Surface Science 603 (2009) 315–319

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Surface reconstruction of clean bcc-Fe{1 1 0}: A quasi-hexagonal top-layer
with periodic height modulation
T.K. Yamada *, H. Tamura, M. Shishido, T. Irisawa, T. Mizoguchi
Faculty of Science, Gakushuin University, 171-8588 Mejiro, Tokyo, Japana r t i c l e

i n f oArticle history:
Received 14 October 2008
Accepted for publication 18 November 2008
Available online 27 November 2008
Keywords:
Surface relaxation and reconstruction
Iron
Whiskers
Single crystal surfaces
Magnetic surfaces
Phase transition
Surface structure, morphology, roughness,and topography
Scanning tunneling microscopya b s t r a c t
Hexagonal-pillar shaped pure Fe single crystal whiskers with six {1 1 0} side planes were obtained bymeans of chemical vapor deposition. Atomically resolved scanning tunneling microscopy images
obtained on the {1 1 0} surface showed a quasi-hexagonal atomic array with mesoscopic-range periodic
height modulation of about 1/3 of an atomic step. This height modulation was found to be a result of
an interference between the quasi-hexagonal top-layer and the sub-surface bcc-Fe{1 1 0} layer. Unit vec  
 
13 1
u~1
p~1
¼
¼
tors of the mesoscopic-range modulation turned out to be expressed as
2 14
p~2
u~2

 
 
 
12 1
s~1
u~1
s~1
, whereandare the primitive vectors of the two-dimensional atomic array
3 15
s~2
u~2
s~2
in the top-layer and those in the sub-surface layer, respectively. The two-dimensional density of atoms in
the top-layer is slightly higher by 0.46% than that in the sub-surface layer.
Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction
Iron is an important popular ferromagnetic metal which has
been widely used since the ancient age in practical applications
owing to its strength and abundance. It is a typical bcc-metal atroom temperature, however, it takes fcc c-phase 1185–1667 K
and bcc d-phase (1667–1811 K: melting point) at 1 atm [1], suggesting that the free energy depends delicately on the crystal structure [2]. In a bcc crystal each atom has 8 nearest and 6 second
nearest neighbors (NN) in bulk, while an atom at the surface has
reduced coordination, i.e. 4 NN and 5 second NN for {0 0 1} and 6
NN and 4 second NN for {1 1 0}. In general, a break down of thesymmetry of atomic interactions generates stress, which causes
surface reconstruction in the case that the stress exceeds the elastic limit. There have been found several surface reconstructions on
metal surfaces ([3] and references therein). There are three types ofthem; (1) surface atoms move parallel to the surface to form a larger unit cell, e.g. W{0 0 1}-c(2  2) [4]. (2) A top surface atomic
layer of noble metals forms a hexagonal lattice, e.g. Au{0 0 1}(5  20), Pt{0 0 1}-(5  20), Ir{0 0 1}-(5  1) [3,5]. (3) Periodic missing atomic rows are formed on the surface, e.g. Pt{1 1 0}-(1  2) [6].

* Corresponding author. Tel.: +49 721 608 3441; fax: +49 721 608 6103.
E-mail address: bb96@pi.uni-karlsruhe.de (T.K. Yamada).
0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2008.11.010

Since impurities on metal single crystal surfaces induce surface
reconstruction [7,8], one must pay a lot of attention whether thesurface reconstruction is of surface intrinsic origin. Absorbates of
the impurities induce reconstruction on Fe surfaces [7,8]. So-called
Fe single crystals which were made by a strain-anneal method include several impurities, such as C, P, and S in bulk. These segregate
on the surface after every sample-annealing process and cover the
Fe surface. Therefore, for a study of clean Fe surfaces, bcc aFe{0 0 1} single crystals made by a chemical vapor deposition(CVD) technique, which are called Fe-whisker single crystals, havebeen used since the whiskers consist of only Fe in bulk [9–13].
Although many investigations have been made on clean purebcc-Fe-whisker single crystals, so far no surface reconstruction
has been reported on {0 0 1} surfaces.
There have been plenty of investigations on Fe ﬁlms of different
modiﬁcations grown epitaxially on single crystal substrates, e.g. W,
GaAs, Cu, or Au [14–18]. These Fe ﬁlms suffer large stress caused bylattice mismatch between the Fe ﬁlms and the substrate, and thesurfaces are frequently reconstructed.
In this study, we discovered a new surface reconstruction onclean bcc-Fe{1 1 0} surfaces of three different pure hexagonal-pillar
shaped a-Fe-whisker single crystals. The top surface layer is reconstructed to a quasi-hexagonal lattice with periodic height modulation in mesoscopic-range due to the interactions with the subsurface bcc-{1 1 0} layer.

316

T.K. Yamada et al. / Surface Science 603 (2009) 315–319

2. Experimental
CVD has been used in order to get bcc a-phase Fe single crystals.
From the gas phase, extremely high quality Fe-whiskers can begrown [9–13]. Most of the produced whiskers were rectangular pillar shape with six {0 0 1} surfaces [10]. We found, however, that avery few crystals had a hexagonal prism shape as shown in
Fig. 1a. Laue X-ray diffraction patterns (Fig. 1b) and four-circle Xray diffraction data (Fig. 1c–h) show that these whiskers growalong h1 1 1i direction with six side planes of bcc-{1 1 0} surfaces.
Contaminations on the Fe-whiskers were investigated by Auger
spectroscopy and scanning tunneling microscopy (STM) in ultrahigh vacuum (UHV). Before cleaning, the Fe-whisker was coveredby oxide layers. The whisker was cleaned by Ar ion sputtering at
600 °C in a preparation chamber by following the procedure described in Ref. [12]. After these treatments, Auger spectra showedno oxygen. The clean Fe-whisker of hexagonal-pillar shape(Fig. 1a) was mounted in our STM chamber (<1  108 Pa). A W
tip, which was cleaned by Ar ion sputtering and electron bombardment, approached the side plane of the whisker. All STM measurements were performed at room temperature (RT), and the STM
images were obtained at negative bias voltages to obtain topography of sample surfaces without effects of sample local density ofstates [19]. Atomically resolved STM images showed an oxygen
contamination below 1%.
3. Results and discussions
STM topographic images obtained on the bcc-Fe{1 1 0} surface
shows several terraces with a step height of 0.21 ± 0.03 nm,
pﬃﬃﬃwhichis consistent with the bcc-Fe{1 1 0} plane thickness of 2a=2 ﬃ
0:203 nm, where a = 0.287 nm is the lattice constant in the conventional bcc unit cell of a-Fe. We observed a regular array ofbright patches of 4 nm in diameter on a single terrace of anFe{1 1 0} crystallographic plane in topographic images as shownin Fig. 2a. Fourier transform of this pattern is shown in the inset
of Fig. 2a, which indicates that the pattern is aligned nearly along 1 1; ½0 0 1 and ½1
 1 1
 directions on Fe{1 1 0}. Note that thethe ½1bcc-{1 1 0} planes do not have hexagonal symmetry, but they have
only two-fold symmetry.
The pattern was observed on the {1 1 0} side planes of three different hexagonal-pillar shaped Fe-whiskers. This implies that theapattern comes from a surface reconstruction intrinsic to the{1 1 0} planes of bcc-Fe. The same topographic image in higher resolution (14  14 nm2) is shown in Fig. 2b, where not only the pattern but also atomic arrangement can be observed. The heightvariation along the broken arrow in Fig. 2b is shown in Fig. 2c.
The height of the pattern is roughly 0.07  0.08 nm, about 1/3 ofthe step height. The periodicity is about 14 atomic spacings. A
two-dimensional Fourier transformed image of Fig. 2b is shownin Fig. 2d. The elements inside the solid circle in the center of theimage indicate the same symmetry as the inset of Fig. 2a. White
dots inside the six dotted-circles apart from the center show thesymmetry of the surface atomic arrangement. Solid and dottedlines show a perfect hexagonal symmetry and a bcc-{1 1 0} symmetry, respectively. Positions of the six dotted-circles almost ﬁt to thehexagonal symmetry (solid lines) but not to the bcc-{1 1 0} symmetry, which indicates that the surface atoms do not have a bcc-{1 1 0}
symmetry, but they have almost hexagonal symmetry in spite of
the fact that the X-ray measurements in Fig. 1 showed bcc{1 1 0}. These six dotted-circles are arranged at every
61.5 ± 2.5°and the distances from the center of the image to thesix dotted-circles are not exact constant (±3%). These experimental
results show that the top surface layer of the bcc Fe{1 1 0}-whisker
has a quasi-hexagonal two-dimensional lattice plane. This will be
the essential idea for our interpretation of the experimentally observed surface reconstruction of the Fe{1 1 0} surface.
An inverse Fourier transformation with elements inside the six
dotted-circles and the center circle in the Fourier transformed image (Fig. 2d) give an image shown in Fig. 2e, which shows a clear
periodicity of the patterned modulation in brightness as well as
the atomic array in the top-layer. From this image, we can get
the unit vectors of the height modulation pattern as



p~1
p~2




¼

13

1

2 14




u~1
;
u~2

ð1Þ

where u~1 and u~2 denote primitive vectors of the atomic arrangement in the top-layer. We set a whisker crystal on our STM stage
as shown in Fig. 2a, i.e. the direction of one of the unit vectors of
periodic modulation, p~1 , was set in almost [0 0 1] crystalline direction. The length of p~1 was observed to be about 3.65 nm in
Fig. 2e, i.e. j p~1 j =a  12:7. Angle between p~1 and another unit vector of p~2 is /p  63.8°, and k ¼j p~2 j = j p~1 j 0:920, i.e.
j p~2 j =a  11:7.

c

d

e

f

g

h

b

Fig. 1. (a) Scanning electron microscopy image of an Fe-whisker in hexagonal-pillar shape. (b) Laue X-ray image obtained on a side plane of the whisker in (a). An inset sketchshows the crystalline structure of the whisker. (c–h) Diffraction spectra were measured by rotating the whisker at U = 0° (c), 60° (d), 120° (e), 180° (f), 240° (g), and 300° (h).
Six side planes of the hexagonal Fe-whisker were identiﬁed to be {1 1 0} using a four circle X-ray diffract meter.

T.K. Yamada et al. / Surface Science 603 (2009) 315–319

317

Fig. 2. (a) An STM image obtained on the bcc-a-Fe{1 1 0} surface (34  34 nm2). The inset image in (a) denotes a Fourier transformed image of (a). (b) An atomically resolved
STM image of the {1 1 0} surface. The pattern array as well as the atomic array is observed. (c) A line proﬁle along the broken arrow in (b). (d) A Fourier transformed image of(b). (e) An inverse Fourier transformation of (d).

The surface reconstruction pattern is formed by a superpositionof a two-dimensional quasi-hexagonal atomic array of the toplayer and the sub-surface bcc-{1 1 0}, which is simply interpretedusing a solid-sphere model in Fig. 3. Surface-atoms in the centerof the darker areas in the STM-topographic images in Fig. 2 areconsidered to sit just on the hollow sites of the sub-surface bcc{1 1 0} layer, what we cannot see in STM. Let us take unit vectors
 0 directions on the {1 1 0} sub-sur^^ along the [0 0 1] and ½1 1
x and yface of bcc-Fe. Using a lattice constant a = 0.287 nm, primitive vecthe 
two-dimensional{110} sub-surface plane
tors of s~1 and s~2 in 

^
1
0pﬃﬃﬃ
x
s~1
¼a
. A solid-sphere
are expressed as,^
1=2 1= 2ys~2model of the sub-surface bcc- Fe{1 1 0} is shown in Fig. 3a, where
hollow sites are indicated by black dots, what makes a triangularlattice with two-fold symmetry different from the quasi-hexagonallattice of atomic sites in the top-layer.
Since the observed height modulation pattern appears as theinterference between the atomic array of the top-layer and the hollow sites on the sub-surface layer, the unit vectors of the modula~j ðj ¼ 1; 2Þ, must also be expressed by the primitive vectors
tion, p~sj ðj ¼ 1; 2Þ, of the hollow sites on the sub-surface layer, i.e.,



p~1
p~2




¼

m1

n1

m2

n2



s~1
s~2



pﬃﬃﬃ ! ^x
m1 þ n1 =2 n1 = 2
pﬃﬃﬃ
¼a
;
^
y
m2 þ n2 =2 n2 = 2ð2Þwhere m1,n1,m2, and n2 are integers, which determine p~1 and p~2 ex~j (j = 1, 2) andxÞ direction are giactly. Angles between
pﬃﬃﬃp the ½0 0 1ð^
2nj =ð2mj þ nj Þ ; ðj ¼ 1; 2Þ.
ven by /j ¼ arctan~j andIf a correct set of integers, m1, n1, m2, and n2, are obtained, p~j are related to ~sj which is strictly deﬁned by the lattice conalso ustant due to constrain of bcc structure in three dimensions. Quantitatively precise results, which improve upon the direct STM
image, can be obtained. First, we put n1 as an integer near zero(e.g. 0, ±1, . . . ±5 in Table 1) since the sample is mounted with /1
not far from zero. Then, an integer m1 is selected to give a minimum deviation, D1 ¼ kp~1 exp j =a j p~1 cal j =a j, where j p~1 exp j =a denotes the experimentally obtained j p~1 j =a  12:7, andqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
j p~1 cal j =a ¼ ðm1 þ n1 =2Þ2 þ n21 =2. Integers n2 and m2 are determined so as to give a minimum deviation in components ofpﬃﬃﬃ
j p~2 exp j =a; Dy ¼j ðj p~2 exp j =aÞ sinð/1 þ /p Þ  n2 = 2 j; Dx ¼j ðj p~2 exp j=aÞ cosð/1 þ /p Þ  ðn2 =2 þ m2 Þ j, where j p~2 exp j =a denotes theexperimentally obtained j p~2 j =a  11:7, and /p  63.8°. The total
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
deviation D ¼ D21 þ D2y þ D2x can be useful to judge the most reasonable set of n1,m1,n2, and m2. Table 1 shows several sets ofcandidate integers. Each set gives different /j(j = 1, 2). In these sets,
the most reasonable relation with the minimum total deviation
is

318

T.K. Yamada et al. / Surface Science 603 (2009) 315–319acbFig. 3. Solid-sphere models on the surface of a-Fe{1 1 0}. White circles and black dots show Fe atoms and hollow sites, respectively. (a) A conventional bcc-a-Fe{1 1 0} latticeplane. s~1 and s~2 are primitive vectors. (b) Relations of the primitive vectors of the quasi-hexagonal top-layer (u~1 and u~2 ), the sub-surface (s~1 and s~2 ) layer and the modulation
pattern (p~1 and p~2 ). Lines are parallel to the sub-surface primitive vectors. (c) A superposition of the quasi-hexagonal top-layer lattice plane and the sub-surface conventionalbcc-{1 1 0}.

Table 1
Obtained integers for n1, n2, m1 and m2. /j denotes the angle between the [0 0 1]
direction and p~j ðj ¼ 1; 2Þ. The total deviation is shown as D ¼ ðD21 þ D2y þ D2x Þ0:5 .
n1

m1

n2

m2

/1

/2

D

5
4
3
2
1
0
1
2
3
4
5

15
14
14
14
13
13
12
12
11
10
10

12
13
13
14
14
15
15
16
16
16
16

2
1
0
1
1
2
3
4
5
5
6

16.1
12.8
9.6
6.4
3.2
0.0
3.2
6.4
9.6
12.8
16.1

46.7
50.8
54.7
58.8
63.2
62.6
67.0
70.5
75.1
75.1
80.0

0.34
0.43
0.43
0.46
0.80
0.47
0.25
0.49
0.36
0.50
0.33



p~1
p~2




¼

12

1

3 15



s~1
s~2



12:5

¼a

4:5

pﬃﬃﬃ ! 
^x
1= 2
pﬃﬃﬃ
^
y
15= 2

ð3Þ

The relation between the top-layer and the sub-surface layer
can be deduced from Eqs. (1) and (3) as follows:



u~1
u~2




¼

13

1

2 14

1 

12

1

3 15



s~1
s~2



ð4Þ

This relation is graphically shown in Fig. 3b, where the twodimensional lattice of the top-layer is not any longer a perfect hexagonal lattice. The angle between u~1 and u~2 is 59.3°, and u~1 rotatesby 0.2°from s~1 , i.e. they are nearly parallel though p~1 rotates by
3.2 (3.4)°from s~1 ðu~1 Þ. Absolute values of primitive vectors are as
follows,j s~1 j¼ a >j u~1 j¼ 0:927a >j u~2 j¼ 0:883a >j s~2 j¼ 0:866a. A
model is made with these primitive vectors, where the hollow sites
on the sub-surface layer marked as black dots are superposed bysurface atoms marked by the white circles. This superposition represents a periodic pattern as shown in Fig. 3c, which is consistent
with the obtained STM topographic image of Fig. 2.

According to the solid-sphere contact model, the maximum
pﬃﬃﬃ
Dh ¼
3
heightdifferenceofthemodulationispﬃﬃﬃ
2Þa=2 ﬃ 0:046 nm. The experimentally obtained STM images at
negative bias voltages show the height difference of 0.07–
0.08 nm, which is somewhat larger than the value suggested by
the solid-sphere contact model. Since the tunneling currents, i.e.
STM images, obtained at negative bias voltages are not strongly
inﬂuenced by sample electronic states [19], this height differenceof 0.07–0.08 nm can be considered as a real height difference.
Then, the larger different height may have physical meaning. Since
the radius of the solid-sphere in the solid-sphere model is estimated for an atom surrounded by eight nearest neighbors in thebulk bcc-Fe, the model does not include inﬂuences of the different
symmetries, i.e. coordination numbers, of the surface atoms. In the
top surface layer, atoms on the hollow sites have a higher coordination number than the atoms on the atomic sites. Therefore, anexperimentally obtained height difference larger than the model
expects indicates an atomic distance larger than the distance inbulk for the atoms on the atomic sites, which can be also explainedby the fact that the NN distance in bulk is shorter than the potential minimum distance between two atoms, i.e. atoms with a lower
coordination number prefer to take a larger atomic distance.
Two-dimensionalpﬃﬃﬃ density of atoms in the sub-surface bcc-{1 1 0}
is 1= j s~1  s~2 j¼ 2=a2 , while that in the top surface layer is
1= j u~1  u~2 j¼ 1:0046= j s~1  s~2 j. This slight difference of less than
0.5% is within errors in direct experimental observation, however,in our procedure of analysis it can be meaningful. This fact that asurface of condensed matter has higher density of atoms than abulk due to the so-called surface tension, which is caused by thebreak down in symmetry of interactions between the atoms.
The observed height difference between dark and bright regionsin the STM image of top-layer is larger than that expected from thesimple hard-contact solid-sphere model. The number of atoms in
an unit cell of the periodic pattern of the height modulation in

T.K. Yamada et al. / Surface Science 603 (2009) 315–319

the ﬂat sub-surface bcc-{1 1 0} layer is j p~1  p~2 j = j s~1  s~2 j¼ 91:50,
while that in the top-layer is j p~1  p~2 j = j u~1  u~2 j¼ 91:92. Thisslight excess number of atoms is accommodated in bright concave
regions in the non-ﬂat top-layer.
There may be another possibility to cause the reconstruction on
the Fe{1 1 0}. Although our Auger spectroscopy and atomically resolved STM images detected only oxygen atoms with a concentration below 1%, these techniques cannot detect hydrogen.
Theoretical calculations and low-energy electron diffraction results
showed a hydrogen-induced (2  2) reconstruction on the Fe{1 1 0}
surface at low temperatures (40 K) by introducing hydrogen gas
under the base pressure in a range of 108–109 Pa [20,21], a pressure that is comparable to our experimental setup. (The Fe single
crystal used in Ref. [21] includes impurities of S, P, C in bulk.) So
far, hydrogen-induced (2  2) reconstruction was found only below 300 K and we did not observe a short-period reconstruction,
like (2  2), on our Fe{1 1 0} surface at 300 K. Therefore, we
consider that the mesoscopic-range reconstruction that we foundon the clean Fe{1 1 0} surface is likely not caused by hydrogenatoms.
4. Conclusion
Clean bcc-{1 1 0} surfaces of three different pure hexagonal-pillar shaped a-Fe-whiskers was investigated by means of STM at RT
in UHV. The top surface layer was found to be reconstructed to aquasi-hexagonal atomic array with periodic height modulation.
Unit vectors of the modulation turned out to be expressed as  
 
  
 
13 1
12 1
u~1
u~1
s~1
p~1
¼
¼
, where
and
2 14
3 15
p~2
u~2
s~2
u~2
 
s~1
are the primitive vectors of the two-dimensional atomic ars~2
ray in the top-layer and those in the sub-surface layer, respectively.
The two-dimensional density of atoms in the top-layer is slightly
higher by 0.46% than that in the sub-surface layer.

319

Acknowledgements
We would like to appreciate to Prof. Dr. W. Wulfhekel, Prof. Dr.
H. van Kempen and Prof. Dr. F. Spaepen for helpful discussions.
Kind guidance for CVD for Fe-whisker by Dr. D.T. Pierce isacknowledged.
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