High-Pressure Behavior of Silver Fluorides up to 40 GPa - Inorganic

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High-Pressure Behavior of Silver Fluorides up to 40 GPa Adam Grzelak,†,‡ Jakub Gawraczyński,†,‡ Tomasz Jaroń,‡ Dominik Kurzydłowski,‡,△ Armand Budzianowski,‡ Zoran Mazej,§ Piotr J. Leszczyński,‡ Vitali B. Prakapenka,∥ Mariana Derzsi,*,‡ Viktor V. Struzhkin,*,⊥ and Wojciech Grochala*,‡ †

Faculty of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland Center of New Technologies, University of Warsaw, ul. Banacha 2C, 02-097 Warsaw, Poland § Department of Inorganic Chemistry and Technology, Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia ∥ Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, United States ⊥ Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, D.C. 20015, United States △ Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Warsaw 01-038, Poland

Inorg. Chem. 2017.56:14651-14661. Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SANTA BARBARA on 06/28/18. For personal use only.

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S Supporting Information *

ABSTRACT: A combined experimental−theoretical study of silver(I) and silver(II) fluorides under high pressure is reported. For AgI, the CsCl-type structure is stable to at least 39 GPa; the overtone of the IR-active mode is seen in the Raman spectrum. Its AgIIF2 sibling is a unique compound in many ways: it is more covalent than other known difluorides, crystallizes in a layered structure, and is enormously reactive. Using X-ray diffraction and guided by theoretical calculations (density functional theory), we have been able to elucidate crystal structures of high-pressure polymorphs of AgF2. The transition from ambient pressure to an unprecedented nanotubular structure takes place via an intermediate orthorhombic layered structure, which lacks an inversion center. The observed phase transitions are discussed within the broader framework of the fluorite → cotunnite → Ni2In series, which has been seen for other metal difluorides.

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compounds are known because of the fact that fluorine is the most electronegative element (4.0 on the Pauling scale); thus, fluorides are ionic to a larger extent than other halides. The crystal structure of AgF2 consists of corrugated sheets made up of [AgF4] square units, somewhat reminiscent of CuF2, but the AgF2 unit cell is orthorhombic (Pbca space group) and the sheets are oriented differently relative to one another compared to CuF2.6 While silver(I) fluoride (AgF) can be considered to be a classic ionic solid (with a rock-salt-type structure), AgF2 has been shown to host largely covalent bonds.7 Indeed, the studies on the nature of chemical bonding in silver fluorides have indicated that the Ag−F bond becomes increasingly covalent with increasing oxidation state of silver, as evidenced by X-ray photoelectron spectroscopy.7 In this work, we focus on the high-pressure behavior of AgF2 and AgF up to 40 GPa. In order to understand the phase transitions of compressed AgF2, it is helpful to compare them with those of other difluorides, which have been extensively studied.8,9 It is common for many of these compounds to adopt a cotunnite (PbCl2) structure upon compression, as exemplified by CaF210 or MnF2.11 Such a transition increases the CN of the

INTRODUCTION Compounds with the general formula MF2 (difluorides) exhibit a large variety of structures and properties. One of the earliest known difluorides is CaF2, which occurs in nature as the mineral fluorite. The crystal structure of fluorite1 [Fm3̅m; metal coordination number (CN) equal to 8] is adopted by many other compounds in this family, e.g., SrF2, BaF2, TiF2, CdF2, PbF2, and HgF2. Another common structural type among difluorides is that of rutile (TiO2; metal CN = 6): examples include difluorides of transition metals such as Mn, V, Fe, Co, Ni, and Pd as well as Mg and Zn. BeF2, on the other hand, which forms a quartzlike structure,2,3 is a rare example of the MF2 system with CN = 4. Several interesting structures of difluorides arise from distortions of the aforementioned prevalent types, caused by the electronic structure of the metal ion. A notable example is CuF2, which bears some resemblance to rutile but is distorted because of the Jahn−Teller effect, which causes elongation of two axial Cu−F contacts.4 The resulting structure is monoclinic and consists of layers made up of [CuF4] squares connected diagonally via F atoms. A similar deformation, although much less pronounced, can be seen in the structure of CrF2.5 Our work focuses on silver(II) fluoride (AgF2) because it is a rare example of a covalent difluoride. Relatively few such © 2017 American Chemical Society

