Hydrogen modes in KH$_2$PO$_4$ under pressure from ab initio calculation and inelastic neutron scattering

TL;DR

This work addresses the longstanding question of the nature of the OH-stretching triplet in KH$_2$PO$_4$ under pressure by combining ab initio phonon calculations with inelastic neutron scattering. The calculations predict a hardening of OH-bending modes and a softening of OH-stretching modes with pressure, while INS measurements show a hardening of the triplet, implying that the observed spectral features arise mainly from overtones and combinations of bending modes rather than direct OH-stretching excitations. The results are supported by mode assignments linking the observed peaks to bending-mode sums (e.g., $2\beta$, $\beta+\gamma$) and by Debye-Waller and cross-section considerations that enhance overtones and suppress fundamentals. The findings generalize to other hydrogen-bonded materials and emphasize the need for Q-dependent INS studies and complementary spectroscopy to resolve hydrogen vibration assignments.

Abstract

The nature of the phonon triplet in the region of OH-stretching modes in hydrogen-bonded materials is often explained by the interplay of OH-stretching modes and combinations and overtones of OH-bending modes. In order to elucidate the both contributions in KH$_2$PO$_4$ (KDP), we compare the pressure dependence of the OH-bending and stretching modes from ab initio calculation and inelastic neutron scattering (INS) measurements. The ab initio calculation predicts a hardening of OH-bending modes and a softening of OH-stretching modes with pressure. At the same time, INS measurements in the region of OH-stretching modes indicate a hardening of the phonon triplet together with the bending modes. This means that this triplet in INS measurements is mainly due to combinations and overtones of OH-bending modes, while the intensity of OH-stretching modes appears to be relatively low. This conclusion may also apply to other hydrogen-bonded materials.

Figures (8)

• Figure 1: KDP conventional unit cell in the ferroelectric phase. Hydrogen bonds (shown as black dashed lines) lie in the $xy$ planes, connecting two oxygen atoms in adjacent phosphate tetrahedra.
• Figure 2: Potential energy surface of a hydrogen atom along an H-bond approximated by the double-Morse potential lawrence1980lawrence1981robertson1981 for larger (thick solid blue line) and shorter (thick dashed purple line) distances between bonded oxygen atoms. The thin lines correspond to the harmonic approximation of the double-Morse potential in the vicinity of one of its two minima. The harmonic potential frequency decreases with the distance between the two oxygen atoms.
• Figure 3: Calculated ab initio out-of-plane $\gamma_{\text{OH}}$ and in-plane $\beta_{\text{OH}}$ OH-bending modes with symmetry $A_1$. Arrows correspond to ion displacements.
• Figure 4: Calculated ab initio OH-stretching modes $\nu_{\text{OH}}$ according to their irreducible representations. Arrows correspond to ion displacements.
• Figure 5: Calculated ab initio phonon dispersion and DOS of OH-modes in KDP at zero pressure (red) and 1.4 GPa (blue). Capital letters are high symmetry points of the Brillouin zone (BZ), and lowercase letters stand for the end point of one path and the starting point of another path in the BZ, as described in the inset. The path in the BZ corresponds to that reported for KDP menchon2018 and face-centered orthorhombic lattice setyawan2010.