Sponge-like nanoporous single crystals of gold

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### ARTICLE

Received 13 May 2015 | Accepted 8 Oct 2015 | Published 10 Nov 2015 DOI: 10.1038/ncomms9841 OPEN
## Sponge-like nanoporous single crystals of gold

Maria Koifman Khristosov 1,2, Leonid Bloch 1, Manfred Burghammer 3,4, Yaron Kauffmann 1,
Alex Katsman 1 & Boaz Pokroy 1,2

Single crystals in nature often demonstrate fascinating intricate porous morphologies rather

than classical faceted surfaces. We attempt to grow such crystals, drawing inspiration from

biogenic porous single crystals. Here we show that nanoporous single crystals of gold can be

grown with no need for any elaborate fabrication steps. These crystals are found to grow

following solidification of a eutectic composition melt that forms as a result of the dewetting

of nanometric thin films. We also present a kinetic model that shows how this nano-porous

single-crystalline structure can be obtained, and which allows the potential size of the porous

single crystal to be predicted. Retaining their single-crystalline nature is due to the fact that

the full crystallization process is faster than the average period between two subsequent

nucleation events. Our findings clearly demonstrate that it is possible to form single
crystalline nano porous metal crystals in a controlled manner.

1 Department of Materials Science and Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel. 2 Russell Berrie Nanotechnology Institute,
Technion—Israel Institute of Technology, Haifa 32000, Israel. 3 European Synchrotron Radiation Facility, BP 220, Grenoble F-38043, France. 4 X-ray
Microspectroscopy and Imaging Research Group, Department of Analytical Chemistry, Ghent University, Ghent B-9000, Belgium. Correspondence and
requests for materials should be addressed to B.P. (email: [bpokroy@technion.ac.il).](mailto:bpokroy@technion.ac.il)

rystals grown in the laboratory by classical methods of
nucleation and growth have facets dictated by their atomic
structure and by minimization of the surface free energy of
# C
the different crystallographic planes 1 . These features result in
faceted crystals in which the revealed planes are the low-energy
ones. Remarkably, however, biogenic crystals produced by living
organisms often demonstrate unfaceted single crystals with
rounded, intricate and even porous structures. Such single
crystals can be produced via an amorphous precursor phase in
which the precursors can be moulded into any desired shape
before their crystallization 2–4 .

The achievement of intricately shaped nanoporous singlecrystalline materials is undoubtedly of considerable scientific and
technological potential 5 . It was previously shown that
micrometre-sized porous single crystals of calcite can be grown
via bio-inspired routes 6,7 . Even porous metal materials (PMMs)
that are polycrystalline are functionally promising 8,9 for research
and industry in the fields of chemistry 10, medicine 11,
environmental sciences, energy storage and others 12 . Besides
the intrinsic properties of monolithic metals, in PMMs the new
and attractive properties derived from the shape, size and
distribution of pores include changes in specific surface area,
permeability and capillarity to mention just a few. Owing to their
unique structure, such porous metals are widely employed in
catalytic support 13, filtration 14, separation 15, heat exchange 16, fuel
cells 17 and many additional uses. Common methods of preparing
nanoporous metals are dealloying 18, or depositing the metal
within a three-dimensional (3D) mould 19 such as a latex sphere 20
or other soft templates 21 .

A particularly important example of a PMM is nanoporous
gold, which has great potential for applications in catalysis 22,23,
sensors 24, actuators 25 and electrodes for electrochemical uses 26 .
The yield strength of nanoporous gold is very high, equal to or
higher than that of bulk Au, whereas the nanoporous material
also has a much lower density and very large surface area 27 .
A common way to obtain nanoporous gold is by dealloying of an
Au-Ag alloy via selective removal of Ag in a corrosive
environment such as a nitric acid solution 28 .

