Pressure-induced Pb–Pb bonding and phase transition in Pb2SnO4

The structure of Pb2SnO4 is found to strongly distort on compression and a structural phase transition with a change of space group from Pbam to Pnam occurs at ∼11 GPa. Our complementary DFT-based calculations show that at ambient conditions, the channels in the structure host the stereochemically active Pb 6s 2 lone electron pairs which form bonds between the Pb2+ ions with increasing pressure.


Introduction
Lead stannate (Pb 2 SnO 4 ) belongs to a family of stannates with composition M 2 SnO 4 , where M 2+ = Mg, Mn, Ca, Ba, Sr, Pb. Characteristic for these stannates is that the SnO 6 octahedra either form layers by sharing corners in a plane (as in Ba 2 SnO 4 and isostructural Sr 2 SnO 4 ) or chains by sharing edges (as in Ca 2 SnO 4 and Pb 2 SnO 4 ). They represent a fascinating class of compounds and have been studied extensively as they may be suitable for a variety of applications, e.g. as photocatalysts (Qin et al., 2015;Dinesh et al., 2016), as electrode material for Li-ion batteries (Rong et al., 2006;Liang et al., 2016) or as anode-material in solar cells (Tan et al., 2007). Furthermore, stannates doped with rare earth elements, such as Eu, Y, Sm, have been extensively investigated regarding their use as long afterglow phosphors (Chen et al., 2005a,b;Yang et al., 2005;Yamane et al., 2008;Zhang et al., 2010;Stanulis et al., 2014).
Pb 2 SnO 4 has been used since the 14th century as a pigment and was frequently used in oil paintings before 1750. Nowadays the pigment is named lead-tin-yellow type I [see summary by Kü hn (1993)]. Its structure at ambient conditions ( Fig. 1) was first proposed to have tetragonal space group symmetry P4 2 /mbc (Byströ m & Westgren, 1943;Swanson et al., 1972). Later, the structure has been described in the orthorhombic space group Pbam (Gavarri et al., 1981). ISSN 2052-5206 In Pb 2 SnO 4 the edge-sharing SnO 6 -octahedra form chains along the c-direction, interconnected within the (001) planes with Pb 2+ ions. There are channels parallel to the c axis with a diameter of % 3.74 Å (Fig. 1). In Pb 2 SnO 4 the Pb ions form the apex of a trigonal pyramid, i.e. there are only three short Pb-O distances. This points towards the presence of a stereochemically active lone electron pair. In contrast, in Ca 2 SnO 4 , where edge-sharing SnO 6 octahedra also form chains, the Ca ions have seven nearest neighbors forming an irregular polyhedron.
At ambient conditions, the structure of Pb 2 SnO 4 closely resembles that of the mineral minium (Pb 2 PbO 4 ), which crystallizes at ambient conditions in the tetragonal space group P4 2 /mbc. In Pb 2þ 2 Pb 4+ O 4 , the Pb 4+ atoms are octahedrally coordinated. Pb 2 PbO 4 has channels with a diameter of $3.8 Å (Gavarri & Weigel, 1975). Pb 2 PbO 4 undergoes a temperature-induced phase transition below 170 K to space group Pbam (Gavarri et al., 1978), so that Pb 2 SnO 4 and Pb 2 PbO 4 are isostructural at low temperatures, as the former shows no temperature-induced phase transition between 5 K and 300 K (Gavarri et al., 1981). For Pb 2 SnO 4 the deviation from tetragonal symmetry remains small in this temperature range Áab = a À b = 0.0125 (6) Å at 300 K, Áab = 0.0139 (6) Å at 5 K]. Dinnebier et al. (2003) found that Pb 2 PbO 4 undergoes a pressure-induced phase transition from space group P4 2 /mbc at ambient pressure to space group Pbam between 0.11 and 0.3 GPa and a second transition between 5.54 and 6.58 GPa to another orthorhombic phase, also having space group Pbam but with half the length of the c axis. Increasing pressure leads to an anisotropic compression of the a and b axes, with Áab $ 0 Å at ambient conditions to Áab $ 0.9 Å at 0.6 GPa and Áab $ 2.9 Å at 6.7 GPa.
The objective of this study was to characterize pressureinduced changes in structure-property relations of Pb 2 SnO 4 at high pressures, as it was expected that by analogy with Pb 2 PbO 4 the compound would undergo phase transitions and offer insight into the high-pressure behavior of stereochemically active lone electron pairs.
2. Experimental details 2.1. Sample synthesis 2.1.1. Solid-state synthesis. Temperatures between 923 K and 1173 K have been used for the synthesis of Pb 2 SnO 4 powder by solid-state reaction (Gavarri et al., 1981;Hashemi et al., 1992;Clark et al., 1995;Chen et al., 2000;Hradil et al., 2007;Pelosi et al., 2010;Denisov et al., 2012;Agresti et al., 2016). For our experiments we chose a synthesis temperature of 1123 (1) K, in order to avoid the presence of PbSnO 3 which decomposes above 1073 K and to prevent decomposition of Pb 2 SnO 4 which is expected to occur above 1173 K (Xing et al., 2004).
The starting materials were analytical grade and used as purchased: PbO (99.9+% purity, Sigma-Aldrich Chemie, Darmstadt) and SnO 2 (99.9% purity, Alfa Aesar, Karlsruhe). Starting materials were mixed in stoichiometric proportions and ground in an agate mortar. The resulting mixture was pressed to 5 mm-sized pellets with an Across International Desktop pellet press at a pressure of 6 (1) Kbar. The pellets were placed in corundum crucibles with lids, transferred into a Nabertherm L08/14 muffle furnace, heated up to 1123 (1) K and annealed for 24 h. The samples were cooled down to ambient temperature by switching off the power supply. After the synthesis the pellets were ground again and the synthesis process was repeated two times.
2.1.2. Hydrothermal synthesis. Pb 2 SnO 4 single crystals were hydrothermally grown in autoclaves according to a prescription by Wu et al. (1999), following the reaction  Structure of Pb 2 SnO 4 at ambient conditions from single-crystal structure solution. A 2 Â 2 Â 2 supercell is shown along the c axis. The SnO 6 octahedra are shown in gray. A diagonal (3.74 Å ) and a line between two opposite Pb 2+ ions (4.11 Å ) in one of the channels which run along the c axis.

