This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 12753–12759 12753

Layer and orientation resolved bond relaxation and quantum entrapment

of charge and energy at Be surfaces

Yan Wang,a Yan Guang Nie,b Ji Sheng Pan,c Likun Pan,d Zhuo Sund and

Chang Q. Sun*be

Received 31st March 2010, Accepted 23rd June 2010

DOI: 10.1039/c0cp00088d

The chemistry and physics of under-coordination at a surface, which determines the process of

catalytic reactions and growth nucleation, is indeed fascinating. However, extracting quantitative

information regarding the coordination-resolved surface relaxation, binding energy, and the

energetic behavior of electrons localized in the surface skin from photoelectron emission has long

been a great challenge, although the surface-induced core level shifts of materials have been

intensively investigated. Here we show that a combination of the theories of tight binding and

bond order-length-strength (BOLS) correlation [C. Q. Sun, Prog. Solid State Chem., 2007, 35,

1–159], and X-ray photoelectron spectroscopy (XPS) has enabled us to derive quantitative

information, by analyzing the Be 1s energy shift of Be(0001), (10�10), and (11�20) surfaces, for

demonstration, regarding: (i) the 1s energy level of an isolated Be atom (106.416 � 0.004 eV) and

its bulk shift (4.694 eV); (ii) the layer- and orientation-resolved effective atomic coordination

(3.5, 3.1, 2.98 for the first layer of the three respective orientations), local bond strain (up to

19%), charge density (133%), quantum trap depth (110%), binding energy density (230%), and

atomic cohesive energy (70%) of Be surface skins up to four atomic layers in depth. It is affirmed

that the shorter and stronger bonds between under-coordinated atoms perturb the Hamiltonian

and hence the fascinating localization and densification of surface electrons. The developed

approach can be applied to other low-dimensional systems containing a high fraction of under-

coordinated atoms such as adatoms, atomic defects, terrace edges, and nanostructures to gain

quantitative information and deeper insight into their properties and processes due to the

effect of coordination imperfection.

I. Introduction

Interaction between under-coordinated atoms is key to the

fascinating behavior of low-dimensional systems such as

adatoms, atomic defects, atomic chains, tubes, cavities, and

surfaces of bulky solids. The shorter and stronger bonds

between under-coordinated atoms cause local strain and

potential well depression, also called quantum entrapment.

The locally densely trapped energy provides a perturbation in

the Hamiltonian, binding energy density, electroaffinity, and

atomic cohesive energy, which determine the mechanical,

thermal, electronic, optic, magnetic, dielectric, catalytic, and

chemical properties that are completely different from those of

the bulk interior.1 The under-coordinated atoms also serve as

activation centers for many processes such as chemical reactions

and growth nucleation. Although the chemistry and physics of

materials at these sites have been intensively investigated,

determination of the underlying mechanism still remains a

great challenge. Therefore, the elucidation of the electronic

structure and the electronic binding energy at sites surrounding

the under-coordinated atoms is of great importance, since its

clarification can improve our understanding of the origination

of the novel physical properties of surfaces and nanostructures.

From the spectra of X-ray photoelectron spectroscopy (XPS),

the binding energies (BE), being a superposition of the intra-

atomic trapping and the interatomic binding (crystal potential)

contributions, of various elements can be determined but the

discrimination of the two identities from each other is infrequent

and indirect due to the lack of suitable guidelines from the

perspective of the intrinsic Hamiltonian perturbation. One

often takes the bulk component as the reference with zero

shift in energy as the determination of the actual bulk shift

from the energy level of an isolated atom is hardly possible.

Such a zero-bulk-shift assumption annihilates plenty of useful

information such as the energy level of an isolated atom and

its bulk shift which is non-zero according to energy band

theory.

