where 𝑉𝑉 � (ℳ) and 𝑉𝑉 � (Ω i ) are the average volumes per atom for an oxygen-free compound ℳ and its 𝑖𝑖th potential oxide Ω i , respectively. Both ℳ and Ω i are represented by normalized formulae (all stoichiometric coefficients of elements sum to 1), and 𝑥𝑥 𝑖𝑖 is the 𝑖𝑖th entry of 𝑥𝑥 ⃗ = (𝑥𝑥