# Polytypism of incommensurately modulated structures of crystalline bromine upon molecular dissociation under high pressure

Yuqing Yin, Andrey Aslandukov, Maxim Bykov, Dominique Laniel, Alena Aslandukova, Anna Pakhomova, Timofey Fedotenko, Wenju Zhou, Fariia Iasmin Akbar, Michael Hanfland, et al.

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Yuqing Yin, Andrey Aslandukov, Maxim Bykov, Dominique Laniel, Alena Aslandukova, et al. Polytypism of incommensurately modulated structures of crystalline bromine upon molecular dissociation under high pressure. Physical Review B, 2024, 110 (10), pp.104111. 10.1103/PhysRevB.110.104111. hal-05128592

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Distributed under a Creative Commons Attribution 4.0 International License
Polytypism of incommensurately modulated structures of crystalline bromine upon molecular dissociation under high pressure

Yuqing Yin,¹,²,³,* Andrey Aslandukov,¹,⁴ Maxim Bykov,⁵ Dominique Laniel,⁶ Alena Aslandukova,⁶

Anna Pakhomova,⁷ Timofey Fedotenko,⁸ Wenju Zhou,¹ Fariia Iasmin Akbar,¹,⁴ Michael Hanfland,⁷

Konstantin Glazyrin,⁸ Carlotta Giacobbe,⁷ Eleanor Lawrence Bright,⁷ Gaston Garbarino,⁷ Zhitai Jia,²

Natalia Dubrovinskaia,¹,³ and Leonid Dubrovinsky⁴,†

¹Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany

²State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

³Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden

⁴Bayerisches Geoinstitut, University of Bayreuth, 95440 Bayreuth, Germany

⁵Institute of Inorganic Chemistry, University of Cologne, Greinstrasse 6, 50939 Cologne, Germany

⁶Centre for Science at Extreme Conditions and School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

⁷European Synchrotron Radiation Facility, 38000 Grenoble, France

⁸Deutsches Elektronen Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

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(Received 20 September 2023; revised 20 January 2024; accepted 23 August 2024; published 23 September 2024)

Polytypism of incommensurately modulated structures was hitherto unobserved. Here, it was found in solid bromine and iodine upon molecular dissociation under pressure up to 112 GPa. Single-crystal synchrotron x-ray diffraction in laser-heated diamond anvil cells revealed a number of allotropes of bromine and iodine, including polytypes of Br-IIIγ (Fmmm(00γ)s00) with γ varying within 0.18 to 0.3, coexisting at a given pressure. This finding opens a research area in the field of solid-solid phase transitions, disordered states of solid matter, and high-pressure structural studies.

DOI: 10.1103/PhysRevB.110.104111

## I. INTRODUCTION

Studies of the behavior of halogens under pressure provide an insight into how simple molecular systems respond to extreme conditions. Fundamental problems to be addressed are the structure evolution [1], the band-gap closure and metallization [2–4], phase transformations during molecular dissociation [4,5], and others. Extensive theoretical studies based on density functional theory (DFT) calculations [6–9] and experimental investigations using powder x-ray diffraction (XRD) [4,5], x-ray absorption spectroscopy (XAS) [1,10], and Raman spectroscopy measurements [4,11,12] have been carried out to determine the behavior of halogens under pressure. In fact, experimental studies have become especially important, as DFT calculations face challenges in application to halogen systems [13,14].

There are experimental observations suggesting similar phase transitions in chlorine, bromine, and iodine, but at different pressures (Fig. 1). This is consistent with the empirical

rule of high-pressure crystal chemistry [15]: elements behave at high pressures like the elements below them in the periodic table at lower pressures. Iodine at ambient conditions is solid and has the *oC8* molecular structure (called also I₂-I; space group *Cmce*), which is preserved up to 16 GPa [16] (Fig. 1; for crystal structure see Fig. 7(a) in Appendix). Br₂ and Cl₂ solidify at ~0.5 GPa [17] and 1.15 GPa [4], respectively. These solid phases, *Cmce* Br₂-I [17] and *Cmce* Cl₂-I [4], possess the *oC8* crystal structures similar to that of I₂-I [16]. These structures are preserved up to 82 GPa [18] and 223 GPa [4], respectively. Here and following the numbering of halogen allotropes is adopted from the original papers.

Further compression modifies the intra- or intermolecular distances, which results in a series of phase transformations, as presented in Fig. 1. At first, the molecular character of the structures of allotropes of chlorine (Cl₂-I') and iodine (I₂-I') is preserved. The structure of C₂/m Cl₂-I' (*mC8*) [4] [Fig. 1, Fig. 7(b)] was suggested based on powder XRD, as well as that of C₂/m I₂-I' (*mC8*) [19]. However, the latter was not confirmed by the recent single-crystal x-ray diffraction (SCXRD) studies of iodine [16], which showed that at ~16 GPa I₂-I transforms into the orthorhombic phase *Cmc*2₁ I₂-VI (*oC8*) [16] [Fig. 1, Fig. 7(c)], so that I₂-I' [19] is not shown in Fig. 1. Hitherto, there have not been XRD data available for high-pressure bromine above 88 GPa [18], but the molecular phase, next after Br₂-I, was suggested to form above ~25 GPa based on XAS [1] measurements and DFT calculations [6]. Figure 1 shows exclusively the phases for which structural information is available from experimental XRD data.

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

<footnote>*Contact author: yuqing.yin@liu.se</footnote>

<footnote>†Contact author: Leonid.Dubrovinsky@uni-bayreuth.de</footnote>
<figure><img src="image_3.png" /><figcaption>FIG. 1. Schematic diagram presenting experimentally observed high-pressure allotropes of halogens, Cl [4], Br ([17,18] and this work, highlighted in red), and iodine [16,21–23], for which structural information was obtained from XRD data. The allotropes are designated by roman numerals (as adopted in the literature), and space groups and Pearson symbols (in brackets) are provided. The letter *i* added to the Pearson symbol (*i*-oF4) refers to incommensurately modulated structures with the space group *Fmmm* (00*γ*)s00. Phases indicated with the same color possess the same structure type. Crystal structures of all phases shown in the diagram are provided in Appendix Fig. 7.</figcaption></figure>

The pathways of crystalline chlorine and iodine from the molecular phases to the nonmolecular (atomic) ones, *Immm* Cl-II (*oI2*) and *Immm* I-II (*oI2*) [Fig. 7(f)], go through phases with incommensurately modulated structures (further called incommensurate and designated by the letter *i* in front of their Pearson symbols) [4,5,16,20,21]. First structural information for an incommensurate phase of iodine was reported in 2003 by Takemura *et al.* [5] based on powder XRD data. Later, SCXRD (see Ref. [16]) showed that within the same pressure interval there are two iodine phases with incommensurate orthorhombic *i-oF4* structures: *Fmmm* (00*γ*)s00 I₂-VII (*γ* = 0.4837 at 20.8 GPa) at 20.8–24 GPa [Fig. 7(d)] and *Fmmm* (00*γ*)s00 I-V (*γ* = 0.274 at 24 GPa) at 24–32 GPa Fig. 7(e) (I₂-VII turned to be the same as the phase called I-VI in Ref. [20]; see Ref. [16] for details). The incommensurate phase *Fmm*2(α00)0s0 Cl-V (*i-oF4*) was reported for chlorine in the pressure range 223–258 GPa from powder XRD [4]. For bromine, a modulated phase similar to I-V was suggested to form above 80 GPa [12], but the experimental structural data are absent. Theoretical calculations predicted several structures for bromine (*oF*20, *oC*24, *oF*28, and *oC*12) through the commensurate approximation of the *i-oF4* phase [7,13].

For bromine, accurate structural information at high pressures is still missing, and SCXRD data are needed to evaluate the path of its solid-state molecular dissociation. In this work, we present the results of synchrotron SCXRD experiments on solid bromine synthesized in diamond anvil cells (DACs) in the pressure range of 45(3) to 112(3) GPa after the laser heating of a solid precursor to ~2600 K.

## II. MATERIALS AND METHODS

### A. Sample preparation

Experiments were carried out in the pressure range of 45(3) to 112(3) GPa. BX90-type screw-driven DACs [24] equipped with 120-µm or 250-µm culet diamond anvils were used (see Table I for experimental details). A piece of CBr₄ (Sigma-Aldrich, > 99% purity) was loaded in one DAC for the main experiments (DAC 1). A thin (2–5 µm) NaBr plate was loaded together with a piece of CBr₄ (DAC 2) as supplementary experiments in order to test the reproducibility of the bromine’s polytypism. DAC 3 was loaded with Mg + CBr₄, which provided a pressure-volume point for Br₂-I. DAC 4 (NaI + Cl₄) was prepared to test the polytypism behavior of iodine I-V. Rhenium was used as the gasket material.

<table><caption>TABLE I. Summary of the performed high-pressure high-temperature experimental syntheses in laser-heated diamond anvil cells.</caption><thead><tr><th>DAC number</th><th>Culet diameter (µm)</th><th>Starting materials</th><th>Pressure points (GPa, ±3)</th><th>Bromine phases observed</th></tr></thead><tbody><tr><td rowspan="3">1</td><td rowspan="3">120</td><td rowspan="3">CBr<sub>4</sub></td><td>72</td><td>Br<sub>2</sub>-I</td></tr><tr><td>81</td><td>Br-II and Br-III<sub>γ</sub></td></tr><tr><td>96, 105, 112</td><td>Br-III<sub>γ</sub></td></tr><tr><td rowspan="2">2</td><td rowspan="2">120</td><td rowspan="2">NaBr+CBr<sub>4</sub><sup>a</sup></td><td>46, 70, 73</td><td>Br<sub>2</sub>-I</td></tr><tr><td>100</td><td>Br-III<sub>γ</sub></td></tr><tr><td>3</td><td>250</td><td>Mg+CBr<sub>4</sub><sup>a</sup></td><td>45</td><td>Br<sub>2</sub>-I</td></tr><tr><td>DAC number</td><td>Culet diameter (µm)</td><td>Starting materials</td><td>Pressure points (GPa, ±0.5)</td><td>Iodine phases observed</td></tr><tr><td>4</td><td>250</td><td>NaI+Cl<sub>4</sub><sup>a</sup></td><td>25.1</td><td>I-V</td></tr></tbody></table>

<footnote>aThese reagents were put into the DACs in excess.</footnote>
Carbon tetrabromide (CBr₄) was used as a source of bromine because it decomposes at pressures over 40 GPa under heating and releases bromine [25–27]. Raman spectra measured before and after laser heating (Fig. 8) give evidence of full decomposition of CBr₄, as after laser heating there are no features characteristic of C-Br vibrations. As far as in all experiments in DACs carbon from diamond anvils is a part of the system, for it can diffuse during laser heating [28]; the use of CBr₄ does not introduce any additional elements into the pressure chamber. At the same time, this precursor is much easier to load into a DAC than pure bromine.

The samples were first compressed to the desired pressures, which were measured *in situ* using the first-order Raman mode of the stressed diamond anvils [29] up to 81 GPa. At pressures above 81 GPa, the Raman mode from the synthesized diamonds inside the DAC [30] (from the decomposition of CBr₄) starts to coincide with the Raman mode of the stressed diamond anvils, resulting in the insufficient quality of the Raman signal. Thus, the *in situ* pressure was measured according to the equation of state of rhenium [31] above 81 GPa. Double-sided laser heating of the sample at each pressure point (up to ~2600 K in all cases), using CBr₄ as the laser light absorber, was performed at our home laboratory at the Bayerisches Geoinstitut [32] in order to release stresses in the DAC, thus improving the XRD data quality [33]. SCXRD measurements were then made on temperature-quenched samples. The information about high-pressure high-temperature syntheses performed in this work in laser-heated diamond anvil cells is summarized in Table I.

## B. X-ray diffraction

Synchrotron x-ray diffraction measurements of the compressed samples were performed at ID11 ($\lambda$ = 0.2846 Å, beam size ~ 0.75×0.75 µm²), ID15b ($\lambda$ = 0.4100 Å, beam size ~ 1.5×1.5 µm²), and ID27 ($\lambda$ = 0.3738 Å, beam size ~ 1.5×1.5 µm²) of the EBS-ESRF and the P02.2 beamline ($\lambda$ = 0.2910 Å, beam size ~ 2.0×2.0 µm²) of PETRA III. In order to determine the sample position for single-crystal x-ray diffraction data acquisition, a full x-ray diffraction mapping of the pressure chamber was performed. The sample positions displaying the greatest number of single-crystal reflections belonging to the phases of interest were chosen, and step scans of 0.5° from -36° to +36° $\omega$ were performed. The CrysAlisPro software [34] was utilized for the single-crystal data analysis. To calibrate the instrumental model in the CrysAlisPro software, i.e., the sample-to-detector distance, detector's origin, offsets of the goniometer angles, and rotation of both the x-ray beam and detector around the instrument axis, we used a single crystal of orthostatite [(Mg₁.93Fe₀.06)(Si₁.93Al₀.06)O₆], Pbca space group, $a$ = 8.8117(2) Å, $b$ = 5.1832(10) Å, and $c$ = 18.2391(3) Å. At each pressure point high-quality diffraction spots (peaks are intense and relatively sharp) were detected. The obtained data were analyzed using our methodology for processing SCXRD from microcrystalline multiphase samples [35–37] with the implementation of the DAFi program [38]. The crystal structures were then solved and refined using the OLEX2 [39] and JANA2006 software [40]. The crystal structure visualization was made with the VESTA software [41]. The equation of

state was obtained by fitting the pressure-volume dependence data using the EoSFit7-GUI [42]. The crystallographic information of the bromine allotropes synthesized in this work is provided in Tables III–X.

## C. Raman spectroscopy

Raman spectroscopy measurements (Fig. 8) were performed with a LabRam spectrometer equipped with a 50× Olympus objective. Sample excitation was accomplished using a continuous He-Ne laser (632.8 nm line) with a focused laser spot of about 2 µm in diameter. The Stokes Raman signal was collected in a backscattering geometry by a CCD coupled to an 1800 l/mm grating, allowing a spectral resolution of approximately 2 cm⁻¹.

# III. RESULTS AND DISCUSSION

In the main experiment with CBr₄ as a single precursor, SCXRD data were collected at 72(3), 81(3), 96(3), 105(3), and 112(3) GPa. Solid bromine Cmce Br₂-I was found to preserve its *o*C8 molecular structure at 72(3) GPa and room temperature (see Table III for crystallographic data). The analysis of SCXRD did not show any sign of coexistence of other molecular phases with Cmce Br₂-I (Fig. 9), unlike reports for Cl₂-I' [4] and I₂-I' [19].

