Specific heat analyses on optical-phonon-derived uniaxial negative thermal expansion system TrZr (tr = fe and CoNi).

A large uniaxial negative thermal expansion (NTE) along the c-axis has recently been observed in the transition metal (Tr) zirconides TrZr with a tetragonal CuAl-type structure. A recent study on FeZr₂ [M. Xu et al., Nat. Commun. 14, 4439 (2023)] suggests that optical phonons play a critical role in inducing the NTE along the c-axis. In this study, we investigate the thermophysical properties of TrZr₂ compounds (Tr = Fe and CoNi(x = 0, 0.2, 0.4, 0.6, 0.8, 1)) using specific heat measurements, sound velocity data, and theoretical phonon calculations to achieve our aim of clarifying the contribution of optical phonons to the uniaxial NTE along the c-axis observed in both FeZr₂ and CoZr₂. We found that FeZr shows a lattice-specific heat peak structure at 8.90 meV, which corresponds to optical phonon energy with a high population of negative Grüneisen parameter along the c-axis in the phonon dispersion curves in FeZr. In an examination of a chemical substitution effect on the CoNiZr, we found that the lattice-specific heat peak structure disappeared for x ≥ 0.4 and the oscillator intensity decreased. Phonon calculations revealed the existence of low-energy optical phonon branches at the Γ point for CoZr and FeZr with uniaxial NTE along the c-axis. However, the low-energy phonon branches were not found in NiZr with uniaxial positive thermal expansion along the c-axis. The increase in phonon density of states near the above optical phonon energy in CoZr and FeZr is consistent with the lattice-specific heat analyses, and we propose that low-energy optical phonons are essential for the exhibiting of uniaxial NTE along the c-axis in TrZr.