Study of Superlattice Formation in $2H$-Nb${\mathrm{Se}}_2$ and $2H$-Ta${\mathrm{Se}}_2$ by Neutron Scattering

Neutron-scattering studies of $2H$-Nb${\mathrm{Se}}_2$ and $2H$-Ta${\mathrm{Se}}_2$ reveal the strong Kohn anomalies and incommensurate superlattice characteristic of charge-density-wave instabilities. Whereas the Nb${\mathrm{Se}}_2$ superlattice ($T_0=33.5\mathrm{}$ K) remains incommensurate to 5 K, Ta${\mathrm{Se}}_2$ ($T_0=122.3\mathrm{}$ K) locks to a commensurate $3a$ superlattice at 90 K. The temperature dependence of the superlattice wave vector and the lockin behavior are understood using a free energy involving terms third order in atomic displacement. A secondary lattice distortion required by this model is observed.