Richard Haynes wrote:
>
> Doug,
> Thanks for adding your important two cents. Could you show us an example
> with the necessary conversions numbers. Also there is the concept of
> equilivalents/mole where the number of equivalents is effectively the
> valence, i.e. 2 for Cu(+2). There are some cases where n is not an even
> intergal. All is all a dimensional analysis must yield a dimensionless
> number in the exp(E or H or F).
> Thanks
> Richard Haynes
Sure, and I would certainly invite any corrections.
One over-riding theme when using equations is to be
sure of the assumptions by which they have been deduced.
The Arrhenius equation is a good approximation for simple
atoms/molecules. As one moves away from simple atomic
structures to more complex molecules, the idea of "heat"
has to change. Complex atomic structures no longer bang
into one another more so at higher temps than lower.
They begin to do all sorts of strange things like twist,
bend, longitudenally vibrate, etc ... In other words,
different modes of displaying heat come about.
Alright, now that everyone's gone to sleep, here we go.
Using Arrhenius Equation = exp[ (Ea/R)*(1/T1 - 1/T2) ]
where
Ea = Activation Energy
* Note: The less the value, the less sensitive to temp;
the greater the value, the more sensitve to temp.
R = Gas Constant
T = Temperature in degrees Kelvin
How we pick the units of R determines everything else as
far as units go. One form of the gas constant is:
R (Gas Constant) = 8.3144 J/mol*K and 1/R = 0.1203
Thus, AE = exp[0.1203*Ea*(1/T1 - 1/T2)]
This means that if Ea is divided by R, the units K must
remain in the numerator to cancel the K in the denominator
from the (1/T1 - 1/T2) factor. This will leave the final
exponent dimensionless. Thus, Ea should be in the units J/mol.
This form (J/mol) is very different in implications than
simply Joules.
Changing this constant to units that have calories involves
1 calorie = 4.184 Joules
R (Gas Constant) = 1.9872 J/mol*K and 1/R = 0.50322
Thus, AE = = exp[0.50322*Ea*(1/T1 - 1/T2)]
This means Ea is now in the units cal/mol.
The form of Arrhenius with which I'm familiar uses electron volts
(eV's) as units. So, using the conversion
1 eV = 96.485 kJ/mol
leaves R = 8.6172E-5 and 1/R = 11,604.56557
Thus, AE = = exp[11,604.5656*Ea*(1/T1 - 1/T2)]
This means Ea is now in the units eV/mol.
Ea = 0 eV/mol -> temp has no effect.
Ea = 1 eV/mol -> temp has alot of an effect.
Some semi-mfrs use 0.4 or 0.5 for estimates with
CMOS and higher numbers for 0.6 or even 0.7 for
BJTs. It is important to note that since there
is such a mix of semi-conductor material in any
device, it is better to estimate, then empirically
derive (as long as you have enough sampling) the
Ea specific to the product. That will take some
time.
Here's a sample of how they all work out so that
the same AF (acceleration factor) comes out the
same no matter which version of Arrhenius you
choose to use.
-------------------------------------------------------
**** INPUTS ***
-------------------------------------------------------
Test time at T1 = 16,006 hours
666.92 days (interesting)
95.27 weeks
1.83 years
T1 = 30 C (equation converts to K)
T2 = 50 C " " " "
Ea eV/mol = 0.6
J/mol = 57891.00
cal/mol = 13900.00
-------------------------------------------------------
*** OUTPUT ***
-------------------------------------------------------
AF = 4.1490 : 3857.79 hours
160.74 days
22.96 weeks
0.44 years
-------------------------------------------------------
-------------------------------------------------------
Regards, Doug
