Ferroelectric / ferroelastic / ferroic domains are the volumes of a material where polarization / strain / any other order parameter are uniform. Domain patterns usually appear as a result of a structural phase transition between para and ferro-electric phases, which changes the symmetry (including crystal system and the space group type). Domain patterns play the central role for the materials properties, e.g. domain-wall motion may majorly contribute to the enhancement of piezoelectric effect and dielectric permittivity [1]. The knowledge of key parameters of domain patterns (such as orientation / mobility of domain walls, volume fraction of specific domains) can help to characterize, predict and even tailor the properties of ferroelectric materials.

Domain patterns may be extremely complicated, especially for a low symmetry material. Unfortunately, only a handful of experimental techniques are suitable for characterization of domain patterns directly. None of them are powerful enough to image domains in three-dimensional bulk volumes of a material and fast enough to probe their response to alternating external perturbation (e.g. temperature or electric field). Although, high-resolution X-ray diffraction is clearly capable to fill this gap, it still has to be significantly advanced and improved to be efficient and reliable. The geometry of single crystal X-ray diffraction pattern from a multi-domain crystal is as complex as domain patterns themselves. It might be very hard to recognize and observe individual domains types / domain walls in the bulk, especially in the case of monoclinic symmetry where the number of domains and domain walls between them is very large.

The morphology of domain patterns are governed by the lost symmetry elements and conditions of mechanical compatibility, which were found by Fousek, Vanocek [2] and later by Sapriel [3].

The goal of this work is to re-formulate the conditions of mechanical compatibility in the form that it is suitable for the analysis of split peaks in high-resolution X-ray diffraction. We inspect diffraction from multi-domain ferroelectric crystals accordingly and show the way to assign different peak components to the individual domains.

The experimental part of the work is done at the single crystal four-circle X-ray diffractometer in Tel Aviv University (Tel Aviv, Israel) and Swiss-Norwegian Beamlines at the European Synchrotron (Grenoble, France). We used the methodology outlined in [4] to accumulate three-dimension X-ray diffraction intensity distribution in the reciprocal space around split Bragg reflection diffracted from the domains in BaTiO₃ (BT) and Na_0.5Bi_0.5TiO₃ (NBT). The positions of individual sub-peaks in the reciprocal space can be marked and geometrical parameters of the peak groups (e.g. the inter-peak vectors) can be analyzed.

The theoretical part of this work involved the geometrical analysis of domain walls of different symmetry, where a “wall” is defined as a strain-free planar interface between the arbitrary pair of domains. We developed the algorithm and MATLAB-based computer program which predicts the list of mechanically compatible domains / orientation of the domain walls, angle between polarization vectors (if the direction of polarization vector is known) and the matrix of orientation of one domain relative to another.

Furthermore, we proved (analytically) that every pair of mechanically compatible domains produces a pair of Bragg sub-peaks, separated in the reciprocal space along the direction that is perpendicular to the domain wall. This remarkable result is used to recognize possible pairs of domains in the diffraction pattern directly.

We demonstrate such recognition for the simple case of tetragonal domains in BT crystal and use to investigate the formation of the domains in the course of the phase transition to the lower symmetry monoclinic phases in PZT and NBT.

[1] Damjanovic, D. Reports on Progress in Physics, (1999), 61(9), p. 1267, 1999.

[2] Fousek, J., Vanocek, V. J. Appl. Phys., (1969), 40(135), 135-142.

[3] J. Sapriel, “Domain-wall orientations in ferroelastics”, Physical Review B12, p. 5125, 1975. 1974

[4] Gorfman, S., Choe, H., Zhang, G., Zhang, N., Yokota, H., Glazer, A.M., Xie, Y., Dyadkin, V., Chernyshov, D., Ye Z.-G. J. Appl. Cryst. (2020), 53(4), 1039-1050.

Ferroelectricity for the ferroelectric perovskite oxides (ABO)₃have been investigated for decades [1]. In the ferroelectric BaTiO₃, it is well known that the electronic p-d hybridization between empty d orbitals of titanium and filled 2p orbitals of oxygen causes a large ferroelectric polarization [2]. In contrast, magnetic-ordering-induced ferroelectric materials (multiferroics) have also been extensively investigated since a large nonlinear magnetoelectric effect was found in the perovskite TbMnO₃[3]. In tetragonal perovskite BaMnO₃, it is proposed that a large ferroelectricity is induced by the distortion of the Mn and O ions originating from the p-d hybridization in the paramagnetic phase. Since the magnetic Mn⁴⁺ion contributes to the emergence of the ferroelectricity, a large magnetoelectric effect is expected. Sakai et al. grew the tetragonal perovskite Sr_1/2Ba_1/2MnO₃[4]. A large reduction in the ferroelectric polarization is observed below the magnetic transition temperature. The reduction mechanism of the ferroelectric polarization should be unveiled by dividing the ferroelectric polarization into the respective contributions from the p-d hybridization and that from the magnetic interaction.