Sample characterization
2.2.1. X-ray powder diffraction at ambient pressure. The powder samples obtained from solid-state synthesis were characterized with a PANalytical X'Pert Pro powder diffractometer with Bragg-Brentano geometry and a PANalytical PIXcel 3D detector. The diffractometer was equipped with a copper X-ray tube and a Johansson monochromator. The measurements were performed using Cu K1 radiation and 0.25 fixed divergence slits. The samples were measured in the range of 10 < 2 < 90 with a scan speed of 0.036 min À1 . The instrument parameters were refined using a measurement on a high purity (99.999%) Si-standard. Powder samples were mounted on an oriented Si single-crystal sample holder after grinding them in an agate mortar. Crystal structure refinements, based on the Rietveld method (Rietveld, 1969), were carried out using the software package GSAS-II (Toby & Von Dreele, 2013).
2.2.2. X-ray single-crystal diffraction at ambient pressure.
Hydrothermally synthesized crystals were employed for the single-crystal diffraction experiments at ambient conditions. Measurements were carried out on an Oxford Instruments Xcalibur four-circle diffractometer with Kappa geometry and a Sapphire3 charge-coupled-device (CCD) detector. The diffractometer was equipped with a molybdenum X-ray tube and graphite single-crystal monochromator. The samples were measured with Mo K radiation. We measured a full sphere up to a resolution of 0.75 Å À1 and an exposure time of 120 s per frame. The crystals were mounted with Apiezon N grease on the tip of a glass capillary. Crystals of approximate dimensions 80 mm Â 30 mm Â 30 mm were centered in an X-ray beam of diameter 500 mm. The reflections were indexed and integrated using the CrysAlisPRO (v. 39.46) program (Agilent, 2014). The structure solution was performed with SUPERFLIP (Palatinus & Chapuis, 2007) and the refinement with the software package JANA2006 (Petricek et al., 2014).
2.2.3. High-pressure experiments. All high-pressure experiments were carried out using Boehler-Almax-type diamond anvil cells (Boehler, 2006). Depending on the target pressure of the experiments we used culet sizes between 250 mm and 350 mm and tungsten or rhenium as gasket material. Samples were placed in holes in the gasket having diameters between 100 mm and 180 mm. The gaskets were preindented to 40-50 mm and the holes were drilled by a custombuilt laser setup. We used argon below 3 GPa for the powder diffraction and neon for all other experiments as pressuretransmitting media in pressure ranges where they provide a quasi-hydrostatic environment (Klotz et al., 2009). Pressure was determined by measuring the ruby fluorescence shift. We assume an error of 2% for the pressure determination in the quasi-hydrostatic conditions present in our experiments (Dewaele et al., 2004(Dewaele et al., , 2008. 2.2.4. High-pressure synchrotron X-ray diffraction. Highpressure diffraction data were collected at the synchrotron PETRA III (DESY) in Hamburg, Germany on the extreme conditions beamline P02.2 (Liermann et al., 2015). We used a Perkin Elmer XRD1621 detector and wavelengths of 0.2887 Å and 0.2906 Å for data acquisition. The beam size was 2 mm (H) Â 2 mm (V) (FWHM) obtained using a Kirkpatrick-Baez mirror for the powder diffraction experiments and 9 mm (H) Â 3 mm (V) (FWHM) obtained using compound refractive lenses for the single-crystal diffraction measurements.
The powder samples were measured for 10 s while rotating them around a rotation axis perpendicular to the beam by AE10 to improve the counting statistics. For calibrating the detector parameters and the detector to sample distance we measured a CeO 2 powder standard. We used the program DIOPTAS (Prescher & Prakapenka, 2015) to integrate and calibrate the diffraction patterns.
For single-crystal diffraction the samples were rotated around a rotation axis perpendicular to the beam by AE33 . Frames were collected in 0.5 steps with 0.5 s acquisition time per frame. Pt-filters were used to reduce the primary intensity to prevent oversaturation of the detector. The diffractometer/ detector geometry was calibrated by measuring an enstatite single crystal. Data treatment and crystal structure refinement were performed in a similar manner as for ambient-pressure single-crystal diffraction data.
The lattice parameters from the high-pressure powder diffraction data were obtained applying the Le Bail method (Le Bail et al., 1988), using the software package GSAS-II (Toby & Von Dreele, 2013). The bulk modulus from the highpressure powder data was obtained by using the EoSFit7-GUI software package (Gonzalez-Platas et al., 2016), fitting a second-order Birch-Murnaghan equation of state (EoS) (Murnaghan, 1944;Birch, 1947) to the unit-cell volume.
High-pressure resistance measurements were carried out in diamond anvil cells (Fig. 2) using a mixture of epoxy resin and Al 2 O 3 as pressure-transmitting medium. We assume an error  of the pressure determination due to non-hydrostatic conditions of 6% (Mao et al., 1986). We performed both two-point and four-point measurements using a Keithley DMM7510 multimeter for the data collection as described in Zimmer et al. (2018).
2.2.6. Raman spectroscopy. Raman spectroscopy was carried out with a custom set-up described in detail in Bayarjargal et al. (2018). We used an OXXIUS S.A. Laser-Boxx LMX532 laser ( = 532.14 nm) and a Princeton Instruments ACTON SpectraPro 2300i spectrograph equipped with a Pixis256E CCD camera. All Raman spectra were background corrected with the software package Fityk (Wojdyr, 2010). High-pressure Raman spectroscopy was carried out in diamond anvil cells, similar to the high-pressure synchrotron X-ray diffraction experiments.
2.2.7. Scanning electron microscopy. We used a Phenom World ProX desktop SEM for the acquisition of electron backscatter images (BSE) on single crystals and powder samples. Furthermore, energy-dispersive X-ray spectroscopy (EDX) measurements for a semi-quantitative characterization of the composition were carried out on single crystals and powder samples. The samples were mounted without coating on aluminium stubs using sticky carbon tape. They were measured under low-vacuum conditions to reduce charging effects on the sample with an acceleration voltage of 10 KV for imaging and 15 KV for EDX measurements.

