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First-Principles Studies of Paramagnetic Vivianite Fe3(PO4)2·8H2O
Surfaces
Henry P. Pinto,* Andrea Michalkova, and Jerzy Leszczynski
Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Jackson State University, Jackson, Mississippi 39217, United
States
ABSTRACT: Using density-functional theory, we have
computed the structural and electronic properties of paramagnetic vivianite crystal Fe3(PO4)2·8H2O and its (010)-(1 ×
1) and (100)-(1 × 1) surfaces. The properties of bulk vivianite
are studied with a set of functionals: HSE06, PBE, AM05,
PBEsol, and PBE with on-site Coulomb repulsions corrections
(PBE+U). The appropriate U parameter is estimated by
considering the HSE06 results, and it is used to study the
vivianite surfaces. The computed surface energy predicts the
(010) surface to be the most stable. The less stable (100)
surface is observed to have important reconstructions with the spontaneous formation of a water molecule at the surface and two
hydroxide hydrate anions per unit cell. Using thermodynamical considerations within DFT, we have calculated the phase diagram
of the (010) surface in equilibrium with hydrogen gas. The results suggest that under ultralow hydrogen pressure, the (010)
surface with two hydrogen vacancies is stable. The electronic structure calculations for the surfaces are complemented with the
computed scanning tunneling microscopy (STM) images for constant-current mode. The topology is dominated by the surface
Fe-3d states that protrude into the vacuum.
■
INTRODUCTION
The vivianite Fe3(PO4)2·8H2O mineral has been experimentally
well studied, but there are sparse theoretical models that
support those experiments. The surfaces of vivianite have been
experimentally less studied, and no reliable atomic-scale model
exists for the surface structure and their properties. The reason
might be associated with experimental difficulties in preparing
clean surfaces free of impurities. Developing and understanding
structural models for the surfaces of paramagnetic vivianite
Fe3(PO4)2·8H2O is the aim of this work. The vivianite group of
minerals are hydrated iron phosphates having the A32+(XO4)2·
8H2O general formula. A2+ can be any of the following
elements: Co, Fe, Mg, Ni, and Zn. The variable X is either As
or P. They can be found in coatings of water pipes, soils,
morasses, and sediments, which makes them photosensitive.1,2
Vivianite is a typical member of this mineral group with the
Fe3(PO4)2·8H2O chemical formula. The vivianite crystal
structure has a monoclinic lattice with C2/m symmetry and
with cell parameters a = 10.021 Å, b = 13.441 Å, c = 4.721 Å,
and β = 102.84°. 3 The vivianite crystal is also an
antiferromagnet with a Neél temperature TN ∼ 10 K, above
this temperature, vivianite has paramagnetic properties.4
Hydrogen bonding between the H2O ligands holds together
sheets consisting of linked Fe and PO4 polyhedra.5 Vivianite
can be oxidized through auto-oxidation or by the air when Fe2+
is oxidized to Fe3+.1,6 It is typical for anoxic environments and
indicative for geochemical conditions where ferric iron oxides
usually dissolve.7 It has great chemical and thermal stability.
Vivianite can disintegrate into strongly magnetic magnetite and
weakly magnetic hematite upon heating in air.8−10
© 2014 American Chemical Society
Several experimental studies on vivianite have been
published. The early qualitative structure of vivianite11 has
been redetermined by X-ray12 as well as by neutron diffraction.3
The vibrational and rotational atomic properties of bulk
vivianite have been carefully studied by optical and near-IR
spectroscopies.13−15 The magnetic properties of vivianite have
been investigated using different techniques such as NMR,16
specific heat,17 static susceptibility measurements,18 neutron
diffraction,19 and Mössbauer spectroscopy.20 According to our
best knowledge, only one theoretical study of the electronic
structure of vivianite has been published.21 The authors have
investigated the electronic and magnetic structure of vivianite
using the cluster molecular orbital calculations in the local spin
density approach. They have assigned unambiguously the
optical and Mössbauer spectra for ferrous iron. However, the
assignment for ferric iron was not conclusive due to
uncertainties in the geometrical changes accompanying the
oxidation.21
Experiments on vivianite surfaces are scarce, and we are only
aware of the work of Pratt.22 In that study, a X-ray
photoelectron spectroscopy was performed on vivianite (010)
surfaces cleaved in a N2 gas atmosphere. The main result points
an autoreduction−oxidation process triggered by the rupture of
hydrogen bonds leading to the formation of the hydroxyl
groups and ferric sites; this process was originally suggested by
Moore et al.23 and experimentally confirmed by Pratt.22
Received: May 18, 2013
Revised: February 24, 2014
Published: March 2, 2014
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■
Article
COMPUTATIONAL DETAILS AND METHODS
Density-functional theory (DFT) calculations have been
performed using the plane wave basis Vienna ab initio
simulation package (VASP).24,25 We describe the Fe-[Ar], O1s2 and P-[Ne] core electrons with projector augmented wave
(PAW) potentials.26 Using a cutoff kinetic energy of 650 eV
and a Γ-centered Monkhorst−Pack grid with 0.04 Å−1 spacing
between k points (e.g., this is equivalent to 3 × 3 × 5, 6 × 3 ×
1, and 2 × 5 × 1 grids of the corresponding primitive cell of
bulk vivianite, Fe3(PO4)2·8H2O (010)-(1 × 1) slab and
Fe3(PO4)2·8H2O (100)-(1 × 1) slab, respectively), we
converge the total energy to <1 meV/atom. In the case of
the surfaces, they were modeled using periodic slabs with three
layers and 15 Å vacuum along the [001] direction. All the
structures under study were fully relaxed until all the forces
were <0.02 eV Å−1. In this work, the DFT calculations are
performed at 0 K; however, the finite temperature phase of
vivianite (paramagnetic) can be approximated by a nonmagnetic (NM) (i.e., nonspin polarized) solution following the
Stoner theory of magnetism.27 This model suggest that
magnetic moments remain ferrimagnetically (or ferromagnetically) ordered within the temperature range 0 < T < TN. The
local moments decrease with the increasing temperature and
finally vanishes for T ≥ TN. This approximation has been
successfully applied in other DFT studies of paramagnetic
