On the spinodal nature of the phase segregation and formation of stable nanostructure in the Ti–Si–N system

Abstract

The free energy of the mixed Ti–Si–N system is calculated according to a semi-empirical thermodynamic formula based on the sub-lattice model for different activities of nitrogen. The results show that the phase segregation in the ternary Ti–Si–N systems is of chemically spinodal nature at a nitrogen pressure and deposition temperature typically used for the deposition of the superhard nc-TiN/a-Si₃N₄ nanocomposites, i.e. $p_{{\text{N}}_2}\ge {10}^{-3}$ mbar and T_dep 550–600 °C, respectively. Only at much lower nitrogen pressure and much higher temperature, can the chemically spinodal decomposition be restrained. A simple estimate of the interfacial strain energy for a semi-coherent interface, as expected for this system, shows that this contribution is unlikely to hinder the system being also coherently spinodal. It is further shown that kinetic constraints, such as T_dep ≤ 300 °C and low $p_{{\text{N}}_2}$, although within the range where the stoichiometric nitrides should be fully spinodally segregated, will kinetically hinder the system to reach the thermodynamically driven equilibrium.

Introduction

The generic design concept for the preparation of superhard nanocomposites with a high thermal stability and oxidation resistance is based on a strong, thermodynamically driven phase segregation in a binary (or ternary) system, that results in the formation of a nanostructure with “compositional modulation” with a sharp and strong interface [1], [2]. In their original paper [1], Veprek and Reiprich omitted using the term “spinodal” because of lack of unambiguous evidence, and because in some publications, where the hardening of mixed transition metal nitrides and carbides upon annealing was attributed to spinodal decomposition, such evidence was absent. The term “spinodal” was not even mentioned in the references quoted in those papers [3], [4], [5]. Meanwhile, experimental results were obtained that support the spinodal nature of the segregation of the TiN and Si₃N₄ phases during the deposition of the nc-TiN/a-Si₃N₄ nanocomposites, consisting of 3–4 nm small TiN nanocrystals “glued” together by about one monolayer of X-ray amorphous silicon nitride (see Section 4.1 in [6]). This segregation occurs provided the nitrogen pressure and deposition temperature are high enough, as explained in earlier papers [1], [2]:

• When deposited under the conditions of a sufficiently high nitrogen pressure (0.3–1 mbar) that provides the thermodynamic driving force and sufficiently high temperature (≥550 °C) that assures the diffusion rate-controlled phase segregation to be completed during the deposition [1], the crystallite size is fairly uniform [7].

• The morphology, as observed by transmission electron microscopy for nanocomposites deposited by plasma-induced chemical vapor deposition (P-CVD) under conditions that favor the formation of fully segregated, thermally very stable nanostructure, is typical of spinodally segregated systems with a high de-mixing enthalpy [6].

• In systems that display a larger misfit between the phases, such as nc-TiN/a-BN, the “optimum” crystallite size, where the TiN nanocrystals are covered with about one monolayer of BN and hardness reaches a maximum, is larger than in the case of nc-TiN/a-Si₃N₄ where this misfit is smaller [6].

• Coatings that were not deposited under the optimum conditions, so that the phase segregation was not completed during the deposition, show an increase in hardness upon annealing to ≥700 °C. This is accompanied by the “adjustment” of the crystallite size to the “optimum” value of about 3–4 nm that can be larger or smaller than the original crystallite size in the as deposited coatings [8].

Although these findings cannot be considered as final, unambiguous evidence, for the spinodal nature of the phase segregation during the formation of the nanostructure in the nc-TiN/a-Si₃N₄ nanocomposites (see, e.g. [9], [10], [11] and references therein), they provide strong support for this concept. Strong evidence of the spinodal nature can be provided by thermodynamic calculations of the Gibbs free energy of the mixed phases as a function of their relative fraction which yields the “chemical spinodal” curve (i.e. the second derivative of the Gibbs free energy of the mixed system is negative) for the TiN/Si₃N₄ system consisting of immiscible, stoichiometric nitrides (see Section 3).

Because the spinodal nature of the phase segregation upon the deposition of the superhard nc-TiN/a-Si₃N₄ and similar nanocomposites was questioned by some workers recently [12], we shall briefly summarize in the next section the thermodynamic conditions needed for spinodal phase segregation to occur. After presenting the calculations that yield the evidence for chemical spinodal in this system under the conditions outlined in [1], [2], [13], [14], we shall discuss possible effects of the strain energy in this system in order to show that it is unlikely to hinder the TiN–Si₃N₄ system to decompose spinodally. Section 4 will deal with a brief discussion of kinetic conditions that are needed in this system to reach that equilibrium. Two conditions will be identified and briefly discussed: (a) a sufficiently high temperature that is needed to allow the diffusion-controlled phase segregation to be completed during the deposition and (b) a sufficiently high nitrogen pressure that is needed to provide the necessary flux of chemisorbed nitrogen to form stoichiometric nitrides at a given deposition rate. The paper will end with conclusions and outlook for the possibilities of the design of superhard nanocomposites with a high thermal stability [1], [2] in other, advanced systems.