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Shape control in concave metal nanoparticles by
etching†
Qiang Li, a Marcos Rellán-Piñeiro, a Neyvis Almora-Barrios, a
Miquel Garcia-Ratés, a Ioannis N. Remediakis b and Núria López

*a

The shape control of nanoparticles constitutes one of the main challenges in today’s nanotechnology.
The synthetic procedures are based on trial-and-error methods and are difficult to rationalize as many
ingredients are typically used. For instance, concave nanoparticles exhibiting high-index facets can be
obtained from Pt with different HCl treatments. These structures present exceptional capacities when are
employed as catalysts in electrochemical processes, as they maximize the activity per mass unit of the
expensive material. Here we show how atomistic simulations based on density functional theory that take
into account the environment can predict the morphology for the nanostructures and how it is even
Received 1st June 2017,
Accepted 30th July 2017

possible to address the appearance of concave structures. To describe the control by etching, we have

DOI: 10.1039/c7nr03889e

reformulated the Wulff construction through the use of a geometric model that leads to concave polyhedra, which have a larger surface-to-volume ratio compared to that for nanocubes. Such an increase

rsc.li/nanoscale

makes these sorts of nanoparticles excellent candidates to improve electrocatalytic performance.

Introduction
The properties of noble metal nanoparticles depend on their
morphology and surface crystalline orientation and, thus, the
specific control of the architectures is one of the major challenges in nanotechnology.1–7 Shape control has been achieved
and several synthetic methods allow the production of selected
polyhedra limited by convex surfaces (cubes, octahedra, tetrahedra, and rods).8–10 Many of the synthetic processes are
based on the generation of a seed by a fast reduction of a
metal salt, which is then grown on a solution containing
halides and/or surfactants with a milder reductive agent.
Recent studies have shown the efficiency of biomolecules in
recognizing specific crystallographic facets and affecting nanocrystal shapes.11,12 The mechanism of shape control has been
proposed to be kinetic or thermodynamic and is a consequence of the solution ingredients and conditions.13 In recent
years, there has been considerable interest in the synthesis of
concave nanoparticles (see Fig. 1).2,14 These structures have
unique potential in electrocatalysis because of their exposed

a

Institute of Chemical Research of Catalonia, ICIQ, The Barcelona Institute of
Science and Technology, Av. Països Catalans, 16, 43007 Tarragona, Spain.
E-mail: nlopez@iciq.es
b
Department of Materials Science and Technology, University of Crete,
and Institute of Electronic Structure and Laser, FORTH, Heraklion, 71003, Greece
† Electronic supplementary information (ESI) available: Calculated surface and
binding energies, resulting Wulff structures, and details on the ab initio thermodynamics formalism and on the geometric model. See DOI: 10.1039/c7nr03889e

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Fig. 1 Atomic representation of the structures formed during the synthetic process of Pt nanoparticles based on the fast reduction of a metal
salt that grows in a solution with a different amount of HCl. The insets
highlight the most stable surfaces in each stage of the process. The
scheme is adapted from ref. 2. Color code for the surface atoms: Pt in
grey, Cl in green, and H in white.

high-index facets5,15 that encompass a larger surface area compared to that in convex systems and result in more active
sites.14–19 In wet chemistry, two strategies have been proposed
to generate concave nanocrystals of active metals: (i) directionally controlled overgrowth20,21 and (ii) site-specific dissolution.22 Overgrowth relies on the fact that capping agents,
bound to specific facets, modify the relative growth rates
leading to concave polyhedra. This is the case of Pt octapods
exhibiting the {411} facets, or Ag nanostructures that are
formed when amines or Cu2+ ions are added.15,23 Octapods
were also indicated to appear by kinetically controlled overgrowth in the case of Rh with bromide as a capping agent.24