Here, we report the atomic displacements in the ferroelectric and multiferroic phases of the tetragonal perovskite Sr_1/2Ba_1/2MnO₃determined by the crystal-structure analyses [5]. Using a first-principles calculation based on accurate crystal-structure parameters, we quantitatively elucidate the suppression mechanism of the ferroelectric polarization in the multiferroic phase. The synchrotron x-ray diffraction experiments were carried out in the ferroelectric (T = 225 K) and multiferroic (T = 50 K) phases of the tetragonal perovskite Sr_1/2Ba_1/2MnO₃. Using the observed diffraction spots, we performed crystal-structure analyses. Comparisons between observed and calculated structure factors are shown in Fig. 1(a, b). Schematic views of the atomic displacements in the ferroelectric and multiferroic phases are shown in Fig. 1(c, d). To understand the effect of the magnetic order on the ferroelectricity in the multiferroic phase, we simulate the ferroelectric polarization in the ground-state G-type antiferromagnetic (G-AFM) structure. In the multiferroic phase, we consider two mechanisms to induce the ferroelectric polarization: hybridization between Mn 3d and apical O2 2p states (P_hyb) and in-plane Mn-O1-Mn magnetic exchange striction (P_extr), as shown in Fig. 1(e). In G-AFM, the magnetic exchange striction prevents the atomic displacement of the side O1 ion, so that total ferroelectric polarization is reduced. We conclude that only positive P_hybcontributes to the large ferroelectric polarization in the paramagnetic phase. In stark contrast, the magnetic exchange striction induces negative P_extr, causing the suppression of the ferroelectric polarization in the multiferroic phase.

[1] M. Dawber, et al., Rev. Mod. Phys. 77, 1083 (2005).
[2] R. E. Cohen, Nature (London) 358, 136 (1992).
[3] T. Kimura, et al., Nature (London) 426, 55 (2003).
[4] H. Sakai, et al., Phys. Rev. Lett. 107, 137601 (2011).
[5] D. Okuyama, et al., Phys. Rev. Research 2, 033038 (2020).

Rare-earth nickelates (RNiO₃) are strongly correlated-electron materials with electronic, structural and magnetic instabilities, including a rare, spontaneous metal to insulator transition (MIT). The origin of the MIT and the correct description of the structural anomalies are source of intensive debate in the scientific community. Here we investigate the gap opening and the simultaneous charge ordering in PrNiO₃ in a temperature range from 1.5 K to 300 K by combining bulk transport and magnetic properties with high-resolution neutron and synchrotron X-ray powder diffraction. The structural information is analysed in terms of symmetry-adapted distortion modes, an unconventional, but illustrative formalism that reveals the existence of sharp anomalies in all mode amplitudes at the MIT[1] and the appearance of new modes below T_MIT. Our analysis also unravels a linear correlation between the breathing-mode amplitude, representing the charge order, and the staggered Ni magnetization below T_MIT, which in this nickelate coincides with the long-range antiferromagnetic ordering of the Ni magnetic moments. We also observe an intriguing anomaly at T ∼60 K (∼0.4×T_MIT), visible in some lattice parameters, mode amplitudes and the electrical resistivity. Possible origins of this anomaly will be discussed, among them the existence of a hidden symmetry in the insulating phase, which could be caused by polar distortions driven by the non-centrosymmetric magnetic order[2].

Materials with perovskite-type structure are well known for undergoing series of phase transitions during temperature or pressure change, wherein the tilt-scheme of the network of corner-connected octahedra typically changes with respect to an untilted cubic parent structure. Rare-earth scandate perovskites (REScO₃, RE = Pr–Dy) defy this trend, as they crystallize at temperatures above 2000 °C [1] in an orthorhombic structure (Pnma) and do not undergo any known phase transitions when cooled to room temperature. Due to their high chemo-physical stability and because their lattice parameters can be tuned by (partly) exchanging the RE [2], they are widely used as substrate materials for epitaxial growth of other perovskites.

The thermoelastic properties of substrates are of great importance as they can be used to estimate interfacial stress that may develop between substrate and thin-film during temperature change. Thus, we used resonant ultrasound spectroscopy and inductive gauge dilatometry to determine the elastic stiffnesses and thermal expansion coefficients of single crystal NdScO₃, SmScO₃, TbScO₃ and DyScO₃ in situ from 103 K to 1673 K [3]. The elastic stiffness coefficients are indicative of high internal consistency, e.g. c₁₁ > c₃₃ > c₂₂ and c₆₆ > c₄₄ > c₅₅ hold for all crystal species at room temperature. With increasing charge density caused by decreasing RE-radius, the crystal species become stiffer. The anisotropy of the elastic behavior approaches tetragonal symmetry with rising temperature, which is probably caused by decreasing structural tilt as the orthorhombic phases approach hypothetical tetragonal phases [3].

