Svante August Arrhenius (19 February 1859 – 2 October 1927) gave us Arrhenius' Law which teaches us that aging processes are accelerated by two-to-one for each 10°C rise of temperature.
Sometimes, we can see that law at work in a component's data sheet. Consider for example the following extract from a data sheet for chip resistors:
We find two statements of "life" which are actually both statements of aging rates, one at 70°C and the other at 25°C. Assigning a coefficient "alfa" to our aging equation, these two data points should yield an "alfa" value of two according to Mr. Arrhenius.
Whatta-ya-know, the value of "alfa" is almost exactly that.
Therefore, the aging rate of these parts at some other temperature is calculable. For example, if the temperature is 40°C, we would have an aging rate K40 as follows:
"Arrhenius is erroneous." (CALCE, 1990)
Posted by: Clemens Lasance | December 22, 2010 at 03:12 AM
Arrhenius does not suggest a fixed rate of change with temperature - the rate depends on the "activation energy".
It is somewhat of a coincidence that the same "10-degrees per factor 2" applies both to the leakage current of silicon and the dominant aging mechanism in these thin-film resistors; but there are plenty of aging and failure processes where the rate of change is significantly different from this.
As an aside: as suggested by Clemens Lasance, Arrhenius "law" is only truly appropriate for a limited class of processes. Nevertheless, like many laws that include "fitting coefficients", it can be useful even where it is not ideal.
That said: one ageing process for thin film resistors is diffusion into grain boundaries - and this should be a situation where Arrhenius works rather well.
Posted by: George Storm | January 25, 2011 at 05:41 PM