Laser heating of the sample at 81(3) GPa led to the formation of two different kinds of crystalline domains: some with lattice parameters similar to those of Cmce Br₂-I (*o*C8), and others with different lattice parameters [slightly smaller *a* (~4.8 vs ~4.6 Å), slightly larger *b* (~3.3 vs ~3.5 Å), and essentially different *c* (~7.5 vs ~14.3, 24.8, or 53.1 Å)]. The analysis of the diffraction data from the first kind of domain revealed clear splitting of some diffraction spots detected on the reconstructed reciprocal space images (Fig. 10). The diffraction pattern could be described by an orthonhombic F-centered unit cell and a modulation wave vector **q** = $\gamma$**c***, where $\gamma$ slightly deviates from 0.5 (Fig. 10). While a few of the second-order satellites could be observed, the average $F^2/\sigma(F^2)$ values for these reflections were low (~81, ~58, and ~13 for the main reflections, and the first-order and second-order satellites, respectively), and only the first-order satellites were used for final refinements (a detailed comparison of the two refinements can be found in Table IV). Therefore, we accept here the structural model as the bromine phase II (Br-II) at 81(3) GPa, described by the (3+1)-dimensional superspace group Fmmm(00$\gamma$)s00 with structural parameters $a$ = 3.2767(14) Å, $b$ = 4.7924(19) Å, $c$ = 3.7618(16) Å, $\gamma$ = 0.493(3), and $A_1(x) = 0.0742(11)$ (Table IV, CIF deposited at CSD 2289479). Displacive modulations of the Br atom [$u_i(\bar{x}_4)$ for $i$ = x, y, z] are described by a truncated Fourier series, which take into account only the first-order harmonics and due to the symmetry restrictions get the following form [43]: $u_x(\bar{x}_4) = A_1(x) \sin(2\pi\bar{x}_4)$, $u_y = u_z = 0$, where $\bar{x}_4 = t + q\bar{x}$ ($t$ is the phase of the modulation).

The second type of domain at 81(3) GPa has the same structural motif as Br-II (*F*mmm(00$\gamma$)s00), but with different $\gamma$ values. Processing SCXRD data reveals the coexistence of bromine single-crystal domains with similar but distinct values of $\gamma$ (between ~0.25 and ~0.30 at 81 GPa, for ex-
<table><caption>TABLE II. Bromine allotropes synthesized at high pressures. For Br-IIIγ, only selected data are presented.</caption><thead><tr><th>Phase</th><th>Pressure (GPa, ±3)</th><th>Space group</th><th>Lattice parameters, a b c (Å)</th><th>γ</th><th>CSD number</th></tr></thead><tbody><tr><td>Br<sub>2</sub>-I</td><td>72</td><td rowspan="3">Cmce</td><td>4.867(4) 3.3083(8) 7.5901(14)</td><td>—</td><td rowspan="3">2289479</td></tr><tr><td rowspan="2">Br-II</td><td>81</td><td>3.2767(14) 4.7924(19) 3.7618(16)</td><td>0.493(3)</td></tr><tr><td>81</td><td>3.515(2) 4.667(3) 3.552(2)</td><td>0.293(4)</td></tr><tr><td rowspan="10">Br-IIIγ<sup>a</sup></td><td rowspan="10">96</td><td>3.5179(11) 4.6502(12) 3.5441(10)</td><td>0.288(2)</td><td rowspan="10">2289480</td></tr><tr><td>3.523(2) 4.636(3) 3.546(3)</td><td>0.284(3)</td></tr><tr><td>3.5163(11) 4.6360(10) 3.531(2)</td><td>0.281(2)</td></tr><tr><td>3.5222(4) 4.6348(13) 3.5321(17)</td><td>0.2786(19)</td></tr><tr><td>3.5216(18) 4.6176(15) 3.5399(10)</td><td>0.274(3)</td></tr><tr><td>3.5315(7) 4.611(2) 3.5390(5)</td><td>0.2708(12)</td></tr><tr><td>3.5339(6) 4.601(3) 3.5385(10)</td><td>0.265(2)</td></tr><tr><td>3.5297(7) 4.582(4) 3.5529(17)</td><td>0.2577(18)</td></tr><tr><td>3.5234(8) 4.5340(9) 3.5324(7)</td><td>0.2266(9)</td></tr><tr><td rowspan="10">Fmmm(00γ)s00</td><td>3.528(4) 4.530(3) 3.536(3)</td><td>0.2232(17)</td><td rowspan="10">2289481</td></tr><tr><td>3.527(2) 4.5222(13) 3.5183(19)</td><td>0.2157(18)</td></tr><tr><td>3.5084(9) 4.5251(15) 3.5133(8)</td><td>0.2087(13)</td></tr><tr><td>3.5181(12) 4.5133(8) 3.5054(11)</td><td>0.2047(13)</td></tr><tr><td>3.5055(14) 4.497(2) 3.5300(13)</td><td>0.2019(13)</td></tr><tr><td>3.5164(5) 4.4936(5) 3.5002(14)</td><td>0.1962(6)</td></tr><tr><td>3.509(2) 4.477(2) 3.5260(19)</td><td>0.1913(15)</td></tr><tr><td>3.5153(12) 4.474(2) 3.527(2)</td><td>0.1847(5)</td></tr><tr><td>3.5105(19) 4.5352(14) 3.5306(7)</td><td>0.2252(17)</td></tr><tr><td rowspan="2">100</td><td>3.5152(11) 4.5371(17) 3.5202(17)</td><td>0.223(2)</td><td rowspan="2">2289486</td></tr><tr><td>3.5174(9) 4.5221(9) 3.5287(11)</td><td>0.217(2)</td></tr><tr><td rowspan="10">105</td><td>3.5195(9) 4.6201(9) 3.5372(17)</td><td>0.2745(12)</td><td rowspan="10">2289487</td></tr><tr><td>3.521(3) 4.6182(17) 3.545(3)</td><td>0.269(2)</td></tr><tr><td>3.528(2) 4.616(2) 3.534(6)</td><td>0.266(2)</td></tr><tr><td>3.5141(19) 4.5991(13) 3.5351(18)</td><td>0.261(3)</td></tr><tr><td>3.5182(10) 4.592(2) 3.543(3)</td><td>0.256(2)</td></tr><tr><td>3.5164(10) 4.5850(15) 3.5239(14)</td><td>0.2517(16)</td></tr><tr><td>3.5177(9) 4.570(2) 3.5279(10)</td><td>0.2435(18)</td></tr><tr><td>3.525(2) 4.5616(8) 3.5335(8)</td><td>0.239(2)</td></tr><tr><td>3.5285(9) 4.5391(11) 3.516(2)</td><td>0.2254(15)</td></tr><tr><td rowspan="6">112</td><td>3.5244(13) 4.5298(18) 3.5265(13)</td><td>0.2192(17)</td><td rowspan="6">2289490</td></tr><tr><td>3.5260(13) 4.521(2) 3.515(4)</td><td>0.2150(19)</td></tr><tr><td>3.5137(8) 4.5896(10) 3.520(5)</td><td>0.2503(12)</td></tr><tr><td>3.507(3) 4.5729(13) 3.516(5)</td><td>0.245(2)</td></tr><tr><td>3.5249(14) 4.554(3) 3.5291(6)</td><td>0.2370(12)</td></tr><tr><td>3.5260(9) 4.5356(10) 3.5339(7)</td><td>0.2236(16)</td></tr><tr><td></td><td>3.5278(6) 4.5076(7) 3.539(3)</td><td>0.2038(17)</td><td>2289493</td></tr></tbody></table>

ample), which we call Br-IIIγ and consider as polytypes (see the discussion below on the use of the term “polytypes”). Polyp typism of the incommensurate structures is present across a wide pressure range [from 81(3) to 112(3) GPa] and reflects how the bromine structure transforms during molecular dissociation. Some polytypes of Br-IIIγ were selected as examples and deposited in the Cambridge Crystallographic Data Center (CCDC) under the identifiers CSD 2289480 through CSD 2289493. Their crystallographic data are provided in Tables V–IX (grouped by pressure), while Table II shows all bromine allotropes synthesized in the pressure range of 72(3) to 112(3) GPa in this work. Note that, as in the SCXRD studies of iodine [16], all satellite reflections of Br-IIIγ up to second order can be well described by an *oF*4 basic cell with only one modulation vector (Fig. 11, Tables V–IX).