The shear resistance c₄₄ has anomalous positive temperature coefficients at low temperatures; the relevant temperature ranges are shifted to lower temperatures with increasing RE-radius (Fig. 1). This resembles the characteristic behavior of the critical parameter of an orthorhombic to monoclinic phase transition involving shear of the (100)-plane. c^[101] and c^[011] are two effective resistances of plane waves propagating parallel [101] and [011] with respective displacement vectors subparallel [-101] and [0-11] that have positive temperature coefficients at low temperatures in the case of TbScO₃ (Fig. 1). This is indicative of at least one additional competing structural instability for TbScO₃ which may activate a phase transition involving shear of the (120)-plane. Only magnetic phase transitions at very low temperatures are known for these REScO₃, so increasing pressures may be required to activate phase transitions associated with these instabilities [3].

[1] Christen, H. M., Jellison, G. E., Ohkubo, I., Huang, S., Reeves, M. E., Cicerrella, E., Freeouf, J. L., Jia, X. & Schlom, D. G. (2006). Appl. Phys. Lett. 88, 262906.

[2] Uecker, R., Klimm, D., Bertram, R., Bernhagen, M., Schulze-Jonack, I., Brützam, M., Kwasniewski, A., Gesing, T. M. & Schlom, D. G. (2013). Acta Phys. Pol. A 124, 295.

[3] Hirschle, C., Schreuer, J., Ganschow, S., & Schulze-Jonack, I. (2019). J. Appl. Phys. 126, 165103.

Hybrid halide perovskites are currently at the forefront of energy materials research for their appealing optical and electronic features, but applications in working devices are still hindered by chemical/structural stability. To enhance their properties, new hybrid compounds with a wide range of different organic cations have been proposed in the last years. The choice of bulky organic cations can reduce the dimensionality of the inorganic scaffold from 2D to 0D. These lower-dimensional perovskites, best defined as pseudo-perovskites, feature useful structural flexibility that can be further exploited to enhance the materials properties. We present here monodimensional hybrid iodide pseudo-perovskites, with Pb²⁺ and Bi³⁺ as B site cations, and (CH₃)₃SO⁺ (TMSO) in the A site. The Pb or Bi end members are isomorphic, and crystallize in the Pnma space group with wires of [BX₆] octahedra along the a direction. As shown in the figure, the chains are continuous for the Pb sample, or interrupted, for the Bi sample, with a B-site vacancy every third site to maintain charge balance. We prepared doped samples with general formula ((TMSO)₃Pb_3xBi_2(1-x)I₉ with complete miscibility between (0≤x≤1) ^[1]. In the a direction, the structure is especially sensitive to Bi and cation vacancy (whose stoichiometry is (1-x) in the formula above) content. Interestingly, the XRD patterns of the samples with high Bi content (e.g. x=0.33) feature a peculiar broadening of hkl peaks having h ¹ 0, while 0kl peaks remain sharp (Figure 1). This broadening points out to a short-range order in the sequence of Pb-Bi-vacancy of the doped structure chains that can be successfully modeled using a stochastic matrix approach to model the Pb/Bi/V probability sequences and reconstruct the experimental XRD traces. The influence of bismuth doping on the optical properties is also significant: even a few % loading of bismuth lowers the band gap by about 0.5 eV. Further characterization using X-ray spectroscopies (X-ray Raman scattering, XANES) to correlate the local electronic states to Bi content is underway. This work is a first insight into the effect of inorganic cation doping on short-range order and electronic properties of a 1D hybrid pseudo perovskite structure.

[1] C. Pipitone, F. Giannici, A. Martorana, S. Carlotto, M. Casarin, G. Garcìa-Espejo, A. Guagliardi, N. Masciocchi, J. Phys. Chem. C, in press.

This Stoichiometric rare earth nickelates (RNiO₃) are a textbook example of strongly correlated electron materials, which provide a notable opportunity to study the interplay between, lattice, charge, and spin degrees of freedom. Their most remarkable characteristic is the presence of spontaneous, temperature-driven metal-to-insulator transitions (MITs) at temperatures T_MIT that increase for smaller R ionic radii [1]. Since this happens in absence of Ni mixed valence or chemical disorder, nickelates are perfect, extremely clean model systems for the investigation of the boundary between localized and itinerant behaviour in theoretical studies. Although the existence of the MIT in RNiO₃ has been known since 1991 [2], the mechanism(s) at the origin of the spontaneous electronic localization is still the subject of lively debate. In particular, it is unclear how electronic correlations, lattice, and magnetic degrees of freedom interact and lead to the gap opening. Moreover, other interesting phenomena such as an unusual non-centrosymmetric antiferromagnetic ordering [3], superconductivity [4, 5] or multiferroelectricity [6, 7] have been either observed or theoretically predicted.

An important drawback for the advancement in the comprehension of the complex nickelate physics has been the limited amount of experimental information, needed to validate theoretical predictions. The reason behind is their challenging chemistry, which requires the use of high oxygen pressure and high temperature during synthesis. These extreme conditions, has prevented to date the growth of sizable bulk single crystals with R ≠ La, Pr and Nd. Here we present the first successful growth of RNiO₃ single crystals with R = Nd, Sm, Gd, Dy, Y, Ho, Er, and Lu with sizes up to ~100 μm, achieved by applying the solvothermal method in temperature gradient under 2000 bar oxygen pressure [8]. We also report a detailed structural and physical property characterization illustrating the excellent quality of the obtained bulk RNiO₃ crystals, long time considered impossible to growth.