The nanoporous gold prepared by dealloying has a nanocrystalline structure 29 . Formation of nanoporous gold from an
original Au-Ag micrometre-sized grained ingot has been
reported 30, but it was prepared by dealloying. This result can
be clearly observed from the decrease in X-ray coherence length,
observed in the broadening of the diffraction peaks and the
increase in lattice misorientations. A few examples of singlecrystalline porous gold have been described, but these nanometric
structures were only two-dimensional 31 . Besides possessing the
attractive properties of polycrystalline porous gold, a nanoporous
single crystal of gold is likely to have additional novel properties.
Studies have shown that grain boundaries in thin films of gold
enhance the electrical resistivity of nanometric thick films owing
to grain boundary-induced scattering of the electrons 32–34 . Not
only would the conductivity of the porous single crystal be higher
than that of porous polycrystalline gold, but as single crystals
their 3D crystallographic orientation could also be selected. The
higher conductivity expected from such nanoporous structures
could increase the efficiency of electrodes for electrochemical
supercapacitors, as described elsewhere 26 . Another advantage of
the absence of grain boundaries in such structures is to be found
in the higher thermal stability of their micro- and nanoframework. This results from lower rates of self-diffusion,
which are attributable in turn to the total elimination of grain
boundary diffusion routes. The latter adventitious property could
be helpful in cases where such structures are utilized in catalysis
when operational temperatures in the range of 20 � 200 �C are
needed 35,36 . As one of the most prevalent applications of

nanoporous gold is in catalysis, we feel that this property could
be of interest to others working in this field.

In this paper, we present a simple method to grow micrometresized nanoporous single crystals of gold with intricate morphologies. Unlike any other examples to date, our structures are
formed via thermodynamically driven self-formation. Thin films
of two components are evaporated onto a nonreactive surface,
followed by heating to above the eutectic temperature. This
procedure causes the films to melt, producing a eutectic melt on
the surface. Because of the low surface energy of the appropriately
chosen substrate, dewetting takes place and isolated droplets of
the melt are produced all over the substrate’s surface. Fast cooling
preserves the shapes of both the droplets and the eutectic
microstructure. Finally, by selectively etching one of the
components, a porous single-crystal structure of the other
component is obtained. We demonstrate this general principle
on an Au-Ge eutectic system, which yields nanoporous single
crystals of gold. Furthermore, we present a model that explains
our experimental findings and enables us to calculate the
conditions needed to obtain rationally designed single-crystalline
porous structures. It also enables us to predict the size limits of
such an approach.

Results
Preparation process description. Thin films comprising two
layers were evaporated at relative thicknesses appropriate for the
eutectic ratio, which in the Au-Ge system is 28 at% Ge (ref. 37).
Annealing above the eutectic temperature resulted in melting of
these thin films and formation of a eutectic melt. Choice of SiO2
as a substrate enabled droplets of this melt to be formed by
dewetting. Cooling to below the eutectic temperature resulted in
solidification of the eutectic liquid to form a eutectic-like solid
structure. Wet etching of the samples to remove the germanium
revealed droplets of porous gold, as seen in Fig. 1a,b by highresolution scanning electron microscopy (HRSEM). Analysis of

a b

c d

Porous Au Pt

Figure 1 | Nanoporous single-crystal particles of gold. (a) High-resolution
scanning electron microscopy (HRSEM) micrograph of the droplets on a
SiO2 surface, large area view (scale bar, 20 mm). (b) HRSEM micrograph of
a eutectic gold droplet after wet etching, top view (scale bar, 2 mm).
(c) HRSEM micrograph of a cross-section of the droplet shown in b,
obtained using a focused ion beam (FIB), reveals the nano-porous structure
of gold after wet etching of Ge (scale bar, 1 mm). The droplet was covered
with Pt in order to protect it during the ion beam etching. (d) HRSEM
micrograph of high magnification in c (scale bar, 500 nm).

the microstructure by energy-dispersive X-ray spectroscopy
confirmed that the Ge was fully removed during the etching
process (Supplementary Table 1). Using a focused ion beam
(FIB), we were able to visualize a cross-section of the droplets and
obtain a view of the gold microstructure within a droplet
(Fig. 1c,d).

TEM diffraction of the gold nanoporous single crystal. A thin
cross-section of a sample droplet was prepared by FIB and
examined by transmission electron microscopy (TEM). A highangle annular dark-field scanning TEM micrograph of the crosssection is presented in Fig. 2a. Selected area diffraction on an area
with a diameter of approximately 4 mm in the centre (the main
part) of the droplet (Fig. 2b) revealed a diffraction pattern
characteristic of a single crystal that could be fully indexed within
the gold structure (Fig. 2c). This indicates that the gold in the
eutectic-like structure within the droplet had solidified into an
intricately shaped single crystal.

Synchrotron scanning diffractometry. To further verify that this
porous gold is indeed a single crystal, we utilized another state-ofthe-art characterization technique, namely synchrotron submicron scanning diffractometry (ID13; European Synchrotron
Research Facility (ESRF), Grenoble, France), on a FIB-sectioned
gold crystal. The same cross-section as that of the droplet
investigated by TEM (Fig. 2) was now examined by scanning
diffraction. Diffraction patterns were scanned over the entire
cross-section of the droplet (Fig. 3). Figure 3a depicts a map of a
single reflection ({200} plane, 0� rotation). The same reflection
occurs throughout the droplet at nearly the same radial and
azimuthal coordinates, with only some slight variations in
intensity. Figure 3b depicts the average of all the diffraction scans
taken from the entire area of the droplet. This can be compared
with Fig. 3c, which shows a single diffraction from the droplet’s
centre. From a comparison of these images, it is evident that the
major reflections are identical, and do not shift their positions
even though the figure integrates a large number of individual
scans (317 in all). Figure 3d represents the azimuthally regrouped
central diffraction with markings for gold crystallographic planes,
and Fig. 3e depicts a rocking curve for the same reflection. Shown
are the mean intensity over the droplet and its 10, 30, 70 and 90%
percentiles. Results for the {220} planes are shown in
Supplementary Fig. 1. The results obtained from the TEM and the
scanning diffractometry provide conclusive proof that the nanoporous gold crystals are indeed single crystals.

Controlling the micro- and nanostructure. By altering the
cooling rates of the samples, micro- and nanostructures of

different sizes could be obtained (Fig. 4). Ligament sizes in the
solid droplet after cooling at a fast rate (35 �C s � 1 ) were about
57 ± 12 nm for gold and 43 ± 8 nm for germanium (Fig. 4a). At a
slow cooling rate (0.6 �C s � 1 ), the approximate ligament sizes of
the gold and the germanium were 300 nm (or larger) and
39 ± 8 nm, respectively (Fig. 4b). This phenomenon resulted
from a coarsening of the solid eutectic phase during the longer
cooling phase.

Surface area and thermal stability. In addition, by analysing the
cross-sectional HRSEM micrographs, we estimated the surface
area of the porous Au crystals. For this purpose, we assumed a
homogeneous microstructure and used a previously described
methodology 38 . Our calculations yielded an estimated surface
area of 3.1 m 2 g � 1, which is in the range of other known
nanoporous metals 39–41 approximately 3–10 m 2 g � 1 .

We then compared the thermal stability of our singlecrystalline nanoporous nanostructures to that of nanoporous
gold prepared by the dealloying method 28 . The results are shown
in Supplementary Figs 2–5. After annealing both types of porous
gold samples, one prepared by our eutectic decomposition
method as described here, and the other by dealloying, at
200 �C for 15 min and for 45 min, and at 250 �C for 15 min, we
compared their nanostructures. The samples prepared by the
dealloying method failed at lower treatment time and
temperatures: grain boundaries developed into cracks, porous
particles were found to be damaged at the edges and coarsening
was clearly observed. In conspicuous contrast, samples prepared
by our method retained their porous nanostructure and showed
no evidence of damage.

