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Zn(CN)2 and Ni(CN)2 are known for exhibiting anomalous thermal expansion overa wide temperature range. The volume thermal expansion coefficient for thecubic, three dimensionally connected material, Zn(CN)2, is negative ({\alpha}V= -51 x 10-6 K-1) while for Ni(CN)2, a tetragonal material, the thermalexpansion coefficient is negative in the two dimensionally connected sheets({\alpha}a=-7 x 10-6 K-1), but the overall thermal expansion coefficient ispositive ({\alpha}V=48 x 10-6 K-1). We have measured the temperature dependenceof phonon spectra in these compounds and analyzed them using ab-initiocalculations. The spectra of the two compounds show large differences thatcannot be explained by simple mass renormalization of the modes involving Zn(65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structureand bonding are quite different in the two compounds. The calculated pressuredependence of the phonon modes and of the thermal expansion coefficient,{\alpha}V, are used to understand the anomalous behavior in these compounds.Our ab-initio calculations indicate that it is the low-energy rotational modesin Zn(CN)2, which are shifted to higher energies in Ni(CN)2, that areresponsible for the large negative thermal expansion. The measured temperaturedependence of the phonon spectra has been used to estimate the totalanharmonicity of both compounds. For Zn(CN)2, the temperature- dependentmeasurements (total anharmonicity), along with our previously reported pressuredependence of the phonon spectra (quasiharmonic), is used to separate theexplicit temperature effect at constant volume (intrinsic anharmonicity).

Relationship Between Phonons and Thermal Expansion in Zn(CN)2 and Ni(CN)2 from Inelastic Neutron Scattering and Ab-Initio Calculations