[time-nuts] Is quartz crystal aging really a logarithmic curve?

[Don Cross]

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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