Thermodynamics of the goethite-diaspore solid solution

Enthalpies of mixing and lattice parameters were determined for a series of Al-substituted synthetic goethite samples by high-temperature oxide-melt calorimetry and Rietveld refinement of X-ray diffraction patterns, respectively. Lattice parameters of Al-goethite deviate from Vegard's law (ideal mixing). The enthalpies of mixing can be fitted by a regular solution polynomial ΔH_mix = WX_goethite (1-X_goethite), where W = 79 ± 14 kJ/mol. Small positive vibrational excess entropy terms may exist in Al-goethite but, regardless of the excess entropy, the equilibrium solubility of Al in goethite is negligible, and Al-goethite is metastable with respect to goethite and diaspore. The large positive enthalpies of mixing in Al-hematite (Majzlan et al., 2002) and Al-goethite can be rationalized on the basis of ionic size mismatch between Fe³⁺ and Al³⁺. Despite large positive ΔH_mix in these two solid solutions, a number of more complex structures with Fe³⁺/Al³⁺ substitution show ideal mixing, suggesting that more complex structures cope with substitution better, as suggested by the systematics provided by Davies & Navrotsky (1983). Aluminum substituted iron oxides are an example of metastable compounds that can persist for geological time because of small energy difference between the stable and metastable phases.