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Alternatively, concave nanoshapes can be formed by partial
dissolution of a larger nanoparticle. The region that experiences the faster dissolution evolves into a concave surface.
Therefore, the strength of the etchants needs to be finely
tuned in order to obtain the desired shape.25
Halides and hydrogen halides form dense phases on metal
surfaces.26 For Au and Ag, halides are employed as structure
directing coatings that show a large preference for the {100}
planes, and thus for cubes.27 This has been recently confirmed
computationally, showing a thermodynamic control of the
nanoparticle shape.28 Experiments on more reactive metals,
like Pt or Pd, have found that hydrogen halides at certain concentrations lead to the formation of concave nanoparticles.2,3,29 In these cases, the process of the formation of
high-index facets requires available low index-planes like {100}
and {111} surfaces that serve as templates.14
The morphology of nanoparticles can be explored through
the systematic use of theoretical tools based on Density
Functional Theory, DFT, coupled with the Wulff construction,
either in the continuum30,31 or atomistic versions,32,33 or by
creating the environment through first-principles thermodynamics.34 In the experiments, concave nanoparticles are
produced in an acid/watery environment, in open air and with
the Pt precursor in the solution. The full theoretical study
would require addressing all the stages from nucleation to
growth and including all the reactive ingredients which make
the prediction of the shape computationally unaffordable.
Alternatively, we have shown previously28,35 that a much better
understanding of the shape controlling factors can be obtained
by addressing the problem of the nanoparticle shape through
first principles and by sequentially increasing the level of
complexity (i.e. with the presence of the solvent, additives). The
lack of a methodology equivalent to the Wulff construction for
concave objects poses an additional challenge. In this study, we
aim at describing the formation of cubic Pt nanoparticles and
how they lead to concave structures when HCl concentration
increases and at describing an alternative to the Wulff construction for concave structures.

Methods
We have performed DFT calculations with the Vienna ab initio
simulation package code (VASP version 5.3.3)36,37 with the
Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional.38 Inner electrons were represented by projector augmented wave (PAW) potentials39,40 with a kinetic cutoff energy
of 400 eV, and dispersion contributions with D2 parameters
complemented with our reparametrized values for metals.41,42
The corresponding k-point samplings were denser than
0.3 Å−1. We considered several low-index planes, (100), (111),
and (110), and also the open surfaces that might be present in
particle-etched concave structures, that is, (211), (311), (411)
and (511) planes which contain the {111} steps and the {100}
terraces. The models for all the Pt surfaces were constructed
with 5–9 layers depending on the degree of openness of the

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surfaces to ensure convergence in all cases. The topmost 2–4
layers were relaxed during optimization, while the remaining
layers were kept fixed to mimic the bulk. The structures were
interleaved under 12 Å vacuum. HCl was adsorbed only on the
topmost surface and the dipole correction was employed to
correct potential spurious terms arising from the asymmetry of
the slabs.43 We used ab initio atomistic thermodynamics to
understand the effect of the concentration of different
adsorbed species on the stability and growth of Pt nanoparticle
surfaces.34 Solvent contributions were added via the
VASP-MGCM (VASP-Multigrid Continuum Model).44 To illustrate how theoretical simulations can account for the etching
of Pt nanoparticles, we have generated a finite cubic model of
16 Å side, representing the most likely growth morphology.
The surface was completely covered with HCl and the
total stoichiometry was 365 Pt atoms and 148 HCl units in the
form of a monolayer of a rock-salt-like structure (see Fig. S2†).
The so-built structure was then allowed to relax and
during this step some HCl molecules were formed and left the
surface due to the repulsion between them. These molecules were
then removed from the simulation box leaving the final Pt-cube
structure surrounded by 119 HCl units. Pitting was then tested at
different positions of the naked Pt365 and Pt365(HCl)119: in the
middle of a facet, in the edge, and at the corner positions.
Finally, we computed the change in energy due to the addition
of an extra Pt atom to the Pt365 and Pt365(HCl)119 at the face positions. A data-set collection of computational results is available
in the ioChem-BD repository.45

Results and discussion
Experiments have evidenced that Pt nanoparticles present
concave faces upon exposure to high concentrations of HCl.2
Simulations have been carried out to explain these observations. The present simulations might seem simple but we
would like to point out the following: (i) this is the first ever
approach that involves the use of density functional theory to
explore the appearance of concave nanoparticles by etching.
(ii) Solvent contributions are employed when needed through
a continuum model. Although this is not the best situation,
because explicit water molecules could have a role, it simplifies
the chemical approach whilst avoiding a discussion based only
on gas-phase energies. (iii) The contribution of oxidants (O2)
that might be present in the solution has not been considered.
Again, a proper representation of the full phenomena of shape
control would be needed to integrate the mechanistic contribution of these species. (iv) However, even if the models presented here are rather simple, they do allow the formulation of
a concave version of the Wulff construction. The Wulff construction has served to understand the equilibrium structure
of nanoparticles since 1901. To our knowledge, this is the first
attempt to predict the theoretically concave shapes of nanoparticles in a generalized framework.
The first point that is addressed in the simulations is the
estimation of the adsorption energy of HCl molecules on all