Computational details
First-principles calculations were carried out within the framework of density functional theory (DFT) (Hohenberg & Kohn, 1964), employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation function (Perdew et al., 1996) and the plane wave/pseudopotential approach implemented in the CASTEP (Clark et al., 2005) simulation package. 'On the fly' norm-conserving or ultrasoft pseudopotentials generated using the descriptors in the CASTEP data base were employed in conjunction with plane waves up to a kinetic energy cutoff of 990 eV or 630 eV, for norm-conserving and ultrasoft pseudopotentials, respectively. The accuracy of the pseudopotentials is well established (Lejaeghere et al., 2016). A Monkhorst-Pack (Monkhorst & Pack, 1976) grid was used for Brillouin-zone integrations with a distance of < 0.023 Å À1 between grid points. Convergence criteria included an energy change of < 5 Â 10 À6 eV atom À1 for scf-cycles, a maximal force of < 0.008 eVÅ À1 , and a maximal component of the stress tensor < 0.02 GPa. Phonon frequencies were obtained from density functional perturbation theory (DFPT) calculations. Raman intensities were computed using DFPT with the '2n+1' theorem approach (Miwa, 2011) and a scissor operator of 5 eV. It should be stressed that all calculations are carried out in the athermal limit, i.e. the influence of temperature and zero-point motion is not taken into account.

