  The crystallization proceeds by the advance of the crystal faces into the
disordered phase at the expense of the supersaturation which is not sustained
in our model. Using a conservation constraint for the transformation ratio and
a kinetic law, we derive a general equation for the rate of transformation. It
is integrated for the six combinations of the three spatial dimensions D = 1,
2, 3 and the two canonical values of the growth order (1 and 2). The same
equation with growth order 1 is obtained when taking only the linear term from
the Taylor's expansion around 0 transformation of the model of
Johnson-Mehl-Avrami-Kolmogorov(JMAK). We verify our model by fitting it with
JMAK. We start the validation of our model in 2D with published results.
