Surface Science Volume 295 issue 1-2 1993 [doi 10.1016%2F0039-6028%2893%2990202-u] S. Blonski; S.H....

7/23/2019 Surface Science Volume 295 issue 1-2 1993 [doi 10.1016%2F0039-6028%2893%2990202-u] S. Blonski; S.H. Garof

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Surface Science 295 (1993) 263-274

North-Holland

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surface science

Molecular dynamics simulations of a-alumina and y-alumina surfaces

S. Blonski 1 and S.H. Garofalini

Depart ment of Cerami cs and Int erfacial M olecular Science Laboratory , Insti tut e for Engineered M aterials, Rutgers U nioersit y,

P.O. Box 909, Piscataw ay, NJ 08855-0909, USA

Received 18 January 1993; accepted for publication 15 June 1993

Molecular dynamics simulations of crystalline aluminum oxide were performed for cu-Al,O, and y-Al,O, phases. Both bulk

crystals and surfaces of each phase were studied. For each of the surfaces, several possible atomic terminations were examined and

surface energies, density profiles, and atom configurations have been calculated. It was found that due to processes of surface

relaxation and reconstruction some terminations of the a-alumina surfaces become more likely to appear. For y-alumina, the

occurrence of cation vacancies in the crystal structure has a significant influence on surface morphology. On the surfaces,

additional active sites were observed which are not predicted by idealized models which omit vacancies.

1. Introduction

Aluminum oxides have a great number of tech-

nological applications. While a-alumina is mainly

seen as a structural, optical and electronic mate-

rial, y-alumina is usually used as a catalytic sup-

port. Because surface properties of the crystals

affect the successful application of these alumi-

nas, the surfaces have been an object of a number

of theoretical and experimental studies. For (Y-

alumina, only one possibility of surface termina-

tion has been considered for each surface studied

by theoretical modeling. However, experimental

studies show that there exist different terminating

layers on a-alumina surfaces [1,2]. Thus, to fill

this lack of knowledge, molecular dynamics simu-

lations of a-alumina surfaces with different ter-

minating layers of atoms were performed. Con-

versely, for y-alumina, the concept of different

terminations has been known and examined pre-

viously. However, theoretical models of y-alumina

surfaces are usually based on an idealized struc-

ture of the crystal, with an excess of aluminum

atoms [3]. In this study, an extended approach for

On leave from the Department of Applied Physics, Techni-

cal University of Gdansk, Poland.

y-alumina crystals was used to find more realistic

structures of the surfaces. Due to the nature of

the y-alumina crystals, experimental observations

of their surfaces have not yet been done. There-

fore, simulations can show for the first time how

the surfaces look and should allow for a better

understanding of the properties of y-alumina.

Both (Y- and y-aluminas were studied using the

same model to allow for comparison between

properties and behavior of both materials.

2. Computational procedure

Constant-volume simulations were performed

with a fifth-order Nordsieck-Gear algorithm used

to integrate Newtons equations of motion with a

time step of the integration of 0.2 fs. The total

potential energy of the system is composed of

contributions from two- and three-body interac-

tions. The two-body part is a modified Born-

Mayer-Huggins form, given as

Qij =Aij exp( -rij/pij)

+ ( 4i4je2/rij) erfc ij/Pij) >

0039-6028/93/ 06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved


2/12

264

S. Blonski, S.H. Garof ali ni / M olecular dynamics simul ati ons of a- and y-al umina surfaces

where qi and q, are the ionic charges, rij is the

separation distance between ions i and j, e is the

elementary charge, and erfc is the complemen-

tary error function 0[4]. The softness parameter,

pCj, is equal to 0.29 A for all pairs of the ions. The

values for the adjustable parameters, Aij and pIj,

are as follows:

A o_o = 0.0725 fJ,

po_o = 2.34 A,

A ,_,,=0.2490J, /3O_A, = 2.34 A,

A *,_*, 0.0500J,

P/,_A, = 2.35 A.

Similar values of the parameters were used in the

studies of sodium aluminosilicate glasses [5,61,

but for the reason of obtaining a rational value of

the pressure in the simulated bulk crystals, the

parameters were modified for the current studies.

The main difference is for the A,,_,,arameter,

but even in this case the force between two ions

is changed by no more than 6% at the distances

occurring in the simulations. Nevertheless, the

adjustment of the parameters was necessary, be-

cause the previous values were developed for an

amorphous system in which Al formed only a

fraction of the total number of cations and all of

the Al ions were biased toward tetrahedral coor-

dinations so as to test ideas regarding glass prop-

erties [51.

function for the triplet with an oxygen ion at the

vertex has a minimum at about 109 which is

appropriate for the tetrahedral coordination, To

take into account two possible coordinations of

the Al atoms in the alumina crystals, the different

angular function is used for the triplets with an

aluminum ion at the vertex. That function has a

broad minimum for 0 in the range from 90 to

110 as well as another minimum for f3 = 180.

This allows Al atoms to be both tetrahedrally and

octahedrally coordinated. The adjustable paramc-

ters, h j r k , Yi , ,

and R,j,ave the following values:

A ,_o_/,, = 0.001 fJ,

A,~,,_, = 0.024 fJ,

yo_*, = 2.0 A,

y&-o = 2.8 A,

R

omA, = 2.6 A,

R,,_o = 3.0 A.

The same values of the three-body parameters

were used in the previous studies of glasses.

The three-body interactions imposed on all of

the Al-O-Al and O-Al-O triplets have the fol-

lowing functional form:

q j i l k = j i k exP[ Yi j / i , - Rr j )

+Y i k / t T i k -Rzk ) ]a j i k ,

if r i j < Rij and

r ik < Rik;

Pjik 0,

if

r r l 2

Rtj or

rik 2 R,k ;

with the angular part, fljik, given by

fijik = (cos O,ik + l/3)*,

for AI-O-Al;

finirk = [(co, ejik + l/3) sin 19,~~ os tijik]*,

for O-Al-O;

The simulations were run for 50000 time steps

each with the initial 5000 steps being used for

temperature equilibration. All the reported simu-

lations have been performed at 300 K. After the

bulk crystals were simulated, the desired surfaces

were exposed and surface simulations were per-

formed in the way described by Garofalini [4l. A

surface was created by removing periodic bound-

aries in one dimension, while keeping them in the

other two dimensions. Simultaneously, atoms in

the layers most apart from the surface were im-

mobilized, so that they retained their original

bulk-like configuration. Samples consisting of

2560 to 3600 atoms were simulated, respiting in

surface dimensions of appr?ximately 25 A X 25 A

and a height of about 50 A. To allow for move-

ment of as many atoms as possible, the thickness

of the layer of immobile atoms was chosen to only

slightly exceed the interaction cut-off distance

(5.5 A,.

The structures of the simulated crystals were

characterized in terms of radial distribution func-

tions (RDFs) of the atomic positions. The partial

radial distribution functions were calculated for

each pair of ion types from the formula [7 :

g i , t r ) =W j r ) /N o r ) 7

where ejik is an angle formed by the ions j, i, and

where N ,, r) denotes the number of ions of type j

k with the ion

i

placed at the vertex. The angular

in a shell between

r - Ar/2

and

r + Ar /2

around


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S. Blonski, S.H. Garofal ini / M olecular dynamics simul ati ons of a- and y-alumi na surfaces

265

an ion of type i. The average number of atoms,

N&r), in the same shell in an ideal gas at the

same number density p is

N,(r) = (%/3)[(

r + Ar/2)3 - (r - Ar/2)3].

The shells with the thickness Ar = 0.01 A were

used. The number density p was calculated by

dividing the total number of ions in the simulated

crystal by the volume of the simulation cell. The

total radial distribution functions were obtained

by summation of the partial RDFs over all pairs

of ion types.