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Fig. 2 (Left) Surface energy for different planes as a function of the HCl
concentration (c0 = 1 M) at room temperature and (right) side view of
the different surfaces with the densest HCl coverage. The inset represents the nanoparticle morphology, as derived from the Wulff construction at 25% of HCl (dashed line). The shaded area corresponds to
HCl concentrations where pitting occurs, as calculated from our kinetic
model. Color code for the Pt surfaces: (100) green, (110) blue, (111) olive,
(211) orange, (311) red, (411) purple and (511) wine. Atomic color code as
in Fig. 1.

relevant Pt surfaces. These quantities are needed to predict
the equilibrium shape of the nanoparticle in an interacting
environment using the Wulff construction method.30
The interaction of HCl on these surfaces with the densest coverage was calculated with respect to the solvated molecules.
The results for adsorption energies and atom–atom distances
are summarized in section S2.† Fig. 2 (right) shows the side
view of the densest HCl packing on low-index facets, such as
(100), (110), and (111), and also on stepped surfaces
(211), (311), (411) and (511). The HCl molecules have been
found to adsorb preferentially on the (100) Pt surfaces, resulting in a large value for the binding energy per HCl molecule
(−1.11 eV per HCl). Note that the adsorption of NaCl also considered in ref. 2 is almost thermoneutral, so the nanoparticle
shape control would only be induced by Cl− adsorption as in
the case of Ag@Au28 (therefore, we do not discuss it further).
In this surface, the Cl and H atoms are placed on the bridge
sites of the Pt surface at a distance of 1.934 Å and 1.011 Å from
the surface, respectively. Surface energies calculated with DFT
methods are known to deviate from experimental data.46
However, DFT-based results for binding energies are not
affected in the same way.42
To predict the shape of the nanoparticles in the HCl–water
environment, we have adopted an ab initio thermodynamics
framework,34 see section S4,† that allows the estimation of the
surface energy for each of the surfaces as a function of the acid
concentration, c. For this purpose, we considered the chemical
potential of the species as the reference in solution at room
temperature. The results for the surface energy for the HClcovered Pt surfaces, γHCl, at different HCl concentrations are
shown in Fig. 2 (left). The range of HCl concentrations corresponds to values between 0.5% and 100% (see Table S5†).

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The ab initio thermodynamics indicates that the preferred
configurations are dense phases with high concentrations of
adsorbed HCl. The general trend shown in Fig. 2 is that the
(100) surface is the most stable over the whole range of concentrations. With regard to the remaining surfaces, it is important
to note that, although the (311) and (511) faces are less stable
than the (110) surface at low HCl concentrations, the situation
is the opposite for large HCl amounts. In order to validate our
approach, we repeated the calculations for the (100) surface
considering the system solvated by the continuum model in
water. The largest deviation in the calculated γHCl with respect
to the same quantity for the systems in vacuum is lower than
1%. Therefore, unsolvated surface energies were employed and
solvation was considered only for the reference HCl molecule
(section S2†), in the definition of the binding energy. The
inset in Fig. 2 shows that the application of the Wulff construction at 25% of HCl concentration results in a nanocube (see
section S3†).
Increasing the acid concentration led to the erosion of
the cubes. Experiments showed that at a HCl concentration of
37%2 the corresponding structure obtained from our Wulff
construction is no longer valid. Increasing the HCl concentration further causes the formation of bone-like structures
without increasing the nanoparticle size.2 This is due to the
effect of the acid. As the deposition rate starts to become lower
than the etching one, and therefore pitting starts.3 In order to
understand how pitting occurs, we calculated the reaction
energies for dissolution at relevant acid concentrations. We
started by studying this dissolution process on the thermodynamically preferred surface: (100), and on a high-index
plane: the (311) facet. The removal of a Pt atom from the (100)
surface is 0.21 eV easier than that from the (311) one. This
energy difference relies on the different HCl configuration that
we have on both the surfaces. In the case of the (100) facet, H
and Cl atoms are placed at the bridge positions between Pt
atoms, whereas for the (311) surface, H and Cl atoms are
placed on top of the Pt atoms (see Fig. 3a and b). When a Pt
atom is removed from both the surfaces, there is no change in
the configuration of the HCl network in the (100) facet,
whereas for the (311) facet, a Cl atom occupies the hollow left
by Pt. Thus, although for this last surface the Cl atom
approaches a Pt atom, the HCl network is distorted locally and
leads to a less favorable situation in terms of energy compared
to the pitting in the (100) facet.
Similarly, for the Pt365 nanoparticle, we calculated the
energy gain to depositing an isolated Pt atom together with
the energy cost to remove a Pt atom from the corner, step and
the (100) facet. In the case of naked Pt nanoparticles, the
easiest Pt removal corresponds to the lowest atom coordination, the corners being 1.75 eV more thermodynamically
easy to be removed than the atoms at the face centers (see
Table S6†). The situation changes for HCl-covered nanoparticles (see Fig. 3c and d). In this case, the pitting at the
edge and facet positions is almost equivalent and the corresponding configurations are 0.94 eV more stable than removing
one atom at the corner, thus the stability goes as: corner > edge

