Primitive Cell Wigner-Seitz Cell (WS) Primitive Cell

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Primitive Cell Wigner-Seitz Cell (WS) Primitive Cell

Lecture 4 Jan 16 2013 Primitive cell Primitive cell Wigner-Seitz cell (WS) First Brillouin zone The Wigner-Seitz primitive cell of the reciprocal lattice is known as the first Brillouin zone. (Wigner-Seitz is real space concept while Brillouin zone is a reciprocal space idea). Powder cell Polymorphic Forms of Carbon Graphite – a soft, black, flaky solid, with a layered structure – parallel hexagonal arrays of carbon atoms – weak van der Waal’s forces between layers – planes slide easily over one another Miller indices Simple cubic Miller Indices Rules for determining Miller Indices: 1. Determine the intercepts of the face along the crystallographic axes, in terms of un it ce ll dimens ions. 2. Take the reciprocals 3. Clear fractions 4. Reduce to lowest terms Simple cubic d100=? Where does a protein crystallographer see the Miller indices? CtlCommon crystal faces are parallel to lattice planes • Eac h diffrac tion spo t can be regarded as a X-ray beam reflected from a lattice plane , and therefore has a unique Miller index. Miller indices A Miller index is a series of coprime integers that are inversely ppproportional to the intercepts of the cry stal face or crystallographic planes with the edges of the unit cell. It describes the orientation of a plane in the 3-D lattice with respect to the axes. The general form of the Miller index is (h, k, l) where h, k, and l are integers related to the unit cell along the a, b, c crystal axes. Irreducible brillouin zone II II II II Reciprocal lattice ghakblc The Bravais lattice after Fourier transform real space reciprocal lattice normaltthlls to the planes (vect ors ) poitints spacing between planes 1/distance between points ((y,p)actually, 2p/distance) l (distance, wavelength) 2p/l=k (momentum, wave number) BillBravais cell Wigner-SiSeitz ce ll Brillouin zone .

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