First-principles phonon-spectral analysis and deformation response of MOFs: Boson Peak, amorphization and generalized flexibility

Abstract

Understanding the propagation of sound waves in three states of matter has attracted active research interests for more than a century now [7, 8]. With strengths of inter-atomic/molecular interacting forces varying in many orders of magnitude, energy-transfer in gas, liquid and solid medium subjected to pressure due to sound waves occurs via two di erent modes. Highly discordant atomic movements in gases allow absorption of sound waves at lowfrequencies through large collisional excitations [9], while in solids, restrained motion of atoms result in vibratory oscillations [10, 11]. Depending on the viscosity of liquids, their response to sound waves may manifest as collisional or vibrational [12]. Collective vibrational excitations or quanta of vibrational energy are termed as phonons [11], viz. acoustic phonons that are linked with the elasticity, and optical phonons, emerging from harmonious conformity of atomic arrangements in a solid. Liquids transmit only longitudinal acoustic waves at low-frequencies in the long-wavelength limit, but absorb transverse acoustic waves since they lack rigidity [13].