systems such as fcc and bcc iron.24,28,29 In addition, and to get a
better understanding of the electronic structure at the surface,
we simulated scanning tunneling microscopy (STM) of the
surfaces considered in this work. The constant-current mode
STM images and line scans for vivianite surfaces with both
positive and negative bias voltages were computed. For this
purpose, the bSKAN code30,31 was used. This program
implements the Tersoff−Hamman32,33 approximationthat
is, it assumes the tunneling current to be proportional to the
surface local density of states (LDOS) of the surface at the
position of the tip. bSKAN calculates the LDOS using the realspace single-electron wave functions of the slabs computed
previously with VASP. Notice that each point in the space has
associated a LDOS value for a given value of bias voltage. Thus,
the constant-current STM images are the contour of constant
LDOS of the surface within the vacuum above the surface
atoms.30,32,33 Finally, we also computed the work function Φ
defined as the energy to move one electron from the Fermi
level into the vacuum outside the surface. Within our
calculations, this value is computed following the standard
method34that is, as the difference of the electrostatic
potential far from the surface (this lies in the middle of the
vacuum region of the slab) and the Fermi level. This surface
property can be measured using for instance photoelectron
emission spectroscopy or kelvin probe microscopy.35
Functional Choice. Before we proceed to model the
vivianite system, we need to determine the exchangecorrelation functional that describes best the vivianite
Fe3(PO4)2·8H2O crystal. We have tested the performance of
a set of functionals by computing the physical properties of
bulk vivianite. We have considered the following functionals:
the generalized gradient approximation (GGA) by Perdew,
Burke, and Ernzerhof (PBE);36 the PBE functional with
intrasite Coulomb repulsion corrections (PBE+U) within
Dudarev’s approach;37 the meta-GGA functionals such as
PBEsol38 and AM05;39,40 and the hybrid Hartree−Fock DFT
functional HSE0641−43 was used as a benchmark. The above-
mentioned set of functionals were selected because of their
reliability as they have been extensively tested in periodic
systems;36,38−40,44,45 certainly the hybrid functionals could be
considered among the most sophisticated and reliable
approximations used in solids. It is worth mentioning that in
all the calculations of this study, we employed PBE−PAW
potentials as described in the beginning of this section.
Using that set of functionals, we have computed the optimal
lattice parameters and mechanical properties of vivianite by
fitting the calculated data to a third-order Birch−Murnaham
equation of state46 (BM-EOS); thus we computed the optimal
volume of the crystal (V0) and the bulk modulus B0. From the
computed electronic structure, we have estimated the band gap
Eg. In addition, a Bader analysis47 of the charge density has
been performed. In the case of PBE+U, we fitted the Dudarev’s
U parameter to reproduce the band gap predicted by the
HSE06 functional, the reason is because until the date this
study was presented, we are unaware of any experiment that
reports the band gap of vivianite Fe3(PO4)2·8H2O.
Surface Energy. We have computed the surface energies
following the standard procedure:48 the surface energy of a
system, σ, is the energy per unit area required to create a
surface from the bulk. Considering a sufficiently thick slab, σ is
defined as
σ=
1
N
lim (Eslab
− NE bulk )
2A N →∞
(1)
where A is the slab area, the factor 1/2 accounts for the two
surfaces in the slab, ENslab is the computed energy of the slab with
N-atoms and Ebulk is the bulk total energy. In actual
computations, rather than using Ebulk from calculations of the
bulk primitive cell, we use the more consistent value given by
the slope of the linear polynomial fitted to ENslab versus N, as
suggested in previous works.49,50 When the slab is sufficiently
thick, there is a linear dependence of ENslab with respect to N
N
Eslab
≈ 2Aσ + NE bulk
(2)
and so the slope is the bulk energy, which is then replaced in eq
1 to yield the surface energy. In our calculations, the linear
trend is reached when the slabs have at least three layers, where
each layer contains one Fe3(PO4)2·8H2O formula unit; Ebulk of
eq 2 was computed using slabs with three up to five layers. It is
worth mentioning here that in all the cases, ENslab is the total
energy of the fully relaxed slab. To properly consider the
thermodynamics of hydroxylated vivianite surfacesthat is,
changing the number of H atoms at the surface; we employ the
formalism of ab initio thermodynamics,51−54 and thus we could
assume that the surface can exchange the H atoms with a
surrounding gas phase. In thermodynamic equilibrium between
the surface and the gas phase, the most stable surface
compositionat a given gas pressure p and temperature T
is given by the minimum of the surface Gibbs free energy. In
this work, we are only interested in the relative stability of the
surface structures with respect to the pristine surface, and then
we can estimate the differences in the Gibbs free energy
ΔG(p,T) between the defective and pristine surface:
ΔG(p , T ) =
1
[G(p , T )slab − nH − G(p , T )slab
2A
− ΔNHμH (p , T )]
(3)
where A is the surface area of the surface unit cell, G(p,
T)slab−nH is the Gibbs free energy of the defective surface
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Table 1. Computed Physical Properties of Vivianite Depending on the Functionala
functional
a (Å)
b (Å)
c (Å)
β°
HSE06
PBE
PBEsol
AM05
exptb
exptc
9.884
9.909
9.713
9.769
10.021
10.080
13.146
13.215
12.783
12.922
13.441
13.430
4.568
4.587
4.513
4.524
4.721
4.700
104.97
104.99
104.90
105.00
102.84
104.50
V0 (Å3)
573.382
580.204
541.456
551.699
619.982
619.993
(−7.5%)
(−6.4%)
(−12.7%)
(−11.0%)
B0 (KBa)
Eg (eV)
401.87
413.57
573.37
490.30
3.3
1.1
1.0
1.1
a
The lattice parameters a, b, and c are in Å, the β angle is in degrees and by symmetry constraints α = γ = 90° (see Figure 1 for lattice parameters
definitions); the optimal volume V0 is in Å3 (between parentheses is the error with respect to the experimental value of ref 3), the bulk modulus B0 in
KBa and the band gap Eg in eV. All the structures were predicted to have C2/m symmetry in agreement with experiment.3,11 bRef 3. cRef 11.