The Be 1s core level shift (CLS) of the hcp(0001), (11�20),

and (10�10) surfaces of Be(1s22s2) has been intensively investigated

experimentally using XPS and theoretically based on a density

functional premise and in terms of the ‘‘initial-final states’’

a School of Information and Electronic Engineering,Hunan University of Science and Technology, Xiangtan 411201,China

b School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore 639798

c Institute of Materials Research and Engineering, A*STAR,Singapore 117602

d Engineering Research Center for Nanophotonics & AdvancedInstrument, Ministry of Education, Department of Physics,East China Normal University, Shanghai 200062, China

e Institute of Quantum Engineering and Micro-nano Energy,Key Laboratory of Low-dimensional Materials and ApplicationTechnologies, Xiangtan University, Changsha 411105, China

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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convention in the past decades.2–8 Using synchrotron radiation,

Johansson et al.6–8 measured the Be(0001) surface 1s CLS and

identified three distinct components of shifts with energies of

�825 � 30 (S1), �570 � 25 (S2), and �265 � 20 (S3) meV with

respect to the low energy (large absolute value) component at

111.835 (B) eV. For the Be(10�10) surface, three components

were identified to shift by �700 (S1), �500 (S2) and �220 (S3)

meV2,7–9 but two components would suffice for the (11�20)

surface.9 These CLS were assigned as negative shifts according

to the ‘‘initial-final states’’ convention, i.e., the surface layers

add states at higher energies (smaller absolute values) than the

bulk component. This assignment is in contrast with the mixed

shift proposed by Hofmann et al.10 who suggested that the

largest negative shift is instead caused by the second surface

layer. Disregarding the discrepancy regarding the number and

the order of the surface components, Johansson et al.6,7,9

reported that the intensities of the high-energy (surface)

components increase with the incident beam energy from

123 to 165 eV. The intensities of the high-energy components

also increased when the emission angle (between the photo-

electron beam and the surface normal) was reduced from 361

to 01.11 Higher beam energy or smaller emission angles means

that the incident beam can penetrate deeper into the bulk and

therefore collect more bulk information.12 From this perspective,

the higher energy component corresponds to the B component,

instead.

A low-temperature scanning tunneling microscope (STM)

investigation13 revealed that the Fermi contour of the

Be(10�10) surface state is located at the boundary of the surface

Brillouin zone, and the surface-state electrons provide the

main part of the charge density near the Fermi energy. Highly

anisotropic standing waves of the surface charge density were

observed on Be(10�10) near the step edges and the point

defects, which is consistent with STM observations from

Au–Au chain ends,14 Au island edges,15 graphite vacancies16,17

and graphene edges.18,19 It is our opinion20,21 that the standing

waves correspond to the edge states due to charge localization,

polarization and densification induced by the densely and

deeply trapped core electrons. On the other hand, in a

theoretical calculation, Hjortstam et al.22,23 found a 25%

inward surface relaxation of the Be(10�10) surface, which is

attributed to the pronounced surface states close to the Fermi

energy.

Although the physics of materials at defects and surfaces

has been extensively investigated, the laws governing the

energetic behavior of electrons and the property change of

materials in the surface region remain unclear. In order to

understand the physical origin of the unusual behavior of

surface electrons and to derive quantitative information

regarding the structure relaxation, binding energy and the

quantum trap depth, we have analyzed the XPS characteristics

of Be(0001),5–7 Be(10�10),2,7,8 and Be(11�20)5,9 surfaces from the

perspective of chemical bond–crystal potential–energy band

correlation.24,25 Using a combination of the tight binding

approximation and the bond order-length-strength (BOLS)

correlation algorithm,1 we have been able to derive quantitative

information from measurements regarding: (i) the energy level

of an isolated Be atom and its bulk shift; (ii) the layer and

orientation resolved local strain and quantum entrapment and

(iii) the relative binding energy density and the relative atomic

cohesive energy at the surfaces. Recent progress25,26 and the

current work affirmed that the shorter and stronger bonds

between under-coordinated atoms provide perturbation in the

Hamiltonian that globally defines the positive core-level shift.

