Copper Iodide (CuI) can form in either a table-salt like cubic lattice structure

Question

Copper Iodide (CuI) can form in either a table-salt like cubic lattice structure, or the complex structure shown below. In the salt-like structure, CuI is a good iodine supplement for the plant goats, who keep the grass on the hillside cut short (an important safety function credited in the FSAR to prevent loss of offsite power through grass fires). However, in the complex structure at right, the material can be fatal to your safety-related goats. Calculate the density of each phase, so that the purchasing department can verify that they are obtaining the correct form of CuI. Note: you would have to make some assumption in order to calculate the edge length of the unit cell at right, but let’s say that it is a cube and that the two interior atoms are at the bcc center position and the center of the bottom face, which is close enough for a rough density value.

Explanation / Answer

LEFT SIDE PHASE IS FCC MODEL LATTICE .

RIGHT SIDE PHASE IS BCC LATTICE(AS PER GIVEN INFORMATION AND DESIGN)

DENSSITY OF FCC LATTICE

d = mass /volume = number of atoms in fcc unit cell*volume of singleatom/volume of the cube

number of atoms in fcc unit cell= 4

volume of singleatom = (4/3)pi r3

volume of the cube = a3 note for fcc lattice r = 1.414*a/4 [ a= side of the cube]

on substituting the values & calculationwe density of phase on the left side = 22/21*1.414 = 0.74 gr/cc(cgs units)

for bcc lattice r = 1.732 8a/4

for bcc number of atoms in the unit cell =2

so substituing values and calculatiing we have density of bcc lattice = 1.732.*22/56 = 0.68 gr/cc (cgs unis)

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