Pilling-Bedworth Ratio (PBR)
Calculate the Pilling-Bedworth ratio, PBR = (M_oxide × ρ_metal) ÷ (n × M_metal × ρ_oxide), comparing the volume of oxide formed with the volume of metal consumed in oxidation. The dimensionless result predicts whether the oxide layer protects the metal: PBR < 1 gives a porous, non-protective oxide (continuous oxidation, as in alkali metals); 1 < PBR < 2 forms an adherent, protective layer (aluminium and chromium, the basis of passivation); PBR > 2 produces an oxide under compression that tends to crack and spall. Enter the molar masses, densities and the number of metal atoms per oxide molecule.
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Pilling-Bedworth ratio (PBR)
When a metal oxidizes, an oxide layer forms on the surface — and the big question is whether that layer protects the metal, barring diffusion and slowing the oxidation, or is useless. The Pilling-Bedworth ratio gives the first criterion for an answer, comparing the volume of oxide formed with the volume of metal consumed to form it: PBR = (M_oxide × ρ_metal) ÷ (n × M_metal × ρ_oxide), where n is the number of metal atoms per oxide molecule. The interpretation splits into three ranges. With PBR < 1, the oxide takes up less volume than the metal consumed: the layer turns out porous and in tension, fails to cover the surface and offers no protection — the case of the alkali and alkaline-earth metals (Mg, Li, Na). With 1 < PBR < 2, the oxide covers the surface well and forms an adherent, compact and protective layer — the ideal situation, seen in metals that passivate such as aluminium (PBR ≈ 1.28), chromium, titanium and nickel, the basis of the resistance of stainless steels. With PBR > 2, the oxide grows with excessive volume and ends up under strong compression, tending to crack, flake and spall, exposing fresh metal — the case of iron at high temperature (PBR ≈ 2.1) and of tungsten. The criterion is a first approximation: other factors, such as adhesion, plasticity and the thermal expansion coefficient, count as well. Enter the molar masses, the densities and the number of metal atoms per oxide molecule.
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