Doug, Thanks. To be complete we need to go over the changes that can occur with E(voltage) affects the rate of electrochemical reaction such as corrosion. It takes a bit to do this and I must wait until I finish some material for a client. Perhaps Fri. if anybody is interested. Looking forward to meeting and discussing things with you. Richard P.S. I will be in the valley Oct 1-2. What will you be doing or perhaps at EMC-Denver -----Original Message----- From: Douglas Mckean <[email protected]> To: Richard Haynes <[email protected]> Cc: emc-pstc <[email protected]>; accelerated-stress-testing <[email protected]>; Parker, Thomas P (Paul) <[email protected]> List-Post: [email protected] Date: Wednesday, July 29, 1998 9:31 PM Subject: Re: AST Tutorial on the Use of Tempature to increase Acceleration Factor
>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 >
