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Here is what I know:

Sapphires are composed primarily of $\ce{Al2O3}$ (in pure form colorless) as well as Fe and Ti (trace impurities responsible for the color). I know that the proportion and identity of trace elements gives rise to various colors but I just want to focus on the combination that gives blue right now.

The explanation that I could find online says that the reason we see blue is because of intervalence charge transfer between the iron and titanium ions. Specifically Ti(IV), Ti(III), Fe(III), and Fe(II) are involved. The ground state configuration is controversial but is presumed to be both ions in their 3+ state. It could also be Ti(IV)-Fe(II). The first part of my question is what is the exact equation for the process occurring? I could not find a redox potential for the reaction $\ce{Ti(IV) + e^- -> Ti(III)}$ so I'm not sure which direction the electrons flow. The half reaction $\ce{Fe(III) + e^- -> Fe(II)}$ has a positive reduction potential of +0.77 V. I assumed that a photon provides enough energy for the fourth ionization energy of Ti (4174.65 kJ/mol) and that electron is transferred to Fe(III). I don't think this can be correct though because that energy would be in the ultraviolet region on the J/atom scale. This is the same for the third ionization energy of Fe. I was expecting to see something closer to yellow light region ~575nm. So from this its clear that I'm probably missing the idea regarding the physics occurring here.

The second part of my question has to deal with color subtraction in general. Why does a sapphires absorption of yellow light lead to blue color in the first place? I've seen an explanation that you imagine white light as a mixture of only the primary colors red, blue, and green light. Also its stated that the secondary colors are formed as follows: red + green = yellow, blue + green = cyan, and red+ blue = magenta. Then if a sample absorbs for example yellow light (R+G) then only blue light remains from the original R+G+B=W combination. This makes sense at face value for me but I wanted to go a bit further. I assume the origin of this color addition and subtraction theory is that humans have cones specific for detection of red, blue, and green light (with a range of wavelengths of course to cover the whole spectrum). My difficulty with the color subtraction answer for the color origin is the fact that our cones detect a range of wavelengths. If the sapphire only removes a single wavelength of light close to 575nm (yellow), how is the effect so dramatic to make the stone blue? Won't the stimulation of the cones not have changed dramatically?

Feel free to answer as in depth as possible! Thanks-

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    $\begingroup$ Trying to use atomic energy levels for impurities incorporated in a crystal tends to not work well. Those ‘ions’ are immersed in electric fields from the surrounding crystal. $\endgroup$ – Jon Custer Jul 20 at 23:02
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    $\begingroup$ Actually sapphires can be any color other than red. If it is red colored aluminum oxide then it is a ruby. $\endgroup$ – MaxW Jul 21 at 1:19
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    $\begingroup$ As @MaxW states, any color, including clear., e.g. edmundoptics.com/f/sapphire-windows/12234 $\endgroup$ – DrMoishe Pippik Jul 21 at 4:44
  • $\begingroup$ Thank you @Jon, MaxW, DrMoishe I know. That is in my first paragraph $\endgroup$ – Joe Jul 21 at 15:31
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The blue of sapphires is produced by the elements titanium and iron that are both present. There is a process called charge transfer causing the transfer of an electron between Ti$^{4+}$ and Fe$^{2+}$ to Ti$^{3+}$ and Fe$^{3+}$ to fit together with the Al$^{3+}$ of the corundum lattice. Those ions give the blue sapphire its colour.

Note that the ions in a crystal are different from isolated ions in the gas phase, they tend to have larger absorption bands instead of sharp lines. Also the distances in the lattice are important and may modify the colour, anisotropy can lead to colour dichroism, the sapphire may be blue viewed from one side and green from another.

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