Received: October 4, 2017 Published: November 15, 2017 14651

DOI: 10.1021/acs.inorgchem.7b02528 Inorg. Chem. 2017, 56, 14651−14661

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Inorganic Chemistry

Raman Spectroscopy. Raman spectra were collected using a 532 nm line and a 1200 slits/mm diffraction grating. The Rayleigh line was cut off using a pair of notch filters. Three experiments were carried out, in which AgF2 samples were compressed in two different pressure ranges: ca. 7−47 and 22−40 GPa. However, we have found out that the sample of AgF2 photochemically and/or thermally decomposes when illuminated with the 532 nm beam available to us, and we could not use Raman spectroscopy to support our X-ray data. The Raman spectra are thus shown in the Supporting Information (SI) only for AgF. Powder X-ray Diffraction (XRD). The XRD patterns were measured using the Advanced Photon Source (APS) synchrotron at Argonne National Laboratory (ANL). The results from two different XRD experiments are discussed in this paper: (a) Experiment “XRDA” was carried out at wavelength 0.3344 Å (37.08 keV) with a diameter of the beam raster of 7 μm. Neon (loaded at ca. 170 MPa) was used as a pressure-transferring medium. The sample was compressed in the range of ca. 5−26 GPa. (b) Experiment “XRD-B” was carried out at wavelength 0.4113 Å (30.14 keV), with a diameter of the beam raster of 6 μm. Slivers of fluorinated ethylene propylene were used as a pressure-transferring medium. The sample was compressed from ca. 12 to 36 GPa and then decompressed to ca. 17 GPa. The very high reactivity of AgF2 resulted in its chemical transformation to AgF in several samples and despite all precautions, and most of such samples were not studied. However, one XRD experiment involved compression of what turned out to be almost entirely AgF, resulting from the in situ reaction of AgF2 with gasket material and/or diamond. This sample was compressed in the range of ca. 3−39 GPa. This enables us to obtain an equation of state (EoS) of the high-pressure polymorph of AgF (see the SI); this compound was inevitably found in nearly all samples of “AgF2”. These findings enabled us to use AgF as another (internal) pressure gauge in experiments with AgF2 because XRD data indicate that AgF is present in both (“XRD-A” and “XRD-B”) samples of AgF2. Thus, pressure values for XRD data in text and figures are given as determined from the EoS of the in situ reference, AgF. The mass fraction of AgF relative to the sum of both silver fluorides varies between 0.12 and 0.47 (with the exception of 0.66 at one data point), with a mean value of 0.28 across the range of both experimental runs. Structure Solution and Refinement. Jana2006 was used for the Rietveld refinement of the XRD patterns.30 “VESTA” was used for drawing crystal structures.31 “Fityk” was used for drawing XRD and Raman spectra.32 Rietveld refinement of XRD patterns was carried out using pseudo-Voigt functions for profiles and Legendre polynomials for background. The March−Dollase parameter was used to account for the preferred orientation of neon and, whenever required, highpressure phases of AgF2. Rietveld fits and their parameters for selected pressures and structures are shown in the SI. While diffraction patterns of all structures for any given set of lattice constants are very similar, they have a different number of low-angle reflections (below 7.5° at 30.14 keV radiation), which renders the assignment reliable. In some of the diffraction patterns, two minor reflections at ca. 8° and 13° remain unassigned. Possible impurities that may give rise to these peaks could include products of the reaction of rhenium gasket or tungsten carbide with AgF2. The scarcity and low intensity of these reflections prevent us from determining the exact origin of these impurities. They do not appear systematically for sample A (i.e., they are seen only in some of spots probed by the X-ray beam), and they are completely absent for sample B. Further details of the crystal structures may be obtained from the Cambridge Structural Database, CSD, on quoting the CSD numbers 1576174 and 1576176, 1576177, 1576175 and 1576173, as well as 1576178, 1576172 and 1576179, for the LP structure compressed to 4.9 and 8.5 GPa, HP-I structure at 10.0, 11.7, and 13.5 GPa, and HP-II structure at 16.9, 25.3, and 36.2 GPa, respectively. Theoretical Calculations. Spin-polarized DFT (hybrid DFT) calculations were performed using the plane-wave VASP package.33−37 The structural models were fully optimized, using the PBEsol functional,38 a plane-wave cutoff of 520 eV, and a k spacing of 0.2 Å−1 at several pressure points within 0−40 GPa (a higher pressure

metal atom from 8 to 9. Those difluorides, which under ambient pressure crystallize in a rutile structure, commonly undergo a transition to a CaCl2-type structure (e.g., NiF212 and ZnF213), which can be described as a slightly distorted rutile. A special case is that of PdF2: it transforms into a cubic structure that features deformed [PdF6] octahedra and can also be traced back to a heavily distorted rutile lattice.14,15 Such deformation allows more efficient packing of the [MF6] octahedra, which is favored under high pressure. Interestingly, this polymorph has also been obtained at ambient pressure.16 This type of structure is also adopted by MgF2, which undergoes a series of transitions: rutile → CaCl2 → HP-PdF2 → cotunnite.17 Interestingly, the fluorite structure, which can be thought of as intermediate between rutile and cotunnite in terms of packing, is not found at any point during the compression of MgF2, a result initially supported by theoretical calculations.17 However, most recent calculations contrastingly found the fluorite polytype to be the energy-favored structure at pressures exceeding 280 GPa.18 Upon decompression, MgF2 has been reported to transform into α-PbO2-type structure.17,19,20 Compounds that exhibit the cotunnite structure at ambient pressure can undergo pressure-induced transitions to even more closely packed systems. PbF2 has been found to transform above 10 GPa into a postcotunnite structure17,21 that features metal atoms coordinated by 10 ligands and is known from highpressure experiments with several other heavy-metal halides.22 The highest CN in MF2 compounds, 11, has been achieved in the Ni2In-type structure of SrF223 and in BaF2.24,25 Previous works on the high-pressure structure of AgF2 suggested either a transition analogous to that of HP-PdF2 (experiment)26 or flattening of the corrugated sheets at pressures above 15 GPa (theory).27 However, recently published preliminary results of our studies on AgF2 under high pressure show that a nanotubular polymorph of AgF2 forms at 15 GPa.28 The following work is an expansion on the subject based on data in the pressure range ca. 5−40 GPa. Pressure-induced phase transitions and crystal structures of HP polymorphs of AgF2 are investigated using a combined theoretical (density functional theory, DFT) and experimental [X-ray diffraction (XRD) and Raman spectroscopy] approach. Although the high-pressure structures reported here are seemingly very different from those adopted by other metal difluorides upon compression, through a careful analysis we have been able to show how they are related to other known MF2 compounds.

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EXPERIMENTAL PROCEDURES AND THEORETICAL CALCULATIONS

Diamond Anvil Cell (DAC) Setup. Samples were compressed using standard symmetrical DAC. Diamonds used in all experiments had 200-μm-wide culets with no bevel. Rhenium plates (250 μm thick) were used as gasket materials. Gaskets were preindented in two steps to 20 GPa, and then 120-μm-wide holes were cut using a laser drill. The high-edge frequency of the first-order Raman band of diamond was used for the initial pressure determination,29 instead of ruby (because AgF2 is very reactive to oxides). Samples. AgF2 was prepared by standard fluorination of the AgNO3 precursor in anhydrous HF. Polycrystalline samples of freshly prepared AgF2 were loaded in an inert atmosphere (argon). Possible contaminants in all samples stem from the decomposition of AgF2 in contact with reducing agents or not fully fluorinated compounds or from parts of measurements in the chamber and equipment, for example, shards of rhenium gasket, pieces of tungsten needle, or tungsten carbide from a seat. 14652


