1. General Kinetics Byeong-Joo Lee Phase Transformations POSTECH - MSE

2. 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

3. 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.

4. 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
          ⇒         

5. 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 
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.

6. General Kinetics - Retarded growth due to the impingement
□ assume linear growth law

7. General Kinetics - Retarded growth due to the impingement

8. 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!!