Role of alkali ions in the near-zero thermal expansion of NaSICON-type AZr2(PO4)3 (A = Na, K, Rb, Cs) and Zr2(PO4)3 compounds

Zero thermal expansion (ZTE) is a rare phenomenon of great importance in the field of materials design. AZr2(PO4)3 (A = Na, K, Rb, Cs) exhibit near-zero thermal expansion. In this work, we perform first principles calculations in AZr2(PO4)3 (A = Na, K, Rb, Cs) and Zr2(PO4)3 compounds to elucidate the effects of A cations on the thermal expansion behavior. Structural and vibrational analysis shows that the near-zero thermal expansion is strongly related to the dynamics of the "lantern" units of [Zr2(PO4)3], where the ZrO6 and PO4 polyhedra are rigid. The calculated Gruneisen parameters reveal that different A-site alkali metal atoms heavily affect the phonon modes of A atoms and the rotation of ZrO6 and PO4 polyhedra, as well as the acoustic phonon modes, thus resulting in a different thermal expansion behavior of AZr2(PO4)3 (A = Na, K, Rb, Cs). The absence of A atoms in Zr2(PO4)3 facilitates the structural flexibility and therefore the occurrence of a stronger negative thermal expansion. This work provides insights into the modulation of thermal expansion of these NaZr2(PO4)3-type compounds.