Number density profiles in the direction per-

pendicular to a surface were calculated by count-

ing the

surface.

w each

cell.

number of ions in slabs parallel to that

The slabs have the thickness of about 0.1

depending on the size of the simulation

3. Structures of bulk crystals

The initial structure of a-alumina was defined

according to Wyckoff [8], with the lattice parame-

ters given by Newnham and de Haan [9]. Fig. 1

shows the radial distribution function obtained

from the simulation of bulk cy-Al,O, composed

of 3600 atoms, i.e. 120 crystallographic cells with

hexagonal symmetry. For comparison, the static

pair distribution for the structure given by Wyck-

5

4

3

C

xl

2

1

0

simulation

diffraction

2 4

r [Al

6 8

10

Fig. 1. Total radial distribution function for a-alumina: solid

line is from the simulations, dotted lines are from the X-ray

diffraction studies [8].

off is also shown. The excellent agreement be-

tween crystallographic data and simulation re-

sults indicates that the potentials used in the

simulations adequately describe the structure of

a-alumina, preserving the initial configuration of

atoms in the molecular dynamics simulations.

The structure of y-Al,O, is still a matter of

discussion; the common assumption being that

-y-alumina is a defective spinel. The defects have

to occur because the stoichiometry of Al,O, does

not fit the spine1 structure. If all of the cation

positions of the spine1 structure were filled by

aluminum atoms, there would be an excess of

aluminum atoms. Thus, some cation positions of

the spine1 structure have to be vacant in y-

alumina. Cation sites of two kinds appear in the

spine1 structure: octahedral and tetrahedral. The

question which remains is where the vacancies

are located. Most of the experimental data sug-

gest that vacancies occur mainly on tetrahedral

sites [lo], but just the opposite statements can

also be found in the literature [ll]. Nevertheless,

it was assumed in the simulations that all vacan-

cies are located on tetrahedral sites. Recently

published results of other molecular dynamics

studies of bulk y-alumina support such an as-

sumption [12]. Those simulations were started

from configurations which had the vacancies

placed randomly among all cation sites of the

spine1 structure. During the time-evolution of the

system, nearly all of the octahedral vacancies

were filled by aluminum atoms and the vacancies

survived almost exclusively on tetrahedral posi-

tions.

In the present simulations the initial structure

of the bulk crystal of y-Al,O, was defined as the

cubic spine1 described by Wyckoff [8]. Locations

of eight cation vacancies per every 3 crystal cells

were chosen randomly. Initially, simulations of

200 different configurations of vacancies were

performed. The configuration with the lowest en-

ergy was chosen for further studies. It was noted

that among all of the configurations, differences

in energy were no greater than 1.3 kJ/mol.

Moreover, ali the samples of y-alumina have

higher energies than the crystal of a-alumina.

