Oxygen deficient perovskites are investigated as oxygen carriers for many different energy applications, based on the possibility to change their oxygen content while maintaining the cation framework. The most well-known oxygen deficient perovskite type structure is brownmillerite, with alternating layers of octahedra and tetrahedra. However, even for this common structure there are complexities such as ordered rotations of tetrahedra that are often missed during structure determination using, for example, powder diffraction, resulting in the persistent use in literature of inaccurate structure models for DFT calculations and properties explanations. When the extra reflections corresponding to the anion related order are picked up in single crystal neutron or X-ray diffraction, the refinement is often still hindered by high amounts of twinning or correlated disorder. In such cases, TEM can shed a light on the structure, in the past through mostly qualitative techniques like high resolution imaging of the structure and visualization of the reflections using electron diffraction, nowadays also through refinement of the structure from single crystal 3DED data. Electron diffraction is more sensitive to low Z atoms such as oxygen next to heavier atoms than X-rays and can be used on submicron sized crystals; the problems there once were with dynamical scattering are overcome using 3DED [1] combined with dynamical refinement [2]. Using TEM, compounds that were commonly accepted to be brownmillerites were proven to have a completely different anion deficient perovskite type structure, for example Pb₂Fe₂O₅ [3] and related compounds, "disordered" brownmillerites like Sr₂Fe₂O₅ [4] and Sr₂Co₂O₅ [5] were shown be ordered, and clear oxygen-vacancy order that escaped characterization with other techniques was found in many oxygen deficient perovskites, such as in LaSrCuO_3.5 [6] and SrMnO_3.5 [7]. So far, such crystal structures were derived in TEM experiments after reduction outside the microscope, however, the results of the first in situ 3DED redox experiments will also be shown, which allow to follow the structure evolution between oxygen deficient and oxidized perovskite by acquiring in situ 3DED data on submicron sized single crystals in different oxidizing and reducing gasses. In short, I will show that there might be more complexity underlying still many published structures, which we are now better equipped to uncover using electron crystallography, no longer only by observing the superstructures but now also by quantifying them, reliably refining the structures and taking control of the oxygen content during the TEM experiments themselves.

[1] Kolb, U., Gorelik, T., Kübel, C., Otten, M.T., Hubert, D. (2007) Ultramicroscopy 107, 507. [2] Palatinus, L., Petříček, V., Antunes Corrêa, C. (2015) Acta Crystallogr., Sect. A: Found. Adv. 71, 235-244 [3] Abakumov, A.M., Hadermann, J., Bals, S., Nikolaev, I.V., Antipov, E.V., Van Tendeloo, G.(2006) Angew. Chemie Int. Ed. English. 45, 6697–6700

[4] D’Hondt, H., Abakumov, A.M., Hadermann, J., Kalyuzhnaya, A.S., Rozova, M.G., Antipov, E.V., Van Tendeloo, G., (2008) Chem. Mater. 20, 7188–7194

[5] Sullivan, E., Hadermann, J., Greaves, C. (2011) J. Solid State Chem. 184, 649–654

[6] Hadermann, J., Pérez, O., Créon, N., Michel, C., Hervieu, M. (2007) J. Mater. Chem. 17, 2344

[7] Gillie, L.J., Wright, A.J., Hadermann, J., Van Tendeloo, G., Greaves, C. (2002) J. Solid State Chem. 167, 145–151

Ferroelectric perovskite oxides have recently been used in solar applications because their polarity allows for the separation of photocarriers when under illumination to generate a photocurrent. Oxides, however, often have band gaps that are beyond the solar-optimal regime (>3.3 eV); for this reason, perovskite-structured chalcogenides have been proposed as suitable candidate materials owing to their lower band gaps (≈ 2 eV). An understanding of the thermal expansion behavior of photovoltaic materials is important so as to prevent large stresses and strains during fabrication and operation of the photovoltaic device. Here, we evaluate the structural, lattice dynamical, and thermodynamic properties of Ruddlesden-Popper chalcogenide Ba_n+1Zr_nS_3n+1 (n=1,2,3, ∞) using the self-consistent quasi-harmonic approximation within density functional theory. These responses are compared to the thermal expansion of Ruddlesden-Popper oxides and recent experimental data, which allows us to suggest guidelines for engineering thermal expansion in the Ruddlesden-Popper structure type with diverse chemistries.

