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

TL;DR

This study investigates how phonon behaviors relate to the unusual thermal expansion in Zn(CN)2 and Ni(CN)2 using inelastic neutron scattering and ab-initio calculations, revealing the role of low-energy rotational modes.

Contribution

It provides a detailed analysis of phonon spectra and their pressure and temperature dependence, linking low-energy modes to negative thermal expansion in these materials.

Findings

Zn(CN)2 exhibits large negative thermal expansion due to low-energy rotational phonon modes.

Ni(CN)2 shows different phonon spectra with shifted modes, explaining its less negative or positive thermal expansion.

Ab-initio calculations successfully connect phonon behavior with thermal expansion anomalies.

Abstract

Zn(CN)2 and Ni(CN)2 are known for exhibiting anomalous thermal expansion over a wide temperature range. The volume thermal expansion coefficient for the cubic, 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 thermal expansion coefficient is negative in the two dimensionally connected sheets ({\alpha}a=-7 x 10-6 K-1), but the overall thermal expansion coefficient is positive ({\alpha}V=48 x 10-6 K-1). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab-initio calculations. The spectra of the two compounds show large differences that cannot 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 structure and bonding are quite different in the two compounds. The calculated pressure dependence 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 modes in Zn(CN)2, which are shifted to higher energies in Ni(CN)2, that are responsible for the large negative thermal expansion. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN)2, the temperature- dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).