The lower-energy y-alumina crystals are usually

characterized by a more uniform spatial distribu-


4/12

266

S. Blonski, S.H. Garof ali ni / M olecular dynamics simul ati ons of a- and y-alumi na surfaces

2,

I

o-o

1

~~~

I,:

: ,,

, ,:

~ I /

~\

\ \

0

Fig. 2. Partial radial distribution functions for y-alumina:

solid and dashed lines are from the simulations with lattice

constants 8.03 and 7.91 A, respectively; dotted lines are from

the X-ray diffraction studies [8].

tion of the vacancies, but the correlation between

the energy and the distribution is rather weak.

To obtain a reasonable value of the pressure in

the sample, a lattice constant of 8.03 A was used,

which is slightly greater than values usually re-

ported in the literature (7.91 A> [ll]. Fig. 2 shows

partial radial distribution functions (PDFs) for

the relaxed structures obtained from the simula-

tions of the crystals with both lattice constants.

Although the expansion is clearly visible, the

shapes of the PDFs are unchanged. The simu-

lated PDFs agree well with the PDFs calculated

for the static structure found by Verwey from

X-ray crystallography [ 131. The most significant

difference is an additional peak near 2.4 A in the

simulated oxygen-oxygen PDF. However, such a

peak occurs in the radial distribution function of

a-alumina (both experimentally and in the simu-

lation; see fig. 1). It originates from distorted

oxygen octahedra which are detectable in the

sharp diffraction spectra of a-alumina. Since the

spectra of y-alumina are more diffuse, the distor-

tion could have been omitted in the generation of

the crystallographic structure of y-alumina.

4. Surfaces of cu-alumina

Three surfaces of a-alumina were simulated:

(000 l),

11 001

and (1 120). These are the sur-

faces which frequently occur in natural and artifi-

cial corundum crystals and have been the subject

of several experimental studies [14-161. From

density profiles of the crystals with different ori-

entation, it was observed that each of the surfaces

can be formed by terminating at a different layer

of atoms. Such different atomic terminations of

surfaces could be formed during fracture of the

bulk crystal. In previous static calculations of

a-alumina surfaces, such a possibility was not

taken into account [17,18]. Therefore, all possible

terminating layers which could preserve a two-di-

mensional periodicity on the surfaces were simu-

lated. Surface energies obtained from our simula-

tions are presented in table 1, along with the

energies obtained from other theoretical studies

of a-alumina surfaces. Experimental values of

surface energy for a-alumina are known only for

Table 1

Calculated surface energies of cu-alumina

Surface Surface energy (J m-*)

This Ref.

Ref.

Ref.

work

[I71

[I81 [211

Unr ela xed surfaces

(0001) A

12.77

_ _ _

B 12.85

C

5.04 6.53 5.95

6.72

(1120) A 14.32

_ _ _

B 3.49 5.17 4.37

_

C

14.41

_ _ _

(iioo) A 5.56 6.87 6.46

5.65

Relaxed surf aces

(0001) A 8.04

_ _ _

B 2.19

_ _ _

C 2.04

2.97 2.03 5.32

(1120) A 8.39

_ _

B

2.21 2.65 2.50

_

C

4.17 -

_ _

CliOO) A 2.35 2.89

2.23

5.59


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S. Blonski, S.H. Garofal ini / M olecular dynamics simul ati ons of a- and y- alumi na surfaces

267

d

E, = 8.04 J m-z

3

I

I

E, = 2.19 J m-*

m

I

E

2

I

I

E, = 2.04 J mz

1

Height [A]

CB

Fig. 3. Density profiles for various terminations of the (0001)

surface of a-alumina and for the bulk crystal in this direction.

Dashed lines show the periodic boundaries for the bulk crys-

tal and the limit of the immobile layer for the surfaces.

elevated temperatures: Kingery reported 0.9 J/m2

at 2123 K [19]. This is less than the values from

our room temperature simulations, but it is known

that surface energy of ceramics decreases with

increasing temperature [20]. Although the experi-

mental value of surface entropy, which describes

the temperature dependence of the surface en-

ergy, is also unknown, estimations made by Tasker

[17] and Mackrodt [18] suggest that the calculated

surface energies presented in table 1 are correct.

Simulation results for the particular surfaces are

discussed in detail in the following subsections.

4.1,

0001)urface

Three possible terminations of the (0 0 0 1) sur-

face are shown in fig. 3. Two of them (B and C)

are terminated by the layers of aluminum atoms.

These terminations have a surface energy signifi-

cantly lower than the third one (A), which is

terminated by a layer of oxygen atoms. The sur-

face with the terminating layer C has the lowest

surface energy among all surfaces studied for

a-alumina. Therefore, this should be the surface

which most frequently occurs in a-alumina crys-

