Density functional study of the stability of various -Bi2O3 surfacesYan-Hua Lei and Zhao-Xu Chen

Citation: The Journal of Chemical Physics 138, 054703 (2013); doi: 10.1063/1.4788667 View online: http://dx.doi.org/10.1063/1.4788667 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Photo-driven oxidation of water on -Fe2O3 surfaces: An ab initio study J. Chem. Phys. 140, 064703 (2014); 10.1063/1.4865103 Density functional theory study of rutile VO2 surfaces J. Chem. Phys. 137, 154706 (2012); 10.1063/1.4758319 Intrinsic defect in BiNbO4: A density functional theory study J. Appl. Phys. 112, 043706 (2012); 10.1063/1.4747919 Surface effect on electronic and optical properties of Bi2Ti2O7 nanowires for visible light photocatalysis J. Appl. Phys. 111, 124306 (2012); 10.1063/1.4729553 The crystalline surfaces of -PdH{111}: Ideal surface terminations of a stoichiometric bulk compound relevant toheterogeneous catalysis J. Chem. Phys. 118, 5623 (2003); 10.1063/1.1528911

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

THE JOURNAL OF CHEMICAL PHYSICS 138, 054703 (2013)

Density functional study of the stability of various α-Bi2O3 surfacesYan-Hua Lei and Zhao-Xu Chena)

Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistryof MOE, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093,People’s Republic of China

(Received 5 August 2012; accepted 7 January 2013; published online 1 February 2013)

Bi2O3 is an important metal oxide in catalysis. In this paper we employed density functional theoryand slab model to investigate the surface energies and structures of various α-Bi2O3 surfaces. We firststudied ten different terminations along [100] direction which has both polar and nonpolar termina-tions due to alternating stacking of Bi layers and O layers. Our calculated surface free energies showthat the stoichiometric symmetric terminations are most stable at both high and low oxygen pres-sures, followed by the T2O/T4O terminations at low/high oxygen pressures. In the low Miller indexplanes, the (010) plane is the most stable whereas the (110) plane is the least stable. Analyses revealthat relaxation may change the surface structures significantly and there is a nice linear relationshipbetween the surface density of broken short Bi–O bonds and the surface energy before relaxation.© 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4788667]

I. INTRODUCTION

Selective oxidation/ammoxidation of lower olefins toaldehydes/nitriles is of commercial importance, representing25% of the chemicals used in the production of industrial andconsumer products.1 Bismuth oxide Bi2O3 is one of the mostimportant components of the catalyst for these processes.Bi2O3 can also be used as nanocatalyst,2 superconductor,3

gas sensors, and pumps.4 Bismuth oxide has four main crys-tal phases: monoclinic α-Bi2O3, tetragonal β-Bi2O3, cubic(BCC) γ -Bi2O3, and cubic (FCC) δ-Bi2O3. The α phase ismost stable at relatively low temperatures, and δ phase is sta-ble when the temperature is above 1000 K. The β and γ

phases are high temperature metastable phases.5 The selectiveoxidation catalysis reactions always take place at the temper-ature less than 750 K, which means that the α-Bi2O3 phaseplays crucial roles for the reaction.

Despite its importance, theoretical and experimentalcharacterizations of α-Bi2O3 surfaces are lacking. The feweravailable theoretical papers focused on the properties ofα-Bi2O3 bulk. The geometric and electronic structure ofpure and Zn-doped α-Bi2O3 was calculated by GGA PW-91method.6 The formation energy for a Zn impurity was 1.34eV, resulting in a maximum Zn concentration of 7.1 × 10−6%at 1000 K. The nature of bonding and the stereochemically ac-tive Bi electron lone pair in α-Bi2O3 were examined by gener-alized gradient approximation-Perdew, Burke, and Ernzerhof(GGA-PBE) method.7 The authors found that the majority ofthe Bi 6s states were present at low energy. Mixing of O 2pwith Bi 6s states was found to be significant in producing theasymmetric electron density on Bi.

Heterogeneous catalysis reactions always take place oncatalyst surfaces. Surface properties and stability are criticalto rationalizing and investigating reaction mechanisms. As far

a)Author to whom correspondence should be addressed. Electronic mail:zxchen@nju.edu.cn. Tel.: +86-25-83593353. Fax: +82-25-83686553.

as we know, there is little information about the relative sta-bility, geometries, and electronic structures of Bi2O3 surfaces,which hinders the understanding of the properties and reactiv-ity of Bi2O3. Regarding the relative stability of surfaces, atten-tion is often paid to two aspects: which plane is most stableand which termination is dominant for a specific plane. Sincesurfaces of metal oxides are usually much more complicatedthan metal surfaces, more efforts have been devoted to theformer. For example, α-Fe2O3 (0001)8 and α-Al2O3 (0001)9

were selected to investigate the environment effect on surfacestability and properties of metal oxides. Unlike mono-metallicsurfaces, metal oxide surfaces are often polar. On the basis ofa simple point charge model, Tasker categorized metal oxidesurfaces into three groups: two groups of nonpolar surfacesand one group of polar surface which has a dipole momentperpendicular to the surface.10 According to Tasker, the po-lar surface is electrostatically unstable. On the other hand, thepolar surface (usually nonstoichiometric) is often exposed fa-vorably in a practical environment.11 In this paper we explorethe stabilities of various surfaces and examine the effect ofenvironmental oxygen pressure on the surface stability. Theresults may not only help select the relevant surface modelsfor future mechanistic density functional theory (DFT) stud-ies, but also assist in experimental characterization of activecatalyst surfaces.

II. COMPUTATION METHOD

All the calculations were performed using the Viennaab initio simulation program.12 The generalized gradient ap-proximation PBE functional13 was applied to account forexchange-correlation effects. The electron-ion interaction isdescribed by the projector augmented wave method.14 TheKohn-Sham equations were solved using a plane-wave basisset with a cutoff energy of 500 eV. We employed the Gaus-sian smearing method to determine how partial occupancies

0021-9606/2013/138(5)/054703/7/$30.00 © 2013 American Institute of Physics138, 054703-1

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-2 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

FIG. 1. The bulk structure of α-Bi2O3. Purple: Bi atoms; red: O atoms.

are set for each wavefunction. Spin polarization and dipolecorrection were considered where necessary.

Monoclinic α-Bi2O3 belongs to the space group P21/c.15

There are four formula units (4Bi2O3) in the primitive bulkunit cell (Fig. 1). For bulk optimization, the sampling ofthe Brillouin zone was performed using a Monkhorst-Packscheme16 of (5 × 3 × 3). The optimized lattice parameterswith that grid are 5.92, 8.30, and 7.58 Å, and β = 112.9◦,which agree well with the experimental results: a = 5.8486,b = 8.1661, c = 7.5097, β = 113.0◦.15 Relativistic effect af-fects the lattice parameters negligibly, as shown by the opti-mized parameters a = 5.92, b = 8.31, c = 7.60, β = 112.9◦.We chose the termination T2Bi(I) (see Sec. III B for the mean-ing of T2Bi(I)) to test the convergence of slab thickness. Theenergies of the slab with different thicknesses characterizedby the repeat unit n (here n means one repeat unit containingfour Bi2O3 of ten layers) are listed in Table I, together withthe calculated bulk energies with formula (7) and surface en-ergies with formula (6). The bulk energies used to calculatesurface energies are the averaged value over the layer rangefrom 4 to 9. As can been seen from Table I, the differenceof surface free energies is less than 1.0 meV/Å2 when thick-ness n ≥ 4. This case is similar to κ-Al2O3, where there arealso ten layers and the convergence of slab thickness can alsobe achieved when n ≥ 4.17 We have also checked the influ-ence of slab thickness on surface energies using (110) plane.

TABLE I. The calculated surface energy γ of relaxed T2Bi(I) termination of(100) plane as a function of the repeat units n in the slab. Ebulk

Bi2O3 is the energyof bulk; γ is obtained from Eq. (6).

n Eslab (eV) EbulkBi2O3 (eV)a γ (meV/Å2)

1 − 114.082 − 229.63 − 115.55 25.683 − 345.88 − 116.25 25.844 − 462.33 − 116.45 26.335 − 578.68 − 116.35 26.666 − 694.99 − 116.31 27.317 − 811.46 − 116.47 26.668 − 927.77 − 116.31 27.319 − 1044.22 − 116.45 26.82Averageb − 116.39

aObtained using Eq. (7).bCalculated using the values from n = 4 to 9.

TABLE II. The area (Å2), surface energies γ (meV/Å2), the surface densityof total broken Bi–O bonds (SDBBt, in bonds nm−2), and the surface densityof broken short Bi–O bonds (SDBBs) of different stoichiometric low Millerindex planes. γ rel and γ unrel refer to the surface energy with and withoutsurface relaxation. For the planes having more than one termination, only theone that has the lowest energy after relaxation is reported.