Table 2. Computed PBE+U Physical Properties for Different Values of Ua
U (eV)
a (Å)
b (Å)
c (Å)
β°
V0 (Å3)
B0 (KBa)
Eg (eV)
0.0
2.0
4.0
6.0
HSE06
9.909
9.952
9.994
10.044
9.884
13.215
13.224
13.276
13.298
13.146
4.587
4.610
4.625
4.644
4.568
104.99
104.93
104.94
104.99
104.97
580.204
586.202
592.805
599.126
573.382
413.57
407.12
398.10
396.57
401.87
1.1
1.9
3.2
4.5
3.3
a
In this table, we also display the predictions of HSE06 functional for comparison. Notice that standard GGA-PBE calculation corresponds to U =
0.0 eV.
without n H atoms, G(p, T)slab is the Gibbs free energy of the
pristine surface, ΔNH is the difference of the H atoms between
the defective and pristine surface, and μH(p, T) is the chemical
potential of the H atoms that is related to the Gibbs free energy
of the molecular hydrogen in gas phase:
μ H (T , p) =
functionals, are displayed in Table 1. In that table, we have also
included the available experimental data. The results displayed
in Table 1 suggest that all the functionals tested reproduce the
physical parameters in good agreement with available
experimental data.3,11 From Table 1, we can conclude that
HSE06 and PBE are the functionals that better reproduce the
experimental volume with errors of −7.5% and −6.4%,
respectively. Experimental data concerning the bulk modulus
or the band gap of vivianite are unavailable or nonexistent. It is
well-known that HSE06 functional is capable of correctly
predicting the band gap within the DFT calculations and is well
documented that it provides the most accurate electronic
structure predictions of crystals including lattice and mechanical
properties;44,45,57 for these reasons, we assume that vivianite is
better described by HSE06: it suggest that paramagnetic
vivianite has band gap of 3.3 eV, and its bulk modulus is ∼402
KBar.
The computed volume with the PBE functional has an error
of −6.4%, and it performs surprisingly better than meta-GGA
functionals PBEsol and AM05: for these functionals the
computed volume has an error of −12.7% and −11.0%,
respectively, almost twice of the PBE error. Here we can only
suggest that perhaps it was an accidental prediction of PBE
since it is expected that overall PBEsol and AM05 improve
standard GGA predictions in solids.38,40
Because of computational restrictions of using HSE06 on
bigger systems, we were unable to apply this method on the
surfaces of vivianite. To tackle this limitation, we have applied
the GGA-PBE functional with on-site Coulomb corrections
between Fe-3d electrons within the Dudarev’s approach;37 we
call it here the PBE+U method. The U parameter was fitted
only to reproduce the HSE06 predicted band gap of 3.3 eV for
bulk vivanite. This fitted U parameter is then applied on the
surfaces as an attempt to improve the description of the
electronic structure since correct bad gap prediction is desirable
for studying possible surface states within the band gap.
Furthermore, the calculations show that for bulk vivianite,
fitting U for reproducing HSE06 Eg has a positive overall effect
on the physical properties as it is shown in Table 2. Finally,
⎛ pH ⎞⎤
1 ⎡ total
⎢E H + μH (T , p◦ ) + kBT ln⎜ ◦2 ⎟⎥
2
2 ⎢⎣ 2
⎝ p ⎠⎥⎦
(4)
EHtotal
2
here
is the computed total energy for isolated H2
molecule, p° is the standard state pressure (0.1 MPa), μH2(T,
p°) accounts for the rotations and vibrations as well as the ideal
gas entropy of the H2 molecule. For μH2(T, p°), we use the
experimental values from thermodynamical tables.55 Assuming
thermodynamical equilibrium of the surface with the H2 gas,
the chemical potential can be directly related to a pressure scale
as a function of the temperature by solving pH2 in eq 4. The
computed ΔG(p, T) can be expressed as a function of ΔμH =
μH(T, p) − μH(T = 0K, p) where
μH (T = 0 K, p) =
1 total
EH
2 2
(5)
and we chose this value to be the zero reference of μH(T, p);
therefore, the maximum value for ΔμH = 0that is, the upper
bound for μH is 1/2Etotal
H2 . For reference purposes, the computed
PBE energy for isolated H2 molecule is −6.78 eV. Finally, it is
important to mention that since we are not adding other atoms
in the system. We could assume that vibrational contributions
to differences in the Gibbs free energy is within the order of 10
meV Å−2 (≡ 0.16 J m−2)as it is suggested in a previous work
of Reuter et al.;53,56 then we could neglect this contribution in
eq 3 without compromising the results and conclusions of this
study.
■
BULK PROPERTIES OF PARAMAGNETIC VIVIANITE
The computed ground state properties for paramagnetic
vivianite Fe3(PO4)2·8H2O, using the above-mentioned set of
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notice that the U parameter is not a universal value for each
atom (here Fe); in fact, several studies have shown that it is a
system-dependent value on the covalent or ionic character of
the material.58−60
In Table 2, we show the computed physical parameters of
vivianite as a function of the U value. The PBE+U(4.0)
reproduces best the HSE06 Eg value of 3.3 eV. Notice that bulk
modulus decreases to ∼398 KBar in better correspondence to
the HSE06 B0 of 402 KBar. In addition, we also observed that
V0 for U = 4.0 eV has a −4.4% error with respect to the
experiment.3
In Table 3, we present the predicted PBE+U(4.0) atomic
parameters for paramagnetic Fe3(PO4)2·8H2O. The iron
Figure 1. The PBE+U(4.0) predicted crystal structure for paramagnetic Fe3(PO4)2·8H2O. (a) Side view of the structure where the
unit cell is delimited by the rectangular box with a, b, and c lattice
vectors; in the same figure we also include the primitive cell denoted
by the rhombohedral box in dotted lines. In this view is possible to
notice the layered structure of vivianite perpendicular to the b lattice
vector, that is, the [010] axis. (b) Perspective view of vivianite crystal
structure.
