I used many similar techniques to the same end of removing quartz which raised its frequency. Grinding materials included abrasives such as jeweler's rouge, cerium oxide, commercial polishes such as Brasso and Silvo and even HF solution. I'd place the quartz on a small section of plate glass and slide it through a slurry of the abrasive periodically testing its frequency until I'd reached my target.

There's an art to this that's too long to mention here except to say abrasives were used strategically, course grinding would get me near the desired frequency and I'd finish off with a fine abrasive. Then there was the job of re-aging the crystal after its recent abuse to increase its stability. Other techniques were involved such as not lowering its Q factor, etc. which I'll not cover here.

The most desired crystal cut was from the XT-plane (being the most stable) but it was generally difficult to get as it's only a small section of the quartz crystal (also each cut oscillates only over a limited range of frequencies). I used to have a book that explained these cuts in detail, their frequency ranges and electronic properties along with the basic crystallography which I lost years ago. A quick glance at the book would have shown that a great deal of science, engineering and skill is involved in the selection of quartz and its manufacture into useful resonators.

BTW, the mentioning of HF will likely horrify chem-phobic readers. We were well aware of its dangers and took special precautions never to come in contact with it.

New fear unlocked

For instance:

https://www.pa3fwm.nl/projects/sdr/

The longer you read, the more amazed you will be.

The quartz crystals themselves were grown with carefully controlled levels of specific impurities (like scandium) in order to reduce their temperature sensitivity.