The question asks for the correct relationship between diffusion coefficients for different paths: lattice ($D_L$), grain boundaries ($D_{GB}$), and free surfaces ($D_S$).
Diffusion Mechanism Comparison
Diffusion rates depend on the atomic mobility along the diffusion path. Different paths offer varying degrees of atomic order and energy barriers:
- Lattice Diffusion ($D_L$): Occurs through the bulk crystal lattice. This path is highly ordered, and atoms require significant energy (often needing vacancies) to jump between lattice sites. It is generally the slowest diffusion mechanism.
- Grain Boundary Diffusion ($D_{GB}$): Occurs along the interfaces between crystal grains. Grain boundaries have a less ordered structure than the lattice, providing easier paths for atomic movement. Diffusion is faster than along the lattice.
- Surface Diffusion ($D_S$): Occurs along free surfaces of the material. Surfaces are the least ordered regions with the highest atomic mobility and lowest energy barriers for movement. This is typically the fastest diffusion mechanism.
Determining the Correct Relation
Based on the relative ease of atomic movement:
- Surface diffusion is the fastest: $D_S$ is the largest.
- Grain boundary diffusion is intermediate: $D_{GB}$ is less than $D_S$ but greater than $D_L$.
- Lattice diffusion is the slowest: $D_L$ is the smallest.
Therefore, the correct relationship is:
$ D_S > D_{GB} > D_L $
This corresponds to Option 4.
Important Questions from Diffusion Fick's Second Law Concentration Profile
During carburizing of a steel, the surface concentration is kept constant at 1.4 wt.% carbon. Diffusivity of carbon for the steel at 950 $^\circ$C is $6.25 \times 10^{-11}$ m$^2$/s. At 950 $^\circ$C, the time required to carburize the steel with an initial composition of 0.2 wt.% carbon to 0.8859 wt.% carbon at a depth of 0.2 mm is ______________ seconds (approximate to the nearest integer).
Use the nearest value of the error function from the table given below for your calculation.
z erf (z) 0.3 0.3268 0.4 0.4284 0.5 0.5205 - What is the depth (in $µm$) from the surface of the specimen at which a composition of 0.4 wt.% C is obtained after carburizing at $870^\circ C$ for 10 h?
For self-diffusion in polycrystalline copper with a lattice diffusion coefficient $D_L$, grain boundary diffusion coefficient $D_{GB}$, and surface diffusion coefficient $D_S$, the correct relationship is
- The concentration $C$ of a solute (in units of atoms$\cdot\text{mm}^{-3}$) in a solid along $x$direction (for $x > 0$) follows the expression
$C = a_1x^2 + a_2x$
where $x$ is in mm, $a_1$ and $a_2$ are in units of atoms$\cdot\text{mm}^{-5}$ and atoms$\cdot\text{mm}^{-4}$,respectively. Assuming $a_1= a_2= 1$, the magnitude of flux at $x = 2 \text{ mm}$ is________ $\times 10^{-3} \text{ atoms} \cdot \text{mm}^{-2} \cdot \text{s}^{-1}$ (answer rounded off to the nearest integer).
Given: diffusion coefficient of the solute in the solid is $3 \times 10^{-3} \text{ mm}^2 \cdot \text{s}^{-1}$. - Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]
Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B.
Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries.
