Oxygen adsorption on (100) surfaces in Fe–Cr alloys

Abstract

The adsorption of oxygen on bcc Fe–Cr(100) surfaces with two different alloy concentrations is studied using ab initio density functional calculations. Atomic-scale analysis of oxygen–surface interactions is indispensable for obtaining a comprehensive understanding of macroscopic surface oxidation processes. Up to two chromium atoms are inserted into the first two surface layers. Atomic geometries, energies and electronic properties are investigated. A hollow site is found to be the preferred adsorption site over bridge and on-top sites. Chromium atoms in the surface and subsurface layers are found to significantly affect the adsorption properties of neighbouring iron atoms. Seventy-one different adsorption geometries are studied, and the corresponding adsorption energies are calculated. Estimates for the main diffusion barriers from the hollow adsorption site are given. Whether the change in the oxygen affinity of iron atoms can be related to the chromium-induced charge transfer between the surface atoms is discussed. The possibility to utilize the presented theoretical results in related experimental research and in developing semiclassical potentials for simulating the oxidation of Fe–Cr alloys is addressed.

Full text

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Oxygen adsorption on (100)
surfaces in Fe–Cr alloys
Matti Ropo1,2, Marko Punkkinen1, Pekko Kuopanportti3, Muhammad Yasir1, Sari Granroth1,
Antti Kuronen3 & Kalevi Kokko1*
The adsorption of oxygen on bcc Fe–Cr(100) surfaces with two dierent alloy concentrations is
studied using ab initio density functional calculations. Atomic-scale analysis of oxygen–surface
interactions is indispensable for obtaining a comprehensive understanding of macroscopic surface
oxidation processes. Up to two chromium atoms are inserted into the rst two surface layers. Atomic
geometries, energies and electronic properties are investigated. A hollow site is found to be the
preferred adsorption site over bridge and on-top sites. Chromium atoms in the surface and subsurface
layers are found to signicantly aect the adsorption properties of neighbouring iron atoms. Seventy-
one dierent adsorption geometries are studied, and the corresponding adsorption energies are
calculated. Estimates for the main diusion barriers from the hollow adsorption site are given.
Whether the change in the oxygen anity of iron atoms can be related to the chromium-induced
charge transfer between the surface atoms is discussed. The possibility to utilize the presented
theoretical results in related experimental research and in developing semiclassical potentials for
simulating the oxidation of Fe–Cr alloys is addressed.
Iron–chromium alloys form the basis for the wide variety of transition metal alloys known as stainless steels. e
most remarkable and distinct property of the stainless steels is their corrosion-resistant surface1. e corrosion
resistivity is due to the protective, self-healing oxide layer, which has a complex structure containing
Cr2O3
,
Fe2O3
and
Fe3O4
oxides2–4. In ferritic steels the corrosion rate drops dramatically when their chromium concentration
increases to 9–10 at%5, and the steels become regarded as stainless. e onset of the decrease of the corrosion
rate correlates with6,7 anomalous surface segregation of Cr that originates from the complex magnetic interac-
tions between bulk and surface atoms8,9.
Due to its considerable economic importance, there has been a lot of interest in the oxidation of Fe–Cr alloys
in scientic literature10–13. Yet the atomic-level understanding of the initial stages of oxidation of Fe–Cr surfaces,
and how the oxide grows, is scarce. Investigations of the initial oxidation, especially computational works, have
focused on cases of pure Fe and Cr. Yuan etal.14 performed calculations based on the density functional theory
(DFT) with the generalized-gradient approximation (GGA) to investigate the eect of segregating alloying
elements on the oxygen adsorption on Fe(100) surfaces. e eects of nine dierent 3d transition metals were
investigated, and oxygen was found to be attracted to those alloying elements that have a lower atomic number
than Fe. Błoński etal.15 investigated electronic and structural properties of oxygen adsorption on Fe(100) and
Fe(110) surfaces. A twofold bridge site for (110) and a hollow site for (100) were found to be preferred. e eect
of the oxygen coverage on electronic, magnetic and structural properties were investigated by Błoński etal.16,
Tan etal.17 and Ossowski and Kiejna18 for Fe(100) and/or Fe(110) surfaces.
ere are few experimental works on the initial or low-pressure oxygen adsorption for Fe or Fe–Cr alloys.
Already in 1976 Leygraf and Hultquist10 investigated the initial oxidation of (110) and (100) surfaces in Fe and
Fe–Cr using Auger electron spectroscopy (AES) and low-energy electron diraction (LEED). ey found that
dierent oxides form on the (100) and (110) surfaces. On the (100) surface mixed Fe and Cr oxides are formed,
whereas on the (110) surface only
Cr2O3
, is formed preventing further oxidation. Using LEED, AES, electron-
energy-loss spectroscopy (EELS), secondary-electron emission spectroscopy (SES) and work-function-change
measurements, Sakisaka etal.19 found that the interaction of oxygen with the Fe(100) surface at 300 K consists
of three stages: (i) dissociative chemisorption of oxygen at the hollow or bridge site, (ii) oxygen incorporation
into the selvedge of the material, and (iii) formation of
γ
-Fe2O3. e magnetic properties of the initial oxygen
adsorption for the (110) surface of Fe were investigated by Busch and Winter20 and by Getzla etal.21. Busch etal.
focused on molecular oxygen on the Fe surface, whereas Getzla etal. focused on the atomic oxygen on the Fe
OPEN
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surface. Initial oxidation of Fe–Cr has also been studied by medium-energy ion scattering (MEIS), Mössbauer
and X-ray photoelectron spectroscopy (XPS)2,22,23.
For the initial oxidation of a Cr surface, only two computational investigations were found. Han and Liu24 have
used a ve-parameter Morse potential to study oxygen adsorption on the (100), (110), (111) and (211) surfaces
of Cr. For the (100) surface a hollow site is preferred, whereas for the rest a quasi-threefold site is preferred. Zim-
mermann and Ciacchi25 have investigated initial oxidation and oxide formation for the Cr(110) surface using
molecular dynamics simulations and static structural DFT calculations. ey found that oxygen forms a perfect
ad-layer before the actual formation of Cr oxides on the surface. More have been done experimentally for Cr
surfaces: Müller and Oechsner26 investigated the initial oxidation of a Cr(110) surface and presented three dier-
ent stages of oxidation. Peruchetti etal.27, Shinn and Madey28 and Baca etal.29 have investigated chemisorption
of oxygen on Cr(100) and Cr(110) surfaces.
To our knowledge, there are only two computational studies that investigate oxygen adsorption on the Fe
surface in the presence of Cr atoms: one by Han etal.30 and another by Yuan etal.14 In both studies the eect of
alloying elements on the adsorption is investigated in the dilute limit with a single Cr atom in the surface. Han
etal.30 investigated ten alloying elements in the
γ
-Fe(111) surface. ey found that Cr has the strongest binding
energy to oxygen and to water of investigated alloys. Yuan etal.14 studied the
α
-Fe(100) surface and nine dierent
alloying atoms in the surface. e hollow site was found to be preferred, followed by the bridge site and then the
on-top site. e subsurface positions for oxygen were the least preferred positions. In both studies the alloying
elements were placed only at one position in the surface.
is paper examines the adsorption of atomic oxygen to (100) surfaces of bcc Fe–Cr alloys with abinitio
DFT calculations. We study the preferred adsorption sites, adsorption energies and how these are aected by the
presence of Cr in the surface. We consider the eect of dierent surface Cr positions up to two Cr atoms in the
surface. We also address the eect of the bulk composition of the Fe–Cr alloy on the adsorption. Since Fe–Cr
alloys are also interesting in terms of magnetism, we further present a summary of the magnetic properties of
the investigated surfaces.
Accurate and detailed atomic-scale data of the energetics and geometry of the adsorption processes of oxygen
on Fe–Cr surfaces is essential not only for modeling the surface oxidation, but also for developing well-perform-
ing multi-targeted semiclassical potentials. Such potential models are essential for large-scale simulation methods
that facilitate the ecient design of more sustainable iron alloys than has been achieved with trial and error.
