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High-temperature materials and creep

The Pilling–Bedworth ratio of a metal's oxide scale (PBR, the ratio of the volume of oxide to the volume of metal used to form it) is calculated as PBR = (M_ox ρ_M)/(n M_M ρ_ox) (M is the molar mass, ρ is the density, and n is the number of metal atoms in one formula unit of the oxide). For magnesium (24.31 g/mol, 1.74 g/cm³) and MgO (40.30 g/mol, 3.58 g/cm³, n = 1), which combination of PBR and scale behavior is correct?

  1. AAbout 1.24, so the scale is under moderate compressive stress and forms a protective film covering the metal
  2. BAbout 0.81, and because it is less than 1 the scale shrinks into a dense layer that protects the metal well
  3. CAbout 0.81, so the scale cannot fully cover the metal surface, cracks easily and is unlikely to be protective
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Answer: C. About 0.81, so the scale cannot fully cover the metal surface, cracks easily and is unlikely to be protective

PBR = (40.30 × 1.74)/(1 × 24.31 × 3.58) = 70.1/87.0 ≈ 0.81. When the PBR is less than 1, the volume of oxide is smaller than the volume of metal consumed, so the scale is under tensile stress and cracks or develops gaps, letting oxygen reach the metal easily. Around 1 to 2, the scale tends to cover the metal without gaps and to be protective, as with aluminum forming Al₂O₃ (PBR ≈ 1.29), whereas well above 2 the compressive stress becomes too large and the scale tends to spall. About 1.24 is the value with numerator and denominator swapped. The PBR is only a guide; protectiveness also depends on the rate of diffusion through the scale and its adhesion.

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