Question

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

• A. D\(_S\) > D\(_{GB}\) > D\(_L\)
• B. D\(_L\) > D\(_S\) > D\(_{GB}\)
• C. D\(_{GB}\) > D\(_S\) > D\(_L\)
• D. D\(_{GB}\) = D\(_S\) = D\(_L\)

Hint:

Think of diffusion paths like different types of roads: - {Surface Diffusion (\(D_S\))} is like a superhighway (most open, fastest). - {Grain Boundary Diffusion (\(D_{GB}\))} is like a main road (less congested than city streets, intermediate speed). - {Lattice Diffusion (\(D_L\))} is like navigating through a crowded city grid (densely packed, slowest).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Diffusion is the thermally activated movement of atoms in a material. In a polycrystalline material, atoms can move through different paths: through the perfect crystal lattice (bulk), along the grain boundaries (interfaces between crystals), and along the free surface. The rate of diffusion depends on the activation energy required for an atom to jump, which in turn depends on the atomic packing of the diffusion path.
Step 2: Detailed Explanation:
Let's compare the three diffusion paths based on their atomic structure:
- Lattice Diffusion (D\(_L\)): This is diffusion through the bulk of the crystal grain. Atoms move by jumping into adjacent vacant lattice sites. This path is the most difficult because the crystal lattice is densely packed, and moving an atom requires significant energy to break bonds and squeeze past neighboring atoms. Therefore, lattice diffusion has the highest activation energy and is the slowest process.
- Grain Boundary Diffusion (D\(_{GB}\)): Grain boundaries are planar defects that separate crystals of different orientations. The atomic arrangement at a grain boundary is more disordered and less tightly packed than in the perfect lattice. This "open" structure provides an easier path for atoms to move. The activation energy for grain boundary diffusion is lower than for lattice diffusion, making it a faster process (\(D_{GB}>D_L\)).
- Surface Diffusion (D\(_S\)): The free surface of the material is the most open structure of all. Atoms on the surface are bonded to fewer neighboring atoms compared to atoms in the bulk or at a grain boundary. This means the energy barrier for an atom to move along the surface is the lowest. Consequently, surface diffusion has the lowest activation energy and is the fastest diffusion mechanism.
Step 3: Final Answer:
Combining these observations, the order of the diffusion coefficients from fastest to slowest is: \[ D_S>D_{GB}>D_L \] Step 4: Why This is Correct:
The relationship is a direct consequence of the atomic packing density of the diffusion paths. More open structures (like surfaces and grain boundaries) have lower activation energies for diffusion and thus exhibit faster diffusion rates compared to the densely packed crystal lattice.