Methods
All abinitio density functional calculations are performed using GPAW31,32 (version 0.11) and the Atomic Simula-
tion Environment (ASE)33 (version 3.9). e valence-core interaction is modeled with the projected augmented
wave potentials (GPAW/PAW version 0.8), and a real-space grid with a 0.2-Ågrid spacing is used to present
the wavefunctions. A
3×3×1
Monkhorst–Pack grid is used for the k points. A generalized-gradient-level
approximation in the form of the Perdew–Burke–Ernzerhof34 functional is used for the exchange-correlation
interaction. e calculations are done using a slab construction where the surface is modeled by a metal-vacuum
lm that is innite in two dimensions and periodically repeates the metal-vacuum structure in the direction
perpendicular to the lm surface. e metal and vacuum parts should be thick enough to give converged results
for the quantities to be calculated. Several useful convergence tests have been published. For instance, Yu etal.35
found that the computational accuracy of the surface energy of Fe(100) is 0.03% at a vacuum thickness of 8 Å.
Moreover, we use a real-space grid technique in which net charges or dipoles present neither conceptual nor
computational diculties36.
e surfaces are modeled with ve-atomic-layers-thick slabs with nine atoms in each layer. A 12-Åvacuum
separates the surfaces. Simulating a dilute Fe–Cr alloy with a 45-atom unit cell, one or two Cr atoms are placed
in the two topmost atomic layers, depending on whether adsorption with one or two Cr atoms is studied. To
simulate the 9 at% Fe–Cr alloy, two of the Cr atoms are placed in the two bottommost atomic layers (maximally
far from each other). en additional one or two Cr atoms are placed in the two topmost atomic layers, as in the
dilute Fe–Cr alloy case. In every calculation the atoms in the two bottommost layers (opposite to the adsorbed
oxygen atom) are xed to their bulk positions, and the rest of the atoms are allowed to relax using the FIRE37
algorithm with a relaxation criteria of 0.05eV/Å. e theoretical lattice constants of 2.846Åand 2.872Åfor pure
Fe and Fe0.91Cr0.09 alloy are used. Atomic charges are calculated using the Bader method implemented in GPAW.
e surface energies are estimated using the formula (due to the asymmetric slab geometry only one of the
surfaces is relaxed)
where
γsurface
,
Eslab
,
Ebulk
, n, A and
γunrelaxed
are the surface energy of the relaxed surface, the energy of the relaxed
slab, the energy per atom for the bulk, the number of atoms in the slab, the area of the surface and the surface
energy of the unrelaxed surface, respectively. e unrelaxed surface energy is calculated with the commonly
used method of Ref.38.
e adsorption energies for an oxygen atom are calculated with the formula
where
Eslab+O
,
Eslab
and
EO2
are the total energies of a slab with an adsorbed O atom, a slab without any oxygen
and an oxygen molecule, respectively. A negative adsorption energy means adsorbate binding.
(1)
γ
surface =
E
slab
−nE
bulk
A
−γunrelaxed
,
(2)
Ead =Eslab+O −Eslab −EO
2
/2,
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Results
We investigate the oxygen adsorption on (100) surfaces of bcc Fe–Cr alloys. Calculations are performed with two
dierent lattice constants: one set of calculations with a pure Fe lattice constant to simulate dilute-limit compo-
sitions and another set with a lattice constant corresponding to the Fe0.91Cr0.09 composition. e compositions
are selected to present two distinct regions of corrosion resistance: in the dilute limit the corrosion rate is high,
whereas at the Fe0.91Cr0.09 composition the corrosion rate is already reduced drastically5. e actual Cr concen-
trations of the dilute alloys with one or two Cr atoms in the surface are 2 at% or 4 at%, respectively, whereas the
actual Cr concentration in the Fe0.91Cr0.09 case is either 7 at% or 9 at% depending on whether oxygen adsorption
with one or two Cr atoms is studied.
e obtained results also shed light on whether the change in the lattice constant due to the change in the alloy
composition aects the interactions between Fe, Cr and O in the surface. e surface of the simulation cell is
illustrated in Fig.1. For both sets of calculations, up to two Cr atoms (to enable the study of Cr–Cr interactions)
are placed in the rst two surface layers. To simulate the bulk concentration of the Fe0.91Cr0.09 alloys, two extra
Cr atoms are placed in the two bottommost (opposite to the adsorption surface) layers of the simulation cell. e
eect of the two extra Cr atoms on the interaction in the surface is estimated to be less than 1meV for the full
simulation cell. ree dierent adsorption sites are considered: on-top (‘ot’, on top of atom 1), bridge (‘br’, between
atoms 1 and 4) and hollow (‘ho’, on top of atom 7) sites. For the numbering of the sites, see Fig.1. A number is
assigned to those rst- and second-layer atomic sites that are needed to construct all non-equivalent atomic
congurations (with respect to translation, rotation and mirror symmetries) for oxygen adsorption at the on-top,
bridge and hollow sites with one or two Cr atoms substituted for Fe atoms in the rst or second atomic layers.
Surface energy and relaxation: oxygen-free surface. First we consider oxygen-free surfaces. e
obtained surface energies are presented in Table1, along with two DFT reference values for pure Fe calculated
using a GGA-level exchange-correlation potential and the VASP program38,39 or the FCD-LMTO method40. Our
estimate is well in line with the previous VASP results.
In addition to the surface energies, Table1 lists the relaxations
�ij =100(dij −d)/d
for the two topmost sur-
face layers; here
dij
and d are the interlayer distances between the layers i and j and in the bulk, respectively. Our
Figure1. Le: Schematic illustration of the numbering of the Fe atoms in the two topmost atomic layers. e
surface-layer atoms are numbered from 1 to 6 and the subsurface-layer atoms from 7 to 10. e three oxygen
adsorption sites considered are the on-top site (‘ot’) over atom 1, the hollow site (‘ho’) over atom 7 and the
bridge site (‘br’) between atoms 1 and 4. Middle: Atomic positions within the unit cell of the dilute Fe–Cr alloy
with two Cr atoms (blue–grey) at sites 1 and 7. e positions of the adsorbed oxygen atom at the on-top, hollow
and bridge adsorption sites are illustrated by the smaller dark blue, red and light blue spheres, respectively.
Right: Same as Middle but with the viewpoint shied so that the vertical positions of the oxygen atoms can be
perceived.
Table 1. Surface energies and relaxations of the rst two surface layers of the investigated systems. e system
label ‘Fe’ indicates that the lattice constant of pure Fe (dilute alloy) is used; ‘FeCr’ indicates the lattice constant
of the Fe0.91Cr0.09 alloy. Here
12
is the percentage change in the distance between the surface layer and the rst
subsurface layer, relative to the layer distance in bulk, and
23
is the percentage change in the distance between
the rst and second subsurface layers.
System surface
γsurf
(
Jm
−
2
)
�12(%)
23
(%)
Fe Fe 2.492
−2.51
1.43
FeCr Fe 2.422
−4.12
1.31
Ref.15 Fe
−3.03
2.14
Refs.38,39 Fe 2.50
Ref.40 Fe 2.430
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results for the clean Fe surface with the pure-Fe lattice constant are somewhat smaller than the corresponding
VASP results15. For both investigated lattice constants, the single Cr atom prefers the top surface layer over the
subsurface layer. In the case of two Cr atoms in the surface, both of them prefer to lie in the top layer, namely,
at sites 1 and 5 in Fig.1 (or other symmetrically equivalent congurations). is result is in agreement with
previous rst-principles calculations8,41. A detailed list of the energies of all calculated atomic congurations is
shown in Supplementary Information.
Oxygen adsorption: preferred sites and geometries. To study oxygen adsorption, both for pure Fe
and for Fe0.91Cr0.09 alloy with all possible substitutional Cr congurations in the two topmost layers, we consider
three adsorption sites: the on-top site over atom 1, the hollow site over atom 7 and the bridge site between atoms
1 and 4 (Fig.1). Given that surface adsorption generally alters surface electrostatics, the following remark about
these adsorption congurations is in order: If the metal lm is asymmetric, it is possible that a spurious dipole
interaction forms between the adjacent metal lms. Oxygen adsorption on an Fe surface increases the surface
dipole moment. Hugosson etal.42 showed that 0.25 monolayer oxygen increases the surface dipole moment by
0.035eÅ and 1 ML of oxygen increases it by 0.087eÅ [here one monolayer (1 ML) adsorption: Fe(100) − p(
1×1
)O]. erefore, from the surface-dipole point of view, our atomic slab with 0.11 ML oxygen is close to a sym-
metric slab, which renders the dipole correction less important43,44.