[1] Gawryluk, D. J. Klein, Y. M. Shang, T. Sheptyakov, D. Keller, L. Casati, N. Lacorre, Ph. Fernández-Díaz, M. T. Rodríguez-Carvajal, J. Medarde, M. (2019). Phys. Rev. B 100, 205137.

[2] Lacorre, Ph. Torrance, J.B. Pannetier, J. Nazzal, A.I. Wang, P.W. Huang T.C. (1991). J. Solid State Chem. 91, 225.

[3] Alonso, J. A. García-Muñoz, J. L. Fernández-Díaz, M. T. Aranda, M. A. G. Martínez-Lope, M. J. Casais, M. T. (1999). Phys. Rev. Lett. 82, 3871.

[4] Chaloupka, J. Khaliullin, G. (2008). Phys. Rev. Lett. 100, 016404.

[5] Li, D. Lee, K. Wang, B. Y. Osada, M. Crossley, S. Lee, H. R. Cui, Y. Hikita, Y. Hwang, H. Y. (2019). Nature 572, 624.

[6] Giovannetti, G. Kumar, S. Khomskii, D. Picozzi, S. van den Brink, J. (2009). Phys. Rev. Lett. 103, 156401.

[7] Perez-Mato, J. M. Gallego, S. V. Elcoro, L. Tasci, E Aroyo, M. I. (2016). J. Phys.: Condens. Matter 28 286001.

[8] Klein, Y. M. Kozłowski, M. Linden, A. Lacorre, Ph. Medarde, M. Gawryluk D. J. (unpublished). arXiv:2104.09873.

Three-dimensional (3D) hybrid perovskites of Pb²⁺ halides have recently gained significant interest due to their use as sensitisers in perovskite solar cells [1]. However, the toxicity of Pb²⁺ has required researchers to look for an alternative to Pb²⁺ containing perovskites. Organic-inorganic (O-I) hybrid Cu²⁺ perovskites containing methylammoniumcations and Cl^- or Br^- halide anion have been studied, as an alternative to Pb²⁺halide perovskites for solar cell applications [2]. Hybrid perovskites of Cu²⁺ halides typically form two-dimensional (2D) layered perovskite structures, even with smaller cations like methylammonium, resulting in band gaps too large for solar cell applications [3]. Despite their large band-gap and low power conversion efficiency, recent studies have shown an improvement in performance of perhalocuprate(II) perovskites, creating opportunity for further research[3]. The 2D hybrid perovskites of Cu²⁺ are of interest as they are low-dimensional magnetic systems and can be used as models for high temperature superconductors [4]. The Cu²⁺ ion is a S = ½ ion, with quenched orbital angular momentum, simplifying the system magnetically, and is typically described by the S = ½ Heisenberg Hamiltonian.

The crystal structures, magnetic properties and magneto-structural correlations of eleven novel bis-(n- carboxyalkylammonium) tetrahalidecuprate(II) compounds, of the forumula ⁺(NH₃(CH₂)_nCOOH)₂[CuX₄]^2- are presented, with n = 2, 3, 4, 5 and 10 and X = Cl^- or Br^-. Thermotropic phase transitions were exhibited by two chlorido members of the series, namely bis-(3-carboxylpropylammonium) tetrachloridocuprate(II), ⁺(NH₃(CH₂)₃COOH)₂[CuCl₄]^2-, and bis-(5-carboxylpentylammonium) tetrachloridocuprate(II), ⁺(NH₃(CH₂)_nCOOH)₂[CuX₄]^2-. Dominant ferromagnetic (FM) interactions are displayed at high temperatures, while the systems shifted to an antiferromagnetic (AFM) state below the ordering temperature, T_c, as shown in Fig. 1. Hysteresis effects, zero field-cooled (ZFC)/field-cooled (FC) cool plots indicated the presence of coercive fields and rememerance effects in some of the compounds. The two-dimensional chlorido structures exhibited an in-plane J value of 14.332 K to 15.109 K and the bromido containing structures displayed an in-plane J value of 18.56 K to 23.65 K.

[1] Smith, I.C., Smith, M.D., Jaffe, A., Lin, Y., Karundadasa, H.I. Chem. Mater, 29 (2017), 1868. [2] S. F. Hoefler, G. Trimmel, T. Rath, Monatsh. Chem. 148. (2017), 795. [3] Cortecchia, D., Dewi, H.A., Yin, J., Bruno, A., Chen, S., Baikie, T., Boix, P.P., Gratzel, M., Mhaisalkar, S., Mathews, N.. Inorg. Chem. 55. (2016), 1044. [4] C.P. Landee, and M.M. Turnbull, J. Coord Chem 63:3 (2014), p. 375.

