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Physics 4340: Introduction to Solid State Physics Lecture 30: More X-ray diffraction Think about the summation: e iK R R For some arbitrary K, and for a large number of unit cells (going towards infinitely large) this sum is likely to yield: A) B) C) D) E) Infinity (infinite number of terms) Zero (equal pos. and neg. contribs) Always goes to 1 Number atoms in unit cell Something else Think about the summation: e iK R R For some special K, this sum has a simple limiting result. What are some special K? A) B) C) D) I like K = 0 I like K = 2p I like K = 2p/R I like something else for special K. What is the sum in that limit? Only 14 distinct styles of lattice in 3-d. (Bravis and Frankenheim) http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bravais.html Only 5 distinct styles of lattice in 2-d. http://staff.chess.cornell.edu/~smilgies/xrd/IntroductionSurfaces.html http://www.atpm.com/8.08/periodic-table.shtml Wigner-Seitz unit cell examples BCC lattice FCC lattice http://what-when-how.com/electronic-properties-of-materials/ energy-bands-in-crystals-fundamentals-of-electron-theory-part-2/ Only 14 distinct styles of lattice in 3-d. Applies equally to the Recip. Lattice, which are the F.T. of direct lattice. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bravais.html