Point defects question: Known that a self interstitial defect has formation ener

Question

Point defects question:

Known that a self interstitial defect has formation energy Q_si and a vacancy defect has a formation energy Q_v. [Q_si = 4 Q_v]. If Q_si = 35 kJ/mol, calculate the temperature when [self interstitials : vacancies = 10^-6 ].

Use following equation:

Here N is the # of atomic sites per unit volume, Nv is the number of vacancies per unit volume, Qv is the activation energy for vacancy formation, k is Boltzmann's constant, and T is the absolute temperature (Kelvin or Rankine).

Explanation / Answer

As Qsi = 4Qv = 35 kJ/mol

Hence, Qv = 35/4 kJ/mol

= 8.75 kJ/mol

Also as per the given equation

Nv = Noexp(-Qv/kT)

And, we want to find temperature, when

Nv = 10-6No

Hence,

10-6No = No exp(-8750/kT)

Or

10-6 = exp(-8750/kT)

Taking natural logarithm on both sides,

-6 ln(10) = -8750/kT

6 x 2.303 = 8750/kT

Hence,

T = 8750/(6 x 2.303 x 1.38 x 10-23)

T = 4.58 x 1021 K

Which is extemely unlikely.

I guess there is something missing or value of number of vacanies may be different.

This is as per the method and information provided by you. If you find any corrections to be made in question, kindly make a comment and I will try to help with that.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects