International
Tables for
Crystallography
Volume I
X-ray absorption spectroscopy and related techniques
Edited by C. T. Chantler, F. Boscherini and B. Bunker

International Tables for Crystallography (2022). Vol. I. Early view chapter
https://doi.org/10.1107/S1574870720004693

X-ray absorption spectroscopy under extreme conditions of pressure

Jean-Paul Itiéa* and Sakura Pascarellib

aSynchrotron SOLEIL, L'Orme des Merisiers, St Aubin, BP 48, 91192 Gif-sur-Yvette, France, and bEuropean Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble, France
Correspondence e-mail:  jean-paul.itie@synchrotron-soleil.fr

X-ray absorption spectroscopy (XAS) has successfully been applied in high-pressure research for over 40 years. The main strengths of XAS make this technique highly complementary to the more commonly used diffraction-based methods. Its strong sensitivity to local structure makes it a powerful probe of pressure-induced changes in disordered matter (liquids and amorphous solids) and of distorted or complex ordered solids where the local structure differs from the average structure. Its element selectivity allows pressure effects on dilute species to be studied, and its high sensitivity to symmetry and charge around the absorbing atom is an asset when phase transitions modify speciation or valence. Developments in the coming years will include 3D hyperspectral mapping on the nanoscale in the diamond anvil cell, and time-resolved studies of chemical reactions and phase-transition kinetics induced by dynamic compression methods.

Keywords: high pressure; phase transitions; diamond anvil cell; Paris–Edinburgh cell.

1. Introduction to extreme conditions

1.1. High-pressure effect

Before emphasizing the interest of XAFS-related techniques for the study of materials under extreme conditions of pressure, it is necessary to highlight the main effects of pressure on matter. From the thermodynamic point of view, pressure is an intensive parameter that is associated with volume as an extensive parameter such as temperature is associated with entropy. In the Gibbs function, the PV term is positive, which means that to minimize the energy at a given pressure, it is necessary to reduce the volume. Therefore, the main effect of pressure on matter will be a reduction in the volume, which can be obtained by a change in the morphology of the material, a reduction of the interatomic distances or a transition to a new denser structure. We also need to note that volume or density is a more appropriate parameter than pressure to describe the properties of materials.

1.2. High-pressure generation and measurement

High-pressure equipment can be divided into two main families: large-volume cells (the Paris–Edinburgh cell, multi-anvil press etc.) and diamond anvil cells (or equivalents with other type of anvils), which have a smaller sample volume but can be operated at a much higher pressure. Although experiments have been performed with large-volume presses (Buontempo et al., 1998[link]; De Panfilis et al., 2002[link]; Arima et al., 2007[link]), diamond anvil cells are clearly the most widely used (Itié, 2004[link]). Details of pressure generation and measurement and of the specific drawbacks of a high-pressure setup for XAS can be found in Aquilanti (2022[link]).

2. The contribution of XAS to high-pressure crystallography

As already mentioned, XAS is a local probe, while X-ray diffraction (XRD) is more sensitive to long-range order. Therefore, under high pressure, XAS will provide specific information around a given atom such as the bond-length variation through the EXAFS oscillations or the symmetry modifications though the XANES and the pre-edge part of the spectrum. This region also probes the electronic and magnetic degrees of freedom, because the transition probability is modulated by the l-projected density of empty states. Changes in valence, reduction or suppression of the band gap as a function of pressure can be studied by XANES. Likewise, changes in ferromagnetic (or antiferromagnetic) order upon compression can be probed using polarized XAS, such as X-ray magnetic circular (or linear) dichroism. These techniques probe magnetic and local structure simultaneously and are therefore very useful to study the correlations between them (Mathon et al., 2004[link]; Torchio et al., 2014[link]).

2.1. EXAFS under pressure: local equation of state

The variation of the EXAFS oscillation period is directly related to the distance variation and, because it is a relative variation from the ambient pressure distances, excellent accuracy can be obtained. Fig. 1[link] shows the evolution with pressure for solid krypton of the first-neighbour distance (R), the square of the Debye–Waller factor (σ2) and the asymmetric coefficient of the distribution β compared with Monte Carlo (MC) simulation (Di Cicco et al., 1996[link]). In the case of krypton the compression is isotropic and the results of EXAFS are similar to the diffraction results. However, under pressure the variation of the interatomic distances is not necessarily isotropic. Therefore, knowledge of the structure is required to determine the local compressibility from X-ray diffraction data, whereas this information can be directly measured from XAFS data. Fig. 2[link] (left) shows the evolution with pressure of the Fourier transform of the EXAFS oscillation measured at the Mn K edge for LaMnO4 (Ramos et al., 2007[link]). The intensity of the first peak increases with increasing pressure, indicating a decrease of the Jahn–Teller distortion around the Mn atom. Fig. 2[link] (right) shows the variation of the two Mn–O distances with pressure: the Jahn–Teller distortion is reduced but remains even at the highest pressure obtained.

