Interplay between Phonons and Anisotropic Elasticity Drives Negative Thermal Expansion in PbTiO_{3}

Giant Negative Thermal Expansion in Ultralight NaB(CN)4

Negative thermal expansion (NTE) is crucial for controlling the thermomechanical properties of functional materials, albeit being relatively rare. This study reports a giant NTE (αV ∼-9.2 ⋅ 10-5  K-1 , 100-200 K; αV ∼-3.7 ⋅ 10-5  K-1 , 200-650 K) observed in NaB(CN)4 , showcasing interesting ultralight properties. A comprehensive investigation involving synchrotron X-ray diffraction, Raman spectroscopy, and first-principles calculations has been conducted to explore the thermal expansion mechanism. The findings indicate that the low-frequency phonon modes play a primary role in NTE, and non-rigid vibration modes with most negative Grüneisen parameters are the key contributing factor to the giant NTE observed in NaB(CN)4 . This work presents a new material with giant NTE and ultralight mass density, providing insights for the understanding and design of novel NTE materials.

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.

Effect of Octahedral Connectivity on the Negative Thermal Expansion of SrZrS3

Sulfide perovskites (ABX₃) are under increasing investigation for use in photovoltaic, optoelectronic, dielectric, and thermoelectric devices due to their favorable band gaps, dynamical properties, environmental stability, and structural diversity. A key material parameter to optimize in such devices is the constituent materials' coefficient of thermal expansion (CTE) in order to minimize thermomechanical stress during fabrication and operation. This can be done by avoiding materials that have large CTE mismatch or by compensating positive thermal expansion by including materials with negative thermal expansion (NTE). Here, we evaluate the CTE of (edge-connected) α- and (corner-connected) β-SrZrS₃ with density functional theory and the self-consistent quasiharmonic approximation. We find that both materials exhibit positive thermal expansion at 0 GPa and host pressure-induced negative thermal expansion. The β phase has a smaller CTE (37 × 10^-6 K^-1) at room temperature and ambient pressure and also has a larger NTE response under pressure due to its more flexible corner-connected framework structure. We use our findings to suggest that corner-shared motifs should be prioritized over edge- or face-shared octahedral networks to maximize NTE arising from vibrational (phononic) mechanisms.