najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-6-668-677najo-282Research ArticleСтатьиMulti-order and structural mechanism of atom nanocluster formation in rhombohedral Cu-Zr-thiospinelsМультипорядок и структурный механизм образования нагнокластеров в ромбоэдрических Cu-Zr-тиошпинеляхhttps://orcid.org/0000-0002-1269-2521ТалановВ. М.TalanovV. M.valtalanov@mail.ruhttps://orcid.org/0000-0002-5416-9579ТалановМ. В.TalanovM. V.mvtalanov@gmail.comЮжно-Российский государственный политехнический университет имени М. И. ПлатоваPlatov South-Russian State Polytechnic UniversityЮжный федеральный университетSouthern Federal University202206062025136668677Copyright © Talanov V.M., Talanov M.V., 20252025Таланов В.М., Таланов М.В.Talanov V.M., Talanov M.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/282

A structural mechanism for the formation of nanoclusters and the rhombohedral modification of CuZr1.86(1)S4 has been proposed. Group-theoretical and crystal-chemical methods are used to study the features of the crystal structure and multi-order in Cu-Zr-thiospinel. A multi-order is a structural organization of a material, in the formation of which different degrees of freedom of a crystal participate. It has been proven that the rhombohedral structure of CuZr1.86(1)S4 is formed as a result of displacements and orderings of all types of atoms. It is theoretically shown that the formation of a rhombohedral phase is associated not only with the lattice, but also with the charge and, possibly, orbital degrees of freedom of the crystal. Theory predicts that the rhombohedral phase must be an improper ferroelastic. An important feature of the rhombohedral structure is metal nanoclusters: “bunch” of dimers, trimers, and tetrahedra. Bunch of dimers are an unusual type of self-organization of atoms in rhombohedral spinel-like structures, formed by atoms of two (tetrahedral and octahedral) frustrated crystal sublattices.

Предложен структурный механизм образования нанокластеров и ромбоэдрической модификации CuZr1.86(1)S4 Теоретико-групповыми и кристаллохимическими методами исследованы особенности кристаллической структуры и мультипорядка в Cu-Zr-тиошпинели. Мультипорядок представляет собой структурную организацию материала, в образовании которой участвуют различные степени свободы кристалла. Доказано, что ромбоэдрческая структура CuZr1.86(1)S4 формируется в результате смещений и упорядочений всех типов атомов. Теоретически показано, что образование ромбоэдрической фазы связано не только с решеточными, но и с зарядовыми и, возможно, орбитальными степенями свободы кристалла. Теория предсказывает что рассматриваемая фаза должна быть несобственным сегнетоэластиком. Важной особенностью ромбоэдрической структуры являются металлические нанокластеры: «гроздья» димеров, тримеры и тетраэдры. Гроздья димеров представляют собой необычный тип самоорганизации атомов в ромбоэдрических шпинелеподобных структурах, образованный атомами двух (тетраэдрической и октаэдрической) фрустрированных подрешеток кристалла.

