Pressure-induced normal-incommensurate and incommensurate-commensurate phase transitions in CrOCl

The high-pressure behavior of layered CrOCl is shown to be governed by non-bonded interactions between chlorine atoms in relation to a rigid framework composed of Cr and O atoms. The competition between optimizing intra- and interlayer Cl–Cl distances and the general trend towards denser packing defines a novel mechanism for high-pressure phase transitions of inorganic materials. CrOCl possesses an incommensurate phase for 16–51 GPa. Single-crystal x-ray diffraction in a diamond anvil cell provides an accurate description of the evolution of the incommensurate wave with pressure. It thus demonstrates a continuous increase of the amplitude up to 30 GPa, followed by a decrease of the wavelength until a lock-in transition occurs at 51 GPa.


Experiments and data processing
Single-crystal X-ray diffraction experiments have been performed on crystals loaded in BX90 diamond anvil cells (DACs) 1 equipped with Boehler-Almax diamonds 2 . Pressures were obtained from the shifts of the R1 fluorescence line of ruby 3 . The fluorescence was measured directly before and immediately after the data collections, in order to establish the magnitudes of pressure variation during each experiment. Neon has been used as pressure-transmitting medium. It crystallizes at approximately 4.8 GPa 4 , but its diffraction peaks became clearly visible only at 13 GPa. Therefore, for higher pressures, the lattice parameter of Ne could be used as an additional pressure indicator 5 . The maximum difference between pressures measured before and measured after the data collections, and determined by different methods did not exceed 0.7 GPa.
Integrated intensities of Bragg reflections were obtained from the measured diffraction images by the software CrysAlisPro 6 . It appeared necessary to convert the format of the Mar555 images to Mar345 format. Custom-made software available at beamline ID09A was used for this purpose.
Perkin Elmer images in .tif format were converted to the esperanto image type 6 that is supported by the latest version of CrysAlisPro 6 . Components of the modulation wave vector were refined simultaneously with the orientation matrix against the observed positions of the reflections, using the computer program NADA 7 as implemented in CrysAlisPro. Outliers were removed according to procedures recently implemented in JANA2006 8 . Equations of state were determined with the software EosFit7c 9 applied to the measured lattice parameters and unit-cell volumes.
For Raman spectroscopy experiments, a BX90 DAC with standard design diamond anvils (250 μm culet size) was used. Raman spectra were measured in backscattering geometry, employing a Dilor XY Raman spectrometer using an Ar + ion laser (Coherent Innova 300) with a wavelength of 514.5 nm, and possessing a spectral resolution of 1 cm −1 . The laser power was kept below 2 mW, in order to avoid laser-heating of the sample. Phonon frequencies were obtained by fitting Pearson VII functions to the experimental peaks.

Structure refinements for the low-pressure phase of CrOCl
CrOCl keeps its ambient-pressure structure up to 14.5 GPa. Crystal structures at these pressures were successfully refined against each of the eight data sets of X-ray diffraction data measured at pressures between 0.0001 and 12.95 GPa (Supplementary Table 1). The structure published by Forsberg 10 was used as starting model. Due to the limited coverage of reciprocal space in the high-pressure diffraction experiments at the ESRF, it appeared necessary to use a smaller number of independent parameters in the refinements than the three coordinates and nine atomic displacement parameters (ADPs) allowed by symmetry. It was chosen to use isotropic ADPs for Cr and O, thus reducing the number of ADP parameters from 9 to 5. The Cl atoms can be expected to possess large and anisotropic displacement amplitudes, because they form the boundary of the Van der Waals gap. Therefore, Cl was given anisotropic ADPs. This model leads to a pronounced drop in R-factors and is supported by a Hamilton test (0.005 significance level), while anisotropic refinement of Cr and O atoms does not lead to a significant lowering of the agreement factors.
Data obtained upon decompression contained more reflections, which allowed refinement anisotropic ADPs for all atoms (Supplementary Table 2).
Larger mosaic spreads at higher pressures reduced the importance of extinction. Therefore, an extinction correction was not applied at pressures above 7.1 GPa. All refinements smoothly converged to excellent fits to the diffraction data (Supplementary Tables 1 and 2).

Structure refinement of the incommensurate high-pressure phase of CrOCl
CrOCl is found to undergo a phase transition at a pressure between 15. 3  were not observed, and therefore only first-order harmonics could be used. The ambient-pressure structure model was used as a starting model for the refinements of the basic structure against the main reflections. Subsequently, small but arbitrary values were given to the modulation amplitudes. Refinement of all parameters against all reflections resulted in a smooth convergence and a good fit to the diffraction data at each pressure (Supplementary Tables 1 and 2). 4 At pressures below 30 GPa, 1 is close to the rational number P21mn for other values of t0. In addition to the refinement of the incommensurate structure model, superstructure models were tested by commensurate superspace refinements with t0 equal to 0, 1 28 and 0.050508, respectively. Differences between the R-factors of these four refinements did not exceed 0.01% (Supplementary Table 3). As a consequence, it is impossible to distinguish between different superstructures and between incommensurate and commensurate modulations, solely on the basis of the refinements. This ambiguity may be the result of having available only highly incomplete data sets. Furthermore, the 14-fold superstructure would allow satellites up to the seventh order, but only first-and second-order satellites were observed, which again diminishes the sensitivity of the diffraction to a possible commensurability of the modulation.
On the other hand, the pressure dependence of the 1 reveals an incommensurate modulation for pressures between 30 and 51 GPa, while phase transitions between 16.4 and 51 GPa were not observed. This strongly suggests the incommensurability of this high-pressure phase of CrOCl.
However, a commensurate-to-incommensurate transition at approximately 30 GPa cannot be entirely excluded on the basis of the present data.

Structure refinement of the incommensurate high-pressure phase of FeOCl at 15 GPa
In FeOCl at 15 GPa satellite reflections can be indexed with the q-vector (0.26, 0,  Table 4).

Structure refinement of the commensurate high-pressure phases of CrOCl
At P = 57.2 GPa the diffraction pattern contains two sets of satellite reflections. One set can be indexed as a lock-in phase of the incommensurately modulated phase at lower pressures, employing 1 =   Table 5 ). On decompression, at P = 47.5 GPa only the lock-in phase survived. It was described by the same superspace group and the same basic structure as the incommensurately modulated structure at lower pressures.
Refinements of the commensurately modulated structure converged smoothly to a good fit to the diffraction data (Supplementary Table 2). The best fit to the diffraction data was obtained for the section t0 =  Table 6). This structure model corresponds to a superstructure with a sixfold, 3a×b×2c supercell with space group Pmmn.

Pressure dependence of the Raman scattering of CrOCl
Raman spectra of CrOCl were recorded at 13 pressures within the range 5-31 GPa ( Supplementary Fig. 1). The full representation of the vibrational modes of CrOCl in space group Pmmn is: where Ag, B2g and B3g are Raman active. At low pressures three strong Raman active modes are clearly observed (Supplementary Fig. 1). They can be identified with Ag modes according to

Tables of interatomic distances and angles
Supplementary