Plane 010 111 011 100 001 101 110

Area 40.43 109.76 62.58 61.33 47.76 91.27 73.45SDBBt 9.89 12.76 9.59 13.04 16.75 10.96 13.61SDBBs 0.0 5.47 0.0 6.52 4.19 6.58 10.89γ rel 16 23 24 26 34 35 50γ unrel 20 67 36 72 55 72 89

From n = 5 to 7, the calculated surface energies are 49.69,49.28, 49.97 meV/Å2, respectively. Thus, for all the planes inTable II, the surface energies are computed using n = 5.

The stability of surfaces is characterized by surface Gibbsfree energy per unit area γ (T, P).11 The γ (T, P) of a bismuthoxide slab with two equivalent surfaces at temperature T andpartial pressure P is calculated by

γ (T , P ) = 1

2A[Gslab − NBiμBi(T , P ) − NOμO(T , P )]. (1)

Here, Gslab is the total Gibbs free energy of the slab, A is thearea of the surface unit cell of the slab, μBi and μO are thechemical potentials of a Bi atom in bulk and an O atom ingas phase respectively. From the fundamental thermodynamicrelation one can get

γ (T , P ) = 1

2A[Eslab + PV − T S − NBiμBi(T , P )

−NOμO(T , P )]. (2)

Assuming the surfaces are connected with bulk Bi2O3,then there is an equilibrium relation between μBi and μO

and the Gibbs free energy of per bulk Bi2O3 formula unitgbulk

Bi2O3(T , P ):

2μBi(T , P ) + 3μO(T , P ) = gbulkBi2O3(T , P ). (3)

Inserting Eq. (3) into Eq. (2) and neglecting the entropiccontribution and PV term leads to (for typical pressure, lessthan 100 atm, and temperature, less than 1000 K, contribu-tions of these two terms to surface free energy are estimatedto be less than 10 meV/Å2. Thus, we did not consider theircontributions, and gbulk

Bi2O3(T , P ) is reduced to ebulkBi2O3 which is

the energy of Bi2O3 per formula unit in bulk structure calcu-lated with DFT):

γ (T , P ) = 1

2A

[Eslab − NBi

2ebulk

Bi2O3

+(

3NBi

2− NO

)μO(T , P )

]. (4)

The chemical potential of an O atom μO can be expressed asthe function of temperature T and partial pressure of O2 P:

μO(T , P ) = μO(T , P ◦) + 1

2kT ln

(P

P ◦

). (5)

Here, P◦ is the standard pressure 1 atm.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-3 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

For the calculated unit cells in which the composition ofBi and O is stoichiometric, the surface free energy does notvary with μO, Eq. (4) can be further reduced to Eq. (6),

γ = 1

2A

(Eslab(n) − nEbulk

Bi2O3

), (6)

where n is the number of repeat bulk units and EbulkBi2O3 is the

energy of four Bi2O3 formula units in bulk (it is four times ofthe value of ebulk

Bi2O3). EbulkBi2O3 is estimated from18

EbulkBi2O3 = Eslab(n) − Eslab(n − 1). (7)

III. RESULTS AND DISCUSSION

A. Bulk Bi2O3

The monoclinic α-Bi2O3 has two types of Bi atoms: Bi(I)and Bi(II), and three kinds of O atoms: O(I), O(II), and O(III),in the primitive bulk (Fig. 1). Each Bi(I) atom has six neigh-boring O atoms, with the experimental bond lengths of 2.224and 2.531 Å to two O(I) atoms, 2.136 and 2.477 Å to twoO(II) atoms, and 2.290 and 2.796 Å to two O(III) atoms.Each Bi(II) atom has five neighboring O atoms, with the bondlengths of 2.209 and 2.636 Å for two Bi(II)–O(I) bonds, 2.174Å for Bi(II)–O(II) distance, and 2.075 and 2.548 Å for twoBi(II)–O(III) bonds. In this paper we classify the Bi–O bondsshorter than 2.41 Å to be short bonds and those longer thanthis value as long bonds. (The effective radius of the O2−

anion which has coordination number 3–4 is 1.36–1.38 Å.The effective ionic radius of Bi3+ cation which has coordi-nation number 5–6 is 0.96–1.03 Å. The sum of these twoionic radii is 2.32–2.41 Å.19) Based on this criterion, bothBi(I) and Bi(II) atoms have three short Bi–O bonds. The cal-culated Bader charges on Bi(I) and Bi(II) atoms are +1.80 |e|and +1.74 |e| respectively. Three types of O atoms have nearlythe same charges: −1.18 |e| for O(I), −1.19 |e| for O(II), and−1.16 |e| for O(III). The similar charges on different typesof oxygen atoms imply that they have essentially the samechemical valence.

