Pilling–Bedworth ratio
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The Pilling–Bedworth ratio (P–B ratio), in
corrosion Corrosion is a natural process that converts a refined metal into a more chemically stable oxide. It is the gradual deterioration of materials (usually a metal) by chemical or electrochemical reaction with their environment. Corrosion engine ...
of metals, is the ratio of the volume of the elementary cell of a metal oxide to the volume of the elementary cell of the corresponding metal (from which the oxide is created). On the basis of the P–B ratio, it can be judged if the metal is likely to passivate in dry air by creation of a protective oxide layer.


Definition

The P–B ratio is defined as: : \mathrm where: * R_ – Pilling–Bedworth ratio * Matomic or
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
* n – number of atoms of metal per molecule of the oxide * \rho – density * V
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...


History

N.B. Pilling and R.E. BedworthN.B. Pilling, R. E. Bedworth, "The Oxidation of Metals at High Temperatures". J. Inst. Met 29 (1923), p. 529-591. 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."ASM Handbook Vol.13 Corrosion", ASM International, 1987


Application

On the basis of measurements, the following connection can be shown: * RPB < 1: the oxide coating layer is too thin, likely broken and provides no protective effect (for example
magnesium Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic ta ...
) * RPB > 2: the oxide coating chips off and provides no protective effect (example
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
) * 1 < RPB < 2: the oxide coating is passivating and provides a protecting effect against further surface oxidation (examples
aluminium Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. I ...
,
titanium Titanium is a chemical element with the symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion in ...
,
chromium Chromium is a chemical element with the symbol Cr and atomic number 24. It is the first element in group 6. It is a steely-grey, lustrous, hard, and brittle transition metal. Chromium metal is valued for its high corrosion resistance and hardne ...
-containing
steel Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant ty ...
s). 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 1.48-1.56, meaning that the oxide is more voluminous than the consumed metal.


Values


References

{{DEFAULTSORT:Pilling-Bedworth ratio Corrosion prevention