Supplementary Material
Figure S1. Van Hove function Gs (r,t) after a short time (0.25 ns) and longer time (1 ns)
exhibiting a transformation from particle localization to a displacement to a distance
about an interparticle distance away. A minimum in this curve at the reduced scale  0.6
defines a natural cut-off for defining the mobile particles.
0.016
0.014
0.012
P(<u2>)
0.01
0.008
0.006
0.004
0.002
0
0.5
1
1.5
2
2.5
3
2
<u >
Figure S2. The distribution of <u2> at T = 1950 K. We note that the distribution of <u2>
does not exhibit any clear bimodal character, despite the clear multi-modal nature of
Gs (r,t) in Fig. S1.
Figure S3. Decay first peak height of Gs (r,t) in Fig. S1. The first peak magnitude at T =
(
)
1950 K, denoted (t), decays an exponential function, F(t) » exp -t / t , to a good
approximation. The time constant  fitted here is  700 ps, which is comparable to the
structural relaxation time s obtained from the self-intermediate scattering function ( 800
ps; See Fig. 9 in text). The structural relaxation time then reflects the persistence time of
the particles in the immobile state, as in glass-forming liquids.87
P (n)
10
T = 1950 K
T = 1920 K
T = 1880 K
T = 1840 K
-1
10-2
n-2.1
10
-3
10-4
n
50
100
150
Figure S4. The distribution of particle cluster sizes P(n) for mobile atoms at four T . The
inset shows the average cluster size for mobile particles as a function of time interval at
different T.
The mobile atoms are identified as these particles by a threshold atomic displacement
condition, 0.6r0 < ri (Dt) - ri (0) < 1.2r0 , involving the average bulk crystal interatomic
spacing, r0. While changing the cut-off value alters the number of mobile particles, the
statistical properties of the size distribution are insensitive to this choice. We then define
a 'mobile particle cluster' as the group of neighboring particles having a separation less
than 1.2 times the interatomic spacing. r0. The power-law cluster size distribution for the
mobile particles in Fig. S.4 is characteristic of branched equilibrium polymers and the
distribution of the mass of the mobile particles exhibits a similar exponent as observed
before for heated crystals of Cu and model glass-forming liquids88 (See Nordlund et
al.85).
Figure S5. Scaling of mobile particle radius of gyration Rg with its average mass M,
Rg ~ M where the inset shows  = 1 / df as a function of T. The exponent  is about 0.4,
corresponding to a fractal dimension df  2.5, consistent with branched equilibrium
polymers with screened excluded volume interactions, i.e., percolation clusters.84,162
Recent simulation estimates of the mobile particles in a model polymer glass-forming
liquid also indicate a fractal dimension of these clusters near 2.5.88