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Inorganic Chemistry range up to 300 GPa, considerably surpassing the experimental pressure range, was probed selectively). A denser k spacing of ∼0.11 Å−1 was used for total energy (enthalpy) calculations. In each case, a proper antiferromagnetic (AFM) model was constructed following the Goodenough−Kanamori rules.39−41 In order to take into account the on-site Coulomb interactions between 3d electrons, the spin-polarized calculations were performed within the GGA+U approach,42 where the values of the Coulomb integral U = 5 eV and Hund’s exchange J = 1 eV were used for the Ag2+ ions (values used in our previous calculations for Ag2+ systems43,44). Calculations of lattice dynamics (phonon dispersions curves) were performed using the direct method of Parlinski, Li, and Kawazoe,45 implemented in PHONOPY.46 The force constants used to construct the dynamical matrices were calculated by taking into account symmetries of the fully relaxed 2 × 2 × 2 supercell containing 96 atoms for both the low-pressure (LP) Pbca and the HP-I Pca21 AgF2 structures. In the case of the HP-I Pca21 form, the phonon dispersion curves were calculated also for the 2 × 4 × 2 supercell (192 atoms). The same results were obtained for the two supercells of the latter structure. The 2 × 1 × 2 supercell was used for computing phonons of the HP-II polytype. The thresholds for electronic and ionic convergence were set to 10−7 and 10−5 eV, respectively. The forces per atom (lattice dynamics calculations) were converged to the maximum value of 0.00001 eV Å−1.

Figure 3 (top left). It can be viewed as an orthorhombic distorted fluorite unit cell with anions displaced from the ideal tetrahedral positions. The crystal structure consists of corrugated AgF2 layers stacked in the b direction. Within the layers, each AgII cation is coordinated by four F atoms in a nearly ideally square-planar fashion. The corrugated [AgF2] layers are thus formed by [AgF4] square units sharing vertices. The AgII cations are additionally linearly coordinated by F atoms from the nearest top and bottom layers, to which they form second nearest Ag···F contacts. These axial contacts complete the coordination sphere of AgII in an angularly distorted elongated octahedron. Finally, a second pair of secondary axial Ag···F contacts completes the severely distorted [AgF8] cubes, a counterpart of the ideal cubic cationic coordination in fluorite. The first XRD pattern collected from sample A corresponds to a pressure of 4.9 GPa (Figure 1); it can be satisfactorily described using the known LP structure of AgF2 (Figure 3, top left, and Table 1; for the Rietveld fit at 8.5 GPa, see the SI). One change of the XRD pattern is seen when the pressure is increased from 8.5 to 10 GPa: an additional reflection appears at ca. 6.8° (marked with an asterisk in Figures 1 and 2). A similar reflection appears for sample B at p = 11.7 GPa (Figure 2). Simultaneously, the remaining part of the XRD pattern does not change dramatically; altogether, this points to a subtle structural change, such as, e.g., symmetry lowering. Indeed, the new low-angle reflection can be satisfactorily accounted for by a new Pca21 structure (Figure 3, top right, and Table 1; for the Rietveld fit, see the SI), to which we will refer as HP-I. The HP-I turns out to arise from the phonon instability of the LP polymorph, as predicted by our PBEsol+U calculations. When subjected to hydrostatic compression, the LP phase becomes dynamically unstable along an optical mode of B2u symmetry that distorts the LP structure, yielding the Pca21 one. According to the PBEsol+U calculations, the B2u mode becomes imaginary at the Γ point of the first Brillouin zone at 6 GPa (Figure 4, left); the higher-precision enthalpy calculations locate the Pbca/Pca21 transition close to 8 GPa. The calculated predicted transition pressure of 8 GPa is not far from the 8.5−10.0 GPa pressure interval, in which the transition is observed in the XRD data, thus supporting the orthorhombic Pca21 structure as the first high-pressure phase of AgF 2 . The symmetry lowering from Pcab (the other representation of Pbca, No. 61) to its Pca21 (No. 29) subgroup preserves the topology of the crystal structure, but it is connected with the disappearance of the inversion center at Ag atom (the number of symmetry operations decreases from 8 to 4), which leads inter alia to the appearance of the weak [110] reflection as discussed above. The dominant atomic motion within the B2u phonon mode is an antiphase displacement of all of the [AgF2] sheets in the b direction (Figure 4, middle) while preserving the presence of corrugated [AgF4/2] sheets. Such a motion modifies the axial intersheet Ag−Fax contacts from undistorted linear to a Vshaped Fax−Ag−Fax geometry with two nonequivalent Ag···F distances (Figure 4, right). Simultaneously, the Ag atoms leave the center of the ideally flat intrasheet [AgF4] unit. This complex motion can be rationalized as an attempt of the AgII cations to avoid the short axial F contacts in order to preserve the local Jahn−Teller distortion because both the antiphase displacement of the AgF2 layers and the shift of the Ag atoms away from the plane of the [AgF4] units guide the AgII cations toward a weaker axial ligand field. At 10 GPa, the calculated

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RESULTS Because AgF2 is extremely reactive and one of the most potent fluorinating agents, contamination of the sample is almost inevitable even when the utmost care is taken during loading. The most common contaminant is AgF, a decomposition product of AgF2. AgF has been previously studied under high pressure and is known to undergo a phase transition at a pressure of ca. 2.7 GPa from a rock salt structure to the more closely packed CsCl-type structure.47 In our own experiments, AgF-rich samples were compressed to ca. 39 GPa, which enabled us to redetermine the EoS parameters of the CsCl-type structure (see the SI) to much higher pressures than previous works,47 which, in turn, served us for applying AgF as an in situ pressure gauge in experiments with other, more AgF2-rich, samples. XRD, Relevant Crystal Structures, and Theoretical Results (PBEsol+U). As outlined in the experimental part, two samples of AgF2 were studied: sample A was compressed in the range of ca. 5−26 GPa (Figure 1), while sample B was compressed from ca. 12 to 36 GPa and then decompressed to ca. 17 GPa (Figure 2). Both samples contained initially the LP orthorhombic form of AgF2 (Pbca)6 and some contamination from AgF. The crystal structure of the LP phase is presented in

Figure 1. XRD-A data (compression only). The characteristic reflection of HP-I is marked with an asterisk and that of HP-II with a square. 14653


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Figure 2. XRD-B data (compression and decompression). The characteristic reflection of HP-I is marked (at compression) with an asterisk and that of HP-II with a square.

