Question

Q3) Using the following data that relates to the formation of vacancy defects in a metallic sample. Determine the following: a) The energy for defect formation in (V) b) The equilibrium number of vacancy defects per cubic meter at 1000 C T°C] Nv/ ml 750 5.7 x 10 1000 ? 1500 5.8 x 1017 Q4) Draw a series of schematics (3 to 4) representing edge dislocation motion up to the surface of a crystal lattice. Clearly show the direction of the shear stress applied.

Can you please solve 3 and 4 with neat handwriting ? Could you explain each step so I can understand?

Answer 1

Multiple questions, as per guideline one to be solved, so as per guideline only first will be solved:

3. Vacancy defects in a metallic crystal are dealt by this equation:

Nv / N = exp. ( -$\Delta$H /kT)

(Nv = No. of vacancies , N = no. of atoms in a crystal )

; $\Delta$H =enthalpy/energy of formation of one vacancy ; k = boltzmann constant)

(a) Energy for defect formation (in eV);

• at, T = 750 C = 1023 K ;   Nv = 5.7*10⁹ / m3

k =   8.62 * 10^–5 eV/K

5.7*10⁹ / m3    / N = exp. ( -$\Delta$H /0.088 eV)   

or ln ( 5.7*10⁹ / m3    / N ) = -$\Delta$H /0.088 eV ...............1

• at, T = 1500 C = 1773 K ;   Nv = 5.8*10¹⁷ / m3

k =   8.62 * 10^–5 eV/K

5.8*10¹⁷ / m3   / N = exp. ( -$\Delta$H /0.153 eV)   

or ln ( 5.8*10¹⁷ / m3 / N ) = -$\Delta$H /0.153 eV ......................2

from 1 and 2

we have   ln ( 5.8*10¹⁷   / N ) /  ln ( 5.7*10⁹   / N ) = 0.575

or we have ( ln 5.8*10¹⁷  ) -( ln  N ) / (ln 5.7*10⁹  - ln N)  = 0.575

or ln N = 65.835 or N = 3.91*10²⁸ /m3

So, Energy for defect formation (in eV)

using data for 750 C ;    (5.7*10⁹ / m3 ) / (3.91*10²⁸ /m3) = exp. ( -$\Delta$H /0.088 eV)

1.458*10^-19 =    exp. ( -$\Delta$H /0.088 eV)

-43.37 =  -$\Delta$H /0.088 eV

or $\Delta$H = 3.82 eV (energy for defect formation)

1(b) No. of equilibrium Vacancy defect per cubic meter at 1000 C

  Nv / N = exp. ( -$\Delta$H /kT)

  Nv /(3.91*10²⁸ /m3) =   exp. (- 3.82 eV /0.1097 eV) = 7.53*10^-16

Nv (@ 1000 C or 1273 K ) = 2.95* 10¹³