Table 3. Crystallographic Data for the Unit Cell of
Paramagnetic Fe3(PO4)2·8H2O Using PBE+U(4.0)a
site
u
v
w
Fe(1)
0.0000
0.0000
0.0000
1.19
qB
Fe(2)
0.5000
0.8907
0.0000
1.23
P
0.6847
0.0000
0.6182
3.65
O(1)
0.6580
0.9013
0.7779
−1.42
O(2)w
0.4050
0.6123
0.1861
−1.23
O(3)w
0.5990
0.2195
0.2799
−1.21
O(4)
O(5)
H(1)
H(2)
H(3)
H(4)
0.8421
0.5988
0.1867
0.1213
0.6247
0.5362
0.0000
0.0000
0.1241
0.0800
0.1911
0.2772
0.6159
0.2864
0.9632
0.6397
0.4866
0.2755
−1.42
−1.41
0.64
0.64
0.64
0.63
dsite−x (Å)
O(2)w = 2.071, O(4) =
2.050
Fe(2) = 2.902, O(1) =
2.099, O(3)w =
2.033, O(5) = 2.040
O(1) = 1.561, O(4) =
1.575, O(5) = 1.553
H(1) = 1.732, H(3) =
1.788
H(1) = H(2) = 1.006,
H(4) = 1.939
H(3) = 0.997, H(4) =
0.987
a
That is, V0 = 592.805 Å3 and symmetry C2/m (cf. Table 2); u, v, and
w are the fractional coordinates. We also included the Bader charge
analysis, qB in e units. The atom labels are according to Figure 1 where
the subindex w stands for water oxygens.
sublattice has two inequivalent octahedral sites: Fe(1) and
Fe(2). The Fe(1) site is coordinated by four O(2)w atoms
(forming water molecules) and two O(4) atoms (see Figure 1).
On the other hand, the Fe(2) site is coordinated by two O(3)w
(forming water molecules) and four O atoms (O(1), O(4), and
two O(5) in Figure 2). The Fe(2) sites form pairs with a
Fe(2)−Fe(2) separation of 2.902 Å along the b lattice vector
(in good agreement with the 2.850 Å observed by Mori et al.11)
̂
of 90.7°. The predicted Fe(1)−O(2)w
and Fe(2)O(5)Fe(2)
and Fe(2)−O(3)w bond lengths are 2.071 and 2.033 Å,
respectively. The experimentally measured Fe−O bond lengths
in vivianite vary. For example, Moore and Araki measured the
Fe(1)−O and Fe(2)−O distances to be shorter by 0.05 and
0.07 Å (2.16 and 2.08 Å)61 than found by Capitelli et al.62 2.21
and 2.15 Å. The P atom site form a PO4 tetrahedron linking the
Fe(1) and Fe(2) octahedral sites. The system clearly has a
laminar structure stabilized by crossed hydrogen bonding
between water molecules corresponding to O(2)w and O(3)w;
they form an interface lying on the ac planethat is, the (010)
plane (see Figure 1). The interaction of the water molecules
lying within that layer can be noticed by the charge of the O
atoms forming those molecules (Ow); they have in average
Figure 2. The computed (a) HSE06, (b) PBE+U(4.0), and (c) PBE
partial density of states for paramagnetic Fe3(PO4)2·8H2O. Notice the
close similarity around EF for HSE06 and PBE+U. The PBE
underestimates Eg as expected. The inset in (b) depicts the electronic
states of isolated water. The displayed PDOS were smeared with a
dispersion of 0.12 eV.
−1.22 e (the charge of those atoms in isolated water molecules
is −1.16 e).
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−0.5 eV has a Fe(1)-3d character, and the peak at ∼ −0.13 eV
has a Fe(2)-3d character with some O-2p contributionthat is,
no water states are involved.
The lower part of the conduction band (CB) has a peak at
∼3.5 eV. It is basically composed of Fe(1)-3d−t2g in the lower
part and Fe(2)-3d−t2g in the upper part of that sub-band; there
are also a small contribution of the O- and Ow-2p states.
Figure 3 depicts the PBE+U(4.0) computed band structure
along the high-symmetry points of the reciprocal primitive cell
In general, both the PBE and PBE+U methods are found to
predict the bond lengths in good agreement with the
experimental data. However, some recent studies have shown
that the PBE approach can underestimate the bond lengths in
minerals. For example, see refs 63 and 64. Similar discrepancy
of 0.1 Å between the observed and calculated structural
parameters was found in another theoretical study of iron
oxyhydroxysulfate, where the experimental Fe−O bond length
is 2.01 Å and DFT calculations gave 1.88 Å.65 Underestimation
of the bond lengths by 0.1 Å using the DFT+U method when
compared with the experimental data was also found in several
theoretical studies of various intermolecular complexes (cf. ref
58).
Figure 2 compares the computed partial density of states
(PDOS) using HSE06, PBE+U(4.0), and PBE. Excepting for
the width and relative position of the bands, the electronic
structure of PBE+U(4.0) is fundamentally similar to the more
accurate HSE06 predictionsthat is, the number of sub-bands
and composition in both calculations matches. The PBEcomputed electronic structure has fundamentally the same
composition and number of sub-bands than HSE06 butas is
expected, PBE underestimates the band gap. We also observed
that the composition of the upper valence band (within −2 to 0
eV in Figure 2c) differs from the HSE06 since it has Fe(1)-3d
states at both edges of that sub-band. The AM05 and PBEsol
computed PDOS (not shown here) present practically the
same features as the PBE results (Figure 2c).
Considering these results, we have decided to use PBE+U(4)
for computing the surfaces of vivianite in the next section: this
post-DFT functional will allow us to have an accurate
description of the electronic structure near the Fermi level (EF).
In the following lines we present the analysis of the
computed PBE+U(4) electronic structure (depicted in Figure
2b). Bear in mind that we have two types of oxygens in the
structure, namely, O and Ow as depicted in Figure 1 and Table
3.
The lower valence band (LVB) is composed of two subbands (cf. Figure 2b). The first sub-band, below −20 eV, has
two peaks: the lower peak at ∼ −21.5 eV has a O-2s with P-3s
contribution; the next peak at ∼ −20.6 eV belongs to the water
statesthat is, the 2a1 composed of Ow-2s and H-1s (see inset
of Figure 2b). The second sub-band is centered around ∼ −19
eV and is composed of O-2s states with small contribution of
the P-3p states. The lower and upper peaks on the LVB clearly
show the O-2s interacting with the P-states 3s and 3p. On the
other hand, the 2a1 water states show a small overlap with the
O-2s and P-states suggesting a small interaction between them.
The upper valence band (UVB) is composed of three subbands (cf. Figure 2b). The lower sub-band (within the energy
range of −10 to −7.7 eV) has basically a water 1b2 state
character Ow-2p + H-1s (this state is responsible for the OH
bonds in water). The broadening of this band is an indication of
the interaction between nearest waters thought H-bondings.