[Figure 1]

Figure 1

Evolution with pressure for solid krypton of the first-neighbour distance (R), the square of the Debye–Waller factor (σ2) and the asymmetric coefficient of the distribution β compared with Monte Carlo (MC) simulation. Reprinted with permission from Di Cicco et al. (1996[link]). Copyright 1996 by the American Physical Society.

[Figure 2]

Figure 2

Left: evolution with pressure of the Fourier transform of the EXAFS oscillation measured at the Mn K edge for LaMnO4. Right: variation with pressure of the two Mn–O distances. Reprinted with permission from Ramos et al. (2007[link]). Copyright 2007 by the American Physical Society.

Because XAFS does not require long-range order, it is well suited for the study of amorphous materials or liquids under high pressure. The bond-length compressibility can be determined and compared, for example, with the same compressibility in its crystalline counterpart. Fig. 3[link] shows the variation of the Ga–Sb distance in amorphous GaSb (aGaSb) and in crystalline GaSb (cGaSb). Locally, the compressibility around the Ga atom is smaller for the amorphous than for the crystalline material (Lyapin et al., 1996[link]). This does not mean that amorphous GaSb is less compressible than crystalline GaSb, but only that the mechanism of compression is different, with the amorphous material being more flexible than the crystalline material because of the rigidity of the crystalline structure.

[Figure 3]

Figure 3

Relative variation of Ga–Sb distance with pressure for amorphous GaSb (circles) and for crystalline GaSb (squares). Reprinted with permission from Lyapin et al. (1996[link]). Copyright 1996 by the American Physical Society.

2.2. EXAFS under high pressure and phase transitions

When phase transitions occur under high pressure, they do not necessarily strongly affect short-range order. However, if there is a bond-length modification, EXAFS becomes very sensitive to the phase transition. The interest of XAS for following phase transitions has already been demonstrated for CuBr (Tranquada & Ingalls, 1986[link]), which exhibits different structures (wurtzite, tetragonal, NaCl) with increasing pressure. In particular, EXAFS is a good indicator of the onset of a pressure-induced transition because when the transition occurs, the distance distribution around a given atom broadens due to the mixing of two different distances belonging to the two different phases. The transition is seen as an increase in the static disorder around a given atom, while X-ray diffraction detects the high-pressure phase only when sufficiently large domains have grown. EXAFS also has higher sensitivity than XRD when phase transitions produce only very subtle changes of the first shell, as is often seen in molecular systems (San-Miguel et al., 2007[link]).

For amorphous samples, EXAFS is extremely well adapted to follow phase transformations, as shown in the pioneering work on GeO2 glass (Itié et al., 1989[link]). This phase transition from fourfold to sixfold coordination around the Ge atom has since been revisited (Baldini et al., 2010[link]), suggesting a possible intermediate phase with fivefold coordination (Fig. 4[link]).

[Figure 4]

Figure 4

Variation of Ge–O distance and σ2 with pressure for GeO2 glass for the compression (top) and decompression (bottom) cycles. Reprinted with permission from Baldini et al. (2010[link]). Copyright 2010 by the American Physical Society.

2.3. XANES under high pressure and phase transitions

XANES is sensitive to intermediate-range order and therefore to pressure-induced modifications of the symmetry around a given atom. However, contrary to EXAFS oscillations, which can be modelled and fitted, the XANES is mainly simulated, requiring knowledge of the structure. In fact, for phase transitions, different structures can be tested and the corresponding simulations compared with the experimental XANES (Briois et al., 1997[link]; Aquilanti et al., 2007[link]). Codes to fit the XANES region have been developed (Benfatto & Della Longa, 2001[link]) but are still mainly used for molecular systems, the structure of which can be described using small atomic clusters.

Fig. 5[link] shows the evolution of XANES with pressure for europium (Bi et al., 2012[link]) measured at the L3 edge (Fig. 5[link]a) and the simulated spectra for different crystallographic structures (Fig. 5[link]b): h.c.p., b.c.c. and orthorhombic. The agreement between experiment and calculations is excellent. It is noticeable that the calculations were performed with a fixed valence state for europium. The fact that the valence of europium remains +2 even at high pressure explains why the superconducting critical temperature at high pressure is much lower than for other rare-earth metals with a +3 valence state.

[Figure 5]

Figure 5

XANES spectra for europium up to 87 GPa (a) compared with FEFF8 simulations up to 75 GPa (b). Reprinted with permission from Bi et al. (2012[link]). Copyright 2012 by the American Physical Society.