Crystal chemistry and chemical bonding characteristics of polytypes Br-II and Br-IIIγ are different. In incommensurate

Br-II, the modulation of the Br-Br distance results in the structure that can be presented as a mixture of Br<sub>2</sub> molecules (at 81 GPa, taking Br<sub>2</sub>-I as a reference [Fig. 2(a)]), intramolecular distances are shorter than ~2.35 Å, and interatomic are longer than ~2.45 Å) and Br<sub>3</sub> zigzag chains (all distances between atoms in the chain are shorter than ~2.4 Å) [Fig. 2(b)]. The Br-IIIγ polytypes do not contain Br<sub>2</sub> molecules (shortest Br-Br distances are ~2.38 Å), but consist of nearly linear Br<sub>3</sub>, Br<sub>4</sub>, and Br<sub>5</sub> atomic chains (angles between atoms in the groups vary from ~177.5° to 180°), and V-shaped (Br<sub>7</sub>) atomic chains [Fig. 2(c)]. The structure of Br-II can be considered intermediate between the structures of Br<sub>2</sub>-I and Br-IIIγ. Unlike for iodine [16], we do not see any evidence of additional molecular phases (like the intermediate I<sub>2</sub>-VI, space group Cmc<sub>2</sub>).

At a given pressure, there are obvious variations of the γ component of the modulation wavevector **q** = γ**c**\* among
<figure><img src="image_4.png" /><figcaption>FIG. 2. Fragments of crystal structures of the bromine allotropes synthesized in this work. (a) Br₂-I (oC8) at 72(3) GPa projected to the *bc* plane; the solid red and dashed black lines represent the intramolecular and intermolecular distances (in Å), respectively. (b) Br-II (Fmmm(00γ)s00; γ = 0.493(3)) at 81(3) GPa projected to the *ac* plane; the bottom figures show the arrangement of bromine atoms in Br-II, which contains both Br₂ molecules and Br₃ zigzag chains. (c) Two examples of the polytypes Br-IIIγ existing in the pressure range of 81(3) to 112(3) GPa: Br-III0.288 at 81(3) GPa and Br-III0.227 at 96(3) GPa (see Table II) projected to the *ac* plane. Some structural elements (Br₃, Br₄, Br₅, and V-shaped (Br₇) atomic chains) are also presented. Br atoms are shown as grey balls. Structure presentations of the incommensurate phases in (b) and (c) are approximate (cut from 5×5×20 cells of the basic oF4 lattice). For all structures, only one plane at y = 0 (x = 0 for Br₂-I in (a)) is presented for simplicity.</figcaption></figure>

different crystallites of Br-IIIγ (Table II). As the difference in γ is small, at first glance it may seem that we are dealing with the same crystalline form of bromine. However, the refined values of γ differ beyond the experimental uncertainty. The analysis of powder XRD data (Fig. 3), collected at the ESRF beamline ID11 with submicron resolution, shows that within a tiny area (0.75×0.75 µm²) coexist numerous domains of Br-IIIγ with distinct values of γ. For example, at one spot the peaks belonging to Br-IIIγ with γ = 0.2266(9), 0.1962(6), and 0.1847(5) appear simultaneously (Fig. 3). There is no evidence of any special spatial distribution of Br-IIIγ crystallites with different γ (Fig. 3 inset), so we suggest that the domains of Br-IIIγ form simultaneously.

Structures of Br-IIIγ with different values of the γ compo-
nent of the modulation vector can be presented as stacking
of distorted close-packed layers of bromine atoms in the
ab plane along the c direction. All layers are identical, as
all bromine atoms occupy a single crystallographic position
(Fig. 12), and the difference in their stacking is defined by
the value of γ. According to Ref. [44], "an element or com-
pound is polytypic if it occurs in several different structural
modifications, each of which may be regarded as built up
by stacking layers of (nearly) identical structure and compo-
sition, and if the modifications differ only in their stacking

sequence.” In this sense, one can consider Br-IIIγ compound
with the varying value of γ as a series of incommensurate
polytypes.

There are striking differences in incommensurate phases
Br-II and Br-IIIγ (Fig. 4): while the values of γ determined
for all domains of Br-II [as for 81(3) GPa] are the same within
the uncertainty, for Br-IIIγ the values of γ vary within ~ 20%
(the uncertainty for γ is only ~1%) at any given pressure
point (Fig. 4). The analysis of XRD data from all domains of
reasonably good quality (giving R<sub>int</sub> < 10%) does not reveal
any remarkable distribution of the number of crystallites with
different values of γ [Fig. 4(b)].

Upon compression, the volume of Br₂-I decreases monotonically between 45(3) and 73(3) GPa (Fig. 5). The experimental data are described by the second-order Birch-Murnaghan equation of state (EOS) with the bulk modulus K₀ = 22(3) GPa, and the volume at ambient pressure, V₀ = 32.10(15) Å³/atom. Extrapolation of the volume of Br₂-I to 81 GPa suggests that the transition from Br₂-I to Br-II does not associate with any significant change in volume (Fig. 5). All analyzed domains of Br-IIIγ at 81(3) GPa show lower atomic volumes than that of Br-II at the same pressure (Fig. 5). The formation of Br-IIIγ indicates that the pressure-induced electron delocalization among the adjacent molecules occurred.
<figure><img src="image_5.png" /></figure>

FIG. 3. Powder XRD pattern taken from sample in DAC 1 at 96(3) GPa after laser heating at ~2600 K. X-ray wavelength is $\lambda$ = 0.2846 Å, beam size is 0.75×0.75 µm². Three bromine polytypes (Br-III$\gamma$, $\gamma$ ~ 0.227, ~ 0.196, and ~ 0.185) were identified in one spot using SCXRD data; the ticks of different colors correspond to calculated powder XRD patterns of these polytypes (red, Br-III0.227; blue, Br-III0.196; magenta, Br-III0.185); two rows of the same color indicate the positions of the main (upper ticks) and satellite (lower ticks) reflections of the same polytype. The inset is an XRD map of the whole sample chamber, which is identified on the reflections with indices (1 1 1 -2) and (1 1 1 -1) for Br-III0.227, (1 1 1 2) and (1 1 3 -2) for Br-III0.196, and (1 1 1 2) and (0 2 0 2) for Br-III0.185. It indicates a mixed distribution of the three polytypes within the sample.

We also noticed that the variation (~ 1.6%, 2.7%, 0.8%, 2.8%, and 1.9% at 81, 96, 100, 105, and 112 GPa, respectively) in atomic volumes of different domains of Br-III$\gamma$ is significantly larger than that for Br-II or Br$_2$-I domains at any pressure point (below 0.6%). Moreover, for Br-III$\gamma$ between 81(3) and 112(3) GPa there is no obvious trend in the volume change with pressure (Fig. 5). This observation suggests that incommensurate polytypes of Br-III$\gamma$ with different $\gamma$ have unique EOSes. The series of Br-III$\gamma$ polytypes that emerged during molecular dissociation can be seen as a signal of a kind of “higher-order phase transitions.” This complex transition process agrees with the pathways from molecular to nonmolecular state of solids towards their pressure-induced ionization—finding delicate balances between electron delocalization (governing bonding) and ionization (governing packing) [45].