Hybrid halide perovskites have made a quite spectacular appearance in the field of photovoltaics, not only because device efficiency has shot over 25 % within 10 years of their development [1], but also because of their specific behaviour that is yet to be fully understood. In structural terms, these materials compare to the oxide perovskites ABO₃ in many respects [2] but also hold some features that are rather distinct and largely related to the molecular cation occupying the A-cation site. [3]

Therefore, a structural categorisation of these materials is greatly beneficial to understand the underlying principles of structure and property relationships. At the core of this work, we will present a fairly comprehensive group-subgroup relationship applied to halide perovskites and double perovskites deriving from the cubic perovskite aristotype in the form of a Bärnighausen tree [3] This is seconded with a discussion of the different distortion modes applying to halide perovskites: atom shifts, octahedral tilting and A-cation orientation, with the latter being a distinct mechanism in hybrid halide perovskites. Furthermore, we will elucidate the implications for the properties and phase transitions given the specific space group settings of the different crystal structures.

We will highlight why the consideration of group-subgroup relationships in halide perovskites materials is not only of structural-systematic interest, but allows direct assumptions on the device performance of perovskite solar cells. For this, we will uncover some of the physical implications of the structural relationships as they arise from the group-subgroup relationships – for instance twinning in the tetragonal phase of MAPbI₃ [4] and a potential crystallographic explanation for the possibility of ferroelectricity in MAPbI₃ [5].

[1] https://www.nrel.gov/pv/cell-efficiency.html, accessed 14/04/2021.

[2] Breternitz, J. & Schorr, S. (2018). Adv. Energy Mater. 8, 1802366.

[3] Breternitz, J. (2021). Crystallography in Materials Science, edited by S. Schorr, C. Weidenthaler, Berlin: de Gruyter, in press.

[4] Breternitz, J., Tovar, M. & Schorr, S. (2020). Sci. Rep. 10, 16613.

[5] Breternitz, J., Lehmann, F., Barnett, S. A., Nowell, H. & Schorr, S. (2020). Angew. Chem. Int. Ed. 59, 424.

The hexagonal perovskite-type oxide 6H-Ba₄Ta₂O₉ undergoes an unconventional symmetry lowering lattice distortion when cooled below 1100 K in the presence of atmospheric water. This temperature corresponds to the onset of hydration, which reaches a stoichiometric value 6H-Ba₄Ta₂O₉.½H₂O by ~500 K. In the study to be presented here, we used a combination of diffraction, ab initio calculations and spectroscopy to show that both processes are due to the incorporation of intact water molecules into the close-packed ionic lattice. The presence of very large Ba²⁺ cations in octahedral interstitial sites (perovskite B sites) forces adjacent vacant octahedral interstitial sites to also expand, making room for occupation by water molecules, while also destabilizing the structure in a way that cannot be adequately addressed by conventional symmetry-lowering pathways on cooling. This gives rise to a synergistic hydration-distortion mechanism, which, to the best of our knowledge, is unique among close-packed ionic compounds. We will discuss the implications of our model for protonic and oxide ionic conductivity in hexagonal perovskites as fuel-cell membrane materials, and for earth sciences given the possibility that more examples could exist under high-temperature and pressure conditions.

Recently, there has been considerable interest in developing high energy density solid-state energy storage systems, where Na_1/2Bi_1/2TiO₃-based materials have also received significant interest for the exceptional large-field electromechanical response. In addition, nonstoichiometric NBT has been reported to be an excellent oxygen-ion conductor. As such, NBT has gained significant interest as the potential new materials for solid-oxide fuel cells and oxygen separation membranes. In this contribution, the effect of Bi non-stoichiometry on the crystal structure has been investigated. Bi non-stoichiometric Na_0.5Bi_xTiO_3-y ceramics with x = 0.485–0.51 were prepared by a conventional solid-state reaction method. The chemical analysis of the 4 sintered samples were performed using ICP-OES. The effects of Bi non-stoichiometry on structural transition and ferroelectric stability of NBT ceramics were systematically investigated by the Neutron diffraction at room temperature (RT), in situ high-temperature X-ray diffraction (HTK-XRD up to 560 °C, see Fig. 1), dielectric analyses, and electromechanical measurements. For all compositions, the room temperature structure was found to be rhombohedral without secondary phases. Whereas at 250 °C and 500 °C, tetragonal phase and cubic were observed, respectively. These results are consistent with previous reports. [1-3] In this study, the temperature-dependent phase transition of nonstoichiometric NBT is presented. The changes in the tilt angle (ω) and octahedral strain (ξ) were calculated from distortion parameters after Megaw and Darlington [4]. An in-depth analysis of the temperature-dependent data shows that the Bi-nonstoichiometry does not alter the average crystallographic structure and phase transition temperatures of the investigated compositions.

[1] Vakhrushev, S. B., Isupov, V. A., Kvyatkovsky, B. E., Okuneva, N. M., Pronin, I. P., Smolensky, G. A. & Syrnikov, P. P. (1985). Ferroelectrics 63 (1), 153-160.

[2] Jones, G. & Thomas, P. (2002). Acta Crystallogr. Sect. B: Struct. Sci. 58 (2), 168-178.

[3] Jones, G. & Thomas, P. (2000). Acta Crystallogr. Sect. B: Struct. Sci. 56 (3), 426-430.

[4] Megaw, H. D. & Darlington, C. N. W. (1975). Acta Crystallographica A 31 (2), 161-173.