During a pressure-induced phase transformation, low- and high-pressure phases can coexist over a large pressure range. The experimental XANES measured in this intermediate range can be reproduced by a linear combination of the XANES of low- and high-pressure phases. This is shown in Fig. 6[link] (left), where the pressure evolution of XANES of GaAs (Besson et al., 1991[link]) is shown. In the right part of Fig. 6[link] the XANES spectrum acquired at 16.4 GPa is compared with a linear combination of the XANES spectra measured at 14.8 and 23.7 GPa with 80% in the low-pressure phase (zinc blende) and 20% in the high-pressure phase (orthorhombic).

[Figure 6]

Figure 6

Left: evolution of the XANES spectrum of GaAs with pressure (increasing pressure: 1, 1.2 GPa; 2, 14.8 GPa; 3, 16.4 GPa; 4, 17.4 GPa; 5, 18.4 GPa; 6, 23.7 GPa; 7, 32.4 GPa; decreasing pressure: 8, 7.7 GPa; 9, 6.2 GPa; 10, ambient). Right: XANES spectrum of GaAs at 16.4 GPa compared with a linear combination of 80% of the XANES spectrum at 14.8 GPa [(b) in the inset] and 20% of the XANES spectrum at 23.7 GPa [(a) in the inset]. Reprinted with permission from Besson et al. (1991[link]). Copyright 1991 by the American Physical Society.

2.4. The pre-edge part of the spectrum

The pre-edge part of the spectrum is very sensitive to electronic properties and to the symmetry around the absorbing atom. In particular, in an octahedral configuration the pre-edge is a fingerprint of the local distortions. A modification of the pre-edge with pressure is a clear indication of a change in the local symmetry. For example, FePO4 undergoes a phase transformation with pressure from a berlinite structure, in which iron is in a tetrahedral configuration, to a mixture of crystalline and amorphous phases (Pasternak et al., 1997[link]). Under increasing pressure, we can observe a strong modification of the pre-edge measured at the K edge of iron in the energy-dispersive mode (Fig. 7[link]; Itié et al., 2005[link]). At low pressure, the intensity is large and the shape corresponds to a tetrahedral environment for the Fe atom. At high pressure, the pre-edge is much smaller and corresponds to an octahedral configuration.

[Figure 7]

Figure 7

Evolution with pressure of the pre-edge part and of the XANES spectra of FePO4 at the Fe K edge. Pressure is indicated in kbar. The spectrum labelled HR was measured on a classical EXAFS beamline with higher resolution. Reprinted from Itié et al. (2005[link]).

3. Trends and future perspectives for high-pressure XAS

Thanks to the increased brilliance of synchrotron-radiation sources and to the possibility of using NPD anvils, new opportunities have arisen for high-pressure XAS. Higher brilliance opens the way to faster measurements for time-resolved and hyperspectral mapping applications. NPD anvils provide the possibility of performing EXAFS at high pressure on classical energy-scanning XAS beamlines, making experiments possible at high energies, in combination with X-ray diffraction (which requires high-energy photons) or with the detection of fluorescence for diluted species.

3.1. Diluted species under high pressure

This is certainly one of the most important improvements in high-pressure crystallography. The use of fluorescence mode for XAS acquisition allows the determination of modification with high pressure of the local environment around a given atom diluted in a matrix, such as chromium in Al2O3 in ruby.

To illustrate this, we present the example of Zn0.95Mn0.05O, a dilute magnetic semiconductor which exhibits a phase transition under pressure from a wurtzite to a rock-salt structure. Under ambient conditions, manganese was shown to substitute zinc in the wurtzite structure (Jin et al., 2003[link]). What happens in the high-pressure phase? What is the compressibility of the Mn–O distance compared with the Zn–O distance (Decremps et al., 2003[link]) in each phase? To answer these questions a fluorescence experiment at the Mn K edge was performed under high pressure (Pellicer-Porres et al., 2006[link]). The main results show that the compressibility of the Mn–O distances is the same in both phases, although Mn–O is longer than Zn–O, and Mn continues to substitute Zn in the high-pressure, sixfold-coordinated phase (see Fig. 8[link]), with an Mn–O distance close to the Zn–O distance.

[Figure 8]

Figure 8

Evolution with pressure (in GPa) of the EXAFS (left) spectrum of Zn0.95Mn0.05O at the Mn K edge and of the pre-edge part of the spectrum (right). A clear change in the XANES and in the EXAFS oscillations is observed at 9.4 GPa together with a strong reduction in the intensity of the pre-edge. Reprinted from Pellicer-Porres et al. (2006[link]), with the permission of AIP Publishing.

