Surface-termination-dependent Pd bonding and
aggregation of nanoparticles on LaFeO3 (001)
The atomic structures and relative stability of LaO- and FeO2-terminated
LaFeO3 (001) surfaces
Since LaFeO3 (001) has alternating LaO+1 and FeO2-1 layers, the surface presents
either a LaO- or an FeO2-termination, and finite slabs should have nonzero dipole
moments. Stabilization of the polar surfaces requires geometric and/or electronic
reconstruction of the atomic layers, even including the formation of vacancies and
adsorption of other species on the surface.1 Indeed, upon full optimization of LaOand FeO2-terminated surfaces, it was found that the geometric and electronic
structures of the two surfaces undergo some modification, as shown in Table S1.
There, dij =dijrelaxed -dijideal is the change in the relaxed interlayer spacing between layer
i and j from the ideal surface structure, where the positions of layers are determined
by the average vertical coordinates of the cations in each layer. Overall, the distortion
of oxygen octahedra and the atomic-layer rumpling in the top two layers are
pronounced, however, it does not penetrate further than 3-4 layers. The distance
between the outermost and second layers of the LaO- and FeO2-terminated surfaces is
compressed by 0.15 and 0.16 Å, while that between the second and the third layers is
expanded by 0.07 and 0.13 Å, respectively, finally converging to values close to zero
for both surfaces. Therefore, it is reasonable to use the 7-layer thick slabs for our
studies of the properties of bare surfaces and the interactions between Pd metal and
LaFeO3 (001).
To stabilize the polar surfaces, the electronic structures usually undergo
self-consistent charge redistribution, which is more complex than that of the classic
model based on the formal ionic charges. Thorough insight can be obtained by Bader
charge analysis.2 The atomic and layer charges for both terminations of LaFeO3 (001),
as well as the bulk values, are presented in Table S1. Because of the strong
hybridization of La and Fe with O, the charges deviate from the perfect ionic limit.
For LaFeO3 bulk, the charges were calculated to be +2.07, +1.92 and -1.33, instead of
the formal +3, +3 and -2 for La, Fe and O, respectively. Similarly, the charges of
electron-rich LaO and electron-poor FeO2 terminations are changed from ±1 to
+0.65 and -0.5, respectively. The additional electrons and holes are also roughly
delocalized over three and four layers of LaO- and FeO2-terminated surfaces,
respectively, with the result that the layer charges are strongly modified. Finally, the
differences between these layer charges and the LaFeO3 bulk values achieve
convergence by the third and fourth layers of the LaO- and FeO2-terminated surfaces,
as presented in Table S1. Correspondingly, the magnitude of the Fe atom magnetic
moments were calculated to be 3.62 and 4.14 μB in the second and fourth layers of
LaO-terminated surface and 4.0 and 4.12 μB in the first and third layers of
FeO2-terminated surface, respectively, while the magnetic moments of O and La
atoms are negligible.
The thermodynamic stability of a surface in contact with an oxygen atmosphere is
closely related to temperature T and oxygen pressure p. If the surface is in equilibrium
with atomic reservoirs, the stability is characterized by the surface Gibbs free energy,
which is defined as:

1
 Eslab  N La La  N Fe Fe  NO O  PV  TS
2A
(1)
At 0 K and typical pressures, the PV and TS terms can be neglected with respect to other
contributions. For the LaFeO3 bulk system, the chemical potential of the compounds
can be written as a sum of the chemical potential of each component within this crystal:
LaFeO  La  Fe  3O
3
(2)
Combining (2) with (1) and eliminating the Fe term, we can obtain:

1
 E slab   N La  N Fe  La  N Fe LaFeO3   N O  3N Fe  O 
2A 
(3)
gas
Introducing the variation of the chemical potentials ( O  12 O2  O and
bulk
La  La
 La ) in Eq.(3), we can obtain:
1
bulk
 E slab   N La  N Fe  La
 N Fe LaFeO3  12  N O  3N Fe  Ogas2 
2A
1

 N La  N Fe  La   N O  3N Fe  O 
2A 

(4)
Since the system is in thermodynamical equilibrium, the surrounding O2 atmosphere
acts as an ideal reservoir for the surfaces. As suggested in Refs. 3-5, the ab initio total
energy of an isolated O2 was chosen as a reference to calculate the oxygen chemical
potential as functions of temperature T and oxygen partial pressure p. It is well known
that traditional DFT methods would overestimate the binding energy of O2.4,
6, 7
However, this intrinsic weakness doesn’t affect the calculations significantly, because
the oxygen chemical potential variation rather than the chemical potential itself is used
as the variable.4, 8 Under the ideal gas approximation, the oxygen chemical potential
variation ΔμO (T, p) can be expressed as:
 p
1
O (T , p)  O (T , p 0 )  k BT ln  0  ,
2
p 
(5)
The μO (T, p0) term determined by the contribution from molecular vibration and
rotation, is given by3:
1
1
O (T , p 0 )   H (T , p 0 )-H (0 K , p 0 )   T  S (T , p 0 )  S (0 K , p 0 ) 
2
2
(6)
At the standard pressure p0 = 1 atm, by using the experimental enthalpy and entropy of
O2 from thermodynamical tables,9 μO (T, p0) can be derived, as listed in Table S2.
Employing Eq. (5), we can obtain the dependence of ΔμO (T, p) as a function of the
given temperature T and oxygen pressure p. Since the surfaces were oxidized in air, the
specific oxygen partial pressure p is approximately 0.2 atm.
Furthermore, ΔμO (T, p) can be varied experimentally within certain boundaries
under the thermodynamic equilibrium conditions. The chemical potential of the
compound can be rewritten as:
LaFeO   bulk  Febulk  32 Ogas  H0f
3
La
(7)
2
Labulk , Febulk , Ogas are the energies of the La atom in the hcp bulk metal, the Fe atom in
2
the bcc bulk structure and the O atom in the gas phase O2 molecule, respectively.
So, we can get the Gibbs free energy of formation H f by
0

