Determination of rhombohedral structure of BiFeO₃ single-domain-like films grown on SrTiO₃ and LaAlO₃ substrates by X-ray diffraction using $(2\bar{1}\bar{3})_{\text{hex}}$

Abstract

The crystal structure of bismuth ferrite (BiFeO3; BFO) epitaxial films was analyzed by X-ray diffraction (XRD) using a two-dimensional detector. The diffraction spots hex (hexagonal notation was used for the rhombohedral structure in this study) specific to the rhombohedral structure (space group: R3c), which clearly separated from the diffractions in other crystal symmetries of BFO, was used for determining the crystal symmetry. The BFO films on the SrTiO3 substrates were unambiguously identified as R3c with the hex diffraction spot, whereas highly strained BFO films (space group: Cm) on the LaAlO3 substrates did not show the diffraction spot. The structure of a single-domain-like sample with R3c could not be determined using variants, i.e., degrees of freedom for crystal orientation, whereas the Bragg’s diffraction of hex can be used to unambiguously distinguish R3c from other space groups. It was proposed that electron diffraction complemented by nondestructive and high-resolution XRD is highly effective to obtain wide-area reciprocal space information for identifying low-symmetric-complex materials such as BFO.

High-Quality Sputtered BiFeO3 for Ultrathin Epitaxial Films

“…So far, by Bragg's reflections specific to the SG of R3c, the crystal symmetry has been identified by electron diffraction 28 and Xray reciprocal space mapping. 20 However, there are few reports on Bragg's diffraction using a high-precision goniometer and scintillation counter of XRD to determine accurately based on the rhombohedral symmetry of the lattice constant and epitaxial strain for the epitaxial BiFeO 3 films. The lattice constant of single-phase BiFeO 3 with an atomically flat surface was determined by fundamental reflections (4 2̅ 6̅ ), (3 1̅ 8̅ ) and rhombohedral-specific reflections (1 1̅ 7̅ ), (2 1̅ 3̅ ) (Figure 3b).…”

“…An accurate evaluation of the crystal symmetry, epitaxial strains, and lattice constant by Braggs' reflection based on a rhombohedral structure instead of pseudo-cubic crystal symmetry has not yet been widely adopted for the BiFeO 3 epitaxial films. There are a few reports on the structural analysis using diffraction specific to the rhombohedral symmetry 20 but not using a high-precision goniometer and scintillation counter of XRD. Obtaining high-quality indicators from the perspective of understanding the overall picture of the physical properties of BiFeO 3 epitaxial films is important.…”

Short range biaxial strain relief mechanism within epitaxially grown BiFeO3

“…It is also noteworthy that the rhombohedral crystal structures found within the current BFO film could be slightly different in terms of the lattice parameter and rhombohedral distortion angle, i.e., α angle, from those found in other BFO films and bulk BFO. This is because the crystallographic details of the rhombohedal BFOs in terms of α angle, lattice parameter, and the locations of basis atoms depend on the characteristic lattice strain statuses, i.e., the amount and type of the particular lattice strain, induced by the particular lattice mismatch with the substrate material 23,24 .…”

“…This is because pseudocubic notation disregards the ~0.55° of rhombohedral distortion in BFO unit cell and subsequent rhombohedral shifts in basis atom locations. As a result, the pseudocubic notation cannot interpret some of Bragg’s reflections that are specifically related to the rhombohedral characteristic as demonstrated in recent reports 21,23,24 . Thus, hereafter, hexagonal notation is used to accurately describe rhombohedral BFO in this work unless otherwise mentioned.…”

“…It should be noted that the hexagonal notation rather than the pseudocubic one is highly recommended to use to accurately describe structural details of the rhombohedral, i.e., SG of R3c , BFO 21,23,24 . This is because pseudocubic notation disregards the ~0.55° of rhombohedral distortion in BFO unit cell and subsequent rhombohedral shifts in basis atom locations.…”