Spin chain oxides containing cobalt and manganese whose structure is closely related to the 2H hexagonal perovskite [1-5] offer a very attractive field for the investigation of magnetic and multiferroic properties. The structure of the prototypic one-dimensional manganate and cobaltate Sr₄Mn₂CoO₉ consists of chains of face-sharing MnO₆ octahedra and trigonal CoO₆ prisms. According to the very important study performed by Perez-Mato et al [2], these spin chain oxides can be described as a composite 2H hexagonal perovskite family A_1+x(Mn_1-Co_x)O₃. Recently the possibility of extra oxygen incorporation during synthesis has been evidenced leading to a large family aperiodic chain structures [6] expressed by the simple formal formula Sr_1+x(Mn_1-xCo_x)O_3+δ; it induces a decrease of the proportion of the number of trigonal prismatic sites (N_P) with respect to the octahedral sites (N_O) within the chains as δ increases and concomitantly the formation of cobalt vacancies on the trigonal prismatic sites. Therefore the structural formula of these oxides must be expressed as Sr_1+y[(Mn_1-xCo_x)_1-z◊_z]O₃.]

The air-synthesized oxide x=3/8-Sr_1+x(Mn_1-xCo_x)O_3+δ is of great interest, since by decreasing the oxygen over stoichiometry to δ=0, one should obtain the oxide “Sr₁₁Mn₅Co₃O₂₄”(x=y, z=0) expected to be built up of trimeric and dimeric polyhedral units according to the sequence [Sr₄Mn₂CoO₉]₂.[Sr₃CoMnO₆]. Such an oxide containing exclusively strontium was never synthesized in air due to the partial oxidation of Co²⁺ into Co³⁺, imposing δ>0. We then have investigated the substitution of calcium for strontium in the pure Sr-phase x=3/8 (δ_~0.09). The objective was to design composite structures built up of trimeric and dimeric units by decreasing δ down to zero through Ca for Sr substitution in order to finally obtain the stoichiometric oxide A₁₁Mn₅Co₃O₂₄ (A=Sr,Ca). We report herein on a series of A_11/8(Mn_5/8Co_3/8)O_3+δ oxides with composite structures, commensurate or incommensurate, built up of trimeric M₃O₉ and dimeric M₂O₆ units (M= Mn, Co, o) with cationic vacancies on the trigonal prismatic sites. We also show the possibility to synthesize the quasi commensurate stoichiometric composite Sr_4.2Ca_6.8[Mn₂CoO₉]₂.[MnCoO₆] (δ=0.002).

[1] J. Darriet, M.A. Subramanian, J. Mater. Chem. 5 (1995) 543-552.

[2] J.M. Perez-Mato, M. Zakhour-Nakhl, F. Weill, J. Darriet, J. Mater. Chem. 9 (1999) 2795-2807.

[3] K. Boulahya, M. Parras, J.M. Gonzalez-Calbet, J. Solid State Chem. 145 (1999) 116-127.

[4] K.E. Stitzer, J. Darriet, H.-C. zur Loye, Curr. Opin. Solid State Mater. Sci. 5 (2001) 535-544.

[5] H.-C. zur Loye, Q. Zhao, D.E. Bugaris, W.M. Chance, Cryst. Eng. Commun. 14 (2012) 23-39.

[6] Caignaert V, Perez O, Boullay P, Seikh MM, Sakly N, Hardy V, Raveau B, J. of Mater Chem. C 8 (2020) 14559-14569

Diffraction enhancement of symmetry (DES) is a phenomenon by which the space-group symmetry suggested by the diffraction pattern of a crystal is higher than the space-group symmetry of the structure that has produced it [1-5]. The most well-known example is that of Friedel’s law, which is however realized only when resonant scattering is not taken into account. In modular structures, DES does occur also when considering resonant scattering. We address this phenomenon in monoarchetypal modular structures [6]. The condition for DES to occur is that both the module and the vector set (set of all interatomic vectors) [7] are invariant under an isometry that is not a symmetry operation for the structure. Only τ-isometries [8], i.e. isometries that do not reverse the polarity of the stacking vectors, can lead to DES once resonant scattering is taken into account. The example of SiC polytypes, where the phenomenon has been confirmed experimentally, is studied in detail. The SiC layer has symmetry p6mm (diperiodic group); the stacking of SiC layer leads to many polytypes, rapidly increasing in number with the number of layers defining the period along to stacking direction. These polytypes can occur in four types of space group: F-43m, R3m P6₃mc and P31m. If the vector set exhibits hexagonal symmetry, than the space group of the polytype can be either of type P6₃mc or of type P31m. In both cases, the diffraction pattern shows hexagonal symmetry although in the latter case the structural symmetry is only trigonal: DES is thus observed. The number of polytypes showing DES increases rapidly with the number of layers, but the fraction of these polytypes with respect to the total number of polytypes decreases. These conclusions apply as well to all modular structures built by layers of the same symmetry, like ZnS.