Synthesis
We synthesized Pb 2 SnO 4 powder by solid-state reaction. The powder is slightly yellow at ambient conditions and does not show any distinct growth morphology [ Fig. 3(a)]. From hydrothermal synthesis we obtained crystals with 50-150 mm lengths. Some crystals form aggregates, but many of them show a tetragonal crystal habit and idiomorphic crystal faces [ Fig. 3b]. Most of those crystals are colorless. The morphology of the single crystals is similar to that observed in an earlier study (Wu et al., 1999). The chemical composition obtained from the EDX measurements on the powders and single crystals do not substantially differ from the expected chemical composition (nominal versus EDX in at.%): PbO: 67/70 (4) and SnO 2 : 33/ 30 (3) for the powders from the solid-state reaction and PbO: 67/71 (4) and SnO 2 : 33/29 (3) for the single crystals from the hydrothermal synthesis. Furthermore, no impurities from other elements were observed in the EDX spectra.

Powder diffraction at ambient pressure
No secondary phase was detected by X-ray powder diffraction within the experimental detection limits of $3%. The phase purity of the powder was also confirmed by Rietveld refinement (Fig. 4). The refinement of the powder data can be carried out in two space groups. A refinement in the tetragonal space group P4 2 /mbc (wR = 12.1%) as well as in its orthorhombic subgroup Pbam (wR = 10.7%) with Z = 4 gave a satisfactory fit of the structural model to the diffraction data. Table 1 summarizes the diffraction data for Pb 2 SnO 4 at ambient conditions. The refined crystallographic parameters for both space groups are also in good agreement with earlier studies (Swanson et al., 1972;Gavarri et al., 1981).
The deviation from a tetragonal metric in the orthorhombic refinement [Áab = 0.0095 (3) Å ] is very small and in good agreement with the value obtained by neutron powder diffraction data from Gavarri et al. (1981) [Áab = 0.0125 (6) Å ]. Furthermore, no peak splitting was observed in the diffraction data. The refinement in space group Pbam shows a slightly lower wR value compared to the refinement in space group P4 2 /mbc. This is caused by the higher reflection to parameter ratio (6.5:1 for Pbam in contrast to 4.5:1 for P4 2 /mbc).

Single-crystal diffraction at ambient pressure
The structure solution for Pb 2 SnO 4 by Gavarri et al. (1981) was performed on neutron powder data; here we carried out the first single crystal data collection and structure refinements. High-quality crystals from our hydrothermal synthesis Rietveld refinements on a Pb 2 SnO 4 powder sample from solid-state synthesis at ambient conditions in space group P4 2 /mbc (a) and Pbam (b) using = 1.54056 Å . Reflection positions are indicated by tickmarks and the residuals between measurement and refinement are shown by the blue line. Table 1 Crystallographic data of Pb 2 SnO 4 at ambient conditions obtained by single-crystal structure solution, Rietveld refinement on powder data and DFTbased calculations in comparison to data from Swanson et al. (1972) and Gavarri et al. (1981). are colorless at ambient conditions and suitable for singlecrystal X-ray diffraction. Similar to the results obtained from the powder diffraction data at ambient conditions, the refinement of the single crystal data gives very satisfactory results in two space groups. Both structure refinements in space group P4 2 /mbc (wR = 2.3%) and in space group Pbam (wR = 2.6%) gave convincing structural models (Table 1), which are in good agreement with the results of earlier studies (Swanson et al., 1972;Gavarri et al., 1981). Table 2 summarizes the atomic positions and anisotropic displacement parameters of Pb 2 SnO 4 for the refinements in both space groups.
The anisotropic displacement parameters do not differ substantially between the structure refinements in space group P4 2 /mbc and Pbam. Lowering of the symmetry from P4 2 /mbc to Pbam space group induces a splitting of the Wyckoff positions of the Pb1 and O1 atoms with 8h ! 4g + 4h, but a detailed analysis showed no significant change in interatomic distances between the two refinements.

DFT calculations at ambient pressure
We cross-checked our experimental results with those of DFT-based calculations in both possible space groups for Pb 2 SnO 4 (Tab. 1). Our DFT-based calculations reproduce the experimental diffraction data satisfactorily with an overestimation of the unit-cell lengths by <3% due to the well established 'underbinding' in DFT-GGA-PBE calculations. The DFT calculations carried out here provide structural and physical parameters in the athermal limit. As has been discussed in the introduction, structurally closely related Pb 2 PbO 4 undergoes a tetragonal $ orthorhombic phase transition at 170 K, so it is actually problematic to neglect temperature in DFT studies of this system. The DFT-based calculations gave the same total energy within the numerical accuracy for the orthorhombic and the tetragonal structure. Fig. 5 shows an isosurface of the electron density difference, i.e. shows charge accumulation with respect to the electron density obtained by overlapping non-interacting atomic densities.
Clearly discernible are the stereochemically-active 6s 2 lone electron pairs of the Pb 2+ ions, which appear in electron density difference isosurfaces as umbrella shaped objects (Friedrich et al., 2010). These electron pairs are located in the channels of the structure.

