The phase transition of Pb8F14I2

Abstract The reversible phase transition of Pb8F14I2 is of continuous type and takes place at about 107 °C as monitored by temperature-dependent single crystal and powder X-ray diffraction measurements, optical microscopy, and differential scanning calorimetry. The low-temperature ferroelastic phase crystallizes in the orthorhombic crystal system (23 °C, Bmmb, Z = 2, a = 6.0699(6) Å, b = 6.0165(6) Å, c = 25.077(2) Å, 1487 structure factors, 41 parameter, R(F 2) = 0.0346, wR(F 2) = 0.0771) and changes its symmetry to the tetragonal crystal system into the high-temperature paraelastic phase (130 °C, I4/mmm, Z = 1, a = 4.2667(12) Å, c = 25.388(7) Å, 430 structure factors, 303 parameter, R(F 2) = 0.0575, wR(F 2) = 0.1564). Group–subgroup relationships between the two structures and a hypothetical intermediate structure are presented. Graphical abstract

The crystal structure of (PbF 2 ) 7 (PbI 2 ) has originally been determined by Aurivillius on the basis of integrated room temperature Weissenberg data in the orthorhombic space group Bmmb (standard setting Cmcm, No. 63) with lattice parameters a = 6.0711(6) Å , b = 6.0198(5) Å , and c = 25.084(2) Å [1]. For that purpose single crystals were originally grown by boiling and recrystallizing a sample with nominal composition of 10PbF 2 ÁPbI 2 in water. The author reported a systematic twinning of the very tiny and thin crystals in the way that the a-and b-axes are interchanged. Due to the method of data collection, the platy crystal form and clearly visible twinning of the investigated single crystal, a straightforward structure refinement was hampered at that time, and the reliability index of 0.109 based on |F| was rather high. However, all atomic positions could be derived, and for Pb and I atoms anisotropic temperature factors were considered in the final model. The nearly equal lengths of the a-and b-axes and an I-centred pseudo-tetragonal subcell make it appear likely that a phase transition from the room-temperature modification (lowtemperature (LT) phase) into a tetragonal high-temperature modification (high-temperature (HT) phase) occurs. Although the author of the original study has theoretically derived an idealized structure model in space group I4/ mmm with the unit cell relations: H8; c ideal. & c LT , neither experimental details regarding a possible phase transition nor structure data of the assumed high-temperature phase were reported at that time or afterwards. Therefore, a more detailed examination of a possible phase transition and a redetermination of the crystal structure of (PbF 2 ) 7 (PbI 2 ) (= Pb 8 F 14 I 2 ) seemed worthwhile.
In this article preparation, ferroelastic behaviour, phase transition and crystal structures of Pb 8 F 14 I 2 at room temperature (LT modification) and at 130°C (HT modification) as well as their relationships are reported.

Phase transition
Examination of Pb 8 F 14 I 2 (LT) single crystals under a microscope in transmitted polarized light revealed clearly visible multiple domains for most of the crystals, in accordance with the observations by Aurivillius [1]. The domain crystals show ferroelastic behaviour [7] and can be partially or completely reorientated by application of stress with a pair of tweezers along the diagonal or parallel to the a-or b-axes (in the setting of space group Bmmb). By heating single crystals in inert silicon oil on a Kofler heating stage, a spontaneous change from a biaxial to an uniaxial crystal system in terms of the change of the birefringence of crystal faces was observed at 107(2)°C, indicating a phase transition from the orthorhombic to the tetragonal crystal system. This process was reversible and showed virtually no hysteresis. The observed transition temperatures are in good agreement with a complementary DSC measurement, with on-set temperatures of 104.6°C (heating; endothermal effect) and 104.0°C (cooling; exothermal effect) (Fig. 1).
The temperature-dependence of the unit cell parameters for the LT-and HT-phases, as evidenced by X-ray diffraction measurements, is given in Fig. 2. The derived transition temperature of the diffraction experiments is somewhat higher (118(8)°C) for this kind of measurement than those from the optical examinations or DSC measurements. This behaviour is ascribed to the more inaccurate temperature measurement during the diffraction studies where the temperature sensing device was displaced a couple of millimetres from the actual sample. Given the different temperature sensing for the three methods, the derived transition temperature from the DSC experiment appears to be that with the highest accuracy.
The evolution of the orthorhombic unit cell parameters a and b (Fig. 2a) reveals a more obvious change of a towards the transition point than that of b. The c unit cell parameter appears not to be directly involved in the transition mechanism (Fig. 2b), with a non-linear behaviour for the temperature-dependence of the LT-phase and a linear behaviour for the HT-phase. The resulting change of the cell volume with temperature is depicted in Fig. 2c. The ratio (ab)/(a ? b), where a and b are the lengths of the orthorhombic unit cell at a given temperature, is a suitable order parameter g for classification of the type (continuous, discontinuous) of the phase transition. The development of the temperature-dependence of g = (ab)/(a ? b) is given in Fig. 2d and indicates a continuous phase transition from orthorhombic to tetragonal symmetry upon heating. This classification is supported by the continuous change of the unit cell volume with temperature close to the transition point and the observation of the very slight hysteresis observed during optical examination of crystals at the Kofler stage in polarized light or in the DSC curve ( Fig. 1) during heating and cooling above and below the transition point.
Above the transition temperature Pb 8 F 14 I 2 is tetragonal, representing the paraelastic phase in space group I4/mmm; below the transition temperature it is orthorhombic, representing the ferroelastic phase in space group Bmmb. There is no direct group-subgroup relation between these two space groups [8,9], because Bmmb (or in its standard setting Cmcm) is not a maximal subgroup but a general subgroup of I4/mmm with Fmmm being the intermediate space group type. The group-subgroup relationships of the paraelastic (HT) and ferroelastic (LT) structures of Pb 8-F 14 I 2 , together with the hypothetical intermediate structure model in Fmmm, are presented in the form of a Bärnighausen family tree [10] in Fig. 3.
The symmetry reduction from I4/mmm to Fmmm is of translationengleiche (t) kind with an index of 2, accompanied by a loss of the fourfold rotation axes present in the higher-symmetry structure. The relationship between the Fmmm structure and Bmmb is of klassengleiche (k) kind with an index of 2 under change of the Bravais centering from F to B. The first translationengleiche transition of index 2 from I4/mmm ? Fmmm is a ferroic transition [11] and explains the presence of two twin domains in the resulting crystals of the LT-Pb 8 F 14 I 2 polymorph.