The second sub-band is extended from −7.6 to −1.5 eV. The
lower part has an overlap between the O-2p and P-3p states. It
was also found a contribution of the water 3a1 states located
around −5.6 eV; these states are interacting with the nearest O
in the form of H-bonds. Around the peak at ∼ −3.2 eV,
contributions from 1b1 (water state), O-2p, and Fe-3d are
observed. The upper part of this sub-band has a peak at ∼ −2.3
which is composed mainly of the O-2p states from the oxygen
atoms that do not form water molecules. Finally, the third subband within the −1 to 0 eV is composed of two peaks: one at ∼
Figure 3. The PBE+U(4.0) computed band structure for paramagnetic
Fe3(PO4)2·8H2O along the highest symmetry points: L(−1/2, 0, −1/
2), M(−1/2, 1/2, −1/2), A(−1/2, 0, 0), Γ (0, 0, 0), Z (0, −1/2, −1/
2), and V (0, 0, −1/2). Here EF denotes the Fermi level. On the right
panel, we also included the raw DOS.
of vivianite. The paramagnetic Fe3(PO4)2·8H2O has an indirect
band gap (Eg) where the CB minimum lies on the M-point and
the maximum of the UBV is along the Z−V direction. The
small dispersion of the occupied bands near the Fermi level
suggests the localized nature of the Fe-3d states.
The calculations of this work consider only paramagnetic
vivianite since this mineral becomes paramagnetic above 10 K,
and we are interested in the properties of this material at room
temperature. We have applied a variety of functionals as
presented in Table 1. Among the set of functionals used for
computing the bulk properties of paramagnetic vivianite
Fe3(PO4)2·8H2O, it is expected that hybrid HSE06 functional
describes more accurately the electronic structure of vivianite;
thus the predicted band gap Eg is 3.3 eV. The computed cell
parameters are in reasonable agreement with experiment: aHSE06
= 9.884(−1.4%) Å, bHSE06 = 13.146(−2.2%) Å, cHSE06 =
4.568(−3.2%) Å, βHSE06 = 104.97°(2%), and V0HSE06 =
573.382(−7.5%)Å3 (percentages within parentheses are the
errors with respect to the experimental values observed by Bartl
et al.3). We were able to satisfactorily reproduce the HSE06
electronic structure using PBE+U(4) that reproduces an Eg =
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belong to O3w1 and O3w2 (these sites correspond to the bulk
sites O(3)w as shown in Figure 1a) relaxed moving away from
each other by ∼0.16 Å; simultaneously, these water molecules
relaxed away from the topmost iron atom Fe2 by 0.03 Å. This
distortion might be better observed by the change in the
̂ 3w2 angle from 88.0° (in the unreconstructed
O3w1 Fe2 O
surface) to 92.9°. The increment of that angle is due to the
breaking of the hydrogen bonds after cleaving the crystal to
form the surface. The surface reconstruction also affects the
water molecules in the sublayer formed by O2w1 and O2w2
(these sites correspond to the O(2)w bulk site),; in this case the
̂ 2w2 angle changed from 87.9° (unreconstructed) to
O2w1 Fe1O
86.7°. The distortion of the atoms beneath the Fe2 is less than
0.02 Å. This is reflected in the PBE+U computed electronic
structure of the (010)-(1 × 1) surface displayed in Figure 6a. As
a consequence of the surface reconstruction, the Fe-3d bands
near the Fermi level are broaden and new peaks appear in both
UVB and LCB, and the band gap drops to ∼2.0 eV (the bulk Eg
is 3.2 eV). The sub-band in the UVB has two peaks. The first
peak at ∼ −1.1 eV is from the Fe2 and Fe3 surface atoms with
3d eg character. The second peak at ∼ −0.3 eV has
contributions from all the surface Fe atoms (Fe1, Fe2, and
Fe3) with Fe2,3-3d eg and Fe1-3d states composition. The LCV
is composed by two peaks. The first peak at ∼3.2 eV has a Fe2,33d t2g character; the second peak at ∼3.7 eV is composed of the
Fe1,2,3 3d t2g states. In addition to the computed PDOS, we
have also performed the Bader charge analysis that is displayed
in Figure 5(a1). A close inspection shows that changes on the
charges compared with the bulk are less than 0.02 e (cf. Table 3
and Figure 5(a1)); these results also reflect the small
reconstruction observed in this surface.
The relaxation of the atoms at the (100)-(1 × 1) surface is
more intricate compared with the (010)-(1 × 1) case; it
undergoes considerable distortions triggered by the dangling
bonds left after cleaving the crystal at the P and O(4) sites (cf.
Figures 1a and 5b). After full relaxation, we notice that O4
captures two hydrogens from the nearest neighbor waters (w1
and w2 in Figure 5b) becoming a water molecule site (cf. H1
and H2 bonding to O4 in 4(b)). This water formation allows
the formation of two hydroxide hydrate anions [HO···H···
OH]−. During this process, the hydrogen H3 (H4) that belongs
to the water molecule on the subsurface w3 (w4) relaxes 0.59 Å
outward from the O3w3 (O3w4) to an equidistant position lying
in between O2w1 and O3w3 (O2w2 and O3w4) where the O−H
distance is 1.23 Å. On the other hand, the surface P atom
undergoes an inward relaxation of ∼0.7 Å toward the
subsurface oxygen atom which also relaxed 0.52 Å toward P;
this allows P to become four coordinated with the nearest
oxygen atoms (see Figure 5b).
These structural changes are also reflected in the electronic
structure of the (100)-(1 × 1) surface (see Figure 6b). This
surface has an insulating ground state with a band gap of ∼2.2
eV. The occupied states near EF show three peaks. The first
peak at EF has the main contribution from Fe-3d with eg
character from the Fe1 atom. The peaks at −1.0 and −1.3 eV
have a Fe-3d character from the Fe2 and Fe3 atoms. The LCV is
dominated by the Fe-3d states with a t2g character: the peaks at
2.5 and 3.1 eV belong to the states from Fe2 and Fe3 atoms, and
the peak at 3.9 eV belongs to the Fe1 atom. The formation of
hydroxide hydrate anions and the new water molecule site near
the surface induces important changes on the water sub-band
(originally located within the range of −10 to −8 eV in the
3.2 eV. Within this approach, the computed cell parameters are
(see Table 2): a PBE+U = 9.994(−0.3%) Å, b PBE+U =
13.276(−1.2%) Å, cPBE+U = 4.625(−2%) Å, β PBE+U =
= 592.805(−4.4%)Å3 (percentages
104.94°(2%), and VPBE+U
0
are errors with respect to experiment3). In overall, the PBE
+U(4) improves the predicted lattice parameters of HSE06
compared with the experiment and corrects the electronic
structure of conventional PBE. The PBE+U(4) computed
PDOS for paramagnetic bulk vivianite (Figure 2b) shows
clearly distinctions between the Fe octahedral sites. This is also
observed in the computed Bader charges between both sites
(see Table 3). The UVB and LCB is dominated by the Fe-3d
states with some contribution of the O-2p states. These results
could explain ultraviolet photoelectron spectroscopy experiments on this material, but we found no published results on
this topic.
