Question

The Pilling-Bedworth ratio is defined as:

• A. Density of oxide/ Density of metal
• B. Mass of oxide/ mass of metal
• C. Volume of oxide/ Volume of metal
• D. Volume of metal/ Volume of oxide

Hint:

Remember the PBR rule of thumb:
- If PBR \( \lt 1 \), the oxide is porous and non-protective.
- If \( 1 \lt \text{PBR} \lt 2 \), the oxide layer is protective and passive.
- If PBR \( \gt 2 \), the oxide film undergoes spallation due to excessive compressive stresses.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the fundamental definition of the Pilling-Bedworth ratio (PBR), which is a key parameter used in metallurgy and corrosion engineering to predict the protective nature of oxide scales formed on metal surfaces.

Step 2: Key Formula or Approach:
The Pilling-Bedworth ratio is mathematically expressed as the ratio of the volume of the metal oxide scale to the volume of the metal consumed to produce that scale:
\[ \text{PBR} = \frac{V_{\text{oxide}}}{V_{\text{metal}}} \]
This can be rewritten in terms of molecular weights and densities as:
\[ \text{PBR} = \frac{M_{\text{oxide}} \cdot \rho_{\text{metal}}}{n \cdot M_{\text{metal}} \cdot \rho_{\text{oxide}}} \]
where:
\( M_{\text{oxide}} \) is the molecular weight of the metal oxide.
\( M_{\text{metal}} \) is the atomic weight of the metal.
\( \rho_{\text{oxide}} \) is the density of the metal oxide.
\( \rho_{\text{metal}} \) is the density of the metal.
\( n \) is the number of metal atoms per molecule of oxide.

Step 3: Detailed Explanation:

• Physical Significance of PBR Values:
-

PBR $\lt $ 1: The volume of the oxide scale is smaller than the volume of metal consumed.
This causes the oxide film to be highly porous and under tensile stress, allowing oxygen to continuously diffuse to the metal surface.
Examples include light metals like sodium and magnesium, which oxidize rapidly and non-protectively.
-

1 $\lt $ PBR $\lt $ 2: The oxide film volume is slightly larger than the consumed metal.
This creates a moderate compressive stress that seals the surface, forming a dense, continuous, and protective passive layer.
Examples include aluminum, chromium, and silicon.
-

PBR $\gt $ 2: The oxide film volume is excessively large compared to the metal.
This generates extremely high compressive stresses that lead to wrinkling, cracking, and eventual spallation (flaking off) of the oxide scale, exposing bare metal to accelerated oxidation.
Examples include iron and copper.


Step 4: Final Answer:
The Pilling-Bedworth ratio is the ratio of the volume of the metal oxide to the volume of the metal consumed.
Thus, the correct option is (C).