The protective or non-protective nature of the oxide film is determined by a rule known as the Pilling-Bedworth rule. The ratio of the volume of the oxide formed to the volume of the metal consumed is called the Pilling-Bedworth rule. According to it, if the volume of the oxide layer is greater than the volume of the metal, the oxide layer is protective and non-porous. On the other hand, if the volume of the oxide layer formed is less than the volume of the metal, the oxide layer is nonprotective and porous.

The P–B ratio is defined as:

RPB = Voxide/Vmetal = Moxide.ρmetal/n. Mmetal.ρoxide

where:

·        RPB 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 – volume.

Thanks Indies. This definition is for oxide. I need to know about sulfide and carbonate. For example if you have one oxide scale with 9.7 to 1.7  PB ratio this scale can cover all metal surfaces but we haven't any criteria for sulfide and carbonate scales.

I think the volume ratio between the formed sulfides or carbonate and the consumed metals is the key.  It is necessary for the protective products to own the volume ration greater than 1.

Usually for oxides:

RPB < 1: oxide coating layer is too thin, likely broken and provides no protective effect (Mg)

RPB > 2: oxide coating chips off and provides no protective effect (Fe)

1 < RPB < 2: oxide coating is passivating and provides a protecting effect against further surface oxidation (Al, Ti, Cr-containing steels)

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.

The Pilling–Bedworth ratio since was suggested in 1923 covered the classification of metals into two categories based on  forming protective oxides or not and according to well defined index as explained @Xinqiang Wu. Therefore, using this ratio for other than metal to metal oxide systems is not easily accepted by others. However, the connecting porosity amount in the scale is the main index for its protective properties since these porosity offer the free path for the electrolyte to access the metal surface where the corrosion takes place.

Best regards  

Thanks for your replies but I have to say that I need one criteria for determining protective and not protective sulfide scales. What do you think? Can we use oxidie criteria? According to my calculations we can't because sulfide pb ratio is usually more than oxides.