In the whole studied pressure range, for Br-III$\gamma$ there is an obvious linear correction between the volume and the value of $\gamma$ [Fig. 4(a)]. Considering that the changes in the volume of Br-III$\gamma$ come almost solely due to the changes in the *b* parameter [Fig. 13(a)], one can notice the decrease of *b* with the decrease of $\gamma$ [Fig. 13(b)]. Structurally, for Br-III$\gamma$ these mean that at a given pressure the decrease in the shortest distance within the chains (in the *ac* plane; D3) of bromine atoms is associated with an increase of the distances between layers of chains (*b* direction; D1 and D2) [Figs. 6(a) and 6(b)]; see Fig. 6(c) for illustration of D1, D2, and D3). Remarkably, at the given pressure points, average distances of bromine atoms

<figure><img src="image_6.png" /></figure>

FIG. 4. Variations of the $\gamma$ component of the modulation vector in the structures of Br-II and Br-III$\gamma$. (a) The relationship between the values of $\gamma$ and the volume per atom; the dotted black line is a guide for the eye. (b) The frequency of the appearance of crystallites (n) with a particular value of $\gamma$. The total number of analyzed crystallites at 81(3), 96(3), 100(3), 105(3), and 112(3) GPa was 27, 16, 9, 20, and 21 respectively. The data related to these pressures are shown in red, blue, magenta, black, and orange, respectively. Only single-crystal domains with sufficient quality ($R_{int}$ < 10% and $R_1$ < 20%) were counted.

within the first coordination sphere remain almost the same for a wide range of $\gamma$ (or volume) [Fig. 6(b)]. This observation reminds of the situation with polytypes based on close-packed structures (in metals, for example)—the interatomic distances are the same in the first coordination sphere, and only change in the second one.

The Br-III$\gamma$ phase is structurally similar to that of the recently reported iodine I-V [5,16]. Like in Br-III$\gamma$, in the pressure range of the existence of the I-V phase (~24 to ~30 GPa) $\gamma$ decreases with decreasing volume (Fig. 14) [5,16]. We have performed our own experiment on iodine, produced by the decomposition of $Cl_4$ upon laser heating at 25.1(5) GPa. Structural data (Table X) closely reproduce the results of Bykova *et al.* [16] for I-V at similar pressure with similar volumes and the ratio of lattice parameters; however, our analysis of numerous domains revealed a significant variation of $\gamma$—from 0.283(2) to 0.300(2)—at a single pressure
<figure><img src="image_7.png" /><figcaption>FIG. 5. Pressure dependence of the volume per atom of bromine at ambient temperature. The dashed gray line represents the fit of our experimental points for Br₂-I at 45, 46, 70, 72, and 73 GPa (see Table I) using the second-order Birch-Murnaghan equation of state (K₀ = 22(3) GPa, V₀ = 32.10(15) Å³/atom) (the volume per atom for Br₂-I at 1 atm from Ref. [46] is also included in the fit). The vertical line indicates the apparent pressure boundary between molecular and nonmolecular allotropes. The data are obtained from all domains which could be analyzed (Rint < 10%). The uncertainties in the volume are smaller than the symbols' sizes. The uncertainty in pressure is 3 GPa.</figcaption></figure>

point. The relation between the volume per atom and $\gamma$ for iodine I-V is similar to that observed for Br-III$\gamma$ (Fig. 14). Thus, there is a clear indication that incommensurate polytypes are present in the I-V phase.

#### IV. CONCLUSION

In summary, we found that bromine preserves its molecular *oC8* structure (Br₂-I) at 72(3) GPa; no sign of other molecular phases was observed. Above 81(3) GPa, we found that bromine forms an incommensurately modulated structure *Fmmm*(00$\gamma$)$_{s00}$ [Br-II; $\gamma$ = 0.493(3)] and, depending on pressure, several incommensurate polytypes of Br-III$\gamma$ similar to Br-II, but with different values of the $\gamma$ components (ranging in the interval of ~0.18 to ~0.3). For I-V at 25.1(3) GPa, $\gamma$ varies from ~0.28 to ~0.30. Thus, Br-III$\gamma$ and I-V are examples of polytypes with incommensurately modulated sequence of layers. These discoveries offer a novel understanding of how solids transition from a molecular to an atomic state under pressure. The diversity of these polytypes and their coexistence at a given pressure, as well as indications that similar behavior may be characteristic of other halogens, suggest that polytypism of incommensurately modulated structures is a common phenomenon for simple halogen systems undergoing transformations from molecular (consisting of strongly bonded units) to nonmolecular crystal states.

#### ACKNOWLEDGMENTS

The authors acknowledge the Deutsches Elektronen-Synchrotron (DESY, PETRA III) and the European Synchrotron Radiation Facility (ESRF) for the provision of

<figure><img src="image_8.png" /><figcaption>FIG. 6. Variation of interatomic distances in Br-II and Br-III$\gamma$ as a function of the $\gamma$ components of the modulation vector. [(a) and (b)] Relations between the Br-Br interatomic distances (D1, D2, and D3) and $\gamma$ at different pressures; (c) notations of D1, D2, and D3 in the *i-oF4* unit cell of bromine. D1 and D2 are the Br-Br distances between the adjacent *ac* planes, and D3 is the distance within the *ac* plane. The four nearest Br-Br distances (D3) in incommensurate phases are continuously distributed between the maximum (Max) and minimum (Min), and their average values are plotted as Avg in (b)</figcaption></figure>
beamtime at the P02.2 and ID11, ID15b, and ID27 beamlines, respectively. Y.Y. acknowledges the financial support provided by the China Scholarship Council (CSC) during her visit to the University of Bayreuth. N.D. and L.D. thank the Deutsche Forschungsgemeinschaft (DFG; projects DU 945-15-1, DU 393-9/2, DU 393-13/1) for financial support. N.D. also thanks the Swedish Government Strategic Research Area in Materials Science on Functional

Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). M.B. acknowledges the support of Deutsche Forschungsgemeinschaft (DFG Emmy-Noether project BY112/2-1). D.L. thanks the UKRI Future Leaders Fellowship (MR/V025724/1) for financial support.