The calculated indirect band gap is 2.45 eV, and the en-ergy gap at � point is 2.68 eV (Fig. 2(a)). When relativis-tic effects are considered, the indirect band gap decreases to2.34 eV and the direct band gap to 2.56 eV. These results com-pare well with the calculated indirect band gap of 2.6 eV usingPW91 method6 and the experimental value 2.5 eV.20 The ear-lier calculation results of 1.68 eV with the Hückel method21

or 6.2 eV with the semi-empirical method complete neglectof differential overlap22 are obviously unreliable. The calcu-lated density of states (Fig. 2(b)) clearly shows that the bot-tom of conduction band ranging from 2.4 to 6.8 eV is mainlycomposed of Bi 6p atomic orbitals (AOs), together with somecontribution from O 2p AOs. The main contribution to thevalence band (−5.0 to 0.0 eV, centered at −2.2 eV) comesfrom the 2p AOs of three types of oxygen atoms, coupled withsome Bi 6p AOs and 5d AOs. Bi 6s AO is mainly populatedfrom −10.0 to −7.6 eV (centered at −9.1 eV) and O 2s AOis located in the range of −18.2 to −16.1 eV (not shown inFig. 2(b)). Experimentally, two wide peaks between −16 and0.0 eV in the x-ray photoelectron spectroscopy experiments

FIG. 2. Band structure (a) and density of states (b) of bulk Bi2O3.

were recorded.20 This first peak centered at −10.5 eV andthe second one at −3.5 eV. According to our calculations, theformer should derive from the bismuth 6s AO while the lat-ter should be originated from the oxygen 2p AOs with somecontribution from the bismuth 6p AOs.

B. Terminations of (100) plane

In bulk Bi2O3, Bi layers and O layers are stacked alter-natively along the [100] direction. Both polar and nonpolarterminations can be got along this direction. Therefore, the(100) plane was selected to study the environmental effect onthe surface stability. Starting from Bi(I), the stacked layersfollow the following periodic sequence (Fig. 1), based on theheight along [100]:

2Bi(I) − 2O(I) − 2O(II) − 2O(III) − 2Bi(II) − 2Bi(II)

− 2O(III) − 2O(II) − 2O(I) − 2Bi(I).

The number 2 in front of each element indicates thenumber of atoms in the corresponding layer in our simulatedcell. According to the above periodic sequence, ten symmet-ric terminations (by “symmetric termination” we mean thatthe top and bottom surface structures and compositions ofthe calculated slab unit cell are identical) can be obtainedalong the [100] direction at different cleavage position. Theseten terminations are: T4Bi(I), T4Bi(II), T2Bi(I), T2Bi(II), T2O(III),T2O(I), T4O(II-III), T4O(II-I), T6O(I-II-III), and T6O(III-II-I). The

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-4 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

FIG. 3. Ten symmetric terminations of Bi2O3(100) surface. The structure ofthe top layer is identical to that of the bottom for each termination. Only onerepeat unit is shown for each termination and the rest four repeat units areomitted for simplicity and clarity.

notation TnE(i) denotes that there are n atoms of type E(i) oneach side of the slab. For example, T4Bi(I) indicates that the topand bottom layers of this termination have four Bi(I) atoms(Fig. 3). Among the ten terminations, only T2Bi(I) and T2Bi(II)

are stoichiometric, i.e., the atomic ratio of Bi to O in the cal-culated unit cell is 2:3, in accord with the formula Bi2O3.These two terminations are also nonpolar. The other eight ter-minations are nonstoichiometric and polar. Because of differ-ent atomic ratios of Bi to O in the unit cell, the surface freeenergies of different terminations behave differently towardsenvironmental condition (oxygen pressure).

The surface free energies of the ten terminations at dif-ferent O chemical potentials are shown in Fig. 4. The range ofμO, marked in Fig. 4 with the vertical dotted lines, is limitedby the conditions that the chemical potential of Bi has to besmaller than that of the bulk Bi atom, and that of oxygen hasto be smaller than half of that of an oxygen molecule in thegas phase. Otherwise, Bi or oxygen condensate will form atthe surface. Equation (5) is used to convert μO into pressuredependence at the fixed temperature 600 K (Fig. 4).

FIG. 4. The surface energies of ten terminations of (100) plane. The dottedvertical lines indicate the allowed range of the oxygen chemical potential.

