of the pressure measurement, those on RI represent the uncertainty from the fits to the measured spectra. As there is no high-pressure q-GeO 2 beyond 5 GPa, we assume a fourfold trend (blue dashed line) parallel to the sixfold trend (red dashed line), further constrained by RI of computed spectra.
We replot computed and measured RI as a function of pressure in Fig. 7 (top and bottom, respectively; note inverse y axis). In the computed results, the trends of fourfold, sixfold, and ninefold coordination are clearly offset from each other (top). The same applies to measured RI of q-GeO 2 and compressed r-GeO 2 (bottom). The trend in the computed RI sequence of sixfold coordination is almost linear up to 60 GPa (dashed red line, top). Above 60 GPa, data on experimentally determined structures is scarce and scattered, which leads to scatter in RI (compare, e.g., two RI values of α-PbO 2 -like GeO 2 from two different studies [19,54]). We plot a nonlinear trend for comparison.
Experimental RI values of r-GeO 2 up to 56 GPa plot on a linear trend. Upon initial compression to 20 GPa, the measured RI values of a-GeO 2 and q-GeO 2 decrease at first, then follow the sixfold trend, with a slight change in slope around 50 GPa. We fit these data (disregarding three outliers at 44, 58, and 79 GPa) by two error functions and two linear trends, one below 55 GPa and one above. The computed trends of q-GeO 2 and PbCl 2 -like GeO 2 (blue and violet dashed line, respectively) have been scaled in onset and slope, such that the trends of measured and computed spectra of r-GeO 2 match.
We convert the fit of measured RI values of compressed amorphous GeO 2 to mean Ge-O distances as a function of pressure, between linear RI trends of fourfold and sixfold coordination (Fig. 7). The resulting curve of mean Ge-O distance in compressed amorphous GeO 2 is shown in Fig. 8 (black line), together with important information on the bond lengths of crystalline polymorphs. Also shown are Ge-O distances in amorphous GeO 2 , obtained from other techniques as reported in the literature. The estimated uncertainty of the average Ge-O distance is 0.02 Å and results mainly from the uncertainty of the function describing the trend of the Ge-O distance in the known crystalline sixfold polymorphs (red curve in Fig. 8). If instead of the red curve a linear fit to crystalline mean Ge-O distances is used as basis (not shown), the resulting Ge-O distance differs especially at high pressures, as shown by a second curve (thin black line). In the pressure region below 5 GPa, RI of compressed q-GeO 2 increases, whereas in amorphous GeO 2 , RI decreases from the beginning, pointing to an earlier onset of coordination increase in amorphous GeO 2 compared to q-GeO 2 , in line with a similar observation in EXAFS measurements of Ge-O distance [5]. The mean Ge-O distances of the sequence of sixfold coordinated GeO 2 are shown in red, together with a monotonic fit (red line), required for conversion of RI to Ge-O distance, as described above. Isostructural compression of any of these structures follows trends dictated by the GeO 6 octahedral bulk modulus of about 300 GPa [42] (four dashed gray lines in Fig. 8). They are tangential to the isostructural mean Ge-O distances (see, e.g., r-GeO 2 and α-PbO 2 -like GeO 2 ). Starting from experimentally determined points of mean Ge-O distances, they extend to higher pressures, describing the expected isostructural evolution of Ge-O distances. However, the effective compression across structural transitions in the octahedral sequence from r-GeO 2 to FeS 2 -like GeO 2 (red line) involves increasing octahedral distortion and thus allows for a much higher effective octahedral bulk modulus. The evolution of Ge-O distances in PbCl 2 -like GeO 2 falls outside the range of the figure, being 1.96 Å at 120 GPa and 2.03 Å at 60 GPa. Instead, the trend of average coordination number 7.5, calculated as the linear intermediate between CN ¼ 6 and 9, is shown.
Our Ge-O distance values increase from 1.75 Å at ambient pressure to 1.85 Å at completion of the fourfold to sixfold coordination transition at 20 GPa, and decrease alongside the trend of effective crystalline octahedral compression up to about 50 GPa, from where on the bond length of amorphous GeO 2 decreases slower and exceeds those of the effective octahedral trend in the crystalline high-pressure sequence. The bond length between 90 and 100 GPa is 1.8 Å, 0.02 Å above the one of the crystalline polymorphs at the same pressure, but in good agreement with FeS 2 -like GeO 2 determined at 108 GPa [19] when the isostructural compressibility of the GeO 6 octahedron is taken into account (rightmost gray dashed line). We take this agreement as an indicator for the FeS 2 -like octahedral distortion in sixfold coordinated amorphous GeO 2 .
Earlier EXAFS studies did not exceed 70 GPa, but reported mean Ge-O distances in good agreement to ours, albeit somewhat lower [5,10,11]. Systematic differences in the absolute bond length between XRD and EXAFS are commonly reported (see, e.g., Ref. [56]), but changes or trends are usually consistent. The only EXAFS study with data above 50 GPa coincides with the mean Ge-O distance of crystalline polymorphs (red line) line between 55 and their highest pressure of 64 GPa (gray circles) [5]. The bond length reported by Kono et al. at 90 GPa is in line with our measurements, but the interpretation concerning the average CN is different; we observe a persistent sixfold coordination, while a mean CN of 7.4 was reported with XRD. The recent ab initio molecular dynamics study of Du and Tse [21], yielding mean germanium CN below 6.5 at 100 GPa, was evaluated for the present study in terms of Ge-O distance (blue open squares). They are about 0.02 Å larger than ours, but almost coincide with those of Kono et al. between 40 and 90 GPa. Figure 8 indicates that a CN of 7.4 at 90 GPa should correspond to a mean bond length of about 1.89 Å, far from any experimental observation.
