Reconciling ab initio and semiempirical approaches to lattice stabilities

Starting around 1970, two methods have been developed that may give information about the lattice stability H-alpha/beta=H-alpha-H-beta, i.e. the enthalpy difference between two phases, alpha and beta, of a pure element or compound. The ab initio method is purely theoretical and relies on electron structure calculations. The CALPHAD method derives a Gibbs energy function G=H-TS from experimental thermodynamic data, including phase diagrams. A long-standings problem has been that the two methods gave very different lattice stabilities for some transition metals, e.g., W. The reason for this discrepancy has recently been clarified, when the role of dynamical lattice instabilities was realised. This paper gives an account of how the discrepancy emerged and is now resolved. The interpretation and practical applicability of the Gibbs energy function in the CALPHAD approach to systems containing dynamical instabilities is clarified.