Figure 3. Relevant polymorphs of AgF2: gray balls, Ag; red balls, F. From left to right: low-pressure Pbca structure (LP) at 4.9 GPa; high-pressure Pca21 structure (HP-I) at 11.7 GPa; high-pressure Pbcn structure (HP-II) at 36.2 GPa; theoretical PbCl2-type structure.

axial Ag−F distances are equal to 2 × 2.373 Å in the LP structure and to 2.373 and 2.414 Å in the HP-I structure. The two shorter and more rigid equatorial intrasheet Ag−F contacts also experience slight expansion during the transition (by 0.013 and 0.015 Å, respectively, at 10 GPa) as a consequence of the displacement of the Ag atoms out of the plane of the ideally flat [AgF4] units (Figure 4, right). This expansion of the silver(II) coordination sphere during the phase transition shows that the B2u mode releases the axial stain that the AgII cations experience under hydrostatic compression. Apart from the above-described changes, the HP-I (Pca21) structure is very similar to the LP one in its two-dimensional character. Under further compression of sample B to 14.8 GPa, the XRD pattern changed noticeably. Aside from marked changes of the diffraction pattern, another weak low-angle reflection appeared at ca. 5.2° (marked with a square in Figures 1 and 2) in most patterns collected. Similar changes were seen for sample A when p is increased from 13.7 to 16.9 GPa. The XRD data at 14.8 GPa and all higher pressures for both samples are best described by yet another orthorhombic structure that we have obtained in theoretical calculations of lattice dynamics. This new structure arises from the pressure-driven phonon instability of the HP-I structure (Figure 5, right); the resulting symmetrized and fully optimized primitive orthorhombic cell belongs to the Pbcn (No. 60) space group, and we will label it here as HP-II (Figure 3, bottom left, and Table 1; for the Rietveld fit, see the SI). The HP-II structure is predicted to be enthalpy-preferred over the HP-I one at 14 GPa (cf. section S4 in the SI), which correlates very well with the experimentally observed pressure of the HP-I → HP-II transition in the pressure range of 13.7−14.8 GPa. Although the lowest-angle reflection characteristic of HP-II is not readily visible at 16.9

and 20.6 GPa in Figure 1, the HP-II structure does, in fact, produce a considerably better fit for these two pressure points than the HP-I phase. The phonon instability that led us to the HP-II phase appears as an imaginary mode at the Y (0.0, 0.5, 0.0) point of the first Brillouin zone of the calculated phonon dispersion curves of the HP-I phase at 70 GPa (Figure 5, left). This mode involves a quite sophisticated motion of the cationic sublattice, which consists of an antiphase displacement of the pairs of Ag atoms along the c direction perpendicular to the [AgF4/2] layers (Figure 5, middle). This leads to the breaking of intralayer Ag− F contacts and creation of new ones perpendicular to the disintegrating layers. Because the Ag atoms move in phase only along the a axis, the imaginary mode leads to the formation of a one-dimensional AgF2 network along this direction. The infinite chains have a shape of channels, in which the repeating unit is built of four AgF2 units and the Ag atoms are found in a distorted square-planar coordination (Figures 3 and 5). Note that the quasi-planar AgF4 units that propagate along the channels of the HP-II structure are similar to those present in the HP-I one. During the transformation, AgF2 tends to preserve as many of these units as possible. In fact, only two Ag−F bonds in every second AgF4 unit are broken at the phase transition, and 75% of the short Ag−F bonds are preserved. The HP-II structure featuring one-dimensional channels is remarkable; to our knowledge, such a structure has never been observed in any transition-metal halide; the uniqueness of this structure has been pointed out in a recent short communication.28 EoS and Compressibility of Various Polymorphs of AgF2. The order of the phase transitions and the EoS of AgF2 are of interest. Interestingly, no volume drop is observed at the 14654


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LP → HP-I transition (Figure 6, bottom), which suggests that the transition is second-order. Such behavior can be understood based on the high similarity of the HP-I and LP structures discussed above; they both consist of puckered [AgF4/2] layers, and no breaking or formation of new bonds is involved in the phase transition (only the secondary interlayer Ag−F contacts are modified). Indeed, the calculated volume change at the pressure of the phase transition is predicted to amount to less than 1%, which is imperceptible in experimental data (especially that both phases may coexist in a finite pressure region). In summary, the LP → HP-I phase transition originates from soft phonon instability, and the associated volume drop is negligible. The calculated EoS of AgF2 in this pressure range (0−15 GPa) agrees very well with the experimental one (Figure 6), i.e., up to 3.3% in terms of volume at a given pressure point. Between 13.5 and 16.9 GPa, the experimental unit cell volume drops suddenly by 6.3%, which is seen as a discontinuity in the V(p) plot (Figure 6, bottom) as well as large changes of the lattice constants (Figure 7). This is strongly indicative of a first-order phase transition, and it is further supported by the results of our PBEsol+U calculations. The calculations predict that the HP-I → HP-II transition should occur at 14 GPa and be accompanied by a volume drop of about 5%. Moreover, the calculated volume change between HP-I at 15 GPa and HP-II at 17 GPa amounts to 6.4%, nicely corroborating the experimental findings. The calculated EoS of AgF2 in this pressure range (15−38 GPa) also agrees very well with the experimental one, with the differences of volume at a given pressure point not exceeding 6.0%. Altogether, a very good agreement of the theoretical and experimental EoS as well as of the unit cell vectors (Figure 7) supports the described scenario involving two consecutive phase transitions for AgF2 under compression. The pressure dependence of the lattice constants is presented in Figure 7. Because all three AgF2 structures belong to different space groups, the representation of the lattice constants is different in each of them. For example, b in LP corresponds to c in HP-I and to a in HP-II. The unit cell also becomes 2 times larger in the b direction as a result of the transition from HP-I to HP-II. This is indicated by the

Table 1. Crystallographic Data for the Three Polymorphs of AgF2: Lattice Constants, Fit Parameters, Atomic Coordinates and Selected Interatomic Distancesa Z=4 a, b, c [Å] α = β = γ (deg) Rp = 0.81% Ag F Ag−F (Å)

Z=4 a, b, c (Å) α = β = γ (deg) Rp = 0.51% Ag F1 F2 Ag−F (Å)