Bulk nanocrystalline samples of La_0.65 Ce_0.05 Sr_0.3 Mn_1-x Cu_xO₃(0 <x < 0.15) manganites are prepared by the sol–gel based Pechini method. The effect of the substitution for Mn with Cu upon the structural and magnetic properties has been investigated by means of X-ray diffraction (XRD), Raman spectroscopy and dc magnetization measurements. The structural parameters obtained using Rietveld refinement of XRD ata showed perovskite structures with rhombohedral (R-3c) symmetry without any detectable impurity phase. Raman spectra at room temperature reveal a gradual change in phonon modes with increasing copper concentration. The analysis of the crystallographic data suggested a strong correlation between structure and magnetism, for instance a relationship between a distortion of the MnO₆octahedron and the reduction in the Curie temperature, Tc. Hence, a theoretical description of the second-order magnetic transition, as well as the magnetic entropy change of La_0.65 Ce_0.05 Sr_0.3 Mn_1-x Cu_xO₃ (x=0 and x=0.15) compounds is presented based on the Bean-Rodbell model of magneto-volume interactions. It is shown that the magnetocaloric properties obtained from initial magnetization isotherms data are in a good matching with the numerical simulations. Within the framework of this specific theoretical model, the magnitude of the spin-lattice interaction, as well as the spin value fluctuation are found to increase upon Cu-doping. These observations shall be taken in accordance with the disorder induced by Cu^2+/Cu³⁺ ions in the system.

Hybrid perovskites of the formula A₂MX₄, A: ammonium substituted organic cation, M: a divalent metal ion and X: a halogen (Cl, Br, I) have attracted considerable attention recently. Their applications include lead-free perovskite solar cell [1], optoelectronic, exitonic and self-assembly quantum well. The properties of these hybrid perovskites OIHs are functions of A, M and X and there are possibilities to tailor the structure, physical and chemical properties according to the application needed [2-3]. The Co hybrid perovskite is a promising material for lead-free perovskite solar cell applications. Mn organic-inorganic hybrid can be used as catalysis and ultraviolet absorbing materials. Cu hybrid can be used in the application of self-assembly quantum well as well as lead-free perovskite solar cell [4]. Some of these materials posses reversible phase transition that may find application as sensors and data storage devises. The presenter has deposited about 15 of these novel hybrid perovskite materials at Cambridge Crystallographic Data Center (CCDC). For further investigation and characterization of diammonium hybrid perovskite materials xrf/xafs has been performed.

Figure 1. Left panel crystal structure of [NH₃(CH₂)₅NH₃]MnCl₂Br₂ at 240 K and right panel layered structure of [NH₃(CH₂)₅NH₃]CoCl₂Br₂ at T = 300 K. [1] Abdel-Aal, S. K., Abdel-Rahman, A. S., Kocher-Oberlehner, G., Ionov, A. & Mozhchil, R. N. (2017). Acta Cryst. A73, C1116. [2] Abdel-Aal, S. K., Abdel-Rahman, A. S., Gamal, W. M., Abdel-Kader, M., Ayoub, H. S., El-Sherif, A. F., Kandeel, M. F., Bozhko, S., Yakimov, E. E. & Yakimov, E. K. (2019). Acta Cryst. B75, 880-886. [3] Abdel-Aal, S. K. & Abdel-Rahman, A. S. (2017) J. Cryst. Growth. 457, 282-288. [4] Abdel-Aal, S. K. & Abdel-Rahman, A. S. (2019) J. Elec. Mat. 48(3) 1686-1693

In this work, SrCo_1-xMo_xO_3-δ(0 ≤ x ≤ 1) powders were synthesized by the gel-combustion method in order to explore two major aspects: the synthesis method and the crystal structure of these systems upon the variation of the Co/Mo relation. Sample SrCo_0.95Mo_0.05O_3-δ, exhibiting a tetragonal phase (space group P4/mmm) at room temperature (RT) was used as the parent compound as it was reported to be a good cathode for intermediate-temperature solid-oxide fuel cells (IT-SOFCs) [1]. The amount of glycine used as fuel in the synthesis route was studied in order to obtain a single-phased material with high homogeneity and reproducibility. Afterward, the relationship between the Co/Mo ratio in the B site of the perovskite was also investigated with the aim of implementing these materials as potential electrodes for intermediate-temperature symmetrical solid-oxide fuel cells (IT-SSOFCs). Thus, both the crystal structure and the reducibility properties of the powders were investigated by X-ray powder diffraction (XPD) and temperature-programmed reduction under diluted H₂ (H₂-TPR) techniques respectively. Additionally, scanning electron microscopy (SEM) was performed for the SrCo_0.95Mo_0.05O_3-δsample in order to study its morphology.