This work was supported by the National Science Foundation’s MRSEC program (DMR-1720139.) at the Materials Research Center of Northwestern University.

Octahedral tilting is integral to the structure and functionality of perovskites: tilt distortions influence the electronic and magnetic properties [1] and reduce the macroscopic symmetry, as rationalised by group theory [2]. Since tilts are driven by the relative sizes of the metal ions, compositional modification can allow for the control of tilt patterns to achieve desired functionality, such as multiferroicity [3]. A class of materials closely related to perovskites are the Prussian blue analogues (PBAs), where cyanide anions replace the oxides to give the formula A_xM[Mʹ(CN)₆]_1−y□_y⋅nH₂O (A is an alkali metal, M and Mʹ are transition metals and □ denotes a vacancy). Like double perovskites, the parent structure (aristotype) adopts the space group Fmm, although ordered A-site cations (x > 1) or vacancies (y > 1) may reduce the symmetry to F3m or Pmm.

Due to the similarity to perovskites, octahedral tilting also features in PBAs and can have a strong impact on the functional response. To illustrate, the tilts in Na₂MnMn(CN)₆ nearly triples the magnetic ordering temperature compared to the cubic Cs₂MnMn(CN)₆ [4]. However, the tilting in PBAs is poorly understood, which is evidenced by considerable confusion in the literature. A systematic understanding of the factors underlying octahedral tilting in PBAs would be highly beneficial and facilitate tilt engineering approaches.

Here, density functional theory (DFT) calculations and literature surveys are used to identify and rationalise the trends in octahedral tilting for PBAs. A high concentration of A-site cations is a prerequisite for tilting and PBAs with x < 1 are almost invariably cubic, even upon cooling. Moreover, the A-site cation radius dictates the particular tilt pattern [Fig. 1], in line with the behaviour of perovskites. Mʹ(CN)₆ vacancies—which have no analogue in oxide perovskites—do not appear to play a major role, but the presence of interstitial water dictates which tilt pattern that appears in response to external or chemical pressure. Functional implications of the tilts include the tilt-driven improper ferroelectricity in the high-pressure Pn phase of RbMnCo(CN)₆ [5], or the undesirable tilt transition upon Na intercalation in cathode materials based on PBAs [6]. More generally, our results help develop a unified picture of the structural behaviour of PBAs and also improve the understanding of tilting distortions in general.

[1] Bull, C. L., & McMillan, P. F. (2004). J. Solid State Chem., 177, 2323.[2] Howard, C. J., Kennedy, B. J., & Woodward, P. M. (1999). Acta Cryst. B, 59, 463. [3] Pitcher, M. J., Mandal, P., Dyer, M. S., Alaria, J., Borisov, P., Niu, H., Claridge, J. B. & Rosseinsky, M. J. (2015). Science, 347, 420.

[4] Kareis, C. M., Lapidus, S. H., Her, J.-H., Stephens, P. W., & Miller, J. S. (2012). J. Am. Chem. Soc., 134, 2246.

[5] Boström, H. L. B., Collings, I. E., Daisenberger, D., Ridley, C. J., Funnell, N. P., & Cairns, A. B. (2021). J. Am. Chem. Soc., 143, 3544.

[6] Asakura, D., Okubo, M., Mizuno, Y., Kudo, T., Zhou, H., Ikedo, K., Mizokawa, T., Okazawa, A., & Kojima, N. (2012). J. Phys. Chem. C, 116, 8364.

