Kyushu University Global COE Program
Journal of Novel Carbon Resource Sciences, Vol. 1, pp. 29-32, Mar. 2010

Determination of a p(3√2×√2)R45° StructureFormed by Sn Adsorption on Cu(001):
A Tensor Low-energy Electron Diffraction Analysis
Hisashi Yoshida*1 and Hiroshi Tochihara*2
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University*2
Faculty of Engineering Sciences, Kyushu University*1(Received December 21, 2009; accepted January 7, 2010)
Low-energy electron diffraction (LEED) have been used to determine the p(3√2×√2)R45° structure formed at300 K by adsorption of Sn atoms on Cu(001). It is confirmed that the same model suggested by previous studies ofsurface x-ray diffraction, density functional calculations and LEED analysis is correct. It contains missing-rows along
the [100] direction. Optimum parameters of the p(3√2×√2)R45° structure reveal that the substitutional Sn atoms
laterally displaced by 0.30 ± 0.05 Å away from ideal fourfold-hollow sites. Distance between the nearest-neighbor
substitutional Sn atoms is 3.02 ± 0.05 Å, suggesting the formation of an Sn dimer. The stabilization mechanism of thep(3√2×√2)R45° structure is discussed.

1. Introduction

It has been demonstrated that various ordered surface
structures are formed on the Cu(001) surface by adsorptionof metals at room or slightly higher temperatures1,2).
Among such adsorption systems, Sn-adsorbed Cu(001)surfaces are extensively studied3-15). The Cu(001)-Sn
system showed five ordered phases at room temperature
in a submonolayer coverage8,13). The first ordered phase isa “p(2×2)” structure formed at Sn coverage of about 0.2
monolayer (ML). The coverage is defined as the ratio ofsurface density of adsorbed metal atoms with respect tothat of the ideal surface Cu atoms. Sn atoms are located at
substitutional sites and form a local p(2×2) structure with
anti-phase domains5). With increasing coverage, a p(2×6)
structure is formed at 0.33 ML. Diffraction patterns of thep(2×6) structure have missing spots, that is, glide planes
are present10). Subsequently observed phase is a c(4×8)
structure, that was discovered recently by scanningtunneling microscopy (STM) studies9,10). The coverage ofa proposed model is 0.375 ML. At 0.5 ML, a p(3√2×√2)
R45° structure is formed. This structure was determinedby several methods including a low-energy electron
diffraction (LEED) intensity-voltage (I-V) analysis. A
half of surface Cu atoms are substituted by Sn atoms
and a sixth of surface Cu atoms are removed leavingvacancies. The vacancies are assembled to be single
missing-rows along the [100] direction6). Very recently,
a double missing-row structure has been locally observed
by STM15). In addition, a reversible phase transitionbetween the p(3√2×√2)R45° and a c(2×2) structure at360 K was observed7). The high-temperature phase is thec(2×2). Upon further deposition of Sn, a c(4×4) structure
is observed at about 0.65 ML and an overlayer model
was proposed3). Recently, a new structure model wasproposed from STM observations10,13). It was suggested
that the c(4×4) structure consists of one substitutional Sn
atom and four Sn adatoms per unit cell.
In the present paper, we report a reinvestigation ofthe p(3√2×√2)R45° structure using LEED I-V analysis.

The determined structure is the same model suggested
by previous LEED study6). However, the structuralparameters are quite different. We discuss the stabilization
mechanism of the p(3√2×√2)R45° structure.

2. Experiment and Calculation

The experiments were carried out in an ultra-highvacuum (UHV) chamber equipped with a commercial
LEED optics. The base pressure in the UHV chamber isless than 4 × 10-10 Torr during experiments. The Cu(001)surface was cleaned by repeated cycles of argon ion
bombardment (0.5 keV, 1.5 μA) and subsequent annealing
to 800 K. Sn atoms were evaporated from a homemade Knudsen cell onto Cu(001) at 300 K. LEED spot
intensities for I-V curves were recorded by a computercontrolled video LEED system at a sample temperatureof 130 K. Details of the experiment were similar to theprevious study16).
A Barbieri/Van Hove symmetrized automated tensor
LEED package was used to calculate I-V curves forstructure models17). The programs searched for agreementwith the experiment by minimizing the Pendry R-factor,
Rp18). The real part of inner potential was determined
during the course of the theory-experiment fit. Thedamping was represented by an imaginary part of thepotential, Voi, of –5.0 eV. The error range of structuralparameters were obtained from the variance of Rp18),
ΔR = Rmin (8 |Voi| / ΔE)1/2, where Rmin is the minimum
Rp factor achieved and ΔE is the total energy range ofmeasured I-V curves for in-equivalent spots.