APPENDIX: FIGURES AND TABLES

<figure><img src="image_9.png" /><figcaption>Incommensurately modulated structures of Cl and I</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Non-molecular structures</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIG. 7. Crystal structures of allotropes of I, Br, and Cl (see also the schematic diagram in Fig. 1) [4,16–19,21–23].</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>FIG. 8. Raman spectra taken from the sample in DAC 1 at different pressures before laser heating (LH), and at 72 GPa and room temperature after LH. After LH there are no features characteristic of C-Br vibrations. The broadened bulge (~240–365 cm⁻¹) at 72 GPa after LH agrees with the A<sub>g</sub> and two B<sub>3g</sub> modes of Br<sub>2</sub>-I [12].</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIG. 10. Reconstructed reciprocal lattice planes of Br-II at 81(3) GPa. Red dashed circles highlight the splitting of the reflections. The details of the structural refinement are presented in Table IV.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>FIG. 9. XRD pattern of the sample in DAC 1 at 72(3) GPa after its laser heating at ~2600 K. Black line is the integrated two-dimensional XRD pattern (in inset) of the sample. Red ticks correspond to the calculated powder XRD pattern of the *Cmce* Br<sub>2</sub>-I (*oC8*) phase (λ = 0.291 Å), whose structure was determined from SCXRD data. All of the diffraction peaks can be assigned to *Cmce* Br<sub>2</sub>-I, thus confirming the absence of any other phases in the sample.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>FIG. 11. Reconstructed precession image of the polytype Br-IIIγ (here γ = 0.1962(6), 96(3) GPa) in the *Fmmm* setting. Satellite reflections are indexed in terms of the modulation vector.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>FIG. 12. A perspective view of the structure of Br-IIIγ, high-lighting the layers of Br atoms in the *ab* plane stacked in the *c* direction. Br atoms are shown as grey balls.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>FIG. 14. The relationship between the values of γ and the volume per atom in the structure of iodine I-V; the dotted black line is a guide for the eye. The results of this work (shown in magenta) are compared to previously reported data (blue and red) from Ref. [16].</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>FIG. 13. Relations between lattice parameters and (a) volume per atom and (b) the γ component for Br-II (solid symbols) and Br-IIIγ (open symbols). Data at 81(3), 96(3), 100(3), 105(3), and 112(3) GPa are shown in red, blue, magenta, black, and orange, respectively. For the γ axis, the uncertainty is smaller than the symbol size.</figcaption></figure>
<table><caption>TABLE III. Crystal structure, data collection, and refinement details of Br₂-I (αC8) at 72(3) GPa.</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td colspan="2"><strong>Crystal data</strong></td></tr><tr><td>Chemical formula</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Cmce</td></tr><tr><td>Temperature (K)</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>72(3)</td></tr><tr><td>a, b, c (Å)</td><td>4.867(4), 3.3083(8), 7.5901(14)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>122.22 (11)</td></tr><tr><td>Z</td><td>8</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.291 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>5.85</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="2"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>LH@P02.2</td></tr><tr><td>No. of measured, independent, and observed [I > 2σ(I)]</td><td></td></tr><tr><td>reflections</td><td>309, 128, 126</td></tr><tr><td>R<sub>int</sub></td><td>0.009</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>1.015</td></tr><tr><td colspan="2"><strong>Refinement</strong></td></tr><tr><td>R[F<sup>2</sup> > 2σ(F<sup>2</sup>)], wR(F<sup>2</sup>), S</td><td>0.033, 0.079, 1.41</td></tr><tr><td>No. of reflections</td><td>128</td></tr><tr><td>No. of parameters</td><td>8</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>1.48, -1.73</td></tr><tr><td colspan="2"><strong>Crystal Structure</strong></td></tr><tr><td>Wyckoff site</td><td>Br1: 8f</td></tr><tr><td>Fractional atomic coordinates (x y z)</td><td>Br1: 1/2 0.3050(2) 0.62284(7)</td></tr><tr><td>U<sub>iso</sub> (Å<sup>2</sup>)</td><td>Br1: 0.0054(3)</td></tr></tbody></table>
<table><caption>TABLE IV. Crystal structure, data collection, and refinement details of incommensurate Br-II at 81(3) GPa. Left column shows the refinement using only the first-order satellite reflections. Right column shows that using the reflections of both the first and second order.</caption><thead><tr><th></th><th>Br</th><th>Br</th></tr></thead><tbody><tr><td>Chemical formula</td><td>Br</td><td>Br</td></tr><tr><td>M<sub>t</sub></td><td>79.91</td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>81(3)</td><td>81(3)</td></tr><tr><td>Wave vectors</td><td>q = 0.493(3)c*</td><td>q = 0.494(3)c*</td></tr><tr><td>a, b, c (Å)</td><td>3.2767(14), 4.7924(19),<br>3.7618(16)</td><td>3.272(2), 4.789(3), 3.759(3)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>59.07(4)</td><td>58.90(7)</td></tr><tr><td>Z</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.41 Å</td><td>Synchrotron, λ = 0.41 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>15.71</td><td>15.76</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="3"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>ESRF ID15b, EIGER2 × 9M<br>CdTe detector</td><td>ESRF ID15b, EIGER2 × 9M<br>CdTe detector</td></tr><tr><td>No. of main reflections: measured, independent<br>and observed [I > 3σ(I)]</td><td>33, 20, 19</td><td>29, 20, 19</td></tr><tr><td>No. of first-order satellite reflections: measured,<br>independent and observed [I > 3σ(I)]</td><td>51, 36, 36</td><td>46, 33, 33</td></tr><tr><td>No. of second-order satellite reflections:<br>measured, independent and observed [I > 3σ(I)]</td><td></td><td>51, 33, 20</td></tr><tr><td>R<sub>int</sub></td><td>0.010</td><td>0.028</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>0.879</td><td>0.880</td></tr><tr><td colspan="3"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.060 / 0.085</td><td>0.105 / 0.145</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.051 / 0.069</td><td>0.072 / 0.093</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.071 / 0.093</td><td>0.140 / 0.167</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td>—</td><td>0.150 / 0.159</td></tr><tr><td>No. of reflections</td><td>56</td><td>86</td></tr><tr><td>No. of parameters</td><td>5</td><td>6</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>4.33, -4.15</td><td>5.95, -9.82</td></tr><tr><td colspan="3"><strong>Crystal Structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>0.0742(11)</td><td>-0.0684(12)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>—</td><td>-0.0032(10)</td></tr></tbody></table>
