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- A family of directions is a set of directions related by symmetry operations of the lattice or the crystal12. In cubic systems, directions that have the same indices are equivalent regardless of their order or sign3. A family of directions is represented by angle brackets and Miller indices, such as < u v w >145. A family of directions can help define planes in the crystal4.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.A set of directions related by symmetry operations of the lattice or the crystal is called a family of directions. A family is a symmetry related set. A family of directions is represented (Miller Index notation) as: < u v w >.scoop.eduncle.com/119-a-family-of-direction-is-repr…Family of Directions It’s a set of directions related by symmetry operations of the lattice.web.iit.edu/sites/web/files/departments/academic-a…Families of Directions (i.e., directions of a form) In cubic systems, directions that have the same indices are equivalent regardless of their order or sign.weavergroup.ua.edu/uploads/4/8/9/0/48901279/08…“Family” of directions is designated as <110>. DIRECTIONS will help define PLANES (Miller Indices or plane normal).nanohub.org/resources/5488/download/ch3_p3.pdfBecause of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes: Indices in angle brackets such as ⟨100⟩ denote a family of directions which are equivalent due to symmetry operations, such as,, or the negative of any of those directions.en.wikipedia.org/wiki/Miller_index
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