3. Results

The p(3√2×√2)R45° structure was previously
investigated by some experimental methods3,4,10,14,15)
including a LEED I-V analysis6). We consider thatthe optimized value of the Rp of 0.26 obtained in theprevious LEED analysis6) is relatively large in spite oflarge number of structural parameters (five complete Culayers are included in the optimization). Here, we have

Journal of Novel Carbon Resource Sciences, Vol.1, Mar. 2010

Fig. 1

Ball models of examined 6 structures ofCu(001)-p(3√2×√2)R45°-Sn (top view).

a very good Rp value of 0.12 for optimized model 1 under
the condition of the same number of structural parameters
as Ref. 6. The Rp of other five models gave above 0.31.
The value of 0.31 is large enough to be excluded, because
the error range of the Rp of the present study is only 0.01.
Thus, we have confirmed model 1 is correct. Optimized
Debye temperatures for Sn, surface Cu and other Cu
atoms were 140, 240 and 343 K, respectively.
Top and cross sectional views of best-fit structure(model 1) are illustrated in Fig. 2. The numbers identify
equivalent atoms. Arrows indicate directions of lateraldisplacements of Sn1 and Cu1 atoms from fourfoldhollow sites in the second layer. Sn2 atom is not allowed
to displace laterally due to the symmetry requirement.
Optimized parameters are summarized in Table 1.
Lateral displacement and height difference are listed
in Table 2 and 3, respectively, in which our results arecompared with those in the previous LEED6), surface
X-ray diffraction (SXRD)14) and DFT15) studies. The
error ranges were obtained from the variance of the Rp
mentioned above18), and they were much smaller, on thewhole, than those in Ref. 6. Comparison of our I-V curves
between of experiment and of theoretical best-fit structureis depicted in Fig. 3. The agreement is very good.

4. Discussion

First, we compare our optimized values of structural
Table 1 Structural parameters for optimized structurein Fig. 2AtomDisplacement along arrow (Å)

Height (Å)

Sn1

0.30 ± 0.05

9.37 ± 0.02

Sn2-

9.43 ± 0.03

Cu1

0.17 ± 0.05

9.06 ± 0.01

Cu20.06 ± 0.05

7.19 ± 0.02

Cu3-

7.11 ± 0.03

Cu40.03 ± 0.06

7.23 ± 0.02

Cu5-

7.27 ± 0.02

Table 2 Lateral displacements of Sn1 and Cu1 atoms in theCu(001)-p(3√2×√2)R45°-Sn structure. Corresponding
atoms are indicated in Fig. 2Displacement along arrow (Å)

Fig. 2 Top and cross sectional views of theCu(001)-p(3√2×√2)R45°-Sn structure.

AtomSn10.26 ± 0.10

0.27 ± 0.01

0.26

0.30 ± 0.05

reinvestigated this structure using a tensor LEED I-V
analysis, because we have obtained a rather large rangeof the total energy of 3977 eV for inequivalent beams(2280 eV in the previous study6)). Six examined structure
models are shown in Fig. 1: surface alloy with single
missing-row model by Pussi et al.6) (model 1); overlayer
model by Argile et al.3) (model 2); overlayer and surface
alloy models by McLoughlin et al.4) (models 3 and 4);
overlayer with subsurface missing-row model by Lalloet al.10) (model 5); and surface alloy with double missingrow model by Fuhr et al.15) (model 6). We have obtained

Cu1

0.01 ± 0.04

0.15 ± 0.03

0.13

0.17 ± 0.05

LEED 6)SXRD 14)

