Question

Titanium (Ti) has an HCP crystal structure and a density of 4.51 g/cm^3. What is the volume of the unit cell in cubic meters? If the c/a ratio is 1.58, compute the values of c and a.

Answer 1

density = (Z*Mwt )/ (NA * Volume of unit cell)

volume of unitcell = (Z*Mwt )/ (NA * density)

Z = for hexagone, it is 6

Mwt of Ti =  47.87 g

NA = 6.023*10²³

density = 4.51 g/cm³

volume = 6*47.87 / (6.023*10²³ * 4.51)

Volume of unitcell = 287.7/27.16*10²³= 10.6*10^-23 cm³

Volume = 3(1.41)a²*c

10.6*10^-23 = 4.2 (a²*c)

a²*c = 2.5 *10^-23

c/a = 1.58 so c=1.58a

a²*1.58a=  2.5 *10^-23

a³ = 1.59 *10^-23

a³ = 15.9 *10^-24

a = 2.52 *10^-8 cm = 252 *10^-10 cm

a = 252 pm

c =a*1.58 = 252*1.58 = 398 pm