Infrared Absorption of Pairs of Coupled Local-Mode Oscillators:H−H−,D−D−, andH−D−Pairs in KCl

Abstract

The prototype for a small-mass local-mode defect, substitutional ${\mathrm{H}}^{\ensuremath{-}}$ (or ${\mathrm{D}}^{\ensuremath{-}}$) in alkali halides, was used to produce pairs of coupled local-mode oscillators. Pairing was achieved by a thermal reaction of mobile interstitial ${\mathrm{H}}_{2}$ molecules with $F$-center pairs ($M$ centers) in KCl. By alignment of the $M$ centers with polarized light, prior to this reaction, the hydrogen-ion pairs could be created aligned in a particular [110] direction. The use of ${\mathrm{H}}_{2}$ and/or ${\mathrm{D}}_{2}$ gas in the hydrogenization process allowed the production of ${\mathrm{H}}^{\ensuremath{-}}$${\mathrm{H}}^{\ensuremath{-}}$, ${\mathrm{D}}^{\ensuremath{-}}$${\mathrm{D}}^{\ensuremath{-}}$, and ${\mathrm{H}}^{\ensuremath{-}}$${\mathrm{D}}^{\ensuremath{-}}$ pairs in any proportion. From the six expected fundamental vibrations of the pair, infrared-absorption measurements can detect the three optically active in-phase modes of the equal-mass pairs (${\mathrm{H}}^{\ensuremath{-}}$${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{D}}^{\ensuremath{-}}$${\mathrm{D}}^{\ensuremath{-}}$). The observed dichroism of the local-mode absorption in crystals with aligned pairs allows a clear identification of the longitudinally and transversally polarized pair modes. For the mixed pair (${\mathrm{H}}^{\ensuremath{-}}$${\mathrm{D}}^{\ensuremath{-}}$), three of the six optically active modes could be detected and identified. A simple model for a pair of localized oscillators is presented, which (after the fit of three coupling parameters between the two hydrogen defects) can quantitatively account for the frequencies and polarization of all observed pair modes. The three coupling parameters can be interpreted to arise predominantly from the electric interaction of the two neighboring vibrating dipoles in their longitudinal and transversal configurations. A quantitative fit to this electric-dipole-coupled oscillator model yields effective charges for the ${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{D}}^{\ensuremath{-}}$ defect close to $1e$. Peculiarities in the widths of the observed local modes are interpreted as arising from transitions between in-phase and out-of-phase pair modes, produced by the emission (or absorption) of an anharmonically coupled lattice phonon.