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.
The other details are fascinating, though - the intersection of mechanical, crystallographic, and RF (?) properties of a crystal that you can adjust through abrasives and selection of the cut.
Teflon is not affected by HF, so if you use only vessels of Teflon to hold the HF solution and tweezers made of Teflon for handling anything that you submerge in the solution of HF, it works fine.
Besides using Teflon for anything that is in contact with the HF solution, you must do all work under a hood that evacuates the vapors of HF emitted by the solution, otherwise handling a HF solution would be very dangerous. It is good that gaseous HF is lighter than air, so after being evacuated it will continue to rise in the air, while becoming more and more diluted.
The book was a harback with a bright yellow dust jacket and I think its title was printed in red. It was about 300 pages and was no lightweight, full of resonance equations, tables etc.—the sort of book you'd find in the lab of a commercial crystal manufacturer.
Can't remember the price but it was damned expensive. At times over the years I've had need to refer to it and I still get a bit peeved when I think about it.
Some of you guys should have picked that up. ;-)
I've seen much more detailed diagrams of the crystal and cuts/cutting angles but I can't find one online. . Those precision diagrams are required by those who cut the quartz at the start of the manufacturing process.
https://xoprof.com/2023/09/unleashing-the-mystery-of-crystal...
And, if you're sneaky, you can add solder.
New fear unlocked
The quartz crystals themselves were grown with carefully controlled levels of specific impurities (like scandium) in order to reduce their temperature sensitivity.
Galvanic deposition of silver has been frequently used for increasing the thickness of thin metal layers that had been deposited in vacuum, in order to adhere to the crystal.
For instance:
https://www.pa3fwm.nl/projects/sdr/
The longer you read, the more amazed you will be.
For electronic circuits such as frequency reference markers where frequency stability is important the lowest practical frequency is 100kHz with 1Mhz preferred, and where frequency tolerances are tight 5 and 10MHz are much preferred with operation in a temperature stabilized oven to minimize frequency drift.
The most frequency-stable crystal cuts are at those frequencies, as frequencies increase (say >10MHz to 100MHz), which at the highest frequencies require the crystal to operate in overtone mode, frequency stability again tends to decrease.
It's much easier to build/buy electrical rather than mechanical LC components to hit audio frequencies ~100Hz-10kHz.