Structure description: LT-phase
The current structure refinement confirms the original model [1]; however, with increased precision and accuracy. The crystal structure is made up of four-layer ''PbF 2 ''-type blocks consisting of four unique Pb 2? cations. The blocks are stacked along [001] with a mean Pb-F distance of 2.63 Å which is in good agreement with the sum of the ionic radii [12] for Pb 2? and F -(2.60 Å ; weighted according to the different coordination numbers as discussed below). The ''PbF 2 ''-type blocks are separated by interstitial Iions that are located at z & and (Fig. 4, left) with a mean Pb-I distance of 3.70 Å . The ''PbF 2 ''-type blocks contain additional ordered Fions (F1) with one close contact of 2.261(10) Å to Pb2. The latter defines one of the boundaries of the blocks and is additionally bonded to the interstitial Iions. Due to the additional F1 ions, the coordination numbers (CN) of the central Pb 2? cations in each block are increased in comparison with fluorite-type PbF 2 (CN = 8), to  (Table 2) are comparable with those of matlockite-type PbFI [6] or the other structures in the system PbF 2 /PbI 2 [1].

HT-phase
In the structure of the HT-phase (Fig. 4, right) only two unique Pb 2? cations are present; the interstitial F1 atom now shows half-occupancy. The central Pb 2? cation (Pb1) of the ''PbF 2 ''-type block has CN = 11 (tricapped cube) and the terminal Pb 2? cation (Pb2) has CN = 9 (four Iand four Fions plus one capping F -; monocapped square antiprism). In comparison with the structure of the LT-  X-ray diffraction and single crystal structure analysis Polycrystalline samples were characterized by X-ray powder diffraction with CuK a1,2 radiation (k = 1.54060, 1.54439 Å ). At room temperature a Philips X'pert system was used. Temperature-dependent measurements were performed on a Philips PW1012/10 diffractometer equipped with a home-built heat controlling system. Unit cell parameters were refined with the program TOPAS [13].
Single crystal X-ray data were collected on a Bruker APEX II CCD diffractometer with MoK a radiation (k = 0.71079 Å ). For single crystal X-ray measurements at room temperature, optically controlled single domain crystals of Pb 8 F 14 I 2 (RT, 23°C) were fixed with cyanoacrylate adhesive on thin silica glass fibres. For hightemperature measurement of Pb 8 F 14 I 2 (HT, 130°C), a more temperature-resistant two-component adhesive was used. Heating was provided with a gas-flow heater using a stream of nitrogen. Diffraction data for the two measurements were corrected for absorption effects with the program HABITUS [14]. Full-matrix least-squares refinements on F 2 for the two data sets and correction of extinction effects were carried out with the program SHELXL-2014 [15].
For the LT-phase the coordinates of the reported structure model [1] were taken as starting parameters for refinement in the space group Bmmb. The measured crystal was twinned by pseudo-merohedry with a rotation by 90°a long [001] as twin element (refined twin ratio of the twin domains 1:1). For the HT-phase the proposed coordinates of the idealized structure model [1] in the space group I4/ mmm were used. For the two models anisotropic displacement parameters for all atoms were refined.
Details of data collections and structure refinements are listed in Table 1. Selected bond lengths are collated in Table 2. Further details of the crystal structure investigations may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (?49)7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, https://www.fiz-karlsruhe.de/icsd.htm) on quoting the appropriate CSD number listed at the end of Table 1. Drawings of structural details were produced using the program ATOMS [16].