That is an interesting chip, our circuits were more discrete  datasheet for your chip. So you are using the crystal  as a series mode transmission structure,  now to get the best phase noise you'd normally match the Zin and Zout of the amplifier to the Rs of the crystal, (as per the oscillator models of Leeson and later Everard ) but the optimum match is pretty soft and it will work very well quite a long way from that equal impedance condition. However this chip seems to be high Z input low Z output and has more in common with the sort of oscillator built into digital watches and PC clocks. For what  you need it may well be more than adequate. In vacuum you may need to keep the dissipation in the crystal lower than you would in the fresh air - I'd aim for tens of microwatts max. (appnote about measuring that) Even with no deposition a fresh crystal ages in two ways, it moves up  in freq as it shakes any dust from the grinding process free, but down as the metal plating of the contacts beds into any voids. To pre-age frequency standards  we would drive hard and then drop the levels to  a few tens of microwatts dissipated in the ESR to give many years of stability,

In your case long term age is not so critical as you zero at the start of the run, but jitter may be,

I'm not sure I am the best placed to answer questions about mounts in your situation as it will have more to do with the constraints of the rest of the experiment around it,  though it may be worth sawing a few commercial crystals open to see how they have done it.  The sort of thing I'd expect is quite gently springy - almost at the compliance level of an O ring with wire wrap so the acoustic impedance is way lower than the quartz ,and it is free to flap.

~I see these chaps are using loops of wire and conductive dag - this is similar size  to what I recall when cutting open HCU49 style ones all those years ago

Image from https://www.researchgate.net/figure/An-image-of-a-quartz-crystal-used-in-the-quartz-crystal-microbalance-when-mounted-in-a_fig4_266038341

Mike.

That was the chip we were using previously, but now I'm thinking of using one of these, STM32H747XI

DS12930_STM32H747xIG.book (arduino.cc)

Purely because it looks like it has the control circuitry for the crystal and can also do the frequency sampling, counting and reporting in a single package, whereas at present that's split out into:

XTAL Driver > AND Gate > Binary Counter > Multiplexer. 

I did see the image you mentioned a few times online, I'm looking into that. One of the worries I had was being able to not just drive the crystal, but heat and cool it too! 

So what you were saying about driving the crystal, presumably you're doing that to standardise the response of the crystal over a production run to ensure they're all as close to each other as they can be? 

That was the chip we were using previously, but now I'm thinking of using one of these, STM32H747XI

DS12930_STM32H747xIG.book (arduino.cc)

Purely because it looks like it has the control circuitry for the crystal and can also do the frequency sampling, counting and reporting in a single package, whereas at present that's split out into:

XTAL Driver > AND Gate > Binary Counter > Multiplexer. 

I did see the image you mentioned a few times online, I'm looking into that. One of the worries I had was being able to not just drive the crystal, but heat and cool it too! 

So what you were saying about driving the crystal, presumably you're doing that to standardise the response of the crystal over a production run to ensure they're all as close to each other as they can be?