When it comes to oxygen adsorption, there are only a few dierences between the two investigated alloys. For
both alloys the fourfold hollow site is the preferred site (Fig.3); the bridge site is the second most favourable and
the on-top site the least favourable. e same order was reported for oxygen adsorption on Fe(100) surfaces by
Yuan etal.14. For the adsorption geometries, the oxygen–metal distances for the two investigated alloys are the
same within
±0.01
Å. For the oxygen at the on-top position, the distance between the oxygen and the underlying
metal atom (be it either Fe or Cr) is 1.64Å.
When the oxygen is at the bridge position, the atomic distances depend on the type of the bridge dimer below
the oxygen. e distances between the oxygen and the metal atoms are shown schematically in Fig.2a. Note
that the two oxygen–metal distances in the Cr–Fe bridge dier signicantly (6%) from each other, the O–Cr
bond being shorter; their average, however, is 1.84Å, which is equal to the average bond distance of the Cr–Cr
and Fe–Fe cases. e DFT calculations with the Perdew–Burke–Ernzerhof exchange-correlation functional for
a pure Fe surface by Yuan etal.14 yield similar results: 1.63Åfor the on-top and 1.83Åfor the bridge position.
e adsorption energy of an oxygen atom at a bridge site depends almost linearly on the type of the bridge atoms:
For both alloy compositions, the adsorption energy for the Fe–Fe bridge is − 3.24eV (Table2). It decreases by
about 0.3eV for the Cr–Fe bridge and again by about 0.3eV for the Cr–Cr bridge for both alloys. is gives
approximately − 1.6eV per O–Fe bond and − 1.9eV per O-Cr bond.
For the hollow site the behaviour is more intricate. e distance to the rst layer depends on which atom is
underneath the oxygen atom (at site 7). Also, in the case of hollow adsorption, if another Cr atom is replaced by
an Fe atom, the distance between the remaining Cr atom and the oxygen atom is shortened, just as in the bridge
case. Although the individual distances from the hollow-site oxygen atom to the ve nearest atoms depend on
whether the atom below the oxygen is iron or chromium, the average distance to the ve nearest atoms is essen-
tially the same in both cases (diering by only 0.5%); this is again similar to the behaviour of the bridge dimer.
Figure2. Schematic gure of the distances (in Å) between an adsorbed oxygen atom and the nearest metal
atoms. Upper panel: Oxygen atom adsorbed to the bridge site atoms, at atomic sites 1 and 4 (see Fig.1 for the
numbering of the sites). Lower panel: Oxygen atom at the hollow site, the Fe and Cr atoms on the side of the
oxygen are atoms at sites 1 and 5.
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e distances in the hollow case are illustrated in Fig.2b. Yuan etal. reported the shortest bond length between
Fe and O for the hollow site of a pure Fe surface to be 2.05Å23.
Adsorption energies. e obtained adsorption energies for zero, one and two Cr atoms in the surface are
given for the dilute Fe–Cr alloy and Fe0.91Cr0.09 in Table2.
As mentioned in the previous section, the strongest binding site is a hollow one. e conguration with Cr
atoms at sites 1 and 4 is the strongest binding bridge case. In fact, its binding is stronger than that of a hollow
site in a conguration where the Cr atoms are at sites 8 an 9. Sites 8 and 9 are next-nearest neighbours to site 7
directly below the hollow site, which suggests that the Cr eect on the oxygen adsorption is predominantly of a
short-range nature (see Fig.4C).
Interestingly, only three of the eleven investigated Cr-containing hollow-adsorption cases (‘3 ho’, ‘9 ho’, ‘8–9
ho’) are less binding than the pure-Fe-surface hollow site (‘- ho’) (Table2 and Figs.3, 4). In these three cases, there
are no Cr atoms within the nearest-neighbour positions of the adsorption site. Placing Cr at site 3, site 9 or sites 8
and 9 raises the adsorption energy of oxygen by 0.016eV, 0.029eV or 0.097eV, respectively. e eect of Cr on the
adsorption of oxygen is therefore ambivalent, that is, Cr within the nearest-neighbour distance from the adsorp-
tion site enhances oxygen adsorption and at farther distances weakens the oxygen adsorption. Similar behaviour
can also be observed for the bridge position in both investigated alloys and for the on-top position in the case of
the pure-Fe lattice constant. For the Fe0.91Cr0.09 alloy with oxygen at the on-top position, the pure Fe surface has
the weakest oxygen binding. For the dilute-limit alloy, the weakest binding occurs when the Cr atom is at site 5
(‘5 ot’ in Table2; see also Figs.1, 3). e overall dierence in the adsorption energies between the dilute-limit
Fe–Cr and Fe0.91Cr0.09 alloys is small. e mean dierence is
(Ead(Fe)−Ead (Fe0.91Cr0.09 ))/N=−0.008
 eV,
and the mean absolute dierence is
|(Ead(Fe)−Ead (Fe0.91Cr0.09 ))|/N=0.037
eV; the sum is over identical
surface congurations with
N=35
.
e energetic stability of the considered Cr congurations can be assessed using the Maxwell–Boltzmann
statistical distribution and the total energies of systems with dierent Cr congurations. e relative probability
of congurations i and j with energies
Ei
and
Ej
at temperature T is
exp [(Ej−Ei)/(kT)]
, where k is the Boltz-
mann constant. To avoid biased energies between systems with dierent numbers of substituted Cr atoms, we
consider the systems with one and two substitutional Cr atoms in the surface region of the unit cell as separate
sets in the probability calculations. Both concentration and temperature aect the occurrence probabilities of Cr
congurations in iron alloys. In order to get a broader view of the Fe–Cr alloys, it is worth mentioning some of
their general properties6,8,41. When the Cr concentration reaches about 10 at% in bulk, the probability of nding
Cr in the surface starts to increase steeply above the bulk value. e occurrence probability of a second-layer
Cr atom stays lower than that of a surface-layer Cr atom. Moreover, the occurrence probability of a Cr dimer
decreases with decreasing distance between the Cr atoms. At higher temperatures, higher-energy Cr congura-
tions become more probable. At a temperature of 300K, the second surface layer contains virtually no chromium.
e probabilities of the ‘1–5’ and ‘1–2’ congurations are, respectively, 96% and 4% in the dilute Fe–Cr alloy and
97% and 3% in the Fe0.91Cr0.09 alloy. At 1100K, the probabilities of the ‘1–5’ and ‘1–2’ congurations are 68%
Figure3. Relative adsorption energies of oxygen in the Fe and Fe0.91Cr0.09 systems (the energy of the ‘1–7 ho’
case is shied to 0eV for both systems, with
Ead
=−
4.37
eV and
−4.35
eV for the Fe and Fe0.91Cr0.09 ‘1–7 ho’
cases, respectively). e dierence between the two systems is minimal except for a few cases. e sites have the
following labels: ‘br’ is a bridge site, ‘ot’ is an on-top site and ‘ho’ is a hollow site. e numbers in front indicate
the position(s) and number of Cr atoms in the surface: one number indicates one Cr atom, and two numbers
separated by a hyphen indicate two Cr atoms in the surface; a hyphen without any numbers indicates a pure Fe
surface. e atomic sites are numbered as in Fig.1. e le (right) vertical line separates all the hollow (bridge)
adsorption cases to its le. From the point of view of energetic stability (see Supplementary Information), the
most relevant congurations are those that have Cr only in the surface layer, i.e. at sites from 1 to 6.
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and 29% in the dilute Fe–Cr alloy and 71% and 28% in the Fe0.91Cr0.09 alloy; the negligible 300K probability of
the ‘1–8’ conguration has increased to about 2% for the dilute Fe–Cr alloy and to 1% for the Fe0.91Cr0.09 alloy.
