# [time-nuts] Crystal Ageing

Bernd T-Online BNeubig at t-online.de
Wed Oct 10 01:34:30 EDT 2007

```Jeffrey Pawlan wrote:
> It was Rick who wrote about crystal aging. It is not predictable whether the
> crystal will go higher or go lower in frequency and there is no guarantee that
> it will age at a linear rate. The worst-case is when a crystal erratically
> jumps.
Indeed, the observed crystal aging is a sum of a larger number of
physical processes.
- Some of them are stronger than others
- some of them decay faster or slower than other others
- many of them show a logarithmic frequency change over time
- a few of them have the shape of an exponential decay.
The usual approximation used to predict frequency aging - as used in
MIL-PRF55310 - is
df/f = f0 + a1*log(a2*t+1),
where a1 can be understood as a measure of the strenght of aging, and
1/a2 is a kind of time constant, i.e. small a2 values stand for slowly
aging processes and large ones for fast agers.
A better approach to describe frequency aging would thus be a
mathematical sum of several logarithmic terms as in the above equation.
As nicely shown in John Vig's tutorial, you can easily get a reversal of
the aging rate (i.e. a change from positive to negative aging or vice
versa), if you simply superimpose a fast and weaker (positive) aging
process with a slower but stronger negative aging process - see attached
copy.

O.K. you now can say: why not make aging prediction by mathematical
fitting of a sum of logarithmic terms through the observed frequency
data over time?
Basically this would/could improve the degree of fitting, correct. BUT:
There is a big leveraging effect, if you make a mathematical prediction
over a long period of time from data taken over a relatively small time
period. In other words: If you just vary one or a few data points by a
very small amount (i.e. to eliminate jumps), the effect on the
extrapolated curve is enormous. Just try it using EXCEL's solver ...
I had published an example for that 10 years ago - see a copy of my
paper " Correlation of predicted and real aging behaviour" on our
website www.axtal.com.
In that paper I used data from about 9 months of aging, and compared the
predictions made from different time periods with the real aging.

From my standpoint the MIL-PRF55310 method of prediction is just a
standardized method to define how the aging numbers in a spec are
"verified" in a reasonable time of 4 weeks, It does not say: "This is
how the crystal will age over decades"

There is much more to say, but I will stop here, hoping that this
contribution gave some time nuts a better understanding - and may kill
their firm believe into aging predictions ;-)

Best regards

Bernd Neubig
DK1AG

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