NaCl crystallizes into a lattice which has alternate Na and Cl atoms along all

# Nacl crystallizes into a lattice which has alternate

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NaCl crystallizes into a lattice, which has alternate Na and Cl atoms along all the edges of the cube as well as through the perpendicular lines running along the middle of the faces. If the atoms were identical then it would be a simple cubic with half the lattice constant. The basis atoms are at (referred to the cubic unit cell): Na : d 1 = (0 , 0 , 0) d 2 = parenleftbigg 1 2 , 1 2 , 0 parenrightbigg d 3 = parenleftbigg 1 2 , 0 , 1 2 parenrightbigg d 4 = parenleftbigg 0 , 1 2 , 1 2 parenrightbigg Cl : d 5 = parenleftbigg 1 2 , 1 2 , 1 2 parenrightbigg d 6 = parenleftbigg 0 , 0 , 1 2 parenrightbigg d 6 = parenleftbigg 0 , 1 2 , 0 parenrightbigg d 6 = parenleftbigg 1 2 , 0 , 0 parenrightbigg 2.2.4 Diamond lattice Carbon, Silicon, Germanium and compounds like GaAs, InSb, ZnS, SiC crytallize in a lattice that is fcc with a two atom basis. The cubic unit cell has 8 atoms in it, each of the four fcc lattice points contributing two atoms. The second atom is displaced along the diagonal of the cube by 1 4 th of the cubes diagonal. So we have for the basis in terms of the cubic lattice vectors a i
2.2. A FEW COMMON LATTICE TYPES 21 Figure 2.9: The NaCl lattice. The cubic lattice constant a = 5 . 6 ˚ A and for KCl , KBr , LiH , AgBr , PbS all have similar lattices. d 1 = (0 , 0 , 0) d 2 = parenleftbigg 1 2 , 1 2 , 0 parenrightbigg d 3 = parenleftbigg 0 , 1 2 , 1 2 parenrightbigg d 4 = parenleftbigg 1 2 , 0 , 1 2 parenrightbigg d 5 = parenleftbigg 1 4 , 1 4 , 1 4 parenrightbigg d 6 = parenleftbigg 3 4 , 3 4 , 1 4 parenrightbigg d 7 = parenleftbigg 1 4 , 3 4 , 3 4 parenrightbigg d 8 = parenleftbigg 3 4 , 1 4 , 3 4 parenrightbigg (2.17)
22 CHAPTER 2. DIFFRACTION AND BASICS OF CRYSTAL STRUCTURE Figure 2.10: The diamond lattice. On the left column, we have used the cubic unit cell, on the right we use the FCC primitive vectors. The cubic lattice constant a = 3 . 57 ˚ A and for Si a = 5 . 43 ˚ A
2.2. A FEW COMMON LATTICE TYPES23PROBLEM : Whichhklreflections would be cut off by this basis, following eqns. 2.18 and 2.19? Considerthe general reciprocal lattice vector to be of the formG=hb1+kb2+lb3Can you see the advantage of making the basis as small as possible?

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• Fall '13
• Crystallography, Cubic crystal system, Reciprocal lattice, Brillouin zone, Lattice points