The contradiction between similar bond lengths in our XES study, in the XRD study by Kono et al., and in the AIMD study by Du and Tse (Fig. 8), but differing coordination number at 90 GPa between 6.0 in our data, 6.4 in the data of Du and Tse, and 7.4 in the data of Kono et al., can be resolved by a closer look at the evolution of the measured mean Ge-O distance as a function of pressure. The mean Ge-O distances of the crystalline high-pressure GeO 2 polymorphs r-GeO 2 , CaCl 2 -like, α-PbO 2 -like, and FeS 2 -like GeO 2 fall on a curved trend (solid red symbols and red line in Fig. 8). The curvature reflects a stepwise increase in octahedral distortion between crystalline polymorphs (Fig. 1). Contrary to this curvature, the mean Ge-O distance of each individual polymorph closely follows a trend described by an octahedral bulk modulus of about 300 GPa (gray dashed lines) [42]. These compression trends, together with the crystalline mean Ge-O distances,  [21], and three EXAFS studies (circles) [5,10,11]. Gray dashed lines indicate the isostructural compression trend described by a GeO 6 octahedral bulk modulus of 300 GPa [42]. The gray shaded area indicates qualitatively the area of octahedral coordination. The expected trend of average CN ¼ 7.5, calculated as linear intermediate between CN ¼ 6 and 9, is indicated (dashed orange line). define the area of octahedral coordination (shaded gray area in Fig. 8). All measured Ge-O distance curves of crystalline and amorphous GeO 2 lie within this area (with a few outliers), regardless of the measurement technique. Thus, the bond length evolution provides evidence for persistent octahedral germanium coordination with increasing distortion.
A mean Ge-O distance consistent with an average CN of 7.0 or higher must plot above the gray shaded area, as indicated by the Ge-O distances of ninefold coordinated PbCl 2 -like GeO 2 , being 2.03 Å at 60 GPa and 2.00 Å at 90 GPa (above the limits of the graph in Fig. 8). Assuming linear bond length increase between sixfold and ninefold coordination, the trend of bond length in average 7.5-fold coordination is indicated by the dashed orange line. It plots significantly above any reported Ge-O distance, indicating that the average germanium coordination remains close to sixfold at least up to 100 GPa. Furthermore, the AIMD data by Du and Tse confirm our view: The predominant sixfold coordination up to 100 GPa (Fig. 5) Fig. 8).
The average germanium CN as high as 7.0 at 60 GPa, reported by Kono et al.
[1], is based on the integration of the first maximum of the total radial distribution function gðrÞ. The Ge CN might be overestimated due to contributions from the first O-O shell to the first peak of the total radial distribution function. Furthermore, the gðrÞ analysis has to rely on extrapolations of the density of amorphous GeO 2 , which are uncertain at high pressure [1]. The XES signal is independent of the abovementioned factors.
The persistent octahedral coordination in compressed amorphous GeO 2 up to 100 GPa, accompanied by increasing octahedral distortion, indicates that the local structure in compressed amorphous GeO 2 follows closely the one found in the sequence of stable crystalline high-pressure phases of GeO 2 . This is consistent with a recent x-ray absorption spectroscopy study on shock compressed amorphous SiO 2 to several hundreds GPa [57], also indicating that the local structure in compressed amorphous SiO 2 follows closely the one found in the sequence of stable crystalline high-pressure phases. GeO 2 and SiO 2 undergo similar structural transitions, although at different pressures [20]. Finally, x-ray Raman scattering spectroscopy data and Brillouin scattering of compressed amorphous SiO 2 both indicate a persistent sixfold silicon coordination up to 120 GPa [15,17], which is at odds with a recent XRD study reporting average silicon CN above six [18].

VII. CONCLUSION
VTC XES spectra of amorphous GeO 2 , quartzlike GeO 2 , and rutilelike GeO 2 have been measured up to 101, 35, and 56 GPa, respectively. Evaluation of the emission energy and the intensity of the Kβ 00 allowed us to track the persistent sixfold coordination of germanium up to 100 GPa. The Ge-O distance, which is in excellent agreement with earlier published values from XRD and EXAFS measurements, indicates persistent octahedral coordination with increasing distortion, like that observed for the sequence of crystalline high-pressure GeO 2 polymorphs. We therefore conclude that on the atomic scale amorphous GeO 2 behaves similarly to the experimentally determined crystalline polymorphs. A density crossover between compressed amorphous GeO 2 and its high-pressure crystalline phases is therefore possible only on the basis of a higher average degree of octahedral distortion, but not on the basis of a coordination increase beyond six.
The Kβ 00 EL evaluation scheme described here is a valuable approach to access both bond lengths and coordination in amorphous material at high pressure. The procedure requires measurements or computational spectra of reference materials. Factors that limit the Kβ 00 EL as a sufficiently intense and separate peak are the overall signalto-noise ratio and the core-hole lifetime broadening of the cation, if its atomic number is too high. However, systems that exhibit the Kβ 00 EL as part of their VTC XES spectra are the compounds of 3d transition metals (or adjacent elements) with ligands from the second or third row of the periodic table. Thus, systems for which the described procedure may be valuable are investigated in a range of scientific fields, from metallic glasses and phase change materials doped with oxygen and nitrogen, nitrides, and oxynitrides for photocatalysis to thin functional amorphous oxide or sulfide films.