Near Atomic Row Matching in the Interface Analyzed in Both Direct and Reciprocal Space

Abstract

Reproducible crystallographic features between new phase and matrix are often observed during phase transformation, including orientation relationship, interfacial orientation, morphology, and so on. The geometrical matching in the interface is the key to understanding the preferred transformation crystallography. Recently, a new geometrical method emphasizing the atomic row matching in the interface, the so-called near row matching method, has been proposed to predict the preferred orientations between two arbitrary crystals. In this work, this method originally expressed in direct space was further extended to the reciprocal space. These two methods were implemented in our free software PTClab (version 1.19). It is found that these two expressions are nearly equivalent. As the near row matching in reciprocal space could be directly measured by the diffraction patterns with transmission electron microscopy (TEM), the condition of atomic row matching would be easily identified in reciprocal space during TEM work, and could be applied to rationalize the experimental observations. Several examples in bothsmall and large misfit alloy systems are shown to apply the near tow matching method in both direct and reciprocal space. Furthermore, the row matching method is compared with other models, and there are some crucial aspects that need extra attention when being applied to prediction.

Study of the epitaxy between ɛ-Fe2O3, hematite and spinel in brown-glazed Chinese ceramics using electron diffraction mapping techniques

“…The corresponding lattice mismatch (in this case, the linear mismatch) between the structures (Gu, 2020) was calculated: 2.80% between the "-Fe 2 O 3 phase and the spinel, 0.92% between the "-Fe 2 O 3 phase and the hematite, and 1.87% between the hematite phase and the spinel. As a mismatch lower than 5% is generally considered to allow epitaxial growth of one species on another (Nahhas et al, 2001;Liu & Zhang, 2020), the situation appears therefore favourable for epitaxial growth of hematite and spinel on "-Fe 2 O 3 in this case.…”

Reproducible Orientation Relationships Developed from Phase Transformations—Role of Interfaces

“…Similarly, one may also obtain the matching correspondence and associated interfacial geometry by conducting the second step in reciprocal space [25]. In the parallel zone axes defined by the pair of good-matching vectors, one arranges the 2D reciprocal points so that rows in different lattices with similar spacing lie parallel to each other to form an OR that meets the near-matching-row condition.…”

“…Compared to the method in direct space, it is straightforward to understand the observed OR, when near row matching is visible in a measured diffraction pattern, since the direction of the near-matching rows is usually normal to a preferred interface. In addition, it is more convenient to conduct the additional second step in the same plane in reciprocal space by a slight change in the OR, and find another pair of planes containing near-matching rows in direct space (i.e., K-S OR and Pitsch OR as demonstrated by Gu and shown in Figure 4 in [25]). Then, the matching correspondence in 3D can be determined in a way similar to the method in direct space.…”

“…The near-matching-row method can also be applied to determine the expression of the measured OR in terms of the proper representative rational OR [25]. Though it is conventional to express the measured OR in terms of low-index vectors of either lattice or both lattices, the expression with a representative rational OR carries an implication of the preferred state.…”

“…Similar to these methods of systematic searching in reciprocal space, the present study suggests using simple steps in the near-row-matching method [20] to search the ORs corresponding to good matching in direct space. A combined search in direct and reciprocal space for planes that meet the near-row-matching condition is also recommended [25]. The range of search with this method is small, since it aims to find geometries that allow the existence of GMS clusters to serve as potential positions for a preferred state, as the core criterion for the OR.…”