Introducing oxygen onto the surface changes the energetic stability of the Cr congurations; the magnitudes
of the changes range from a few percents at room temperature up to tens of percents at high temperatures. At
1100K, the probabilities of the ‘1–5’ and ‘1–2’ congurations are, respectively, 81% and 14% in the dilute Fe–Cr
alloy and 81% and 15% in the Fe0.91Cr0.09 alloy. e negligible 300K probability of the ‘1–7’ conguration has
increased to approximately 4% for the dilute Fe–Cr alloy and 2% for the Fe0.91Cr0.09 alloy. At temperatures where
metal atoms become mobile, the adsorbing oxygen could change the atomic conguration of the Fe–Cr surface.
Temperature, Cr concentration and oxidation can thus signicantly alter the stability of the Cr congurations.
e stabilities of the Cr congurations in Table2 at temperatures of 300K, 700K, 1100K and 1500K are given
in Supplementary Information.
In the case of the Fe surface, our results can be compared with previous investigations of the Fe surface. Cao45
reports the DFT-GGA values
−7.577
eV,
−6.632
eV and
−5.585
eV for the oxygen adsorption energies for the
hollow, bridge, and on-top adsorption sites on a Fe(100) surface, respectively. In Cao’s results, the reference level
includes the energy of a free oxygen atom, in contrast to half the energy of a free oxygen molecule in our case.
Table 2. Adsorption energies (in eV) of an oxygen atom calculated using the lattice constant of pure iron
(‘Fe’) and the lattice constant of Fe0.91Cr0.09 (‘FeCr’). For instance, the notation ‘1–2 br’ means that there are Cr
atoms at sites 1 and 2 (see Fig.1 for the site numbering) and that the oxygen atom is adsorbed at the bridge
position. e sites have the following labels: ‘br’ is the bridge site, ‘ot’ is the on-top site, and ‘ho’ is the hollow
site.
Cr pos. O pos.
Ead
(eV)
Fe FeCr
–br
−3.24
−3.24
–ho
−3.89
−3.90
–ot
−2.41
−1.93
1br
−3.55
−3.54
2br
−3.19
−3.20
6br
−3.18
−3.20
7br
−3.30
−3.26
9br
−3.16
−3.24
1ho
−4.01
−4.01
3ho
−3.86
−3.88
7ho
−4.22
−4.18
9ho
−3.88
−3.85
1ot
−3.23
−3.25
2ot
−2.12
5ot
−2.36
−2.37
7ot
−2.52
−2.50
8ot
−2.43
−2.36
1–2 br
−3.59
−3.58
1–4 br
−3.85
−3.85
1–5 br
−3.58
−3.58
1–7 br
−3.61
−3.59
2–9 br
−3.12
−3.28
8–9 br
−3.11
−3.21
1–2 ho
−4.12
−4.12
1–5 ho
−4.21
−4.20
1–7 ho
−4.37
−4.35
1–8 ho
−3.97
−3.95
4–9 ho
−4.00
−4.00
7–8 ho
−4.20
−4.21
8–9 ho
−3.79
−3.79
1–2 ot
−3.31
−3.34
1–5 ot
−3.30
−3.33
1–7 ot
−3.23
−3.25
1–8 ot
−3.23
−3.23
4–8 ot
−3.55
−3.54
8–9 ot
−2.43
−2.42
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erefore, to compare Cao’s results with our adsorption energies (Table2), we must add half the binding energy
of an oxygen molecule (
1
2
×
6.07
 eV46) to Cao’s results, yielding
−4.542
eV,
−3.597
eV,
−2.550
eV. ese dier
from our results by
−0.7
eV,
−0.4
eV and
−0.2
eV, respectively. However, also the oxygen coverage diers: in
our calculations it is 0.11 monolayers (ML), whereas in Cao’s work it is 0.25 ML. Previous investigations have
shown that the adsorption energy of oxygen decreases with increasing oxygen coverage. Błoński etal.15 report
the DFT-GGA adsorption energies for the oxygen adsorption at hollow site on Fe(100) to be
−3.41
eV,
−3.26
eV
and
−3.09
eV for the coverages 0.25, 0.5 and 1.0 MLs, respectively. e trend of oxygen binding becoming
weaker with increasing adsorbate coverage is also observed for other metal surfaces, such as Pd(111)47, Pt(111)48
and Au(111)49. Using UV and X-ray photoelectron spectroscopy, Maschho and Armstrong50 investigated the
initial oxidation of polycrystalline Fe surface from atomic adsorption to
105
Langmuir (L) exposure in ultra-
high vacuum and up to oxidation in atmospheric conditions. ey found that the initial oxide is FeO. Aer 10
L oxygen adsorption,
Fe3O4
starts to form.
e obtained adsorption energies are useful data, for instance, in Monte Carlo simulations of the growth of
the oxide scale on pristine Fe and Fe–Cr (100) surfaces. ese simulations could provide useful information
about the dierences in the oxidation process between corrosion-resistant and corrosion-susceptible surfaces.
Having a comprehensive atomic picture of the oxidation processes of Fe and Fe–Cr surfaces would be very
benecial for modern alloy design.
Electric charges. Before discussing electric charges of the atoms, we would like to point out that the charge
of an atom in a solid is not an observable but rather relies on a model used to partition the total charge density
of the solid51. Nevertheless, relative changes in atomic charges, calculated using the same method for all systems,
can give relevant physical and chemical information about the atomic processes. e electric charges of the
atoms in the investigated systems are calculated with the Bader program52,53. e Bader method has been bench-
marked and tested in several works53–59. For instance, Bader charges have been tested for Na metal using two
dierent integration methods, the near-grid method and the weight method. For
603
grid points, the near-grid
method underestimates the Bader charge by 0.01e (e is the absolute value of the charge of an electron), while the
weight method underestimates it by 0.005e.
Here again there are no signicant dierences in the charges between the two investigated systems (dilute
and Fe0.91Cr0.09 alloys). e maximum charge dierence between the two systems for the same conguration is
±0.07
e. For the clean Fe surface, the average charge of the Fe atom is 0.09e in the surface layer and -0.10e in
the subsurface layer. (Here a charge is the dierence between the Bader charge of an atom in the material and
the electric charge of a free atom, i.e. the positive value indicates electron deciency). e charge of a single Cr
atom in an oxygen-free Fe surface layer is 0.38e. Yuan etal.14 reported a charge of about 0.5e for Cr in the Fe
surface layer. Our result for a single Cr atom in the subsurface layer is 0.36e. In the case of two Cr atoms in the
rst two surface layers, we obtain the average charges of 0.41e and 0.31e for Cr in the surface and subsurface
layers, respectively.
When there is an oxygen atom at the on-top position (above site 1), it has an average charge of − 0.80e, and
the averages for the metal atoms directly below the oxygen are 0.74e for Cr and 0.33e for Fe. When the oxygen
is at the bridge site, it has a charge of − 0.95e, and the averages for the nearest metal atoms (sites 1 and 4) are
0.72e for Cr and 0.40e for Fe. In the case of oxygen at the hollow position, its average charge is − 1.15e, and
the averages for the nearest metal atoms are as follows: rst-layer Cr 0.60e, rst-layer Fe 0.27e, second-layer Cr
0.27e and second-layer Fe 0.08e.
Electronic properties. To understand the intricate interactions between iron, chromium and oxygen, we
have investigated the highest occupied (HO) states, the lowest unoccupied (LU) states and the density of states
(DOS). e analysis reveals that the HO states are mainly localized at the Fe atoms whereas the Cr atom (or
atoms) contributes strongly to the LU states whenever it is present. Similar DFT-GGA results were reported by
Hu etal.60 for a single Cr atom in the (110) surface. ese conclusions are also supported by our analysis of the
local density of states (LDOS) using projections to the atomic basis. e Fe atoms have large contributions just
Figure4. Illustrations of the three hollow-site congurations in which oxygen is more weakly bound than at
the hollow site of a pure Fe surface. e positions of Cr atoms (indicated with blue-gray color) are (A) site 3, (B)
site 9 and (C) sites 8 and 9. e oxygen position is indicated by the small red sphere.
