C. Miller Indices for Crystal Directions & Planes. Because crystals are usually anisotropic (their properties differ along different directions) it is useful to regard a . Lecture 5: Crystal planes and Miller Indices. Index system for crystal directions and planes. Crystal directions: Any lattice vector can be written as that given by. Miller indices define directional and planar orientation within a crystal . [3] K.J. Hemker, “Crystallography,” [cited Feb 7], Available PDF.

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Miller indices are used to specify directions and planes. • These directions and planes could be in lattices or in crystals. • The number of indices will match with. intuitively understood and hence some time has to be spent to familiarize oneself with the notation. Miller Indices. Directions. Planes. Miller Indices. Lattices. Materials: inorganic, organic, biological, rigid/flexible. • Fabrication: photo/e- beam lithography, self-assembly, 2D/3D print. • Dimensions: quantum dots.

New York: Holt, Rinehart and Winston. That is, the Miller indices are proportional to the inverses of the intercepts of the plane, in the basis of the lattice vectors. For all these reasons, it is important to determine the planes and thus to have a notation system. Although many quasicrystals, such as the Penrose tiling , are formed by "cuts" of periodic lattices in more than three dimensions, involving the intersection of more than one such hyperplane.

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