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phys documents (dragged) 68 - that For the maxima holds: 2...

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Chapter 12 Solid state physics 12.1 Crystal structure A lattice is defned by the 3 translation vectors ± a i , so that the atomic composition looks the same From each point ± r and ± r ± = ± r + ± T , where ± T is a translation vector given by: ± T = u 1 ± a 1 + u 2 ± a 2 + u 3 ± a 3 with u i IN .A lattice can be constructed From primitive cells. As a primitive cell one can take a parallellepiped, with volume V cell = | ± a 1 · ( ± a 2 × ± a 3 ) | Because a lattice has a periodical structure the physical properties which are connected with the lattice have the same periodicity (neglecting boundary eFFects): n e ( ± r + ± T )= n e ( ± r ) This periodicity is suitable to use ±ourier analysis: n ( ± r ) is expanded as: n ( ± r )= ± G n G exp( i ± G · ± r ) with n G = 1 V cell ²² cell ² n ( ± r )exp( - i ± G · ± r ) dV ± G is the reciprocal lattice vector . IF ± G is written as ± G = v 1 ± b 1 + v 2 ± b 2 + v 3 ± b 3 with v i IN , it Follows For the vectors ± b i , cyclically: ± b i =2 π ± a i +1 × ± a i +2 ± a i · ( ± a i +1 × ± a i +2 ) The set oF ± G -vectors determines the R¨ontgen diFFractions: a maximum in the re²ected radiation occurs iF: Δ ± k = ± G with Δ ± k = ± k - ± k ± . So: 2 ± k · ± G = G 2 . ±rom this Follows For parallel lattice planes (Bragg re²ection)
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Unformatted text preview: that For the maxima holds: 2 d sin( ) = n . The Brillouin zone is defned as a Wigner-Seitz cell in the reciprocal lattice. 12.2 Crystal binding A distinction can be made between 4 binding types: 1. Van der Waals bond 2. Ion bond 3. Covalent or homopolar bond 4. Metalic bond. or the ion binding oF NaCl the energy per molecule is calculated by: E = cohesive energy(NaCl) ionization energy(Na) + electron aFfnity(Cl) The interaction in a covalent bond depends on the relative spin orientations oF the electrons constituing the bond. The potential energy For two parallel spins is higher than the potential energy For two antiparallel spins. urthermore the potential energy For two parallel spins has sometimes no minimum. In that case binding is not possible....
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