Z=8 a, b, c (Å) α = β = γ (deg) Rp = 0.29% Ag F1 F2 F3 Ag−F (Å)

Pbca (LP, 8.5(2) GPa) V = 147.93(3) Å3 5.477(3) 5.592(2) 90 90 Rwp = 1.24% GOF = 0.53 0 0 0.3050(5) 0.1309(6) square: 1.999(1) axial: 2.489(2) Pca21 (HP-I, 11.7(5) GPa) V = 141.63(8) Å3 5.586(7) 4.501(8) 90 90 Rwp = 0.70% GOF = 0.13 0.53562 0.76418 0.21860 0.90334 0.86852 0.60639 square: 1.999(5) 2.075(4) axial: 2.402(6) Pbcn (HP-II, 36.2(8) GPa) V = 233.6(8) Å3 5.13(1) 7.85(1) 90 90 Rwp = 0.44% GOF = 0.30 0.20439 0.62693 1 0.64551 1 1.20262 0.32092 0.58270 square: 1.989(4) 2.075(4) interchain: 2.423(5) 2.473(9) intrachain: 2.626(5)

4.831(2) 90 0 0.1846(6) 2.030(1)

5.634(7) 90 0.00760 0.84516 0.11147 2.030(4) 2.089(4) 2.455(4)

5.803(7) 90 −0.55926 −0.25 −0.25 −0.89643 2.028(4) 2.084(4) 2.471(6) 2.591(5) 2.729(10)

a

The atomic coordinates in the HP-I and HP-II phases were derived from theory and were not refined; thus, their uncertainties are not shown. Rietveld fits corresponding to the above data can be found in section S2 in the SI.

Figure 4. Left panel: Phonon dispersion curves calculated for LP AgF2 at two pressure points on the PBEsol+U level. The arrow points to the optical B2u phonon at the Γ point that becomes imaginary (gains a negative force constant) at 6 GPa. Middle panel: LP Pbca structure (top) distorted along the imaginary Γ mode toward the Pca21 structure (bottom). Note how the axial Ag−F contacts are being distorted from the linear to a dumbbell F− Ag−F geometry (dashed lines) because of the antiphase movement (indicated by oppositely oriented arrows) of the AgF2 layers along the a direction of the Pbca cell. Right panel: AgF6 coordination with values of axial Ag−F distances calculated for Pbca and Pca21 at 10 GPa. 14655


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Figure 5. Phonon dispersion curves calculated for the AgF2 HP-I structure at the PBEsol+U level for p = 70 GPa (left) and illustration of the emergence of the Pbcn structure from the imaginary mode at Y (right) indicated with an arrow in the left panel. The arrows in the HP-I supercell point in the directions of the displacements of the Ag atoms within mode Y, and the dashed lines indicate the new contacts created upon such displacements. The displaced structure (before optimization) is shown on the far right (HP1 + imY). Compare with Figure 3 (bottom left).

Figure 7. Pressure dependence of the lattice constant (see the text) of the three AgF2 structures (solid markers, compression; hollow markers, decompression): (top) c lattice constant; (bottom) a and b lattice constants. Error bars are not shown for clarity; for error values, please refer to section S3 in the SI.

Figure 6. Pressure dependence of volume per formula unit for the three AgF2 structures. Top: Results of the PBEsol+U calculations. Bottom: Results from experiment (solid markers, compression; hollow markers, decompression). Lines connecting the pressure points (PBEsol+U results) were added to guide the eye. The dotted lines are not the EoS fits but approximate linear fits to highlight the volume drop between HP-I and HP-II.

and simultaneously is perpendicular to the direction in which these sheets are corrugated. The compression is most significant in the c direction, along which the sheets become increasingly corrugated. The b vector is reduced continuously from LP to HP-I, and its pressure dependence retains roughly the same slope for the HP-II structure within the entire studied pressure range. The unit cell length in this direction corresponds to the separation between sheets in the LP and HP-I structures.

appropriate labels in Figures 6 and 7. In a subsequent description, the lattice constants will be for simplicity referred to as those for the LP structure, regardless of which structure is being discussed. HP-I proves to be least compressible along the a direction, which is one of directions of propagation of the [AgF4/2] sheets 14656


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Figure 8. Evolution of the centered metal dodecahedra in both high-pressure phases of AgF2 relative to the fluorite and cotunnite structures. The change of the orientation of the triangular face between HP-I and HP-II is marked by the black arrow at the bottom.

Near the transition from HP-I to HP-II, a starts to increase and continues to increase up to 32.7 GPa, where it reaches a plateau of ca. 5.8 Å. At the same time, b and c steadily decrease. These counteracting tendencies amount to an overall decrease in the volume with increasing pressure, as is expected for the progressive spatial confinement. As the sheets of HP-I become increasingly corrugated, they rearrange at ca. 14 GPa into compact 1D channels typical of HP-II. The HP-II structure also exhibits mechanical anisotropy: under increasing pressure, these channels become elongated along a but also more closely packed (b and c decrease). Phase Transitions of AgF2 and Other MF2 Systems: From the Fluorite to the Cotunnite Prototype. Crystal structures of AB2 compounds can be divided into four major groups: the quartz group, the rutile group, the fluorite group, and the cotunnite group. Because the metal CN increases here from 4 (tetrahedron) via 6 (octahedron) and 8 (cube) to 9 (elongated tricapped trigonal prism), respectively, the quartz → rutile → fluorite → cotunnite sequence is recognized also as the typical high-pressure sequence in these compounds. This behavior can be exemplified by SiO2, which transforms from coesite (rutile) to stishovite (rutile), or by PbO2, which undergoes several phase transitions on the rutile → fluorite → cotunnite pathway. In fluorides, the above sequence was found to continue to the postcotunnite phases, with the highest so-farobserved CN of the cation equal to 11.23,24 This is exemplified by MF2 (M = Pb, Ca, Sr, Ba), which crystallize in the fluorite or cotunnite structure at ambient or low pressures, while at high pressures, they transform to the even more densely packed Ni2In polytype. However, do polymorphic transitions of AgF2 fit into this picture? Clearly, none of the AgF2 polymorphs corresponds to an ideal fluorite, rutile, or cotunnite type. However, the LP form of AgF2 may be viewed as an orthorhombically distorted fluorite structure, in which the anions are displaced from their ideal positions in the middle of tetrahedral voids formed by a cationic sublattice. This leads to a decrease of the CN from 8 to 6 [although the severely distorted (4 + 2 + 2) coordination is still recognizable]. The similarity between the LP and fluorite is emphasized by the fact that the heavy-atom sublattice of LP is identical with that of the F-centered CaF2 type. Having said that, a phase transition from LP to some sort of cotunnite-type structure (Figure 3, bottom right) is expected for AgF2 at elevated pressures. This, indeed, is the case, as one may judge from the pressure evolution of the cationic sublattice of AgF2 (Figures 8 and 9). Because of the hexagonal and pseudohexagonal dense packing of the fluorite and cotunnite structures, respectively, one may distinguish the centered metal dodecahedra that consist of triangular and square faces in these structures. The dodecahedron is ideal for the high-symmetry fluorite polytype but distorted for the cotunnite type. The main difference between them is that the triangular faces at the bottom and top

