Phenomenological thermodynamics and the structure formation mechanism of the CuTi₂S₄rhombohedral phase

Abstract

The theory of structural phase transition in CuTi2S4 is proposed. The symmetry of order parameters, thermodynamics and the mechanism of the atomic structure formation of the rhombohedral Cu-Ti-thiospinel have been studied. The critical order parameter inducing the phase transition has been found. Within the Landau theory of phase transitions, it is shown that the phase state may change from the high-symmetry cubic disordered Fd3[combining macron]m phase to the low-symmetry ordered rhombohedral R3[combining macron]m phase as a result of phase transition of the first order close to the second order. It is shown that the rhombohedral structure of CuTi2S4 is formed as a result of the displacements of all types of atoms and the ordering of Cu-atoms (1 : 1 order type in tetrahedral spinel sites), Ti-atoms (1 : 1 : 6 order type in octahedral spinel sites), and S-atoms (1 : 1 : 3 : 3 order type). The Cu- and Ti-atoms form metal nanoclusters which are named a "bunch" of dimers. The "bunch" of dimers in CuTi2S4 is a new type of self-organization of atoms in frustrated spinel-like structures. It is shown that Ti-atoms also form other types of metal nanoclusters: trimers and tetrahedra.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4

“…In expression (3), the underlined terms define the multicritical point (a 1 = 0, a 2 = 0), near which the potential (3) is stable. Previously, we presented the results of the stable potential research (3) in order to describe the phase transition in CuTi 2 S 4 (Talanov et al, 2016). In this paper, we present a much more detailed picture of the possible phase equilibrium.…”

“…In many cases, molecular metallic clusters appear in dielectric matrices, formed by the anions and atoms of non-transition elements. Well known examples of such multimers are: linear chains in NaTiO 2 (Takeda et al, 1992;Clarke et al, 1998), LiCoO 2 (Talanov et al, 2007); trimerons in Fe 3 O 4 (Senn et al, 2012a(Senn et al, ,b, 2015Attfield, 2015); dimers in MgTi 2 O 4 (Schmidt et al, 2004;Talanov et al, 2015a;Ivanov et al, 2011), CuTe 2 O 5 (Hanke et al, 1973;Ushakov & Streltsov, 2009), VO 2 (Imada et al, 1998), CuGeO 3 (Hase et al, 1993); bunch of dimers in CuTi 2 S 4 (Talanov et al, 2016); trimers in LiVO 2 (Pen, Tjeng et al, 1997), LiVS 2 (Katayama et al, 2009), NaV 6 O 10 (Kato et al, 2001), BaV 10 O 15 (Liu & Greedan, 1996;Bridges et al, 2004;Kajita et al, 2010), SrV 8 Ga 4 O 19 (Miyazaki et al, 2009), AV 13 O 18 (A = Ba, Sr) (Ikeda et al, 2011), A 2 V 13 O 22 (A = Ba, Sr) (Miyazak et al, 2010), Ba 4 Ru 3 O 10 (Streltsov & Khomskii, 2012); tetramers in A-site-ordered spinel (Talanov, 1986b;, CaV 4 O 9 (Starykh et al, 1996), LiGaCr 4 O 8 and LiInCr 4 O 8 (Okamoto et al, 2013); tetramers in ordered structures with breathing pyrochlore sublattices (Talanov & Talanov, 2017); hexamers in ZnCr 2 O 4 (Lee et al, 2002); heptamers in AlV 2 O 4 (Horibe et al, 2006); octamers in CuIr 2 S 4 (Radaelli et al, 2002); dodecamers in a doubleexchange spin-ice model on a Kagomé lattice (Shimomura et al, 2004).…”

Two Different Mechanisms of Metal Cluster Formation in the Rhombohedral Spinel Structures: AlV2O4 and CuZr1.86(1)S4

“…Each "bunch" consists of three [Cu(2)− Zr( 3 3)) belong to the "bunch" of dimers. Thus, it has been found that CuZr 1.86(1) S 4 is the second compound (after CuTi 2 S 4 38 ) in which such type of metal clusters exists. In the CuZr 1.86(1) S 4 rhombohedral thiospinel structure, Zr(2) atoms occupy a position being equidistant from 12 Zr(3) atoms with a considerable distance between them that practically excludes the possibility of a chemical bonding between them (for comparison, in CuTi 2 S 4 , distance Ti(2)−Ti(3) = 4.488 Å 39 ) (Figure 3a,b).…”

“…These metal clusters were called a "bunch" of dimers. 38 One can suppose that the "bunch" of dimers should exist in the CuZr 1.86(1) S 4 structure, since this substance is isostructural with CuTi 2 S 4 . 39 The structure of the AlV 2 O 4 rhombohedral phase is characterized by the same space group as the CuZr 1.86(1) S 4 structure.…”

Universal mechanism of tetrahedral metal cluster formation in structures with breathing pyrochlore sublattices

“…To find the splitting of Wyckoff positions in the structure of the highly-symmetric phase it is necessary to analyze the composition of permutation and mechanical representations of high-symmetry structure. We have found that the critical one dimensional irrep κ 11 (τ 4 ) enters into the mechanical representation on 16c, 16d, 32e, 48f Wyckoff positions and enters into the permutation representation on 8a, 8b, 32e, 48f Wyckoff positions [11][12][13][14][15].…”