lec-26-Chap11-3_4-1

lec-26-Chap11-3_4-1 - Crystalline Solids 2d unit cell...

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1 48 Crystalline Solids 2 d unit cell unit cell example: • The unit cell is a square. • Each corner contributes ¼ of a circle to the unit cell. • Net of 1 circle/unit cell. • The entire lattice can be formed by adding unit cells to each face 49 Cubic Unit Cells Crystals have 3 d unit cells. There are 7 types . The simplest are the cubic cells with 3 subtypes: – simple (or primitive) cubic (sc). – body-centered cubic (bcc). – face-centered cubic (fcc). Faces meet at 90° with equal-length sides. 50 Cubic Unit Cells Primitive (simple) cubic Primitive (simple) cubic (sc) • Atoms sit at the corners of squares. • Layers stack atom-on-atom. • One atom/cell (8 x 1/8). • Atoms occupy 52 % of the total V . 1 3 2 4 5 6 at rear Each atom has 6 equivalent neighbors: 51 Cubic Unit Cells Body Body -centered cubic centered cubic (bcc) (bcc) • An extra (unshared) atom sits in the center • (8 x 1/8 ) + 1 = 2 atoms/cell 68 % of the space is occupied. 52 Cubic Unit Cells Face Face -centered cubic centered cubic (fcc fcc ) 1 atom at the center of each face. Face atoms are shared by 2 cells. (corner atoms are shared by 4 cells) (6 x ½ + 8 x 1/8 ) = 4 atoms/cell. 74 % of the space is filled by atoms 53 Closest Packing of Spheres Metal crystals have equal-sized atoms (spheres).
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lec-26-Chap11-3_4-1 - Crystalline Solids 2d unit cell...

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