In the present study, the modified Sverjensky–Molling equation, derived from a linear-free energy relationship, is used to predict the Gibbs free energies of formation of crystalline phases of α-MOOH (with a goethite structure) and α-M2O3 (with a hematite structure) from the known thermodynamic properties of the corresponding aqueous trivalent cations (M3+). The modified equation is expressed as ΔG0f,MVX=aMVXΔG0n,M3++bMVX+βMVXγM3+, where the coefficients aMVX, bMVX, and βMVX characterize a particular structural family of MvX (M is a trivalent cation [M3+] and X represents the remainder of the composition of solid); γ3+ is the ionic radius of trivalent cations (M3+); ΔG0f,MVX is the standard Gibbs free energy of formation of MvX; and ΔG0n,M3+ is the non-solvation energy of trivalent cations (M3+). By fitting the equation to the known experimental thermodynamic data, the coefficients for the goethite family (α-MOOH) are aMVX=0.8838, bMVX=?424.4431 (kcal/mol), and βMVX=115 (kcal/mol.?), while the coefficients for the hematite family (α-M2O3) are aMVX=1.7468, bMVX=?814.9573 (kcal/mol), and βMVX=278 (kcal/mol.?). The constrained relationship can be used to predict the standard Gibbs free energies of formation of crystalline phases and fictive phases (i.e. phases that are thermodynamically unstable and do not occur at standard conditions) within the isostructural families of goethite (α-MOOH) and hematite (α-M2O3) if the standard Gibbs free energies of formation of the trivalent cations are known.