Indexing of Trigonal and Hexagonal Systems  Practical Electron Microscopy and Database   An Online Book  

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 (fourindex) unit cell with six prism faces indexed {hkil} and (c) Orthohexagonal unit cell. The zaxis points out of the plane of the page. The threeaxis notation in Figure 3091a (a) can be converted to the fouraxis 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 MillerBravais notation [u v t w] can be given by: For your convenience, the fouraxis notations can be converted to the threeaxis notations with the excel file, vice versa. Figure 3091b shows different crystal planes in hexagonal and trigonal crystal structures with fourindex. The aplanes are given by the {1120} facets, the cplanes by the {0002} facets, the mplanes by the {1100} facets, and the rplanes by the {1102} facets of the hexagonal unit cell. Figure 3091b. Different planes in the hexagonal and trigonal crystal lattices.
Now, we can figure out the MillerBravais notation for vector A in Figure 3091c: Figure 3091c. Example of extractions of MillerBravais notations. For hexagonal structures, the lattice spacing (dspacing) can be given by, (You can download the excel file for your own calculations)  [3091p]


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