<table><caption>TABLE V. Crystal structure, data collection, and refinement details of incommensurate Br-IIIγ at 81(3) GPa.</caption><thead><tr><th></th><th>Br</th><th>Br</th><th>Br</th></tr></thead><tbody><tr><td>Chemical formula</td><td>Br</td><td>Br</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td><td>79.91</td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>81(3)</td><td>81(3)</td><td>81(3)</td></tr><tr><td>Wave vectors</td><td>q = 0.288(2)c*</td><td>q = 0.2708(12)c*</td><td>q = 0.2577(18)c*</td></tr><tr><td>a, b, c (Å)</td><td>3.5179(11), 4.6502(12), 3.5441(10)</td><td>3.5315(7), 4.611(2), 3.5390(5)</td><td>3.5297(7), 4.582(4), 3.5529(17)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>57.98(3)</td><td>57.63(3)</td><td>57.46(6)</td></tr><tr><td>Z</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.41 Å</td><td>Synchrotron, λ = 0.41 Å</td><td>Synchrotron, λ = 0.41 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>16.01</td><td>16.10</td><td>16.15</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="4"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>ESRF ID15b, EIGER2 × 9M CdTe detector</td><td>ESRF ID15b, EIGER2 × 9M CdTe detector</td><td>ESRF ID15b, EIGER2 × 9M CdTe detector</td></tr><tr><td>No. of main reflections: measured, independent and observed [I > 3σ(I)]</td><td>41, 26, 26</td><td>37, 22, 22</td><td>34, 20, 20</td></tr><tr><td>No. of first-order satellite reflections: measured, independent and observed [I > 3σ(I)]</td><td>58, 36, 36</td><td>71, 39, 39</td><td>60, 35, 35</td></tr><tr><td>No. of second-order satellite reflections: measured, independent and observed [I > 3σ(I)]</td><td>68, 39, 13</td><td>68, 41, 30</td><td>73, 40, 19</td></tr><tr><td>R<sub>int</sub></td><td>0.009</td><td>0.011</td><td>0.025</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>0.864</td><td>0.864</td><td>0.851</td></tr><tr><td colspan="4"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.049 / 0.065</td><td>0.078 / 0.097</td><td>0.075 / 0.084</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.048 / 0.069</td><td>0.071 / 0.079</td><td>0.071 / 0.082</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.044 / 0.056</td><td>0.081 / 0.103</td><td>0.060 / 0.077</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td>0.142 / 0.156</td><td>0.094 / 0.108</td><td>0.165 / 0.165</td></tr><tr><td>No. of reflections</td><td>101</td><td>102</td><td>95</td></tr><tr><td>No. of parameters</td><td>6</td><td>6</td><td>6</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>2.70, -2.65</td><td>2.86, -3.18</td><td>4.12, -3.38</td></tr><tr><td colspan="4"><strong>Crystal structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>0.0569(6)</td><td>-0.0607(6)</td><td>-0.0631(8)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>-0.0002(9)</td><td>0.0004(6)</td><td>-0.0022(16)</td></tr></tbody></table>
<table><caption>TABLE VI. Crystal structure, data collection, and refinement details of incommensurate Br-IIIγ at 96(3) GPa.</caption><thead><tr><th></th><th>Br</th><th>Br</th><th>Br</th></tr></thead><tbody><tr><td>Chemical formula</td><td>Br</td><td>Br</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td><td>79.91</td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>96(3)</td><td>96(3)</td><td>96(3)</td></tr><tr><td>Wave vectors<br>a, b, c (Å)</td><td>q = 0.2266(9)c*<br>3.5234(8), 4.5340(9),<br>3.5324(7)</td><td>q = 0.1962(6)c*<br>3.5164(5), 4.4936(5),<br>3.5002(14)</td><td>q = 0.1847(5)c*<br>3.5153(12), 4.474(2),<br>3.527(2)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>56.43(2)</td><td>55.31(2)</td><td>55.47(4)</td></tr><tr><td>Z</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron,<br>λ = 0.2846 Å</td><td>Synchrotron,<br>λ = 0.2846 Å</td><td>Synchrotron,<br>λ = 0.2846 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>5.97</td><td>6.09</td><td>6.07</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="4"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>ESRF ID11, Dectris<br>Eiger2 X CdTe 4M<br>92, 52, 51</td><td>ESRF ID11, Dectris<br>Eiger2 X CdTe 4M<br>89, 33, 25</td><td>ESRF ID11, Dectris<br>Eiger2 X CdTe 4M<br>97, 46, 39</td></tr><tr><td>No. of main reflections: measured, independent and observed [I > 3σ(I)]</td><td>166, 83, 83</td><td>171, 50, 50</td><td>178, 79, 78</td></tr><tr><td>No. of first-order satellite reflections: measured, independent and observed [I > 3σ(I)]</td><td>179, 96, 45</td><td>182, 55, 43</td><td>186, 87, 61</td></tr><tr><td>No. of second-order satellite reflections: measured, independent and observed [I > 3σ(I)]</td><td>179, 96, 45</td><td>182, 55, 43</td><td>186, 87, 61</td></tr><tr><td>R<sub>int</sub></td><td>0.008</td><td>0.028</td><td>0.016</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>1.139</td><td>1.136</td><td>1.124</td></tr><tr><td colspan="4"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.039 / 0.045</td><td>0.032 / 0.035</td><td>0.038 / 0.044</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.033 / 0.042</td><td>0.023 / 0.029</td><td>0.033 / 0.047</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.033 / 0.038</td><td>0.028 / 0.031</td><td>0.036 / 0.039</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td>0.109 / 0.124</td><td>0.059 / 0.063</td><td>0.054 / 0.052</td></tr><tr><td>No. of reflections</td><td>231</td><td>138</td><td>212</td></tr><tr><td>No. of parameters</td><td>6</td><td>6</td><td>6</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>4.89, -2.26</td><td>2.60, -3.29</td><td>3.29, -3.24</td></tr><tr><td colspan="4"><strong>Crystal structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>0.0625(3)</td><td>0.0652(2)</td><td>0.0697(2)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>-0.0002(3)</td><td>0.0005(7)</td><td>0.0000(4)</td></tr></tbody></table>
<table><caption>TABLE VII. Crystal structure, data collection, and refinement details of incommensurate Br-IIIγ at 100(3) GPa.</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td colspan="2"><strong>Crystal data</strong></td></tr><tr><td>Chemical formula</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>100(3)</td></tr><tr><td>Wave vectors</td><td>q = 0.223(2)c*</td></tr><tr><td>a, b, c (Å)</td><td>3.5152(11), 4.5371(17), 3.5202(17)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>56.14(4)</td></tr><tr><td>Z</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.3738 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>12.82</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="2"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>ESRF ID27, EIGER2 X CdTe 9M detector 35, 18, 18</td></tr><tr><td>No. of main reflections: measured, independent and observed [I > 3σ(I)]</td><td></td></tr><tr><td>No. of first-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>68, 38, 36</td></tr><tr><td>No. of second-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>—</td></tr><tr><td>R<sub>int</sub></td><td>0.022</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>0.889</td></tr><tr><td colspan="2"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.061 / 0.072</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.053 / 0.072</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.068 / 0.072</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td></td></tr><tr><td>No. of reflections</td><td>56</td></tr><tr><td>No. of parameters</td><td>5</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>3.51, -3.60</td></tr><tr><td colspan="2"><strong>Crystal structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>-0.0629(10)</td></tr><tr><td>A<sub>2</sub>(y)</td><td></td></tr></tbody></table>
<table><caption>TABLE VIII. Crystal structure, data collection, and refinement details of incommensurate Br-IIIγ at 105(3) GPa.