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Lecture note 3 (09-13-2011)

Lecture note 3 (09-13-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 3 Miller–Bravais indices It should be borne in mind that the general purpose of the Miller procedure is to define the orientation of a family of parallel equidistant planes; the selection of a convenient representative plane is a means to this end. For this reason, it is permissible to shift the origin provided that the relative disposition of a , b and c is maintained. Miller indices are commonly written in the symbolic form ( h k l ). As mentioned previously, it is sometimes convenient to choose a non-primitive cell. The hexagonal structure cell is an important illustrative example. For reasons which will be explained, it is also appropriate to use a four-axis Miller–Bravais notation ( h k i l ) for hexagonal crystals , instead of the three-axis Miller notation ( h k l ). In this alternative method, three axes ( a 1 , a 2 , a 3 ) are arranged at 120 o to each other in a basal plane and the fourth axis ( c ) is perpendicular to this plane (Figure 1.9a). Hexagonal structures are often compared in terms of the axial ratio
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