Mechanism of Negative Thermal Expansion in Monoclinic Cu₂P₂O₇ from First Principles

Negative thermal expansion (NTE) materials generally have high-symmetry space groups, large average atomic volumes, and corner-sharing octahedral and tetrahedral coordination structures. By contrast, monoclinic α-Cu₂P₂O₇, which has a small average atomic volume and edge-sharing structure, has been reported to exhibit NTE, the detailed mechanism of which is unclear. In this study, we investigate the A₂B₂O₇ polymorphs and analyze the NTE behavior of α-Cu₂P₂O₇ using first-principles lattice-dynamics calculations. From the polymorphism investigation in 20 A₂B₂O₇ compounds using 6 representative crystal structures, small A and B cationic radii are found to stabilize the α-Cu₂P₂O₇-type structure. We then analyze the NTE behavior of α-Cu₂P₂O₇ using quasi-harmonic approximation. Our calculated thermal expansion coefficients and anisotropic atomic displacement parameters were in good agreement with those of the experimental reports at low temperatures. From the mode-Grüneisen parameter distribution plotted over the entire first-Brillouin zone, we found that the phonon contributing most significantly to NTE emerges not into the special points but between them. In this phonon mode, the O connecting two PO₄ tetrahedra rotates, and the Cu and O vibrate perpendicular to the bottom of the CuO₅ pyramidal unit, which folds the ac lattice plane. This vibration behavior can explain the experimentally reported anisotropic NTE behavior of α-Cu₂P₂O₇. Our results demonstrate that the most negative mode-Grüneisen parameter contributing to NTE behavior is not always located on high-symmetry special points, indicating the importance of lattice vibration analyses for the entire first-Brillouin zone.