[1] Iwasaki, H. (1972). On the Diffraction Enhancement of Symmetry. Acta Cryst. A28, 253-260.

[2] Perez-Mato, J. M. and Iglesias, J.E. (1974). Acta Cryst. A33, 466-474.

[3] Sadanaga, R. and Ohsumi, K. (1975). Proc. Japan Acad. 51, 179-183.

[4] Sadanaga, R. and Ohsumi, K. (1979). Acta Cryst. A35, 115-122.

[5] Iglesias, J. E. (1979). Z. Kristallogr. 150, 279-285.

[6] Ferraris, G.. Makovicky E. and Merlino, S. (2008). Crystallography of Modular Materials. Oxford: Oxford University Press, 384 pp..

[7] Buerger, M. J. (1950). Acta Cryst. 3, 87-97.

[8] Dornberger-Schiff, K. and Grell-Niemann H. (1961). Acta Cryst. 14, 167-177.

Polytypism in cronstedtite; how various stacking sequences of layers affect diffraction pattern Jiří Hybler¹,

¹Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, CZ-18224 Prague 8, Czech Republic

hybler@fzu.cz

The 1:1 layered silicate cronstedtite (Fe²⁺_3-x Fe³⁺_x)(Si_2-xFe³⁺_x)O₅(OH)₄, of the serpentine-kaoline group forms relative large amount of polytypes. They are subdivided into four OD subfamilies, or Bailey’s groups A, B, C, D according to different stacking rules of identical (structure building) 1:1 layers (equivalents of OD packets) with trigonal protocell a=5.5, c=7.1 Å. Distributions of so called subfamily reflections along the reciprocal lattice rows [2l]* / [11l]* / [2l]* in (l_hex)* / (hhl_hex)* / (2hl_hex)* planes of diffraction pattern is used for subfamily determination. Similarly, distributions of characteristic reflections along [10l]* / [01l]* / [1l]* rows in (h0l_hex)* / (0kl_hex)* / (hl_hex) planes allow determination of particular polytypes. For this purpose, graphical identification diagrams simulating distribution of reflections along named rows are used [1]. Owing modern diffractometers with area detectors and appropriate software, and/or Electron Diffraction Tomography (later EDT) technique, precession-like images of Reciprocal Space (later RS) sections corresponding to above listed planes can be easily and quickly obtained.

Lot of specimens of cronstedtite from various terrestrial localities and synthetic run products were studied by the author [1-5]. RS sections were recorded, and selected ones are presented in the lecture in order to demonstrate the variability of diffraction pattern.

In the subfamily A, the stacking rule comprises ±a_i/3 shifts of consecutive layers. The most common is the 3T, relatively rare are 1M and 2M₁ polytypes. They usually occur in 3T+1M, 3T+2M₁, 1M+2M₁ mixed crystals. Monoclinic polytypes might be affected by twinning by reticular merohedry with 120º rotation as twinning operation. Six-layer 6T₂ and three-layer triclinic 3A polytypes are rare. Another possible twinning by 60º rotation changes obverse setting of the subset of subfamily reflections into the reverse one [1, 4].

In the subfamily D, the stacking rule is characterized by alternating 180º rotations of consecutive layers, combined by ±b/3 (of the orthohexagonal cell) or zero shifts. The most common polytypes are 2H₁ and 2H₂, occurring either isolated or in mixed crystals. Rarely, several six-layer polytypes were found. They usually occur in mixed crystals containing more polytypes, up to six! Diffraction patterns of such crystals are, of course, confusing. Fortunately, in many cases polytypes were isolated simply by cleaving crystals into smaller fragments, later studied separately. Hall et all. [6] derived 24 possible sequences of six-layer polytypes of subfamily D serpentines, valid also for cronstedtite. Their diffraction patterns were modelled, and compared with real RS sections. This simulation revealed, that five pairs of sequences (No. 4+6, 7+18, 8+10, 9+13, 11+12) provided identical diffraction patterns. Polytypes really found correspond to following sequences: 1 (Hall’s 6T₁), 5 (proposed 6T₃), 8+10 (6T₅), 11+12 (6T₄), 24 (6T₆) (trigonal polytypes), 22 (6R₁), 23 (6R₂), (rhombohedral polytypes). The hexagonal polytype 6H₂ corresponding to the sequence 14 was also found. However, the identical diffraction pattern can be produced by the obverse-reverse twin of the rhombohedral polytype 6R₂ (sequence 23).

