[time-nuts] Quartz Crystal Motional Movement

Attila Kinali attila at kinali.ch
Sun Jun 26 05:42:10 EDT 2016

On Sat, 25 Jun 2016 21:30:30 -0400
Bob Camp <kb8tq at n1k.org> wrote:

> Every paper I have ever read on the intrinsic Q of quartz makes the claim that Q * F 
> is a constant ( Q goes up as frequency goes down). 

Yes, same here. But sofar I have not seen any theoretical proof of that.
But then, I have not been looking into those papers that deal with that,
as it would open a big can of wurms (aka a lot of theory to learn to even
understand the most basic stuff).

On Sat, 25 Jun 2016 18:17:58 -0700
Hal Murray <hmurray at megapathdsl.net> wrote:

> > The highest Q I remember seeing were BVA's that reached 2e6 to 3e6 @ 5MHz
> What determines the Q of a crystal?  Is it atomic level impurities?  Crystal 
> defects?  ...

This is a very good question, but unfortunately, I do not have an answer.
It seems (with a big "I am not sure" disclaimer) that modern solid state
physics, or rather the sub-part that deals with crystals, has good
predictive power of what the piezo electric properties of a certain
quartz crystal cut will be. But I do not know how accurate these
predictions really are, whether they apply to any other piezo-electric
material (there is a lot of research going on in this field) and
what limits the predictions accuracy.

>From what I have understood, the bigest contributors to Q are:
* overtone number
* the cut angle
* the form of the crystal (aka energy trapping) and placement of the holder
* the placement of the electrodes and how they are applied

Crystal defects seem to be either only a minor factor, or they can be
kept out of the crystal good enough that they don't matter. The only
references I have seen that deal with this were those from around WWII
that mention twining.

Impurities of crystals do not seem to have any large effect on Q
but determine long term stability and radiation hardness.

> How has that changed over time?  Is there a Moore's law for crystals?

I am not aware of any study of the change of Q of crystal oscillators
over time. Only of those that study the frequency stability. And even
those do not give a lot of information what the factors and the size of
influnce they have. It's mostly "we built this design and measured
it for 3 years" kind of stuff.

> How does the quality of crystals used for timing compare to the crystals used 
> for semiconductors?

Biiiiig difference. Modern crystals for use in semiconductor devices
are optimized for size. 2.5x2mm is today kind of a standard size for
high frequency oscillators, but by far not the smallest. 32kHz tuning
forks can be even smaller (at least in one dimension). These crystal
are a rectangular piece of quartz that is supported on its corners and
usally of constant thicknes. This means that a lot of oscillation energy
is present at the holder contacts, which in turn means it's being damped,
ie the Q is being lowered. For these designs, the stability of quartz
crystals is so high anyways, that some loss of Q is easy to tolerate.

For timing crystals, you want the crystal to be as large as possible
(less influence of holder, higher power) and lens shaped (trapping
the energy in the center of the crystal while keeping the holder
"out of the way").

These differneces in design lead to Q factors in the range of
a couple 1000 to a few 10'000 for the cheap crystals, while the
timing/low noise crystals seem to be usually in the range of
a few 100'000 to 1'000'000.

> Are there any other economically significant uses of high quality crystals?

Anywhere where you need low close in noise and high stability.
Cell phone base stations are probably one of the largest markets
these days. But also telecomunication equipment in general seems
to have a need for stable low noise oscillators.

			Attila Kinali

Malek's Law:
        Any simple idea will be worded in the most complicated way.

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