Figure 9. Metal sublattice of fluorite and LP AgF2 (top panel), HP-I and HP-II structures of AgF2 (two middle panels), and cotunnite (bottom panel). Only selected contacts are drawn in order to highlight fragments of the fluorite structure in the remaining structures. Note that two different projections are shown in the left and right panels.

of the polyhedron (Figure 8) have opposite orientation (i.e., they are related by their inversion center) for the fluorite structure, but they are similarly positioned (i.e., related by the plane symmetry) for the cotunnite form. The shape of the dodecahedra and arrangement of the triangular faces seen for the HP-I AgF2 form are reminiscent of those for fluorite, but for the HP-II form, they resemble those for the cotunnite type. In other words, the HP-I → HP-II transition for AgF2 corresponds to the fluorite → cotunnite transition seen for other metal difluorides.22 The transition from the fluorite to the cotunnite-like structure for AgF2 may also be observed analysis of the topology of the entire 3D cationic network, as seen in two different projections (Figure 9). In all of these structures, corrugated cationic layers can be distinguished when only selected metal−metal contacts are considered. The fluorite structure exhibits the AA stacking of the layers in both projections, while the cotunnite structure shows the AA and AB stacking when viewed along two different directions, respectively (compare the left and right panels in Figure 9). In the LP and HP-I structures of AgF2, the stacking of the layers is the same as that in the fluorite (albeit with some disorder within the layers). Under further compression (HP-I → HP-II), 14657


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Figure 10. Filling of the octahedral and tetrahedral voids by anions in the AgF2 structures with respect to the fluorite and cotunnite structures.

this disorder is accompanied by a shift of the layers with respect to each other, and that results in an ABC stacking pattern when viewed along one of the two directions (Figure 9, right panel). Simultaneously, the corrugated metal sublattice substantially “flattens out” in the HP-II form, as is typical also for the cotunnite type (Figure 9, left panel). From this feature, as well as from the character of the layer stacking in another projection (Figure 9, right panel), it is evident that the metal sublattice in the HP-II phase is heading away from the fluorite toward the cotunnite type; still, one must notice that even for the HP-II form the transformation is not complete, and there are differences between the topologies of the HP-II and cotunnite forms. In the above, we have rationalized the evolution of the metal sublattice in the high-pressure phases of AgF2 along the fluorite−cotunnite pathway. However, what about the anionic sublattice? We will now look at the octahedral and tetrahedral voids that share triangular faces in the cationic fcc sublattice. In the fluorite structure, anions are located in the tetrahedral voids (Figure 10, left), while in LP AgF2, they are found on the oppositely positioned triangular faces (Figure 10, second left). The small distortions within the metallic sublattice of the HP-I phase (compared to the LP one) allow one of the anions to enter the interior of the octahedron, while the second anion remains on the triangular face (Figure 10, middle). Further changes within the metal sublattice upon the second-phase transition bring the two anions toward the central positions of the octahedron and of the neighboring tetrahedron, respectively (Figure 10, second right). The cotunnite structure also features anions within the octahedral and tetrahedral voids in the cationic sublattice (Figure 10, right). This is similar to what is seen for the AgF2 HP-II structure, and therefore this observation serves as another piece of evidence that AgF2 is approaching a cotunnite-related structure under pressure. Note, however, that while the arrangement of the octahedral and tetrahedral voids in the HP-I and HP-II AgF2 polytypes is the same as that in the fluorite structure, it is different from that in the cotunnite structure: here, two of the tetrahedral voids surrounding the central octahedral void are replaced by octahedral ones (Figure 10, right). Overall, the evolution of the anionic sublattice of AgF2 under pressure may be described as the progressive occupancy of the octahedral voids from null for the LP structure (this is similar to the fluorite type), via partial (for the HP-I structure), up to full occupancy of all octahedral voids for the HP-II type (this is similar to what is seen for cotunnite). Still, one should remember that the anionic sublattice of both HP forms of AgF2 is unique and likely driven mostly by the prominent Jahn− Teller effect typical of all silver(II) compounds. Even More Similarities between HP-II and Cotunnite: Connectivity of the [AgF4] Squares and the Role of the Jahn−Teller Effect. Even more similarities between the observed HP-II and the hypothetical cotunnite forms of AgF2 may be detected upon analysis of the local coordination of AgII

cations, as well as the connectivity of the fundamental building blocks present in both structures. It turns out that the projection of both structures on the same bc plane (Figure 11) reveals a striking similarity between half of the Ag sublattice

Figure 11. Illustration of the relationship between half (gray spheres) of the Ag sublattice for the HP-II polytype (left) and the entire metal sublattice for the hypothetical cotunnite type of AgF2 (right). Similarities of the local coordination of AgII in the form of a distorted [AgF4] square are also seen. Only the shortest Ag−F bonds were drawn for clarity.

