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.
Assertion [a] Analysis: Homogenization Rate
The assertion states that the rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B. Homogenization involves the uniform distribution of solute atoms (B) within the solvent (A). This process occurs via diffusion, where atoms move from regions of high concentration to low concentration. In a dilute solution, the movement of B atoms is the primary factor enabling homogeneity. The speed of this atomic movement is directly quantified by the diffusion coefficient, or diffusivity, of the diffusing species, which in this case is B. Therefore, the diffusivity of B, denoted as $D_B$, dictates how quickly the solution homogenizes.
Conclusion: Assertion [a] is true.
Reason [r] Analysis: Atomic Migration Paths
The reason claims that atomic migration cannot occur along dislocations and grain boundaries. However, these crystalline defects significantly influence diffusion rates.
- Dislocations: These are linear defects in the crystal lattice. The atomic packing is less dense along dislocation cores, making it easier for atoms to move.
- Grain Boundaries: These are interfaces between different crystal grains. Atoms are less tightly bound at grain boundaries compared to the bulk lattice, allowing for faster migration.
These regions are often referred to as "short-circuit paths" because diffusion occurs much more rapidly along them than through the bulk lattice. Thus, atomic migration *can* and typically *does* occur readily along dislocations and grain boundaries, especially at lower temperatures where bulk diffusion is slow.
Conclusion: Reason [r] is false.
Final Determination
Based on the analysis:
- Assertion [a] is true.
- Reason [r] is false.
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 $3 \times 10^{-3} \text{ mm}^2 \cdot \text{s}^{-1}$. - A species can diffuse through the lattice (diffusion coefficient, $D_L$), along grain boundaries (diffusion coefficient, $D_{GB}$), and along free surfaces (diffusion coefficient, $D_S$). Which of the following relations is CORRECT?
