Fractional extent fictitious

The concept of fictitious fractional extent was introduced by Johnson and Mehl [JOH 39]. Its purpose is to simultaneously take into account the mutual covering of growing nucleus and the variation of free volume for further nucleatioa... 

The fictitious fractional extent would be the fractional extent of the same reaction for which the growth of the grains would not be limited by meeting with other grains and for which the whole initial volume would be constantly free for nucleation. 

Call Fo the initial volume of the solid reaetant, the fictitious fractional extent is defined by ... 

A.9.1.2. Relation between fictitious fractional extent and realfractional extent... 

The fictitious fractional extent will thus be calculated by not taking account of the phenomenon of mutual blocking of the interfaces and considering that random nucleation can occur, at any moment, at any point of the whole of volume Fq of the initial phase. 

Remark.- At the initial time, the fictitious and real fractional extents are null and at the very first moments, they are practically equal because it is far from probable that two grains meet with each other at the beginning of the reaction. 

In Figure A.9.3a, we plotted the curve of the reduced rate versus k t from equation [A.9.22], and in Figure A.9.3b, the fictitious fractional extent versus the same X-coordinate such as given by [A.9.20]. 

Figure A.9.3. Reduced rate (a) and fictitious fractional extent (b) in an Avrami model...

Figure A.9.4a, which gives the fictitious fractional extent versus kfif, is not a line under the same conditions as above.

Figure A.9.4. Fictitious fractional extent by the Avrami model...

Figure A.9.4b, which gives the same fictitious fractional extent versus is a line under the selected conditions, and thus, obeys [A.9.26] and makes it possible to determine d).

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