</caption><thead><tr><th></th><th>Br</th><th>Br</th><th>Br</th><th>Br</th></tr></thead><tbody><tr><td colspan="5"><strong>Crystal data</strong></td></tr><tr><td>Chemical formula</td><td>Br</td><td>Br</td><td>Br</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td><td>79.91</td><td>79.91</td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>105(3)</td><td>105(3)</td><td>105(3)</td><td>105(3)</td></tr><tr><td>Wave vectors</td><td>q = 0.2745(12)c*</td><td>q = 0.266(2)c*</td><td>q = 0.2517(16)c*</td><td>q = 0.2192(17)c*</td></tr><tr><td>a, b, c (Å)</td><td>3.5195(9), 4.6201(9), 3.5372(17)</td><td>3.528(2), 4.616(2), 3.534(6)</td><td>3.5164(10), 4.5850(15), 3.5239(14)</td><td>3.5244(13), 4.5298(18), 3.5265(13)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>57.52(3)</td><td>57.55(11)</td><td>56.81(3)</td><td>56.30(4)</td></tr><tr><td>Z</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.291 Å</td><td>Synchrotron, λ = 0.291 Å</td><td>Synchrotron, λ = 0.291 Å</td><td>Synchrotron, λ = 0.291 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>6.18</td><td>6.18</td><td>6.26</td><td>6.32</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="5"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>LH@P02.2</td><td>LH@P02.2</td><td>LH@P02.2</td><td>LH@P02.2</td></tr><tr><td>No. of main reflections: measured, independent, and observed [I > 3σ(I)]</td><td>39, 26, 23</td><td>45, 29, 23</td><td>83, 38, 33</td><td>42, 26, 25</td></tr><tr><td>No. of first-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>74, 41, 41</td><td>89, 51, 49</td><td>127, 49, 49</td><td>68, 41, 40</td></tr><tr><td>No. of second-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>84, 44, 30</td><td>—</td><td>139, 62, 25</td><td>86, 50, 20</td></tr><tr><td>R<sub>int</sub> (sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>0.015<br>1.006</td><td>0.023<br>1.036</td><td>0.025<br>1.041</td><td>0.039<br>0.833</td></tr><tr><td colspan="5"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.054 / 0.069</td><td>0.054 / 0.061</td><td>0.050 / 0.062</td><td>0.070 / 0.085</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.061 / 0.079</td><td>0.051 / 0.062</td><td>0.045 / 0.053</td><td>0.065 / 0.088</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.047 / 0.063</td><td>0.056 / 0.061</td><td>0.050 / 0.054</td><td>0.062 / 0.073</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td>0.054 / 0.060</td><td>—</td><td>0.080 / 0.177</td><td>0.133 / 0.137</td></tr><tr><td>No. of reflections</td><td>111</td><td>80</td><td>149</td><td>117</td></tr><tr><td>No. of parameters</td><td>6</td><td>5</td><td>6</td><td>6</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>2.40, -2.86</td><td>3.38, -2.35</td><td>2.86, -3.05</td><td>4.59, -4.11</td></tr><tr><td colspan="5"><strong>Crystal Structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>-0.0606(4)</td><td>-0.0620(7)</td><td>0.0576(4)</td><td>0.0656(7)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>-0.0007(13)</td><td>—</td><td>0.0004(9)</td><td>-0.0008(15)</td></tr></tbody></table>
<table><caption>TABLE IX. Crystal structure, data collection, and refinement details of incommensurate Br-IIIγ at 112(3) GPa.</caption><thead><tr><th colspan="4">Crystal data</th></tr></thead><tbody><tr><td>Chemical formula</td><td>Br</td><td>Br</td><td>Br</td></tr><tr><td>M<sub>r</sub></td><td>79.91</td><td>79.91</td><td>79.91</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>112(3)</td><td>112(3)</td><td>112(3)</td></tr><tr><td>Wave vectors</td><td>q = 0.2503(12)c*</td><td>q = 0.2370(12)c*</td><td>q = 0.2038(17)c*</td></tr><tr><td>a, b, c (Å)</td><td>3.5137(8), 4.5896(10), 3.520(5)</td><td>3.5249(14), 4.554(3), 3.5291(6)</td><td>3.5278(6), 4.5076(7), 3.539(3)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>56.77(8)</td><td>56.65(4)</td><td>56.28(5)</td></tr><tr><td>Z</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.2846 Å</td><td>Synchrotron, λ = 0.2846 Å</td><td>Synchrotron, λ = 0.2846 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>5.93</td><td>5.95</td><td>5.99</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><th colspan="4">Data collection</th></tr><tr><td>Diffractometer</td><td>ESRF ID11, Dectris Eiger2 X CdTe 4M</td><td>ESRF ID11, Dectris Eiger2 X CdTe 4M</td><td>ESRF ID11, Dectris Eiger2 X CdTe 4M</td></tr><tr><td>No. of main reflections: measured, independent, and observed [I > 3σ(I)]</td><td>78, 36, 30</td><td>74, 41, 30</td><td>60, 23, 21</td></tr><tr><td>No. of first-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>144, 48, 45</td><td>145, 77, 73</td><td>99, 30, 29</td></tr><tr><td>No. of second-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>159, 52, 27</td><td>—</td><td>—</td></tr><tr><td>R<sub>int</sub></td><td>0.017</td><td>0.027</td><td>0.073</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>1.063</td><td>1.128</td><td>0.802</td></tr><tr><th colspan="4">Refinement</th></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.033 / 0.034</td><td>0.044 / 0.046</td><td>0.039 / 0.047</td></tr><tr><td>R(obs)<sub>main</sub>/wR(all)<sub>main</sub></td><td>0.024 / 0.028</td><td>0.035 / 0.040</td><td>0.038 / 0.048</td></tr><tr><td>R(obs)<sub>1st order satellites</sub>/wR(all)<sub>1st order satellites</sub></td><td>0.034 / 0.030</td><td>0.050 / 0.050</td><td>0.039 / 0.047</td></tr><tr><td>R(obs)<sub>2nd order satellites</sub>/wR(all)<sub>2nd order satellites</sub></td><td>0.076 / 0.114</td><td>—</td><td>—</td></tr><tr><td>No. of reflections</td><td>136</td><td>118</td><td>53</td></tr><tr><td>No. of parameters</td><td>6</td><td>5</td><td>5</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>1.78, -1.51</td><td>2.75, -2.46</td><td>1.18, -1.34</td></tr><tr><th colspan="4">Crystal Structure</th></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>0.0587(2)</td><td>0.0634(4)</td><td>0.0687(9)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>0.0003(11)</td><td></td><td></td></tr></tbody></table>
<table><caption>TABLE X. Crystal structure, data collection, and refinement details of incommensurate I-V at 25.1(5) GPa.</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td colspan="3"><strong>Crystal data</strong></td></tr><tr><td>Chemical formula</td><td>I</td><td>I</td></tr><tr><td>M<sub>r</sub></td><td>126.9</td><td>126.9</td></tr><tr><td>Crystal system, space group</td><td>Orthorhombic, Fmmm(00γ)s00</td><td>Orthorhombic, Fmmm(00γ)s00</td></tr><tr><td>Temperature (K)</td><td>293</td><td>293</td></tr><tr><td>Pressure (GPa)</td><td>25.1(5)</td><td>25.1(5)</td></tr><tr><td>Wave vectors</td><td>q = 0.2888(18)c*</td><td>q = 0.3004(15)c*</td></tr><tr><td>a, b, c (Å)</td><td>4.2254(13), 5.536(3), 4.249(2)</td><td>4.2221(13), 5.569(6), 4.2550(11)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>99.39(8)</td><td>100.05(12)</td></tr><tr><td>Z</td><td>4</td><td>4</td></tr><tr><td>Radiation type</td><td>Synchrotron, λ = 0.41 Å</td><td>Synchrotron, λ = 0.41 Å</td></tr><tr><td>μ (mm<sup>-1</sup>)</td><td>6.99</td><td>6.95</td></tr><tr><td>Crystal size (mm)</td><td>0.001×0.001×0.001</td><td>0.001×0.001×0.001</td></tr><tr><td colspan="3"><strong>Data collection</strong></td></tr><tr><td>Diffractometer</td><td>ESRF ID15b, EIGER2 × 9M CdTe detector</td><td>ESRF ID15b, EIGER2 × 9M CdTe detector</td></tr><tr><td>No. of main reflections: measured, independent, and observed [I > 3σ(I)]</td><td>46, 33, 30</td><td>58, 34, 31</td></tr><tr><td>No. of first-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>74, 50, 48</td><td>100, 58, 55</td></tr><tr><td>No. of second-order satellite reflections: measured, independent, and observed [I > 3σ(I)]</td><td>95, 58, 27</td><td>112, 60, 31</td></tr><tr><td>R<sub>int</sub></td><td>0.012</td><td>0.035</td></tr><tr><td>(sin θ/λ)<sub>max</sub> (Å<sup>-1</sup>)</td><td>0.872</td><td>0.855</td></tr><tr><td colspan="3"><strong>Refinement</strong></td></tr><tr><td>R(obs)<sub>main+satellites</sub>/wR(all)<sub>main+satellites</sub></td><td>0.044 / 0.048</td><td>0.105 / 0.117</td></tr><tr><td>R(obs)<sub>main/wR(all)<sub>main</sub></sub></td><td>0.041 / 0.046</td><td>0.106 / 0.113</td></tr><tr><td>R(obs)<sub>1st order satellites/wR(all)<sub>1st order satellites</sub></sub></td><td>0.035 / 0.041</td><td>0.092 / 0.115</td></tr><tr><td>R(obs)<sub>2nd order satellites/wR(all)<sub>2nd order satellites</sub></sub></td><td>0.098 / 0.104</td><td>0.154 / 0.204</td></tr><tr><td>No. of reflections</td><td>141</td><td>152</td></tr><tr><td>No. of parameters</td><td>6</td><td>6</td></tr><tr><td>Δρ<sub>max</sub>, Δρ<sub>min</sub> (e Å<sup>-3</sup>)</td><td>2.70, -1.97</td><td>6.68, -5.02</td></tr><tr><td colspan="3"><strong>Crystal structure</strong></td></tr><tr><td>Br (x y z)</td><td>(0 0 0)</td><td>(0 0 0)</td></tr><tr><td>A<sub>1</sub>(x)</td><td>-0.0599(3)</td><td>-0.0587(8)</td></tr><tr><td>A<sub>2</sub>(y)</td><td>-0.0016(7)</td><td>-0.0028(15)</td></tr></tbody></table>
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