Mixed crystals of polytypes belonging to different subfamilies were rarely found. 1M+1T mixed crystal of subfamilies A and C, respectively, was identified by EDT in the synthetic material [1]. The C subfamily is characterized by mere ±b/3 or zero shifts, without any rotation. The mixed crystals of A+D subfamilies were found in some terrestrial samples. Sometimes, the A and D parts of such crystals were separated by cleaving into smaller fragments.

Many RS sections showed diffuse streaking of characteristic reflections along c* due to partial stacking disorder. In extreme cases, reciprocal lattice rows are completely replaced by diffuse streaks.

The total number of ascertained polytypes of cronstedtite, recognized in RS sections, is 15 (+ one questionable).

[1] Hybler, J., Klementová, M., Jarošová, M., Pignatelli, I., Mosser-Ruck, R., & Ďurovič, S. (2018). Clays and Clay Minerals 66, 379–402.

[2] Hybler, J., Sejkora, J., & Venclík, V. (2016). European Journal of Mineralogy, 28, 765–775.

[3] Pignatelli, I., Mugnaioli, E., Hybler, J., Mosser-Ruck, R., Cathelineau, M., & Michau, N. (2013). Clays and Clay Minerals 61, 277–289.

[4] Hybler, J., Števko, M., & Sejkora, J. (2017). European Journal of Mineralogy, 29, 91–99.

[5] Hybler, J., Dolníček, Z., Sejkora, J., & Števko, M., (2020). Clays and Clay Minerals 68, 632-645.

[6] Hall, S. H., Guggenheim, S., Moore, P., & Bailey, S. W. (1976). Canadian Mineralogist 14, 314-321.

Keywords: cronstedtite; polytypism; layer stacking; X-ray diffraction; electron diffraction tomography

Even after decades of solid-state research, there are intriguing binary systems lacking investigation, even exclusively with main group elements. For instance, there are significantly fewer investigations on beryllium compounds than on any other class of light-element materials, even though beryllium-containing phases feature interesting properties for basic and applied research.[1] Owing to its toxicity, efforts to understand the chemistry of Be are rather rare. However, the limited knowledge present promises a rich and unusual structural chemistry. The few results concerning Be compounds with group 15 elements include the disordered diamond-like structure of BeP₂.[2] Yet, the true building blocks, i.e. the arrangement of polyphosphide anions, remained elusive with respect to the description of the average structure. Preliminary work on BeAs₂ and BeSb₂ indicates related structures for both compounds;[3] however, this information is only based on qualitative evaluation of powder X-ray diffraction data. Precise structural data require very accurate diffraction data due to the large difference in scattering factors. Despite the simple stoichiometry, a complete structural analysis proved difficult as the crystals obtained are by far too small for data collection using laboratory diffractometers. We now employed a combined approach using microfocused synchrotron radiation, electron diffraction and HRTEM.

Synchrotron data of a microcrystal of BeSb₂ reveal a coloring variant of the cubic diamond structure (Fig. 1). The corresponding tetragonal superstructure contains twisted chains of Sb atoms interconnected by Be atoms with all atoms showing a distorted tetrahedral coordination. The conformation of the polyanion corresponds to the Ge substructure in Li_~3AgGe₂.[4] This indicates chemical bonding according to a Zintl phase with a “sulfur-like” Sb^- polyanion (comparable to Ge^2-). Yet, BeSb₂ can also be viewed as a Grimm-Sommerfeld semiconductor with an average valence electron concentration of 4. Compared to Be₁₃Sb, which features Be₁₂ icosahedrons in analogy to the NaZn₁₃ type, the bonding situation changes from quasi-molecular entities to typical semiconductors upon varying the relative Be content. Hypothetical intermediate structures may exhibit rather unusual chemical bonding.

For BeP₂ and BeAs₂, our investigations have confirmed the disordered diamond-like / sphalerite-like structures according to the average structures in literature, which can be refined in space group I4₁/amd.[2,3] Diffraction patterns (both with X-rays and electrons, Fig. 2) exhibit pronounced diffuse streaks that indicate stacking disorder. Synchrotron data were collected from microcrystallites on TEM grids that were pre-characterized by electron microscopy. Both the evaluation of synchrotron diffraction data and HRTEM imaging reveal the nature of the disorder and the local structure of the polyanions. Stacking probabilities were derived by simulation diffraction patterns. The degree of ordering varies: diffuse streaks can be almost uniform but, especially in the case of BeAs₂, they may also approach a superstructure.

[1] M. R. Buchner, R. Pöttgen, H. Schmidbaur (2020). Z. Naturforsch. 75b, 403.

[2] P. L’Haridon, J. David, J. Lang, E. Parthé (1976). J. Solid State Chem. 19, 287.

[3] R. Gerardin, J. Aubry (1976). J. Solid State Chem. 17, 239.

[4] A. Henze, V. Hlukhyy, T. F. Fässler (2015). Inorg. Chem. 54, 1152.