Negative Thermal Expansion Properties and the Role of Guest Alkali Atoms in LnFe(CN)₆ (Ln = Y, La) from <i>ab Initio</i> Calculations

Using the ab initio calculations within density functional theory combined with the quasi-harmonic approximation (QHA), we have investigated the negative thermal expansion (NTE) properties of LnFe­(CN)6 (Ln = Y, La) systems and the role of alkali as guest atoms being inserted in LnFe­(CN)6. We have found that both the antiprism mode originated from the torsional vibration of N atoms in LnN6 units and the transverse vibration of CN ligand mainly contribute to the magnitude of NTE in LnFe­(CN)6, and the largest coefficients of negative thermal expansion (CNTE) are found to be approximately −39.3 × 10–6 K–1 at 180 K for YFe­(CN)6 and −50 × 10–6 K–1 at 110 K for LaFe­(CN)6, respectively. The transverse vibration modes of CN ligand are significantly enhanced when Y atoms are substituted by their La counterparts, which results a larger CNTE of LaFe­(CN)6 than that of YFe­(CN)6. Such NTE can be tuned to be smaller, up to zero, or even to positive expansion by inserting one or more gust alkali ions in the vacancy of LaFe­(CN)6 owing to the fact that the guest ions effectively oppose the antiprism vibrational modes. Our study provides not only the understanding of the NTE mechanism but also an approach to tune the NTE properties of LaFe­(CN)6 systems.