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given value for the HCl concentration, when pitting starts, the
deposition and elimination rates shall be equal and we can
write the following equation

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kdep ½Pt365 Š½H2 PtCl6 Š½H3 Oþ Š4 ¼ kel ½Pt365 Š½HClŠ6

Fig. 3 Optimized structures after a Pt atom removal of HCl on (a) the
Pt(100), (b) Pt(311) surfaces, as well as on (c) the Pt365(HCl)119 nanocube,
and (d) after a Pt atom addition in the later system. Atomic color code as
in Fig. 1. The positions of the removed and added Pt atoms are highlighted with a red circle.

≈ facet. However, for a cube with side length a and N atoms
side, the number of edge atoms Ne is linear with N, while the
number of face atoms Nf is quadratic. Therefore, Nf is one
order of magnitude larger than Ne and, thus, the pitting shall
start readily at the facets.
Although the presence of oxidative agents and explicit water
models would be needed to have a complete picture of the
synthesis and shape control of the nanoparticles, the computed
results have already provided some hints on these phenomena.
With the calculated values, we propose a kinetic model to
identify at which HCl concentration the pitting starts. The
energy references have been taken as soluble H2PtCl6 units.
This model relies on two equations:
Deposition Pt365 þ H2 PtCl6 þ 4H3 Oþ ! Pt366 þ 6HCl þ 4H2 O
Elimination Pt365 þ 6HCl ! Pt364 þ H2 PtCl6 þ 4Hþ
The kinetic coefficients47 for deposition and elimination
can be traced back to the values for deposition (−4.63 eV at the
facet of the HCl-decorated Pt365) and elimination (4.17 eV from
the facet of the HCl-decorated Pt365). For simplicity, we
consider the kinetics of the above equations to be governed
by power-low rates. Solvent effects are only considered
through the continuum model. Although an atomistic
insight48 would be relevant to unravel the specific effect of the
solvent, this point is beyond the aim of the present work. At a

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Considering the experimental conditions: room temperature and the concentration of Pt in the solution, [H2PtCl6] =
0.1 M and pH = 0, the [HCl] concentration at which the pitting
starts is 43% HCl. Experimentally, the transition between Pt
nanocubes and bonelike structures is observed at 37%.2 Given
the simplicity of our model, the agreement between the two
thresholds for the pitting is remarkable. In addition, our
results qualitatively agree with the increase in the (100) surface
area of up to 25% HCl (43% in our case) and with its decrease
for higher concentrations. From that point onwards, the
surface area of surfaces like the 311 and 511 (which involve a
higher number of steps and defects) increases.2
As the Wulff theorem always results in convex objects, we
devised a new procedure to consider etched nanostructures
obtained: (i) its final shape, (ii) surface(s) exposed, and (iii) the
surface-to-volume ratio. Starting from the nanocube limited
{100} planes and given that the pitting starts at the center of
the facet, the formation of the convex structure can be found
as a volume excavation from this pitting point.15 Therefore, the
process of forming a high-index faceted concave nanoparticle
consists of the removal of an object (in our case, a tetragonal
pyramid), made of the {hll}-like planes from each face of a
nanocube (h, k, and l are Miller indices with k = l and h > k,
see Fig. 4a). Varying the concentration of HCl would then
correspond to a different degree of intersection between
solids. In the beginning, the facet excavated structures
resemble the bonelike ones reported in ref. 2. In the limit
where the {100} planes are completely excavated out, the resulting structure is an octapod containing, in our case, only the
{311} planes (Fig. 4b). As mentioned above, it is important to
point out that a concave nanoparticle containing just the {311}
planes can only be obtained if the pitting occurs at the center
of the {100} faces. If it occurred either at the corners or at the
edge centers, the resulting structures would always contain the
{100} and {311} planes simultaneously, and would never have
sharp corners. A full derivation of the nanostructure formation, bonelike to octapods in this case, is presented in
section S6.†
The final effect of the degree of penetration of the etching
volume (red in Fig. 4) is represented by the δ parameter, which
is the shortest distance between the corners of the pyramidal
pit and the edges of the cubic particle (see Fig. 4b). The parameter δ depends on the concentration c of HCl (see section
S6.2†). Therefore, for low etching values, the surface area of
the nanoparticle does not change much (Fig. 4c). At intermediate values, the composition of the surface is 50% that of the
{100} and {311} stepped surfaces, and only when the octapods
appear, the total surface area decreases by about 45% of the
initial value, being mostly of the {311} type. The effect on the
volume is more pronounced. Although at δ = 0 the volume is

