The inverse Hall–Petch effect in nanocrystalline ZrN coatings

For the purpose of studying the inverse Hall–Petch effect in nanocrystalline hard coatings, nanocrystalline ZrN coatings have been fabricated using magnetron sputtering with grain sizes ranging from 45 nm to 10 nm by varying negative biases from 0 V to 150 V. The transition from the classical Hall–Petch effect to an inverse Hall–Petch effect in nanocrystalline ZrN coatings is observed at a grain size between 19.0 nm and 14.2 nm. The reality of the inverse Hall–Petch effect in the present study is validated by exclusion of other possible effects on hardness of nanocrystalline ZrN coatings, such as porosity, multiphase, chemical composition, texture, and residual stress. Furthermore, a concise model based on lattice dislocations piling up mechanism is proposed to illustrate the breakdown of the Hall–Petch effect and calculate the critical grain size. The predictions of the model fit well with experimental data in some nitride and carbide nanocrystalline coatings. Both experimental and theoretical results indicate that the inverse Hall–Petch effect is an essential property of nanocrystalline hard coatings as similar to nanocrystalline metals and alloys.