Hi, my name is Don.  I have been lurking on this list for a while, so here is 
my first post.
I am a hobbyist who has just built my second home-made quartz digital clock.  
Both are based on a microcontroller that counts timer interrupts and uses 
software tricks to allow me to tune the clock rate based on comparison with 
atomic time via NTP.  The second clock uses a temperature sensor and a heater 
(a grid of resistors) enclosed with the microcontroller board in a glass jar to 
regulate its own temperature.
Of course, I am noticing a drift in the clock rate over time due to crystal 
aging.  The frequency of the crystal is gradually increasing over time.  For 
example, on June 2, the frequency was 15.99927052 MHz.  As of yesterday it is 
hovering around 15.99927796 MHz.
I have read through several online resources, including the very interesting 
one that was posted here recently:
http://www.am1.us/Papers/U11625%20VIG-TUTORIAL.PDF
On page 4-7 of that document there is a slide titled "Typical Aging Behaviors" 
where it shows that long-term crystal aging can be represented as a sum of 
logarithmic functions.  I was wondering if this is just an approximation, or if 
there is a theoretical reason why logarithms would describe such phenomena?  
Looking at the causes of aging, they seem to do with changes in the bonding 
with the electrodes, deposition or oxidation of the components inside the 
crystal enclosure, etc.
I am thinking about trying to measure the aging process over the coming months, 
and then try to model and even predict future aging.  If I can get that to 
work, perhaps I can even incorporate the formula for predicted aging right into 
my software.  Any insights on this would be much appreciated.
FYI, here is a link to what I did on my first clock.  I have not yet finished 
the web page for the second clock, but I will get around to it, eventually.
http://cosinekitty.com/digitalclock/
I do have the firmware for my second clock online, along with some crude 
schematics, if anyone is interested:
http://cosinekitty.com/thermalclock/thermal_clock_firmware.cpphttp://cosinekitty.com/thermalclock/main_board_schematic.pnghttp://cosinekitty.com/thermalclock/heater_switch.png
- Don                                     
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