bulk
H 0f   La  La
   Fe  Febulk   3O  32 Ogas2

(8)
The chemical potential in compounds for each species must be less than the chemical
potential in its bulk phase, otherwise the compound would be unstable and decompose
into elemental phases. So,
1
La  Labulk , Fe  Febulk and O  Ogas
2
2
Thus,
1
3
(9)
H 0f   O  0 , H 0f  La  0 . Here, H 0f is the 0 K formation heat of
LaFeO3 bulk, which is calculated to be -10.34 eV. The stability of LaO- and
FeO2-terminated LaFeO3 (001) surfaces as a function of temperatures T (at p = 0.2
atm) and oxygen partial pressure (at T = 1000 K) is shown in Figure S1. Note that the
formation of a surface will be exothermic and spontaneous if Ω becomes negative,
leading the crystal to decompose. Therefore, the surface slab can be stable on the
condition that Ω is positive. As illustrated in Figure S1, only the FeO2-terminated
surface is available under conditions where the temperature is higher than 1700 K
(with pO2 = 0.2 atm), which is comparable to the transition temperature of 1500 K
obtained by Lee et. al.,4 or the oxygen partial pressure is lower than 10-10 atm (at T =
1000 K), assuming that the phase transition from orthorhombic to tetragonal or cubic
doesn’t happen. The LaO-terminated surface is thermodynamically more stable under
the oxygen chemical potential μO (T, p) in the range of -2.20~-1.00 eV, i.e., at
temperatures between 800 and 1700 K (pO2 = 0.2 atm) or the oxygen partial pressure
between 100 to 10-10 atm (T = 1000 K). The FeO2-terminated surface turns out to be
more stable under the oxygen chemical potential higher than -1.0 eV, corresponding to
a temperature lower than 800 K (pO2 = 0.2 atm) or the oxygen partial pressure higher
than 100 atm (T = 1000 K). The results are slightly in disagreement with the
conclusion from Ref. 10 in which the authors claimed that the LaO-terminated surface
is not stable over a wide range of oxygen chemical potential, the extent of which was
not explicitly provided.
1
A. Asthagiri and D. Sholl, Phys. Rev. B 73 (2006).
2
R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, New York,
1990).
3
K. Reuter and M. Scheffler, Phys. Rev. B 65 (2001).
4
C.-W. Lee, R. Behera, E. Wachsman, S. Phillpot, and S. Sinnott, Phys. Rev. B 83 (2011).
5
E. Heifets, S. Piskunov, E. Kotomin, Y. Zhukovskii, and D. Ellis, Phys. Rev. B 75 (2007).
6
Y.-L. Lee, J. Kleis, J. Rossmeisl, and D. Morgan, Phys. Rev. B 80 (2009).
7
L. Wang, T. Maxisch, and G. Ceder, Phys. Rev. B 73 (2006).
8
E. Heifets, J. Ho, and B. Merinov, Phys. Rev. B 75 (2007).
9
D. R. Stull and H. Prophet, JANAF Thermochemical Tables, 2nd ed. (U.S. National Bureau of
Standards, Washington, DC, 1971).
10
I. Hamada, A. Uozumi, Y. Morikawa, A. Yanase, and H. Katayama-Yoshida, J. Amer. Chem.
Soc. 133, 18506 (2011).
Table S1 Geometric relaxation ( dij =dij
relaxed
-dijideal in Å) and the atomic Bader charges (AC in e)
and total charge associated with each layer (LC in e) in the LaO- and FeO2-terminated
LaFeO3(001) surfaces.
LaO-terminated
Layer
Δdij
LaO
AC
qLa=1.99
qO=-1.34
FeO2-terminated
LC
Layer
0.65
FeO2
-0.15
FeO2
qO=-1.34
-0.81
LaO
0.07
qO=-1.33
0.74
FeO2
0.03
qFe=1.88
qO=-1.19
-0.5
qLa=2.08
qO=-1.29
0.79
qFe=1.93
qO=-1.31
-0.69
qLa=2.08
qO=-1.32
0.76
0.02
qFe=1.92
Bulk
LC
0.13
qLa=2.07
FeO2
AC
-0.16
qFe=1.87
LaO
Δdij
qO=-1.34
-0.76
LaO
qLa=2.07 qFe=1.92 qO=-1.33
qLaO=0.74 qFeO2=-0.74
Table S2 Temperature dependence of oxygen chemical potential μO (T, p0) at the standard pressure
of p0=1 atm.
T
μO (T, p0)
T
μO (T, p0)
100
300
500
1000
-0.08 eV
-0.27 eV
-0.50 eV
-1.10 eV
1500
2000
2500
3000
-1.75 eV
-2.43 eV
-3.14 eV
-3.87 eV
Figure S1. Surface free energy of LaO- and FeO2-terminated LaFeO3 (001) as functions of
temperature at given oxygen partial pressure p=0.2 atm (left panel) and of oxygen partial pressure
at give temperature of 1000 K (right panel), respectively.