Question

Problem 3. Determine the Miller indices for the plane shown in the following unit cell. If it is copper with an FCC structure, a molar mass of 63.5 g/mol and an atomic radius of 0.128 nm, calculate its planar atomic density in atoms/nm'.

Answer 1

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Miller indices, group of three numbers that indicates the orientation of a plane or set of parallel planes of atoms in a crystal. If each atom in the crystal is represented by a point and these points are connected by lines, the resulting lattice may be divided into a number of identical blocks, or unit cells; the intersecting edges of one of the unit cells defines a set of crystallographic axes, and the Miller indices are determined by the intersection of the plane with these axes. The reciprocals of these intercepts are computed, and fractions are cleared to give the three Miller indices (hkl). For example, a plane parallel to two axes but cutting the third axis at a length equal to one edge of a unit cell has Miller indices of (100), (010), or (001), depending upon the axis cut; and a plane cutting all three axes at lengths equal to the edges of a unit cell has Miller indices of (111)

The x y &z intercepte are x = 1/2 y = 1/2 Z=00 are Taking the reciprocal and the mille indeces (2,2,0) milles indices (220) 4x0.128 Given molar mass = 63.5glmal atomic radius = 0.128 nm Density of unit cell ga nam OBXNA a assidelength far fel crystal = 1 . 47 a = 0.295603 mm NA Avogadros no = 6.02214 15x10 23 De 4 atoms = 4x 63.5 C.295605) x 6.022141542823 = 1.63259x10-20 atomoloma V3 s