for the HP-II polytype and the complete metal sublattice for the cotunnite form. Aside from this, the [AgF4] squares are present in both structures, and the topology of these units in the unit cell is very similar for both polymorphic forms; the main difference is that the [AgF4] squares are linked by another half of AgII cations into a nanotubular structure28 for the HP-II form, while they polymerize along a axis into quasi-1D CuCl2like48 [AgF4/2] chains in the case of the cotunnite structure. Yet another similarity of both polytypes is featured in the distortions of the [AgF4] squares. In both cases, a substantial out-of-plane shift of the central AgII cations is seen, leading to the appearance of the local dipole moment; recall that in most known compounds of AgII the coordination of this cation is in the form of a flat square or of a distorted (compressed or elongated) octahedron, but most often the local quasi-D4h symmetry is preserved. This distortion observed for AgF2 at high pressure (and seen already for the HP-I form; Figure 4) is caused supposedly by the combined effects of the increasing packing and persistence of the strong Jahn−Teller effect. On the one hand, the CN of AgII (equal formally to 4 for the LP form, when the shortest contacts are taken into account) should increase at high pressure to allow for better packing, but, on the other hand, the CN cannot increase to 6 while preserving the octahedral form because this would mean annihilation of the Jahn−Teller effect. Hence, a compromise is adopted in the HPI type where the CN of AgII increases to 5 (i.e., 4 + 1), and there is still some room left for the dz2/p hybrid lone pair at the AgII site. The dz2 orbital benefits from the admixture of the valence Ag 5p orbital, the unoccupied orbital of the two 14658


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Inorganic Chemistry resulting ones is exposed in the direction of the fifth approaching fluoride ligand, and the occupied one sticks out mostly on the other side of the AgII cation where the distance to the adjacent F (the sixth ligand in the coordination sphere of Ag) is larger. That the Jahn−Teller effect for AgII is indeed very strong is testified by the primary (Ag−F) and secondary (Ag···F) bonding in the HP-II AgF2 phase, as calculated for p = 70 GPa. At this pressure, the four shortest Ag−F distances that form the close-to-square-planar [AgF4] unit are predicted to fall in the 1.98−2.03 Å range (average value ∼2.00 Å), while the remaining six Ag···F distances are calculated to be considerably longer (2.28−2.47 Å; average value ∼2.37 Å). The difference between the two average values equals 0.37 Å and thus exceeds 18% of the smaller value. Although this value is much larger than the Jahn−Teller distortion typical for most copper(II) compounds,49 a recent study reports that in CuF2, a copper analogue of AgF2, the Jahn−Teller distortion is equal to 21%, and in certain copper(II) fluorides, it can even reach 23%.50 The extent of the Jahn−Teller effect in HP AgF2 and CuF2 is therefore comparable. It seems that the Jahn−Teller effect should persist to quite high pressures for silver(II) difluoride with all consequences for the crystal, electronic, and magnetic structures of this compound. Will AgF 2 Transform to a Genuine Cotunnite Structure under Further Compression? In view of all similarities discussed above, the question naturally arises as to whether AgF2 can adopt the genuine cotunnite structure at even higher pressures than those reached in current experiments. While one must await a firm answer to this question to be provided by new experiments, theoretical considerations may already be presented. In fact, we have found out that a cotunnite form may be derived from the lattice dynamics of the AgF2 HP-I structure. Apart from the imaginary mode that led us to the HP-II form, the phonon dispersion curves of the HP-I structure show a characteristic softening of yet another mode at the S (0.5, 0.5, 0.0) point of the first Brillouin zone (Figure 5). This mode leads to a hypothetical monoclinic form AgF2 of P21 symmetry and Z = 8 that under optimization converges to the cotunnitetype structure (Figure 12, bottom right). The monoclinic P21 unit cell is doubled along the b direction with respect to the cotunnite Pnma one and as such accommodates AFM AgF2 chains that form along this direction. They consist of edgeshared [AgF4] units, where the AgII cations are in deformed square-planar coordination reminiscent of the AgF2 HP-I and HP-II forms. The same chains can be distinguished in the cotunnite PbCl2 structure along the b axis when selected Pb··· Cl contacts are drawn (Figure 12). The AFM interactions thus break the cotunnite Pnma symmetry to a monoclinic one. However, the crystallographic symmetry remains orthorhombic Pnma. The HP-II and cotunnite-type AgF2 structures become nearly degenerate in volume and enthalpy at 50 GPa, and this degeneracy continues to ∼70 GPa (the highest pressure point in our enthalpy calculations; cf. section S4 in the SI). In conclusion, the HP-II structure turns out to be an alternative to the cotunnite structure type for AgF2 with its Jahn−Telleractive AgII cation at a quite broad pressure range (14−70 GPa). Anti-Ni2In Type: The Ultimate Destiny of AgF2 at High Pressure? The previous research on certain metal difluorides has testified to the fact that the hexagonal anti-Ni2In polytype is better packed even than the cotunnite form, and as such, it

Figure 12. Theoretical 2 × 1 × 1 cotunnite-type AFM AgF2 supercell (bottom) obtained from a soft mode S in the AgF2 HP-I structure (see Figure 4). The cotunnite PbCl2 form (top) is visualized with selected Pb···Cl contacts for a better comparison. Crystal structures highlighting the unit cells and a fragment of the infinite MX2 chains are shown. Big balls are cations (Pb, dark gray; Ag, light gray and black), and small balls are anions (Cl, green; F, blue).

constitutes an ultimate high-pressure polytype of MF 2 systems.23,24,51 Our DFT calculations show that the HP-II structure is dynamically stable up to at least 200 GPa (cf. the SI for phonon dispersion), but the structure progressively approaches that of the anti-Ni2In polytype (Figure 13 and cf. section S9 in the SI for the theoretical cif file). This, together with what has been discussed above, suggests that the pressureinduced phase transitions of AgF2 might fall within the general scheme known for the other metal difluorides, with the (distorted) fluorite → (distorted) cotunnite → (distorted) Ni2In transitions progressively taking place. This hypothesis remains to be verified by experiment at much larger pressures than those reached in experiments reported here.

