Indexing of Trigonal and Hexagonal Systems - Practical Electron Microscopy and Database - - An Online Book - |
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Microanalysis | EM Book https://www.globalsino.com/EM/ | ||||||||
This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers. | ||||||||
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For hexagonal lattices, there are normally three choices of unit cell as shown in Figure 3091a: Figure 3091a. Hexagonal net of the hexagonal P lattice: (a) Primitive hexagonal unit cell with six prism faces indexed {hkl}, (a) Hexagonal (four-index) unit cell with six prism faces indexed {hkil} and (c) Orthohexagonal unit cell. The z-axis points out of the plane of the page. The three-axis notation in Figure 3091a (a) can be converted to the four-axis notation in Figure 3091a (b) with the equations below: For instance, Similarly, the converting of hexagonal zone axes between Miller notation [U V W] and Miller-Bravais notation [u v t w] can be given by: For your convenience, the four-axis notations can be converted to the three-axis notations with the excel file, vice versa. Figure 3091b shows different crystal planes in hexagonal and trigonal crystal structures with four-index. The a-planes are given by the {11-20} facets, the c-planes by the {0002} facets, the m-planes by the {1-100} facets, and the r-planes by the {1-102} facets of the hexagonal unit cell. Figure 3091b. Different planes in the hexagonal and trigonal crystal lattices.
Now, we can figure out the Miller-Bravais notation for vector A in Figure 3091c: Figure 3091c. Example of extractions of Miller-Bravais notations. For hexagonal structures, the lattice spacing (d-spacing) can be given by, (You can download the excel file for your own calculations) --------------------------------- [3091p]
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