The SrCo_0.95Mo_0.05O_3-δsample synthesized by the addition of a non-stoichiometric amount of glycine, was able to stabilize the desired tetragonal phase as shown in Fig. 1. On the other hand, the undoped SrCoO_3-δ sample showed the typical hexagonal structure corresponding to the R32 space group. Samples containing 0.1 ≤ x ≤ 1 Mo, prepared in air flow at RT, presented two additional tetragonal phases (space groups: I4/m and I4₁/a), which correspond to the Sr₂CoMoO_6-d double perovskite and the SrMoO₄ scheelite phase respectively, as depicted in Fig. 2. Recent research has shown that this double perovskite material can become a promising ceramic oxide for anode applications in IT-SOFC [2]. Samples calcinated in a 5 mol% H₂ in Ar flow (50 cm³ (STP) min^-1) during the H₂-TPR experiments showed that, those with the lowest Mo content presented some reduction peaks at 275, 390 and 825 ºC; and the ones with the highest Mo content were partially reduced at 900 ºC. In the latter, a cubic phase was stabilized at RT (Pm-3m space group), which has been considered an ideal phase for its use as IT-SOFCs anode materials [3], meaning a big possibility to obtain other materials at intermediate Co/Mo compositions with optimal properties for IT-SSOFCs electrodes.

The prototype antiferroelectric material PbZrO₃ (PZO) features a peculiar transition from cubic (Z=1, Pm-3m) to orthorhombic (Z=8, Pbam) phase in which off-centre shifts of Pb²⁺ cations are accompanied with rotations of oxygen octahedra. These two displacive modes are present already in the cubic phase giving rise to strong structured diffuse scattering. Their coupling is considered to be at the core of the antipolar modulation of the PZO’s ground-state structure.

Here we show that partial substitution of Zr⁴⁺ cations with Sn⁴⁺ adds another level of complexity to this system [1]. For 28% of Sn two new intermediate phases appear before crystal reaches the known orthorhombic structure. The higher-temperature one is characterized by ordered system of octahedral tilts and signatures of incommensurate modulation. The latter properly develops at lower temperatures in the second intermediate phase. We track changes in the diffraction patterns in the wide temperature range, showing how diffuse scattering signal transforms to orders of magnitude stronger signal marking a critical growth of displacive modes correlation. These changes are discussed in the context of modes coupling.

[1] I. Jankowska-Sumara, M. Paściak, M Podgórna, A. Majchrowski, M. Kopecký and J. Kub, APL Materials 9, 021101 (2021).

A quantitative experimental charge density study was undertaken for the double antiperovskite mineral – sulphohalite [Na₆(SO₄)₂FCl]. High-resolution X-ray diffraction data was collected employing AgKα radiation (λ = 0.56087 Å) to a resolution of 0.3941 Å at 100K. Electron density (ED) distribution – ρ(r) was modelled, in compliance with the Hansen-Coppens formalism[1], by consecutive least-square multipolar refinements. Based on such experimental distribution of charge, QTAIM topological analysis[2] was undertaken. Full-volume property integration over delineated atomic basins (AB’s) yielded their appertaining charges [Q_AB-Cl = -0.836e^-; Q_AB-S = 03.168e^-; Q_AB-Na = 0.910e^-; Q_AB-F = -1.334e^-; and Q_AB-O = -1.227e^-] and volumes [V_AB-Cl = 38.920ų; V_AB-S = 5.656ų; V_AB-Na = 7.931ų; V_AB-F = 14.178 ų and V_AB-O = 17.416 ų]. The percentage of unaccounted electrons and volume per unit cell was respectively 0.010% and 0.406%. Within the uncertainty range of performed numerical integration, such percentages can be unheeded. A total of 6·BCP’s [∇²ρ(r_Cl···S) = 0.120e^-·Å^-5; ∇²ρ(r_Cl···Na) = 0.575e^-·Å^-5; ∇²ρ(r_S-O) = -31.00e^-·Å^-5; ∇²ρ(r_Na···O) = 1.931e^- ·Å^-5; ∇²ρ(r_Na···F) = 3.022e^-·Å^-5 and ∇²ρ(r_F···O) = 0.868e^-·Å^-5], 5·RCP’s [∇²ρ(r_I) = 0.912e^-·Å^-5; ∇²ρ(r_II) = 0.332e^-·Å^-5 and ∇²ρ(r_III,IV,V) = 0.201e^-·Å^-5] and 4·CCP’s [∇²ρ(r_I,II) = 0.514e^-·Å^-5 and ∇²ρ(r_III,IV) = 0.401e^-·Å^-5] were identified (Figure 1). Hence, Morse’s ‘characteristic set’ condition was met[3]. The study of primary bundles (PB’s), as proposed by Pendás[4], revealed the interconnection between AB’s and CP’s onto basins of attraction or basins of repulsion. The nature of interatomic interactions was assessed through the dichotomous classification[3]. The S–O contact was acknowledged as a covalent with a shared-shell. The remaining contacts were characterized as non-covalent closed-shell (Cl···Na, Na···O and Na···F) or weak van der Waals closed-shell (Cl···S and F···O).