II. Principles

2.1 Bond–potential–band correlation

Interatomic bonding plays a pivotal role in differentiating the

behavior of a bulk solid as opposed to that of individually-

isolated constituent atoms. For instance, the energy levels of

an isolated atom evolve into bands that shift downward in

energy upon bulk formation; phase transition can only happen

to the bulk rather than to single atom; an isolated atom does

not have a detectable melting point or mechanical strength as

the bulk counterparts do. Without interatomic bonding,

neither solid nor liquid could form. Therefore, the performance

of a material is determined uniquely by the constituent atoms

and the interactions among them.

The interatomic bonding at site r in an extended bulk solid

(B) is represented by the periodic crystal potential, Vcry(r,B), a

resultant of attraction and repulsion of many-body effects.

Electrons in different orbits of the constituent atoms will

experience the Vcry(r,B) but the value of Vcry(r,B) varies for

electrons in different orbits or energy levels because of the

screening effect. The Vcry(r,B) for electrons in the inner shells is

much weaker. Normally, the Vcry(r,B) has a magnitude of

several eVs, much weaker than the intra-atomic trapping,

Vatom(r), of the inner electrons up to the 103 eV level in the

deepest level. Under the equilibrium conditions of a bulk, the

maximum value of Vcry(r,B) p Eb is the cohesive energy per

bond. The coupling of the Vcry(r,B) with the relevant Bloch

wave functions determines the entire band structure and

related properties of a specimen such as the band gap, core

level shift, band width, and the dispersion relations and the

allowed energy states in the valence band and below, as well as

the dielectrics and electroaffinity according to energy band

theory.

In the crystallite-imperfect regions such as at sites surrounding

defects, adatoms, edges, surfaces and the skins of nano-

structures, the single-body Hamiltonian is perturbed because

of the bond strain, bond nature alteration and the associated

band energy gain, also called quantum entrapment.27 We can

introduce the perturbation coefficient, DH = g(zi) � 1, with

g(zi) = ci(zi)�m being the bond energy enhancement coefficient,

to the Hamiltonian of an extended bulk,

HðgÞ ¼ � �h2r2

2mþ VatomðrÞ

� �þ gðziÞVcryðr;BÞ ð1Þ

The terms in the brackets correspond to the Hamiltonian of an

isolated atom. Vatom(r) is the potential of the intra-atomic

trapping that determines the nth atomic energy level of an

isolated atom, Ev(0) = hfv(ri)|Vatom(r)|fv(ri)i, from which the

core level shifts when the crystal potential is involved. fv(ri) is

the specific Bloch wave function for the tightly-binding core

electron at site ri, which satisfies hfv(ri)|fv(rj)i= rdij, where dijis the Kronecker delta function and r the charge density.

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According to the tight-binding approximation, the non-zero

shift of a particular nth level, DEv(B), from the Ev(0), is

determined by the exchange and overlap integrals,

DEnðgÞ¼gDEnðBÞ¼gðbþzaÞ/gEb ðCore level shiftÞ

gb¼�hfnðriÞjVcryðrÞ½1þDH�jfnðriÞi/gEb ðOverlap IntegralÞ

ga¼�hfnðriÞjVcryðrÞ½1þDH�jfnðrjÞi/gEb ðExchange IntegralÞ

8>><>>:

ð2Þ

Since the wave functions of the tight binding electrons in the

inner shells are not overlapped, a is much smaller than b.From the XPS spectrum bulk component whose maximal

width is 2za (0.1–1.0 eV level), one can estimate that a is of

the order of 10�2–10�1 eV.28 z is the atomic coordination

number (CN). b is at the 100 eV level. Therefore, the BE shift is

dominated by b and proportional to the bond energy. Hence,

the chemical bond, potential well, and the core level shift can

thus be correlated.

2.2 Surface local strain and quantum entrapment

According to the BOLS correlation theory, bonds between

under-coordinated surface atoms are shorter and stronger.