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below the Fermi level, whereas the Cr atoms have large contributions just above the Fermi level. Previous DFT
calculations with the local density approximation by Papanikolaou etal.61 similarly revealed a large Cr contribu-
tion above the Fermi level in the LDOS of the Cr-containing Fe(100) surface.
Figure5 shows the DOSes for pure and Cr-containing Fe surfaces in both oxygen-free (Fig.5A) and oxygen-
containing (Fig.5B) cases, with the conguration corresponding to the strongest binding case for the hollow
site. For the oxygen-free surfaces (Fig.5A) there are clear dierences between DOSes of pure and Cr-containing
Fe surfaces (most clearly seen in the double peak at the top of the up d band). Chromium atoms increase the
dierence (spin splitting) between the up and down DOSes (by about 0.2 eV, measured for the DOS peaks at
the top of the up and down d bands). An oxygen atom on the surface also increases the spin splitting (0.2 eV),
as observed by comparing Fig.5A,B. However, aer adding oxygen on the surface the eect of chromium atoms
on the spin splitting is considerably reduced (Fig.5B).
As mentioned above, LDOSes were also analysed for selected atomic sites to shed light on the behaviour of
dierent atoms in dierent congurations. e LDOSes for the adsorbed oxygen atom, as well as for chromium
atoms near the oxygen atom, are shown in Fig.6 for oxygen at on-top, bridge and hollow sites. e states of the
adsorbed oxygen are much lower (around 7eV below the Fermi level) for the hollow site than they are for the
bridge and on-top sites (around 5eV and 4eV below the Fermi level, respectively). ere is also a strong overlap
between some of the chromium and oxygen states, just below − 6eV for the hollow site, below − 5eV for the
bridge site and below − 4eV for the on-top site. e Fe DOS shows similar behaviour, although its overlap with
oxygen is not as strong as that of chromium. As Fig.6 shows, the band energy (
E
F
0
E[DOS↑(E)−DOS↓(E)]d
E
)
of oxygen decreases with the adsorption sites in the order ot–br–ho, in agreement with the adsorption energies
of these sites. e strong overlap between oxygen and chromium states at low energies suggests stronger bonding
of oxygen to chromium than to iron.
Magnetic properties. Here we mainly focus on the magnetic-moment data of the dilute Fe–Cr alloy (data
for Fe0.91Cr0.09 is given in parentheses). e atomic magnetic moments for all calculated Cr congurations are
presented in Supplementary Information. e moments of Fe atoms in Cr-free surfaces are 2.968
µB
(2.963
µB
)
for an atom in the rst layer and 2.340
µB
(2.398
µB
) for an atom in the second layer. For comparison, the mag-
Figure5. DOSes (positive values for up and negative values for down spin channels) for (A) an oxygen-
free surface with zero (red), one (green) or two (blue) Cr atoms corresponding to the strongest binding
conguration; (B) as (A) but with an oxygen atom at the hollow site. e horizontal axis is energy in eV relative
to the Fermi energy, and the vertical axis is the DOS in arbitrary units. e numbers in the legends indicate the
position(s) of the Cr atom(s) (see Fig.1 for the numbering scheme). e lone hyphen indicates the absence of
Cr atoms in the surface.
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netic moment of bulk Fe is 2.186
µB
per atom. e substitution of one Fe atom by a Cr atom reduces the moments
of the nearby Fe atoms, on average, to 2.884
µB
(2.865
µB
) in the surface layer and to 2.228
µB
(2.248
µB
) in the
second layer. Two Cr atoms, placed in the rst or second (or both) atomic layer(s), reduce the moment of an Fe
atom in the surface layer to 2.752
µB
(2.769
µB
) and in the second layer to 2.198
µB
(2.219
µB
). In general, there
are only minor dierences in magnetic moments between the dilute Fe–Cr alloy and Fe0.91Cr0.09 alloy.
e magnetic moment of a single Cr in the rst layer is
−3.133

µB
(
−3.149

µB
) and
−1.984

µB
(
−2.226

µB
)
in the second layer. e average of the moments of two Cr atoms, either in the rst or second (or both) atomic
layer(s) is
−3.114

µB
(
−3.132

µB
) in the rst layer and
−1.840

µB
(
−1.957

µB
) in the second layer. e obtained
magnetic moments are in line with the moments calculated for random substitutional Fe–Cr alloys using the
coherent potential approximation8.
Next we consider the magnetic moments when oxygen is adsorbed in the bridge, hollow or on-top positions
on the surface. Because we have calculated a large number of dierent Cr congurations, we present here only
the moments at sites 1 (rst layer) and 7 (second layer) and take an average over all calculated congurations
with one Cr in the rst or second layer (Table3). e absolute value of the magnetic moments of rst-layer Fe
and Cr is reduced by the adsorbed O in all three adsorption sites. is reduction for Cr is much larger than
for Fe. e eect of O on the moments in the second layer is generally smaller than in the rst layer and both
decrease and increase in the absolute value of the moment is obtained. Increasing the Cr content in Fe–Cr from
the dilute limit to 9 at% changes the magnetic moments by less than 1%, except for the moment of Fe at site 1
(
−21
%) and the moment of Cr at site 7 (
−4
%) when oxygen is adsorbed in the on-top position. e magnetic
moment of oxygen is highest for the bridge adsorption (0.164
µB
with the pure Fe surface) and lowest for the
on-top adsorption (0.096
µB
with two Cr atoms in the surface).
Discussion and summary
To gain atomic-level understanding of why oxygen bonding is stronger for some of the Cr-containing Fe surfaces
than for the corresponding pure Fe surface, let us analyse the intricate interaction between iron, chromium
and oxygen more closely. Previously Hu etal.60 reported that Cr in a Fe(110) surface changes the charge of
Figure6. Comparison of the local densities of states of oxygen and chromium atoms calculated with a
projection to an atomic basis located at the atomic sites. e labels ‘ho’, ‘br’ and ‘ot’ indicate whether the oxygen
is at a hollow, bridge or on-top site. e second label tells the type of atom under consideration (Cr or O), and
the number indicates the Cr position (see Fig.1 for the site numbering). e horizontal axis is energy in eV
relative to the Fermi energy, and the vertical axis is the DOS (both up and down spin channels) in arbitrary
units.
Table 3. Magnetic moments at atomic sites 1 and 7 (see Fig.1) in the dilute-limit Fe–Cr alloy with one Cr
atom in the rst or second surface layer. e Fe moments are averaged over Cr congurations with Cr in the
nearest- or next-nearest-neighbour position to Fe. e magnetic moments (m) of Fe and Cr are shown with O
adsorbed at either the bridge (‘br’), hollow (‘ho’) or on-top (‘ot’) site. e eect of the adsorbed O is measured
by the dierence
�mX
=
mX(with O)
−
mX(without O)
, w here
X=Fe
or Cr. e magnetic moments without
adsorbed O are
mFe
=
2.868 µB
and
mCr
=−
3.133 µB
at site1 and
mFe
=
2.243 µB
and
mCr
=−
1.984 µB
at
site7.
Adsorption site of O
Site 1 Site 7
mFe
(
µB
)
mCr
(
µB
)
mFe
(
µB
)
mCr
(
µB
)
With O
mFe
with O
mCr
with O
mFe
with O
mCr
br 2.790
−0.078
−2.378
0.755 2.351 0.108
−2.297
−0.313
ho 2.853
−0.015
−3.041
0.092 2.409 0.166
−1.886
0.098
ot 1.955
−0.910
−1.734
1.400 2.220
−0.023
−1.921
0.063
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neighbouring Fe atoms, thereby increasing their electron donor capabilities and prompting the adsorption of
positive
H+
ions. In the case of oxygen on the (100) surface, we found the eect of Cr to be twofold. A Cr atom in
the nearest-neighbour position to the Fe atom under the oxygen renders that Fe atom more attractive to oxygen
regardless of the adsorption site. For the on-top adsorption, a Cr in any other neighbour position also renders
the Fe atom (under oxygen) more attractive to oxygen except in the dilute alloy where a Cr at site 5 makes Fe less
attractive to oxygen. For bridge and hollow adsorptions in both alloys, a Cr in a beyond-the-nearest-neighbour
position renders Fe less attractive to oxygen. is means that a Cr atom within the two topmost surface layers
produces an eective ‘driving force’ to escort a diusing oxygen atom closer to the Cr atom. e energy dierence
that gives rise to this ‘driving force’ is, depending on the atomic conguration, about 0.06–0.38eV, measured in
terms of the oxygen adsorption energy. Our data sheds light on the issue of whether this Cr-induced change in the
bonding between an oxygen atom and the surface is directly related to the changes in the atomic charges or not.