Discussion
By using state-of-the-art characterization techniques such as
TEM and synchrotron submicrometre scanning diffractometry,
we were able to show that the porous gold structure
within the eutectic droplets is a single crystal. Use of these
techniques further revealed continuous growth of a single gold
crystal during formation of the eutectic-like two-phase structure
during its solidification. Although nanoparticles of nanoporous
gold have been demonstrated previously 19–21,28, our method is
novel in that we do not use the dealloying mechanism (a ‘topdown’ approach); instead, our porous single crystals grow from a
liquid phase during eutectic decomposition, which is a
spontaneous ‘bottom-up’ approach. Growth of the porous
single crystal by the latter method occurs rapidly and is
a self-forming process (eutectic decomposition). The outcome is
a nanoporous single crystal of gold, with the germanium residing
only in the pores. Another advantage of our method is that by

a b c

(111)

(220)

(311)

Figure 2 | TEM investigation of a nanoporous single crystal. (a) A high-angle annular dark-field scanning TEM (HAADF-STEM) micrograph of a crosssection of a droplet, showing microstructure of gold after Ge etching (scale bar, 500 nm). (b) TEM image of the area of the droplet from which the
diffraction pattern was acquired, showing the selected area aperture in a (scale bar, 500 nm). (c) Diffraction pattern taken from the area shown in b, fully
indexed within the gold structure; zone axis [121].

a b c

{200} {200}

150

100

–50

–100

–150

Mean

30% → 70%
10% → 90%

–8 –6 –4 –2 0
Angle (°)

2 4 6 8

0 10 20 30 40
_q_ (nm –1 )

50 60

Figure 3 | Synchrotron submicron scanning diffractometry of the gold nanoporous single crystal. (a) Reflection map for the {200} planes of the sample
shown in Fig. 2. (b) The average diffraction pattern from the drop area. (c) Diffraction pattern from the centre of the drop, marked with a white square on a.
(d) Azimuthally regrouped central diffraction pattern, q ¼ 2p/d, j—radial axis. (e) Rocking curve of a reflection from the {200} planes.

a b

Figure 4 | Controlling the micro- and nanostructures of the single-crystal
nanoporous gold. HRSEM micrograph of a FIB cross-section of the
eutectic microstructure at (a) 35 �C s � 1 and (b) 0.6 �C s � 1 . Scale bar,
200 nm.

means of a simple, fast and low-cost process we obtain freestanding porous particles whose shape can be determined by the
original droplets wetting properties and which can easily be used
in other processes with no need to cut the bulk material by any
type of fabrication technique.

When comparing our method with the conventional dealloying
procedure in the formation of nanoporous gold, it should be
borne in mind that not all that appears to be a single crystal is
indeed a single crystal. Several studies 30,42 have implied that given
the apparently unchanged morphology and orientation of the
original grains before and after dealloying, the nanoporous gold
products are still single crystals of the same original size. This was
demonstrated on the basis of grain morphology and electron
back-scattered diffraction in SEM. However, the only way to
unambiguously prove that a grain is in fact a single crystal is by
the use of high-resolution X-ray diffraction techniques, as we did
in this study. For further verification, we performed in-situ
dealloying with high-resolution powder diffraction at the
synchrotron (ID22; ESRF) on AuAl2 intermetallic. The results

clearly showed how the coherence length of the gold that remains
after dealloying is drastically reduced (Supplementary Fig. 6).
Although the structure of AuAl2 is different than that of pure
gold (both are cubic), the literature shows the exact same
phenomenon when dealloying silver from gold 30 .

One of the nano porous’ gold promising applications is a lowtemperature catalytic CO oxidation 35,36 to CO2. This process can
be undertaken at temperatures in the range of 20–200 �C, and
usually is performed utilizing nanoporous gold prepared by
dealloying or gold nanoparticles. The disadvantage of the
nanoporous gold prepared by dealloying is coarsening of the
nanoporous structure because of the temperature-induced
diffusion. Although our samples have slightly larger ligament
size as compared with the ligament size of the dealloyed gold
counterpart, and therefore slightly lower surface area, the former
demonstrate superior thermal stability. This relative
improvement is due to the lack of grain boundaries within
single crystals.

Discerning the mechanism governing the growth of nanoporous crystals that maintain the characteristics of a single crystal is
important not only for basic scientific knowledge but also to allow
this technique to be applied, in a controlled manner, in
technologically important crystalline systems. We therefore felt
it necessary to develop a kinetic model that could explain how
these nanoporous single crystals are formed, and would allow us
to estimate the maximal achievable size of such crystals.

