Self-reduction of the native TiO2 (110) surface during cooling after thermal annealing – in-operando investigations

We investigate the thermal reduction of TiO2 in ultra-high vacuum. Contrary to what is usually assumed, we observe that the maximal surface reduction occurs not during the heating, but during the cooling of the sample back to room temperature. We describe the self-reduction, which occurs as a result of differences in the energies of defect formation in the bulk and surface regions. The findings presented are based on X-ray photoelectron spectroscopy carried out in-operando during the heating and cooling steps. The presented conclusions, concerning the course of redox processes, are especially important when considering oxides for resistive switching and neuromorphic applications and also when describing the mechanisms related to the basics of operation of solid oxide fuel cells.


SUPPLEMENTARY X-RAY PHOTOELECTRON SPECTROSCOPY DATA FOR THE SAMPLES PREVIOUSLY ANEALED AT 1100 °C.
Figure S1. The XPS Ti 2p core line spectrum of TiO2 (110) surface; (a) after annealing at 1100 °C and removing the surface layer with the use of the diamond scraper; (b) during cooling down after annealing in 1100 °C when the temperature level reaches 600 °C.
The XPS investigations proved the surface localization of the intense reduction process. The surface of the reduced TiO2 with the Ti 3+ concentration, as presented in Figure 2(e) in the main text, was removed with the use of the diamond scraper. Such a process performed in-situ in an XPS UHV chamber uncovered the subsurface layers of the crystal, which indicated no presence of Ti 3+ oxidation states, as presented in Figure S1(a).
The TiO2 (110) surface is mainly reduced during cooling of the sample down from 1100 °C, when the temperature is still above 500 °C. This is visible when analysing the concentration of Ti 3+ oxidation states at particular temperatures and is presented in Figure S1(b), where XPS data measured at 600 °C are shown. At this temperature, the concentration of Ti 3+ states was at a level of 8%, while it only increased to 12% after cooling down to room temperature.

THERMODYNAMIC MODEL INCLUDING CONFIGURATIONAL ENTROPY
In the manuscript we derived a relationship between the surface and bulk concentration of vacancies, neglecting the configurational entropy. Then, considering the exchange of vacancies between the surface and bulk layers, S B1 B2 …, the rate equations can be written: In the steady state limit, it follows that: (1) in the main text.
To include vibrational entropy, we consider a TiO2 film consisting of 24 layers and an overall concentration of oxygen vacancies of 0.5%, where the topmost layer will be denoted as the surface. The difference between the vacancy formation energies on the surface and bulk is again E = Eb-Es > 0. As discussed in the main text, the vibrational entropy at the surface is assumed to be 0.3 kT lower than in the bulk. A layer with defect concentration c will have a configurational entropy of ( ) = This expression can be minimized with respect to cb for a given temperature T to find cb(T). Combining the last two terms of this equation in ∑ cf (cb), we can derive these values from the equation: Figure S2. Figure S2. The black line illustrates eq. (S1) for S v =0.3kT. If E/kT > 0.9, the bulk vacancy concentration tends to zero and all vacancies gather at the surface layer. For E/kT < 0.3, the surface layer gets depleted with respect to the bulk -an effect of the vibrational entropy difference. Note that the number of layers, N, is 24. Due to the boundary conditions, cb cannot exceed 0.52%. The blue (dotted) and the red (dashed) lines are computed for N=48 and N=100 layers, respectively.
We see that for E = 0.8eV it is not possible to stabilize any vacancies in the bulk if kT < 0.88eV. This corresponds to an unreasonably high temperature of 10200K. Assuming E = 57 meV and T=1100 C, the bulk concentration is about 0.4% and, at the surface, cs=2.8%. Lowering the temperature to 500 C is already sufficient to stabilize 10.5% of the vacancies at the surface layer, while at RT all vacancies are located at the surface.

DE/kT
Of course, the model presented here is fairly crude, both in the treatment of vibrational entropy (assuming the Vineyard-Dienes model), as well as in the configurational entropy (using the point defect limit). However, we must see that S v merely vertically shifts the curve in Figure S2 and adds or subtracts a linear term in E/kT. In reality, we also assume a narrowing in the configuration space in both the surface and bulk layers, corresponding to a rescaling of the derivative of  cf and lowering of cb for a given temperature. We assumed that during the heating and cooling cycles, the topmost 24 layers are accessible to the newly created vacancies. It should be noted though that this number is merely illustrative and the model can be generalized to N layers with the same total number of vacancies in the film. As is shown in Figure S2, the general features are not significantly affected if we scale the bulk concentration with the number of layers.