3.2. EXAFS at high energy using nano-polycrystalline diamonds

The problem of Bragg diffraction from single-crystal diamond anvils has hindered the development of EXAFS applications at very high pressures in general, and in particular for studies at high-energy absorption edges. The availability of nano-polycrystalline diamond anvils (Irifune et al., 2003[link]) represents a real revolution for high-pressure studies by EXAFS. An illustration of this is given in Fig. 9[link], where EXAFS has been applied to investigate a possible direct reaction between xenon and oxygen at high pressure and temperature. The noble gases are the most inert atomic group, but can become reactive under extreme conditions. Xe K-edge EXAFS, coupled to XRD and ab initio modelling, has revealed the structure of new xenon oxides synthesized above 78 GPa, indicating that xenon is reactive at pressures relevant in the Earth's interior (Dewaele et al., 2016[link]).

[Figure 9]

Figure 9

Xe K-edge XAS of a 36% Xe–64% O2 mixture at ∼82 GPa. (a) XANES before and after laser heating. (b) and (c) EXAFS and amplitude of FT (blue, data; green and red, two different fitting models) for the oxide phase. Reprinted from Dewaele et al. (2016[link]). Copyright 2016 Springer Nature.

3.3. Heterogeneities and phase transitions in the laser-heated diamond anvil cell

The laser-heated diamond anvil cell (LH-DAC) allows rough coverage of the P/T conditions within our planet. Partitioning of iron in mantle minerals down to the core–mantle boundary (Andrault et al., 2010[link]) and metallic melts to megabar pressure (Aquilanti et al., 2015[link]) have been probed by XAS studies in the LH-DAC. Recent studies have shown that molten matter is unstable under continuous laser heating: chemical reactions or decompositions occur at extreme P/T conditions which alter the chemical state and speciation of the absorber. Laser heating also often induces sample-geometry variations or element segregation. While the nanometre scale is still out of reach of XAS, hyperspectral XAS mapping, in which each pixel of the map contains a full XAS spectrum, has been applied to probe heterogeneities at the micrometre scale in samples subject to high P and T in the LH-DAC (Muñoz et al., 2008[link]). The example in Fig. 10[link] shows that element segregation, chemical decomposition or reactions, if any, can be efficiently monitored across the laser-heated spot (Kantor et al., 2018[link]).

[Figure 10]

Figure 10

Absorption-jump maps of a metal foil in the diamond anvil cell before (a) and after two melting events using laser heating (b, c) at around 30 GPa. A hole in the sample is visible in (c). Reprinted from Kantor et al. (2018[link]), with the permission of AIP Publishing.

The trend towards diffraction-limited storage rings (DLSRs) with extremely low emittance will boost 2D and 3D imaging applications at higher spatial resolution in the years to come. Breakthroughs in this domain are expected by the coupling of the DLSR to the development of new-generation double-crystal monochromators for XAS, with the required stability and speed for EXAFS imaging applications with nanometre resolution.

3.4. Time-resolved XAS experiments under high pressure

The increase in flux at synchrotron XAS beamlines is increasingly being exploited for time-resolved studies at high pressure. Recent work has shown that third-generation synchrotrons provide sufficient flux to record an EXAFS spectrum with a single 100 ps X-ray pulse. This feature has been exploited to probe laser-shocked, dynamically compressed matter, enabling the exploration of extreme states of matter beyond the static limit of the diamond anvil cell, to mimic the conditions of the interior of the Earth and other planets (Torchio et al., 2016[link]). These are `exotic' states of matter such as warm dense matter (WDM), where most of the approximations used in condensed-matter physics or in plasma physics break down. To date, this field of research had only been successfully pursued at large high-power laser facilities. In particular, EXAFS has been used to probe shocked matter on nanosecond timescales by employing a laser-imploded target as an X-ray source (see, for example, Yaakobi et al., 2005[link]; Ping et al., 2013[link]).

The first feasibility experiment on a synchrotron beamline was devoted to the study of warm dense iron, Fig. 11[link] compares measured (left) and calculated (right) Fe K-edge XANES data for pure iron shocked to two different P, T conditions along the Hugoniot curve. While the theory is capable of grasping the main changes in the data (indicated with arrows), the experimentally measured value of the shift of the absorption edge at 500 GPa with respect to ambient conditions (top left) is found to be smaller than the theoretical prediction (top right), stimulating further work to improve the electronic treatment of WDM in the DFT framework.

[Figure 11]

Figure 11

Left: enlargement of the edge region of data collected at 120 GPa (bottom) and 500 GPa (top). a, b, c and d indicate regions where major changes are observed. Right: ab initio molecular-dynamics simulations. Reprinted from Torchio et al. (2016[link]).

4. Conclusion

XAS is a useful technique which provides new information on matter under high pressure with excellent complementarity to X-ray diffraction. An overview of XAS applications in high-pressure research is made, with selected examples that highlight its strengths and its complementarity to XRD methods. Developments in the coming years will include 3D hyperspectral mapping at the nanoscale in the diamond anvil cell and time-resolved studies of chemical reactions and phase-transition kinetics induced by dynamic compression methods

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