Chapter 5, Problem 5.61P

Interpretation Introduction

(a)

Interpretation:

The carbon content at 0.05cm beneath the surface needs to be calculated, if iron in BCC is given also carbon present is 0.05% is heated at 912⁰C at atmosphere which produces 1.20% C at the surface and held for 24hr.

Concept Introduction:

Fick's second law equation is given by the following relation:

  $\frac{Cs-Cx}{Cs-Co}=erf(\frac{x}{2\sqrt{Dt}})$ ---------------- (a)

Here,

D = diffusion coefficient

Cs = constant concentration for the material surface of diffusion atoms.

Co = initial concentration of diffusion on

Cx = diffusing concentration atom at location x

T = time

Also diffusion coefficient for carbon in BCC by Arrhenius type equation relation is as follows:

  $D_{acc}=D_o\exp (\frac{-Q}{RT})$ -------------------- (b)

Where,

Dacc = diffusion coefficient

Do = constant

Q = activation energy

R = Gas constant

T = absolute temperature

Interpretation Introduction

(b)

Interpretation:

The carbon content at 0.05 beneath the surface needs to be determined, if the iron is FCC, also given that iron-containing 0.05% c is heated at 912⁰C, 1.20% C at the surface, time is 24 hr. The diffusion in iron in BCC and in FCC needs to be explained.

Concept Introduction:

Fick's second law equation is given by the following relation:

  $\frac{Cs-Cx}{Cs-Co}=erf(\frac{x}{2\sqrt{Dt}})$ ---------------- (a)

Here,

D = diffusion coefficient

Cs = constant concentration for the material surface of diffusion atoms.

Co = initial concentration of diffusion on

Cx = diffusing concentration atom at location x

T = time

Also diffusion coefficient for carbon in FCC by Arrhenius type equation relation is as follows:

  $D_{acc}=D_o\exp (\frac{-Q}{RT})$ -------------------- (b)

Here,

Dacc = diffusion coefficient

Do = constant

Q = activation energy

R = Gas constant

T = absolute temperature