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The '''Pilling-Bedworth ratio''' ('''P-B ratio'''), in [[corrosion]] of metals, is the ratio of the volume of the [[Crystal_structure#Unit_cell|elementary cell]] of a metal oxide to the volume of the elementary cell of the corresponding metal (from which the oxide is created).
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On the basis of the P-B ratio, it can be judged if the metal is likely to [[Passivation (chemistry)|passivate]] in dry air by creation of a protective oxide layer.
 
==Definition==
The P-B ratio is defined as:
: <math>\mathrm{R_{PB} =\frac{V_{oxide}}{V_{metal}}= \frac{ M_{oxide} \cdot \rho_{metal}} {n \cdot M_{metal} \cdot \rho_{oxide}} }</math>
 
where:
* R<sub>PB</sub> 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<ref>N.B. Pilling, R. E. Bedworth, "The Oxidation of Metals at High Temperatures". J. Inst. Met 29 (1923), p. 529-591.</ref> 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.<ref name="ASM">"ASM Handbook Vol.13 Corrosion", ASM International, 1987</ref>
 
== Application ==
On the basis of measurements, the following connection can be shown:
* R<sub>PB</sub> < 1: the oxide coating layer is too thin, likely broken and provides no protective effect (for example [[magnesium]])
* R<sub>PB</sub> > 2: the oxide coating chips off and provides no protective effect (example [[iron]])
* 1 < R<sub>PB</sub> < 2: the oxide coating is passivating and provides a protecting effect  against further surface oxidation (examples [[aluminium]], [[titanium]], [[chromium]]-containing [[steel]]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. (citation needed)
 
== Values ==
 
{| class="wikitable"
! Metal    !! Metal oxide    !!  R<sub>PB</sub>
|-
| [[Zinc]] || [[Zinc oxide]] || 1.58
|-
| [[Calcium]] || [[Calcium oxide]] || 0.64 <ref name="ASM"/>
|-
| [[Magnesium]] || [[Magnesium oxide]] || 0.81
|-
| [[Aluminium]] || [[Aluminium oxide]] || 1.28
|-
| [[Lead]] || [[Lead(II) oxide]] || 1.28 <ref name="ASM"/>
|-
| [[Platinum]] || [[Platinum(II) oxide]] || 1.56 <ref name="ASM"/>
|-
| [[Zirconium]] || [[Zirconium(IV) oxide]] || 1.56
|-
| [[Hafnium]] || [[Hafnium(IV) oxide]] || 1.62 <ref name="ASM"/>
|-
| [[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 <ref name="ASM"/>
|-
| [[Vanadium]] || [[Vanadium(V) oxide]] || 3.25 <ref name="ASM"/>
|-
|}
 
==References==
<references/>
 
[[Category:Corrosion]]

Revision as of 13:39, 7 February 2014

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