tals. Some observations have show that it is really

the case [14]. This surface has also been chosen

as the subject of earlier theoretical studies (see

table 1). The surface is only slightly relaxed and

has the symmetry of the bulk crystal. As fig. 4

shows, for all of the terminations there exists a

two-dimensional periodicity on the surfaces. Sur-

faces B and C are surprisingly similar, consider-

ing the difference between the initial configura-

tions from which they were created. There is an

excess of aluminum atoms on the unrelaxed B

surface, which during relaxation shift toward the

inside of the crystal. This causes other Al atoms

to move deeper into the crystal and to create

interstitial defects in the bulk. Thus. the surface

layer

layer

Fig. 4. Atom configurations for the terminations of the (000 1)

surface of a-alumina. For the layers B and C, only the

aluminum atoms located above the surface are shown.


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26X S. Blonski, S.H. Garofal ini / M olecular dynamics simulat ions of a- and y-al umina surfaces

Al atoms are the source of the crystal defects and

their occurrence increases the surface energy, but

they do not influence the appearance of the outer

surface layer itself.

Both B and C surfaces are stoichiometric and

on both of them exist under-coordinated alu-

minum atoms which can significantly influence

the chemical properties of the surface. For the

third terminating layer, the A surface, there are

mainly oxygen atoms on the surface. This can also

be seen as a deficiency of the aluminum atoms on

the unrelaxed surface. Due to the field of unbal-

anced electric dipoles, aluminum atoms from the

Al layer adjacent to the surface move toward the

surface during the relaxation. Some Al atoms

from the deeper aluminum layer also move in the

same direction and cause the A surface to be

non-stoichiometric. In the simulated samples,

there are 90 oxygens in each oxygen layer, there-

fore, there should be 60 Al atoms in each alu-

minum layer. However, fig. 4 shows that there are

69 Al atoms in the uppermost aluminum layer of

the termination A. The excess Al atoms originate

from the deeper aluminum layer, hence there is

also a deficiency of Al atoms in the deeper layer.

Because of the similarity of the B and C sur-

faces, the simulations show that only two differ-

ent regions should be observed on the (000 1)

surface. Recent experiments indicate that this

may, in fact, be the case [16]. Two regions were

observed in reflection electron microscopy experi-

ments performed under different resonance con-

ditions. Contrast reversals suggest that the atomic

configurations in the regions are different, very

possibly due to the surfaces terminated at differ-

ent layers within one crystal cell. However, the

observations are not fully understood yet. Results

of further studies might be very important to

clarify the problem. However, simulation results

presented here provide a useful interpretation of

the experimental features.

4.2. (I I 20) surface

Three terminations of the (1 120) surface have

been studied. Density profiles obtained from the

simulations are shown in fig. 5, in comparison

with a density profile of the bulk crystal. The

E, = 4.77 1 m-

Height [A]

CBA

3

Fig. 5. Density profiles for various terminations of the (1 1 ZO)

surface of a-alumina and for the bulk crystal in this direction.

termination B, which is formed when the crystal

is split at the plane lying between two oxygen

layers, has the lowest surface energy. Surpris-

ingly, it is achieved with only modest relaxation of

the surface. The surface profile remains very sim-

ilar to the profile of the bulk crystal. It is contrary

to the behavior of the (000 1) surface, for which

the density profile peaks are significantly broader

than for the bulk crystal.

For the terminating layer A, a significant re-

construction of the surface occurs. The depth

involved in the reconstruction has a thickness of

about 7 A. Despite the reconstruction, the sur-

face energy of this termination is high. As a result

of the reconstruction, there is a layer of non-

bridging oxygen (NBO) atoms at the top of the

surface. The NBOs and aluminum atoms bonded

to them also form a regular pattern on the sur-

face (see fig. 6). This layer of NBOs might result

in strong reactivity of the surface. For the termi-

nating layer C the reconstruction is even deeper

than for the layer A, because there is initially a

layer of Al atoms on the top of the termination C.


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S. Blonski, S.H. Garofal ini / M olecular dynamics simulat ions of LX- nd y-al umina surfaces 269

;

layer

a-A O,

11

TO)

layer c

Fig. 6. Atom configurations for the terminations of the (1120)