In the case of a fully eutectic structure, the volume ratio
VAu/VGe ¼ 1.92 (calculated on the basis of the eutectic composition) enables gold crystals to grow continuously throughout the
entire droplet, accompanied by repeated nucleation and growth of
rod-like germanium crystal channels surrounded by a gold
matrix. When considering a crystallization process in the Au-Ge
eutectic system, it should be remembered that normal crystallization of a non-equilibrium eutectic liquid usually starts with

the heterogeneous nucleation of one solid phase, in the present
case probably Au. The nucleation also most probably takes place
at the liquid/substrate interface. In the next stage, the adjacent
liquid is substantially enriched by Ge, providing heterogeneous
and, if possible, epitaxial nucleation of Ge crystals at the surface
of this Au crystal. The formation is governed by the free energy
gain as a result of undercooling to below the eutectic temperature,
DT ¼ (Teut–T), while atoms are being transferred from the liquid
phase to the growing crystal:

DGtr ¼ ðTeut � TÞDStr; ð1Þ

where DStr is the entropy change in the L (eutectic) Au(s) þ Ge(s) transformation. Obviously, additional
energy is needed to create the solid/liquid and
Au(s)/Ge(s) interfaces. The epitaxial nucleation and
growth of Ge on Au are possible in the crystallographic
orientation relationships Auð111Þ½ 11 � 2�==Geð111Þ 11½ � 2� and
Auð � 1 � 11Þ½ 11 � 2�==Geð111Þ½ 11 � 2� 43, which may provide relatively
low interfacial energies. Growth of the eutectic structure is
limited by volume diffusion in the liquid in front of the freezing
solid/liquid interface. The growth rate can be evaluated according
to the simple model suggested by Turnbull 44 :

The rate of heterogeneous nucleation of gold crystals,
presumably at the substrate/liquid interface, can be deduced on
the basis of classical kinetic theory 52,53 :

Jss ¼ J0 expð - W � =kTÞ; ð4Þ

where W* is the height of the heterogeneous nucleation barrier
and J0 is a pre-exponential factor. As shown in Supplementary
Note 2 and Supplementary Fig. 8, for reasonable material
parameters, the pre-exponential factor can be evaluated as J0 E
(4�6) - 10 20 s � 1 mm � 3, and at the moment when the first stable
nucleus appears, the heterogeneous nucleation rate in the
droplet reaches Jssðt1Þ ¼ J0DVde � y 1 2 - 2y B1 30a nuclei per second (see

droplet reaches Jssðt1Þ ¼ J0DVde � y 1 2 - 2y B1 30a nuclei per second (see

Supplementary Note 2 for details), which for the cooling rate
a ¼ 1C� s � 1 (used in most of the present experiments) provides
about (0.8�1.0) nuclei per second. Comparison of the average time
Dt12 - B a 0 2lny21 3 between the two first nucleation events with the time

Dt12 - B a 0 2lny21 3 between the two first nucleation events with the time

of full crystallization of the droplet tc allows us to formulate a
criterion for the appearance of a monocrystal porous structure
described in the previous sections:

ln2

- 1: ð5Þ
2y1 3

¼ VB0

Rda

w ¼ Dt12

V ¼ kD D l X

X

l ¼ kD D l X0

1 � l�
l X0 l

-
1 � l� ; ð2Þ

where D is the diffusion coefficient in the liquid, DX is the
difference in composition of the liquid above the freezing
interface across the eutectic lamellar spacing l, DX0 is the
difference in composition for l-N, kB1 is a geometrydependent coefficient and l* is the critical lamellar spacing
defined by Zener 45 :

l � ¼ 2gabvmol

DGtr

¼ 2gabvmol

DTDStr

; ð3Þ

For typical values of parameters (see Supplementary Tables 2 and 3,
and Supplementary Note 2 for details): B 0 ¼ 700 �C, y1 ¼ 6.5,
w - 0:88V
Rdað�C s � 1 Þ ~~.~~ For droplets with radii Rdr10 mm and cooling