It is revealed from Fig. 4 that the ten surface free energylines can be divided into three groups, based on the variationwith respect to the environmental oxygen chemical potentialsμO: A type terminations including T4Bi(I), T4Bi(II), T2O(I), andT2O(III), whose surface free energies increase with the valueof μO; B type terminations containing T6O(III-II-I), T6O(I-II-III),T4O(II-I), and T4O(II-III) whose surface free energies decreasewith the oxygen chemical potentials; C type terminations hav-ing T2Bi(I) and T2Bi(II) whose surface free energies are indepen-dent of the oxygen chemical potentials, forming horizontallines (Fig. 4).

The four A type terminations are Bi-excess surfaces. Atpoor oxygen limit, their surface free energies are: 73 forT4Bi(I), 57 for T4Bi(II), 57 for T2O(I), and 32 meV/Å2 for T2O(III).From the poor oxygen region to the rich oxygen limit, theirsurface free energies increase by 102 meV/Å2 for the two Bi-most excess terminations T4Bi(I) and T4Bi(II), and 34 meV/Å2

for the Bi-less excess terminations T2O(I) and T2O(III). Theslopes of the surface free energy line for the two T4Bi termina-tions are identical because they have the same Bi to O atomicratio. Similar situation is found with the two T2O terminations.On the other hand, the slope of the surface free energy line ofT2O is smaller than that for the T4Bi, due to smaller Bi to Oatomic ratio of T2O terminations compared with that of T4Bi

ones.The four B type terminations are O-excess surfaces. Their

surface free energies decrease with the increase of oxygenchemical potentials. The lines for T6O(III-II-I) and T6O(I-II-III) aresteeper than those for T4O(II-I) and T4O(II-III), due to the Bi toO atomic ratio in the former being smaller than the one in thelatter. The surface free energies of T6O(III-II-I) and T6O(I-II-III)

terminations are 172 and 166 meV/Å2 at the O poor chemicalpotential point and they decrease by 102 meV/Å2 to 70 and63 meV/Å2 at the O rich chemical potential point. T4O(II-I) andT4O(II-III) terminations have lower surface free energies thanT6O(III-II-I) and T6O(I-II-III) terminations in all of the permittedO chemical potential range. For instance, the surface free en-ergies of T4O(II-I) termination decrease from 82 to 48 meV/Å2

from the oxygen poor limit to the rich oxygen limit. FromFig. 4 one can find that the absolute magnitude of the slopeof the free energy lines for T4Bi equals to that for the T6O.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-5 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

Similar situation is found between T2O and T4O terminations.This phenomenon is understandable because the atom ratio ofthe number of excess Bi atoms in T4Bi/T2O terminations to thenumber of excess oxygen atoms in T6O/T4O terminated sur-faces is stoichiometric (2:3). The C type terminations T2Bi(I)

and T2Bi(II) have the lowest free energies among all the ten ter-minations of (100) plane, with the corresponding values of 27and 26 meV/Å2, respectively. Because these two terminationsare stoichiometric, their surface free energies do not changewith the oxygen chemical potentials.

Now we discuss the stability of the ten terminations. Atconstant pressure and temperature, the smaller the surface freeenergy, the more stable the surface. According to this cri-terion, we can easily identify the stable termination. FromFig. 4 one can see that between the upper and lower limit ofoxygen chemical potentials, the surface free energy of T2Bi(II)

is smallest, next is T2Bi(I). Due to neglecting the entropic con-tribution and the finite basis set, the computation uncertaintyis estimated to be about ±10 meV/Å2. Therefore, the moststable terminations are T2Bi. In other words, Bi2O3 will ex-pose the T2Bi terminations most favorably. At the oxygen poorregion, the surface free energies of T2O(III) are close to thoseof T2Bi, with a difference less than 10 meV/Å2, indicating thatexposure of these terminations is also likely in this case. Onthe other hand, at the oxygen rich region, T4O(II-I) becomesmore stable than T2O(III). Since the surface free energies ofT2Bi are much smaller than those of T4O and T2O, T2Bi arethe most stable terminations in all the allowed range of oxy-gen chemical potentials. The most Bi-excess/most O-excessterminations are most unstable at O-rich/O-poor conditions,respectively. The largest (absolute) value of the slope for thesurface free energy lines shows that they are most sensitive tothe environmental oxygen pressure.

The above analyses show that in the permitted range of Ochemical potentials, the surface free energies of the eight po-lar terminations are larger than the two nonpolar terminations.The most polar terminations T6O or T4Bi are the least stable,while the nonpolar terminations T2Bi are the most stable. Thisconclusion is qualitatively consistent with Tasker’s rule basedon simple ionic model that surfaces with a dipole moment inthe repeat unit perpendicular to the surface are less stable.10 Itis worth to mention that this rule is too coarse.11

C. Other low Miller index planes

The surface free energies of other low Miller index planeswere also computed for comparison. According to the findingfrom the above calculations on the (100) plane, we selectedthe stoichiometric (that is, the Bi to O atomic ratio in the cal-culated unit cell is 2:3) and symmetric terminations of theseplanes. If two or more terminations meet the above criteria,only the termination that has the lowest energy (after relax-ation) is reported. The fractional cleavage sites are 0.20 for(010) plane, 0.50 for both (100) and (001) planes, and 0.0 forthe rest planes (Fig. 5).

Table II displays the calculated surface free energies forthe seven planes. The most stable plane under study is the(010) with the calculated surface energy 16 (after relaxation)

FIG. 5. Side view of six low Miller surfaces of Bi2O3.

and 20 (before relaxation) meV/Å2. The weak relaxation ef-fect can be rationalized by the surface structure. This termi-nation is created by breaking four long Bi–O bonds formedby two Bi (one is Bi(I) and the other is Bi(II)) and two Oatoms (by “long Bi–O bonds” we mean those that are longerthan 2.41 Å while those less than this value are short bonds.See Sec. III A). Therefore, each atom has one bond brokendue to this cleavage. The number of broken bonds is the leastamong all the planes listed in Table II, and the surface den-sity of total broken Bi–O bonds (SDBBt) is the second lowest(9.89 bonds nm−2).

The second most stable plane is the (111) plane, whichhas the calculated surface free energies 23 (after relaxation)and 67 (before relaxation) meV/Å2. The free energy after re-laxation is only about 1/3 of the free energy before relaxation,which reflects strong relaxations. This notable strong relax-ations make (111) plane change from the fourth stable planebefore relaxation to the second one after relaxation. FourteenBi–O bonds are cut to create this plane. The number of bro-ken Bi–O bonds is the largest in all planes studied. Since thisplane also has the largest surface area, the SDBBt is interme-diate (12.76 bonds nm−2).

Similar to the (010) plane, no short Bi–O bond is cut toform the (011) plane. Therefore, it also has much low surfacefree energy, especially before relaxation. The surface free en-ergy before relaxation is 36 meV/Å2, which is only higherthan that of the (010) plane. But the relaxation effect is weakfor this plane and only 12 meV/Å2 is stabilized due to the re-laxation. Six long Bi–O bonds are broken to create this plane:four Bi(I)–O bonds and two Bi(II)–O bonds. The value ofSDBBt is the lowest (9.59 bonds nm−2).

Formation of the (100) termination needs to break fourshort and four long Bi–O bonds (the SDBBt is 13.04 bondsnm−2). The surface free energy before relaxation is inter-mediate, with the value 72 meV/Å2. Relaxation effect forthis plane is also notable and the surface free energy after

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-6 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

FIG. 6. The surface energies before relaxation γ unrel (meV/Å2) vs the sur-face density of broken short Bi–O bonds SDBBs (bonds nm−2).

relaxation is 26 meV/Å2. As stated above, this plane has typ-ical alternate stacking metal layers and oxygen layers, we se-lect it as an example to examine the relaxation effect in detailin the following.

Something interesting can be found when the (001) planeis formed. The surface density of broken total Bi–O bondsSDBBt is the highest (16.75 bonds nm−2). However, both therelaxation induced surface energy decrease and the surfaceenergy before relaxation are smallest among the five planeshaving broken short Bi–O bonds (it means that the (010) and(011) planes are excluded, since they have no short Bi–Obonds cut). To rationalize this phenomenon, we examined therelation between the surface energies and the surface densityof broken Bi–O bonds. It is found that the surface energiesbefore relaxation and surface density of broken short Bi–Obonds (SDBBs) correlate linearly for all the surfaces stud-ied (Fig. 6) whereas there is no such relationship betweenthe value of SDBBt and the surface energies. This means,the denser the surface density of broken short Bi–O bonds,the larger the surface energy before relaxation. This smallersurface energy before relaxation and smaller relaxation in-duced surface energy decrease of the (001) surface is due to itssmaller SDBBs of 4.19 bonds nm−2 (Table II) because amongeight broken bond only quarter of them are short Bi–O bonds.

