The self-intermediate scattering function .
The 13A icosahedral cluster and clusters that have icosahedral-like structure. Clusters 11E and 12D occur at α-interlocking icosahedral sites, 13 the rest are contained within a single icosahedron. Clusters in dotted rectangles are ground state clusters of n particles for the Wahnström mixture. 37 The colors of the particles and the bonds highlight the detection methods in the TCC algorithm. Grey particles are part of 3, 4, or 5 membered shortest path rings. These rings are shown by the white, blue, pink, and green colored bonds. Yellow particles are spindle particles for the shortest path rings which together form the basic clusters. Red particles are additional particles bonded to smaller clusters forming a new cluster. The detection routines for clusters are described in Ref. 38 .
(a) Non-Arrhenius increase in structural relaxation time versus the inverse of temperature. The data are fitted with an Arrhenius exponential at high temperatures and VFT at low temperatures. The onset temperature of the super-Arrhenius behavior is T* = 1.48 (vertical dashed line in both (a) and (b)). (b) The fraction of particles detected within icosahedral 13A clusters of all lifetimes N 13A(τℓ ⩾ 0)/N. Note the fast increase in N 13A(τℓ ⩾ 0)/N starts around T*.
(a) Cluster lifetime correlation functions P(τℓ > t) for icosahedral (denoted 13A—solid line), octahedral (6A—dashed line), and HCP13 (dotted line) at T = 0.604. All clusters with structure distinct from icosahedral order fall in the grey shaded region between P(τℓ > t) for 6A and HCP13. (b) The fraction of particles detected within icosahedral clusters with lifetime τℓ > t (T = 0.604). (c) The mean-square displacement ⟨δr 2(t)⟩ of all particles (black line) and particles starting within icosahedral clusters with lifetime τℓ > t as specified in the legend (colored lines—T = 0.604).
(a)–(c) Domains of icosahedral clusters form on cooling from high to low temperature (slices through 3D simulation box). Particles in icosahedral clusters are shown full size in green, other particles are blue dots. (d) The radius of gyration R g of the domains versus the number of particles in the domain m for T = 0.620. R g is well fitted by m 0.47 indicating the domains have a fractal dimension d f ≃ 2. (e) The mean lifetime of icosahedral clusters versus the domain size m. (f) Icosahedral domains retard the motion of neighboring particles. The MSD ⟨δr 2(τ h )⟩ as a function of distance from icosahedral domains d (solid line). The dotted line is the MSD over τ h of all particles not in icosahedra, independent of d. Note that the particles located around d = 1 amount to 40% of the system at this temperature.
(a) The relationship between icosahedra and spatial heterogeneities in the dynamics at T = 0.604 (2D slice of simulation box). Mobility (⟨δr 2(τ h )⟩) is depicted by the size of the particle. Large particles have ⟨δr 2(τ h )⟩ < 0.043, small particles otherwise. Particles always within icosahedral clusters with lifetime are colored green, and others are grey. (b) Growing structural ξ Rg (squares) and ξ S13A (crosses), and dynamical ξ4 (circles) correlation lengths.
(a) Relationship between icosahedral 13A domains and the crystalline “Frank-Kasper,” and icosahedral clusters for T = 0.604. The quantity N c(τℓ > t)/N is the fraction of particles detected within clusters lifetime τℓ > t. The dashed line is for Frank-Kasper clusters, and the dotted line is for icosahedral clusters with B-particles in the center, and arrangements of A- and B-species in the shell of the icosahedron compatible with the bulk crystal phase. 17 Both of these clusters exist in the MgZn2 structure of the Wahnström crystal. The solid line is for all icosahedra, irrespective of the arrangement of A- and B-species. (b) Snapshot at T = 0.604 showing the overlap between icosahedral domains and Frank-Kasper clusters. Green particles are the icosahedral domains, red particles are those in both Frank-Kasper and icosahedral clusters, and black are Frank-Kasper particles not in icosahedral domains. The small blue particles are not members of icosahedral or Frank-Kasper clusters.
(a) The four-point dynamic susceptibility χ4(t). The maximum of χ4(t) occurs at time τ h . (b) The four-point dynamic structure factor S 4(k, τ h ). The solid lines are fits to the data with the Ornstein-Zernike equation (Eq. (4) ). (c) The structure factor of the icosahedral particles S 13A (k). The solid lines are fits to the data with the OZ function.
The ground state clusters of the Wahnström mixture in TCC notation for n = 5–13 particles containing n A A-species particles. The energy E is the binding energy of the cluster. Clusters highlighted in bold face are the lowest energy states for a given value of n. The final column is the cluster detected by the Topological Cluster Classification algorithm from the ground state configuration. Note that for the Wahnström mixture the ground state clusters with n A = 0 and n A = n are identical for each n as the AA and BB Lennard-Jones interactions are the same. The n A = 0 clusters have therefore been omitted from the table for brevity.
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