Mechanically stiffened and thermally softened bulk modulus of BaXO ₃ (X=Ti,Zr,Nb) cubic perovskites

Although the physics behind the bulk modulus, B (T,P), as a function of temperature (T) and pressure (P), has been intensively investigated, an atomic scale understanding of this attribute remains a high challenge. Here, we show that the B (T,P) for BaXO₃ (X=Ti,Zr,Nb) can be established by connecting the B directly to the bond length and bond energy and their response to the applied T and P in the form of binding energy density, B [E/d³ (T,P)]. Besides an estimation of the Debye temperature and single bond energy, outcomes clarified that the thermally softened B arises from bond expansion and bond weakening due to lattice vibration and the mechanically stiffened B results from bond compression and bond strengthening due to mechanical work hardening.