The potential well becomes deeper; an additional potential

trap is added to the under-coordinated atoms and hence the

energy levels of these atoms will drop correspondingly. If

nonbonding electrons exist such as the otherwise conduction

electrons in the half-filled s-orbits, polarization of the non-

bonding electrons by the densely trapped bonding electrons

may take place. Such occurrence of surface polarization may

add density-of-states to the upper edges of both the valence15

and the core band, such as those identified from Rh(5s1).21 The

polarization is responsible for the observed Be(10�10) edge13

and Au chain end and edge states as well.14,15

Because of the local bond strain, densification of charge,

energy, and mass will occur at the local sites. Thus, the

broken-bond-induced local strain and quantum entrapment

provides perturbation to the Hamiltonian in the ith atomic

layer region characterized by an effective atomic CN of zi,

DH¼DðziÞ¼ gðziÞ�1¼ cðziÞ�m�1 ðHamiltonian perturbationÞ

ciðziÞ¼ 2=f1þ exp½ð12� ziÞ=ð8ziÞ�g ðBond strain coefficientÞ

cðziÞ�m¼EiðziÞ=E0 ðQT depth or bond energy gainÞ

8>>><>>>:

ð3Þ

where m is the bond nature indicator.20 For metals, m = 1.

According to band theory and the BOLS correlation, the

surface-induced energy shift of the nth level, En(0), follows

the relation:

Ev(i) � Ev(0) = [Ev(B) � Ev(0)] � (1 + Di) (4)

where Ev(B) � Ev(0) = DEv(B), thus we have the relation

EnðiÞ � Enð0ÞEnði0Þ � Enð0Þ

¼ 1þ Di

1þ Di0¼ ciðziÞ

�1

ci0 ðzi0 Þ�1 ; ði

0aiÞ ð5aÞ

If taking the XPS spectrum bulk component as a reference,

we have

EnðiÞ � EnðBÞEnði0Þ � EnðBÞ

¼ ciðziÞ�1 � 1

ci0 ðzi0 Þ�1 � 1; ði0aiÞ ð5bÞ

Given an XPS profile with clearly identified En(i) and En(B)

components of a surface (i= 1, 2, . . .), one can easily calculate

the atomic En(0) and bulk DEn (B) with the relations derived

from eqn (5):

Enð0Þ ¼ð1þDi0 ÞEn ðiÞ�ð1þDiÞEnði0ÞDi0 �Di

¼ ciðziÞEn ðiÞ�ci0 ðzi0 ÞEn ði0ÞciðziÞ�ci0 ðzi0 Þ

;ði0aiÞ

DEnðBÞ ¼EnðBÞ�hEnð0Þi

8<:

ð6Þ

If a total of l components are used to decompose a set of XPS

spectra from different surfaces of a specimen, En(0) should

take the mean value of the N = C(l,2) = l!/[(l � 2)!2!] possible

combinations with a standard deviation s. The minimal

standard deviation may serve as a criterion for the accuracy

of spectral decomposition which involves the peak energies

and the corresponding effective CNs. The latter is the unique

parameter for fitting. The intrinsic En(0) and DEn(B) values

should not be affected by experimental conditions, chemical

reactions, crystal size or orientation, or surface relaxation.

However, crystal orientation may lead to a fluctuation of the

component peak energies and the number of components

because of the slight difference in the effective atomic CNs.

Accuracy of the determination is strictly subject to the

XPS data calibration.29 Furnished with this approach and

decomposing rule, we would be able to elucidate the core-level

positions of an isolated atom and the strength of the bulk crystal

binding, and related properties from an XPS measurement.

Based on the above discussion, we may establish the rules

for decomposing the surface-induced XPS core-level shift:

1. An XPS profile can be decomposed into a number of

peaks according to contributions from different-coordinated

atoms in the bulk and surface layers denoted as B and Si. The

maximal i value is subject to the interlayer distances and the

cross section of the atomic diffraction. For heavier atoms, i is

smaller; for lighter atoms, i is greater. The i value is also

smaller for densely packed surfaces. If adatoms or defects exist

or if polarization occurs, there should be an A component

representing the trapped states of the even lower coordinated

adatoms or defects and a P component for the polarized states.

