Pilling-Bedworth Ratio (P-B Ratio)
The Pilling-Bedworth ratio explain the protective nature of an oxide layer formed on a metal surface during oxidation. It is defined as the ratio of the volume of the metal oxide formed to the volume of the metal consumed.
Mathematically, the P-B ratio is calculated by using the following formula-
Where, Moxide is the molecular mass of the metal oxide.
ρmetal is the density of the metal.
n is the number of metal atoms per molecule of the oxide (e.g., n=1 for MgO, n=2 for Al2O3).
Mmetal is the atomic mass of the metal.
ρoxide is the density of the metal oxide.
The Pilling-Bedworth ratio indicates whether the oxide layer formed on a metal surface is likely to be protective against further oxidation.
The Pilling-Bedworth ratio is less than one (RPB < 1):
If the Pilling-Bedworth ratio is less than one then the amount of oxide consumed is less than the amount of metal. This usually results in a thin, porous or cracked oxide layer that does not provide effective protection against further oxidation. Alkali and alkaline earth metal oxides forms oxides of volume less than the volume of metals. Magnesium (MgO, RPB ≈ 0.81) is a common example. The oxide film is not protective, so magnesium corrodes easily.
The Pilling-Bedworth ratio is less than two and greater than one (1 < RPB < 2):
If the Pilling-Bedworth ratio is in between 1 and 2 then the amount of oxide is greater than the amount of metal consumed, causing compressive stress in the oxide layer. This generally results in a dense, coherent, and protective oxide layer that can neutralise the metal surface and prevent the further oxidation. Heavy metals such as Al, Cr, Pb, Sn etc. form a protective oxide layer and prevent further corrosion. Some metals with their P-B ratio are aluminium (Al2O3, RPB ≈ 1.28), titanium (TiO2, RPB ≈ 1.73) and chromium (Cr2O3, RPB ≈ 2.07).
The Pilling-Bedworth ratio is greater than 2 (RPB > 2):
The amount of oxide is much higher than the amount of metal consumed. This can lead to high compressive stress in the oxide layer, causing it to break, crack or expand thus not providing long-term protection. The ferrous Fe2O3 (RPB ≈ 2.14) is an example where the oxide layer, while initially somewhat protective, can become very thick and unstable.
Remember:
PBR = 1.0: Oxide layer will be relatively stable and protective, preventing further oxidation and corrosion.
PBR < 1: Oxide layer is likely to be tensile stressed and prone to cracking, resulting in poor protection.
PBR > 1: Oxide layer may be compressive stressed and prone to buckling, potentially leading to poor protection.
Importance and Limitations of Pilling-Bedworth Ratio
The Pilling-Bedworth ratio is a useful criteria to predict the protectiveness of oxide layers. It is particularly important in studies under high-temperature oxidation and also in the design of corrosion-resistant materials. For example, in nuclear fuel cladding made of zirconium alloys (RPB ≈ 1.48-1.56 for ZrO2), the P-B ratio indicates the oxide layer is more voluminous than the consumed metal, influencing the mechanical integrity of the cladding.
However, it's important to note that the P-B ratio is a simplified model and has some limitations. It assumes that the growth of oxide is uniform and does not account for factors such as:
- Oxide growth mechanism: The P-B ratio assumes oxygen diffusion through the oxide layer, but in actual practice, the diffusion of metal ion to the oxide-air interface can be dominant.
- Temperature: High temperatures can affect the rate of diffusion and oxide's morphology.
- Stress Relief Mechanisms: Creep or plastic deformation in the oxide or metal can relieve stresses.
- Alloy composition: For alloys, the oxidation behaviour and P-B ratio can be more complex, involving selective oxidation of certain elements.
For oxide layer to be protective, the Pilling Bedworth ratio should be
A. close to 1
B. less than 0.5
C. nearly 5
D. greater than 10
View Answer
Option A is correct answer. close to 1
- P–B < 1: Oxide film is porous/cracked, not protective (e.g., Mg).
- 1 ≤ P–B ≤ 2: Oxide film is compact and protective (e.g., Al, Ti).
- P–B > 2: Oxide film is thick, prone to cracking/spalling, not protective (e.g., Fe).