Structural complexity in monodisperse systems of isotropic particles

Engel, Michael; Trebin, Hans‐Rainer

doi:10.1524/zkri.2008.1040

Cited by 26 publications

(32 citation statements)

References 32 publications

(41 reference statements)

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“…It has been shown that the LJG system forms a glass at r G = 1.4σ and ε = 1.8ε 0 [2] or at r G = 1.47σ and ε = 1.5ε 0 [4][5][6]. We also found that the LJG system cannot be crystallized in the parameter region near these points.…”

Section: Sa020-4mentioning

confidence: 52%

“…With the aim of realizing single-component glasses, atoms interacting through the LennardJones-Gauss (LJG) potential [1,2] have been studied by molecular dynamics (MD) simulations in two dimensions [3] and three dimensions, [4][5][6] and it has been shown that the LJG system forms a longlifetime glass when the liquid is cooled. In equilibrium, the system forms crystals and quasi-crystals depending on the parameter region of the LJG potential [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…In equilibrium, the system forms crystals and quasi-crystals depending on the parameter region of the LJG potential [1,2]. Up to now, the thermodynamic origin of the complex phase diagram has not been fully understood.…”

Section: Introductionmentioning

confidence: 99%

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Application of Phase Transition Theory to a Glass-Forming System

et al. 2012

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We have investigated the crystallization of a monatomic simple liquid in equilibrium, where the constituents interact through the Lennard-Jones-Gauss (LJG) potential. By incorporating a perturbation expansion into a density functional approach, we obtain a phase diagram covering a wide range of the parameter space. The phase diagram agrees qualitatively with that obtained by molecular dynamics (MD) simulations. The MD simulations show that the system cannot be crystallized, even if the temperature is sufficiently low, in a certain region of the parameter space. In this parameter region, we find that the coexisting density of the fcc crystal is unexpectedly high owing to a decrease in the free energy and show that the third-nearest-neighbor site of the fcc crystal coincides with the second minimum in the LJG potential.

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Section: Sa020-4mentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

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Application of Phase Transition Theory to a Glass-Forming System

et al. 2012

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“…Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14]. The ingredients for 2D quasipattern formation are, first, a propensity towards periodic density modulations with two characteristic wave numbers k 1 and k 2 [15][16][17][18]. The ratio k 2 =k 1 must be close to certain special values; e.g., for dodecagonal QCs the value is 2 cosðπ=12Þ.…”

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confidence: 99%

Three-Dimensional Icosahedral Phase Field Quasicrystal

et al. 2016

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We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize threedimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation. DOI: 10.1103/PhysRevLett.117.075501 Periodic crystals form ordered arrangements of atoms or molecules with rotation and translation symmetries, and possess discrete x-ray diffraction patterns, or equivalently, discrete spatial Fourier spectra. In contrast, quasicrystals (QCs) lack the translational symmetries of periodic crystals, yet also display discrete spatial Fourier spectra. QCs made from metal alloys were discovered in 1982 [1] and attracted the Nobel prize for chemistry in 2011. QCs can be quasiperiodic in all three dimensions (e.g., with icosahedral symmetry), or can be quasiperiodic in two (or one) directions while being periodic in one (or two). The vast majority of the QCs discovered so far are metallic alloys (e.g., Al/Mn or Cd/Ca). However, QCs have recently been found in nanoparticles [2], mesoporous silica [3], and soft matter [4] systems. The latter include micellar melts [5,6] formed, e.g., from linear, dendrimer or star block copolymers. Recently, three-dimensional (3D) icosahedral QCs have been found in molecular dynamics simulations of particles interacting via a three-well pair potential [7].In recent years, model systems in two dimensions (2D) have been studied in order to understand soft matter QC formation and stability [8][9][10][11][12]. Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14]. The ingredients for 2D quasipattern formation are, first, a propensity towards periodic density modulations with two characteristic wave numbers k 1 and k 2 [15-18]. The ratio k 2 =k 1 must be close to certain special values; e.g., for dodecagonal QCs the value is 2 cosðπ=12Þ. Second, strong reinforcing (i.e., resonant) nonlinear interactions between these two characteristic density waves are required [17,19,20]. Earlier work on quasipatterns observed in Faraday wave experiments reveals similar requirements [19,[21][22][23]. We demonstrate here, following Mermin and Troian [24], that these same requirements suffice to stabilize icosahedral QCs in 3D. In contrast, nonlinear resonant interactions between density waves at a single wavelength are important in stabilizing simple crystal structures, such as body-centered cubic (bcc) crystals [25] although, with the right coupling, QCs can also be stabilized [26].We consider a 3D phase field crystal (PFC) model, appropriate for soft matter systems, that generates modulations with two l...

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“…The session was devoted to the role of electron microscopy in quasicrystal research. Festivities included a conference tour of Jerusalem, where the group photo in Figure 1 was taken, a special Jubilee Dinner, as well as the award of prizes for the best student presentations, sponsored by Journal of Physics D. The second prize was shared by Ruben Ma¨der and Alon Bahabad [19], and the first prize was awarded to Michael Engel [20].…”

mentioning

confidence: 99%

Quasicrystals–The Silver Jubilee

2008

Philosophical Magazine

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Structural complexity in monodisperse systems of isotropic particles

Cited by 26 publications

References 32 publications

Application of Phase Transition Theory to a Glass-Forming System

Application of Phase Transition Theory to a Glass-Forming System

Three-Dimensional Icosahedral Phase Field Quasicrystal

Quasicrystals–The Silver Jubilee

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