The purpose of the topaz lecture is two fold - firstly to introduce topaz as a gem and - secondly to cover the issue of how the appearance of a gem is changed by irradiation.
Gem color change by irradiation is a big business, and a very important topic in gemology! Check out the shopping channel or the display cases in department stores for that oh-so-common pale blue topaz!!
The most important method by which the color of topaz is manipulated involves irradiation of the gemstone. This can be done in a number of ways, perhaps the use of a linear accelerator is easiest to understand.
In the case of irradiation using a linear accelerator, the gemstone is bombarded with electrons that are travelling really fast. The electrons penetrate the crystal and at some point hit an atom or displace an electron from an atom or create some other kind of damage. Electrons are really small (much smaller than an atom), so the damage that they do is of atomic proportions.
A simple example of the result of such damage is that an atom is displaced from its regular site and an electron is trapped in the resulting "hole". This electron can absorb light energy, which causes it to "jiggle". The energy is dissipated through the motion of the electron, so a subset of the light wavelengths with appropriate energies is used up.
In most cases, only a small range of wavelengths = energies can be absorbed by an electron trapped on one specific type of site, and so the visible spectrum only looses that set of wavelengths = colors. We see the color of the remaining light (the principles of absorption and transmission should now be familiar). If the irradiated stone has two or more types of color centers (e.g., involving electrons trapped in two or more different types of sites) then the color will be the net result of all color centers.
In the specific case of topaz, two types of color centers (e.g., trapped electrons) are created by irradiation. The first absorbs energy at the blue end of the spectrum, giving a yellowish / brownish color. The second type absorbs at the red end, giving a blue color. The result = yellow-brown + blue = yakky green. This is not popular.
It so happens that the yellow-brown color centers are much less stable than the blue color centers. In other words, if the topaz is heated up a bit, the electrons, (displaced atom, or whatever other damage is involved) can relocate themselves, "healing" the crystal (repairing the color-forming defect). We see the color of the remaining light (the principles of absorption and transmission should now be familiar).
In this case: yakky green -minus- yellow-brown => blue.
That is it. end of story. If a mistake is made and the stone is heated too hot, it will become colorless (assuming that all color was due to color centers)! But this is no problem! The stone can simply be irradiated again and it will turn yakky green!