параметр порядкамультипорядокструктурный механизмромбоэдрическая модификациянанокластерыorder parametermulti-orderstructural mechanismrhombohedral modificationnanoclusterReferencesBitoh T., Hagino T., et al. Superconductivity in Thiospinel CuRh2S4. J. Phys. Soc. Jpn., 1992, 61 (8), P. 3011-3012.Bitoh T., Hagino T., et al. Superconductivity in Thiospinel CuRh2S4. J. Phys. Soc. Jpn., 1992, 61 (8), P. 3011-3012.Hagino T., Seki Y., et al. Superconductivity in spinel-type compounds CuRh2S4 and CuRh2Se4. Phys. Rev. B, 1995, 51 (18), P. 12673-12684.Hagino T., Seki Y., et al. Superconductivity in spinel-type compounds CuRh2S4 and CuRh2Se4. Phys. Rev. B, 1995, 51 (18), P. 12673-12684.Suzuki H., Furubayashi T., et al. Metal-Insulator Transition and Superconductivity in Spinel-Type System Cu1-xZnxIr2S4. J. Phys. Soc. Jpn., 1999, 68, P. 2495-2497.Suzuki H., Furubayashi T., et al. Metal-Insulator Transition and Superconductivity in Spinel-Type System Cu1-xZnxIr2S4. J. Phys. Soc. Jpn., 1999, 68, P. 2495-2497.Cao G., Kitazawa H., et al. Superconductivity in Zn-doped CuIr2S4. Physica C: Superconductivity, 2000, 341-348, P. 735-736.Cao G., Kitazawa H., et al. Superconductivity in Zn-doped CuIr2S4. Physica C: Superconductivity, 2000, 341-348, P. 735-736.Cao G., Furubayashi T., et al. Suppression of metal-to-insulator transition and appearance of superconductivity in Cu1-xZnxIr2S4. Phys. Rev. B, 2001, 64, 214514.Cao G., Furubayashi T., et al. Suppression of metal-to-insulator transition and appearance of superconductivity in Cu1-xZnxIr2S4. Phys. Rev. B, 2001, 64, 214514.Ito M., Hori J., et al. Pressure-Induced Superconductor-Insulator Transition in the Spinel Compound CuRh2S4. Phys. Rev. Lett., 2003, 91, 077001.Ito M., Hori J., et al. Pressure-Induced Superconductor-Insulator Transition in the Spinel Compound CuRh2S4. Phys. Rev. Lett., 2003, 91, 077001.Sekine T., Uchinokura K., et al. Electrical and thermal properties in CuV2S4. Solid State Commun., 1984, 51, P. 187-189.Sekine T., Uchinokura K., et al. Electrical and thermal properties in CuV2S4. Solid State Commun., 1984, 51, P. 187-189.Mahy J., Colatis D., Van Dyck D., Amelinck S. Electron diffraction evidence for domain structures in the low-temperature incommensurate phase in CuV2S4. J. Solid State Chem., 1987, 68, P. 320-329.Mahy J., Colatis D., Van Dyck D., Amelinck S. Electron diffraction evidence for domain structures in the low-temperature incommensurate phase in CuV2S4. J. Solid State Chem., 1987, 68, P. 320-329.Radaelli P.G., Horibe Y., et al. Formation of isomorphic Ir3+ and Ir4+ octamers and spin dimerization in the spinel CuIr2S4. Nature, 2002, 416, P. 155-158.Radaelli P.G., Horibe Y., et al. Formation of isomorphic Ir3+ and Ir4+ octamers and spin dimerization in the spinel CuIr2S4. Nature, 2002, 416, P. 155-158.Furubayashi T., Suzuki H., Kobayashi N., Nagata S. Large negative magnetoresistance in thiospinel CuCrZrS4. Solid State Commun., 2004, 131, P. 505-508.Furubayashi T., Suzuki H., Kobayashi N., Nagata S. Large negative magnetoresistance in thiospinel CuCrZrS4. Solid State Commun., 2004, 131, P. 505-508.Plumier R., Sougi M., Lecomte M. Observation of an unusual short range magnetic ordering in spinel Cu1/2In1/2Cr2S4. Phys. Lett. A, 1977, 60, P. 341-344.Plumier R., Sougi M., Lecomte M. Observation of an unusual short range magnetic ordering in spinel Cu1/2In1/2Cr2S4. Phys. Lett. A, 1977, 60, P. 341-344.Isoda M., Mori S. Magnetic Correlation and Breakdown of Fermi Liquid Picture in Frustrated Itinerant Electron Magnet Magnetic. J. Phys. Soc. Jpn., 2000, 69, P. 1509-1516.Isoda M., Mori S. Magnetic Correlation and Breakdown of Fermi Liquid Picture in Frustrated Itinerant Electron Magnet Magnetic. J. Phys. Soc. Jpn., 2000, 69, P. 1509-1516.Anderson P.W. Ordering and Antiferromagnetism in Ferrites. Phys. Rev., 1956, 102, P. 1008-1013.Anderson P.W. Ordering and Antiferromagnetism in Ferrites. Phys. Rev., 1956, 102, P. 