Study of pressure induced structural phase transitions in perovskites has received considerable attention as it can tune many physical properties like band gap, resistivity, piezoelectric coefficients and ferroelectric polarization, etc. PbTiO₃ (PT) is one such model compound whose high pressure behaviour has been a topic of extensive research in recent years because of its technological importance as the end member of the commercial piezoelectric solid solution compositions in the electronics industry [1]. However, the structural phase transition sequence of PT at high pressures has remained very controversial with two entirely different propositions. As per the first principles calculations of Wu & Cohen [2] and subsequent experimental studies [3], pressure can induce polarization rotation due to a tetragonal to monoclinic phase transition much in the same way as the composition does in the morphotropic phase boundary (MPB) based commercial piezoelectric solid solution systems. First principles calculations and experimental studies by Kornev and his co-workers [4], on the other hand, present a completely different picture whereby PT undergoes a pressure induced antiferrodistortive (AFD) structural phase transition, albeit with decreasing tetragonality, until a ‘pseudo-cubic’ like non-ferroelectric phase appears which is followed by the emergence of a reentrant ferroelectric phase at still higher pressures. However, the evidence for AFD superlattice reflections were not observed at moderate pressures predicted theoretically [4]. Recently, we have addressed these controversies by carrying out a careful study of high pressure structural phase transitions in a tetragonal composition of PbTiO₃ solid solution containing 50% BiFeO₃ (PT-0.5BF) using synchrotron x-ray diffraction measurements at P02.2 Extreme Conditions Beamline of PETRA III at DESY. A tetragonal composition in the solid solution of PbTiO₃ with BiFeO₃ was chosen to enhance the AFD instability and hence the intensity of the superlattice peaks [5]. Our results [5] show that even at moderate pressures (~2.15 GPa), the tetragonal P4mm phase of PT-0.5BF system transforms to a monoclinic phase in the Cc space group, which permits MPB type rotation of ferroelectric polarization vector as well as oxygen octahedral tilting induced by a concomitant AFD transition (see Fig. 1). The transition pressure is very close to the theoretically predicted moderate pressure values for pure PT [4]. Our results also show that with increasing pressure, the ferroelectric distortion decreases and the structure acquires a pseudo-cubic character at intermediate pressures, as expected on the basis of Samara’s criterion [6] (see Fig. 2). But interestingly, our studies reveal that the ferroelectric distortion starts increasing above a critical pressure (~7 GPa) due to the emergence of a reentrant ferroelectric phase through an isostructural phase transition in which the oxygen octahedral tilting provides an efficient mechanism for volume reduction. Our results show that the DFT based theoretical predictions of both the groups [2,4] are correct in parts but none of the two provides the complete picture. Our results not only resolve the existing controversies but also provide an insight towards designing of new environmentally friendly Pb-free piezoelectric compositions.

Metal halide perovskites (MHPs) has shown impressive results in solar cells, light emitting devices, and scintillator applications, but its complex crystal structure is only partially understood and many open questions are still to be answered [1]. In particular, a method to image the dynamics of the nanoscale ferroelastic domains in MHPs requires a challenging combination of high spatial resolution and long penetration depth. With the recent development in X-ray optics it is now possible to focus X-rays down to the nanoscale. Combining the traditional high sensitivity to lattice spacing and tilt, as well as its characteristic to probe deep into the sample, nanofocused scanning X-ray diffraction is a unique powerful technique on the study of MHPs domain dynamics [2].

