Pilling–Bedworth ratio

Definition

The P–B ratio is defined as : R_{PB} =\frac{V_\text{oxide}}{n \cdot V_\text{metal}} = \frac{ M_\text{oxide} \cdot \rho_\text{metal}} {n \cdot M_\text{metal} \cdot \rho_\text{oxide}},

where

• M is the atomic or molecular mass,
• n is the number of atoms of metal per molecule of the oxide,
• \rho is the density,
• V is the molar volume.

History

N.B. Pilling and R.E. Bedworth suggested in 1923 that metals can be classed into two categories: those that form protective oxides, and those that cannot. They ascribed the protectiveness of the oxide to the volume the oxide takes in comparison to the volume of the metal used to produce this oxide in a corrosion process in dry air. The oxide layer would be unprotective if the ratio is less than unity because the film that forms on the metal surface is porous and/or cracked. Conversely, the metals with the ratio higher than 1 tend to be protective because they form an effective barrier that prevents the gas from further oxidizing the metal.

Application

On the basis of measurements, the following connection can be shown:

• RPB
• RPB 2: the oxide coating chips off and provides no protective effect (example iron)
• 1 PB

However, the exceptions to the above P–B ratio rules are numerous. Many of the exceptions can be attributed to the mechanism of the oxide growth: the underlying assumption in the P–B ratio is that oxygen needs to diffuse through the oxide layer to the metal surface; in reality, it is often the metal ion that diffuses to the air-oxide interface.

The P–B ratio is important when modelling the oxidation of nuclear fuel cladding tubes, which are typically made of Zirconium alloys, as it defines how much of the cladding that is consumed and weakened due to oxidation. The P–B ratio of Zirconium alloys can vary between 1.48 and 1.56, meaning that the oxide is more voluminous than the consumed metal.

Values

References

References

1. N.B. Pilling, R. E. Bedworth, "The Oxidation of Metals at High Temperatures". J. Inst. Met 29 (1923), pp. 529–591.
2. "ASM Handbook Vol.13 Corrosion", ASM International, 1987
3. Callister, Jr., William D. "Materials Science and Engineering: An Introduction". 7th Edition. John Wiley and Sons 2007. pg. 653.
4. (December 2018). "Oxidation Behavior of Tungsten Carbide-6% Cobalt Cemented Carbide". Metallography, Microstructure, and Analysis.
5. (November 2017). "The corrosion of Zr(Fe, Cr)2 and Zr2Fe secondary phase particles in Zircaloy-4 under 350 °C pressurised water conditions". Corrosion Science.