Question

Given that for a typical metal the energy for vacancy formation is on the order of 1 eV/atom, melting point is 10^3 K, molar mass is 10^2 g/mol and density is 10 g/cm3.

1.) Near melting point the fraction of vacant lattice sites is:
a) <10^-5
b) 10^-5 to 10^-3
c) 10^-3 to 10^-2
d) 10^-2 to 10^-1

2.) The number of vacant sites per cm^3 is typically:
a) <10^3
b)10^3 to 10^6
c) 10^6 to 10^9
d) > 10^9

3.) By what factor does the number of vacant sites increase when going from 300K to 400K for the typical 'order of magnitude' metal above?

Answer 1

a.) Given,

energy for vacany formation= 1eV/atom ie Q_V=1eV/atom , T=1000k

N_v/N=exp[-Q_v/KT]

N_v/N= exp[-1/(8.62x10^-5eV/atom-k)(1000)]

=exp[-1/0.082]

= 10^-5 therefore answer is a.) 10^-5

^{b.) number of vacant sites per cm.cube at 1000k}

^N_V = N exp [-Q_v/KT]

=Na P/ A exp [-Q_V/KT]

= [((6.022x10²³atoms/mol)(10)g/cm³)/100g/mol]x 10^-5

⁼ 6.022x10¹⁷ cm³

therefore d.>10⁹

c.) N_v/N = exp (-delta H_s/ 2KT);

as temperature increases vacancy sites increases.

number of vacany sites increased by the factor of 2