MatCalc version: 6.01 - …
Author: P. Warczok
Created: 2018-12-19
Revisions:
This paper describes the available options for the definition of the precipitate nucleus composition. Depending on the chosen option, the relevant nucleation rate is calculated by MatCalc.
Nucleus composition of the given precipitate phase is one of the parameters that determine the value of the nucleation driving force ($-\Delta G_\text{chem}$) and the precipitate/matrix interface energy $\gamma$. Hence, various nucleus compositions will result in different critical nucleation energy $G^*$ the nucleation rate $J$ values.
\[J=N_0Z\beta^*\exp\left({-\frac{G^*}{k_\text{B}T}}\right)\exp\left({-\frac{\tau}{t}}\right)\]
\[ G^*=-\frac{2\gamma}{\left(\Delta G_\text{chem}+\Delta G_\text{el} \right)} \]
MatCalc gives the following options for the nucleus composition assumption:
In many cases, the “ortho-equilibrium”, “minimum critical nucleation energy” and “maximum nucleation rate” result in almost identical values of nucleus composition.
Nucleus composition is evaluated by MatCalc which results in the highest value of the nucleation driving force ($-\Delta G_\text{chem}$) for the precipitate phase at the given system state.
Nucleus composition is taken as close to the matrix composition as possible. This is realized with identical u-fraction values of substitutional elements for matrix and precipitate phase.
Nucleus composition resulting in the highest driving force is taken, considering the composition constraints defined for the parent equilibrium phase.
The site fractions of various elements in the nucleus are to be defined by the user.
Nucleus composition which yields the minimal value of $G^*$ is evaluated and taken for the nuclei.
Nucleus composition appears in the nucleation rate formula at the critical nucleation energy ($G^*$) and atomic attachment rate ($ß^*$). With this option, the composition which yields the maximal value of $J$ is evaluated and taken for the nucleus.