High-pressure single-crystal diffraction
We performed high-pressure single crystal X-ray diffraction measurements on Pb 2 SnO 4 crystals up to 21.0 (4) GPa and solved and refined the crystal structure at numerous pressures (Table 3). From the single crystal data we found that on pressure increase the unit cell of Pb 2 SnO 4 is immediately strained and Áab increases from 0.0025 (4) Å at ambient pressure to its maximum of 2.799 (1) Å at 12.4 (3) GPa. After a pressure increase above $0.5 GPa the structure of Pb 2 SnO 4 cannot be described in space group P4 2 /mbc anymore and only a refinement in space group Pbam is satisfactory. At 7.8 (2) GPa (wR = 14.0%) and 10.0 (2) GPa (wR = 18.5%) the refinements of the structure in the space group Pbam yield increasingly worse reliability factors, but attempts to improve Isosurface of the electron density difference at 0.03 e Å À1 . Sn atoms, oxygen atoms and lead atoms are represented by violet, red and gray spheres, respectively. The yellow circle highlights a channel running parallel to [001], which hosts the 6s 2 stereochemically active lone electron pairs of the Pb 2+ ions, which appear as umbrella shaped surfaces. Table 2 Atom positions and anisotropic displacement parameters of Pb 2 SnO 4 in space groups P4 2 /mbc and Pbam from single-crystal structure refinement.
Lattice parameters a, b, c in Å and atomic displacement parameters U ij in Å 2 .
Atom Site a b c U eq U 11 U 22 U 33 U 12 U 13 U 23 P4 2 /mbc Pb 8h 0.16055 (5) 0.14197 (5)  the description of the data by changing the structural model to another space group were unsuccessful. On further pressure increase we observed that Pb 2 SnO 4 undergoes a phase transition from the orthorhombic space group Pbam (No. 55) to Pnam (No. 62) between 10 GPa and 12 GPa. At 12.4 (3) GPa (wR = 2.3%), the refinement in the high-pressure space group Pnam is convincing. We chose the unconventional Pnam setting of space group No. 62 in order to facilitate a comparison to the low-pressure structure. A symmetry check with the PLATON package (Spek, 2003) was carried out to confirm the space group symmetry.
After pressure release we measured the same crystal in an opened diamond anvil cell at ambient conditions. The structure refinement shows that the pressure-induced straining of the unit cell and the pressure-induced phase transition is fully reversible on pressure release (Table 3).

High-pressure powder diffraction
The high-pressure X-ray powder data complement the single-crystal data, as they have been measured for pressures up to 50 (1) GPa. We used the results from the single crystal refinement on Pb 2 SnO 4 as starting model for the refinements of the powder diffraction data. Fig. 6 shows a Rietveld refinement of data collected at 12.0 (2) GPa, close to the pressure-induced structural phase transition. The refinement was carried out in space group Pnam. The anisotropic displacement parameters of the oxygen atoms were constrained to be identical and we applied restraints to ensure that the Sn-O bond distances are $2 Å . The high background is caused by diamonds and the pressure transmitting medium. The agreement between the experimental data and the structural model is convincing. The results obtained from  Table 3 Selected crystallographic data of Pb 2 SnO 4 obtained between ambient conditions and 21 GPa by synchrotron-based single-crystal structure refinements.  (6) 6.6337 (6) 6.4498 (9) 6.4046 (6) 6.3282 (6) c (Å ) 6.3048 (2) 6.3047 (2) 6.2893 (7) 6.3250 (7) 6.3553 (2) 6.3808 (2) 6.4096 (2) 6.3727 (2) 6.3110 (2)

Figure 6
Rietveld refinement of Pb 2 SnO 4 at 12.0 (2) GPa in space group Pnam (wR = 2.7%) using = 0.2906 Å . Reflection positions are indicated by tickmarks and the residuals between measurement and refinement are shown by the blue line. Diamond and neon reflections were masked before data integration.