rates r1 �C s � 1, with V ¼ (30�50) mm s � 1, formation of Au-Ge
eutectics with the monocrystal gold matrix seems to be highly
probable. On the other hand, with faster cooling, for example with
the rate a ¼ 35 �C s � 1, such a structure is unlikely to be formed. In
other words, for cooling rates B1 �C s � 1 the second nucleus
appears (0.7�0.9)s on average after the first one, and this period is
long enough to allow full crystallization of the (2�10) mm droplets
before the second nucleation event occurs. At the same time, for
droplets with radii RZ20 mm and/or high cooling rates
aZ10 �C s � 1, several nuclei can appear during crystallization (for
details, see Supplementary Fig. 7).

In conclusion, in each droplet during cooling of the sample,
two processes are competing—nucleation and crystal growth. The
times taken for the full crystallization process in the micrometresized droplets investigated here appeared to be substantially
shorter than the average period between the two subsequent
events of nucleation of gold crystals from the eutectic melt. This
can explain why the gold matrix of the eutectic structure was
formed as a single crystal. To further validate our kinetic model,
we studied how changing the cooling rates of the process affects
the number of single-crystal domains in each droplet. As our
model suggests, an increase in the cooling rate from 0.6 to
35 �C s � 1 is followed by a clear transition from single crystal to
polycrystalline droplets (Supplementary Fig. 7).

To conclude, using the relatively simple method of dewetting
from thin films, and by exploiting thermodynamic phenomena
such as crystallization from a eutectic melt, we demonstrated here
that it is possible to produce nanoporous gold single crystals. We
have developed a kinetic model that explains this phenomenon
and shows that the full crystallization process is faster than the
average period between two subsequent nucleation events, a key
factor allowing the intricate 3D single crystals of gold to retain
their single-crystalline nature. Based on our calculations, we can
predict that this method allows for the growth of nanoporous
single crystals of gold of up to several hundred micrometres in
size. We also clearly showed that nanoporous single crystal
prepared by eutectic composition demonstrate superior thermal
stability as compared with their counterpart nanoporous gold
prepared by dealloying, which is essential for catalysis. We believe

where gab is the energy of the solid/solid (Au/Ge) interface and
vmol is the liquid molar volume. Using the transformation entropy
value for the Au-Ge system 46 DStr ¼ 23.9 J mol � 1 K � 1, and
assuming gab ¼ (0.2�0.4) J m � 2 and DT ¼ (10�20) K, we can
estimate from equation (3) the critical width of lamellae as
l* ¼ (8�32) nm, which is comparable to the half of the observed
ligament size (40�60) nm. The relatively minor observed
supercooling is attributable to the heterogeneous character of
the nucleation. The supercooling corresponds to a difference in
composition of the couple zone of the Au/Ge phase diagram 46
DX0 ¼ 0.01�0.02. From viscosity experiments at high
temperatures 47, the self-diffusion coefficient in the liquid
gold was found to be in the range of 2.02 � 10 � 9 to
3.35 � 10 � 9 m 2 s � 1 at temperatures between 1,063 and
1,364 �C with an activation energy of Ea ¼ 0.316 eV. The
diffusion coefficient in the undercooled eutectic liquid can be
evaluated by extrapolation of these values to temperatures below
the Au\Ge eutectic temperature. D ¼ D0 exp ( � Ea/kBT) with
D0 ¼ 3.1 � 10 � 8 m 2 s � 1, yielding B8.5 � 10 � 11 m 2 s � 1 for the
eutectic temperature. We can now estimate the growth rate and
the time to achieve full crystallization of the eutectic structure.
The growth rate is evaluated as V ¼ (10�30) mm s � 1
and the total crystallization time in droplets (2�5) mm in size is
tc ¼ Rd/V ¼ (0.07�0.5) s, where Rd is the droplet size.

