Particles on curved surfaces: A dynamic approach by a phase-field-crystal model

Backofen, Rainer; Voigt, Axel; Witkowski, Thomas

doi:10.1103/physreve.81.025701

Cited by 33 publications

(38 citation statements)

References 33 publications

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“…From this probability we determine that the icosahedral packing, which has the fewest defects, is indeed entropically more favourable than the D 5h , confirming that the ground state can exhibit excess defects, similar to experimental observations and computational results for very much larger systems in the form of grain boundary scars 6,7 and for packings of electrons on a sphere (the Thomson problem).…”

supporting

confidence: 79%

“…6 The equilibrium packings follow from the interplay between the curvature of the sphere and the interaction between the particles. For fixed particle size and surface coverage, increasing the radius of curvature of the surface leads to packings that exhibit varying numbers of isolated point defects that for large enough particle numbers condense into clusters of defects.…”

Section: Introductionmentioning

confidence: 99%

“…For fixed particle size and surface coverage, increasing the radius of curvature of the surface leads to packings that exhibit varying numbers of isolated point defects that for large enough particle numbers condense into clusters of defects. 6,7 Here, defects are particles that do not have the ideal six-fold coordination. Studies of particles on unduloids and catenoids have shown that for small particle numbers a Lennard-Jones potential produces different minimum energy structures compared to a purely repulsive Coulomb potential, showing that the range and type of interaction also affect the geometry of particle packings on curved surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Energetically favoured defects in dense packings of particles on spherical surfaces

et al. 2016

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The dense packing of interacting particles on spheres has proved to be a useful model for virus capsids and colloidosomes. Indeed, icosahedral symmetry observed in virus capsids corresponds to potential energy minima that occur for magic numbers of, e.g., 12, 32 and 72 identical Lennard-Jones particles, for which the packing has exactly the minimum number of twelve five-fold defects. It is unclear, however, how stable these structures are against thermal agitation. We investigate this property by means of basin-hopping global optimisation and Langevin dynamics for particle numbers between ten and one hundred. An important measure is the number and type of point defects, that is, particles that do not have six nearest neighbours. We find that small icosahedral structures are the most robust against thermal fluctuations, exhibiting fewer excess defects and rearrangements for a wide temperature range. Furthermore, we provide evidence that excess defects appearing at low non-zero temperatures lower the potential energy at the expense of entropy. At higher temperatures defects are, as expected, thermally excited and thus entropically stabilised. If we replace the Lennard-Jones potential by a very short-ranged (Morse) potential, which is arguably more appropriate for colloids and virus capsid proteins, we find that the same particle numbers give a minimum in the potential energy, although for larger particle numbers these minima correspond to different packings. Furthermore, defects are more difficult to excite thermally for the short-ranged potential, suggesting that the short-ranged interaction further stabilises equilibrium structures.

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supporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energetically favoured defects in dense packings of particles on spherical surfaces

et al. 2016

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“…We can confidently apply this assumption here (τ zx = C zx zx ) to obtain results in terms of stress, which can be directly compared with Eq. (15). Expected errors are < 1 − 2% for zx 0.05.…”

Section: Dissociation Width Vs Applied (Escaig) Strainmentioning

confidence: 91%

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

et al. 2012

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The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable defect structures that maintain high numerical efficiency. The general framework combines both long-range elastic fields and basic features of atomic-level core structures, with defect dynamics operable over diffusive time scales. Fundamental elements of the resulting defect physics are characterized for the case of fcc crystals. Stacking faults and split Shockley partial dislocations are stabilized for the first time within the PFC formalism, and various properties of associated defect structures are characterized. These include the dissociation width of perfect edge and screw dislocations, the effect of applied stresses on dissociation, Peierls strains for glide, and dynamic contraction of gliding pairs of partials. Our results in general are shown to compare favorably with continuum elastic theories and experimental findings.

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“…[25]. Perfect dislocations and simple grain boundaries in 2D triangular and 3D BCC crystals have also been examined in various contexts [14,15,[27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Phase field crystal modeling as a unified atomistic approach to defect dynamics

et al. 2014

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Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and nonconservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-type glide mechanisms involving closed dislocation loops or grain boundaries as well as Bardeen-Herring-type climb mechanisms involving precipitates, inclusions, and/or voids. Both source classes are naturally and simultaneously captured at the atomistic level by PFC descriptions, with arbitrarily complex defect configurations, types, and environments. An unexpected dipole-to-quadrupole source transformation is identified, as well as various new and complex geometrical features of loop nucleation via climb from spherical particles. Results for the strain required to nucleate a dislocation loop from such a particle are in agreement with analytic continuum theories. Other basic features of FCC and BCC dislocation structure and dynamics are also outlined, and initial results for dislocation-stacking fault tetrahedron interactions are presented. These findings together highlight various capabilities of the PFC approach as a coarse-grained atomistic tool for the study of three-dimensional crystal plasticity.

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Particles on curved surfaces: A dynamic approach by a phase-field-crystal model

Cited by 33 publications

References 33 publications

Energetically favoured defects in dense packings of particles on spherical surfaces

Energetically favoured defects in dense packings of particles on spherical surfaces

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

Phase field crystal modeling as a unified atomistic approach to defect dynamics

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