Phase field crystal models and fast dynamics

Research output: ThesisDoctoral ThesisCollection of Articles


Emergent microscale structural properties of crystalline materials have been puzzling scientist since the dawn of modern solid state physics. The microstructure of crystalline materials is affected by disorder: topological defects such as vacancies and grain boundaries can fundamentally change both the electronic and structural properties of materials. The microstructure is determined by the manufacturing process, the most famous being solidification from melt. Understanding the solidification process can be used to produce materials with specific properties in a controlled way. Classical density functional theory (CDFT) and its computationally more efficient counterpart, the phase field crystal (PFC) model, have emerged as efficient tools for studying microscopic crystalline properties of materials at diffusive time scales, avoiding the unnecessary short time scale of thermal vibrations. In this thesis we further develop the PFC methodology. First, we use the DFT and PFC methods to calculate the free energy of the solid–liquid boundary of the well-known Yukawa system. In the second part – the main body of the work – we develop fast dynamics for the PFC framework. The last part is dedicated to computational work: we propose an efficient numerical scheme for solving the dynamics of the PFC amplitude system. Developing fast dynamics tackles an old problem of diffusive dynamical systems. The presence of collective vibrations of atoms is characteristic of metallic materials. In principle all the dynamical theories that describe elasticity of materials should also include these vibrations. However, diffusive dynamics are unable to describe such vibrations. To this end, we propose two approaches. In the first approach the elastic excitations that create these vibrations are explicitly equilibrated. In the second approach we develop a hydrodynamic theory for the PFC framework based on physical conservation laws. In both cases we demonstrate the viability and the importance of the approach. The latter theory is more general and can be used to describe a larger spectrum of fast phenomena such as advective mass transport. The theories developed in this thesis allow studying previously inaccessible problems such as fast solidification. In addition they should produce better understanding of many problems where fast dynamics are present. These include problems where relaxation of elastic excitations is important, such as polycrystalline coarsening, and problems where mass transport is important e.g. certain type of dendritic solidification. Another advantage of the methods presented here is that the theoretical framework is general and can be extended to different systems.
Translated title of the contributionFaasikenttäkidemallit ja nopea dynamiikka
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Ala-Nissilä, Tapio, Supervising Professor
  • Ala-Nissilä, Tapio, Thesis Advisor
Print ISBNs978-952-60-6861-9
Electronic ISBNs978-952-60-6862-6
Publication statusPublished - 2016
MoE publication typeG5 Doctoral dissertation (article)


  • phase field crystal models
  • elasticity
  • hydrodynamics


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