Figure 7
Pressure-dependent behavior of the Pb 2 SnO 4 lattice parameters, from single-crystal diffraction (blue), powder diffraction (red) and DFT calculations (black). The lattice parameter a is shown with black squares, b with filled circles and c with red diamonds.
the refinements of the powder data are in good agreement with the single crystal data collected up to 21 GPa. Fig. 7 shows the behavior of the Pb 2 SnO 4 lattice parameters between ambient conditions and 30 GPa from single crystal and powder diffraction data in comparison to DFT-based calculations. Based on the single crystal and powder diffraction data we observed that the pressure dependence of the unit-cell parameters are very different up to pressures of $12 GPa. In this pressure regime, the a axis expands on pressure increase, the b axis shrinks, and the c axis remains essentially unchanged. This observation is supported by the DFT-based calculations. The pressure-dependence of the Pb-Pb and Sn-O distances in Pb 2 SnO 4 are shown in Fig. 9. We observed that the SnO 6 octahedra behave as quasi-rigid units in the crystal structure. The Sn-O bond lengths in the SnO 6 octahedra remains approximately constant ($2 Å ) and are only slightly decreasing with increasing pressure. At ambient conditions the SnO 6 octahedra have a volume of V SnO 6 = 11.9 Å 3 which is decreasing to V SnO 6 = 11.1 Å 3 at 21.0 (4) GPa. The distance between the opposite Pb 2+ ions, forming the channels at ambient conditions (Fig. 1), is decreasing by 1 Å with increasing pressure from $4.1 Å at ambient conditions to $3.1 Å at 12.4 (3) GPa. After the phase transition the Pb-Pb distance is almost independent of pressure.

Description of the high-pressure crystal structure
The experimental finding of a phase transition was also supported by DFT-based calculations. The calculations imply, based on the enthalpy difference ÁH ¼ H Pbam À H Pnam , that the phase transition from space group Pbam to Pnam occurs just below 10 GPa. The experimentally determined transition pressure and the results from the DFT-based calculations are therefore in good agreement.
The DFT calculations show a rather peculiar behavior of the stereochemically active lone electron pairs. While it is well established that such lone electron pairs may persist at high pressures [e.g. Friedrich et al. (2010)] Fig. 10 shows that in Pb 2 SnO 4 the lone electron pairs overlap on increasing pressure, i.e. there is bond formation along the Pb-Pb contacts both within the (001) planes and along the c direction.   Pb-Pb and Sn-O distances with increasing pressure from single-crystal diffraction (filled square) and DFT-based calculations (filled circle). Lines represent fits to the experimental data points.

Figure 10
Electron density difference maps obtained by DFT calculations of the pressure induced evolution of the stereochemically active lone electron pairs (highlighted by white circles) show that at high pressures there is a charge accumulation along the Pb-Pb contacts, i.e. Pb-Pb bonds have been formed by transferring 6s electrons of a Pb atom into empty 6p orbitals of a Pb atom <3 Å away. 2 Â 2Â 2 supercells are shown along the c axis.
The formation of Pb-Pb bonds has been discussed earlier [see e.g. reviews by Fischer & Power (2010) and Nagase (2013)] in diplumbenes, which have Pb-Pb bonds with bond distances of 2.9-4.1 Å . In the present case, the change in the electron density suggests the formation of dative bonds between the Pb 2+ ions, i.e. bonds due to the interaction of the stereochemically active lone electron pairs of the donor atom with unoccupied orbitals of the acceptor atom. A Mulliken population analysis shows that the Pb 6p orbitals are filled slightly more on bond formation and the bond population between neighboring Pb 2+ ions rises up to 0.28 e Å À3 at 80 GPa.

