These processes could be recrystallization (grain growth), densification during sintering or hot-pressing treatment and so on..., except creep data, which are just available for me. In reality, these values should be called "apparent activation energies" or even simply "temperature dependence coefficients" as they only evaluate quantitively how temperature change can increase/decrease the rates of the processes.
Dear Igo, Image that you don't have any idea what type of reaction kinetics involved in your measurements still you can calculate the apparent activation energy if you are sure that it is diffusion controlled.
First of all you have to run at least three experiments at three different temperatures. Normally one has to plot those experimental results as the fraction of reaction or transformation (also it is called as as the degrees of advancement of reaction) ,, Y is accomplished versus the time t required for that. The most of the curves you got are S-type curves if you plot them on a semi-logarithmic paper. Then you take for an example: Y= 0.75 or 0.90 and you obtain t1 for T1, t2 for T2 and t 3 for T3. Don't forget Y changes from zero to unity.
Then plot Ln t versus 1/T on a linear paper for the each fraction of transformation , you suppose to get a straight line through those there points on that graphical representation. The slope is equal to Q/R, where Q is the apparent activation enthalpy, which is also called energy, and R is the gas constant. If you repeat that for various values of Y fraction you should get bunch of parallel line having exactly the same slopes. Best regards.
Dear Tarik,
Many thanks to you. To be honest, I am aware of plenty methods for the calculation of apparent activation energies, including all those you have described in your message. However, I need the obtained experimental results published in the literature for HfC...
With my best regards,
Igor
Dear İgor, We are teaching that staff in the physical metallurgy course offered for the sophomore year students but it is not very much appreciated by those in chemistry department , where they are using isoconventional method. For me it is not sound method if one deals with diffusion controlled reactions, where D t bi-product term appears as a single arguments because governing PDE is parabolic type. Best Regards.
Dear Igor,
Such data you can find in:
Kumachiro Y. High-temperature characteristics. In: Kumashiro Y, editor. Electric
refractory materials. New York–Basel: Marcel Dekker, Inc.; 2000.
Best regards
Mikhail
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