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The Pilling-Bedworth ratio (P-B ratio), in corrosion 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). Template:Tocright 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:

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

where:

• R_PB is the Pilling-Bedworth ratio,
• M - the atomic or molecular mass,
• n - number of atoms of metal per one molecule of the oxide
• ρ - density, and
• V - 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:

• 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. (citation needed)

Values

Metal	Metal oxide	RPB
Zinc	Zinc oxide	1.58
Calcium	Calcium oxide	0.64
Magnesium	Magnesium oxide	0.81
Aluminium	Aluminium oxide	1.28
Lead	Lead(II) oxide	1.28
Platinum	Platinum(II) oxide	1.56
Zirconium	Zirconium(IV) oxide	1.56
Hafnium	Hafnium(IV) oxide	1.62
Nickel	Nickel(II) oxide	1.65
Iron	Iron(II) oxide	1.7
Titanium	Titanium(IV) oxide	1.73
Chromium	Chromium(III) oxide	2.07
Iron	Iron(II,III) oxide	2.10
Iron	Iron(III) oxide	2.14
Silicon	Silicon dioxide	2.15
Tantalum	Tantalum(V) oxide	2.47
Vanadium	Vanadium(V) oxide	3.25