Khomotso P Maenetja1, Phuti E Ngoepe1. 1. Materials Modelling Centre, University of Limpopo Private Bag X1106, Sovenga, 0727, South Africa.
Abstract
Metal-air batteries have attracted extensive research interest owing to their high theoretical energy density. However, most of the previous studies have been limited by applying pure oxygen in the cathode, without taking into consideration the effect of the catalyst, which plays a significant role in the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Adsorption of oxygen on (110) Na-MO2 is investigated, using density functional theory (DFT) calculations, which is important in the discharging and charging of Na-air batteries. Adsorption of oxygen on Na/MO2 was investigated, and it was observed that the catalysts encourage the formation of the discharge product reported in the literature, i.e., NaO2. The surface NaO2 appears to have bond lengths comparable to those reported for monomer NaO2.
Metal-air batteries have attracted extensive research interest owing to their high theoretical energy density. However, most of the previous studies have been limited by applying pure oxygen in the cathode, without taking into consideration the effect of the catalyst, which plays a significant role in the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Adsorption of oxygen on (110) Na-MO2 is investigated, using density functional theory (DFT) calculations, which is important in the discharging and charging of Na-air batteries. Adsorption of oxygen on Na/MO2 was investigated, and it was observed that the catalysts encourage the formation of the discharge product reported in the literature, i.e., NaO2. The surface NaO2 appears to have bond lengths comparable to those reported for monomer NaO2.
Metal-air batteries are
ideal for applications where weight is
a major consideration. Since oxygen is not stored in the battery,
the cathode is much lighter compared to that of a lithium-ion battery.
The metal-air battery has the potential of providing energy densities
up to three times that of conventional lithium-ion batteries found
in electronics devices, not to mention the incoming wave of electric
vehicles.[1] It is well-known that Na-air
has a lower energy density compared to Li-air batteries;[2−4] thus, we look at the effect of a catalyst in the formation of NaO2. Lithium oxygen batteries have a theoretical gravimetric
energy density of 3456 Wh kg–1, assuming lithium
peroxide (Li2O2) as the stable discharge product.[5] The theoretical gravimetric energy density of
sodium oxygen (Na-O2) batteries depends on the assumed
discharge product and is 1605 Wh kg–1 or 1105 Wh
kg–1 for sodium peroxide (Na2O2) or sodium superoxide (NaO2), respectively. The attention
given to sodium-air batteries is due to their high theoretical energy
density but also because sodium is an abundant resource.[6] The known discharge products in Na-air batteries
are shown in the following equations:Conversely,
in a Na-air, the formation of
the discharge products NaO2 and Na2O2 competes due to the equilibrium potentials of 2.27 and 2.33 V, respectively
shown in eqs and 2. Importantly, Kang et al. concluded from computation
that Na2O2 is more stable in the bulk phase,
whereas NaO2 is more stable at the nanoscale.[7] Although both the peroxide[8,9] and
superoxide[10,11] have been reported as the discharge
products of a Na-O2 battery, which discharge product is
favored is still not understood. The formation of NaO2 may
be kinetically preferred due to the requirement of only a one-electron
transfer compared to two electrons for Na2O2.In the absence of an oxygen evolution reaction catalyst,
sodium-air
batteries have a cycle life of 80 cycles; after an alloy catalyst
was applied, the charge potential showed a decrease from over 4.0
V to below 2.7 V, resulting in an improved energy efficiency. The
cells are cycled based on the reversible formation and decomposition
of the discharge product, Na2O2·2H2O. This is an improvement toward real applications in the
field of energy storage of metal-air batteries. The oxygen crossover
effect is largely suppressed by replacing the oxygen with air, whereas
the dense solid electrolyte interphase formed on the sodium anode
further prolongs the cycle life. The increased charge overpotential
is likely due to the accumulation of side products on the air electrode
to cover the active sites of the catalyst.[12]Among transition metal oxides, manganese dioxide has been
widely
investigated as the catalyst in nonaqueous metal–oxygen batteries,
mainly due to its environmental friendliness and easy preparation.[13−15] A question has always been posed as to why MnO2 is a
preferred metal oxide (TiO2 and VO2) catalyst
in metal-air batteries. To elucidate and gain a better comprehension
of this observation, it is necessary to unravel how such a compound,
together with other related metal oxides, plays a role in the promotion
or inhibition of the growth of dominant discharge products Li2O2 or LiO2 in Li-air batteries, or NaO2 and Na2O2 in Na-air batteries, for
example.Adsorption of oxygen on sodium-adsorbed surfaces was
carried out
where oxygen atoms were placed in a bulk-like composition, and oxygen
molecules were placed in a peroxo form on Na-MO2. Coadsorption
of oxygen was performed in order to simulate the discharge cycle of
the metal-air battery whereby oxygen molecules from the atmosphere
combine with Na from the anode to form discharge products of Na-air
batteries.Comparison between the metal oxides was investigated
in order to
validate which of the metal oxides make a better catalyst based on
the discharge products’ stability and formation, and whether
the catalyst encourages formation of the products or not.
Results
Oxygen Adsorption on MO2 Surfaces
To discuss the redox properties of MO2’s (110)
surface, we calculated the adsorption energies of various stoichiometries.
We only took into account variations in the oxygen content (the number
of M atoms is fixed). If we stick to bulk-like oxygen positions, there
are five possible values of = 0 (stoichiometric surface), = 1 and
2. Total oxidation refers to the addition of a full layer of oxygen
ions generating manganyl-like, titanyl ,and vanadyl terminations on
top of the previously unsaturated M sites. “Mono-peroxo”
and “bridging-peroxo” modes of O2 adsorption[16] are shown in Figure .
Figure 1
MO2 (110) (a) MnO2, (b)
TiO2,
and (c) VO2 with different amounts of surface oxygen. Γ
= 1 and 2 are the partially and totally oxidized surfaces; the bridging
and mononuclear peroxo compositions.
MO2 (110) (a) MnO2, (b)
TiO2,
and (c) VO2 with different amounts of surface oxygen. Γ
= 1 and 2 are the partially and totally oxidized surfaces; the bridging
and mononuclear peroxo compositions.The oxygen adsorption energies for MnO2 have been discussed
previously discussed in detail[16] together
with those on the VO2 (110) surface.[17] The adsorption energy of an oxygen atom on a five-fold
coordinated Ti site (where Γ = 1) yielded 2.41 eV. When compared
to other configurations, the configuration with Γ = 2 has more
electron transfer from the titanium atom to the adatom.The
calculated adsorption energy obtained in this configuration
is 0.69 eV and implies that oxidation of the surface has undergone
an endothermic process; hence, it is thermodynamically unfavorable.
We further adsorbed oxygen as bridging-peroxo unit (O22–), split between two Ti surface cations, which requires
the least charge transfer per Ti cation of all oxidation possibilities.
The mononuclear configuration gives the adsorption energy of 0.070
eV, and the bridging configuration gives 0.37 eV; these values show
that the processes are endothermic, which implies a nonspontaneous
process shown in Table . The mononuclear configuration is energetically most stable configurations
where the oxygen molecule is adsorbed in different orientations. The
adsorption energies shown in Table reveal that VO2 adsorbs oxygen strongly[17] both in the form of an atom or molecule.
Table 1
Adsorption Energies with Different
Amounts of Oxygen Adsorbed Surfaces of MO2
number of oxygens and configuration
MnO2 Ads energy (eV)[16]
TiO2 Ads energy (eV)
VO2Ads energy (eV)[17]
Γ= 1
1.36
2.41
–2.10
Γ = 2
1.16
0.67
–1.56
bridging
–1.56
0.37
–3.28
mononuclear
–0.02
–0.07
–3.30
Adsorption
of Oxygen on Na/MO2 (110)
Surface
We then interrogated the impact of MnO2, TiO2, and VO2 catalysts on the formation
of NaO2 and Na2O2, during the cycling
of Na-air batteries. Figure shows structures of possible discharge products and their
related O–O separations, i.e., bulk NaO2 in pyrite
(1.34 Å), marcasite (1.28 Å), Fm3̅m polymorphs, and the corresponding NaO2 monomer
(1.43 Å). Moreover, the bond lengths of O–O in the bulk
(1.49 Å) and monomer (1.56 Å) Na2O2 are depicted. A variety of oxygen adsorption configurations have
been investigated, with some assuming molecular bonding and others
assuming dissociative adsorption. Figure depicts four different stable configurations
that have been discovered.
Figure 2
Structures of NaO2 (a–d) pyrite,
marcasite, Fm3̅m, and a monomer,
respectively,
and structures of Na2O2; (e, f) P6̅2m and its monomer respectively showing
the relaxed O–O distances.[18]
Figure 3
(i–iv) Various configurations that can be adopted
by Na–O2 peroxos when oxygen is adsorbed on different
sodiated metal
oxide surfaces.
Structures of NaO2 (a–d) pyrite,
marcasite, Fm3̅m, and a monomer,
respectively,
and structures of Na2O2; (e, f) P6̅2m and its monomer respectively showing
the relaxed O–O distances.[18](i–iv) Various configurations that can be adopted
by Na–O2 peroxos when oxygen is adsorbed on different
sodiated metal
oxide surfaces.The first considered configuration
is where one oxygen atom is
directly located on top of each Na as a stationary point, which is
in fact unstable, since this arrangement subsequently relaxes (if
the symmetry of the initial configuration is broken) to a peroxo where
two oxygen atoms are bonded to one Na atom, as shown in Figure (i). In the superoxide configuration,
the oxygen adsorption energy is −2.18 eV/O2, −3.94
eV/O2, and −5.33 eV/O2 for metal oxides
surfaces shown in Figure . The resulting bond length of 1.29 Å for the O–O
associated with the MnO2 catalyst is consistent with those
of the bulk marcasite phase of NaO2. Furthermore, this
configuration is the most stable for all MnO2-based catalysts.
For NaO2, the bond length of 1.44 Å (O–O) induced
by the TiO2 catalyst is consistent with that of the NaO2 (1.43 Å) monomer and is the second most stable configuration
for TiO2. However, the bond length of (O–O) in NaO2 where VO2 is the supporting catalyst compares
well with the bond length (O–O) in the pyrite form of NaO2, which is 1.34 Å, and it is the least stable configuration.The Na-peroxo adsorption configuration is not the only stable peroxo
adsorption configuration: a peroxo group perpendicular to the surface
and binding to Na on one end and to M on the other end, as in Figure (ii) (Eads = −1.55 eV/O2, −3.40 eV/O2, −5.96 eV/O2 for the metal oxides as they
are shown in Figure ), are stable. In the case of MnO2 and TiO2 catalysts such configuration is least stable, whereas for VO2 it is the most stable arrangement. The molecular form of
oxygen is maintained with a bond length ranging from 1.40 to 1.44
Å, which is comparable to the O–O bond length of 1.43
Å in the NaO2 monomer. The length of such a bond is
likewise closer to that of the bulk Na2O2, namely,
1.49 Å.Another configuration occurs when locating oxygens
above two previously
unsaturated M cations, as in Figure (iii). Upon relaxation, the oxygens remain separated
with bond lengths ranging from 2.55 to 3.07 Å, mainly suggesting
a dissociated configuration, which is, however, stable as shown by
the adsorption energies (Eads= −1.91
eV/O2, −4.98 eV/O2, −5.68 eV/O2 for MnO2, TiO2, and VO2 respectively).
The configurations in Figure (iii) are the second most stable for MnO2 and VO2, but for TiO2, it is the most stable. Figure (iv) shows an additional
stable dissociative configuration with an oxygen atom on the “bulk-like”
positions on top of each of the M cations but with additional bonds
formed with the Na adatoms, as in Figure (iv) (Eads =
−1.73 eV/O2, −3.62 eV/O2 and −5.96
eV/O2). In general, it is the second least stable configuration
in Figure . Large
O–O separations ranging from 2.93 to 3.09 across all metal
oxides further confirm the dissociation.There is no trend in
terms of the most stable surface; for MnO2, the most stable
configuration is the peroxo group on sodium,
which clearly shows or encourages the formation of NaO2. The most stable configuration for the adsorption of oxygen on the
Na-TiO2 is the configuration with the peroxo on Ti, while
the most stable configuration for the adsorption of oxygen on Na-VO2 is the configuration with peroxo on the surface V and adsorbed
Na. The adsorption energy for oxygen adsorption on Na-MO2 is negative, indicating an exothermic reaction that does not require
energy to occur and is therefore spontaneous.The dissociated
and peroxo on Ti/Na are the least stable configurations
relative to other configurations but still stable compared to pure
TiO2 surface which depicts similar tendencies as MnO2.Oxidation on Na/VO2 is also stable relative
to the Na
free surface that is shown in Figure , which extends to −1 eV and which is 0.9 eV
below the threshold of the Na free surfaces. According to the order
of the plots, it is observed that the most stable configuration is
the peroxo on V/Na followed by the dissociated’, whereas the
superoxide and the dissociated are the least stable configurations.
Figure 5
Surface free energies
of the oxygen coadsorbed on Na/TiO2 (110) surfaces with
respect to Na/MnO2 (without oxygen
on the surface).
All plots for different compositions (Figures , 5, and 6) appear to be most stable in
all three metal oxides because the relative surface free energies
are negative with a very slight increase in the oxygen chemical potential.
The order of stability on the plots is in agreement with the calculated
adsorption energies of the oxygen adsorption on Na-MO2.
Figure 4
Surface
free energies of the oxygen coadsorbed on Na/MnO2 (110)
surfaces with respect to Na/MnO2 (without oxygen
on the surface).
Figure 6
Surface free energies
of the oxygen coadsorbed on Na/VO2 (110) surfaces with
respect to Na/MnO2 (without oxygen
on the surface).
Surface
free energies of the oxygen coadsorbed on Na/MnO2 (110)
surfaces with respect to Na/MnO2 (without oxygen
on the surface).Surface free energies
of the oxygen coadsorbed on Na/TiO2 (110) surfaces with
respect to Na/MnO2 (without oxygen
on the surface).Surface free energies
of the oxygen coadsorbed on Na/VO2 (110) surfaces with
respect to Na/MnO2 (without oxygen
on the surface).
Discussion
Effect of Metal Oxide Catalysts in the Cathode
Reaction in a Na-Air Battery
Na-air batteries have emerged
parallel to the study of Li-air batteries as an alternative, based
on the substitution of lithium by sodium, in spite of their lower
theoretical energy density, which can exhibit better reversibility
and much lower overpotentials compared to lithium-based cells.[19,20] During the battery discharge process, molecular oxygen is reduced
in the cathode, in the presence of Na cations and electrons, forming
sodium superoxide (NaO2) particles:This is subsequently decomposed upon
charging
in the reverse reaction (Na+ + O2 + e– ↔ NaO2). Other less prevalent discharge products
such as sodium peroxide (Na2O2) and peroxide
dehydrate (Na2O2·2H2O) have
been reported.[21−23] This is in contrast to nonaqueous Li-air batteries,
where Li2O2 was unequivocally identified as
the final discharge.The effects concerned with the MnO2 (110) surface as a catalyst are summarized in Figure . First, three bulk polymorphs, Fm3̅m, marcasite, and pyrite, of
the Na-O2 battery superoxide discharge product, NaO2, are shown in Figure , and their respective formation energies are −2.14,
−2.69, and −2.74 eV[18,24] with corresponding
O–O bond lengths of 3.80, 1.28, and 1.34 Å. A competing
discharge product is the peroxo Na2O2 (symmetry P6̅2m) with a formation energy of
−2.63 eV and related O–O bond length of 1.49 Å.
Furthermore, it is apparent that energies of formation of bulk marcasite
(−2.74 eV) and pyrite (−2.69 eV) NaO2 are
lower than adsorption energies of sodium oxides at the MnO2 (110) surface for all configurations, i.e., from the least stable
(−1.55 eV) to the most stable (−2.18 eV) arrangements.
In addition, the energy of the bulk P6̅2m peroxo Na2O2 is also lower than
those of all MnO2 surface-catalyzed products, which implies
that surface MnO2 promotes nucleation and formation of
the discharge products.
Figure 7
Surface adsorption of MnO2 (110)
and sodium oxide bulk
energetics.
Surface adsorption of MnO2 (110)
and sodium oxide bulk
energetics.This is consistent with the experimental
observation that NaO2 is the main product of the cathode
reaction in Na-air batteries,
with some Na2O2 as a byproduct (both in the
presence and in the absence of MnO2).[19] Indeed, the O–O bond length of the most stable surface
configuration (1.29 Å) is nearly equivalent to that of the marcasite
(1.28 Å) and not adversely far from one of the pyrite (1.34 Å)
phases. On the other hand, the length of the O–O bond of the
least stable configuration (1.40 Å) is 6% smaller than that of
the bulk phase of the peroxo Na2O2. Formation
of the dissociated configurations, corresponding to large O–O
separations, is also enhanced by the MnO2 catalyst. All
such evidence suggests the MnO2 catalyst for promoting
nucleation and growth of NaO2 and Na2O2 discharge products.We now consider the TiO2 (110)
surface as a viable catalyst
for the formation of NaO2 products during discharge. A
closer look at the energies of formation of bulk NaO2 polymorphs
Na2O2 is shown in Figure ; the energy of formation of the surface
sodium oxide at configuration (peroxo on Ti/Na, dissociated, dissociated’,
and superoxide) indicates that the former (bulk) is higher by 0.93
eV/Na, 2.29 eV/Na, 1.25 eV/Na, and 0.71 eV/Na respectively in all
stable configurations for oxygen adsorption on Na-TiO2 surfaces.
This means that the formation of NaO2 and Na2O2 will be discouraged in such configurations because
the clusters are too stable and will stick to the surface. In all
configurations, the initial reduction of oxygen in the cathode occurs
less favorably, i.e., peroxo on Ti/Na, dissociated, and superoxide.
Although the energetics do not show the benefit of the TiO2 (110) surface as a catalyst in the formation of expected discharge
products, their associated O–O bond lengths are closer to those
of Na2O2 bulk and dissociated configurations.
Figure 8
Surface
adsorption of TiO2 (110) and sodium oxide bulk
energetics.
Surface
adsorption of TiO2 (110) and sodium oxide bulk
energetics.Finally, a comparison of the energy
of formation of bulk NaO2 and Na2O2, shown in Figure , and the energy of formation
of the sodium oxides on the VO2(110) surface (dissociated,
dissociated’, superoxide, and peroxo on V/Na) is informative.
Figure 9
Surface
adsorption of VO2 (110) and sodium oxide bulk
energetics.
Surface
adsorption of VO2 (110) and sodium oxide bulk
energetics.It indicates that the energy of
formation for the bulk is higher
compared to those of all stable sodium oxide configurations induced
by the VO2 (110) surfaces. This suggests that formation
of NaO2 and Na2O2 will not be enhanced
by the VO2 (110) surface catalyst since the clusters are
too stable and would stick to the surface.Consequently, nucleation
and growth of discharge products will
not be enhanced by such metal oxides. However, the O–O bond
lengths of generated sodium oxides, which are mediated by the catalysts,
though not energetically feasible, are closer to those of NaO2 pyrite (1.36 Å), Na2O2 (1.44 Å),
and dissociated configurations (3.07 Å).Similar to rechargeable
Li–O2 batteries, recent
studies have alluded to the importance of catalysts in enhancing the
performance of Na–O2 batteries. Carbonaceous materials
have been used to accelerate the sluggish behavior of the oxygen reduction
reaction (ORR) and oxygen evolution reaction (OER) kinetics in rechargeable
Na–O2.[22,25,26] Although transition metal oxides catalysts have been employed extensively
in Li-O2 batteries,[27−33] owing to the advantages of low cost, high abundance, being environmentally
benign, and having considerable catalytic activity in both aqueous
and aprotic electrolytes, their use in Na-O2 batteries
is limited.It has, however, been clearly shown that the porous
micro-nanostructured
CaMnO3 electrode is an efficient electrocatalyst in Na-O2 batteries[34] and delivers a high
rate capacity and enhanced cyclability. In addition, a composite of
NiCo2O4 nanosheets/Ni foam, as a carbon-free
and binder-free electrode for Na-air, has been identified as a highly
efficient electrode for nonaqueous Na-air cells. The nanosheets of
the discharge products, composed of Na2O2 and
Na2CO3, were observed after discharging in sodium-air
batteries.[35] Similarly, our current study
has demonstrated that MnO2, as a catalyst, promotes nucleation
and growth of both Na2O and Na2O2. On the contrary, other metal oxides such as TiO2 and
VO2, do not depict this catalytic effect toward the formation
of discharge products in Na-O2 batteries.It is further
interesting to discuss the current results in light
of computations reported by Ceder et al. (2014),[7] which were carried out in the absence of catalysts. They
showed that while sodium peroxide (Na2O2) is
the stable bulk phase of Na in an oxygen environment at standard conditions,
sodium superoxide (NaO2) is considerably more stable at
the nanoscale regime. Hence, the superoxide requires much lower nucleation
energy than the peroxide, which explains why NaO2 is reported
as the discharge product in some Na-O2 batteries. Our study
proposes that the presence of catalysts, such as the MnO2 (110) surface, would further lower the nucleation energy for the
superoxides and peroxides, and enhance their growth, whereas the TiO2 and VO2 would not be effective.Figure summarizes
the surface adsorption and coadsorption of Li and oxygen atoms in
comparison to the formation energies of different bulks of NaO2 as illustrated in Figures –6. This clearly shows
the stability of the adsorbed surfaces and the formation energies
of the bulk for the metal oxides. The more stable the adsorption energy
of the catalyzed systems (compared to the formation energy of the
bulk NaO2), the more unfavorable the configuration, which
implies that NaO2 will stick to the surface, and thus the
catalytic property of the metal oxide is not recommended.
Figure 10
MO2 surface (110) adsorption and sodium oxide bulk energetics.
MO2 surface (110) adsorption and sodium oxide bulk energetics.
Conclusion
The formation
of surface sodium oxide (NaO2) is more
energetically favorable than the formation of gas-phase sodium superoxide
(NaO2) monomers but is less favorable than the formation
of NaO2 bulk, implying that the presence of β-MnO2 in the cathode of a Na-air battery lowers the energy for
the initial reduction of oxygen. In the presence of TiO2 and VO2, the formation of the surface NaO2 is more favorable than the monomer and NaO2 bulk, which
implies that the discharge products will stick to the surface.For the most stable configurations in the most favored or preferred
catalyst, which is MnO2 in the case for Li-MO2 and Na-MO2, it is observed that the stable products predicted
are indeed Li2O2 and NaO2, which
are observed in the dissociated composition for the Li-MnO2 surface, while it is the most stable configuration in the Na-MnO2 surface, which encourages the formation of NaO2. The discharge products formed in Li-air batteries supported by
the metal oxide surface catalyst (MnO2, TiO2, and VO2) have the same bond lengths with their bulk
and monomer structures. In summary, in Li-air batteries, that Li2O2 is not the only product formed; there is a trace
of LiO2, which is confirmed by the bond length similar
to that of the calculated LiO2 monomer.[33]The metal oxide catalyst employed in this study (MnO2, TiO2, and VO2) supports the formation
of
NaO2 in Na-air batteries, which is the most stable discharge
product, and this was supported by the bond length comparison of the
clusters (NaO2) formed with the bulk NaO2 and
NaO2 monomer calculations.
Computational
Methods
Periodic density functional theory (DFT) computations
were carried
out using the Vienna Ab initio Simulation Package (VASP) code[36,37] in the form of the Perdew, Burke, and Ernzerhof (PBE) exchange correlation
functional[38] in the generalized gradient
approximation (GGA). A cutoff kinetic energy of 600 eV was utilized
to determine the number of planewaves, and the Monkhorst–Pack
Brillouin zone sampling approach with 6 × 6 × 9 and 6 ×
6 × 1 k-points mesh for the bulk and surface structures, respectively,
was used. We adopted Liechtenstein’s nonsimplified rotationally
invariant Hubbard correction with the effective Coulomb parameter
set U = 2.8 eV and exchange parameter J = 1.2 eV and U = 4.6 eV and exchange parameter J = 0.0 eV.[39,40] The VO2 calculations
were done without the Hubbard correction and were not spin calculations.
We first considered the stability of the (110) surface by performing
periodic calculations in a slab with stoichiometric composition, thicknesses
14 Å (depending on the oxidation state), and vacuum gaps of ∼14
Å (Figure ).
The two surfaces of each slab are symmetrically equivalent, and this
equivalence was kept during all of the calculations, preventing the
formation of the electric dipole moments that can be associated with
asymmetric slabs.With variances of roughly +0.8% and −3.1%
for a and c, respectively, and 1.6%
in the cell volume
for the MO2 indicated in Table , the lattice parameters were in good agreement
with the experimental results. When the bulk structure was allowed
to relax fully and cleaved a (110) surface which was allowed to converge
as well, and the surface energy was obtained using the expressionwhere Eslab denotes
the energy per slab unit cell, Ebulk denotes
the energy of an equivalent amount of bulk solid, and A is the surface area. The adsorption and coadsorption of sodium and
oxygen on clean (110) surfaces are carried out in such a way that
stoichiometry and symmetry are maintained throughout the calculations.
More information on the methodology can be found elsewhere.[44,45]Equatiom is used to calculate
the adsorption energy where EAds is the
adsorption energy, Esystem is the energy
of the slab together with its adsorbate,
and Eadsorbate is the energy of the adsorbate.
Authors: Pascal Hartmann; Conrad L Bender; Joachim Sann; Anna Katharina Dürr; Martin Jansen; Jürgen Janek; Philipp Adelhelm Journal: Phys Chem Chem Phys Date: 2013-07-28 Impact factor: 3.676