The piezoelectric effect in natural quartz crystals

Question

Background

I have recently started doing a lot of research on the piezoelectric effect with the hopes of gaining a better understanding of the topic. When I can I like to do experiments on top of reading because it helps cement the knowledge I learned more effectively. The main topic I am looking into right now is quartz crystals. I have researched the molecular structure of quartz and what causes the piezoelectric effect but I am having a hard time finding out how the shape effects the frequency. I have mostly found resources on what makes small perfectly made factory quartz crystals oscillate but I have not been able to find any information on the processes of natural quartz.

The main thing I hope to gain from your knowledge is the understanding of how natural quartz crystals behave when a force or voltage is applied to them. I have a collection of quartz crystals ranging in sizes but I cant complete any successful tests with them on a larger scale.

Questions

Question 1- What effect would a force have on a cluster of natural quartz crystals? I ask this because the molecular structure would be intertwined so I wonder how it would be polarized when a force is applied and what kind of oscillation would be caused. Also how much would the efficiency drop by when compared to a perfect set of quartz crystals?

Question 2- When I have a single quartz crystal that is not uniform how can I determine its internal lattice structure to best predict its poles for any possible experiments I may conduct? I have been unable to read any voltage being created when a force is applied to any of my non uniformed crystals.

Question 3- I know that irregular quartz crystals with deformations will be less efficient but is it even possible to apply a force and read a return voltage with conventional tools and if so how would this best be done with that larger set of crystals.

Answer 1

Even well-ordered single crystals have many resonance modes at different frequencies. A natural cluster of quartz crystals might have a confusing jumble. Like doing resonance analysis of a model doing a catwalk strut.

Bragg x-ray diffraction was (is?) used to probe lattice structure to find alignment of crystal planes. X-ray tools can also be used to probe stress applied to crystals.

Answer 2

The bigger problem you'll have, I think, is that without cutting wafers, you'll have an impossibly high impedance to couple to. And the resonant frequencies will be quite low (whether by thickness modes, flexture at the root of a crystal, or between other crystals in the cluster). The equivalent circuit manifests as a capacitance (largely the electrode capacitance), exhibiting various resonances (modeled as series RLC resonant tanks wired in parallel with the capacitor). The resonances are very weak, i.e. they manifest as small variations in impedance relative to the capacitive reactance. So, if that capacitance is a few pF, and the strongest expected resonances are in the 10s to 100s of kHz, then the impedance is at least some megaohms.

What slicing does, is make the capacitance larger, and the coupling stronger. The frequency is also increased (the preferred modes are thickness-wise), so that quite reasonable values are had, say some kohms impedance in the low MHz.

Unfortunately, slices don't look as pretty. I'm not sure that there's much to do, with respect to both having a pretty cluster, and doing something electronic with it; at least not very easily. But that's the kind of thing you'd need, if you want to give it a real try: an AC bridge circuit, to couple to quite high impedances (megaohms), nulling out the capacitance and coupling to the resonances as best you can.

I wouldn't even try for low frequency (applied mechanical force / generated electric charge) experiments; again, the impedance is so high, you might get a few faint sparks from banging on it with a hammer for example, but it's just going to be such a pain to work with, sticking with a fixed assembly and probing its frequency response seems the easier thing to do.

Answer 3

During WW 2, the USA used submarines to bring Brazilian quartz into US hands.

The "natural quartz" was crucial, but the quartz was ground and etched into very thin regions.

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regarding thicknesses, etc, I've heard the central part of a standard crystal, etched very thin, and plated on both sides of the thin region with silver, with the thicker edges clamped in a holder, is the mechanical approach.

And why would natural quartz be crushed and re-melted and then a mono-crystal slowly drawn from the melt? Because fewer inclusions, and thus cleaner energy storage and higher quality_factor and narrower resonant peaks will result.

I'm not sure "more reliable oscillation" is what results with a MELT/REGROW.

I've seen circuits that can make a Q=200 (poor quality ceramic resonators) oscillate.

However, purer crystals and the use of Low_Thermal_Noise (Boltzmann, Johnson, Nyquist noise) circuitry and PI_filter interfaces and careful Power_supply filtering and careful Gound layout and shielding, can produce oscillations with close-in-phase-wander.

Such very clean close_in waveforms allow Synthetic Aperature Radar success, and allow communication receivers to handle information even in the presence of strong adjacent_channel jamming.

Thus the spacecraft mapping Venus, or the military satellites using radar to look thru clouds and track ships on oceans, or mapping the Brazilian Jungle using side_looking Radar in the 1960s (Motorola built those), need purer crystals and attendant circuits.

Answer 4

Alpha-quartz crystals have electrical and mechanical couplings, that mean that a stress generates electricity and application of electricity deforms the crystal shape. Using them as an oscillator stabilizing element requires identifying an echoing sonic excitation that couples to an electrical polarization. In (common) AT-cut crystals this is shear mode movement in a disc-shape with electrodes on the flat faces. Shear mode is like a bit of Jello sitting on a plate, quivering left-right at the top while the base remains stationary (stuck to the plate).

In wristwatch crystals, the quartz is tuning-fork shaped; the two tines flex to narrow and expand their separation.

There are four considerations in making an oscillator quartz timing element. First, you want it to be supported in a way that doesn't damp the desired oscillation (that tuning fork is cemented to its base at the non-quivering end). Second, you want the echo-chamber effect of sound reinforcement to occur preferentially at ONE frequency, with provision for damping of spurious resonant modes. Third, you want the resonance to have minimal age and temperature sensitivity. Fourth, you want the electrical connection that excites the sound to be simple metallized patches on some accessible surfaces.

The 'insensitive to temperature' requirement is why AT-cut is popular; the A direction, and the T direction (A and T are names for facets of a quartz crystal and specify a direction perpendicular to those faces) are negative and positive temperature coefficient choices, so there's a zero coefficient orientation inbetween the two.