Computational scheme for ab-initio predictions of chemical compositions interfaces realized by deposition growth
Introduction
Density functional theory calculations are today routinely applied to characterize structural and electronic properties of condensed matter systems. They serve as an important complement to and extension of experimental methods [1]. Atomic (and electronic) structure and chemical composition are inseparably interwoven. Information about chemical composition at, for example, interfaces (including surfaces) is therefore of great importance for reliability of such calculations.
Traditional ab initio atomistic thermodynamics methods aim at describing and predicting compositions at oxide surfaces [2], [3]. These schemes assume that equilibrium is established between the oxide and surrounding O2. This criterion is often justified for oxide surfaces that are in direct contact with an O-rich environment. For (solid–solid) interfaces, the situation is more complicated. Interfaces are typically exposed to the surrounding environment only at the moment of creation.1 Furthermore, oxides are seldomly grown directly from O2, and it is not clear what gas(es) they are in (dynamic) equilibrium with during deposition, if at all. A generalization of the ab initio atomistic thermodynamics scheme from surfaces to interfaces [4] can therefore be problematic. In fact, we have shown [5] that the equilibrium configuration at the interface between TiC and alumina predicted by such a generalized scheme does not describe the wear-resistance of TiC/alumina multilayer coatings [6]. We have attributed this inconsistency to the fact that the scheme does not account for the actual growth conditions. This may be a serious shortcoming also for other interfaces realized by deposition growth.
This paper presents a computational scheme that explicitly accounts for deposition conditions. At the same time no a priori equilibrium assumptions are introduced. The scheme is therefore capable to predict chemical compositions at interfaces (including surfaces) as they arise in a deposition process. While kinetic accounts are generally required to describe the full nonequilibrium nature of growth, the Bell–Evans–Polanyi (BEP) principle [7] motivates an effective thermodynamic description inspired by chemical reaction theory.
The key elements of our scheme are the use of Gibbs free energies of reaction as a predictor for the chemical composition and a modeling of the deposition conditions in terms of rate equations describing the deposition environment. Our approach extends the method of ab initio thermodynamics of deposition growth for surfaces [8] to interface modeling. Applying the scheme to the TiC/alumina interface in a chemical vapor deposition (CVD) environment we predict the formation of strongly adhering structures in agreement with the wear-resistance [6] of CVD TiC/alumina multilayers.
The paper is organized as follows. Section 2 motivates the use of the Gibbs free energy of reaction as a predictor of chemical composition. Section 3 contains the details of our modeling. Results are presented in Section 4 and Section 5 contains our conclusions.
Section snippets
Predictor for as-grown chemical composition
We use the Gibbs free energies of reaction as a predictor for the prevalent chemical composition at surfaces and interfaces realized by deposition growth. We justify the use of as predictor using chemical reaction theory [9], [10] and the BEP principle [7].
A description of nonequilibrium growth generally requires a kinetic description. The prevalent surface or interface composition will in principle depend on the reaction barriers for all relevant processes. However, the BEP principle [7]
Materials background
We illustrate our computational scheme by studying the interface composition between TiC and alumina. TiC/alumina multilayers are commonly used as wear-resistant coating on cemented-carbide cutting tools [6]. They are routinely fabricated by chemical vapor deposition (CVD).
Fig. 2 illustrates the experimental setup for CVD of alumina [12]. A H2-AlCl3-CO2 supply gas mixture is injected into a hot chamber which is kept at a fixed temperature and a fixed total pressure. The CVD process proceeds in
Results
In Fig. 4 we plot the free energies of reaction for the two films shown in Fig. 3 as functions of the scaled reaction rate . Deposition parameters (supply gas composition, total pressure, and deposition temperature) as specified in Ref. [12] have been used. In this illustration of the approach we assume for simplicity . Furthermore, the scaled reaction rate is limited to the right by the limit of dynamic equilibrium in (7), indicated by the vertical line.
We find that, over
Summary and conclusions
We have presented a novel computational scheme to predict chemical compositions at interfaces as they emerge in a growth process. The scheme uses the Gibbs free energy of reaction associated with the formation of interfaces with a specific composition as predictor for their prevalence. We explicitly account for the growth conditions by rate-equation modeling of the deposition environment.
An earlier study of TiC/alumina interfaces [5] documented that the predicted composition at this interface
Acknowledgements
We thank Carlo Ruberto and Gerald D. Mahan for valuable discussions. We gratefully acknowledge support from the Swedish National Graduate School in Materials Science (NFSM), from the Swedish Foundation for Strategic Research (SSF) through ATOMICS, from the Swedish Governmental Agency for Innovation Systems (VINNOVA), from the Swedish Research Council (VR) and from the Swedish National Infrastructure for Computing (SNIC).
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