TY - JOUR A1 - Ivanov, V.V. A1 - Tielemann, Christopher A1 - Avramova, K. A1 - Reinsch, Stefan A1 - Tonchev, V. T1 - Modelling crystallization: When the normal growth velocity depends on the supersaturation N2 - The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor’s expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. We show further how the values of n depend on the value of αupper to which the fit is performed starting always from 0. Towards building a validation protocol, we start with validating α21 with published results. KW - Crystallization KW - Supersaturation KW - Growth kinetics KW - Growth rate KW - JMAK model PY - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-581706 SN - 0022-3697 VL - 181 SP - 1 EP - 10 PB - Elsevier Ltd. AN - OPUS4-58170 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -