Supplemental Material
Towards CH4 dissociation and C diffusion during
Ni/Fe-catalyzed carbon nanofiber growth: A density
functional theory study
Chen Fan,1 Xing-Gui Zhou,1 De Chen,2 Hong-Ye Cheng,1 Yi-An Zhu1,a)
1
State Key Laboratory of Chemical Engineering, East China University of Science
and Technology (ECUST), Shanghai 200237, China
2
Department of Chemical Engineering, Norwegian University of Science and
Technology (NTNU), N-7491 Trondheim, Norway
a)
Authors to whom correspondence should be addressed. Electronic mail:
yanzhu@ecust.edu.cn (Yi-An Zhu).
I. SEGREGATION ENERGY AND SURFACE MIXING ENERGY
The segregation energy and surface mixing energy of Fe atoms in Ni are calculated
in the following way. First, one surface Ni atom of a four-layer p(3×3) Ni(111) slab
(36 Ni atoms in total) is replaced by one Fe atom, and the calculated the total energy
of the slab is denoted as Es. Then, one bulk Ni atom (e.g., in the third layer) of the
same slab is replaced and recalculated the total energy, as notated as Eb. Then the
segregation energy can be calculated as,
Es e g E s E
(1)
b
It is found that Eb is about 0.22 eV lower than Es, which indicates that the Fe atom
dissolving into the Ni bulk to form a bulk alloy is energetically more favorable than
staying on the surface. Furthermore, with the content of Fe increased, Eb is much
lower than Es (See Table SI). The distribution of Fe atoms in Ni was also qualitatively
investigated. Two systems with different Fe distributions were calculated. In the both
systems, three surface Ni atoms of the Ni(111) slab are replaced by three Fe atoms. In
one system, the three Fe atoms are separated with each other, and in another one, the
Fe atoms gather together to form a Fe island. It is found that the former system is 0.19
eV more stable than the later system, which indicates that phase separation of the
Ni/Fe is unfavorable.
TABLE SI. The calculated Es and Eb for different Fe atoms in Ni.
Number of Fe
atoms in Ni
1
2
3
Es (eV)
Eb (eV)
Eseg (eV)
-191.9720
-194.8599
-197.6562
-192.1874
-195.1530
-192.0268
0.2154
0.2931
0.3704
II. K-POINT CONVERGENCE TESTS
The total energy convergence tests with the increasing K-point sampling are
performed. The K-point samplings which are finally utilized for the calculation are
highlighted in the yellow notation in Table SII and Table SIII.
TABLE SII. The total energy convergence with the increasing K-point sampling of the
NiFe(111) surface.
K-point sampling
3×2×1
4×2×1
5×2×1
5×3×1
6×3×1
Total energy (eV)
-212.8190
-212.6380
-212.5554
-212.5692
-212.5570
TABLE SIII. The total energy convergence with the increasing K-point sampling of
the Ni2Fe(111) surface.
K-point sampling
1×1×1
2×2×1
3×3×1
4×4×1
Total energy (eV)
-221.9832
-224.2829
-223.5292
-223.4981
III. OTHER LESS STABLE ADSORPTION CONFIGURATIONS ON NIFE(111)
The adsorption of H and CHx (x = 0- 3) at the bridge and atop sites are also
calculated to gain the full information of the potential energy surface on NiFe(111).
The initial adsorption configurations are shown in Fig. S1. The adsorption energies
are shown in Table SIV. For most cases of the adsorption, the bridge and atop sites are
not stable, and the adsoabates move to the nearby hollow sites during the geometry
optimization. For some cases of the adsorption, the adsorbates can adsorb. However,
the adsorption energies at these sites are much lower than that at the three-fold hollow
sites (see Table I in the text for comparison). Therefore, it can be concluded that the
hollow sites are most favorable for the adsorption of atomic H and CHx on NiFe(111).
Thus, only hollow sites are considered for the adsorption of H and CHx on Ni2Fe(111).
Table SIV. Calculated adsorption energies (eV) of atomic H and C on NiFe(111)
Species
bri1
bri2
bri3
atop1
atop2
H
-2.78
to hcp2
to hcp2
-2.34
to fcc1
C
-6.65
-6.60
to hcp2
to fcc2
to fcc1
CH
to fcc1
to fcc2
to fcc1
to fcc1
to hcp2
CH2
to fcc1
to fcc2
to fcc1
to fcc1
to hcp2
CH3
to fcc1
to fcc2
to fcc1
-1.58
-1.63
FIG. S1. Schematic representations of the atomic H and C adsorption on the NiFe(111)
surface. The light blue balls denote Ni atoms; the dark blue balls denote Fe atoms; the
white balls represent the adsorption sites.
IV. H ADSORPTION ON FCC-STRUCTURED FE(111)
The bulk fcc-Fe model is built by optimizing a Fe4 cell in fcc structure. The lattice
constant and magnetic moment of bulk fcc-Fe is calculated to be 3.63 Å and 2.54 μB,
respectively, which is good agreement with the previous theoretical results (3.64 Å
and 2.62 μB) [D. Jiang and E. Carter, Phys. Rev. B 67, 214103 (2003)]. Then the H
adsorption on fcc-Fe(111) is investigated. The initial configuration for H adsorption is
shown in Fig. S2(a). After the geometry optimization, the fcc-Fe(111) surface is
reconstructed to bcc-like Fe(110) structure, as shown in Fig. S2(b).
Fig. S2. Initial (a) and final (b) configurations of atomic H and C adsorption on
fcc-Fe(111). The dark blue balls denote Fe atoms; the white balls denote H atoms.
V. OTHER LESS STABLE TRASITION STATES
FIG. S3. Schematic representations of the less stable transition states of CH4
dissociation on the NiFe(111) (TS1-TS4) and Ni2Fe(111) (TS5-TS8). The light blue
balls denote Ni atoms; the dark blue balls denote Fe atoms; the black balls denote C
atoms; the white balls denote H atoms.
TABLE SV. Calculated energy barriers of the less stable TSs on the alloyed Ni/Fe
surfaces
NiFe(111)
Ni2Fe(111)
TS
TS1
TS2
TS3
TS4
TS5
TS6
TS7
TS8
Ea (eV)
0.96
0.69
0.41
1.27
0.97
0.81
0.37
1.19
VI. CALCULATED IMAGINARY FREQUENCIES OF THE TRASITION
STATES
Only the metal atoms in the first layer and the adsorbates are allowed to relax in the
frequency calculations. For each TS, only one negative mode was found in the
frequency calculation.
TABLE SVI. Calculated imaginary vibrational frequencies (cm-1) of TSs in Fig. 6 of
the manuscript
TS1
937.19i
NiFe(111)
TS2
TS3
876.46i 785.46i
TS4
866.17i
TS5
853.11i
Ni2Fe(111)
TS6
TS7
802.12i 701.78i
TS8
612.49i