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determines the final nanoparticle shape. A detailed balance
between the number of potential pitting points – corners,
edges, and facets – and the thermodynamic demand for this
particular elimination is required to obtain the etched shape.
Once the starting pitting point, in our case the face center, has
been determined, the final equilibrium structure can be
obtained by a geometrical model involving the intersection of
our nanoobject with a polyhedron composed of the next stable
surface at the pitting point. The impact on the geometric parameters can then be described through a model which, in our
particular case, results in a surface-to-volume enhancement of
up to 3–4-fold which improves the atom economy in these
types of materials.

Conclusions

Fig. 4 (a) The formation of etched nanoparticles exhibiting the {311}
planes can be described as a process where a tetragonal pyramid
composed of the {311} planes intersects a cube at each face center.
(b) Resulting structures for different HCl concentrations in the y–z plane
(concentration increases from left to right). The gray line corresponds to
the intersection between the tetragonal pyramid with the plane x = a/2.
The parameter δ (see section S6†), which is shown for some of the
cases, is measured from the edge of each face. (c) Surface area (left),
volume (middle) and surface-to-volume ratio (right) for the nanoparticles as a function of δ. All quantities are scaled by the respective
values for a cube with side length a. The color code for the surfaces is
the same as shown in Fig. 2.

about 80%, when the octapod is formed the volume is only
around 20% that of the nanocube. The most striking characteristic of these nanoobjects is the increase in the surface-tovolume ratio upon etching. At intermediate values of δ, the
effect is not pronounced (marginal 10% increase), but it exponentially grows for δ/a larger than 0.25. Thus, after this severe
etching (represented by the fourth structure in Fig. 4b), the
surface-to-volume ratio is doubled and, under the most favorable conditions, it reaches a 3–4-fold increase. Such atom
economy is essential to improve electrocatalytic performance.
To sum up, the acid control on the shape of the nanoparticle works as follows. Firstly, the nanostructures grow exhibiting the {100} surfaces as predicted from ab initio thermodynamics and reinforced by the Wulff construction. Once the
chemical potential of the acid in the solution is too high, the
deposition and consequent growth are no longer preferred
over elimination and etching. This can be inferred by considering the chemical potential in the corresponding microkinetic
equations. Here, the starting pitting point is important as it

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Theoretical calculations hold the key for an atomistic understanding of the control in the synthesis of nanostructures even
when concave structures are generated. We have presented a
formulation that describes the formation of concave Pt nanoparticles in the HCl–water environment. Our results based on
ab initio thermodynamics predict cubic nanoparticles for any
HCl concentration. However, at a certain HCl concentration,
the gain for adding an extra Pt atom to the nanoparticle equilibrates with that of etching. Therefore, pitting starts at the
most favorable elimination position, the facets. From this
point, a geometric model based on the intersection of a nanocube and a polyhedron made of the {hll} planes predicts the
equilibrium nanoparticle shape as a function of the degree of
intersection, δ, between both the figures. When this parameter, which can be correlated with HCl concentration, adopts
its maximum value, the structures are the octapods but
resemble bonelike for smaller values as in the experiments.
For the limiting case of octapods made of the {311} planes, the
volume decreases 80% with respect to that for the cubic nanoparticle and the surface-to-volume ratio reaches a 3–4-fold
increase. The resulting insights advance the understanding of
the role of additives during metal nanoparticle growth and
etching and can be extended to other metals and structures,
thus opening a new perspective in understanding the control
of new shapes and architectures.

Conflicts of interest
There are no conflicts of interest to declare.

Acknowledgements
The authors acknowledge the MINECO ( project CTQ201568770-R and grants FPDI-2013-16194, SEV-2013-0319, and
SEVP-2014-068237) for financial support. We are grateful to
Professors J. M. Feliu and L. M. Liz-Marzan, for useful
discussions.

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