# Pilling-Bedworth ratio

In chemistry and materials science, the Pilling-Bedworth ratio (PBV, or PBR from Pilling-Bedworth ratio ) is the ratio of the molar volumes of a metallic element and its oxide. The PBV can be used to estimate whether a metal is permanently resistant to dry air through the formation of a protective oxide layer ( passivation ). Since the oxide formation sometimes takes place in several stages and mixed oxides can be formed in alloys, the PBV does not allow any reliable statements. This applies in particular to atmospheric corrosion, which almost always occurs via hydroxides due to the ubiquitous water.

## definition

${\ displaystyle \ mathrm {PBV = {\ frac {V_ {Oxide}} {{n} \ cdot V_ {Metal}}} = {\ frac {M_ {Oxide} \ cdot \ rho _ {Metal}} {M_ { Metal} \ cdot {n} \ cdot \ rho _ {oxide}}}}}$

M denotes the molar mass , ρ the density , V the (molar) volume and n the number of metal atoms in the empirical formula of the oxide.

## effect

The following relationship can be shown on the basis of measurements:

Schematic representation of the oxide structure and the Pilling-Bedworth ratio
PBV <1: tearing of the oxide layer, no protective effect (example magnesium oxide on magnesium )
PBV> 2: flaking of the oxide layer, no protective effect (example rust on iron )
PBV = 1 ... 2: Formation of a permanent, passivating oxide layer (examples aluminum , titanium , chrome layer on steel)

## Numerical values

metal Metal oxide PBV
magnesium Magnesium oxide 0.81
aluminum Alumina 1.28
Zirconium Zirconium (IV) oxide 1.56
nickel Nickel (II) oxide 1.65
iron Iron (II) oxide 1.7
titanium Titanium (IV) oxide 1.73
chrome Chromium (III) oxide 2.07
iron Iron (II, III) oxide 2.10
iron Iron (III) oxide 2.14
iron Iron (III) oxide hydroxide ( rust ) 3.6
Silicon Silicon dioxide 2.15
Tantalum Tantalum (V) oxide 2.47