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Journal Name
Why are Zn-rich Zn-Mg nanoalloys optimal protective
coatings against corrosion? A first-principles study of
the initial stages of the oxidation process†
P. Álvarez-Zapatero,∗aA. Lebon,∗bR.H. Aguilera del Toro,aA. Aguado,aA. Vegaa
ZnMg alloys of certain compositions in the Zn-rich side of the phase diagram are particularly
efficient, and widely used, as anticorrosive coatings, but a sound understanding of the physico-
chemical properties behind such quality is still far from being achieved. The present work focuses
on the first stage of the corrosion process, namely the initial growth of a sacrificial surface ox-
ide layer, whose characteristics will condition the next stages of the corrosion. A comprehensive
ab-initio study, based on the density functional theory, is carried out on ZnMg nanoalloys with
20 atoms and different compositions, which serve as model systems to simulate the complex
processes that occur in extended granular surfaces. The structural and electronic properties,
when progressive oxidation of the nanoalloys takes place, are analyzed in detail with the help of
structural descriptors, energetic descriptors such as the oxygen adsorption energies and excess
adsorption energies, as well as with electronic ones based on the topological analysis of the elec-
tron density and the electron localization function, from which a detailed analysis of the bonding
patterns is extracted. We explain why small amounts of Mg create a very positive synergy be-
tween Zn and Mg that increases the reactivity to oxygen while reducing, at the same time, the
stress induced on the cluster substrate, both facts working in favor of promoting the growth of
the oxide crust whilst protecting the core. Moreover, we also show that stoichiometries close to
the Mg2Zn11 and MgZn2compositions are the best candidates to optimize the protection against
corrosion in Zn-Mg alloys, in agreement with the experimental observations.
1 Introduction
The use of protective coatings containing zinc1is a general prac-
tice in automotive, building, and other industries to extend the
lifetime and appearance of products. Zinc-magnesium alloys with
low magnesium content have been shown to provide very good
protective coating properties that even outperform those of pure
zinc. For instance, corrosion tests in automotive laboratories2
have shown that the time for growing significant amounts of red
rust under spraying with NaCl is three times longer when apply-
ing coatings consisting of a MgZn2alloy than if pure Zn coat-
ings are employed. The pH dependence in an aqueous NaCl solu-
tion environment has been thoroughly investigated3. Protection
against oxidation was also investigated, the optimal magnesium
content in the coating being 4-8 wt.%; for this particular alloy, the
aDepartamento de Física Teórica, Atómica, y Óptica. Universidad de Valladolid, E-
47011 Valladolid, Spain. E-mail: pablo.alvarez.zapatero@uva.es
bLaboratoire de Chimie Électrochimie Moléculaire et Chimie Analytique, UEB/UBO,
UMR CNRS 6521, 29238 Brest Cedex, France. E-mail: alexandre.lebon@univ-brest.fr
† Electronic Supplementary Information (ESI) available: See DOI:
00.0000/00000000.
weight loss is up to 10 times lower than that measured for pure
Zn4. The microstructure and the possible multilayer arrangement
of Zn-Zn/Mg has been also carefully investigated5since the coat-
ing properties do not only depend on the resistance to a corrod-
ing agent but also on the microstructure of the protective layers.
The influence of macrosegregation, microstructure evolution and
microstructure length scale on the corrosion properties of a Zn-
5.0wt.%Mg alloy casting were also analyzed6. Finally, the corro-
sion problem is a very general subject that is not limited to Zn or
Zn-Mg systems. For instance, an ab-initio study was performed
on Fe-Cr alloy surfaces in order to analyse at an atomic level the
initial oxidation stages in these surfaces7, in a similar way as we
shall show in this work.
For a given protective coating under particular external condi-
tions, the corrosion process is quite complex, involving physical,
chemical, thermodynamical and kinetic mechanisms, as well as
several stages that are yet far from being completely understood
in the time scale. It is known, for instance, that the improved
anticorrosive properties of MgZn2, derived from the decrease of
the charge transfer across the interface as compared to pure Zn
coatings, are a consequence of the different proportion of hydrox-
Journal Name, [year], [vol.],
1–14 | 1
ide and carbonate species in the final corrosion products, which
increase the work function of the surface8. It is also known9
that the thickness of the corrosion film of the ZnMg coating is
thicker than that of a pure Zn coating, which favors passivation
of the surface in a chloride-rich atmosphere due to the lowering in
the gradient of the electrostatic potential across the metal-oxide
interface. In the first stage of the corrosion process, the forma-
tion of an oxide surface layer is observed4.The improved coating
properties of Zn-Mg alloys are closely connected with the supe-
rior capability of Mg atoms to promote the protective surface ox-
ide layer, being more stable than the oxide surface that pure Zn
would form. Oxygen preferentially binds to Mg and even favors
Mg enrichment at the surface, which produces an oxide surface
layer with more Mg concentration than the nominal concentra-
tion in the alloy.
The physical and chemical mechanisms that determine the
corrosion process along the different stages are triggered by
fundamental structural and electronic properties of the system
which are difficult to understand in depth without a quantum-
mechanical analysis. For example, the granularity that character-
izes usual protective coatings can decisively modify their proper-
ties10. The microstructure of the coating must also be considered
with special care, since penetration and fast diffusion of the cor-
roding agents are easier through local defects.
In previous works11–13, we have reported first-principles cal-
culations for ZnMg in vacuum nanoalloys of several sizes and
composition ratios, to obtain hints into the fundamental physico-
chemical properties that might ultimately explain the reasons for
the improved capability of ZnMg coatings against corrosion. A
noticeable charge transfer from Mg to Zn atoms was identified
and rationalized, modulated by composition-dependent features.
We also showed that Mg atoms are more reactive than Zn atoms,
so that the oxidation of the nanoalloy surface is a faster and more
exothermic process as compared to oxidation of pure, all those
facts being consistent with the experimental evidences. The re-
sults of these initial works also allowed us to generate a signifi-
cant number of accurate nanoalloy structural models as an input
for the explicit corrosion studies, and to determine fundamental
indicators that point to certain Zn-Mg compositions as the optimal
ones for protective coatings.
The present work, on the contrary, focuses on the first stage
of the corrosion process, that is the formation of an oxide sur-
face layer and related structural and electronic properties that
can be relevant for the next stages of the corrosion process. For
this purpose, ZnMg nanoalloys of 20 atoms have been chosen, for
which the reactivity indicators were analyzed in detail in our ini-
tial work11. We have investigated, at a first-principles level, both
the molecular and dissociative adsorptions of O2for several com-
positions. The results allow to better understand now why certain
compositions are better suited to the design of optimal protective
ZnMg coatings, taking into account that the characteristics of the
formed oxide surface layer will condition the next stages of the
process.
Small nanoalloy clusters are used in this work since these are
simple yet useful computational models for an initial study of the
intricate processes that operate in the real extended surfaces. A
perfectly periodic slab model would not necessarily be closer to
the realistic situation, because the real materials are granular in
nature and the defects or cracks associated with the microstruc-
ture of the sample have been found to be essential for corrosion,
as explained above. Thus, the local features of the surface play a
critical role in the overall corrosion process14–16. Additionally, it
is relevant in our opinion to study nanoclusters as most coating
techniques involve sputtering or spray methods where the mate-
rial could be fragmented through surface-induced dissociation as
expected in physical vapour deposition technology4, either while
hitting the surface or by collision of powder crystallites during
the deposition process. In such a case, the beginning of oxida-
tion could occur in regions of nanometer size that are expected to
be formed around cracks and that are ill-measured by electronic
microscopy techniques. It is worth emphasizing that nanoalloys
offer the possibility to simulate the variety of local environments
that appear in real granular surfaces, and as will be shown in this
paper, corrosion/oxidation processes are ultimately related to the
local reactivity. Finally, in one of our recent studies13, we have
obtained the global minimum structures of (MgZn2)Nnanoalloys
of varying sizes, and compared them to the bulk Laves structure.