■
ENERGETICS AND STRUCTURAL PROPERTIES OF
VIVIANITE SURFACES
Having resolved the bulk structure for paramagnetic vivianite,
we proceed to investigate the (010) and (100) surfaces. The
cleaving planes have been chosen in the following manner: if
the structure of vivianite is observed along the c lattice vector
(see Figure 1a) then it is possible to realize the layered
structure of vivianite formed by Fe3(PO4)2·8H2O blocks staked
along the b lattice vector (notice a sublayer of water molecules
lying in the ac plane). Therefore, it can be defined a cleaving
{010} plane that crosses those water sublayer forming the
(010) surface. On the other hand, considering the same Figure
1a, it is possible to identify a {100} plane that cuts the P−O
bondings (in Figure 1a one of such planes would be crossing
the bonding between P and O4); thus, the formed surface is the
(100) surface. Other index surfaces are unlikely to be observed
given the number of bonds to brake, making the resulting
surface more unstable or with higher surface energy. To
minimize the dipole moment in the supercells, we built the
slabs with similar surfaces in each side of the slab and kept
Fe3(PO4)2·8H2O stoichiometry throughout. Furthermore, our
computations show that a vacuum of at least 15 Å is adequate
to minimize the artifact interactions between slab-images.
In Table 4 we present the computed surface energy (σ) for
(010) and (100) with (1 × 1) surface reconstruction (see eqs 1
Table 4. PBE+U(4.0) Computed Surface Energies for (100)
and (010) Surfaces with (1 × 1) Reconstructionsa
surface
slab size (atoms)
σ (J m−2)
Φ (eV)
thickness (Å)
(100)-(1 × 1)
(010)-(1 × 1)
111
111
0.77
0.23
3.84
5.07
13.22
20.59
a
The computed work function Φ and actual thickness of the slab are
also included.
and 2). The results suggest that the most stable surface is the
(010) which has a water layer termination.
Figure 4 depicts the fully relaxed atomic structure of the
(010) and (100) surfaces with (1 × 1) reconstruction. The
(010) surface has a H2O−Fe−O termination where the water
molecules form rows along the [001] axis (see Figure 4 (a1)
and (a2)). On the other hand, the (100) surface has a O−P−
H2O termination, where the surface P atoms are fourcoordinated forming rows along the [010] axis.
The relaxation of the atoms at the (010)-(1 × 1) surface is
small (see Figure 5a). The topmost water molecules that
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Figure 4. The PBE+U(4) computed surface structure of (a) (010)-(1 × 1), (a1) top view and (a2) side view; and (b) (100)-(1 × 1) surface, (b1)
top view and (b2) side view. The orange lines denote the (1 × 1) surface unit cell and the color of the atoms are in correspondence with Figure 1; in
these images we label selected sites as discussed in the text and also shown in Figure 5. Notice that all the Fe atoms labeled in these figures are
beneath the water layer.
Figure 5. Atomic relaxation of (a) (010)-(1 × 1) and (b) (100)-(1 × 1) surfaces. The images show the surface unit cell delimited by the black lines
and the relaxation is displayed with green arrows magnified 10 times for better visualization. (a1) and (b1) are perspective views, while (a2) and (b2)
are top views of the surfaces. The color of the atoms are in correspondence with Figure 1.
bulk, Figure 2b). This sub-band shifts ∼1 eV toward EF where
the O4-2p states form a peak at −7.7 eV. We also notice the
formation of a new surface state at ∼ −11.1 eV that
corresponds to the interaction of surface P with subsurface O
(see Figure 5b). The computed Bader charges for selected
atoms are displayed in Figure 5b. We have found that the
charge of P atom at the surface changes slightly compared with
its original charge in the perfect lattice (3.65 e from Table 3).
This can be explained by the final four-coordination of the P
atom with the surrounding O atoms induced by the large
relaxation of P (this is the same coordination as in the bulk).
The formation of a water molecule at the O4 site causes a
charge decrease by 0.23 e compared with the charge in the bulk
(cf. Table 3). This can be considered as a local reduction.
Simulated STM Images of Vivianite Surfaces. The band
gap of both (010) and (100) surfaces are around ∼2 eV, and
therefore it is likely that they can be probed using STM. To
complement the electronic structure calculations, in Figures 7
and 8 are displayed the computed STM images (constantcurrent mode) and line scans for surfaces (010)-(1 × 1) and
(100)-(1 × 1). As a reminder, the computed STM data are
obtained using bSKAN as detailed in the methodology section.
Figure 7 depicts the computed STM images corresponding
to sample bias voltages (VBIAS) of −0.5, −1.0, −1.5 V (Figure
7a) and +2.5, +3.0, +3.5 V (Figure 7b). The topology of the
images are basically bright stripes along the [001] axis.
Considering the line scans, for negative VBIAS (occupied states),
the corrugation basically increases with decreasing the voltage
(more negative voltage). On the other hand, for positive VBIAS
(empty states), we observe a decrease of the corrugation when
the voltage increases. Before we explain the computed STM
topology, it is important to bear in mind that the STM signal is
proportional to the local density of states (LDOS) at the
surface;32,33 therefore, one can consider the previously
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no accessible to the STM tip. In all the STM images and line
scans, the minimum (or dark stripe) is above the subsurface Fe1
atom rows along the [001] axis.
Figure 8 illustrates the computed STM images and line scans
for a VBIAS range of −0.6, −1.0, −1.5 V (Figure 8a) and +2.8,
+3.5, +4.4 V (Figure 8b). The topology shows a bright stripe
along the [010] axis pointing to the location of the Fe1 (Fe2
and Fe3) atom rows for negative (positive) VBIAS. The
computed STM images show a change of contrast depending
on the VBIAS. The explanation is related to the main
contribution to the LDOS near EF. The computed STM
images for negative VBIAS show a main bright stripe along the
rows formed by the Fe1 atoms (Figure 8a). This is explained by
the main contribution to the PDOS near EF: the main states
below EF are Fe-3d eg from the Fe1 atom (cf. Figure 6b).
