The figure shows the cubic lattice cell of nickel. Nickel has a face-centered cr

Question

The figure shows the cubic lattice cell of nickel. Nickel has a face-centered crystal structure, an atomic number of 28, atomic mass of 58.69, valance of 2+, and an atomic radius of 1.25 angstroms. (1 angstrom = 10^-10 meters and Avogadro's Number = 0.602*10^24) Show all calculations to determine:

a) The value of the atomic packing factor in the face-centered cubic crystal structure.

b) The density of nickel in grams/cm^3

c) The indices for the direction going from point "2" to the point "4" of the figure and the linear density of the nickel atoms along this direction.

d) The Miller indices of the plane going through the points "2", "4", and "6" and the planar density of the nickel atoms on this plane.

Explanation / Answer

1)atomic packing factor = volume occupied by element/total volume of cell now atomic size r = a /2*sqrt2, where a is cell dimension, so atomic packing factor = 4*4/3pi*r^3/ a^3 = 0.74. 2) density = mass/volume = 4*(Z/avogadro number)/a^3 = 8.85kg/m^3. Miller Indices 2:4:6 1/2:1/4::1/6 6:3:2

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