Let us disregard the oxygen for a moment and consider oxygen-free Fe–Cr surfaces from the Bader-charge
perspective. In a clean Fe surface, with no Cr, the Fe atoms in the surface and subsurface layers have electric
charges of 0.09e and - 0.10e, respectively. But what happens to these charges when Cr is introduced to the
surface? Let us analyze three dierent Cr congurations: (i) a single Cr atom in the surface layer; (ii) a single
Cr atom in the subsurface layer; and (iii) two Cr atoms in the subsurface layer (positions 8 and 9 in Fig.1). In
case(i), the single Cr atom in the surface layer changes the charges of neighbouring surface-layer Fe atoms to
0.05e and the charges of the nearest subsurface-layer Fe atoms to − 0.14e. In other words, their Bader charges
decrease by 0.04e compared to the pure Fe surface case, indicating a net gain of electrons. In case(ii), where the
single Cr atom is in the subsurface layer, the nearest Fe atoms in the surface layer have a charge of 0.03e, and the
nearest Fe atoms in the subsurface layer have a charge of − 0.12e; therefore also in this case the Bader charges
have decreased relative to the pure-Fe case. In case(iii), with two Cr atoms at the subsurface sites 8 and 9, the
Fe atoms in the surface layer again acquire more electrons: Fe at site 5 between the two Cr atoms has a charge
of − 0.02e, and the Fe atoms at sites 2 and 4 have a charge of 0.00e. e Cr-induced changes in the charges of
Fe atoms are summarised in Fig.7. Comparing these trends in the electronic charge transfer from Cr to Fe with
our results for the oxygen adsorption shows that the extra electrons acquired by the Fe atoms from a nearby Cr
atom are not generally available for forming stronger bonds between the iron and oxygen atoms. It would also
be instructive to use other methods in addition to the Bader method to relate the changes in the atomic charges
to observable physical quantities. For example, the Helmholtz method would provide a way to study surface
polarization and the work function55,62,63.
e hollow, bridge and on-top adsorption sites for an oxygen atom were studied. e most favourable adsorp-
tion site in both investigated alloys was found to be the hollow site. Eleven dierent Cr congurations were
studied for the hollow-site oxygen adsorption. For both alloys, the maximum variation among these 11 adsorp-
tion energies is about 0.6eV. Among all the investigated adsorption sites and Cr congurations, the maximum
variation in the oxygen adsorption energy is about 2.0eV for the dilute alloy and 2.4eV for the Fe0.91Cr0.09 alloy.
e variation of the oxygen adsorption energy between dierent Cr congurations is generally larger among
cases with two Cr atoms than among cases with one Cr atom. e adsorption energies of an oxygen atom on the
Fe–Cr(100) surface, when analysed in order of magnitude, show clear steps and terraces (Fig.3). at feature
could be studied using the experimental techniques suitable for investigating energetics of adsorption64.
Figure7. e charge of an Fe atom versus Cr congurations (with the neutral atom, of charge 0e, as the
reference level). e axis labels ‘Pure Fe’, ‘Cr in 1L’, ‘Cr in 2L’ and ‘2Cr in 2L’ refer to pure Fe surface, one Cr atom
in the surface layer, one Cr atom in the subsurface layer and two Cr atoms in the subsurface layer at sites 8 and
9 (Fig.1). e green curve with square markers shows the charge of the subsurface Fe atom nearest to the Cr
atom. e blue curve with lled circles gives the charge of the surface Fe atom nearest to the Cr atom. For the
‘2Cr in 2L’ case, the red branch (open circle) shows the charge of the Fe atom at site 5, and the blue branch (lled
circle) shows the charge of an Fe atom at sites 2 and 4.
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Insertion of dierent Cr-atom congurations into the two topmost atomic layers of a pure Fe surface can
either increase or decrease the oxygen adsorption energies: Cr under an oxygen atom makes the oxygen bonding
stronger and Cr farther away from the adsorption site makes the oxygen bonding weaker. is two-way eect
is further enhanced when there are two Cr atoms in the surface layers. is demonstrates the general eect of
Cr on the Fe surface: Cr attracts oxygen more than Fe and, at the same time, makes beyond-nearest-neighbour
Fe atoms less attractive to oxygen than they would be in a pure-Fe surface. is Cr eect is strongest for bridge
adsorption and weakest for on-top adsorption.
At the bridge site of the bcc Fe(100) surface, the shape of the minimum of the oxygen potential energy sur-
face (PES) is very shallow along the minimum-energy diusion path towards the hollow site compared to the
shape of the minimum of the oxygen PES at the hollow site65. Consequently, the adsorption-energy dierence
between bridge-site and hollow-site oxygen gives a good approximation for the diusion barrier of an oxygen
atom escaping from a hollow site. For the Cr-free surface this dierence is 0.65eV (0.894eV according to Cao
etal.65), and for the hollow site with a Cr atom beneath the oxygen the dierence is 0.91eV. e lowest dierence,
0.27eV, is for oxygen moving from a hollow site to a bridge site between two Cr atoms. e highest dierence,
1.09eV, occurs for an oxygen atom moving from the strongest-bonding hollow-site conguration (Cr at sites 1
and 7) toward the bridge site between two iron atoms. All calculated dierences are provided in Supplementary
Information. All in all, the barrier analysis demonstrates that the oxygen anity of chromium is higher than
that of iron and, therefore, the surface diusion of an oxygen atom on the bcc Fe–Cr(100) surface tends to be
biased towards Cr atoms.
In summary, we have carried out abinitio density functional calculations to investigate the adsorption of
atomic oxygen for two dierent Fe–Cr alloy compositions, namely, the dilute Fe–Cr alloy with the lattice constant
of pure Fe and the Fe0.91Cr0.09 composition. Up to two chromium atoms were inserted in the two topmost surface
layers. e two dierent investigated alloys were found to have the same order of preference for adsorption sites,
hollow > bridge > on-top (from most to least favoured); the distances between the oxygen atom and the nearest
metal atoms also turned out to be nearly identical for the two compositions. Although there were some dierence
in absolute adsorption energies, the relative adsorption energies were practically the same except in a few cases.
e oxygen was found to prefer congurations that have a subsurface chromium atom right beneath the hollow
adsorption site. A Cr atom was shown to reduce the oxygen anity of Fe beyond the nearest neighbours of the
Cr atom. is eect that the adsorption sites between the Cr sites become less favorable to oxygen, combined
with the fact that the most favorable adsorption site of an oxygen atom is near to the Cr atom, leads to a biased
oxygen diusion probability towards Cr atoms and, thereby, an eective ‘pulling force’ that acts on the oxygen
atoms towards the Cr atoms.
Received: 17 August 2020; Accepted: 26 February 2021
References
1. Oleord, I. e passive state of stainless steels, surface problems in materials science and technology. Mater. Sci. Eng. 42, 161–171.
https ://doi.org/10.1016/0025-5416(80)90025 -7 (1980).
2. Lince, J. R., Didziulis, S. V., Shuh, D. K., Durbin, T. D. & Yarmo, J. A. Interaction of O2 with the Fe0.84Cr0.16(001) surface studied
by photoelectron spectroscopy. Surf. Sci. 277, 43–63. https ://doi.org/10.1016/0039-6028(92)90611 -9 (1992).
3. Donik, Č et al. XPS study of duplex stainless steel oxidized by oxygen atoms. Corros. Sci. 51, 827–832. https ://doi.org/10.1016/j.
corsc i.2009.01.021 (2009).