2. The surface-induced core level shift should be positive

with the lower-z component shifting the most to deeper

energies. However, the P states should move oppositely to

the low-z states, to the upper of the bulk component. If

polarization dominates, a negative core level shift could be

possible.

3. The energy shift of each component due to trapping is

proportional to the magnitude of the bond energy, which

follows the relationship: DEv(i) :DEv(B) = Ei :Eb = ci(zi)�m

(i=A, S1, S2,. . .). The values of Ev(0) and DEv(B) are intrinsic

and remain constant for a given material.

Fig. 1a illustrates the decomposition of the surface CLS

with P, B, Si and A components representing the states due to,

from high (small absolute value) to low, polarization, bulk,

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surface layers, and adatoms. The number of Si components for

a specific surface is subject to the atomic number and the

interlayer spacing. For heavy metals such as Cu, Ag, W and

Pd, i= 2 would suffice. For the light Be atom and the hcp high

index surfaces,25 i may be larger as demonstrated in the

spectral decomposition. Fig. 1b shows an hcp crystal unit cell

with the hcp(0001), (10�10), and (11�20) surfaces indicated.

2.3 Surface binding energy density and atomic cohesive energy

We have the expression for the coordination-resolved core

level shift and local lattice strain:30

E1s(z) = E1s(0) + DE1s(B)c�1z

e(z) = c(z) � 1 = 2/{1 + exp[(12 � z)/(8z)]} � 1 (7)

As the detectable quantities can be directly connected to the

binding identities such as bond nature, order, length, and

strength,20 we are able to predict coordination dependence

of the relative binding energy density, Ed(z) = Ei(z)/di3, and

the relative cohesive energy per atom, Ec(z) = ziEi(z), in each

atomic layer,27,31

Ed(z)/Ed(B) = ci(zi)�4

Ec(z)/Ec(B) = zibci(zi)�1 (8)

with zib = z/12. Subscript i represents the atomic layers

counted from the outermost inwards. The binding energy

density and the atomic cohesive energy are related to the local

elastic modulus31 and the local melting point27 at the specific

atomic site, respectively. More details regarding the inter-

dependence of various physical and chemical properties have

formed the subjects of recent thematic reports.1,20

III. Calculation algorithm

Based on the criteria established in section 2.2, we fit the XPS

spectra by using Gaussian components with respect to the

energy shifts given by Johansson et al.6–8,11 for Be, as listed in

Table 1. For Be(0001), the initial four components are

sufficient. An addition of the S1 component in the lower end

of the spectrum is needed to represent the under-coordinated

Be atom in the outermost Be(10�10) layer. The effective CNs

determined here are consistent with those for Rh(0001) and

(10�10) surfaces,25 indicating the reliability of this approach.

We need to point out that the quantities of En(0) and En(B)

are intrinsic constant values for a given material disregarding

Fig. 1 (a) Schematic illustration of the P, B, Si (i = 1, 2, 3. . .), and A

components of the positive surface CLS. The reference point for the

shifts is the energy level of an isolated atom En(0), instead of the En(B)

component. The DEn(B) and En(0) values are intrinsic and remain

constant for a given material disregarding the crystal orientation or

experimental conditions. If polarization occurs, a P state presents at an

energy above the B component; if adatoms are present, A states appear

with energy even lower than the S1 because of the lowered CN.

(b) Illustration of an hcp crystal structure with the (0001), (10�10),

and (11�20) planes indicated.