Bulk modulus of Pb 2 SnO 4
We used the X-ray powder diffraction data to obtain the unit cell volume of Pb 2 SnO 4 from ambient conditions up to 50 (1) GPa (Fig. 11). These data sets were used to compute the values of the bulk modulus K for the low-pressure phase (Pbam) and the high-pressure phase (Pnam). We fitted a second-order Birch-Murnaghan equation of state to unit cell volume data up 10.4 (2) GPa for the low-pressure structure. The ambient-pressure volume V 0 was not refined due to the limited data range for this structure and fixed to the volume obtained from ambient-pressure X-ray diffraction. For the high-pressure phase we fitted a second-order Birch-Murnaghan equation of state to the experimental data between 12.0 (2) GPa and 50 (1) GPa, refining the ambient-pressure volume V 0 also. Table 4 lists the experimental values of K for both phases. The bulk moduli of the ambient-pressure phase [K Pbam = 36 (2) GPa] and the high-pressure phase (K Pnam = 117 (6) GPa) differ significantly. 4.10. Resistance measurements 4.10.1. Calibrating the experimental set-up. We performed electrical resistance measurements as a function of pressure in diamond anvil cells. These measurements were calibrated by measuring pure silicon (99.999% purity, Alfa Aesar). At ambient pressure silicon crystallizes in space group Fd " 3 3m (No. 227) (Cohen & Chelikowsky, 1989). Between 8 GPa and 12.5 GPa silicon undergoes a phase transition into the -Sn structure with space group I4 1 (No. 141) (Garg et al., 2004;Olijnyk et al., 1984;Weinstein & Piermarini, 1975;Hu & Spain, 1986;Gupta & Ruoff, 1980;Hu et al., 1986;Yin & Cohen, 1982;McMahan & Moriarty, 1983;Chang & Cohen, 1985;Mizushima et al., 1994), accompanied by a decrease of the electrical resistance by $10 7 (Garg et al., 2004;Minomura & Drickamer, 1962).
Our measurements from ambient conditions to 21 (1) GPa show a change of the resistance of > 10 6 (Fig. 12). The resistance decreases by 10 4.5 within $2.5 GPa in the region of the phase transition from Si-I to Si-II and we determined a transition pressure of 8.4 (5) GPa. Garg et al. (2004) measured a decrease of the resistance by 10 4.5 within $5 GPa and a transition pressure of 10.2 GPa using mylar embedded Al 2 O 3 as pressure transmitting medium. In comparison to Garg et al. (2004) the phase transition occurs in a much narrower pressure-range in our experiments, but at slightly lower pressures. The transition pressure obtained here is in good agreement with the data from Hu et al. (1986) who found that the phase transition occurs at lower pressures of $8.5 GPa in a nonhydrostatic environment in comparison to a transition pressure of 11.3 (2)-12.5 (2) GPa for quasi-hydrostatic conditions. Gupta & Ruoff (1980)  Pressure dependence of the unit-cell volume of Pb 2 SnO 4 from X-ray powder diffraction data. The second-order Birch-Murnaghan equation of state fitted to the experimental data for the low-pressure phase is shown in blue and for the high-pressure phase in red.

Figure 12
Electrical resistance measurements on Si for calibrating and testing the experimental set-up as function of pressure using the four-point probe method up to 21 (1) GPa in comparison to data of Garg et al. (2004).
phase transition to uniaxial stress and observed a change in the pressure-dependent resistance at 8 GPa by applying uniaxial stress along [111]. In summary, these calibration measurements show that our set-up allows us to accurately measure pressure-induced changes in the resistance but the sample environment is not hydrostatic. 4.10.2. Pressure-dependent resistance of Pb 2 SnO 4 . Pressure increase leads to a significant color change of Pb 2 SnO 4 powder and single crystals. At ambient pressure, the crystals are colorless and the powder is lightly yellow. With increasing pressure the light yellow powder at ambient pressure and the single crystals became yellow ($3 GPa), red ($6 GPa) and brown ($8 GPa). On further pressure increase the sample becomes opaque (Fig. 13). All pressure-induced color changes are fully reversible on pressure release without hysteresis.
The change in color is caused by a change in the absorption of visible light by the sample, indicative of a decrease in the band gap. Electrical resistance measurements were carried out between ambient pressure and 48 (3) GPa using two-point and four-point measurements (Fig. 2). Below 14.2 (9) GPa the electrical resistance was above the detection limit of our experimental set-up (10 Â 10 9 ).
The electrical resistance of Pb 2 SnO 4 decreases by at least six orders of magnitude when the pressure is increased from ambient to $40 GPa (Fig. 14). Due to the limitations of our experimental setup we were not able to determine the resistance of the sample across the structural phase transition. An extrapolation of the resistance to ambient pressure [using f(x) = A 1 Áexp(Àx/f 1 ) + y 0 ] suggests a resistivity > 10 14 m for Pb 2 SnO 4 , similar to insulators such as quartz or corundum. The results from the two-point probes and the four-point probes method are mutually consistent, as it is expected that two-point measurements will yield systematically higher values due to the additional contact resistance of the junction between the sample and the wires.
We calculated the band gap energy E g between 0 and 50 GPa by DFT-based calculations and present it together with the electrical resistance measurement (Fig. 14). The results of these calculations indicate that the band gap is closing between 40 GPa and 50 GPa. However, it is well established that DFT-GGA-PBE calculations underestimate the band gap energy by up to 50% and while the pressuredependence of the experimentally determined electrical resistance and predicted band gap energy is similar, a quantitative evaluation would require more advanced model calculations. The closing of the band gap is also consistent with the observed pressure-induced change in color.