This relationship is further illustrated with the last twoplanes, the (101) and (110) planes. The (101) plane has aSDBBs value 6.58 bonds nm−2 which is much closer to thevalue of the (100) plane, it has a free energy before relax-ation much closer to the (100) plane surface with the value 72meV/Å2. Meanwhile, the (110) plane has the largest SDBBs

10.89 bonds nm−2. So its surface energies are the largestwith the value 89 (before relaxation) and 50 (after relaxation)meV/Å2, respectively. The above finding indicates that thestability of the surface is controlled by the surface density ofbroken short Bi–O bonds and the long Bi–O bonds do not playimportant role in this aspect.

As relaxation stabilizes the surface significantly, here wetake the termination T2Bi(II) of the (100) plane to make a de-tailed analysis. Before relaxation, the layer sequence is asfollows:

2Bi(II) − 2O(III) − 2O(II) − 2O(I) − 2Bi(I) − 2Bi(I)

− 2O(I) − 2O(II) − 2O(III) − 2Bi(II).

TABLE III. Interlayer relaxation data for the T2Bi(II) termination of Bi2O3

(100).

Interlayer distance (Å)

Interlayer Unrelaxed Relaxed Change Relaxation (%)

Bi(II)-O(III) 1.10 1.00 − 0.10 − 9.1O(III)-O(II)a 0.16 0.00 − 0.16 − 100.0O(II)-O(I) 0.12 0.04 − 0.08 − 66.7O(I)-Bi(I) 0.96 1.04 +0.08 +8.3Bi(I)-Bi(I) 0.44 0.49 +0.05 +11.4Bi(I)-O(I) 0.96 0.91 − 0.05 − 5.2O(I)-O(II) 0.12 0.18 +0.06 +50.0O(II)-O(III) 0.16 0.12 − 0.04 − 25.0O(III)-Bi(II) 1.10 1.17 +0.07 +6.4Bi(II)-Bi(II) 0.26 0.23 − 0.03 − 11.5

aThe sequence for the initial three O layers has changed from O(III)-O(II)-O(I) beforerelaxation to O(II)-O(I)-O(III) after relaxation.

The interlayer distances of two adjacent layers can becategorized into three types: those between two O layersd2O(III)-2O(II) and d2O(II)-2O(I); those between two Bi layersd2Bi(I)-2Bi(I) and d2Bi(II)-2Bi(II) (the latter exists because in ourmodel there are 5 repeating sequences as illustrated above);those between one Bi layer and one O layer d2Bi(II)-2O(III)

and d2Bi(I)-2O(I). The interlayer distance between the Bi layerand O layer (d2Bi(II)-2O(III) and d2Bi(I)-2O(I)) before relaxationis the largest in the three types of interlayers. For exam-ple, the interlayer distance between Bi(II) and the adjacentO(III) layer, d2Bi(II)-2O(III), is 1.10 Å and the interlayer distancebetween Bi(I) and the adjacent O(I), d2Bi(I)-2O(I), is 0.96 Å(Table III). The interlayer distances of two O layersd2O(III)-2O(II) and d2O(II)-2O(I) are the least, with the value 0.16and 0.12 Å, respectively. The interlayer distance between thetwo Bi(I) layers (d2Bi(I)-2Bi(I)) is 0.44 Å and that between thetwo Bi(II) layers (d2Bi(II)-2Bi(II)) is 0.26 Å.

In the unrelaxed slab, each Bi(II) atom in the first layerhas three neighboring O atoms. Compared with the bulk Bi(II)atom, two Bi(II)–O bonds are broken due to the surface for-mation. After relaxation the interlayer distances between thetop three O layers are shortened so that the three oxygenlayers become essentially one layer. For example, the calcu-lated d2O(III)-2O(II) is negligible and dO(II)-O(I) is 0.04 Å. Thesechanges of the O layers make each Bi atom possess fourneighboring O atoms, compared to three O atoms before re-laxation. The topmost Bi(II) layer contracts inward by 0.10 Å.The interlayer distance variations of three other Bi and O lay-ers (d2Bi-2O) are among the ranges from 0.05 to 0.08 Å. Thedistance between the two Bi(I) layers (d2Bi(I)-2Bi(I)) increasesby 0.05 Å and the two Bi(II) layers (d2Bi(II)-2Bi(II)) decreases0.03 Å.