1008-1013.Attfield J.P. Magnetism and the Trimeron Bond. Chem Mater., 2022, 34 (7), P. 2877-2885.Attfield J.P. Magnetism and the Trimeron Bond. Chem Mater., 2022, 34 (7), P. 2877-2885.Furubayashi T., Matsumoto T., Hagino T., Nagata S. Structural and Magnetic Studies of Metal-Insulator Transition in Thiospinel CuIr2S4. Phys. Soc. Jpn., 1994, 63, P. 3333-3339.Furubayashi T., Matsumoto T., Hagino T., Nagata S. Structural and Magnetic Studies of Metal-Insulator Transition in Thiospinel CuIr2S4. Phys. Soc. Jpn., 1994, 63, P. 3333-3339.Isobe M., Ueda Y.Y. Observation of Phase Transition from Metal to Spin-Singlet Insulator in MgTi2O4 with S = 1/2 Pyrochlore Lattice. Phys. Soc. Jpn., 2002, 71, P. 1848-1851.Isobe M., Ueda Y.Y. Observation of Phase Transition from Metal to Spin-Singlet Insulator in MgTi2O4 with S = 1/2 Pyrochlore Lattice. Phys. Soc. Jpn., 2002, 71, P. 1848-1851.Schmidt M., Ratcliff W., et al. Spin Singlet Formation in MgTi2O4: Evidence of a Helical Dimerization Pattern. Phys. Rev. Lett., 2004, 92, 056402.Schmidt M., Ratcliff W., et al. Spin Singlet Formation in MgTi2O4: Evidence of a Helical Dimerization Pattern. Phys. Rev. Lett., 2004, 92, 056402.Talanov V.M., Shirokov V.B., Ivanov V.V., Talanov M.V. Theory of Structural Phase Transition in MgTi2O4. Crystallogr. Reports, 2015, 60 (1), P. 101-110.Talanov V.M., Shirokov V.B., Ivanov V.V., Talanov M.V. Theory of Structural Phase Transition in MgTi2O4. Crystallogr. Reports, 2015, 60 (1), P. 101-110.Matsuno K.I., Katsufuji T., et al. Charge Ordering in the Geometrically Frustrated Spinel AlV2O4. J. Phys. Soc. Jpn., 2001, 70, P. 1456-1459.Matsuno K.I., Katsufuji T., et al. Charge Ordering in the Geometrically Frustrated Spinel AlV2O4. J. Phys. Soc. Jpn., 2001, 70, P. 1456-1459.Horibe Y., Shingu M., et al. Spontaneous Formation of Vanadium Molecules in a Geometrically Frustrated Crystal: AlV2O4. Phys. Rev. Lett., 2006, 96, 086406.Horibe Y., Shingu M., et al. Spontaneous Formation of Vanadium Molecules in a Geometrically Frustrated Crystal: AlV2O4. Phys. Rev. Lett., 2006, 96, 086406.Talanov M.V., Shirokov V.B., et al. Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4. Acta Crystallogr. B, 2018, 74, P. 337-353.Talanov M.V., Shirokov V.B., et al. Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4. Acta Crystallogr. B, 2018, 74, P. 337-353.Khomskii D.I., Streltsov S.V. Orbital Effects in Solids: Basics, Recent Progress, and Opportunities. Chem. Rev., 2021, 121 (5), P. 2992-3030.Khomskii D.I., Streltsov S.V. Orbital Effects in Solids: Basics, Recent Progress, and Opportunities. Chem. Rev., 2021, 121 (5), P. 2992-3030.Talanov M.V., Talanov V.M. Structural Diversity of Ordered Pyrochlores. Chem. Mater., 2021, 33, P. 2706-2725.Talanov M.V., Talanov V.M. Structural Diversity of Ordered Pyrochlores. Chem. Mater., 2021, 33, P. 2706-2725.Talanov V.M., Shirokov V.B., Talanov M.V. Unique atom hyper-kagome order in Na4Ir3O8 and in low-symmetry spinel modifications. Acta Crystallogr. A, 2015, 71, P. 301-318.Talanov V.M., Shirokov V.B., Talanov M.V. Unique atom hyper-kagome order in Na4Ir3O8 and in low-symmetry spinel modifications. Acta Crystallogr. A, 2015, 71, P. 301-318.Talanov M.V., Shirokov V.B., Talanov V.M. Phenomenological thermodynamics and the structure formation mechanism of the CuTi2S4 rhombohedral phase. Phys. Chem. Chem. Phys., 2016, 18, P. 10600-10606.Talanov M.V., Shirokov V.B., Talanov V.M. Phenomenological thermodynamics and the structure formation mechanism of the CuTi2S4 