The Pilling-Bedworth ratio (P-B ratio), in corrosion

Corrosion

Corrosion is the disintegration of an engineered material into its constituent atoms due to chemical reactions with its surroundings. In the most common use of the word, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen...

 of metals, is the ratio of the volume of the elementary cell of a metal oxide to the volume of the elementary cell of the corresponding metal (from which the oxide is created).

On the basis of the P-B ratio, it can be judged if the metal is likely to passivate

Passivation

Passivation is the process of making a material "passive", and thus less reactive with surrounding air, water, or other gases or liquids. The goal is to inhibit corrosion, whether for structural or cosmetic reasons. Passivation of metals is usually achieved by the deposition of a layer of oxide...

 in dry air by creation of a protective oxide layer.

Definition

The P-B ratio is defined as:

where:

• R_PB 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 - the molar volume.

History

N.B. Pilling and R.E. Bedworth suggested in 1923 that metals can be classed into two categories: those that form protective oxides, and those that cannot. They ascribed the protectiveness of the oxide to the volume the oxide takes in comparison to the volume of the metal used to produce this oxide in a corrosion process in dry air. The oxide layer would be unprotective if the ratio is less than unity because the film that forms on the metal surface is porous and/or cracked. Conversely, the metals with the ratio higher than 1 tend to be protective because they form an effective barrier that prevents the gas from further oxidizing the metal.

Application

On the basis of measurements, the following connection can be shown:

• R_PB < 1: the oxide coating layer is too thin, likely broken and provides no protective effect (for example magnesium
  Magnesium
  Magnesium is a chemical element with the symbol Mg, atomic number 12, and common oxidation number +2. It is an alkaline earth metal and the eighth most abundant element in the Earth's crust and ninth in the known universe as a whole...
  
  )
• R_PB > 2: the oxide coating chips off and provides no protective effect (example iron
  Iron
  Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
  
  )
• 1 < R_PB < 2: the oxide coating is passivating and provides a protecting effect against further surface oxidation (examples aluminum, titanium
  Titanium
  Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....
  
  , chromium
  Chromium
  Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...
  
  -containing steel
  Steel
  Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...
  
  s).

However, the exceptions to the above P-B ratio rules are numerous. 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. (citation needed)

Values

Metal	Metal oxide	RPB
Calcium Calcium Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...	Calcium oxide Calcium oxide Calcium oxide , commonly known as quicklime or burnt lime, is a widely used chemical compound. It is a white, caustic, alkaline crystalline solid at room temperature....	0.64
Magnesium Magnesium Magnesium is a chemical element with the symbol Mg, atomic number 12, and common oxidation number +2. It is an alkaline earth metal and the eighth most abundant element in the Earth's crust and ninth in the known universe as a whole...	Magnesium oxide Magnesium oxide Magnesium oxide , or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium . It has an empirical formula of and consists of a lattice of Mg2+ ions and O2– ions held together by ionic bonds...	0.81
Aluminium Aluminium Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....	Aluminium oxide Aluminium oxide Aluminium oxide is an amphoteric oxide with the chemical formula 23. It is commonly referred to as alumina, or corundum in its crystalline form, as well as many other names, reflecting its widespread occurrence in nature and industry...	1.28
Lead Lead Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...	Lead(II) oxide Lead(II) oxide Lead oxide is the inorganic compound with the formula PbO. Lead oxide occurs in two polymorphs, red, having a tetragonal crystal structure and yellow, having an orthorhombic crystal structure...	1.28
Platinum Platinum Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...	Platinum(II) oxide	1.56
Zirconium Zirconium Zirconium is a chemical element with the symbol Zr and atomic number 40. The name of zirconium is taken from the mineral zircon. Its atomic mass is 91.224. It is a lustrous, grey-white, strong transition metal that resembles titanium...	Zirconium(IV) oxide	1.56
Hafnium Hafnium Hafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869. Hafnium was the penultimate stable...	Hafnium(IV) oxide Hafnium(IV) oxide Hafnium oxide is the inorganic compound with the formula HfO2. Also known as hafnia, this colourless solid is one of the most common and stable compounds of hafnium. It is an electrical insulator with a band gap of approximately 6 eV. Hafnium dioxide is an intermediate in some processes that...	1.62
Nickel Nickel Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...	Nickel(II) oxide Nickel(II) oxide Nickel oxide is the chemical compound with the formula NiO. It is notable as being the only well characterized oxide of nickel . The mineralogical form of NiO, bunsenite, is very rare. It is classified as a basic metal oxide...	1.65
Iron Iron Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...	Iron(II) oxide Iron(II) oxide Iron oxide, also known as ferrous oxide, is one of the iron oxides. It is a black-colored powder with the chemical formula . It consists of the chemical element iron in the oxidation state of 2 bonded to oxygen. Its mineral form is known as wüstite. Iron oxide should not be confused with rust,...	1.7
Titanium Titanium Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....	Titanium(IV) oxide	1.73
Chromium Chromium Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...	Chromium(III) oxide Chromium(III) oxide Chromium oxide is the inorganic compound of the formula Cr2O3. It is one of principal oxides of chromium and is used as a pigment. In nature, it occurs as the rare mineral eskolaite.-Structure and properties:...	2.07
Iron Iron Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...	Iron(II,III) oxide Iron(II,III) oxide Iron oxide is the chemical compound with formula Fe3O4. It is one of a number of iron oxides, the others being iron oxide , which is rare, and iron oxide also known as hematite. It occurs in nature as the mineral magnetite. It contains both Fe2+ and Fe3+ ions and is sometimes formulated as FeO ∙...	2.10
Iron Iron Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...	Iron(III) oxide Iron(III) oxide Iron oxide or ferric oxide is the inorganic compound with the formula Fe2O3. It is one of the three main oxides of iron, the other two being iron oxide , which is rare, and iron oxide , which also occurs naturally as the mineral magnetite. As the mineral known as hematite, Fe2O3 is the main...	2.14
Silicon Silicon Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...	Silicon dioxide Silicon dioxide The chemical compound silicon dioxide, also known as silica , is an oxide of silicon with the chemical formula '. It has been known for its hardness since antiquity...	2.15
Tantalum Tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as tantalium, the name comes from Tantalus, a character in Greek mythology. Tantalum is a rare, hard, blue-gray, lustrous transition metal that is highly corrosion resistant. It is part of the refractory...	Tantalum(V) oxide	2.47
Vanadium Vanadium Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...	Vanadium(V) oxide Vanadium(V) oxide Vanadium oxide is the chemical compound with the formula V2O5. Commonly known as vanadium pentoxide, this brown/yellow solid is the most stable and common compound of vanadium. Upon heating it reversibly loses oxygen...	3.25