Phase field crystal modeling of two-dimensional materials

Petri Hirvonen

Research output: ThesisDoctoral ThesisCollection of Articles


Pristine two-dimensional (2D) materials display many exceptional properties unseen in conventional bulk materials. However, techniques scalable to large-scale production yield polycrystalline microstructures with grains in different orientations and grain boundary line defects between them. Grain boundaries can impair the unique properties of these materials. Better control of the growth process is needed to avoid defects or at least to control their distribution. Unfortunately, the formation of 2D microstructures is poorly understood due to the large span of length and time scales involved. Phase field crystal (PFC) models are a recent approach to multiscale modeling of defected materials. PFC holds great promise for studying complex large-scale microstructures and their slow evolution over long, diffusive time scales. In the work reported in this thesis, we have extended the PFC framework to quantitative modeling of real 2D materials. We first assessed the suitability of PFC for modeling the grain boundaries and triple junctions found in polycrystalline graphene. After detailed comparisons with experimental evidence and atomistic calculations, we found realistic defect structures and formation energies. Finally, we studied the coarsening and characteristics of different crystalline and quasicrystalline microstructures using PFC. We observed that many microstructural properties are universal and independent of the underlying lattice symmetry. Having identified a PFC model capable of yielding realistic graphene structures, we exploited it in a multiscale approach to produce sample model systems for heat transport molecular dynamics studies. These realistic, highly-relaxed samples allowed multiple new discoveries. For example, we showed that the in- and out-of-plane phonon modes in graphene are scattered very differently by grain boundaries. We repeated these analyses for PFC samples of hexagonal boron nitride and observed qualitatively similar behavior. In addition to new knowledge about 2D microstructures and heat transport through them, we developed various computational techniques to facilitate our research. These methods are related to sampling low-energy defect configurations, converting PFC density fields to discrete atomic coordinates and analyzing microstructures. As an example, we developed a method for detecting the local lattice orientation and defects in crystalline and quasicrystalline microstructures, and for extracting the grain structures in them. This was the first method of this kind applicable to quasicrystals. The work in this thesis has laid a solid foundation for application of the PCF methodology to study other 2D materials or further physical properties of them, such as their mechanical or electronic transport properties.
Translated title of the contributionKaksiulotteisten materiaalien faasikenttäkidemallintaminen
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Ala-Nissilä, Tapio, Supervising Professor
  • Ala-Nissilä, Tapio, Thesis Advisor
  • Elder, Ken, Thesis Advisor
Print ISBNs978-952-60-8607-1
Electronic ISBNs978-952-60-8608-8
Publication statusPublished - 2019
MoE publication typeG5 Doctoral dissertation (article)


  • phase field crystal
  • two-dimensional materials
  • graphene
  • hexagonal boron nitride
  • quasicrystals
  • microstructure
  • defect structures
  • formation energy
  • heat transport


Dive into the research topics of 'Phase field crystal modeling of two-dimensional materials'. Together they form a unique fingerprint.

Cite this