Bicrystallography in two dimensions: A graphical procedure. Andrew Maas Portland State University Department of Physics Nano-Crystallography Group
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1 Bicrystallography in two dimensions: A graphical procedure Andrew Maas Portland State University Department of Physics Nano-Crystallography Group 1
2 What s a bicrystal? A bicrystal in this talk is two crystals with identical structure joined together, with a planar grain boundary. The first crystal is on the left of the boundary, the second to the right. Crystal 1 Boundary/ Interface Crystal 2 SrTiO3 bicrystal viewed edge-on, [001] tilt axis (z- axis is into the screen) 2
3 Bicrystallography? Describes ideal bicrystals at the atomic level Correlates physical properties to internal structure (ShubnikovCurie principle) Real 3D bicrystals related to ideal ones by free energy minimization Z-contrast STEM image of a structural variant of a Σ 13a grain boundary in SrTiO3 3
4 State of the Field Approx. 6,000 pages of information in the International Tables of Crystallography Less than 10 pages of these 6,000 dedicated to Bicrystallography A Google search for crystallography yielded in May of 2015 about 8 million results, while bicrystallography yielded only about 750 4
5 Objective Understanding of bicrystal structures is needed High quality sub angstrom (~1 Å) resolution images available to us for the first time (Pacific Northwest National Lab) Create straightforward and generalizable method to make predictions for, and to help interpret, the experimental images Z-contrast STEM image of another structural variant of a Σ 13a grain boundary in SrTiO3 5
6 Why 2D Bicrystallography? Growing availability of aberration corrected STEM images Projection technique, 2D output 6
7 Terms and Abbreviations Simple (SC), Body Centered (BCC), and Face Centered Cubic (FCC), refers to a crystal lattice that has a cube shaped unit cell: 7
8 Terms and Abbreviations (510) refers to a plane drawn through a crystal; the plane that intersects the unit cell at (1/5,1, ). (Miller Indices) The sectioning line (gray) follows this plane in 2D projection. Tilt axis is [001] throughout this presentation. BCC or FCC metal in [001] projection 8
9 Modeling a Bicrystal in 2D A method shown in A Roadmap For The Use of Interfacial Symmetry Groups by G. Kalonji Published in 1985, did not account for boundary migration and expansion Our method can demonstrate all of these steps, and is carried out in the drawing program GIMP ( 9
![MATLAB to Create Simulated Images MATLAB code outputs: Crop, copy, and expand to desired lattice size Code outputs [001] projections](/docs-images/96/128030273/images/10-1.jpg "of Crystal Structures with Simple, Body Centered, and Face Centered Cubic lattices ReO3, a SC Bravais lattice in [001] projection 10")
10 MATLAB to Create Simulated Images MATLAB code outputs: Crop, copy, and expand to desired lattice size Code outputs [001] projections of Crystal Structures with Simple, Body Centered, and Face Centered Cubic lattices ReO3, a SC Bravais lattice in [001] projection 10
11 Create Projections of two Crystals After expanding the projected monocrystal lattice, create a copy of it in GIMP These are to be the two interpenetrated crystals BCC or FCC metal in [001] projection 11
12 Apply Rotation Mg2Sn, two FCC Bravais lattices in [001] projection 12
13 Skip rigid body shift In general grain boundary cases, when there is no Coincidence Site Lattice with a low, there can be rigid body shifts, this presentation is only concerned with special cases. 13
14 Section Line Locations and their Symmetries Select a mirror line (Green) to create an 11m boundary. Select a glide line (Blue) to create an 11g boundary. Section with any type of line not shown to create an 1 boundary. The gray box outlines the CSL unit cell. p4m m Dichromatic complex of BCC or FCC metal that produces a desired Coincidence Site Lattice (CSL with Σ = 13) in [001] projection. 14
15 Section Dichromatic Pattern / Complex The lower extreme of the selected area acts as a sectioning line. Remove from the lower crystal the selected area. Invert selection and remove from the upper crystal. Desired dichromatic complex of SrTiO3 in [001] projection, oxygen atoms faintly visible 15
16 Remove partially resolved columns Desired sectioned dichromatic pattern (CSL grain boundary) of a BCC or FCC metal in [001] projection 16
17 Remove partially resolved columns Exclude partial columns if their corresponding lattice point is not on that side of the section line. The white dots represent a lattice of mathematical points after sectioning. Desired CSL grain boundary in a BCC or FCC metal in [001] projection 17
![62o [001] tilt axis in grain](/docs-images/96/128030273/images/18-2.jpg "boundary view")
18 Results SC 11m ReO3 Σ13a (510) 22.62o FCC 11g Cu Σ13a (510) 22.62o [001] tilt axis in grain boundary viewed edge on, i.e. in [001] projection 18
19 Results BCC 11m W Σ5 (310) 36.87o FCC 11m MgO Σ5 (310) 36.87o 19
20 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
21 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
22 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
23 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
24 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
25 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
26 Comparison to Experiment Figures a, c are predicted structures, Figures b, d are Z-contrast STEM images, Material is SrTiO3 P. Moeck et al. Cryst. Res. Technol. 49 (2014)
27 The Future of the Project MatLab code improvements, other projections Integration into Open Access Crystallography (resources available at nanocrystallography.research.pdx.edu) 27
28 Thank you for listening! This work was performed in support of a a platform presentation by Prof. Peter Moeck, on August 5th 2015, at the Annual Meeting of the Microscopy Society of America. Shubnikov-Curie Principle relates bicrystallography to physical properties, G. Kalonji, A roadmap for the use of interfacial symmetry groups, J. Phys. Colloq. 46 (1985) C
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