Phonon dispersion and Grüneisen parameters of zinc dicyanide and cadmium dicyanide from first principles: Origin of negative thermal expansion

Zinc dicyanide, $\mathrm{Zn}{(\mathrm{C}\mathrm{N})}_{2}$, and the isostructural cadmium dicyanide show negative thermal expansion over a broad range of temperatures. By the use of density functional theory calculations, we determine the phonon dispersion curves of these materials and show that the transverse acoustic modes give rise to a relatively sharp feature at about $2--4\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ in the phonon density of states. In addition, we compute the Gr\uneisen parameters of these modes and show that they have large negative values, indicating that they are the primary contributors to the negative thermal expansion in this material. Our results are in broad agreement with recent neutron scattering experiments on $\mathrm{Zn}{(\mathrm{C}\mathrm{N})}_{2}$ and the rigid unit mode analysis of these materials.