The ‘random’ square–triangle tiling: simulation of growth

Rubinstein, Boaz; Ben-Abraham, Shelomo I.

doi:10.1016/s0921-5093(00)01142-4

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…This vertex presents 83.7% of all vertices in the model by Stampfli 76 and 84.7% of those obtained by simulation in which the condition was enforced that square tiles should be next to triangular ones. 79 The 3 2 .4.3.4 vertex represents 100% of vertices in the P4 2 /mnm phase (Fig. 8b).…”

Section: Liquid Quasicrystalmentioning

confidence: 99%

Frank–Kasper, quasicrystalline and related phases in liquid crystals

2005

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Section: Liquid Quasicrystalmentioning

confidence: 99%

Frank–Kasper, quasicrystalline and related phases in liquid crystals

2005

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“…He found a discontinuous phase change for a special energy condition, from a mean-field calculation, which he suggested to be analogous to a change of association number from one liquid phase to another. The noninteracting version of the model was employed later in the study of quasi-crystals [18,19,20], observed in alloy systems such as V-Ni and V-Ni-Si, in an attempt to explain their mechanism of formation.…”

Section: The Modelmentioning

confidence: 99%

Tiling in the geometric model for water

Girardi¹,

Figueiredo²,

Guisoni³

et al. 2004

Braz. J. Phys.

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Hydrogen bonded liquids like water present a rich thermodynamic behaviour due to the strength and directionality of the bonds. In a recent paper a geometric model based on Bernal's model for liquids was proposed to study the effects of the hydrogen bonds on the phase transitions of water, under pressure and temperature variations. Water molecules were assumed to stay at the vertices of coordination r (r = 4, 5, 6) of perfectly tiled polygons, and to have four links which allow up to four hydrogen bonds per particle. Mean field calculations yielded a phase diagram with three phases of different densities and a critical point at the end of the coexistence line between the high and low density phases. The three phases were considered to be liquids of different densities. In the present work we have shown that applying some geometric constraints to particle arrangements (thus correcting the system entropy, which was overestimated in the previous work), and allowing a variable number of links per molecule, leads to substantial alteration of the phase diagram. Three phases of different densities are still present, but no critical point appears. Two of the phases are solid, and one phase is amorphous.

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“…This relatively new class of solids was first identified in 1984 [2] and since then, considerable research has been conducted in the field leading to reports of quasicrystalline phases in over 100 systems with several metals serving as the primary constituent, i.e., Al [3,4], Cu [5,6], Ga [7], Mg [8,9], Ni [10], Ta [11,12], Ti [13,14], Zn [15,16] and Zr [17,18]. In the last decade, there have been significant efforts to identify commercial applications that might benefit from the QC phases [8,19,4] especially in those alloys where these phases appear to enhance the mechanical properties or render the material with distinct functional properties [9].…”

Section: Introductionmentioning

confidence: 99%