First Principles Calculation

Theoretical calculations in this thesis, were done by our collaborators Dr. Sophia Heiden ((11-20) surface) and Dr. Giacomo Melani ((0001) surface) from Prof. Dr. Peter Saalfrank’s group in University of Potsdam. Here the calculation method will be briefly introduced since the results will be compared with experimental observations in the following chapters. Periodical density functional theory (DFT) in the Kohn−Sham scheme and supercell models were employed to describe the adsorption of water on α- Al2O3. The DFT calculations[40] were carried out with the Vienna Ab Initio Simulation Program, version VASP5.2, employing the Projector Augmented Wave (PAW) method[41, 42]. Exchange and correlation were treated in the Generalized Gradient Approximation (GGA) using the Perdew-Becke- Ernzerhof (PBE) function[43]. A plane-wave cutoff of 400 eV and Grimme’s D2 correction[40], to account for dispersion interactions, were adopted. These settings were applied for a slab model of both (0001) and (11-20) surfaces. For the structure of (0001) clean surface, Al-I termination, which was

proved to be the most stable structure under UHV conditions by the theoretical work of Kurita[44] and others[45] and also in experiment[46-48], is applied in this work while the O-I termination is the most stable structure under both UHV and high water pressure for the clean (11-20) surface. The atomic layer sequence of (1x1) unit cell of the clean α-Al2O3(0001) surface is -Al-O3-Al-Al-O3- while it is -O-O2- Al4-O2-O- of clean α-Al2O3(11-20) surface.

To allow for low water coverage, we applied a (2x2) super cell model with 10 atom layers for water adsorption on α-Al2O3(11-20) which is confirmed to be sufficiently accurate both for vibrational frequencies and reaction pathways when compared with more atom layers (25 layers). The upper five- layers were optimized to allow for surface relaxation, while the lower five-layers were fixed at the bulk geometry. The surface normal direction of the slab is chosen with a length of 20.5 Å. As a result, the vacuum gap is ∼17 Å which is large enough to get rid of spurious interactions between individual slabs. After the termination of clean surface was optimized, a single water molecule will be brought onto the surface of (2×2) super cell, which in principle with 0.08 tML(theoretically defined monolayer, where we think all the Al active sites are occupied by dissociated water thus 12 water on 2x2 super cell) water coverage that is reasonable to compare to a low coverage situation as in experiment. It is difficult to define a monolayer water adsorption in theory, but this model is thermodynamically favorable at low water coverage. The stable structures with adsorbed water is found by optimizing the topmost five-layer slab and water fragments together. To evaluate the thermodynamic properties of the structure, Gibbs free energies G(T) were calculated for both stable species and transition states, according to

G(T) = H(T) − TS(T) ≈ E + Gvib(T)

where the enthalpy H(T), the entropy S(T), the absolute temperature T, the self-consistent field (SCF) total energy E, and the vibrational part of the free energy, Gvib(T). Since in this thesis understanding the reactivity of water on each surface of α-Al2O3 is one important task to solve, it is necessary to calculate the rates of interconversion of the various possible forms of interfacial water. For this purpose, Eyring’s transition state theory was applied:

𝑘(𝑇) =𝑘𝐵𝑇 ℎ 𝑒−𝛥𝐺

‡_{(𝑇) 𝑘} 𝐵𝑇

⁄

Here, h and kB are Planck’s and Boltzmann’s constants, and ΔG⧧ = G⧧ − G(educt) is the activation free energy for the reaction in question, with G⧧ being the free energy of the transition state. We located transition states using the Nudged Elastic Band (NEB) with Climbing Image (CI) method[49]. The vibrations are treated in the harmonic approximation by diagonalizing the dynamical matrix at the Γ- point. Only coordinates arising from atoms that were not frozen were considered.

The OH (OD) stretching vibration frequencies are determined based on the above methods on α- Al2O3(11-20). For the surface phonon vibrations on α-Al2O3(11-20), we applied a thicker slab with 25 atomic layers which is revealed to result more accurate frequencies than the thinner ones. Besides, the dipole square of normal modes of surface phonons were also evaluated as to have a quantitative understanding of SFG experimental results. For α-Al2O3(0001) surface, also 2x2 super cell with 25 atomic layers slab was used to calculate the normal mode of surface phonon vibrations.

The calculated stable water adsorbed structures and vibrational results of water fragments and surface phonon of α-Al2O3 will be introduced in the lateral part: chapter 3 water adsorption on α-Al2O3(11-20) surface, chapter 5 surface phonon on α-Al2O3(11-20) and chapter 6 surface phonon on α-Al2O3(0001).

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