Positive and negative monoclinic deformation of corundum-type trigonal crystal structures of M ₂O₃ metal oxides

Abstract

are studied using synchrotron radiation X-ray powder diffraction. The observed angular dependence of the integral breadths is described by two models: (i) the distorted corundum-type structure model described by the space group C2/c and (ii) the Stephens model of anisotropic Bragg peak broadening. These two models are shown to be equivalent. Ti 2 O 3 , V 2 O 3 and Cr 2 O 3 show a 'positive' distortion which is related to the possible metal-metal bond suggested by Goodenough in the literature (the deformation leads to shorter metal-metal distances) whereas Al 2 O 3 and -Fe 2 O 3 show a 'negative' distortion which leads to relatively longer metal-metal distances. 2017) can be described by: (i) a Rietveld refinement with a crystal structure model with monoclinic symmetry, C2/c, or (ii) using the Bragg peaks broadening due to anisotropic strains ). In the present paper, it is shown that these two approaches agree with each other, i.e. the anisotropic strains (Stephens, 1999) induce a change of symmetry from trigonal to monoclinic for a substantial part of the crystallites.This study is focused on other oxides classified in the corundum-type structure, , which show a variety of interesting magnetic and electronic phenomena. Just to give a few examples: the metal-insulator transition in V 2 O 3 and Ti 2 O 3 (Morin, 1959;McWhan et al., 1969), magnetoelectric coupling in Cr 2 O 3 (Astrov, 1960) and weak ferromagnetism in -Fe 2 O 3 (Né el & Pauthenet, 1952;Dzyaloshinsky, 1958). Goodenough (1963) introduced the concept of the metal-metal bond, as explained in detail for corundum-type compounds by Prewitt et al. (1969). These metal-metal bonds were reported in V 2 O 3 , Ti 2 O 3 , Cr 2 O 3 but were absent in Al 2 O 3 and -Fe 2 O 3 (Prewitt et al., 1969). This is why V 2 O 3 , Ti 2 O 3 and Cr 2 O 3 are denoted as 'positively' distorted compounds, while Al 2 O 3 and -Fe 2 O 3 are denoted as 'negatively' distorted in the present study.The main questions are: (i) will M 2 O 3 compounds show a systematic Bragg peaks' broadening indicative for a distortion from trigonal symmetry? (ii) will the metal-metal bond influence the character of these distortions?The paper is organized in the following parts: x2 describes in detail the samples and the experimental setup; x3.1 presents the Rietveld refinements with the trigonal (undistorted) structures; x3.2 explains the pseudohexagonal (distorted) setting which is equivalent to the monoclinic symmetry model and presents the results of the Rietveld refinements in the distorted setting; x3.3 discusses the model of anisotropic strains (Stephens, 1999) and its application to the SR diffraction patterns; x3.4 shows the equivalence between the monoclinic (pseudohexagonal) symmetry model and the anisotropic strains model of Stephens (1999). Discussion and conclusions are given in x4. research papers Acta Cryst. (2018). B74, 660-672 Fabrykiewicz et al. Positive and negative monoclinic deformation of M 2 O 3 661 research papers Acta Cryst. (2018). B74, 660-672 Fabrykiewicz et al. Positive and nega...

Nanoscale self-organization and metastable non-thermal metallicity in Mott insulators

“…The non-primitive hexagonal unit cell contains six formula units, and has the lattice vectors shown in Fig. 1b , where 28 , 36 , 37 and, by convention, we choose a H ∥ x and c H ∥ z . The vanadium atoms form honeycomb planes with ABC stacking, see also Supplementary Note 2 (See the Supplementary Material).…”

Nanoscale self-organisation in Mott insulators: a richness in disguise

“…We can therefore identify the vector ǫ 2 in (5) with the two-component order parameter of the rhombohedral to monoclinic transition. Specifically, using the structural data of the corundum and monoclinic structures across the transition 32,41,42 , and in our reference frame, the shear strain order parameter ǫ 2 just after the transition has magnitude ǫ 2 ≃ 0.01756, and three possible orientations, i.e., monoclinic twins, defined by the phases, see Eq. ( 5),…”

“…The non-primitive hexagonal unit cell contains six formula units, and has the lattice vectors shown in Fig. 2, where 32,41,42 a…”

Nanoscale self-organisation and metastable non-thermal metallicity in Mott insulators

“…The nonprimitive hexagonal unit cell contains six formula units, and has the lattice vectors shown in Fig. 2, where [31,41,42]…”

“…We can therefore identify the vector 2 in (S36) with the two-component order parameter of the rhombohedral to monoclinic transition. Specifically, using the structural data of the corundum and monoclinic structures across the transition [31,41,42], and in our reference frame, the shear strain order parameter 2 just after the transition has magnitude 2 0.01756, and three possible orientations, i.e., monoclinic twins, defined by the phases, see Eq. (S36),…”