Question

Is there an expansion or a contraction as titanium transforms from hep to body-centered Cubic ? The atomic radius of titanium is `145.8` pm in hep but `142.5` pm is bcc.
A. Expansion of `3.2 %`
B. Expansion of `1.016`
C. Contraction of `3.2 %`
D. Contraction of `1.016`

Answer 1

Correct Answer - B
The volume change is a result of two partically contracting factors: (1) different
packing fraction (f), and (2) different radii
`(V("bcc"))/(V("hcp"))=(f("hcp"))/(f("bcc"))xx(V("bcc"))/(V("hcp"))`
f(hcp)=0.7404,f(bcc)=0.6802
`(V_("bcc"))/(V("hcp"))/(V_("hcp"))=(0.7404)/(0.6802)xx((142.5)^(3))/((145.8)^(3))=1.016`