Finally, we would like to make a comparison of Bi2O3

with other metal oxides. We find that the surface energiesof the seven low Miller planes are notably small, comparedwith other metal oxides. For example, the surface energy ofthe most stable stoichiometric termination of α-Al2O3 (0001)is about 247 meV/Å2,18 that of α-Fe2O3 (0001) is about95 meV/Å2,8 and that of RuO2 (110) is 80 meV/Å2.11 Thesmaller surface energies (and small surface energy difference)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41

054703-7 Y.-H. Lei and Z.-X. Chen J. Chem. Phys. 138, 054703 (2013)

may be ascribed to the weak bond energy of Bi–O bond,which has a value of 1.06 eV,23 while other metal-oxygenbonds, such as Al–O bond, are much stronger with a bondenergy in the range of 3.42–4.37 eV.24 The small surface en-ergies, in particular, the quite small surface energy differenceof α-Bi2O3 imply that many planes may coexist in commonexperimental conditions, which will make rationalization ofreaction mechanisms on Bi2O3 much difficult. To get one spe-cial plane of α-Bi2O3 single crystal, the experimental condi-tions should be more carefully controlled. On the other hand,the small and close surface free energies of these terminationsalso make this oxide function multifaceted.

IV. CONCLUSIONS

We have employed density functional theory and slabmodels to study the surface stability of various surfaces ofBi2O3 and examined the influence of environmental oxygenpressure on the stability of ten terminations for Bi2O3 (100)plane. The calculations show that in all the permitted chemi-cal potentials the stoichiometric symmetric T2Bi terminationsare most stable, and the nonstoichiometric T2O/T4O termina-tion may also expose at low/high oxygen pressures. In the lowMiller index planes, the (010) plane is found to be the moststable, while (110) plane is the least stable one. We demon-strate that relaxation can lead to great variation of surfacestructures, and the surface energies before relaxation correlatelinearly with the surface density of broken short Bi–O bonds.

ACKNOWLEDGMENTS

The authors acknowledge the financial support from theNatural Science Foundation of China No. 20973090 and theNational Key Basic Research Development Program of China

(973 Program) 2011CB808604 and 2003CB615804. All cal-culations were done in the high performance computing cen-ter of Nanjing University.

1S. Pudar, J. Oxgaard, and W. A. Goddard, J. Phys. Chem. C 114, 15678(2010).

2A. Hameed, T. Montini, V. Gombac, and P. Fornasiero, J. Am. Chem. Soc.130, 9658 (2008).

3R. J. Cava, B. Batlogg, J. J. Krajewski, R. C. Farrow, L. W. Rupp, Jr., A. E.White, K. T. Short, W. F. Peck, Jr., and Y. Kometani, Nature (London) 332,814 (1988).

4J. A. Switzer, M. G. Shumsky, and E. W. Bohannan, Science 284, 293(1999).

5T. P. Gujar, V. R. Shinde, C. D. Lokhande, R. S. Mane, and S. H. Han,Appl. Surf. Sci. 250, 161 (2005).

6M. C. Johan, H. Bo, S. D. Helder, and D. B. Paul, Phys. Rev. B 65, 205122(2002).

7A. Walsh, G. W. Watson, D. J. Payne, R. G. Edgell, J. H. Guo, P. A. Glans,T. Learmonth, and K. E. Smith, Phys. Rev. B 73, 235104 (2006).

8X. G. Wang, W. Weiss, S. K. Shaikhutdinov, M. Ritter, M. Petersen, F.Wagner, R. Schlögl, and M. Scheffler, Phys. Rev. Lett. 81, 1038 (1998).

9R. D. Felice and J. E. Northrup, Phys. Rev. B 60, R16287 (1999).10P. W. Tasker, J. Phys. C 12, 4977 (1979).11K. Reuter and M. Scheffler, Phys. Rev. B 65, 035406 (2001).12G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).13J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).14P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).15G. Malmros, Acta Chem. Scand. 24, 384 (1970).16H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).17C. Ruberto, Y. Yourdshahyan, and B. I. Lundqvist, Phys. Rev. Lett. 88,

226101 (2002).18C. Ruberto, Y. Yourdshahyan, and B. I. Lundqvist, Phys. Rev. B 67, 195412

(2003).19R. D. Shannon, Acta Crystallogr., Sect. A 32, 751 (1976).20T. P. Debies and J. W. Rabalais, Chem. Phys. 20, 277 (1977).21V. P. Zhukov, V. M. Zhukovskii, V. M. Zainullina, and N. I. Medvedeva, J.

Struct. Chem. 40, 831 (1999).22R. A. Evarestov, V. O. Shapovalov, and V. A. Veryazov, Phys. Status Solidi

B 183, K15 (1994).23V. Dimitrov and T. Komatsu, J. Non-Cryst. Solids 356, 258 (2010).24K. H. Sun, J. Am. Ceram. Soc. 30, 277 (1947).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.115.103.99 On: Sat, 04 Oct 2014 11:06:41