NMR study of interacting $\mathrm{F}$ centers in ${\mathrm{Na}}_8{[\mathrm{Al}}_6{\mathrm{Si}}_6{\mathrm{O}}_{24}{]\mathrm{Cl}}_2$ sodalite

Hyperfine interactions between randomly distributed $\mathrm{F}$-center electrons and the surrounding magnetic nuclei in mixed $\mathrm{Cl}$/electrosodalite, ${\mathrm{Na}}_8{[\mathrm{Al}}_6{\mathrm{Si}}_6{\mathrm{O}}_{24}{]\mathrm{Cl}}_x·{\left(e^{-}\right)}_{2-x}$, give rise to multiple nuclear magnetic resonances due to quantized variations in the local electron density at the nuclear site. This enables one not only to account for the number of $\mathrm{F}$ centers surrounding a crystallographic site, but also to estimate the percentage of cages filled with $\mathrm{F}$ centers and their spatial distribution. Complete assignments of ${}^{23}\mathrm{Na}$, ${}^{27}\mathrm{Al}$, and ${}^{35}\mathrm{Cl}$ MAS NMR spectra are provided and the NMR evidence for spin correlation effects of interacting $\mathrm{F}$-center electrons is presented. It is proposed that the spin pairing is a general feature of paramagnetic cage-structures with $s$-like electrons, owing it to the Pauli exclusion principle.

Figure 1

The body-centered cubic (bcc) lattice of face-sharing sodalite cages with examples of salt-free, salt-bearing, and $\mathrm{F}$-center-containing sodalite cages. The corners of the truncated octahedra are occupied by regularly alternating $\mathrm{Al}$ and $\mathrm{Si}$ atoms, bridged by divalent oxygen. Salt-free sodalite cages have only three charge-compensating sodium cations (dark circles) while salt-bearing ones carry an excess $\mathrm{NaCl}$ unit with the chloride ion in the center. The $\mathrm{F}$-center electron, symbolized by “$e^{-}$,” is formed by the inclusion of one sodium atom in the salt-free sodalite cage. A high electric field inside the salt-free sodalite cages ionizes incoming sodiums atom to form a tetrahedral ${\mathrm{Na}}_4^{3+}\equiv \left\{4{\mathrm{Na}}^{+}\left(e^{-}\right)\right\}$ center.

Figure 2

The ${}^{23}\mathrm{Na}$ MAS NMR spectrum of SCl/ES with 60% of cages with $\mathrm{F}$ centers. (a) The $1_2$ and $n_3+n_4$ resonances are shifted with respect to resonance 0 by the hyperfine interactions between $\mathrm{F}$-center electrons and the sodium nuclei. The remaining resonances are due to sodium surface species (see the text for details). Spinning sidebands are marked by asterisks. (b) Shown is the first downfield spinning sideband pattern for the $n_3+n_4$ resonances, which suffers from less overlap than the MAS center-band. Dotted curves represent Gaussian lineshape components used for peak deconvolution. The experimental intensity profiles for $n_3+n_4$ resonances (light bars) are compared to those expected from binomial distribution (dark bars). The assignment of $n_3+n_4$ resonances, labeled here by letters, is given in Table .

Figure 3

The ${}^{27}\mathrm{Al}$ MAS NMR spectra of SCl/ES samples with 17%, 60%, and 84% of cages with $\mathrm{F}$ centers. For clarity, $m_1$ and $m_2$ resonances are labeled only in the sample with 60% cages with $\mathrm{F}$ centers. These resonances arise due to two groups of $\mathrm{F}$ centers at a distance of $5.0\mathrm{\AA }$ (dark circles) and $8.1\mathrm{\AA }$ (light circles), respectively, each surrounding aluminum nuclei in tetrahedral geometry. Shown by the inset is the fine structure of the $1_1$ resonances in the sample with 17% of cages with $\mathrm{F}$ centers, consisting of four components due to different $\left[m_2\right]$ configurations of next nearest $\mathrm{F}$-center electrons. Dotted curves represent Gaussian lineshape components used for peak deconvolution. For all samples, experimental intensities of the $m_1$ resonances (light bars) are compared with those calculated from binomial distribution (dark bars).

Figure 4

The ${}^{35}\mathrm{Cl}$ MAS NMR spectra of SCl/ES samples with 17%, 60%, and 84% of cages with $\mathrm{F}$ centers. The $m_1$ resonances are due to $\mathrm{F}$-center electrons in the neighboring cages sharing the hexagonal cage-windows (dark circles). These electrons are located at the corners of the sodalite unit cell, separated from the ${}^{35}\mathrm{Cl}$ nucleus at the cage center by $7.6\mathrm{\AA }$. The $m_2$ resonances are due to more distant $\mathrm{F}$-center electrons (light circles) located in the neighboring cages sharing the smaller square windows and are only visible in the sample with 17% of cages with $\mathrm{F}$ centers. The experimental intensities for $m_1$ resonances (light bars) are compared with those calculated from a binomial distribution (dark bars).

Figure 5

Experimentally determined paramagnetic shifts of ${}^{27}\mathrm{Al}$ (squares) and ${}^{35}\mathrm{Cl}$ (rhombs) MAS NMR $m_1$ resonances (with respect to resonance 0) as a function of the number of nearest $\mathrm{F}$-center electrons. The continues lines depict the dependence of the paramagnetic shifts for two nuclei in the absence of electron-electron interactions.