Most metals oxidize when exposed to air, this can result in rusting as we are all familiar with. Some noble metals, such as platinum and gold, do not react with oxygen and do not rust. Other metals do react with oxygen but the process of oxidation results a thin oxide layer or scale that, once formed, prevents further oxidation and protects the material. Aluminum does this naturally and stainless steels are alloyed with chromium to achive a protective layer. A protective scale should cover the surface of the metal evenly and completely, be stable, and have a low ionic permeability to effectively isolate the metal from the envirnment. The Pilling-Bedworth ratio (PBR) is a numerical value used as a first assessment of whether a metal will develop a protective layer. This ratio compares the volume per metallic ion of the unit cell of the metal with that of the oxide. If the volume of the oxide is much larger, the oxide scale will be in compression and would crack, lossing effectiveness. On the the hand, if the volume of the oxide is much smaller, it would result in poor coverage. In the Goldilocks zone, one can expect a smooth stable scale. 

The PBR is the ratio between molar volume of the oxide and metal layers per metallic ions. This value roughly describes tendencies towards adhesion, cracking, or buckling behaviors. The volume of elementary unit cells between oxide and metal are compared from which internal stresses between the metal and the oxide scales due to size mismatch can be estimated.

Researchers should cite this work as follows:

• Zachary D McClure, Alejandro Strachan (2022), "Pilling-Bedworth Ratio Calculator," https://nanohub.org/resources/pbratio. (DOI: 10.21981/1AD4-5468).

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