The image above represents frenkel defect.

To compute for frenkel defect, four essential parameters are needed and these parameters are **N, activation energy (Q _{fr}), Boltzmann’s Constant (K)** and

**temperature (T).**

The formula for calculating the frenkel defect:

N_{fr} = N exp (^{-Qfr }/ _{2KT})

Where:

N_{fr} = Frenkel Defect

Q_{fr} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the frenkel defect when the activation energy is 34, N is 22, Temperature is 12 and the boltzmann’s constant is 1.38064852e-23.

This implies that;

Q_{fr} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

N_{fr} = N exp (^{-Qfr }/ _{2KT})

N_{fr} = (22)exp(^{-(34) }/ _{2(1.38064852e-23)(14)})

N_{fr} = (22)exp(^{(-34) }/ _{(3.865815856e-22)})

N_{fr} = (22)exp(-8.795038684325786e+22)

N_{fr} = (22)(0)

N_{fr} = 0

Therefore, the **frenkel defect **is **0.**

**Calculating the Activation Energy when the Frenkel Defect, the Boltzmann’s Constant and the Temperature is Given.**

Q_{fr} = – (In (^{Nfr} / _{N}) x 2KT)

Where;

Q_{fr} = Activation Energy

N_{fr} = Frenkel Defect

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Given that the frenkel defect is 20, the boltzmann’s constant is 5, the temperature is 2 and N is 10. Find the activation energy?

This implies that;

N_{fr} = Frenkel Defect = 20

K = Boltzmann’s Constant = 5

T = Temperature = 2

N = 10

Q_{fr} = – (In (^{Nfr} / _{N}) x 2KT)

Q_{fr} = – (In (^{20} / _{10}) x 2 x 5 x 2)

Q_{fr} = – (In 2 x 20)

Q_{fr} = – (In 40)

Q_{fr} = – 3.688

Therefore, the **activation energy **is **– 3.688.**

Continue reading How to Calculate and Solve for Frenkel Defect | Ceramics