4. Goncharov, O. Y. & Kanunnikova, O. M. High-temperature oxidation of Fe–Cr alloys in air. Inorg. Mater. 43, 515–519. https ://doi.
org/10.1134/S0020 16850 70501 47 (2007).
5. Lev y, A. V. & Yong-Fa, M. Erosion-corrosion mechanisms and rates in Fe–Cr steels. Wear 131, 39–51. https ://doi.org/10.1016/0043-
1648(89)90244 -5 (1989).
6. Ropo, M. et al. eoretical evidence of the compositional threshold behavior of FeCr surfaces. Phys. Rev. B 76, 220401. https ://
doi.org/10.1103/PhysR evB.76.22040 1 (2007).
7. Levesque, M. Anomalous surface segregation proles in ferritic Fe–Cr stainless steel. Phys. Rev. B Condens. Matter Mater. Phys.
87, 1–5. https ://doi.org/10.1103/PhysR evB.87.07540 9 (2013).
8. Ropo, M. et al. First-principles atomistic study of surfaces of Fe-rich Fe–Cr. J. Phys. Condens. Matter Instrum. Phys. J. 23, 265004
(2011).
9. Levesque, M., Gupta, M. & Gupta, R. P. Electronic origin of the anomalous segregation behavior of Cr in Fe-rich Fe–Cr alloys.
Phys. Rev. B Condens. Matter Mater. Phys. 85, 1–6. https ://doi.org/10.1103/PhysR evB.85.06411 1 (2012).
10. Leygraf, C. & Hultquist, G. Initial oxidation stages on FeCr(100) and FeCr(110) surfaces. Surf. Sci. 61, 69–84. https ://doi.
org/10.1016/0039-6028(76)90408 -8 (1976).
11. Vesel, A., Mozetič, M. & Zalar, A. Oxidation of AISI 304L stainless steel surface with atomic oxygen. Appl. Surf. Sci. 200, 94–103
(2002).
12. Gheno, T., Monceau, D. & Young, D. J. Kinetics of breakaway oxidation of Fe–Cr and Fe–Cr–Ni alloys in dry and wet carbon
dioxide. Corros. Sci. 77, 246–256. https ://doi.org/10.1016/0025-5416(80)90025 -70 (2013).
13. Ranganath, S.B., Wick, C.D. & Ramachandran, B.R. Role of structure and oxidation states in the passivation of stainless steel by
chromium. In 8th Annual International Conference on Sustainable Energy and Environmental Sciences (SEES 2019), 10–14. https
://doi.org/10.5176/2251-189X_SEES1 9.65 (2019).
14. Yuan, X.-S. et al. Segregation of alloying atoms on the Fe(100) surface and their eects on oxygen adsorption. Phys. B Condens.
Matter 425, 42–47. https ://doi.org/10.1016/0025-5416(80)90025 -71 (2013).
15. Błoński, P., Kiejna, a & Hafner, J. eoretical study of oxygen adsorption at the Fe (110) and (100) surfaces. Surf. Sci. 590, 88–100.
https ://doi.org/10.1016/0025-5416(80)90025 -72 (2005).
16. Błoński, P., Kiejna, A. & Hafner, J. Oxygen adsorption on the clean and O-precovered Fe (110) and (100) surfaces. J. Phys. Condens.
Matter 19, 96011. https ://doi.org/10.1016/0025-5416(80)90025 -73 (2007).
17. Tan, X., Zhou, J. & Peng, Y. First-principles study of oxygen adsorption on Fe(110) surface. Appl. Surf. Sci. 258, 8484–8491. https
://doi.org/10.1016/0025-5416(80)90025 -74 (2012).
Content courtesy of Springer Nature, terms of use apply. Rights reserved


Vol:.(1234567890)
Scientic Reports | (2021) 11:6046 | 
www.nature.com/scientificreports/
18. Ossowski, T. & Kiejna, A. Oxygen adsorption on Fe(110) surface revisited. Surf. Sci. 637–638, 35–41. ht t ps ://do i .org/10.1016/0025-
5416(80)90025 -75 (2015).
19. Sakisaka, Y., Miyano, T. & Onchi, M. Electron-energy-loss-spectroscopy study of oxygen chemisorption and initial oxidation of
Fe(100). Phys. Rev. B 30, 6849–6855 (1984).
20. Busch, M., Gruyters, M. & Winter, H. Spin polarization and structure of molecular oxygen adsorbed on Fe(1 1 0). Surf. Sci. 600,
4598–4604. https ://doi.org/10.1016/0025-5416(80)90025 -76 (2006).
21. Getzla, M., Bansmann, J. & Schönhense, G. Oxygen on Fe(110): Magnetic properties of the adsorbate system. J. Magn. Magn.
Mater. 192, 458–466. https ://doi.org/10.1016/0025-5416(80)90025 -77 (1999).
22. Headrick, R. L., Konarski, P., Yalisove, S. M. & Graham, W. R. Medium-energy ion scattering study of the initial stage of oxidation
of Fe(001). Phys. Rev. B 39, 5713 (1989).
23. Idczak, R., Idczak, K. & Konieczny, R. Oxidation and surface segregation of chromium in Fe–Cr alloys studied by Mössbauer and
x-ray photoelectron spectroscopy. J. Nucl. Mater. 452, 141–146. https ://doi.org/10.1016/0025-5416(80)90025 -78 (2014).
24. Han, L. L. & Liu, T. Adsorption of O atom on Cr (100), (110), (111), and (211) surfaces: An 5-parameter Morse potential method
study. Bull. Korean Chem. Soc. 33, 1867–1872. https ://doi.org/10.1016/0025-5416(80)90025 -79 (2012).
25. Zimmermann, J. & Ciacchi, L. C. Mechanisms of initial oxidation of the Co (0001) and Cr (110) surfaces. J. Phys. Chem. C 114,
6614–6623 (2010).
26. Müller, M. & Oechsner, H. Insitu STM and AES studies on the oxidation of Cr(110). Surf. Sci. 387, 269–278. https ://doi.
org/10.1016/0039-6028(92)90611 -90 (1997).
27. Peruchetti, J., Pirri, C., Bolmont, D. & Gewinner, G. Evidence for two oxygen chemiroption sites on the Cr (100) surface at room
temperature. Solid State Commun. 59, 517–519 (1986).
28. Shinn, N. D. & Madey, T. E. Oxygen chemisorption on Cr(110). I. Dissociative adsorption. Surf. Sci. 173, 379–394. https ://doi.
org/10.1016/0039-6028(92)90611 -91 (1986).
29. Baca, A., Klebano, L., Schulz, M., Paparazzo, E. & Shirley, D. e initial oxidation of Cr(100). Surf. Sci. 171, 255–266 (1986).
30. Han, C. et al. Eects of alloying on oxidation and dissolution corrosion of the surface of
γ
-Fe(111): A DFT study. J. Mol. Model.
21(181), 1–9. https ://doi.org/10.1016/0039-6028(92)90611 -92 (2015).
31. Mortensen, J. J., Hansen, L. B. & Jacobsen, K. W. Real-space grid implementation of the projector augmented wave method. Phys.
Re v. B 71, 035109. https ://doi.org/10.1016/0039-6028(92)90611 -93 (2005).
32. Enkovaara, J. et al. Electronic structure calculations with gpaw: A real-space implementation of the projector augmented-wave
method. J. Phys. Condens. Matter 22, 253202 (2010).
33. Larsen, A. H. et al. e atomic simulation environment’s python library for working with atoms. J. Phys. Condens. Matter 29,
273002 (2017).
34. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868. https
://doi.org/10.1016/0039-6028(92)90611 -94 (1996).
35. Yu, J., Lin, X., Wang, J., Chen, J. & Huang, W. First-principles study of the relaxation and energy of bcc-Fe, fcc-Fe and AISI-304
stainless steel surfaces. Appl. Surf. Sci. 255, 9032–9039. https ://doi.org/10.1016/0039-6028(92)90611 -95 (2009).
36. Feldman, B., Seideman, T., Hod, O. & Kornik, L. Real-space method for highly parallelizable electronic transport calculations.
Phys. Rev. B 90, 035445. https ://doi.org/10.1103/PhysR evB.90.03544 5 (2014).