Table 1 Atomic-layer and crystal-orientation resolved effective CN (z), local strain (c(z) � 1), relative binding energy density (c(z)�4), and relativeatomic cohesive energy (zib/c(z) with zib = z/12) determined from the measured XPS profiles of Be(0001), (10�10), and (11�20) surfaces under theestablished approach and the criteria. The energy shift E1s(i) � E1s(B) for each component is the input and the effective CNs are the adjustableparameters. The 1s core level of 106.416 � 0.004 eV and the B component at 111.11 eV should be identical for all the surfaces. The coordinationdependence of the Be 1s core level shift is expressed as E1s(z) = E1s(0) � s + DE1s(B)/c(z) = 106.416 � 0.004 + 4.694/c(z) eV wherec(z) = 2/{1 + exp[(12 � z)/(8z)]}

i E1s(i)/eV z c(z) � 1 (%) c(z)�4 zib/c(z)

Be B (z = 12) 111.110 12 0.00 1.00 1.00(10�10) Ref. 7,8 S4 111.330 7.00 �4.46 1.20 0.61

S3 111.590 4.83 �9.25 1.47 0.44S2 111.830 3.83 �13.25 1.77 0.37S1 112.122 3.10 �17.75 2.19 0.31

(0001) Ref. 6,11 S3 111.370 6.53 �5.23 1.24 0.57S2 111.680 4.39 �10.79 1.58 0.41S1 111.945 3.50 �15.06 1.92 0.34

(11�20) Ref. 9 S4 111.400 6.22 �5.80 1.27 0.55S3 111.650 4.53 �10.29 1.54 0.42S2 111.870 3.71 �13.90 1.82 0.36S1 112.190 2.98 �18.71 2.29 0.31

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the orientation. Therefore, we can refer the energy shifts of all

surface components to the En(B) before knowing the En(0).

According to the tight binding and BOLS theories, a positive

shift is preferred. The given energy shifts enable us to determine

the effective atomic CN as the unique variable in the present

exercise for each component and the En(0) using eqn (5) and

(6). It is emphasized that the effective CN is different from the

apparent CN.1 Incorporating the BOLS correlation mechanism

into the measured surface relaxations,32,33 the effective CN for

the fcc(001) outermost surface is four instead of six.

IV. Results and discussion

Fig. 2 shows the XPS decomposition of the Be(0001), (10�10),

and (11�20) surfaces. The intensities of the atomic-layer and

crystal-orientation resolved components also change with the

incident beam energy. Including the B component that was

counted only once, there are a total of l = 12 components for

the Be surfaces considered, as shown in Table 1. There will be

a combination of C(12,2) = 12!/(12 � 2)!2! = 66 = j values of

En(0). Using the least-root-mean-square approach, we can find

the average of hEv(0)i =P

NEvi(0)/j and the standard

deviation, s = {P

21(Evi(0) � hEv(0)i)2/(j(j � 1))}1/2. A fine

tuning of the CN values will minimize the s value and hence

improve the accuracy of the effective CNs, the local strain, the

binding energy density and the cohesive energy per discrete

atom in differently oriented surface layers.

According to the decomposition criteria, the B component

must exist in all the surfaces. The invisibility of the B component

in the Be(11�20) surface spectrum indicates that the high-mass

density of the low-index Be(11�20) surface prevents the incident

beam from penetrating into the bulk underneath the first four

atomic layers. The fitting indicates that the Be surface skin is

formed by at most four surface atomic layers because of the

lower atomic cross section and the packing density. For a Ni

surface34 and a 3.5 nm sized gold cluster,35 the surface is only

two interatomic spacings thick. The lack of bulk information

in the Be(11�20) spectrum also indicates the penetration depth

of the 135 eV X-ray beams is limited to the outermost three

atomic layers.

The optimal s value is 0.004–0.0042. The derived E1s(B) =

106.416 � 0.004 eV and the bulk shift is DE1s(B) = 4.694 eV

with three decimal places being sufficient with respect to the

measurement precision. The derived effective CNs, the local

strains, and the predicted trends of the local binding energy

Fig. 2 The decomposed XPS spectra for (a) the Be(0001), (b) (10�10),

and (c) (11�20) surfaces with information derived as summarized in

Table 1. The 1s core level of 106.416 � 0.004 eV and the B component

at 111.11 eV should be identical for all the surfaces of the same

material.

