General Kinetics
Byeong-Joo Lee
POSTECH - MSE
[email protected]
Byeong-Joo Lee
cmse.postech.ac.kr
Content
0. Thermally activated process - Concept of Energy barrier
1. Rate of Transformation - time dependence of reaction
2. Empirical rate Equation - degree of reaction
· General approach vs. J-M equation
3. Temperature Dependence of reaction rates
4. Determination of Activation Energy
· Rate constant technique : @ constant Temp.
· Time for constant fraction technique
· The change of slope technique
5. Significance of the Activation Energy
Relation with Mechanism
Parallel Process vs. Serial Process
6. Classification of Phase Transformations
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Rate of Transformation
□ The parabolic growth law
in cases where the diffusion distance increases during the reaction
ex) oxidation, precipitation
R = G·t1/2, V ∝ t3/2
□ The linear growth law
in cases where the diffusion distances do not change during the reaction
ex) oxidation yielding a porous oxide layer,
precipitation of needles or plates
formation of pearlite
R = G·t, V ∝ t3
※ One can expect different laws for particles of different shapes.
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Rate of Transformation
□ Introduction of degree of reaction f as the ratio between momentary
total volume and final volume of the reaction product
1. assume all the nuclei are present at time zero.
f = K·tn
ex) complete growth of pearlite : Vfinal = V
density of nuclei
: N (#/volume)
total volume of specimen : V
assume no impingement
⇒
ex) precipitation
: Vfinal < V
⇒
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Rate of Transformation
2. combination of rate of nucleation and rate of growth
suppose that new nuclei form all the time with the rate N
per unit time and unit volume
assume linear growth law and Vfinal = V
total volume of all particles which have formed up to the time t is
※ time exponent
for a precipitation of spherical particles with continuous nucleation = 5/2
for plates when all nuclei were present at the beginning = 5/2
⇒ detailed mechanism of a reaction cannot be uniquely determined
by simply studying the overall reaction rate.
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Retarded growth due to the impingement
□ assume linear growth law
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Retarded growth due to the impingement
Byeong-Joo Lee
cmse.postech.ac.kr
General Kinetics
- Temperature Dependence of Reaction Rates
□ apply the concept of activation energy in a purely formal way as a means
of representing the temperature dependence of complicated reactions
define a time tf which is required in order to bring the reaction to a certain stage f.
ex) Suppose that a reaction goes to f = 0.1 in half the time at 900oC compared to 800oC.
Try to estimate how past the reaction will be at 1100oC.
What assumption do you need?
※ Several mechanisms often affect the rate!!
Byeong-Joo Lee
cmse.postech.ac.kr