A simple procedure for accurately assessing the stoichiometry and structural disorder of TiN ceramics by X-ray diffractometry

Abstract

Accurately assessing the stoichiometry and structural disorder of TiN ceramics is very important for understanding their properties, but is often not done because it requires complex Rietveld refinements of the corresponding X-ray diffraction (XRD) patterns. As an alternative, a simple procedure is developed here that allows such information to be extracted from the XRD patterns without Rietveld refinements. For this purpose, the stability ranges of super-stoichiometric and sub-stoichiometric TiN are first determined theoretically mathematically from the general principles of Wyckoff position occupation and electrical charge neutrality, and then constrained by theoretical thermodynamic calculations of the Gibbs potential. Subsequently, theoretical simulations of the XRD patterns of a large set of super-stoichiometric and sub-stoichiometric TiN ceramics in their stability ranges are used to reveal the existence of linear relationships between the stoichiometry and the intensity ratio of the hkl peak to the 200 peak (i.e., Ihkl/200 (%) with hkl being 111, 220, 311, 222, 400, and 331), which is then exploited to formulate an analytical model that easily assesses the stoichiometry and structural disorder of TiN ceramics from I111/200 (%). Finally, as an experimental validation and example of application, the stoichiometry of a TiN ceramic fabricated by spark plasma sintering is experimentally evaluated using both the Rietveld method and the proposed model showing marked agreement between their results.