rhombohedral phase. Phys. Chem. Chem. Phys., 2016, 18, P. 10600-10606.Talanov M.V. Two different mechanisms of metal cluster formation in the rhombohedral spinel structures: AlV2O4 and CuZr1.86(1)S4. Crystal Growth & Design, 2018, 18, P. 3433-3440.Talanov M.V. Two different mechanisms of metal cluster formation in the rhombohedral spinel structures: AlV2O4 and CuZr1.86(1)S4. Crystal Growth & Design, 2018, 18, P. 3433-3440.Trighet L., Rouxel J. Le spinelle direct CuZr2S4. C.R. Acad. Sc. Ser. C, Sci. Chim., 1968, 267 (18), P. 1322-1324.Trighet L., Rouxel J. Le spinelle direct CuZr2S4. C.R. Acad. Sc. Ser. C, Sci. Chim., 1968, 267 (18), P. 1322-1324.Dong Y., McGuir M.A., Yun H., DiSalvo F.J. Synthesis, crystal structure, and properties of the rhombohedral modification of the thiospinel CuZr1.86(1)S4. J. Solid State Chem., 2010, 183, P. 606-612.Dong Y., McGuir M.A., Yun H., DiSalvo F.J. Synthesis, crystal structure, and properties of the rhombohedral modification of the thiospinel CuZr1.86(1)S4. J. Solid State Chem., 2010, 183, P. 606-612.Kovalev O.V. Representations of Crystallographic Space Groups. Irreducible Representations, Induced Representations and Co-representations. Ed. by H.T. Stokes and D.M. Hatch, Taylor and Francis Ltd., London, 1993, 349 p.Kovalev O.V. Representations of Crystallographic Space Groups. Irreducible Representations, Induced Representations and Co-representations. Ed. by H.T. Stokes and D.M. Hatch, Taylor and Francis Ltd., London, 1993, 349 p.International tables for crystallography, volume A, Space-group symmetry. Ed. by T. Hahn, Fifth edition, Springer, 2005, 911 p.International tables for crystallography, volume A, Space-group symmetry. Ed. by T. Hahn, Fifth edition, Springer, 2005, 911 p.Talanov V.M., Shirokov V.B. Tilting structures in spinels. Acta Crystallogr. A, 2012, 68, P. 595-606.Talanov V.M., Shirokov V.B. Tilting structures in spinels. Acta Crystallogr. A, 2012, 68, P. 595-606.Talanov V.M., Shirokov V.B. Atomic order in spinel structure - a group-theoretical analysis. Acta Crystallogr. A, 2014, 70, P. 49-63.Talanov V.M., Shirokov V.B. Atomic order in spinel structure - a group-theoretical analysis. Acta Crystallogr. A, 2014, 70, P. 49-63.Sahnenko V.P., Talanov V.M., Chechin G.M. Group-Theoretic Analysis of the Full Condensed Complex Arising upon Structural Phase Transformations. Fiz. Met. Metalloved., 1986, 62, P. 847-856.Sahnenko V.P., Talanov V.M., Chechin G.M. Group-Theoretic Analysis of the Full Condensed Complex Arising upon Structural Phase Transformations. Fiz. Met. Metalloved., 1986, 62, P. 847-856.Sakhnenko V.P., Talanov V.M. Deformational phase transitions in crystals of cubic classes. Deformations of Stretching. Phys. Solid State, 1980, 22, P. 785-792.Sakhnenko V.P., Talanov V.M. Deformational phase transitions in crystals of cubic classes. Deformations of Stretching. Phys. Solid State, 1980, 22, P. 785-792.Stokes H.T., Hatch D.M., 2007, ISOTROPY, URL: http://stokes.byu.edu/iso/isotropy.html.Stokes H.T., Hatch D.M., 2007, ISOTROPY, URL: http://stokes.byu.edu/iso/isotropy.html.Stokes H.T., Kisi E.H., Hatch D.M., Howard C.J. Group-theoretical analysis of octahedral tilting in ferroelectric perovskites. Acta Crystallogr. B, 2002, 58, P. 934-938.Stokes H.T., Kisi E.H., Hatch D.M., Howard C.J. Group-theoretical analysis of octahedral tilting in ferroelectric perovskites. Acta Crystallogr. B, 2002, 58, P. 934-938.

The authors declare that there are no conflicts of interest present.