  We report $^{7}$Li, $^{29}$Si, and $^{13}$C NMR studies of two different
carbon-rich SiCN ceramics SiCN-1 and SiCN-3 derived from the preceramic
polymers polyphenylvinylsilylcarbodiimide and polyphenylvinylsilazane,
respectively. From the spectral analysis of the three nuclei at room
temperature, we find that only the $^{13}$C spectrum is strongly influenced by
Li insertion/extraction, suggesting that carbon phases are the major
electrochemically active sites for Li storage. Temperature and Larmor frequency
($\omega_L$) dependences of the $^7$Li linewidth and spin-lattice relaxation
rates $T_1^{-1}$ are described by an activated law with the activation energy
$E_A$ of 0.31 eV and the correlation time $\tau_0$ in the high temperature
limit of 1.3 ps. The $3/2$ power law dependence of $T_1^{-1}$ on $\omega_L$
which deviates from the standard Bloembergen, Purcell, and Pound (BPP) model
implies that the Li motion on the $\mu$s timescale is governed by continuum
diffusion mechanism rather than jump diffusion. On the other hand, the rotating
frame relaxation rate $T_{1\rho}^{-1}$ results suggest that the slow motion of
Li on the ms timescale may be affected by complex diffusion and/or
non-diffusion processes.
