Direct Observation of Entropic Stabilization of bcc Crystals Near Melting

Crystals with low latent heat are predicted to melt from an entropically stabilized body-centered cubic symmetry. At this weakly first-order transition, strongly correlated fluctuations are expected to emerge, which could change the nature of the transition. Here we show how large fluctuations stabilize bcc crystals formed from charged colloids, giving rise to strongly power-law correlated heterogeneous dynamics. Moreover, we find that significant nonaffine particle displacements lead to a vanishing of the nonaffine shear modulus at the transition. We interpret these observations by reformulating the Born-Huang theory to account for nonaffinity, illustrating a scenario of ordered solids reaching a state where classical lattice dynamics fail.

Figure 1

Top: Phase diagram as a function of colloid volume fraction $\varphi$. Confocal microscopy images (middle) and structure factors $S(q_x,q_y)$ (bottom) are given for $\varphi =0.050$ [(a), fluid], 0.063 [(b), fluid-bcc coexistence], 0.130 [(c), bcc], and 0.350 [(d), fcc]; $S(q_x,q_y)$ in (b) is separated into that of the coexisting crystal (left) and fluid (right).

Figure 2

(a) Lindemann parameter ${\delta }_L$. Inset: Mean-squared displacements $⟨\mathrm{\Delta }{r}^2(t)⟩$ for (top to bottom) $\varphi =0.030$, 0.060, 0.080, 0.141, 0.221, and 0.301. (b) fraction of “hot” particles $n_L$. Inset: Distributions of Voronoi volumes $P(v)$ for hot particles (red circles) and all others (blue squares). (c)–(e) Computer-generated renderings of experimental data, where hot particles are color coded according to cluster size, where blue, orange, and yellow are first, second, and third largest clusters, respectively, for $\varphi -{\varphi }_c=0.095$ (c), 0.011 (d), and 0.005 (e).

Figure 3

(a) Experimental affine elastic constant $C_{44}$ (squares) and nonaffine shear modulus $G_0$ (circles), and prediction from the reformulated Born theory (line). Inset shows the amplitude of nonaffine displacements $⟨D^2⟩$. (b) Illustration of how a heterogeneous distribution of hot particles (red) in a bcc lattice disrupts the local force balance between “cold” particles (blue) bonded by green arrows.

Figure 4

(a) Cluster size distributions $P(n)$, for $\varphi =0.066$ (diamonds), 0.101 (triangles), 0.129 (squares), and 0.190 (circles); drawn lines are fits to a power-law distribution with exponential cutoff. (b) Comparison of experimental $P(n)$ for $\varphi =0.101$ (filled circles) and a distribution for a randomized placement of the same number of hot particles (open squares). (c) Cluster radius of gyration $R_g$ versus size $n$, for 6 different $\varphi$ between 0.17 and 0.066; drawn line indicates $d_f=1.70$. (d) Characteristic cluster size $⟨n⟩$ taken as the time-averaged size of the largest cluster (squares) or the time- and ensemble-averaged size of all clusters (circles); lines indicate a power-law divergence: $⟨n⟩\propto {[(\varphi -{\varphi }_c)/{\varphi }_c]}^{-3/4}$.