Volume change and non-local driving force in crystallization (Q2505114)

The author develops a model for crystallization of substances experiencing a volume change upon phase change. A distinctive feature of the model is the use of the following set of variables: momentum density, temperature, pressure, and degree of crystallinity. The model accounts for the volume expansion through a dissipative mass current density. The core of the model consists in the definition of certain matrices \(G, M\) governing the evolution of the vector \(\vec{x}\) of the above mentioned quantities through the equation \[ \dfrac{d\vec{x}}{dt}=L(\vec{x})\cdot\dfrac{\delta E}{\delta \vec{x}}+ M(\vec{x})\cdot\dfrac{\delta S}{\delta \vec{x}}, \] where \(E, S\) are the total energy and entropy functionals, respectively, and \(\delta /\delta \vec{x}\) denotes the functional derivative. The matrices \(L, M\) have to satisfy several conditions imposed by physics, including \[ L(\vec{x})\cdot\dfrac{\delta S}{\delta \vec{x}}=M(\vec{x})\cdot\dfrac{\delta E}{\delta \vec{x}}=0 \] which leads to associate \(L\) with irreversibility and requires that \(M\) does not affect \(E\). The construction of \(L, M\) is discussed at length, with particular attention on how to incorporate the diffusive current. The model is applied to the specific case of aluminum. A perturbation analysis around a stationary state is also performed.