37. Bitzek, E., Koskinen, P., Gähler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Phys. Rev. Lett. 97, 170201. https
://doi.org/10.1016/0039-6028(92)90611 -97 (2006).
38. Tran, R. et al. Surface energies of elemental crystals. Sci. Data 3, 160080. https ://doi.org/10.1016/0039-6028(92)90611 -98 (2016).
39. Tran, R. et al.Data from: Surface energies of elemental crystals. https ://doi.org/10.5061/dryad .f2n6f (2016).
40. Vitos, L., Ruban, A., Skriver, H. & Kollár, J. e surface energy of metals. Surf. Sci. 411, 186–202. https ://doi.org/10.1016/0039-
6028(92)90611 -99 (1998).
41. Kuronen, A. et al. Segregation, precipitation, and
α
-
α
phase separation in Fe–Cr alloys. Phys. Rev. B 92, 214113 (2015).
42. Hugosson, H. W., Cao, W., Seetharaman, S. & Delin, A. Sulfur- and oxygen-induced alterations of the iron (001) surface magnetism
and work function: A theoretical study. J. Phys. Chem. 117, 6161–6171. https ://doi.org/10.1021/jp310 2496 (2013).
43. Natan, A., Kronik, L. & Shapira, Y. Computing surface dipoles and potentials of self-assembled monolayers from rst principles.
Appl. Surf. Sci. 252, 7608–7613. https ://doi.org/10.1016/j.corsc i.2009.01.0211 (2006).
44. Natan, A. et al. Real-space pseudopotential method for rst principles calculations of general periodic and partially periodic
systems. Phys. Rev. B 78, o75109. https ://doi.org/10.1103/PhysR evB.78.07510 9 (2008).
45. Cao, W. eoretical and experimental studies of surface and interfacial phenomena involving steel surfaces. Ph.D. thesis, Division of
Materials Process Science Department of Materials Science and Engineering Royal Institute of Technology (2010).
46. Behler, J., Reuter, K. & Scheer, M. Nonadiabatic eects in the dissociation of oxygen molecules at the Al(111) surface. Phys. Rev.
B 77, 115421. https ://doi.org/10.1103/PhysR evB.77.11542 1 (2008).
47. Kitchin, J. R. Correlations in coverage-dependent atomic adsorption energies on Pd(111). Phys. Rev. B 79, 205412. https ://doi.
org/10.1103/PhysR evB.79.20541 2 (2009).
48. İnoğlu, N. & Kitchin, J. R. Simple model explaining and predicting coverage-dependent atomic adsorption energies on transition
metal surfaces. Phys. Rev. B 81, 045414. https ://doi.org/10.1103/PhysR evB.82.04541 4 (2010).
49. Shi, H. & Stampgl, C. First-principles investigations of the structure and stability of oxygen adsorption and surface oxide formation
at Au(111). Phys. Rev. B 76, 075327. https ://doi.org/10.1103/PhysR evB.76.07532 7 (2007).
50. Maschho, B. L. & Armstrong, N. R. in Oxide Layers on Clean Iron Surfaces: Formation under Vacuum and Characterization
by Photoelectron spectroscopy and electrochemical reactions of probe molecules at the oxide/electrolyte interface. Langmuir 7,
693–703 (1991).
51. Walsh, A., Sokol, A. A., Buckeridge, J., Scanlon, D. O. & Catlow, C. R. A. Electron counting in solids: Oxidation states, partial
charges, and ionicity. J. Phys. Chem. Lett. 8, 2074–2075 (2017).
52. Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for bader decomposition of charge density. Comput.
Mater. Sci. 36, 354–360. https ://doi.org/10.1016/j.corsc i.2009.01.0217 (2006).
53. Yu, M. & Trinkle, D. R. Accurate and ecient algorithm for bader charge integration. J. Chem. Phys. 134, 064111. https ://doi.
org/10.1016/j.corsc i.2009.01.0218 (2011).
54. Choudhuri, I. & Truhlar, D. G. Calculating and characterizing the charge distributions in solids. J. Chem. eory Comput. 16, 5884.
https ://doi.org/10.1021/acs.jctc.0c004 40 (2020).
55. Zornio, B. F., d Silva, E. Z. & San-Miguel, M. A. eoretical insights into 1D transition-metal nanoalloys grown on the NiAl(110)
surface. ACS Omega 3, 8819–8828. https ://doi.org/10.1021/acsom ega.8b008 17 (2018).
56. Lebon, A., Aguado, A. & Vega, A. Nanoscale reactivity of ZnxMg20?x investigated by structural and electronic indicators. Corros.
Sci. 124, 35–45. https ://doi.org/10.1134/S0020 16850 70501 471 (2017).
57. Alvarez-Zapatero, P., Vega, A. & Aguado, A. Incorporating charge transfer eects into a metallic empirical potential for accurate
structure determination in (ZnMg)N nanoalloys. Nanoscale 12, 20432–20448. h t t ps ://do i.o r g/10.1134/S0020 16850 70501 472 (2020).
58. Jones, T. E., Miorelli, J. & Eberhart, M. E. Reactive cluster model of metallic glasses. J. Chem. Phys. 140, 084501. https ://doi.
org/10.1134/S0020 16850 70501 473 (2014).
59. Saikia, U., Sahariah, M. B., González, C. & Pandey, R. Vacancy assisted He-interstitial clustering and their elemental interaction
at fcc-bcc semicoherent metallic interface. Sci. Rep. 8, 3844. https ://doi.org/10.1038/s4159 8-018-22141 -y (2018).
Content courtesy of Springer Nature, terms of use apply. Rights reserved


Vol.:(0123456789)
Scientic Reports | (2021) 11:6046 | 
www.nature.com/scientificreports/
60. Hu, J. et al. A d-based model on the adsoprtion behavior of h2o, h+, cl-, and oh- on clean and cr-doped fe(110) planes. Coatings
8, 51. https ://doi.org/10.1134/S0020 16850 70501 475 (2018).
61. Papanikolaou, N., Nonas, B., Heinze, S., Zeller, R. & Dederichs, P. H. Scanning tunneling spectra of impurities in the Fe(001)
surface. Phys. Rev. B 62, 11118–11125. https ://doi.org/10.1103/PhysR evB.62.11118 (2000).
62. Bagus, P. S., Käfer, D., Witte, G. & Wöll, C. Work function changes induced by charged adsorbates: Origin of the polarity asym-
metry. Phys. Rev. Lett. 100, 126101. https ://doi.org/10.1103/PhysR evLet t.100.12610 1 (2018).
63. Lousada, C. M., Johansson, A. J. & Korzhavyi, P. A. Adsorption of hydrogen sulde, hydrosulde and sulde at Cu(110)—Polariz-
ability and cooperativity eects. First stages of formation of a sulde layer. ChemPhysChem 19, 2159–2168. https ://doi.o r g/10.1002/
cphc.20180 0246 (2018).
64. Maurer, R. J. et al. Adsorption structures and energetics of molecules on metal surfaces: Bridging experiment and theory. Prog.
Surf. Sci. 91, 72–100. https ://doi.org/10.1134/S0020 16850 70501 479 (2016).
65. Cao, W., Delin, A. & Seetharaman, S. Calculation of oxygen and sulfur average velocity on the iron surface: A two-dimensional
gas model study. Steel Res. Int. 81, 949–952. https ://doi.org/10.1002/srin.20100 0110 (2010).
Acknowledgements
We have received funding from the Academy of Finland (Grant No. 308633). e computer resources of the
Finnish IT Center for Science (CSC) and the Finnish Grid and Cloud Infrastructure (FGCI; urn:nbn::research-
infras-2016072533) project are gratefully acknowledged. e services of Turku University Center for Materials
and Surfaces (MatSurf) are acknowledged.
Author contributions
M.R. performed the computations and analysed the results. M.R., M.P. and K.K. wrote the manuscript. PK., M.Y.,
S.G. and A.K. discussed the results and commented on the manuscript.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https ://doi.
org/10.1038/s4159 8-021-85243 -0.
Correspondence and requests for materials should be addressed to K.K.
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