Pilling–Bedworth ratio

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).

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:

where:

History

N.B. Pilling and R.E. Bedworth[1] 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.[2]

Application

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

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.

Values

Metal Metal oxide RPB
Zinc Zinc oxide 1.58
Calcium Calcium oxide 0.64 [2]
Magnesium Magnesium oxide 0.81
Aluminium Aluminium oxide 1.28
Lead Lead(II) oxide 1.28 [2]
Platinum Platinum(II) oxide 1.56 [2]
Zirconium Zirconium(IV) oxide 1.56
Hafnium Hafnium(IV) oxide 1.62 [2]
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 [2]
Vanadium Vanadium(V) oxide 3.25 [2]

References

  1. N.B. Pilling, R. E. Bedworth, "The Oxidation of Metals at High Temperatures". J. Inst. Met 29 (1923), p. 529-591.
  2. 1 2 3 4 5 6 7 "ASM Handbook Vol.13 Corrosion", ASM International, 1987
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