A more sophisticated theory of steady-state eutectic growth
was developed by Jackson and Hunt 48 and then modified by
several authors 49–51 . The estimations based on this theory are
presented in Supplementary Note 1. According to evaluations
based on the Jackson and Hunt theory, the freezing rates,
V ¼ (30�60) mm s � 1, are slightly higher (and the total
crystallization times are lower) than those obtained from the
Turnbull model 44 .

that this method can also be employed in other crystal systems,
thereby opening the door to new technological capabilities.

Methods
Sample preparation. SiO2 (100 nm) was grown on (001) Si wafers by
thermal oxidation at 1,100 �C. The oxide layer served as a diffusion barrier for
preventing Si migration from the wafer. Gold and germanium films (99.999%
pure, Sigma-Aldrich) were successively evaporated onto the SiO2 substrate in an
e-beam-equipped AircoTemescal FC-1800 evaporating system under a high
vacuum of 10 � 7 Torr at room temperature, yielding a deposition rate of
8 Å s � 1 . The gold and germanium films were 150 and 78 nm thick, respectively.
Samples were thermally annealed at 550 �C for 5 min in a MILA-5000 ULVACRIKO rapid thermal annealer or in a Jiplec JetFirst-100 rapid thermal annealer in
an ambient flow of Ar-H2 (15% H2; 99.999%, 150 s.c.c.m.) or vacuum (10 � 5 Torr)
at a heating rate of 10 �C s � 1 . The cooling rates were 35 and 0.6 �C s � 1 . Samples
were wet-etched in two steps: (i) immersion in a solution of NH4OH:H2O2
(1:25% vol) for 1 h and then rinsed, first in deionized water and then in ethanol;
(ii) immersion in KOH solution (1.25 M) for 16 h and then rinsed again in water
and ethanol. Cross-sectional samples were prepared by an FEI Strata 400S
dual-beam FIB. Low-voltage argon ion milling was then applied for final thinning
and cleaning of surface using the Gentle Mill, model IV8 (Technoorg Linda).
Thermal stability experiments were performed in Jiplec JetFirst-100 rapid thermal
annealer in 200–250 �C for altering times in vacuum (10 � 5 Torr).

Sample characterization. Surfaces were imaged with a Zeiss Ultra Plus HRSEM,
combined with energy-dispersive X-ray spectroscopy. Images of the cross-sections
were acquired with the Strata 400S dual-beam FIB. TEM imaging and electron
diffractions were obtained using an FEI Cs corrected Titan 80–300 KeV
FEG-S/TEM operated at 300 KeV. Single-crystalline droplets were characterized by
nanofocus X-ray beam analysis on ID13 of the ESRF . The samples were rotated
from - 45� to 45�, with 1� intervals. After each interval, the sample was scanned
with an X-ray beam at a wavelength of 0.83189 Å, focused to approximately
200 � 150 nm (full-width at half-maximum) at the sample plane.

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Acknowledgements
Thin films were fabricated at the Micro-Nano Fabrication Unit (MNFU) at the
Technion—Israel Institute of Technology, Haifa. We are grateful to Dr Tzipi
Cohen-Hyams, Dr Alex Berner and Michael Kalina for their help in preparing samples
and operating the electron microscopes. We thank Boris Haimov for useful discussions,
and Avigail Aronhime Bracha and Yael Etinger for helping with sample preparation. We
thank Professor Eugen Rabkin for use of the rapid thermal annealer. The research leading
to these results received funding from the European Research Council under the
European Union’s Seventh Framework Program (FP/2007–2013)/ERC Grant Agreement
no. 336077. M.K.K. is grateful for financial support by the Israeli Ministry of Science,
Technology and Space. Nanofocusing lenses were kindly provided by the group of
Professor Dr Christian Schroer from TU Dresden, Germany.

Author contributions
B.P. conceived the work; M.K.K. performed the experiments; L.B. analysed the synchrotron data; A.K. developed the theoretical model; M.B. performed the synchrotron

measurements; Y.K. performed the TEM measurements; M.K.K. and B.P. wrote the
manuscript with comments from all authors.

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How to cite this article: Khristosov, M. K. et al. Sponge-like nanoporous single crystals
of gold. Nat. Commun. 6:8841 doi: 10.1038/ncomms9841 (2015).

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