In this work, we demonstrate in situ temperature-dependent imaging of ferroelastic domains in a single nanowire of metal halide perovskite, CsPbBr₃, using scanning X-ray diffraction with a 60 nm beam [3] to retrieve local structural properties for temperatures up to 140 °C [4]. We observed a single Bragg peak at room temperature, but at 80 °C, four new Bragg peaks appeared, originating in different real-space domains, as depicted in Fig. 1 (left panels). The originally random domains were arranged in periodic stripes in the center and with a hatched pattern close to the edges, as one can see in Fig. 1 (right panels). Reciprocal space mapping at 80 °C was used to quantify the local strain and lattice tilts, revealing the ferroelastic nature of the domains. The domains display a partial stability to further temperature changes. Our results show the dynamics of nanoscale ferroelastic domain formation within a single-crystal perovskite nanostructure, which is important both for the fundamental understanding of these materials and for the development of perovskite-based devices.

[1] Zhang, W.; Eperon, G. E.; Snaith, H. J. (2016). Nature Energy 1 (6), 16048. DOI: 10.1038/NENERGY.2016.48 [2] Chayanun, L.; Hammarberg, S.; Dierks, H.; Otnes, G.; Bjorling, A.; Borgstrom, M. T.; Wallentin, J. (2019). Crystals 9 (8), 432. DOI: 10.3390/cryst9080432 [3] Bjorling, A.; Kalbfleisch, S.; Kahnt, M.; Sala, S.; Parfeniukas, K.; Vogt, U.; Carbone, G.; Johansson, U. (2020). Opt. Express 28 (4), 5069. DOI: 10.1364/OE.386068 [4] Marçal, L. A. B.; Oksenberg, E.; Dzhigaev, D.; Hammarberg, S.; Rothman, A.; Björling, A.; Unger, E.; Mikkelsen, A; Joselevich, E; Wallentin, J. (2020). ACS Nano 14, 15973. DOI: 10.1021/acsnano.0c07426

Antiferroelectric perovskites form an important family of functional electric materials, which have high potential in energy storage and conversion applications. However, a full understanding of their crystal structural formation is still lacking. PbZrO₃-based materials can serve as a model system for investigation, not only because PbZrO₃ was the first discovered antiferroelectric, but also because it undergoes a typical phase transition sequence from a high-temperature paraelectric to the low-temperature antiferroelectric phase, passing through a possible intermediate (IM) phase that is poorly understood. The IM phases usually exist only in a narrow temperature interval in pure PbZrO₃, and therefore it is hard to capture them. On the other hand, with a small amount of Ti substitution, the Zr-rich PbZr_1-xTi_xO₃ (PZT, x ≤ 0.06) also displays a room-temperature antiferroelectric structure and goes through the same phase transition process as PbZrO₃. In this case, the temperature range of the IM phase becomes wider, which makes a detailed study of the IM structures possible.

Here we employ a combination of optical and scattering experiments and theoretical calculations to reveal the nature of the intermediate state. Experimental results show that the IM phase is not a pure phase but a state containing a mixture of several short- and long-range correlated structural components that compete energetically in a complicated way. To emphasize this, we shall henceforth refer to it as the IM state rather than the IM phase. There are several types of superstructure reflections that appear in the IM state temperature range in the single-crystal diffuse scattering pattern (Fig. 1). With the aid of synchrotron powder total scattering and high-resolution neutron diffraction data analysis, we constructed the complex structural models in this temperature range [1]. Evidence is found that this peculiar state consists of multiple short-range and long-range structural components, as well as complex mesoscopic domain structure [2]. External stimuli such as temperature change or chemical substitution can easily alter each component’s energy landscape and thereby change the materials' electrical properties. These findings provide new insights in understanding antiferroelectric-ferroelectric competition and hence in designing new antiferroelectric materials.

[1] An, Z., Yokota, H., Zhang, N., Pasciak, M., Fábry, J., Kopecký, M., Kub, J., Zhang, G., Glazer, A. M., Welberry, T. R., Ren, W., & Ye, Z.-G. (2021) Phys. Rev. B 103, 054113.

[2] An, Z., Xie, S., Zhang, N., Zhuang, J., Glazer, A. M., Ren, W., & Ye, Z.-G. (2021) APL Mater. 9, 030702.