Moreover, the images at VBIAS −1.0 and −1.5 V show a
secondary bright feature in between the main bright stripes
along the [010] axis just above the Fe2 and Fe3 atoms rows.
That feature is explained by the 3d states lying at −1.0 and −1.3
eV from EF that belong to those atoms (see Figure 6b). The
computed STM images for positive VBIAS show a bright stripe
above the Fe2 and Fe3 atoms row along the [010] axis. This is
related to the main character of the bands just above EF: from
PDOS (Figure 6b), the main contribution is from the Fe-3d
states with t2g character that belongs to the Fe2 and Fe3 atoms;
the secondary bright feature that appears at VBIAS = +4.4 V
corresponds to the 3d t2g states (lying at 3.9 eV; see Figure 6b)
from Fe1.
Figure 6. PBE+U(4) computed PDOS for surface (a) (010)-(1 × 1)
and (b) (100)-(1 × 1). Both surfaces show an insulating ground state.
Displayed PDOS with Gaussian smearing of 0.12 eV.
computed PDOS (cf. Figure 6). The STM images and line
scans suggest that the Fe-3d states are playing the dominant
role in the topology and corrugation: for occupied (empty)
states was found that near EF the 3d-eg (3d-t2g) states from the
Fe2 atom is the main character of the electronic structure with a
tiny contribution of water states (see Figure 6a); for that reason
the bright features are above the Fe2 rows along the [001] axis
(see Figure 7). Notice that subsurface Fe1-3d states also
contribute to the occupied states, but its depth (position along
z axis with respect to the topmost atom) is 1.41 Å lower than
the Fe2 site (see Figure 5); therefore, it produces less
protrusion on the STM images. The surface water molecules
have almost no effect on the LDOS since the details of its
bonding is energetically located in lower-lying orbitals that are
■
SURFACE RECONSTRUCTION OF (010)-(1 × 1)
WITH HYDROGEN DESORPTION
The vivianite (010)-(1 × 1) surface is water molecules
terminated; then by thermodynamic considerations, it is
important to explore the phase diagram of this surface in
equilibrium with hydrogen gas. Figure 9 depicts the computed
differences in the surface Gibbs free energies ΔG (see eq 3 with
respect to the hydrogen chemical potential ΔμH for several
stable surfaces where either one or two H2 molecules were
Figure 7. PBE+U(4) computed STM images for the (010)-(1 × 1) surface and corresponding line scans on the right for (a) negative VBIAS (blue)
and LDOS of 10−10 states/eV and (b) positive VBIAS (red) for a LDOS of 10−5 states/eV. The computed line scans are along A−A′. The atomic
structure of the surface unit cell is superimposed on two STM images for reference. The labeled Fe atoms and colors are in correspondence with
Figure 5a.
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Figure 8. PBE+U(4) computed STM images for the (100)-(1 × 1) surface and corresponding line scans on the right for (a) negative VBIAS (blue)
and LDOS of 10−9 states/eV and (b) positive VBIAS (red) for a LDOS of 10−6 states/eV (10−5 states/eV for VBIAS = +4.4 V). The atomic structure of
the surface unit cell is superimposed on two STM images for reference. The labeled Fe atoms and colors are in correspondence with Figure 5b.
stable for ΔμH ≈ −2.1 eV. It is relevant to mention that we
have also considered the case where all the water molecules
dissociate forming a (010) surface where all the surface O sites
are hydroxylated. This configuration is highly unstable and
relaxes back again to the pristine (010) reconstruction. To
complement the thermodynamical picture of (010) with the
change of the H coverage, in Figure 10 we plot the PBE+U(4)
Figure 9. PBE+U(4) computed free energy ΔG for the (010) surface
with different hydrogen coverages as a function of the hydrogen
chemical potential ΔμH. In the top x axis, the conversion of ΔμH to H2
pressure p and expressed as ln(p/p°) has been carried out for T = 300
K (eq 4). The inset shows the pristine surface structure pointing the
H-sites from where the H atoms were extracted. In this figure, the
nomenclature H1,2 means a (010) surface without the H1 and H2
atoms.
Figure 10. PBE+U(4) computed pressure−temperature phase
diagram for (010) with respect to the H coverage at the surface.
Here p refers to the H2 pressure. The image shows the regions of
stability of the most stable phases: (010):pristine (blue), (010):H1,2
(red), and (010):H1,2,3,4 (green). The nomenclature is in correspondence with Figure 9.
extracted from the surface. We only consider the desorption of
H2 molecules since isolated single hydrogen atoms are
energetically unstable and prone to form the H2 molecules.
The results displayed in Figure 9 suggest that for ΔμH ∼
−1.7 eV (it corresponds to a ultralow H2 pressure of 5.9 ×
10−51 atm @ 300 K), the (010):H1,2 reconstruction becomes
more stable than pristine (010) surface. However, the
termination (010):H1,4 could occur since it is only ∼0.1 J
m−2 less stable than (010):H1,2. The reconstructions named
here H1,2′ is a variation of H1,2 with the OH group between two
consecutive Fe2 surface atoms. We have also considered the
surface with four hydrogen vacancies (H1,2,3,4) where all the
topmost hydrogen were removed; this surface become the most
computed pressure−temperature phase diagram (using eqs 3
and 4). The pristine phase is dominant but for ultralow H2
pressure and high enough temperatures, the stability regime of
the H1,2 can be seen.
Figure 11 depicts the computed electronic structure of the
(010):H1,2 and (010):H1,4 surfaces. The PDOS for (010):H1,2
shows a sub-band on the UVB with two peaks (Figure 11b).
