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# Pilling-Bedworth Ratio (P-B Ratio)

Last updated: July 19, 2024

## What Does Pilling-Bedworth Ratio (P-B Ratio) Mean?

The Pilling-Bedworth ratio (P-B ratio), in terms of metal corrosion, is the ratio of elementary cell volume of metal oxide to the elementary cell volume of the equivalent metal where the oxide has been created.

By using the P-B ratio, it can be determined if it is possible for the metal to undergo passivation in the presence of dry air by building a protective oxide film.

## Corrosionpedia Explains Pilling-Bedworth Ratio (P-B Ratio)

Metallurgy relies on guidelines to determine protective oxide film for the purpose of protecting against corrosion. These coatings or films should be free from pinholes. For this, the guidelines created for these protective films can be utilized for the protective oxides in terms of integrated circuits.

The term Pilling-Bedworth ratio was derived from a 1923 research paper about metal oxidation in high temperatures that was presented by N. Pilling and E. Bedworth to the Institute of Metals (IM). In the paper, these two linked the metal oxide porosity to specific density 1. The metal oxide P-B ratio can be best described as the ratio of the metal oxide volume produced by the oxygen and metal reaction to the consumed value of metal. This can be further defined in the equation:

RPB = Voxide/Vmetal = (Moxide × Pmetal)/(n × Mmetal × Poxide)

Where:

RPB is the Pilling-Bedworth Ratio

M is the molecular or atomic mass

n is the metal atom per one oxide molecule

V is the molar value

P is the density

Using the P-B ratio as the basis for gauging protective films, the following can be assumed:

• If the P-B ratio is less than 1, the oxide film is too thin and will most likely break down, such as in magnesium.
• If the P-B ratio is grater than 2, the oxide film chips off and offers no protection, such as in iron.
• If the P-B ratio is greater than 1, but less than 2, the oxide film is passivating and offers protection from surface oxidation such as in titanium, aluminum and chromium.