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I'm having a hard time finding data about an experiment that I know has been done a bunch of times:

I have a sheet of single crystal rutile $\ce{TiO_{2}}$ (110) that I want to reduce to various $\ce{TiO_{2-x}}$ forms where the x is what I want to vary. I want to try to avoid conversion to the other Magnéli phases if possible $(\ce{Ti_{n}O_{2n-1}})$. To do this reduction, I have a high temp oven that I can flow with 95% $\ce{N_2}$ and 5% $\ce{H_2}$ or simply evacuate. I can set the flow rate to cubic centimeters per second. I need a chart that will tell me what temperature, flow rate, and duration I need to convert my sheets surface to a desired reduced value (i.e., I want a specific x).

I then want to reoxidize the surface by using lower temperatures in a furnace that I can fill with oxygen at different pressures. I need a chart that will tell me what temp, partial pressure of $\ce{O_2}$, and duration I need to re-Oxidize the surface.

The goal here is not to simply get the surface, but to test other properties. I was hoping this step (finding the proper charts) would have been fairly straightforward, but my literature searches haven't turned up quite what I need. I was hoping someone here can point me to a resource that has this data.

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I can't post a comment, so this is not a true answer but I think can help. If I've understand what you mean you want to perform a Temperature-programmed reduction (TPR) followed by a temperature-programmed oxidation (TPO). In this case I think this old book can help: Temperature-programmed Reduction for Solid Materials Characterization. I don't know much about single crystal but I think that many things from TiO2 studies of nanomaterials can be consider valid for your case, this online book can be helpful to understand all the variables.

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