The free-energy barrier was then determined from
The phase behavior of this system can be compared to
previous experimental and theoretical studies of binary
hard-sphere mixtures. Vermolen et al. examined various
methods for growing binary NaCl hard-sphere crystals in-
cluding gravitational and electric ﬁelds, epitaxial templates,
and dielectrophoretic compression from a binary mixture
with size ratio q ¼ 0:3 . However, the crystal structures
they found all included a signiﬁcant number of vacancies of
the small colloids ( > 10%). This result is in keeping with
the phase behavior observed in Fig. 1. Hunt et al. also
examined binary hard-sphere mixtures of particles with
q ¼ 0:39 and 0.42 and reported the presence of NaCl
. However, from their presented results it is impossible
to distinguish between an ISS and a NaCl crystal. On the
theoretical side, the closest size ratios examined in literature
using free-energy calculations are the phase diagrams pre-
sented for binary hard-sphere mixtures with q ¼ 0:2 
and 0.414 . For q ¼ 0:2, the phase behavior is expected to
be signiﬁcantly different than that for q ¼ 0:3 as the small
particles can ﬁt in both the tetragonal and octahedral holes.
However, the phase behavior for a binary hard-sphere mix-
ture with q ¼ 0:414 is likely to be qualitatively the same as
that of q ¼ 0:3. In both cases, the smaller particles both ﬁt
and are restricted to reside in the octahedral holes at
close packing. MD snapshots included in Ref.  for the
q ¼ 0:414 mixture show a coexistence between a solid and
ﬂuid phase which the authors identiﬁed as a monodisperse
fcc phase and a binary liquid phase. However, the fcc phase
depicted in their snapshots contains some small particles,
and is more likely an ISS phase. To summarize, the NaCl
phases previously identiﬁed experimentally  and theo-
retically  were most likely ISSs. Additionally, we remark
that there are a vast number of other colloidal and nano-
particle systems which may form an ISS phase. In particular
we have also found an fcc-based ISS phase in experiments
on binary mixtures of oppositely charged colloids with size
¼ 0:73 (Supp. Figs. S6 and S7 ) thereby
indicating that the ISS phase is not restricted to hard-sphere
systems. Moreover, we would also expect binary mixtures
of charged colloids to form body-centered-cubic (BCC)
based ISSs since the BCC lattice is stable for monodisperse
particles interacting via a Yukawa potential.
In conclusion, we have demonstrated that the ISS is
thermodynamically stable in binary hard-sphere mixtures
and is likely stable for a wide variety of particle interac-
tions. Our ﬁnding on the stability of ISS phases is of vital
importance for a wide range of applications as it provides a
method to grow large, defect-free single colloidal ISS
crystals with unprecedented control of the sublattice dop-
ing. For instance, a transistor based on a regularly doped
semiconductor has been realized with a binary nanocrystal
solid . Similarly, intriguing structural color tuning has
previously been achieved by interstitial doping of an fcc
photonic crystal with light absorbing nanoparticles .
Extending this to the ISS phase present in our model, we
would expect more control over the color tuning. More
generally, the availability of a simple model system which
is both theoretically and experimentally realizable will be
of great value for the understanding of the many ISS phases
arising in atomic and molecular systems. The nucleation of
molecular ISSs can be very complex due to the different
time scales on which both species equilibrate. Realizing a
stable ISS phase in a colloidal system allows one to study
the nucleation process in real space on reasonable time
scales. Additionally, this ISS is an ideal system for exam-
ining interactions between equilibrium interstitial defects
for any concentration.
We acknowledge J. Hoogenboom for particle synthesis
and F. Smallenburg and M. Marechal for fruitful discus-
sions. We acknowledge ﬁnancial support from Nanodirect,
NWO-CW, a NWO-VICI grant, NanoNed, and FOM.
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PRL 107, 168302 (2011)
PHYSICAL REVIEW LETTERS
14 OCTOBER 2011