Theory of the martensitic phase transformations in lithium and sodium

A phenomenological model is proposed which describes the static and dynamical properties observed in connection with the martensitic transformations in lithium and sodium. The martensite structure is shown to result from a coupling between the mechanisms associated with the $\mathrm{bcc}-9R,$ bcc-hcp, and bcc-fcc transformations. These mechanisms are expressed in terms of primary displacive order parameters, involving definite critical shifts, and of additional spontaneous symmetry breaking strains. The theoretical phase diagrams in which the bcc and martensite phases are inserted are worked out. They contain regions of stability for intermediate phases. The existence or absence of softening of the ${\Sigma }_4$ phonon branch with temperature, as a precursor effect to the transformation, is shown to depend on the distance of the experimental thermodynamic path to the corresponding intermediate phase. The nonlocalized character of the softening region on the ${\Sigma }_4$ branch reflects the coupling of the different structural mechanisms involved in the transformation. The irrational values found for the wave vectors at the phonon dips are interpreted by an implicitly incommensurate character of the transformation, which originates from the distinct coherency stresses between the potentially stable close-packed structures and the bcc matrix. It results in the creation of strain fields acting inhomogeneously on the effective transformation order parameter, and explains the observed incubation times and response of the crystals to elastic and plastic deformations. These properties are shown to be consistent with a nucleation process on elastic defects which is activated only close to the transformation.