Fig. 3 Comparison of the BOLS prediction with the derived CN

(layer)- and orientation-resolved values for (a) bond strain and the

relative change of atomic cohesive energy (Ec), (b) potential trap depth

and, (c) the relative energy density.

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density and the atomic cohesive energy are given in Fig. 3 and

Table 1. The derived bond contraction is consistent with recent

findings35 using a combination of molecular dynamics

calculations, Pauling’s correlation, and coherent electron

diffraction, which revealed that individual Au nanocrystals

of 3.5 nm in diameter demonstrate inhomogeneous relaxations

occurring at the outermost two atomic layers. The under-

coordination-induced bond contraction involves large out-

of-plane bond length contractions for the edge atoms

(B0.02 nm, 7%), a significant contraction (B0.013 nm,

4.5%) for {100} surface atoms, and a much smaller contraction

(B0.005 nm, 2%) for atoms in the middle of the {111} facets.

In the current system the maximal contraction is around 19%,

a value between the theory prediction22,23 for Be(10�10) and the

measurement for Au.35

Results show that the positive core-level shift assignment is

more proper than the assignment of negative or mixed shift

and hence the criteria established herewith are essentially true.

The positive shift assignment allows us to derive the energy

level of an isolated atom and its bulk shift. The derived

fundamental factors are of great importance in determining

the surface properties and surface processes.

Furthermore, the experimentally observed incident beam

energy and emission angle trends6,8,9,11 provide evidence for

the assignment of surface positive CLS, as the higher incident

beam energies or smaller emission angles collect more

information from the bulk than from the surface.12,36 Speranza

and Minati36 reported that increasing the angle between the

surface normal of graphite and the emission beam from 0 to

851, decreases the penetration depth from 8.7 to 0.7 nm.

The surface-induced positive BE shift is consistent with a

model of the surface interlayer relaxation mechanism.32,33 For

Nb(001)-3d3/2 example, the first layer spacing contracts by

12% associated with a 0.50 eV core-level shift.32 A (10 � 3)%

contraction of the first layer spacing has caused the

Ta(001)-4f5/2(7/2) level to shift by 0.75 eV.33 The assignment

of a positive core-band shift has been elegantly favoured by

XPS measurements6,32,33,37–43 revealing that the intensity of

the low-energy bulk component often increases with the

incident beam energy or with decreasing the angle between

the incident beam and the surface normal in the measurement.

Most strikingly, a recent X-ray absorption diffraction spectro-

scopic study34 revealed that the Ni 2p levels of the outermost

three atomic layers shift positively to higher binding energies

discretely, with the outermost atomic layer shifting the most.

Dominated by the under-coordinated atoms, the core-level

features (both the main peak and the chemical satellites) of

nanostructures move simultaneously towards lower binding

energies and the size of the shifts depends on both the original

core-level position of the components and the shape and size

of the particle.

V. Conclusion

We have systematically analyzed the Be 1s energy shift of

Be(0001), (10�10), and (11�20) surfaces from the perspective of

bond–potential–band correlation and elucidated information

regarding: (i) the binding energy of an isolated Be atom, (ii)

the bulk shift of Be 1s, (iii) the effective atomic CNs and the

corresponding local strains, and, (iv) prediction of the trends

of coordination resolved binding energy density and cohesive

energy per discrete atom in the surface of skin depth. The

developed approach enhances the power of the conventional

XPS technique for more quantitative information regarding

surface processes and properties. The concepts of local strain

and quantum entrapment may be essential for understanding

the bonding and electronic behavior in the surface and atomic

defect sites.

Acknowledgements

Financial support from Nanyang Technological University

and Agency for Science, Technology and Research, Singapore,

Nature Science Foundation (No. 10772157) of China,

Shanghai Natural Science Foundation (No. 07ZR14033),

Shanghai Pujiang Program (No. 08PJ14043), Special Project

for Nanotechnology of Shanghai (No. 0752nm011), and

Applied Materials Shanghai Research & Development Fund

(No. 07SA12) are all gratefully acknowledged.

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