exercise2 - MTPA 1 Condensed Matter Theory I Exercise sheet...

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MTPA 1 : Condensed Matter Theory I Exercise sheet 2, 10.10.2014 LPTM, Universit´ e de Cergy-Pontoise Prof. Andreas Honecker Exercise 2.1 Hexagonal closed-packed “lattice” A hexagonal closed-packed (hcp) structure is called “ideal” if it corresponds to a close packing of spheres centered around its lattice points. (a) Show that c/a = 8 / 3 for an ideal hcp structure. (b) Sodium metal transforms from bcc to hcp at about 23 K (the “martensitic” transformation). Assuming that the density remains fixed through this transition, find the lattice constant a of the hexagonal phase, given that a = 4 . 23 ˚ A in the cubic phase and that the c/a ratio is ideal. Exercise 2.2 Reciprocal lattice Given a set of primitive vectors a i of a d -dimensional direct lattice and a set of primitive vectors b j of the reciprocal lattice with
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