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CONCLUSIONS We were able to identify and characterize two new polymorphs of AgF2, which arise during compression in the range up to 40 GPa. Using phonon dispersion calculations to look for HP structures (as has been previously done in the case of AgO52), we found the HP-I and HP-II structures that match the experimental data very well. These two polymorphs do not, at first glance, resemble any of the typical systems of other MF2 compounds, which adopt (in the order of increased packing) rutile, fluorite, cotunnite, or Ni2In structures (or a slight modification thereof). However, we were able to demonstrate that all three structures of AgF2 do, in fact, arise from the wellknown fluorite and cotunnite structures via deformations of the anionic sublattice due to the Jahn−Teller effect, which is very pronounced in compounds of AgII. Specifically, it can be shown that the HP-I-to-HP-II transition is analogous (from the point of view of the cationic sublattice) to the transition from fluorite to cotunnite found in many other difluorides.10,12,17,23 Because AgII is a paramagnetic spin-1/2 cation, the electronic and magnetic properties of various polymorphs of AgF228 at increasing confinement are of immediate interest. The HP-I (Pca21) polymorph is a result of only a slight distortion of the ambient-pressure structure, but this distortion can have farreaching consequences for the electric and magnetic properties of AgF2. Importantly, it lacks an inversion center, which renders it an attractive candidate for a multiferroic material. Moreover, the lack of planarity of [AgF4] seen in the HP-I and HP-II 14659


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Figure 13. Projection of the theoretical unit cell for cotunnite (left), AgF2 in the HP-II structure at three different pressure values (middle), and antiNi2In (right), showing the similarities and differences between them (Pb and In, black; Cl and Ni, green; Ag, gray; F, blue).

(ARRS) for support within the research programme P1-0045 Inorganic Chemistry and Technology. The quantum-mechanical calculations were carried out using ICM supercomputers (ADVANCE-PLUS and GA67-13). Portions of this work were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), APS, ANL. GeoSoilEnviroCARS is supported by the National Science Foundation (NSF), Earth Sciences (Grant EAR-1128799), and Department of Energy, GeoSciences (Grant DE-FG02-94ER14466). This research used resources of the APS, a U.S. Department of Energy (DOE) Office of Science User Facility, operated for the DOE Office of Science by ANL under Contract DE-AC02-06CH11357. Portions of this work were performed at HPCAT (Sector 16), APS, ANL. HPCAT operations are supported by DOE-NNSA under Award DE-NA0001974, with partial instrumentation funding by the NSF.

forms should destroy the annihilation of the orbital angular momentum (typical of the LP form) and may lead to substantial spin−orbit coupling and concomitant complex magnetic properties. Our preliminary theoretical calculations suggest that, in contrast to the previous suggestions,27 AgF2 cannot be metallized at pressures as low as 40 GPa, and its fundamental band gap should be on the order of 1.4 eV and quite pressure independent (see the SI). Because fluoroargentates are considered to be good candidates for the precursors of superconducting materials,53 the electronic and magnetic properties of various forms of AgF2 will be carefully scrutinized in a separate contribution.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02528. EoS of AgF, Rietveld fits to the collected powder XRD patterns for characteristic pressure points, lattice constants of AgF2 at different pressures obtained from XRD experiments, theoretical enthalpies of the relevant structures, the closest F···F contacts in the observed crystal structures, Raman spectroscopy of AgF and AgF2, electronic band gap at the Fermi level (theoretical PBEsol+U data), and analysis of phonons of the HP-II phase (PDF)

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DEDICATION This work is dedicated to Prof. Neil W. Ashcroft on his birthday.

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(1) Bragg, W. L. The Analysis of Crystals by the X-Ray Spectrometer. Proc. R. Soc. London, Ser. A 1914, 89, 468−489. (2) Ghalsasi, P.; Ghalsasi, P. S. Single Crystal X-Ray Structure of BeF2: α-Quartz. Inorg. Chem. 2011, 50, 86−89. (3) Rakitin, M. S.; Oganov, A. R.; Niu, H.; Esfahani, M. M. D.; Zhou, X.-F.; Qian, G.-R.; Solozhenko, V. L. A novel phase of beryllium fluoride at high pressure. Phys. Chem. Chem. Phys. 2015, 17, 26283− 26288. (4) Billy, C.; Haendler, H. M. The Crystal Structure of Copper(II) Fluoride. J. Am. Chem. Soc. 1957, 79, 1049−1051. (5) Jack, K. H.; Maitland, R. The Crystal Structure and Interatomic Bonding of Chromous and Chromic Fluorides. Proc. Chem. Soc. 1957, 232. (6) Jesih, A.; Lutar, K.; Ž emva, B.; Bachmann, B.; Becker, S.; Mueller, B. G.; Hoppe, R. Einkristalluntersuchungen an AgF2. Z. Anorg. Allg. Chem. 1990, 588, 77−83. (7) Grochala, W.; Egdell, R. G.; Edwards, P. P.; Mazej, Z.; Ž emva, B. On the Covalency of Silver-Fluorine Bonds in Compounds of silver(I), silver(II) and silver(III). ChemPhysChem 2003, 4, 997−1001. (8) Barreda-Argüeso, J. A.; López-Moreno, S.; Sanz-Ortiz, M. N.; Aguado, F.; Valiente, R.; González, J.; Rodríguez, F.; Romero, A. H.; Muñoz, A.; Nataf, L.; Baudelet, F. Pressure-induced phase-transition sequence in CoF2: An experimental and first-principles study on the crystal, vibrational, and electronic properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 214108. (9) Stavrou, E.; Yao, Y.; Goncharov, A. F.; Konôpková, Z.; Raptis, C. High-pressure structural study of MnF2. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 54101. (10) Morris, E.; Groy, T.; Leinenweber, K. Crystal Structure and Bonding in the High-Pressure Form of Fluorite (CaF2). J. Phys. Chem. Solids 2001, 62, 1117−1122.

Accession Codes

CCDC 1576172−1576179 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.D.). *E-mail: [email protected] (V.V.S.). *E-mail: [email protected] (W.G.). ORCID

Zoran Mazej: 0000-0003-3085-7323 Wojciech Grochala: 0000-0001-7317-5547 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS W.G. thanks the Polish National Science Center (NCN) for funding this work (Project Harmonia “HP” 2012/06/M/ST5/ 00344). Z.M. acknowledges the Slovenian Research Agency 14660


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Inorganic Chemistry

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High-Pressure Behavior of Silver Fluorides up to 40 GPa - Inorganic

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