Chemical-bonding and lattice-deformation mechanisms unifying the stability and diffusion trends of hydrogen in TiN and AlN polymorphs

The continuous development of hydrogen-permeation barriers (HPB) based on metal nitrides highly desires a generic unification of the key thermodynamic and kinetic mechanisms therein. This work employs first-principles calculations to study the stability and diffusion trends of H impurity in the rock-salt, wurtzite, and sphalerite phases of the prototypical TiN and AlN. The formation energies ($E_f$) of H at various interstitial and vacant sites in these nitrides are calculated, and the underlying chemical-bonding and lattice-deformation mechanisms are self-consistently revealed by the systematic structual, energetic, and electronic-structure analyses. This leads to the discovery of a generic volcanic trend of $E_f$ in terms of the electron number on H ($Q_H$), which well portrays how the covalent-ionic H–N and H–metal bondings determine its stability in different atomistic environments. Then, the kinetic properties (e.g., potential barriers, diffusion coefficients, and isotope effects) of interstitial H in these nitrides are calculated, where the volcanic $E_f$–$Q_H$ relationship is applied to better understand the joint contributions of chemical bonding and lattice deformation. Finally, the revealed mechanisms and volcanic $E_f$–$Q_H$ relationship are generalized to successfully describe the behaviors of H in some important grain boundaries of c-TiN and c-AlN, including the $\Sigma 3\left\{112\right\}〈110〉$ twin frequently observed in c-TiN and the $\Sigma 5\left\{210\right\}〈001〉$ twin prototypical to many rock-salt materials. The widely varying hydrogen permeabilities measured in experiment on many nitride coatings are successfully explained, inspiring more useful chemical principles to guide the design of HPB coatings facing harsh environments with long-term reliability.