where 𝑉𝑉 � (𝑀𝑀 𝑎𝑎 𝐵𝐵 𝑏𝑏 ) is the molar volume of 𝑀𝑀 𝑎𝑎 𝐵𝐵 𝑏𝑏 oxide, and 𝑉𝑉 � (𝑀𝑀) is the molar volume of metal 𝑀𝑀, both in their crystal phases. Note this represents the volume change of crystal 𝑀𝑀 at its surface after oxidation: the denominator represents the volume of mole amount of 𝑀𝑀 consumed in forming the numerator. A PBR between 1 and 2 is considered suitable for self-passivation.