The anharmonicity of the lead-halide bond influences the optoelectronic properties of hybrid perovskites. Since many optoelectronic properties undergo large changes during the orthorhombic/tetragonal phase transformation, this temperature range is the focus of our investigation. The aim of this study was to determine the anharmonicity of the lead-halide bond in chlorine-substituted MAPbI₃ by combining temperature-dependent synchrotron XRD and Pb L3-edge EXAFS measurements from 20 K to 265 K. The partial negative thermal expansion (NTE) behavior of the [PbX₆] octahedra observed with XRD is related to the negative tension effects of the lead-halide bond in MAPbI₃ and MAPbI_2.94Cl_0.06 observed with EXAFS, whereas in MAPbCl₃ the positive bond expansion towards higher temperatures is predominant. The experimentally observed EXAFS parameters showed clear effects at 100 % chlorine substitution. The lead-halide bond in the orthorhombic phase of MAPbCl₃ was much less anharmonic than in pure MAPbI₃. However, after the phase transition to the room temperature phase, MAPbCl₃ showed much greater anharmonicity, indicating a significantly changed state of the lead-chlorine bond. At 2 % chlorine substitution, smaller changes became apparent compared to MAPbI₃. But significant differences between MAPbI₃ and MAPbI_2.94Cl_0.06 could be observed in the degree of anisotropy γ and the asymmetry parameter C₃/C₂^3/2. By determining the structural parameters that are required for the conversion of the effective force constants k₀ and k_3, into the Morse potential parameters α and D, we found our results to be in conformance with other experimental findings.

Catalytic processes are indispensable in energy research. It is essential to enhance their environmental friendliness and resource‑efficiency by exploring and optimizing new reaction routes for future sustainability. One major topic in this context is the chemical energy storage using eg. hydrogen, in a pure state or hydrogen-carrier molecules. The release of hydrogen from carrier molecules, such as ammonia (NH₃), is achieved by a catalytic reaction. Among others, promising catalysts for ammonia decomposition are nickel-based catalysts [1]. Perovskites, eg. LaNiO₃, can serve as catalyst precursors.

The synthesis of LaNiO₃ was conducted via incipient wetness impregnation of mesoporous carbon spheres and subsequent sintering [2]. Detailed microstructure analysis was performed via transmission electron microscopy that enabled the identification of Ruddlesden-Popper faults. These [LaO]-[LaO] shear faults have been reported in the past to be present in LaNiO₃ thin films grown on various substrates [3, 4]. With this information, a Rietveld refinement of synchrotron powder diffraction data could be performed using a stacking fault model based on the superstructure, space group Pm-3m, of the original LaNiO₃ crystal structure, space group R‑3cH (Fig. 1 a). In addition, the local structure of the perovskite was investigated by total scattering neutron and synchrotron experiments and subsequent pair distribution function analysis.

The aim of this work is the correlation of structure properties with the catalytic performance of perovskites with different chemical compositions. The catalytic performance of the synthesized material was tested during NH₃ cracking experiments. For LaNiO₃, a conversion of 70% could be achieved at 550°C with a gas flow of 15000 ml/g^-1h^-1 of 100% NH₃. The structural behavior during the reaction was investigated by in situ synchrotron diffraction experiments at the high-resolution powder diffraction beamline P02.1 (PETRA III, DESY). A decomposition of the perovskite via intermediate states and the reduction to the active phase of metallic Ni on La₂O₃ could be observed (Fig. 1 b).

We investigated the pulsed-laser deposition of epitaxial layers of hexagonal LuFeO₃ by measuring the x-ray diffraction intensity in the quasi-forbidden reflection 0003 in situ during deposition. For this purpose we used a growth chamber attached to the NANO beamline at KARA storage ring of Karlsruhe, Germany.

The dependence of the diffracted intensity exhibited characteristic oscillating behaviour, the period of the oscillation is inversely proportional to the growth rate and the decay of the oscillation visibility is connected with the growth kinetics, especially to the transition from two-dimensional to three-dimensional growth mode.

The experimental data were compared to numerical simulations, for which we developed a novel growth model. The model is based on the solution of equations describing the time evolution of monolayer coverages and numbers of mobile particles at surface terraces. From the model it follows that the widths of the monolayer coverage profiles exhibit a power law dependence on the deposition time and the exponent of this law sensitively depends on the width of the diffuse Ehrlich-Schwoebel barrier, as well as on the effective temperature of two-dimensional gas of mobile molecules on the growing surface.

[1] Bauer, S., Lazarev, S., Molinari, A., Breitenstein, A., Leufke, P., Kruk, R., Hahn, H., Baumbach, T. (2014) J. Synchr. Rad. 21, 386.

[2] Holý, V., Bauer, S., Rodrigues, A., Horák, L., Jin, X., Schneider, R., Baumbach, T. (2020) Phys. Rev. B 102, 125435.

[3] Bauer, S., Rodrigues, A., Horák, L., Jin, X., Schneider, R., Baumbach, T., Holý, V. (2020) Materials 13, 61.

The work was supported by the Czech Science Foundation (project No. 19-10799J) and by the project NanoCent financed by European Regional Development Fund (ERDF, project No. CZ.02.1.01/0.0/0.0/15.003/0000485). The additional funding by the German Research Foundation within the framework of the projects SCHN 669/11 and BA 1642/8-1 is gratefully acknowledged.