Large and tunable negative thermal expansion induced by a synergistic effect in M2II[MIV(CN)8] Prussian blue analogues

Abstract

Designing negative thermal expansion (NTE) materials with a larger NTE coefficient and a wider temperature window is a great challenge nowadays, leading to the limitation of existing NTE materials such that only about 150 kinds of NTE materials have been discovered since 1996. Here, using first-principles calculations combined with the quasi-harmonic approximation (QHA), we find that the synergistic effect of different vibrational modes can significantly enhance the NTE in open framework compounds. We systematically investigate the NTE properties of the M₂^IIM^IV(CN)₈ (M^II = Ni, Co, Fe, and Mn; M^IV = Mo and W) family, which is the first kind of Prussian blue analogues (PBAs) with a 2D and 3D topology structure, to explore the synergistic enhancement effect in NTE. We reveal that both the optical modes of the rotational motion of [W(CN)₈] and [Ni(NC)₄] rigid units and the low frequency acoustic modes of the transverse vibration contribute significantly to the NTE. Furthermore, the coefficients of NTE increase monotonously with increasing ionic radius upon substituting Ni in M₂^IIW(CN)₈ with Co, Fe, or Mn, respectively. Analyzing the vibrational modes of the substituted systems indicates that the dramatic changes in NTE originate from a highly synergistic effect, in which all the frequencies of these NTE modes have the same trend, i.e. the lower the frequencies, the larger the coefficient of NTE. This work clearly presents a synergistic mechanism of enhancing NTE in PBA materials, and sheds light on designing new materials with better properties.