Tolerance Factor for Huntite-Family Compounds
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Tolerance Factor for Huntite-Family Compounds M. S. Molokeeva, b, * and S. O. Kuznetsova a Siberian
b
Federal University, Krasnoyarsk, 660041 Russia Kirensky Institute of Physics, Krasnoyarsk Scientific Center, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia *e-mail: [email protected] Received June 3, 2020; revised June 3, 2020; accepted June 26, 2020
Abstract—85 RM3(BO3)4 (R is the rare-earth element (Y, La–Lu) and M = Al, Sc, Cr, Fe, or Ga) compounds with the huntite structure have been analyzed. The analysis of the structures has made it possible to determine critical atomic displacements during the phase transition R32 ↔ P3121 and establish how these critical displacements can be controlled by varying the ionic radii. A tolerance factor has been derived and its threshold value below which the structure is stable in the R32 phase and above it, in the distorted P3121 phase, has been found. The formula has been tested on more than 30 huntite-family compounds and good agreement has been obtained. Therefore, it can be used with confidence to predict new compounds. At the moment, the tolerance factor has allowed us to establish previously unknown regularities in huntites. Keywords: huntites, tolerance factor, phase transition, structural stability, crystal structure DOI: 10.1134/S1063783420110190
1. INTRODUCTION In the last few decades, borate crystals have evoked a great interest due to a wide variety of their structures [1]. Borates are optically transparent in a wide spectral range and have the high chemical and mechanical stability. Borates with a huntite structure (CaMg3(CO3)4 huntite, sp. gr. R32) attract close attention by their valuable magnetoelectric [2, 3] and spectroscopic [4– 6] properties promising for engineering applications. The general formula of the huntite-family borates is RM3(BO3)4, where R is the rare-earth element (Y, La–Lu) and M is Al, Sc, Cr, Fe, or Ga. The RM3(BO3)4 crystal structure type depends on chemical composition and crystallization conditions (Table 1). In each structure, three types of coordination polyhedra are distinguished: trigonal prisms RO6, octahedra MO6, and polyhedra BO3 in the form of triangles. In the most wide-spread phase with the R32 symmetry, there is one RO6, one MO6, and two BO3 in the independent part of the cell (Fig. 1). Along with the R32 phase, the trigonal P3121 and P321 and monoclinic C2/c, Cc, and C2 phases have been noted. However, for huntites, no quantitative measure has been proposed yet that would allow one to estimate the formation of a desired phase and make a quick symmetry forecast. Such a measure, as a rule, is the tolerance factor, which is an indicator of the stability and distortion of crystal structures [7]. Initially, it was only used to describe the perovskite structure [8], but, at present, the tolerance factors are used also, e.g., for ilmenite
[9], garnets [10], pyrochlores [11], and chalcogenides with the general formula ABCX3 [12]. In this work, we propose a tolerance factor for determining the sta
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