Quantitative characterization of high temperature oxidation using electron tomography and energy-dispersive X-ray spectroscopy

We report quantitative characterization of the high temperature oxidation process by using electron tomography and energy-dispersive X-ray spectroscopy. As a proof of principle, we performed 3D imaging of the oxidation layer of a model system (Mo3Si) at nanoscale resolution with elemental specificity and probed the oxidation kinetics as a function of the oxidation time and the elevated temperature. Our tomographic reconstructions provide detailed 3D structural information of the surface oxidation layer of the Mo3Si system, revealing the evolution of oxidation behavior of Mo3Si from early stage to mature stage. Based on the relative rate of oxidation of Mo3Si, the volatilization rate of MoO3 and reactive molecular dynamics simulations, we propose a model to explain the mechanism of the formation of the porous silica structure during the oxidation process of Mo3Si. We expect that this 3D quantitative characterization method can be applied to other material systems to probe their structure-property relationships in different environments.

model), molecular dynamics with mobility of all atoms was performed for 200 ps at 298 K. To test the influence of systems size on the pores formed, simulations were carried out with the initial 5.8 nm model, 20, 40 and 100 nm models using the same simulation protocol. The 100 nm model contained 64 million atoms and rules out any artifacts due to periodic boundary conditions. Supplementary Fig. 2b shows the oxidation of large (40 nm) 3 Mo3Si models that feature a 20 nm thick silica layer upon completion of oxidation. Supplementary Figs. 3c, d and e show representative one nanometer thin slices of the silica layer obtained after simulation of the Mo3Si oxidation reaction from the 5.8, 40 and 100 nm models, respectively. The quantitative analysis of the size and distribution of pores in hundreds of slices indicates irregular pore sizes between 1 and 2 nm with less than 1 nm contact length. The results are independent of the model dimensions and represent the thermodynamic equilibrium state when disregarding the effects of MoO3 sublimation. Therefore, it can be concluded that the large and irregular pore distribution of the amorphous silica layer on the (001) surface of Mo3Si observed in experiment is a non-equilibrium structure that results largely from the kinetics of MoO3 evaporation.
Major limitations of the simulation results are the neglect of MoO3 evaporation, also called "pesting" process 2 , and minor uncertainties from the silica force field (see next section). The simulation protocol of the reaction relies on the assumption of a layer-by-layer process. While there is no direct evidence, an interval in between oxidation of subsequent layers allows better qualitative comparisons to the long time scales (seconds) in experiment. The reported results do not depend on the layer thickness, verified by tests with larger incremental layer thickness of 2 nm. The simulation protocol also keeps computational cost at a manageable level, especially for the large-scale simulations up to 100 nm size.

Force Field.
A new force field for bulk silica was created for the reactive simulation of the oxidation of the Mo3Si (001) surface. The potential energy expression consist only of nonbonded parameters to allow changes in chemical bonding, including a term for Coulomb energy and a 12-6 Lennard-Jones (LJ) term, Epot = Ecoulomb + ELJ. The parameterization is based on the INTERFACE force field approach 3 and higher atomic charges account for the neglect of covalent bonding in silica. This force field is also compatible with other common force fields such as CHARMM, CVFF, and AMBER for interfacial simulations 4,5 . The parameters reproduce the local tetrahedral geometry, Si-O bond length, and density of crystalline silica phases (quartz, cristobalite). In total, four different atom types were defined including two for Mo and Si in the alloy phase as well as two for Si and O in silica. Mo and Si in the alloy carry no atomic charges (zero) and are described by LJ parameters (σ, ε) only which amount to (2.99 Å, 5.0 kcal/mol) and (4.55 Å, 3.0 kcal/mol), respectively. Si and O atoms in silica carry atomic charges of +2.4e and -1.2e, respectively, as well as LJ parameters of (1.

EDS and high-resolution images of MoO2 islands
To get statistical results, except for the 0 o projection EDS maps of flakes characterized by electron tomography, around 5 more spectra of similar flakes oxidized at each temperature were also collected and then averaged for Fig. 3c. One typical fitted EDS spectrum of Mo and Si are shown in Supplementary Figs. 3a and 3b. and the raw spectrum is shown in Supplementary Fig. 3c.   Supplementary Fig. 3. Quantification of Mo/Si ratio. Fitted spectra of Mo (a) and Si (b) from an EDS map. c, An EDS spectrum of a Mo3Si porous structure. The Cu and C signals are from the TEM grid. The oxidation temperature was 900 o C.
We used a table of Cliff-Lorimer factors calculated for 200kV accelerating voltage to convert the integrated peaks to atomic concentration using Bruker Software. We used the K-edges of all elements, because the scattering cross-sections of the K-edge are better known. Consequently, the calculated CL factors are more accurate. As we do statistical analysis for multiple flakes at the same oxidation temperature, the error bar for Mo/Si ratio comes from the results of analysis of 5 EDS maps of different sample flakes. The magnitude of the error bar is usually ±1% (~15 to 20% of error). To confirm the analysis without an absorption correction is not a problem for our results, we repeated the quantification using an absorption correction and found the change in mole fraction to be less than 10 relative % of the reported values for both Si and Mo. For the density we used the density of non-porous SiO2 (2.7 g/cm -3 ), which is the dominant phase. We quantified the spectra using a thickness of 50, 200 and 500 nm which spans the extremes of the thickness of our flakes. Results for one spectrum of one sample oxidized at 800 o C for 5min are shown in Supplementary Table 1 below. The difference between these two extremes (50 and 500 nm) was smaller than the error bars in quantifying different flakes. We therefore conclude that the absorption correction is negligible; this makes sense considering both the low Z of most of the material as well as the fact that it is porous. We fixed the stoichiometry of the oxides to be dioxides to get a more accurate result, as SiO2 and MoO2 are the most likely oxides we have in the porous structure during high temperature oxidation 6 . We also calculate the results if we don't assume fixed stoichiometry. The result for Mo/Si ratio is within 5% accuracy between the results with and without fixed stoichiometry. The oxide is MO1.7 (M stands for Si or Mo) without fixed stoichiometry without absorption correction. The lower estimation of oxygen is due to the absorption. We also calculated the crystal lattice constant based on the HR-STEM images measurement ( Supplementary Fig. 4d), and it is ~5.5 Å for both a and c which is close to the literature published 7 (5.54 Å for a and 5.63 Å for c, Supplementary Fig. 4c). Supplementary Fig. 5 shows the overlay of Mo, Si and O signal obtained from EDS mapping. Clearly, Mo signal is associated with O signal while no Si signal can be seen at the same region (white circles in Supplementary Fig. 5b). The oxygen peak can be seen from these regions in EDS spectrum ( Supplementary Fig. 5c). It indicates the Mo forms MoO2 embedded in silica.

Supplementary
Supplementary Fig. 4. a, Fig. 6. STEM images at 0 before (a) and after (b) acquiring a full tomographic tilt series of a sample oxidized at 1100 o C for 30 minutes. The 3D reconstruction of the tilt series is shown in Fig. 4c. STEM images before (c) and after (d) measuring an EDS map of a sample oxidized at 800 for 5 minutes. The EDS map is shown in Fig. 3.