Phase Field Crystal Modeling Of Quasicrystal Growth

Quasicrystal(QC),as a solid structure with no translational order but with 5-,7-and higher-fold forbidden rotational symmetry in traditional crystallography,reforms our understanding of the notion of "order",which usually equals to periodicity.QC has attracted substantial interest in materials science and condensed matter physics since its first discovery.Huge amount of experimental reports of QCs from multiple alloy systems with the order of magnitude of a few angstroms represented by Al-based systems to various soft matter system with the order of magnitude of sub-micron represented by the polymer self-assembly,and rapid development of mathematical tools for analyzing the quasiperiodic structures,make us understand more and more about this new state of matter.However,we still have many confusions about this delicate quasiperiodic pattern,one of which is,how do QCs grow?Consequently,this thesis focuses on the topic of exploring the growth mechanism of QCs,and its main body is organized and presented as following.Computer simulations has been employed to explore the stability mechanism of QCs in recent years.And the idea of two length scales with a specific ratio in a model is recognized as a powerful and effective requirement to recover QC patterns.Herein,we studied perfect-tiling growth mode,random-tiling growth mode and a multistep growth mode with multiple metastable states via a phase-field crystal model incorporating a two-length-scale potential.Firstly,in this two-mode phase field crystal model,perfect-tiling and random-tiling growth modes exist in different regions of temperature parameter,and these two modes can convert to each other by simply manipulating the softness of the potential of the system.After decomposing the total free energy to idea entropy term and particle-particle interaction term,which represent the disorder and the order of the system respectively,we demonstrate that controlling the magnitude of temperature parameter and the softness parameter of the system will alter the contribution of the interaction term in the total free energy of the system,that is,alter the competitive relation between the entropy term and interaction term,and hence result in entropy-driven random-tiling growth mode and energy-driven perfect-tiling growth mode.Next,in the same model system,under certain thermodynamic parameters,both quasicrystal growths via heterogeneous and homogeneous nucleation may be associated with a multistep behavior and the transient appearance of triangular and intermediate phases,different from classical nucleation pathways.The metastable intermediate phase spontaneously occurs to bridge the triangular phase and quasicrystal nuclei of different orientations to reduce the total free energy of the system.Decomposition of an undercooled fluid phase into quasicrystal phase shows a multistep pathway wherein the triangular phase and the intermediate phase may occur faster than the quasicrystal phase,when the growth rate of one length-scale ordering is significantly different from the other and the subsequent competing and coupling of both length scales are involved.The calculated structure factor,radial distribution function,and the aperiodic tiling structure of the intermediate phase reveal that it's a one-dimensional QC structure between two-dimensional crystal structure and two-dimensional QC structure,and its structure units,which finely match the transformation from crystals to QCs,explain why it appears during the quasicrystal formation.