DFT 15)this study

Table 3 The rumplings of Sn-Sn and Sn-Cu in theCu(001)-p(3√2×√2)R45°-Sn structure comparedwith Ref. 6, 14, and 15 shown in Fig. 2
rumpling
dSn1-Sn2
dSn1-Cu1
dSn2-Cu1

LEED 6)
0.12 ± 0.08
0.27 ± 0.07
0.39 ± 0.07

Value (Å)
SXRD 14)
DFT 15)0.13 ± 0.03
0.12
0.22 ± 0.02
0.41
0.35 ± 0.03
0.53

this study
0.06 ± 0.03
0.31 ± 0.02
0.37 ± 0.02

Determination of a p(3√2×√2)R45° Structure Formed by Sn Adsorption on Cu(001)

Finally, we discuss the origin of the stabilizationof the p(3√2×√2)R45° structure. The formation of Sndimers becomes possible by removing surface Cu atoms
along the [100] direction. This suggests that the dimer
formation results in a considerable gain of the adsorptionenergy at the cost of surface vacancy formation energy.
The coverage of surface Cu vacancies is 2/3 ML in thep(3√2×√2)R45° structure, while 1/2 ML in the c(2×2)
structure. The dimer formation provides an additional
gain of the adsorption energy: Surface Cu (Cu1 in Fig.
2) atoms can displace away from Sn2 atoms to allow
Sn2 atoms go down deeper. Then, Sn2 atoms become
possible to interact with the second layer Cu atoms more
effectively. Thus, the p(3√2×√2)R45° structure stabilizes
more than the c(2×2) substitutional structure. The DFTcalculations15) conclude that the p(3√2×√2)R45° structure
is more stable than the c(2×2) substitutional structure by
90 meV/Sn atom: The adsorption energy of Sn atom in
the former is 4.03 eV, while that in the latter is 3.94 eV.

5. SummaryFig. 3 Comparison between the experimental (solid line)
and best-fit theoretical (dashed line) I-V curves forCu(001)-p(3√2×√2)R45°-Sn.

parameters with those obtained by the previous LEED6),SXRD14) and DFT15) studies. Table 2 is one of suchcomparisons for lateral displacements of Sn1 and Cu1 inFig. 2, while Table 3 for height differences among surface
atoms of Sn1, Sn2 and Cu1. In both tables our values areobtained from Table 1. Bond distances such as Sn1-Sn1
are obtained also from Table 1. In Table 2, values of thedisplacement of Sn1 are very similar in four studies6,14,15).
On the other hand, previous studies reported considerably
different values for Cu1. SXRD14) and DFT15) studies
show relatively large displacements but the previous
LEED study6) concluded almost no displacement. Our
LEED study confirms that Cu1 atoms laterally displaceconsiderably from the hollow sites.
Second, we discuss features of the p(3√2×√2)R45°
structure on the basis of structural parameters obtainedin this study. This structure is a new type of surface
ordered alloys. Basically it may be classified into thec(2×2) check-like surface alloys. However, there is a
big difference: Every third Cu atoms at the surface arecompletely removed away along [100] directions inducedby Sn adsorption. In the removed area, pairs of Sn atoms
are aligned along the [100] directions (see Fig. 2). The
bond distance of the paired Sn atoms is obtained to be
3.02 ± 0.05 Å (see Table 3), suggesting the formation ofSn dimers. The nearest Sn atom distance in β-tin is 3.016
Å19). The dimers are arranged like dimer-rows along the[100] directions, but it is noted that the distance between
neighboring dimers is 3.61 Å, indicating there are little
direct chemical bonds.

Sn adsorbed Cu(001) surface has been studied by LEEDat room temperature. We succeeded the determinationof p(3√2×√2)R45° structure by the tensor LEED I-Vanalysis. Our result showed a previously suggested
structure that contains single missing-row along [100]direction is correct. Large lateral displacements of Sn1and Cu1 atoms from ideal fourfold-hollow sites in Fig. 2
are observed. Sn1 atoms are stabilized by formation of
dimers to gain an additional adsorption energy.
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