Characteristic Phonon Spectrum of Negative Thermal Expansion Materials with Framework Structure through Calorimetric Study of Sc₂M₃O₁₂(M = W and Mo)

To study the relation between the structural characteristics and the phonon property in the negative thermal expansion (NTE) compounds, the heat capacities of Sc 2 W 3 O 12 and Sc 2 Mo 3 O 12 were measured. Spectrum analysis of heat capacity provided their effective phonon densities of states (DOS). The DOS of Sc 2 W 3 O 12 shows three features; low-energy phonon modes with negative mode-Grüneisen parameter (γ i ) around 5 meV, high-energy phonon modes, and separation of phonon DOS into two regions with a wide gap. The relative contribution of γ i C i, where C i is heat capacity of each vibrational mode i, reveals that the low-energy phonon modes with negative γ i cause the NTE and that the latter two features are necessary to maintain the NTE in a wide temperature range. Sc 2 Mo 3 O 12 has the low-energy mode with the negative γ i . This fact indicates that Sc 2 Mo 3 O 12 potentially has the NTE property even in its low-temperature phase showing positive thermal expansion. A comparison of the phonon DOS with other oxides shows that the phonon features are common in the NTE oxides and related to their common chemical and structural characteristics, “strong bond” and “framework structure”. This finding gives us an important guide to search for new actual and/or potential NTE compounds.