Raman spectroscopy
Raman spectroscopy was performed on powder samples and on a single crystal. Experimentally determined ambientpressure Raman spectra of Pb 2 SnO 4 were satisfactorily reproduced by a theoretical spectrum from DFT-based calculations independent of their synthesis route [ Fig. 15(a)]. The theoretical Raman spectra for structures with space group symmetry of Pbam or P4 2 /mbc are almost identical, therefore both reproduced the experimental data. The experimentally obtained Raman spectra are also in good agreement with the measurements from e.g. Clark et al. (1995) or Pelosi et al. (2010).

Figure 14
Electrical resistance measurements on Pb 2 SnO 4 as function of pressure using the two-point probes and the four-point probes method (black). f(x) shows an exponential fit to the two-point probes measurement. Due to the limitation of the Keithley instrument employed, high resistances could not be observed. The DFT-calculated band gap is shown in red. mental and calculated Raman modes in Pb 2 SnO 4 together with the corresponding assignment to the irreducible representation from DFT-based calculations for Pbam. Fig. 15(b) shows experimental Raman data at 16.0 (3) GPa in comparison to results from DFT-based calculations at 15.2 GPa. The agreement between the peak positions from the experimental data and DFT-based calculations for the high-pressure structure with Pnam space group symmetry is convincing and all experimentally observed Raman peaks can be assigned to their irreducible representations (À Raman = 12 A g + 9 B 1g + 12 B 2g + 9 B 3g ). Table 6 shows the experimental and theoretical Raman data together with the corresponding assignment to the irreducible representation for the highpressure space group Pnam.

Discussion and conclusion
The ambient pressure X-ray diffraction data of Pb 2 SnO 4 can be successfully refined in two space groups (P4 2 /mbc or Pbam) with very similar R values. Neither Raman spectroscopy nor DFT calculations can be used to unambiguously distinguish between the two space groups. While the structure of Pb 2 SnO 4 is undoubtedly very nearly tetragonal, both earlier studies (Gavarri et al., 1981) and the present experiments lead to the conclusion that there is a small deviation from P4 2 /mbc and that hence the space group Pbam is the preferred choice for the structure of Pb 2 SnO 4 at ambient conditions.
The high-pressure X-ray diffraction data and DFT-based calculations show a significant pressure-induced distortion from the quasi-tetragonal metric present at ambient conditions with increasing pressure. Pb 2 SnO 4 with Pbam space group symmetry is stable up to 8-10 GPa, when a structural phase transition to a high-pressure structure with space group symmetry Pnam occurs. The experimentally observed structural phase transition is consistent with the results from the DFT-based calculations and Raman spectroscopic data. We observed no further phase transition of Pb 2 SnO 4 up to 50 GPa.
The pressure-induced structural changes lead to a rearrangement of the Pb ions, while the chains formed by the edgeshared SnO 6 octahedra remain essentially unchanged. The high-pressure phase is stabilized by the formation of Pb-Pb bonds. The presence of the Pb-Pb bonds at high pressures  Table 5 Peak positions (cm À1 ) of selected Raman modes of Pb 2 SnO 4 from experimental data and DFT-based calculations at ambient conditions together with DFT-based mode assignments to irreducible representation.

Figure 15
Ambient-pressure Raman spectra of Pb 2 SnO 4 powder and a single crystal in comparison to results from DFT-based calculations (a) and Experimental Raman spectra of a Pb 2 SnO 4 single crystal at 16.0 (3) GPa in comparison to results from DFT-based calculations at 15.2 GPa carried out in space group Pnam (b). The frequencies of the calculated Raman spectrum were rescaled by 8%.
has been inferred from a Mulliken analysis of the electron density obtained from DFT calculations and from electron density difference maps. Our findings are consistent with earlier results on Pb-Pb bonding based on NMR measurements (Gabuda et al., 1999;Dybowski et al., 2001), in which it was concluded that the Pb 2+ 6p electron is involved. The pressure-induced structural changes are accompanied by changes in the physical properties, such as a dramatic change in color and a large change in the resistivity. The experimentally obtained bulk moduli for the low-and highpressure phase of Pb 2 SnO 4 differ significantly [K Pbam = 36 (2) GPa and K Pnam = 117 (6) GPa]. A similar drastic change in the bulk moduli between the low and high-pressure phase has also been observed for the phase transition from phase II [K phase II = 20.8 (4) GPa] to phase III [K phase III = 98 (3) GPa] in structurally closely related Pb 2 PbO 4 (Dinnebier et al., 2003). The pressure-induced changes in the structural and physical properties are fully reversible on pressure release.
In summary, Pb 2 SnO 4 was shown to display an interesting high pressure behavior which is associated with a change of the properties of the stereochemically active lone electron pairs present at ambient conditions and the formation of Pb-Pb bonds. Studies to further characterize these bonds are currently underway.