That study demonstrates that the nanoalloys look very similar to
the bulk material as regards the short-range skeletal and compo-
sitional orders, which adds to our idea that the nanoalloys are
good model systems, representative of extended samples at least
locally, but additionally displaying a larger variety of similar envi-
ronments as expected in a granular sample. The only significant
size effect is that bond lengths are homogeneously scaled down
in nanoalloys as compared to the bulk limit (this is generally true
for nearly all metallic nanoparticles). We will discuss the expected
size effects on the oxidation process, and argue that they do not
fundamentally alter the identified mechanisms.
The theoretical approach, based on the density functional the-
ory, is first detailed in the next section. Then the putative ground
state configurations are analyzed with the use of structural and
energetic descriptors together with indicators deduced from a
quantum chemical topology analysis. The selected nanoalloys,
ZnxMg20−xwith x=0,10,13,15,17,20, are subjected to a progres-
sive oxidation with the addition of up to 6 oxygen atoms. The Mg
content is low for the majority of the analyzed stoichiometries,
which were selected on the basis of the experimental results that
demonstrate that the best coating properties are found for Zn-rich
alloys. On the other hand, the x=17 and x=13 stoichiometries
are in the range that mimics the alloys at 4-8 wt %for the former
and the MgZn2for the latter.
2 Theoretical and Computational Methods
Ground state (GS) configurations (both atomic structure and
chemical order) of the bare ZnxMg20−xnanoalloys were taken
from a previous work11. Density Functional Theory calculations
of molecular and dissociative O2adsorption on all non equivalent
surface sites of those nanoalloys have been performed employ-
ing the code VASP17,18. Electron-ion interactions are described
with the projector-augmented-wave (PAW) potentials available
within VASP code. Exchange and correlation effects were de-
scribed with the generalized gradient approximation of Perdew,
2 | 1–14
Journal Name, [year], [vol.],
Burke and Ernzerhof (PBE)19. This functional was found to pro-
vide accurate enough results regarding the structural, energetic
and elastic properties of zinc and magnesium oxides20–22, which
are the essential properties we need in our discussion. A hybrid
functional would be needed, however, to describe some proper-
ties of the electronic density of states, as for example the HOMO-
LUMO gap, which for metal oxides are not properly captured by
semilocal functionals. An energy cutoff of 500 eV was used for
the plane wave basis set. The tolerance for the electronic den-
sity in the selfconsistent calculation was set at 10−4. We checked
all our calculations for spin polarization, and found that all GS
configurations are in a singlet spin state.
Each calculated cluster is placed in a 30 ×30 ×30 Å3supercell.
The calculations include only the Γpoint as appropriate for finite
size systems. The structure is optimized by relaxing the atomic
positions until the force on each atom is smaller than 0.01 eV/Å.
Local atomic populations were derived with the Bader’s
method23 following the algorithm of Henkelman24. To analyze
the changes in local reactivity of the Zn-Mg system upon O2ad-
sorption, the Fukui f+and f−25–27 functions have been com-
puted. The Fukui functions can be presented either as isosurface
(contour) plots or in its condensed form which is obtained by in-
tegrating them over the Bader atomic basins25. Further details
can also be obtained from our previous work11. Following the
common practice of approximating the derivatives by finite dif-
ferences, the expressions for a cluster with Neelectrons are:
f+
Ne(⃗r) = ρNe+1(⃗r)−ρNe(⃗r)(1)
f−
Ne(⃗r) = ρNe(⃗r)−ρNe−1(⃗r)(2)
The corrosion process is accompanied with drastic changes in
the structure and energetics of the clusters. To determine how
the stability changes when ZnxMg20−xclusters are exposed to ox-
idation, two excess energy indicators have been defined. The first
one is the standard excess energy definition, adapted to deal with
partially oxidized metals:
Eexc(ZnxMg20−xOm) =
=E(ZnxMg20−xOm)−xE(Zn20Om)
20 −(20 −x)E(Mg20Om)
20 ,
(3)
where E(Zn20Om)and E(Mg20 Om)are the energies of the ox-
idized Mg20 and Zn20 clusters. This definition reduces to the
excess energy of Zn-Mg nanoalloys when m=0. For m̸=0, it
quantifies how much favorable it is the formation of the oxidized
nanoalloy as compared to an ideal mixture of oxidized Zn and
oxidized Mg clusters of the same size. Next, we use the oxygen
adsorption energies:
Eads (ZnxMg20−xOm) =
=1
2E(O2) + E(ZnxMg20−xOm−1)−E(ZnxMg20−xOm),
(4)
to define an excess adsorption energy:
Eexc−ads(ZnxMg20−xOm) =
=Eads (ZnxMg20−xOm)−xEads(Zn20 Om)
20 −(20 −x)Eads (Mg20Om)
20 ,
(5)
When positive, this excess energy demonstrates that oxygen ad-
sorption is more exothermic in the oxidized nanoalloy than in a
statistical mixture of the separately oxidized Mg and Zn metals.
Its dependence with mdetermines how the oxygen content influ-
ences the adsorption energetics of additional oxygen atoms.
The progressive oxidation of the ZnxMg20−xnanoalloys is ex-
amined through a topological analysis of the electron density (ρ)
and electron localisation function (ELF)28 scalar fields. Regard-
ing the electronic density, the examination of its critical points un-
veils the character of bonding23. The analysis of electron density
gradients reveals maximal density lines connecting two atoms,
and the minimum along this line is called a bond critical point
(BCP). Several indicators are then determined at the BCPs, such
as the value of the electronic density ρb, its Laplacian ∇2ρb, and
the total electronic energy density Hb, which together make it
possible to identify the nature of the bonding interaction29–31.
The different types of bonds, according to Matta’s classification32,
range between electron-sharing bonds and closed-shell interac-
tions. All the data at the BCPs are provided in atomic units.
The ELF quantifies the amount of Pauli repulsion at each point
of the molecular space28,33, which is partitioned into bonding,
non bonding and core basins. The latter reproduce the atomic
core shell structures and are labeled by C(X) for an atom X. The
valence basins (either bonding or non bonding) are classified ac-
cording to their degree of synapticity. A disynaptic basin is a basin
common to two atoms A and B, and is labeled as V(A,B). Non
bonding basins are called monosynaptic since they are localized
around a single A atom, and they are noted as V(A). They tipically
correspond to lone pairs. The average population of each basin
is derived after integrating the electronic density within the basin
volume, and the population variance is similarly obtained from
integration of the pair density.
In this study the optimized VASP structures served as input
for single point calculations with the well-established quantum
chemistry code Gaussian1634. These are motivated by the fact
that the PAW-generated ELF and ρdisplay spurious minima
around the cut-off radius35. As a consequence, compared to an
all-electron calculation, there are differences in the building of
the electron density or the ELF function. All Gaussian16 calcu-
lations are done at the same level of theory as the VASP calcula-
tions, employing a 6-311g(d) basis set. The gradient of the elec-
tron localization function (ELF) and the electronic density were
computed with the codes TOPMOD0936 and DGRID5.137.
3 Results and Discussion
3.1 Structural trends along the initial oxidation path
In a previous study, the GS structures of ZnxMg20−xnanoalloys
were determined through self-consistent DFT calculations, with
the same considerations and methodology as here. Global and
Journal Name, [year], [vol.],
1–14 | 3
local reactivity descriptors were determined to inquire about the
reactivity of the bare cluster11. Here, we have started with those
GS configurations for the bare nanoalloys, that correspond to
ZnxMg20−xOmfor m=0.
Fig. 1 Putative GS structures of ZnxMg20−xOmfor m=0−6, and x=
0,10,13,15,17 and 20. Brown, yellow and red spheres represent Zn, Mg
and O atoms, respectively.
The putative GS structures of the oxidized and non-
oxidized nanoalloys ZnxMg20−xOm(with m=0−6and x=
0,10,13,15,17,20) are shown in Fig. 1. Our first relevant com-
ment is that molecular chemisorption of O2is not even a stable
local minimum in most cases, i.e. the molecule readily dissoci-
ates during the optimization process, demonstrating that, if an
activation barrier exists for the dissociation process, it must be
negligibly small. Only in very few runs could we obtain a local
minimum with a chemisorbed O2molecule, and all those config-
urations were between 3 and 4 eV less stable than the correct
GS structure. Once it was clear that only dissociative chemisorp-
tion is relevant in these systems, the GS structures for the oxi-
dized nanoalloys were located by trying various initial locations
for each additional adsorbed oxygen atom, including “hollow”,
bridge and atop positions over the cluster surface. The hollow
sites correspond to the center of the triangular facets where the
oxygen is bonded to three metal atoms, and are always the most
stable adsorption sites. When other sites like bridge or atop po-
sitions were tested, either the calculation converged to a hollow
site after relaxation, or the final relaxed structure was a highly
excited isomer at more than 2 eV with respect to the GS. After
having relaxed all the candidates with a single O atom, the most
stable configuration was chosen as the new starting point to lo-
cate the optimal adsorption site for the second oxygen atom, and
so forth. This search strategy was initially guided by calculations
of the nucleophilic condensed Fukui functions f−, performed on
each ZnxMg20−xOmnanoalloy right before addition of the next
oxygen atom (see Fig. S1 in the ESI). Considering that large f−
values are related to the propensity of an atomic site to experi-
ence an electrophilic attack, the initial position for the O atom
was proposed in the vicinity of those regions with higher f−.
However, with increasing oxygen content, we observed that the
electrophilic attack can preferentially occur at other sites, i.e. f−
itself is not sufficient to unambiguously predict the adsorbed site
of the additional oxygen atoms. The oxygen atom rather goes
to a surface site where the bonding interactions with magnesium
are maximized. For given values of oxygen content and nanoal-
loy composition, approximately 30 different adsorption configu-
rations were tested, including those based on the largest f−sites
and those close to Mg-rich surface regions.
By adding the oxygen atoms one at a time and varying just the
position of the newly added atom, we are obviously constraining
the number of sampled configurations. When moxygen atoms are
added on top of a given nanoalloy structure (with a given atomic
skeleton and chemical order), and if there are Nshollow surface
sites available on the substrate, a total of Ns
mdifferent configu-
rations exist in principle for the oxidized system, which may be
too many to try them all explicitly. Therefore, we can not claim to
have located the absolute global minimum structure for moxygen
atoms on the surface of a Zn-Mg nanoalloy. On the other hand,
we have performed additional optimizations for the m=2case
not using that assumption (i.e. varying the possible adsorption
sites of the two oxygen atoms) and have not located a more sta-
ble structure than when fixing the position of the first adsorbed
oxygen. These additional tests justify our assumption and make
us confident that the main structural trends have been correctly
identified, i.e. that the obtained structures are representative of
the true situation, even if there may be similar structures which
are slightly more stable.
This dedicated procedure enabled us to finally obtain a bench
of 42 putative GS structures that is representative of the initial
oxidation scenario expected for these systems in the thermody-
namic equilibrium limit corresponding to a low oxidation rate,
because we are assuming that each oxygen atom reaches its most
stable adsorption site before the next oxygen atom is added. To
provide explicit support for our assumption, we have calculated
the diffusion barriers of an oxygen adatom over the surface us-
ing the Nudged Elastic Band method38,39 (see Fig. 2). In order
to move between two neighboring triangular facets on the clus-
ter substrate, an oxygen atom has to surmount a barrier which
is between 0.3-0.6 eV. As we will later show, these barriers are
between 5 to 10 times smaller than the oxygen adsorption en-
ergy, so right after adsorbing each oxygen atom, the cluster has
enough internal energy for the oxygen atom to surmount the dif-
fusion barriers before the excess heat is dissipated.
We first describe the main structural trends that can be ex-
tracted from a detailed visual inspection of the GS structures
(Fig. 1), including a comparison with the initial oxidation stage
in sodium clusters, that was analyzed in previous reports40,41.
There are some systematic differences between the initial oxida-
tion behaviors of Na, Mg, Zn and Zn-Mg systems that can be cor-
related with their specific structural properties. In sodium clus-
ters, to start with, the oxygen atoms get absorbed at octahedral
interstices that exist within the subsurface layer of the metal host,
and when several oxygen atoms are added, they prefer to occupy
neighboring interstices, thus generating a single sodium oxide
4 | 1–14
Journal Name, [year], [vol.],
Fig. 2 Diffusion path analyzed for the oxygen atom in the Zn13Mg7com-
position. The diffusion path comprises two different barriers, where the
oxygen atom moves from a hollow position to another one, almost 4.5
Å away. Reddish colors represent Zn atoms, golden colors depict Mg
atoms while oxygen atom is depicted in blue color. For the first barrier,
the same elastic constant was employed for all the images, while for the
second barrier a kmax=2kmin scheme was used, in order to increase the
resolution around the saddle point. Also the atomic configurations are
shown for maximum and minimum energy values along the path.
sub-cluster well segregated from the metallic host40,41. The static
coexistence of oxidized and metallic phases separated by an inter-
face is in line with the bulk behavior42. Similarly, Na clusters are
not able to dissolve the oxide molecule because the elastic defor-
mation energy of the metal host when the oxygen impurities are
dissolved is bigger than the energy cost of the interface. Purely
steric factors finally explain the preference for subsurface sites:
with an average interatomic distance of about 3.7Å, the octahe-
dral interstices in sodium clusters have just the appropriate size
to house an oxygen impurity without disrupting the whole clus-
ter structure. Nevertheless, the oxidized region locally contracts,
and puts the metallic host under a tensile stress which can not be
fully compensated by elastic deformation mechanisms. Obviously
a metal like sodium would be useless for corrosion protection as
the oxide nucleation centers grow inside the metallic host right
from the start, thus getting easy access to attack the core region.
The initial oxidation of Mg20 shares many similarities with the
sodium case. In effect, the initial oxygen adatoms tend to be close
to each other on the surface of the pure Mg20 cluster, thus pref-
erentially attacking a specific local region of the cluster surface
and inducing strong distortions in the structure of the metal host.
As an example of these distortions, we observe that some oxygen
atoms become coordinated to four metal atoms, while the shell
of the pristine Mg20 cluster is well triangulated and only three
metal-oxygen bonds would be expected if distortions were small
(in other words, the initial hollow sites are not structurally sta-
ble). At the highest oxygen content here considered (m=6), the
local shrinking around the oxidized region puts the shell under a
high tensile stress so the metallic bonds at the surface have sig-
nificantly weakened; in order to alleviate the tension, some struc-
tural defects are created in the cluster shell, in the form of large
square or even pentagonal “windows” through which additional
oxygen atoms might penetrate inside the cluster core. Opposite to
sodium clusters, however, the average Mg-Mg distance in the pure
cluster is about 3.1Å, the inner interstices are much smaller than
in sodium, and the oxygen atoms prefer to be adsorbed rather
than absorbed. Nevertheless, some oxygen atoms sit in an “in-
plane” position within the shell, i.e. they are at a borderline sep-
arating adsorption from absorption. Thus, although the scenario
is slightly more favorable due to steric factors, pure magnesium
does not seem able to restrain the oxide from eventually perco-
lating towards the interior of the metal, and it should be useless
as a corrosion-protecting coating as well. The whole scenario is
qualitatively identical in the equiatomic nanoalloy (x=10), which
suggests that all Mg-rich Zn-Mg alloys should be discarded in cor-
rosion protection applications, in agreement with the experimen-
tal observations.
The initial oxidation stage is qualitatively different in Zn20,
which is much more efficient in dissolving the oxide impurities. In
effect, the initial oxygen impurities adsorb at well separated sur-
face sites, and at the highest oxygen content (m=6) two separate
oxide islands have formed on the cluster surface. With an average
Zn-Zn distance of about 2.7Å, the oxidized region locally expands
instead of shrinking as in the Mg case. All of the oxygen atoms
get adsorbed at sites which are completely external to the metal
shell, and thus more separated from the cluster core in a natural
way because of purely steric factors. The number of structural
defects in the cluster shell is much smaller than in Mg or Mg-
rich clusters, suggesting that the tension stored in the metallic
bonds is not so high as in Mg-based materials. The square or pen-
tagonal defects are not only less abundant, but also significantly
less reactive, as they never become the preferred adsorption site,
while they were readily occupied by oxygen in Mg-rich alloys. In
fact, when an oxygen atom is adsorbed on top of a square de-
fect, the oxygen seals the aperture during optimization and ends
up bonded to only three Zn atoms, thus naturally preventing the
oxygen from approaching the cluster core. Thus, our calculations
provide support and theoretical interpretation for the experimen-
tal observations of Zn being better suited than Mg as a sacrificial
metal for corrosion protection applications.
Finally, the oxidation scenario is even better, and close to op-
timal, in Zn-rich nanoalloys. It is convenient to emphasize here
that the functional material in real applications is the fully oxi-
dized surface layer, i.e. it is the oxide crust formed on the surface
that provides protection against corroding agents; but during the
initial oxidation stages analyzed in this paper, it is the metal sur-
face that must protect the core until the oxide crust is fully formed
and, at the same time, it must strongly react with oxygen so that
the oxide crust forms as soon as possible. A small amount of Mg
added into Zn makes the initial oxidation reaction more exother-
mic (because oxygen atoms preferentially attach to Mg atoms),
without increasing significantly the volume of the subsurface in-
terstices or the average interatomic distances, both factors con-
tributing to a more efficient oxidation of just the cluster shell, as
the oxygen adatoms occupy clearly external positions. Addition-
ally, and as shown in our previous works 12,13 , Mg atoms tend to
segregate to the surface of ZnMg nanoalloys due to their bigger
atomic size, i.e. there is a slight Mg-enrichment of the shell in
the nanoalloys, and this is another factor favoring shell oxidation
Journal Name, [year], [vol.],
1–14 | 5
as compared to core oxidation. At the same time, the nanoal-
loys are maximally mixed on the cluster shell, so the number of
Mg-Mg bonds is minimized and the number of the strongest Mg-
Zn bonds is maximized. Therefore, at low Mg concentrations,
Mg atoms occupy well separated and highly-coordinated surface
sites. In the initial stages of oxidation, those Mg atoms in the
shell act as attractors that anchor the oxygen adatoms, creating
several nucleation centers evenly distributed across the cluster
surface. The initial growth of the oxide phase thus displays a
multi-center nature and evenly affects the whole surface, instead
of concentrating into a single local region of the surface. This is
expected to result in a much more uniform distribution of stress
across the metal surface. Finally, the Mg atoms guide the oxygen
atoms precisely towards those local regions in the surface that
contain the strongest Zn-Mg metallic bonds, which are expected
to be the most resistant ones at a structural level. Any square
or pentagonal defects in the shell occur in Zn-rich regions so the
Mg atoms also protect those defects from being attacked by oxy-
gen in the initial stages of oxidation. All of these properties seem
to conspire precisely to promote the growth of the oxide crust
whilst protecting the core, an example of a very positive synergy
between Zn and Mg for this particular application. As an exam-
ple, the optimal composition here seems to be x=17: for m=3
there is one oxygen close to each Mg atom in the shell, for m=6
two oxygen atoms bonded to each Mg. Thus it seems that the
three islands grow independently and at the same rate. The only
potential problem with this multi-center growth can occur during
the last stages of oxidation, not covered yet in the present study.
Some line defects might be generated at the interface where two
independent oxide islands meet. We will consider this problem in
future works, but for the time being our results suggest that some
mild annealing post-processing treatment of the material might
be beneficial for the microstructure of the oxide crust.
In what follows, we analyze several energetic, structural, and
electronic indicators to provide a more quantitative support for
our claims in the previous paragraphs. In Fig. 3 we plot the cu-
mulative adsorption energies, representing the energy gain upon
adsorption of moxygen atoms on the bare cluster, against the
number of metal-oxygen X-O bonds (with X=Mg or Zn). The
non-cumulative adsorption energies are separately shown in the
ESI. The number of bonds is ascertained by the existence of a
BCP in between two nuclei, as explained in the previous section.
A multivariate fitting on the whole set of data (as shown in the
upper part of the figure) shows that the average energy gain upon
formation of a Mg-O bond (1.17 eV/bond) is superior to the cor-
responding gain in the formation of a Zn-O bond (0.62 eV/bond).
This accounts for the observation that the atom with the high-
est f−value is not necessarily the best site for O adsorption in
these systems. A supplementary condition must be fulfilled re-
garding the local chemical environment, specifically it must con-
tain Mg atoms. Because of this preferential formation of Mg-O
bonds, the excess adsorption energies (not shown explicitly) are
positive for all nanoalloys (the curve for Zn15Mg5, for example, is
closer to the pure Mg curve than to the pure Zn curve in Fig. 3,
despite being a Zn-rich nanoalloy). Additionally, all of the cumu-
lative adsorption energies display a slightly positive curvature, so
Fig. 3 Cumulative adsorption energies as a function of the number of
metal-oxygen X-O bonds (X=Zn or Mg) for the pure clusters and some
representative nanoalloys. The discontinuous red lines are the result of a
multivariate fitting in terms of Zn-O, Mg-O and X-O bonds, performed on
the whole set of data as shown in the upper insert. The mean absolute
error (MAE) of the fit is also shown.
that oxygen adsorption becomes a more exothermic process the
larger the oxygen content (see Fig. S2 in the ESI), and the ox-
ide phase grows at an accelerated rate at least during its initial
growth stage. Therefore, the structural changes induced by oxy-
gen attachment weaken the metal-metal bonds and increase the
reactivity of the metallic part.
Notice that, despite the difference of energy gain in forming a
Mg-O bond with respect to a Zn-O bond, the average Mg-O and
Zn-O interatomic distances are very much the same, since for all
values of the oxygen content mboth bonds are measured at ≈
1.95 Å. Among the investigated metallic compositions, some of
them display almost equal Zn-O and Mg-O distances irrespective
of the number of adsorbed oxygen atoms, in particular Zn17Mg3
and Zn13Mg7. The similarity of these distances is consistent with
the systematic placement in hollow sites of the adsorbed oxygen
atoms, and with the fact that the larger atomic radius of Mg (≈
1.50 Å) as compared to Zn (≈1.35 Å) is compensated by the
stronger Mg-O interaction. The nearly constant metal-oxygen
distances can be contrasted with significant variations observed
in the Zn-Zn, Mg-Mg or Zn-Mg bond distances. As metal-oxide
bonds are approximately 5 times stiffer than metal-metal bonds,
the elastic deformation energy is dominantly stored in the metal
phase. The Zn-Mg skeleton of the nanoalloys is, therefore, with-
standing the deformation generated by the adsorption of oxygen
atoms.
Table 1 lists the number of Mg-O and Zn-O bonds for the whole
set of nanoalloys investigated, as these are not easily appreciated
from a visual inspection of Fig. 1. Once again we stress the fact
6 | 1–14
Journal Name, [year], [vol.],
that the number of bonds has been unambiguously determined
within the QTAIM theoretical approach instead of just counting
neighbors within a given cutoff distance. Table 1 confirms that
the oxygen atoms generally sit on positions where one O atom
is bonded to three atoms, but exceptions to this rule occur in
the pure Mg cluster and also in the Zn10Mg10 nanoalloy, where
some of the O atoms bind to four metal atoms. These exceptions
can only be explained by a more important surface reconstruction
upon oxygen adsorption, or a higher reactivity of square rings, in
Mg-rich nanoalloys, confirming our previous claims. Concerning
Zn-rich nanosystems, we observe some regularities for composi-
tions x=13 and x=17: in the Zn17Mg3nanoalloy, oxygen adsorp-
tion occurs on top of a MgZn2triangular hollow site as these are
the only Mg-containing facets at such a low Mg concentration;
in Zn13Mg7, however, the oxygen preferentially attach to Mg2Zn
triangles as long as they are available. In summary, these trends
demonstrate that oxygen atoms would fill the available hollow
triangular sites in the following order: Mg3, Mg2Zn, MgZn2and
finally Zn3triangles. As all the nanoalloys with x≥10 are well
mixed12, there are no Mg3facets naturally occurring on their
surfaces. Nevertheless, Table 1 shows that some oxygen atoms
attach to three Mg atoms for the x=10 composition, demonstrat-
ing that the presence of oxygen induces segregation of Mg atoms
towards a local region of the shell.
Fig. 4 displays the excess energy of the oxidized and non-
oxidized nanoalloys according to eq. 3. For oxygen-free alloys,
we know from previous works11 that x=10 is the most stable
composition, because it contains the largest possible number of
the strongest Zn-Mg metallic bonds. This figure now confirms
that alloying of the oxidized metals is a more exothermic process
than the alloying of the pure metals, and more so the larger the
oxygen content. The reason for this behavior is apparent from the
results in Fig. 3, that demonstrate a positive oxygen adsorption
excess energy: as compared to an ideal statistical mixture of the
oxidized metals (governed by Vegard’s law), the oxidized nanoal-
loy is much more stable because the number of the strongest Mg-
O bonds is larger than in the statistical mixture.
Fig. 4 Excess energy of ZnxMg20−xOmnanoalloys, for all different oxygen
contents.
In order to quantify the global structural changes undergone
by the metallic skeleton upon oxygen adsorption, we first analyze
the evolution of its volume and its shape as a function of oxygen
content. Fig. 5 displays the volume of the inertia ellipsoid and
the Hill-Wheeler asphericity parameter β43,44, which is obtained
from the principal moments of inertia I1≥I2≥I3(evaluated with
all the atomic masses set to unity) as:
Ik=2
3r21+βsin(γ+(4k−3)π
6),(6)
where r= (I1+I2+I3)/2is a measure of the average cluster ra-
dius. βquantifies the quadrupole shape deformation, and γ(not
shown explicitly) determines if that deformation is prolate or
oblate. The maximum value of βis 0.5 for oblate clusters and
1 for prolate clusters. Both indicators are calculated considering
only the metal atoms and excluding the oxygen atoms. Addi-
tionally, explicit results are shown only for Mg20 Omand Zn20Om
limits as all the nanoalloys present an intermediate behavior be-
tween these limits. One can notice that all clusters experience a
similar global volume expansion upon oxidation, that increases
as more and more oxygen atoms are added to the system. Metal
clusters are known to become more reactive when expanded45,
so the results in Fig. 5 provide an explanation for the acceler-
ated oxidation rate detected in Fig. 3. The global expansion is
somehow expected for Zn, because oxidation induces a signifi-
cant expansion of metal-metal bonds in the local region around
oxygen atoms, but it is more strange in Mg because in this case
the oxidized region locally shrinks. An additional conclusion from
Fig. 5 is that, while the pure clusters are very spherical at the
quadrupolar level, oxidation induces a shape deformation away
from sphericity, which is more marked in Mg-rich systems. This
last observation apparently confirms that Mg-based materials un-
dergo a more significant reconstruction upon oxidation, although
we emphasize that Fig. 5 only quantifies the global geometrical
response of the whole metallic skeleton: by including all metal
atoms, it misses relevant local information regarding the differ-
ent structural response of the oxidized and metallic parts of the
cluster.
In order to obtain a more detailed picture of the structural dis-
tortions induced by oxidation, we have partitioned the whole set
of metal atoms into two subsets: the first subset contains all metal
atoms not directly bonded to an oxygen atom. We call d0the
average metal-metal distance within this subset, which is repre-
sentative of the “metallic” part of the cluster; the second subset
contains all metal atoms bonded to oxygen atoms, so it is rep-
resentative of the metal oxide phase. Within this second subset,
we further differentiate between metal-metal bonds linked to a
single oxygen atom (whose average distance is called d1), and
metal-metal bonds linked to two oxygen atoms (whose average
distance is called d2). Notice that each metal-metal bond sep-
arates two neighboring hollow sites, so this classification is ex-
haustive, i.e. there are no metal-metal bonds with more than
two oxygen atoms attached. Finally, we define dint as the aver-
age length of the bonds formed between a metal atom in the first
subset and a metal atom in the second subset. This distance is
representative of the metal-oxide interface. These distances are
plotted in Fig. 6 for Mg20Omand Zn20 Omclusters, as a function of
Journal Name, [year], [vol.],
1–14 | 7
Table 1 Number of Zn-O and Mg-O bonds in ZnxMg20−xOm. The first number is for Mg-O the second for Zn-O
x/m 1 2 3 4 5 6
20 –/3 –/6 –/9 –/12 –/15 –/18
17 1/2 2/4 3/6 4/8 5/10 6/12
15 2/1 4/2 5/4 6/6 8/7 9/9
13 2/1 4/2 6/3 8/4 10/5 11/7
10 2/1 4/2 6/3 9/4 11/4 14/4
0 3/– 7/– 10/– 13/– 17/– 20/–
0 1 2 3 4 5 6
m
100
120
140
160
Volume (Å3)
Mg20Om
Zn20Om
1 2 3 4 5 6
m0
0.05
0.1
0.15
0.2
0.25
β (adimensional)
Fig. 5 The volume of the inertia ellipsoid (left panel) and the asphericity
parameter β(right panel) are displayed as a function of the oxygen con-
tent.
the total oxygen content. As happened with the previous figure,
the nanoalloys display an intermediate behavior between these
figures, so it is enough with displaying the pure limits to get the
whole qualitative picture.
A simple visual inspection of Fig. 6 already demonstrates that
Mg and Zn substrates respond in different ways to the oxida-
tion process, mostly due to the different size mismatch at the
metal-oxide interface, although there are also some similarities
between both systems. In order to attain equally optimal lengths
for the stronger metal-oxygen bonds, Mg-Mg bonds slightly con-
tract when put in contact with a single oxygen atom (see d1results
as a red line), while Zn-Zn bonds significantly expand. Therefore,
addition of a single oxygen atom induces a stronger stress on the
Zn skeleton compared to the Mg skeleton. However, for both sys-
tems d2is significantly shorter than d1, and this has interesting
consequences: as more oxygen atoms are added to the system,
the oxidation process accumulates a growing tensile stress in the
Mg skeleton (as d2distances are very much contracted as com-
pared to d0distances in Mg); meanwhile, for the Zn cluster, the
same oxidation process gradually releases most of the compres-
sive stress initially incurred (as d2is only slightly longer than
d0for the Zn substrate). In fact, it is interesting to notice that
d1values (around 3Å) and d2values (around 2.7Å) are similar
in both substrates, demonstrating that it is the metal that struc-
turally adapts to provide the optimal environment to the oxygen
atoms. To summarize, the oxidation induces a growing tensile
2.7
2.8
2.9
3
3.1
3.2
d(Mg-Mg) (Å)
0 1 2 3 4 5 6
m
2.4
2.5
2.6
2.7
2.8
2.9
3
d(Zn-Zn) (Å)
d0
d1
d2
dint
Fig. 6 Locally averaged Mg-Mg distances in Mg20Om(upper graph) and
Zn-Zn distances in Zn20Om(lower graph) are shown as a function of
the oxygen content. d0refers to metal-metal bonds in the non-oxidized
(metallic) part of the cluster, d1and d2to the same bonds but in the ox-
idized region of the cluster; finally dint are the metal-metal distances at
the metal-oxide interface. See the main text for more details. d0values in
the bulk limit are also shown (black arrows), to appreciate the degree of
bond length contraction at the nanoscale.
stress in the Mg substrate, a cumulative effect of an “exploding”
nature; while it induces a compressive stress in the Zn substrate,
which has a “self-healing” nature. Obviously, the Zn scenario is
more appealing for the goal of keeping the metal shell intact while
the oxide crust is growing, thus protecting the core.
It is also very interesting that both systems behave similarly
concerning their metallic part. In effect, the bond distances in
the metallic part of the clusters (d0) are hardly affected by the
oxidation process. The metal and oxide phases seem to be quite
independent from each other in their coexistence, and the metal
does not significantly respond to the imposed stress, irrespective
of its tensile or compressive nature. Therefore, it must be the
metal-oxide interface that concentrates the whole of the strain re-
sponse, and we have observed that this response is also of a very
different nature in Mg/MgO and Zn/ZnO interfaces. For Zn20Om
clusters, Fig. 6 shows that interfacial Zn-Zn bonds (dint ) are com-
pressed, and by a similar amount to the expansion observed in
d2. The elastic deformation energy is thus dominantly stored in
the interfacial bonds, which retain their integrity and sustain the
local expansion of the substrate in the oxide phase. On the con-
trary, the Mg/MgO interface is not able to sustain the much big-
ger tensile stress induced by oxidation, and it does not retain its
8 | 1–14
Journal Name, [year], [vol.],
integrity, i.e. we have checked that several Mg-Mg bonds are bro-
ken (or dissociated) in the interfacial region after addition of each
oxygen atom. The surviving bonds keep a short dint length, and
this is why we have decided not to plot them in Fig. 6, as they
are not representative of the observed phenomenon. The cluster
volume expands (as shown in Fig. 5) even if all the bond lengths
contract, simply because the structure becomes less compact be-
cause of a reduced number of Mg-Mg bonds. It is indeed expected
that bond breaking (which generates some of the open square or
pentagonal rings close to the interfacial region) is a mechanism
that can alleviate a sufficiently strong tensile stress by creating
structural defects in the substrate. This detailed picture confirms
that Mg-rich substrates are much more disrupted by the oxida-
tion process, and so are less capable of properly protecting the
core against oxygen attack.
It is now easy to understand why Zn-rich nanoalloys are opti-
mal for corrosion applications. In effect, the presence of Mg is
beneficial because of its higher reactivity with oxygen, but only in
small amounts as we have just demonstrated why Mg-rich mate-
rials are deleterious for corrosion protection. The Zn17Mg3clus-
ter shows optimal properties in this study: first, it has no Mg-Mg
bonds which are the most disruptive ones when two oxygen atoms
are attached to them; second, it has an average metal-metal bond
length slightly longer than in pure Zn20, so the compressive stress
at the interface will be even smaller than in pure Zn; moreover,
oxygen atoms are initially guided towards Zn-Mg bonds, which
are locally slightly longer (2.75-2.80Å) than Zn-Zn bonds, so that
oxygen attaches to Zn-Mg bonds at almost zero induced stress
cost. In summary, there is an optimal synergy that increases the
reactivity while reducing the induced stress at the same time.
The metal-metal shortest interatomic distances in the bulk limit
are also shown in Fig. 6. Both metals crystallize in an hcp struc-
ture, with d0values of (rounded off to the first decimal digit) 2.9Å
for Zn and 3.2Å for Mg. As expected, these are both longer than
in the small clusters considered in this work. The most important
comment is that employment of the bulk d0values (instead of the
cluster ones) would not fundamentally alter the main conclusions
of the paper, although it is interesting to observe that the purely
steric factors are size dependent, as they depend of the specific
d0reference values. If we make the sensible assumption that the
optimal metal-oxygen bond lengths are roughly size-independent
(this is in fact expected as the metal-oxygen interaction is the
strongest one in these systems), we can use our results to further
discuss the expected size effect on corrosion protection proper-
ties. With a longer d0, bulk Mg would sustain even a stronger
tensile stress upon oxidation than Mg nanoparticles do, i.e. bulk
Mg would be expected to be even worse than nanoscale Mg for
corrosion protecting applications. Meanwhile, bulk Zn would re-
main approximately at the same quantitative stress level than our
studied nanoparticle, but the stress would have a different sign: it
would be slightly tensile in the bulk crystal, as opposed to slightly
compressive in Zn20. This reasoning suggests that the cluster size
is an important extra parameter to fine-tune the corrosion protec-
tion properties of nanoparticles, as expected indeed of any cluster
study where size does matter. Pure Zn nanoparticles of bigger size
than here studied, and with d0≈2.75Å will undergo no distortion
upon oxidation, as for them d0≈d2. This would also happen for
Zn-rich Zn-Mg nanoalloys at some optimal size.
3.2 Analysis of electronic properties
Now that we have exhausted the purely structural analysis, let’s
consider what else can be learnt about the corrosion protecting
features from the analysis of electronic indicators. What makes
Mg and Zn clusters so different, and what makes a certain com-
position of those elements particularly suitable in the context of
optimal coating properties as regards the formation of the surface
oxide? It is the aim of the following discussion to provide hints at
possible answers for these questions.
Fig. 7 displays the atom condensed Fukui function f−averaged
over all the atoms of each chemical element and discriminating
the central (or core) atom from the surface atoms. Several strik-
ing features are evident at first sight. The Fukui function of oxy-
gen atoms is smaller than that of Zn and Mg surface atoms, and
of the same order as that of the core atom. This means that, in
principle, an attacking oxygen atom should not sit in the vicinity
of an already adsorbed oxygen atom. In effect, we do not observe
any O-O bond, although oxygen atoms can sit relatively close to
each other, for example when on the surface of the pure Mg clus-
ter. Obviously, the Fukui function can not anticipate the structure
relaxation that occurs after oxygen adsorption as it is an indicator
calculated on the fixed geometry of the cluster before the oxy-
gen atom is adsorbed, and this is why it was used just to provide
some guide but not to completely determine the structural search.
Coming back to the central atom, the very weak reported f−val-
ues indicate that upon electron capture, only a very slight change
of the charge takes place at the core atom; the charge variation
occurs mainly at the surface of the oxidized or non oxidized clus-
ters. The central atom is expected to be the least reactive atom.
This is quite noteworthy in the case of the Zn17Mg3nanoalloy.
In fact, whatever the oxygen content, the electrophilic f−Fukui
function of the central atom lies below the f−of the oxygen atoms
for this sole stoichiometry (middle right panel of Fig. 7). Finally,
this figure shows that the behavior of the electrophilic f−Fukui
functions of the Zn and Mg surface atoms is at odds. Indeed, for
x=10,13,15 and 17, the f−of Zn atoms is almost constant while
the f−of Mg are either decreasing or presenting a descending
oscillation. This last trend underlines the effect of the progressive
oxidation, that affects more the Mg atoms environment.
Fig. 8 displays, in its top part, the positions of the BCPs with
respect to the atomic sites for both the bare nanoalloy with x=17,
and the same nanoalloy with the maximum number of O atoms
attached. The BCPs, plotted as small green balls identify the dif-
ferent bonds. In all the composition range Zn-Zn, Mg-Mg, Zn-
Mg, Zn-O and Mg-O bonds are detected. All these bonds can be
classified according to a scheme proposed by Matta32 and their
average values (for all the composition range) are listed in Ta-
ble 2. Zn-O bonds have a ρbvalue that amounts to 0.09 a.u.,
with a positive Laplacian and a ratio of the potential energy to
the kinetic energy close to 1.0; Hbis also small and negative.
All these features point towards a dative bond, a special kind of
two-center, two-electron ionocovalent bond where the two shared
Journal Name, [year], [vol.],
1–14 | 9
Fig. 7 Atom condensed f−Fukui functions of ZnxMg20−xOmnanoalloys.
Blue, red and green circles stand for the average value of f−for Mg, Zn
and O surface atoms, respectively. f−values for the central atom is also
sketched as square symbols.
electrons are mainly contributed by one of the atoms, Zn in this
case. The Mg-O bonds (ρb≈0.05 a.u) have many features in com-
mon with the Zn-O bonds, except for a positive Hb, which char-
acterizes this bond as ionic. The bottom panels of Fig. 8 display
a representative ELF isosurface (at η=0.8) for the Zn20O6and
Mg20O6clusters. The different nature of Zn-O and Mg-O bonds
is also appreciated in the ELF scalar field. In fact, the absence of
V(Mg,O) disynaptic basins is an evidence of the ionic character
of the bonding, whereas the presence of V(Zn,O) basins close to
the O atoms is typical of a dative bonding interaction. V(Zn,O)
basins are detected with a population of about 0.8 electrons of
which the analysis of the atomic contribution indicates that 0.7
electrons are contributed by the oxygen atom. This last number
is in agreement with the traditional picture of the dative bonds
between a transition metal (TM) atom and oxygen, that is de-
scribed by a σdonation of the TM atom and a πback donation
of the oxygen atom. Here the πcontribution is due to the oxygen
atom and the σcontribution to the TM element. The ionocova-
lent picture of the bond is then illustrated in Fig. 8 with two gray
and pink concentric spheres around the O atoms for the Zn20O6
structure (being the ionic nature of the bonding more intense),
while the pure ionic bonding in Mg20O6is depicted with single
pink spheres around the O atoms.
Prior to entering into the details of the Zn-Zn, Mg-Mg and Zn-
Mg bonding interactions, we note that their ρb≈0.025 a.u. values
are at least twice smaller than in the Zn-O and Mg-O bonds. This
observation can be connected to the trends discussed above for
the interatomic distances and their evolution throughout the ox-
Mg20 Zn20
h=0.8
Zn17Mg3Zn17Mg3+6O
Mg20+6O Zn20+6O
Fig. 8 BCPs and ELF isosurfaces for selected structures of ZnMg
nanoalloys. The top part displays the BCPs as small light green balls
whereas Zn, Mg and O atoms are shown with grey, dark green and red
balls, respectively. Middle and low panels illustrate the ELF isosurface
at ELF=0.8 for both the pure Mg and Zn clusters, and the same clus-
ters oxidized with 6 O atoms. Gray, pink and blue isosurfaces stand for
polysynaptic, monosynaptic and core basins, respectively. The small red
spheres in the ELF are the oxygen atoms.
idation process. The Zn-Zn bonds belong to a third category of
bonding, the metallic bonding. In fact, small values of ρbare
obtained and the rest of features also correspond to a metallic
bonding, since Hband ∇2ρbare slightly negative. The Mg-Mg
bonds should be termed as metallic in spite of a negative ∇2ρb
at -0.0006 a.u. It should be noted that very few data for ∇2ρb
are available for bulk metals and they are reported at 0.0002 and
-0.0046 a.u. for Na(bcc) and Al(fcc), respectively. The weakness
of the Laplacian is assumed to be a signature of metallicity rather
than its sign46.
To better capture the differences in the nature of Mg-Mg and
Zn-Zn bonds, the ELF has been plotted also for the bare Mg20 and
Zn20 clusters (middle panels in Fig. 8). Surprisingly, there are
no polysynaptic basins in the Zn cluster, whereas almost exactly
the opposite happens in the Mg cluster. In fact, for Zn20 , the ELF
depicts an assembly of monosynaptic basins for every Zn atom,
an exception being the central one where all the charge is accu-
mulated in a single core basin. Each monosynaptic valence basin
has its attractor located on top of a Zn surface atom at an average
10 | 1–14
Journal Name, [year], [vol.],
Table 2 Average values of the electronic density, its Laplacian, as well
as the energy and the ratio of the potential energy to the kinetic energy at
the BCPs for all the composition range. See the section of Computational
details for the units. For X-Y bonds with X and Y being Mg or Zn, two
values are given. The first one is related to X-Y bonds between two
atoms at the surface. The second number is for a X-Y bond between a
central atom (X) and a surface atom (Y)
ρb∇2ρbHbVb
Gb
Zn-Zn 0.03/0.015 0.08/ 0.03 -0.003/-0.001 1.2/1.0
Mg-Mg 0.02/0.02 -0.006/-0.002 -0.003/-0.003 2.7/2.1
Zn-Mg 0.027/0.026 0.03/ -0.007 -0.006/-0.007 1.4/2.3
Zn-O 0.09 0.4 -0.015 1.1
Mg-O 0.05 0.4 0.01 0.9
distance of 1.9Å. By contrast, for Mg20, polysynaptic basins are
mostly observed between pairs of Mg atoms, except for the three
apical atoms which sustain monosynaptic basins as well. The data
listed in Table 3 show that the electronic population of the core
basin associated to the Zn central atom is 30 electrons, which is
exactly the electronic population of an isolated Zn atom. This
observation suggests that the central Zn atom is isolated from the
surface in practical terms. This last point is in line with a previous
analysis of the isolation of the core of Zn clusters with respect to
their surface47. Opposite to this behavior, the Mg central atom
is connected to the surface atoms by as many as 5 polysynap-
tic basins. Turning now our attention to the surface atoms, the
ELF of the Mg clusters exhibits di- and trisynaptic valence basins,
with electronic populations comprised between 0.5 and 2.0 elec-
trons and a large variance of the populations that ranges between
0.4 and 1.4 electrons, suggesting a high degree of electron de-
localization. By comparison, an average value of 2.0 electrons is
computed in the V(Zn) monosynaptic basins with an average pop-
ulation variance of 1.4 electrons. Hence, for both pure clusters,
a large variance is reported for the valence basin populations;
additionally, in Zn20 , each monosynaptic valence basin shares a
boundary with the monosynaptic valence basins of neighboring
Zn atoms, thus forming a connectivity network that percolates the
whole cluster surface pointing to a high degree of electron delo-
calization. Therefore, both Zn20 and Mg20 have a metallic charac-
ter at their surface but with a marked difference in the nature of
that metallicity, as the electron localization attractors are located
at very different positions. The exotic type of metallicity observed
in Zn clusters can be ascribed to its peculiar sp−hybridization pat-
tern, that was analyzed in a previous work47: there, we observed
that the 4p−orbital pointing along the radial direction was com-
pletely unoccupied for each surface atom, producing something
similar to a sp2hybridization mechanism along the directions tan-
gential to the cluster surface. The delocalization associated with
this hybridization occurs exclusively along this tangential direc-
tion, explaining why the monosynaptic valence basins of the ELF
field are only tangentially connected and why the localization at-
tractors occur along the radial direction. Finally, the character-
ization of the Zn-Mg bond must be addressed; at the surface it
resembles that of the Zn-Zn metallic bond, whereas for a Zn cen-
tral atom connected to a surface Mg atom, the bond is like the
Mg-Mg metallic bond. The data reported in the column ∇2ρbof
Table 2 confirms the above assessments.
Having discussed the nature of the reported bonds, it is valu-
able to investigate how the bonding around the central atom de-
pends on the composition of the nanoalloy. In fact, a good pro-
tective layer should isolate the core from the surface, and one
expects that the best coating conditions are met when the inter-
actions between the surface and the core regions are kept mini-
mal even after the corrosion process has started. In this respect,
Table 3 is not only interesting as far as the two pure metals are
concerned. As soon as a small amount of Mg is added to a Zn
cluster (x=17), the core basin population of the central atom
drops rapidly but without implying connections to the surface of
the cluster since no polysynaptic basins are identified involving
the central atom. The addition of more Mg atoms (x=10,13,15)
results in a stronger interaction between the central atom and the
surface, but it is mainly an interaction of the central Zn atom with
other Zn atoms. Note that the interaction of the central Zn atom
with Mg atom at the surface is kept at a low value with even can-
cellation for the x=13 composition. This feature reinforces the
fact that x=17 and x=13 stoichiometries, close to the Mg2Zn11
and MgZn2compositions, are the best candidates to optimize the
protection against corrosion in Zn-Mg alloys, in agreement with
the experimental observations.
In addition to the previous analysis, the bare ZnxMg20−xand
the 6 O atoms loaded nanoalloys have been analyzed within the
framework of QTAIM. The data are summarized in Table 4. Let
us start the analysis with the Mg20 cluster. The central Mg atom
interacts with the Mg surface atoms exactly in the same manner
as two Mg atoms at the surface do (see line Mg-Mg in Table 2).
The oxidation with 6 O atoms on the surface gives way to an in-
crease of interaction of the Mg central atom with the Mg surface
atoms for the x=0(Mg20) stoichiometry. In contrast, for the pure
Zn stoichiometry, and if the standard deviation is included, the
ρbvalues remains roughly constant despite oxidation. Overall,
the interaction drops between the central and the surface atoms,
however the large standard deviation after 6 O atoms oxidation
suggests that locally there is a connection to the surface of the
cluster. Two noticeable trends are observed in Zn-rich nanoal-
loys. For the x=13 stoichiometry, the Zn-Zn core-shell interac-
tion falls down but the single Zn-Mg interaction increases. For
the x=17 stoichiometry, both the Zn-Zn and Zn-Mg core-shell
interactions drop. Interestingly, the higher degree of isolation of
the core from the surface takes place for x=13 and x=17. The
x=17 stoichiometry was found above to be characterized by the
lowest f−Fukui function on the central atom. There is an overall
agreement between the data provided by the different geometri-
cal and electronic descriptors throughout this work. This supports
the idea that nanoalloys close in composition to Mg2Zn11 have op-
timal properties to act as protective coating. Finally, it is worth
stating that for all the 42 structures investigated, no direct inter-
action between the central atom and an oxygen atom has been
found. In fact, neither a BCP nor a disynaptic basin of the ELF
appears between the central atom and an attacking O atom.
4 Conclusions
We conducted a comprehensive ab-initio study of the initial oxida-
tion stages in ZnxMg20−xnanoalloys with different compositions
Journal Name, [year], [vol.],
1–14 | 11
Table 3 Number (N) and populations (Pop) of ELF basins for the ZnxMg20−xnanoalloys. XCdenotes the central atom, and XAand XBother atoms.
Populations are given as a number of electrons. In parenthesis, we show the population of a disynaptic valence basin involving the XCatom and a Mg
surface atom
Mg20 Zn20 Zn17Mg3Zn15 Mg5Zn13Mg7Zn10 Mg10
N(V(X)) 3 19 16 13 11 8
N(V(XA, XB)) 36 0 21 27 35 36
N(V(XC, XA/B)) 5 0 0 16 9 8
Pop(C(XC)) 10.0 30.0 27.7 27.8 27.6 27.6
Pop(∑V(XC, ...)) (3.78) 0 0 7.92(0.68) 9.68(0.00) 12.25(0.76)
Table 4 Average value of the electronic density at the BCPs connecting the central atom to surface atoms. First two rows are for the bare cluster, and
last two for the oxidized nanoalloys with 6 oxygen atoms. Within the set of two rows, the first row corresponds to the connection to a surface Zn atom
and the second one to the connection with a Mg surface atom Standard deviations are given in parenthesis when more than one value was available
ZnxMg20−xx=20 x=17 x=15 x=13 x=10 x=0
central atom Zn Zn Zn Zn Zn Mg
ρb0.024(3) 0.024(3) 0.026(3) 0.027(1) 0.025(2)
pristine 0.0253(1) 0.0209(5) 0.0198 0.0200 0.0154(2)
ρb0.019(7) 0.015(2) 0.023(5) 0.019(4) 0.022(3)
6 O atoms 0.0134 0.0261 0.0217 0.020(1) 0.0179(4)
(x=0,10,13,15,17,20), with the goal of understanding why the
Zn-Mg mixtures in the Zn-rich side of the phase diagram are op-
timal as anticorrosive coatings. We focused on the formation of
the sacrificial surface oxide layer, which constitutes the first step
in the corrosion process, and whose characteristics will condition
the next stages. These nanoalloys are model systems to simulate
the local environments and related complex processes that occur
in extended granular surface coatings.
The results were analyzed from different perspectives, includ-
ing structural, energetic and electronic indicators, which allowed
us to characterize: (a) the local atomic and chemical environ-
ments, both in a local neighborhood around the oxygen attack
site and in the oxygen-free metallic part; (b) the subtle interplay
between the selective reactivity of different parts of the system
and the resulting structural rearrangements induced by oxida-
tion, with particular interest in the degree of protection of the
core region provided by the oxygen crust; and (c) the different
bonding patterns and how they reveal an electronic redistribu-
tion that might be optimal in certain cases for protecting the core
from the attack of other radicals in the presence of the already
formed surface oxide crust.
We found that oxygen adsorption becomes a more exothermic
process the larger the oxygen content, so that the oxide phase
grows at an accelerated rate at least during its initial growth
stage. At low Mg concentrations, Mg atoms occupy well sepa-
rated and highly-coordinated surface sites. In the initial stages
of oxidation, those Mg atoms in the shell act as attractors that
anchor the oxygen adatoms, creating several nucleation centers
evenly distributed across the cluster surface. The Mg atoms guide
the oxygen atoms precisely towards those local regions in the sur-
face that contain the strongest Zn-Mg metallic bonds, which are
the most resistant ones at a structural level, as a consequence of
which Mg atoms also protect surface defects from being attacked
by oxygen in the initial stages of oxidation. All these proper-
ties conspire precisely to promote the growth of the oxide crust
whilst protecting the core, an example of a very positive synergy
between Zn and Mg for this particular application.
As metal-oxide bonds are approximately 5 times stiffer than
metal-metal bonds, it is mainly the metallic region close to the
metal-oxide interface the one that deforms in response to the
stress incurred upon oxidation. The Zn17 Mg3composition shows
optimal properties in this study: first, it has no Mg-Mg bonds
which are the most disruptive ones upon oxygen adsorption; sec-
ond, it has an average metal-metal bond length optimal to mini-
mize the compressive stress at the interface between the oxidized
part and the metallic part of the system; moreover, oxygen atoms
are initially guided towards Zn-Mg bonds at almost zero induced
stress cost. We have also discussed the expected cluster size de-
pendence of the induced local deformation and stress, suggesting
that there exist optimal sizes for which the induced stress is min-
imal.
The electronic indicators show that as soon as a small amount
of Mg is added to a Zn cluster, the atom at the core becomes
the least reactive atom in the system and is disconnected from
the surface in practical terms. Further addition of Mg within the
Zn-rich side of the phase diagram results in a stronger interac-
tion between the central atom and the surface, but it is mainly
an interaction of the central Zn atom with other Zn atoms while
the interaction of the central Zn atom with Mg atoms at the sur-
face remains very weak. These features reinforce the conclusion
that x=17 and x=13 stoichiometries, close to the Mg2Zn11 and
MgZn2compositions respectively, are the best candidates to opti-
mize the protection against corrosion in Zn-Mg alloys, in agree-
ment with the experimental observations. We strongly believe
that our results will serve to better guide the design of specific
protective coatings based on Zn and Mg. The present work could
be extended along several lines. One of them would be to con-
sider larger nanoalloys with a bigger core, and to analyze the
structural and electronic properties of the fully oxidized crust.
Further studies should also focus on the response of the oxidized
Zn-Mg nanoalloys to the attack of chloride ions, of prime impor-
tance to understand the resistance to corrosion in an oceanic at-
mosphere, but also quite relevant in the domain of biomedical
materials where Zn-Mg alloys are used to manufacture orthopedic
12 | 1–14
Journal Name, [year], [vol.],
prosthesis. These lines will be pursued in our long-term project
devoted to unveiling the fundamental aspects that trigger the op-
timal anticorrosive properties of Zn-Mg coatings.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
The financial support of the Spanish Ministry of Economy and
Competitiveness (Grant PGC2018-093745-B-I00) is gratefully ac-
knowledged. Facilities provided by the Pole de Calcul Intensif
pour la Mer (DATARMOR, Brest) are also acknowledged.
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