Transient behaviour of the formation of primary dendrite arms

Abstract
In this work a model describing the formation of new primary dendrite arms within a grain or single crystal during directional growth is presented. Therefore it is assumed that the initial distribution of primary dendrite arms has to be rearranged in order to provide locally sufficient space of undercooled interdendritic liquid. A two dimensional arrangement of three equidistant dendrites growing parallel to the imposed temperature gradient is investigated. The idea is to calculate the changes in the undercooled liquid and thereby in the free enthalpy in the free growth zone when the middle dendrite moves laterally in order to provide space for a new dendrite. An activation enthalpy for this mechanism is derived and the rate of formation is estimated. In analogy to the classical nucleation theory for equiaxed solidification the free enthalpy curve as a function of time or process advance exhibits the characteristic energy barrier (the maximum) to overcome and then a drop when a dendrite has formed as this is a step towards the stationary state. Therefore the process may be characterized as a nucleation mechanism.