Pilling–Bedworth ratio

The P–B ratio is defined as:[1]

${\displaystyle \mathrm {R_{PB}={\frac {V_{oxide}}{V_{metal}}}={\frac {M_{oxide}\cdot \rho _{metal}}{n\cdot M_{metal}\cdot \rho _{oxide}}}} }$

where:

• ${\displaystyle R_{PB}}$ – Pilling–Bedworth ratio
• ${\displaystyle M}$ – atomic or molecular mass
• ${\displaystyle n}$ – number of atoms of metal per molecule of the oxide
• ${\displaystyle \rho }$ – density
• ${\displaystyle V}$ – molar volume

N.B. Pilling and R.E. Bedworth[2] 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.[3]

Scheme of the oxide structure and the Pilling-Bedworth ratio.

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

• R_PB < 1: the oxide coating layer is too thin, likely broken and provides no protective effect (for example magnesium)
• R_PB > 2: the oxide coating chips off and provides no protective effect (example iron)
• 1 < R_PB < 2: the oxide coating is passivating and provides a protecting effect against further surface oxidation (examples aluminium, titanium, chromium-containing steels).

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.