Date of Award

Spring 2012

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Materials Science and Engineering


Nikolas Provatas



Committee Member

Jeffrey J. Hoyt, Hatem Zurob, Sumanth Shankar


Crystal growth has been recognized as a paradigm for non-equilibrium pattern formation for decades. Scientific interest in this field has focused on the growth rates and curvature of branches in snow flake-like structures patterned after a solid's crystallographic orientations. Similar patterns have been extensively identified in solidification of metals and organic metal analogues and are known as dendrites, which is originated from a Greek word "dendron" meaning tree.

Dendritic spacing and morphology established during casting often sets the final microstructure and second phase formation that develops during manufacturing of alloys. This is particularly true in emerging technologies such as twin belt casting of aluminum alloys, where a reduced amount of thermomechanical processing reduced the possibility of modifying microstructure from that determined at the time of solidification. Predicting and controlling these microstructure of cast alloys has thus been a driving force behind various studies on solidification of materials.

Mg-based alloys are another class of materials gaining importance due to the high demand for weight reduction in the transportation industry which accordingly reduces the gas consumption. While the solidified microstructure and its effect on the material properties have been the subject of intensive studies, little is known about the fundamental mechanisms that determine dendritic microstructure in Mg alloys and its evolution under directional growth conditions.

This thesis investigates the relationship between the microstructure and cooling conditions in unsteady state upward directional solidification of Al-Cu and Mg-Al alloys. The four-fold symmetry of Al-Cu alloys are used to study the dynamical spacing selection between dendrites, as the growth conditions vary dynamically, whereas, the Mg-Al system with a six-fold symmetry is used to study a competition between neighbouring, misoriented grains and the effect of this as the resulting microstructure. Mg-Al also presents a situation wherein the cooling conditions dynamically vary from the preferred crystallographic growth direction. Analysis of phase field simulations is used to shed some light on the morphological development of dendrite arms during solidification under transient conditions. Our numerical results are compared to new casting experiments.

Chapter three studies spacing selection in directional solidification of Al-Cu alloys under transient growth conditions. New experimental results are presented which reveal that the mean dendritic spacing versus solidification front speed exhibits plateau-like regions separated by regions of rapid change, consistent with previous experiments of Losert and co-workers. In fact, The primary spacing of a dendritic array grown under transient growth conditions displays a distribution of wavelengths. As the rate of change in solidification front velocity is decreased, the evolution of the spacing follows the prediction of the geometrical models within a band of spacing fluctuations. The width of the band is shown to highly depend on the rate of the solidification front velocity acceleration, such that the higher the rate, the wider the band of available spacings. Quantitative phase field simulations of directional solidification with dynamical growth conditions approximating those in the experiments confirm this behavior. The mechanism of this type of change in mean dendrite arm spacing is consistent with the notion that a driven periodically modulated interface must overcome an energy barrier before becoming unstable, in accord with a previous analytical stability analysis of Langer and co-workers.

In chapter four, it is demonstrated both computationally and experimentally that a material's surface tension anisotropy can compete with anisotropies present in processing conditions during solidification to produce a continuous transition from dendritic microstructure morphology to so-called seaweed and fractal-like solidification microstructures. The phase space of such morphologies is characterized and the selection principles of the various morphologies explored are explained. These results have direct relevance to the microstructure and second phase formation in commercial lightweight metal casting.

McMaster University Library

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