The peak at −0.19 eV is composed of the Fe1-3d states (eg and
t2g contributing in the same amount). The lower peak of this
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Figure 11. PBE+U(4) computed PDOS for surface (a) pristine (010)
shown here for reference, (b) (010):H1,2 and (c) (010):H1,4. Displayed
PDOS with Gaussian smearing of 0.12 eV.
sub-band at ∼ −0.5 eV is composed by the Fe2-t2g states
mainly. Besides, as a consequence of the formation of two
hydroxyl groups at the Fe2-site, we observe a new surface state
at 1.86 eV above EF with a Fe2-t2g character mainly (Figure
11b). Figure 12a shows the fully relaxed atomic structure of
(010):H1,2 together with the computed STM images for VBIAS =
−0.5 and +3.0 V. The formation of two hydroxyl groups at the
Fe2 oxidizes that site since the computed Bader charge qB is
1.67 e (cf. Figures 5a and 12a). The Fe2−OH distance and
̂ 3w2 angle are 1.76 Å and 100.2°, respectively. It is
O3w1 Fe2 O
important to mention that the STM images for VBIAS ranging
from ∼2.0 to 3.0 V show no differences since there are no states
within the energy range of 2.0−3.0 eV (see Figure 11b). The
computed STM images have similar features observed in the
pristine (010) surface (see Figure 12a); the bright (dark)
stripes along the [001] direction point to the position of the
Fe2 (Fe1) sites. Moreover, the STM image for VBIAS = +3.0 V
shows a small protrusion on the bright stripes just above the
OH sites. In Figure 12c, it sketches the line scans of the STM
images. The computed corrugation for the (010):H1,2 surface
with positive (negative) VBIAS is ∼1.5 (1.1) Å.
On the other hand, the PDOS for (010):H1,4 shows a subband on the UVB composed of three peaks (Figure 11c). The
peak at EF is an overlap of Fe1-t2g with Fe1-eg and O-2p
(oxygens forming the hydroxides at Fe1- and Fe2-sites). The
peaks at ∼ −0.42 eV and −1.38 have mainly a Fe2-3d character.
The LCB is formed by a band with three peaks. The two peaks
at 2.6 and 3.4 eV correspond to Fe2-t2g; the peak at 2.9 eV has a
Fe1-t2g character (Figure 11c). Figure 12b depicts the atomic
structure of the fully relaxed surface as well as the computed
STM images for VBIAS = −0.5 and +3.0 V. In this case, the
formation of the hydroxyl group at Fe1 and Fe2 oxidizes those
Figure 12. Most stable surface reconstruction of (010) with hydroxyl
termination and corresponding STM images for (a) (010):H1,2 and
(b) (010):H1,4. (c) The computed line scans are along A−A′ where
red (blue) corresponds to the (010):H1,2 ((010):H1,4) surface. The
images for VBIAS = −0.5 (+3.0) V correspond to a LDOS of 10−10
(10−8) states/eV. The atomic structure of the surface unit cell is
displayed on the left side, and it is also superimposed on the STM
images for reference. The labeled Fe atoms and colors are in
correspondence with Figure 5a.
sites as we computed the qB of 1.48 and 1.53 e, respectively (cf.
Figure 5b and 12b). The formation of hydroxyl group induces
structural changes where the Fe2−OH1, Fe1−OH4, Fe2−O3w2,
and O3w1 Fe2 ̂ O3w2 are 1.81 Å, 1.84 Å, 2.01 Å, and 86.9°,
respectively. The corresponding STM images for this surface
are also displayed in Figure 12b. The images show the same
features observed in pristine and (010):H1,4: the bright (dark)
stripes along the [001] direction are located above the Fe2
(Fe1) sites. The image for VBIAS = +3.0 V shows a modulation
on the bight stripe where the maxima are above the OH1 and
O3w2 sites. Figure 12c shows the line scans of the STM images;
for (010):H1,4 the computed corrugation for positive (negative)
VBIAS is 1.25 (0.55) Å.
The predicted stability of either (010):H1,2 or (010):H1,4
surfaces at ultralow H2 pressure and above determinate
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temperature together with the changes on the electronic
structure suggest the actual desorption of H2 molecules and the
formation of the hydroxyl group at the Fe1 or Fe2 sites. Those
sites are left oxidized during the process. This theoretical result
is in agreement with the experimental X-ray photoelectron
spectroscopy results by Pratt22 who observed an autoreduction−oxidation process triggered by the rupture of hydrogen
bonds leading to the formation of the hydroxyl groups and
ferric sites.
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■
CONCLUSIONS
Using density-functional theory within the PBE+U approach,
we have computed and reported for the first time the properties
of paramagnetic surfaces of vivianite Fe3(PO4)2·8H2O. The
starting point was the accurate computation of the paramagnetic bulk vivianite using a set of functionals. We used the
HSE06 results as a benchmark and within the PBE+U
approximation, and we fitted the intrasite Coulomb repulsion
U between the Fe-3d electrons to replicate the HSE06 band
gap. The PBE+U computed bulk structure for vivianite was
cleaved to form the (100)- and (010)-(1 × 1) surfaces. Surface
energies of 0.77 and 0.23 J m−2 were computed for the (100)
and (010) surfaces, respectively. The (010) surface is observed
to undergo small atomic reconstruction. On the other hand, the
less stable (100) surface presented important reconstructions
with the formation of two hydroxide hydrate anions [HO···H···
OH]− and one water molecule per unit cell. Computation of
the differences in the Gibbs free energy between the defective
and pristine surface allows us to explore thermodynamically
favorable reconstructions of (010) changing the H content at
the surface. The main result is the stability of (010):H1,2 and
(010):H1,4 surfaces at ultralow H2 pressure. The surface
reconstructions and computed electronic structure of these
surfaces suggest an autoreduction−oxidation process. Finally,
the topology of the vivianite (010) and (100) surfaces at the
nanoscale was studied by modeling of the constant-current
mode STM images depending on the VBIAS applied. The STM
images for pristine and hydroxylated (010) surfaces show
similar features where the local density of states at the surface
protrude more into the vacuum at the Fe2 sites for a VBIAS
ranging from −1.5 to +3.5 V. The STM images for (100)
present a change in contrast depending on the VBIAS that ranges
from −1.5 to +4.4 V: it protrudes more into the vacuum at the
Fe1 (Fe2,3) sites for negative (positive) bias voltage.
■
Article
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was jointly supported by NSF and the NASA
Astrobiology Program under the NSF Center for Chemical
Evolution, CHE1004570. The computation time was provided
by the Extreme Science and Engineering Discovery Environment (XSEDE) by National Science Foundation Grant No.
OCI-1053575 and XSEDE award allocation number
DMR110088. H.P.P. acknowledges the generous grants of
computing time from the Center for the Scientific Computing
(CSC), in Espoo, Finland.
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The Journal of Physical Chemistry C
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