Discovering Large Isotropic Negative Thermal Expansion in Framework Compound AgB(CN)₄ via the Concept of Average Atomic Volume

Exploring isotropic negative thermal expansion (NTE) compounds is interesting, but remains challenging. Here, a new concept of “average atomic volume” is proposed to find new NTE open-framework materials. According to this guidance, two NTE compounds, AgB­(CN)₄ and CuB­(CN)₄, have been discovered, of which AgB­(CN)₄ exhibits a large NTE over a wide temperature range (α_v = −40 × 10^–6 K^–1, 100–600 K). The analysis by extended X-ray absorption fine structure spectroscopy and first-principles calculation indicate that (i) the NTE driving force comes from the transverse vibrations of bridge chain atoms of C and N, corresponding to the low-frequency phonon modes; and (ii) the same transverse vibration direction of C and N atoms is a key factor for the occurrence of strong NTE in AgB­(CN)₄. The present concept of “average atomic volume” can be a simple parameter to explore new NTE compounds especially in those open-framework materials.