surface of a-alumina.

The resulting surface has energy higher than the

layer B, but lower than the layer A. As can be

seen in fig. 6, the surface C is partially disor-

dered. From the results, it is believed that longer

simulations are needed to form an entirely peri-

odic surface. Additionally, it should be noted

that, although there are only octahedrally coordi-

nated aluminum atoms in bulk a-alumina crys-

tals, the surface Al atoms are often four- or

five-coordinated, as indicated in fig. 6.

4.3. 1700)

surface

There is only one possible termination of the

(1iOO) surface. After splitting the crystal at that

level, the surface undergoes significant recon-

struction. In the most external layer, two-coordi-

nated oxygens move slightly above the surface

formed by three-coordinated oxygens and four-

coordinated aluminum atoms. Other changes also

occur in deeper layers, even 5 A from the surface

(see fig. 7b). The formed surface, shown in fig. 7a,

displays two-dimensional periodicity. The energy

of the (liO0) surface is higher than that of the

lowest-energy terminations of the (0 00 1) and

(112 0) surfaces. Therefore, contrary to results of

Tasker [17] and Mackrodt et al. [18], the order of

surface energies predicted in the present work is:

(0001) < (1120) < (iioo),

which coincides with the statistical observations

presented by Hartman [141.

5. Surfaces of y-alumina

The crystal structure of -y-alumina is much

more complicated than the structure of cy-

alumina. In a-alumina, Al atoms have only octa-

hedral coordination, but in y-alumina, aluminum

atoms are coordinated octahedrally as well as

tetrahedrally. Occurrence of vacancies at some

(a>

20

k

10

a-AI,O,

(iioo)

layer A

0

(b) lox

I

,

I

4

E, = 2.35 J me2

Height [A]

A

Fig. 7. (a) Atom configurations on the (IiOO) surface of

a-alumina; (b) density profile for this surface and for the bulk

crystal in this direction.


8/12

270


Table 2

Calculated surface energies for y-alumina (letters in paren-

theses show notation of surfaces used by other authors [3])

Surface

(001) A (EJ

B (F)

(110) A (D)

B (Cl

(111) A (A)

B (B)

Surface energy (J rn-)

Unrelaxed Relaxed

surfaces

surfaces

3.24

1.94

3.37 0.79

4.62

2.54

4.62

1.21

9.45 0.87

14.08

0.88

cation sites creates another complication to the

structure. Hence, surfaces of y-alumina have a

more complex structure than a-alumina. In par-

ticular, surface relaxation in y-alumina can vary

in different regions depending on the distribution

of Al vacancies in the atomic layer below the

surface. Such behavior was observed in the simu-

lations.

Therefore, in order to find the average proper-

ties of the y-alumina crystal surfaces, 12 to 16

different samples for each of the surfaces were

studied. Three y-alumina surfaces were exam-

ined: (00 l>, (1 lo), and (111). The average sur-

face energies obtained are shown in table 2. The

surface energies for y-alumina are for the most

part lower than the energies for a-alumina. The

surfaces which have the lowest energies became

amorphous during reconstruction. However, sim-

ulations of bulk amorphous alumina resulted in

higher energy than the crystalline y-alumina, in-

dicating that the crystal is the more stable bulk

structure and the amorphization of the surface is

not an artifact.

Surface disordering during simulations is ac-

companied by a change in coordination of alu-

minum atoms: the number of tetrahedral Al atoms

increases. For each of the surfaces studied, there

is an apparent dispersion of the values of surface

energy, but the structural characteristics are simi-

lar. Neither the number of defects nor the extent

of disordering was directly related to the surface

energy. However, the energy is lower for the

surfaces which contain more vacancies located in

the layer adjacent to the surface. Results for

particular surfaces of y-alumina are discussed in

more detail in the following subsections.

5.1. 001)

urface

There are two possible terminating layers of

the (0 0 1) surface. Fig. 8 shows density profiles of

both surfaces compared with the one of the bulk

crystal. To enhance details, only top regions of

the crystals are shown. Density profiles of the

entire crystals show that surface relaxation in

y-alumina is extended to a depth similar to that

in the a-alumina crystals, but interesting features

occur close to the surface level. The crystal struc-

ture of y-alumina is preserved quite well on the

(00 1) surface. For the A-layer only some oxygen

atoms move slightly above the surface. For the

B-layer, which has a surface energy significantly

lower than the A-layer, some aluminum atoms

were located above the surface at the beginning

of the simulation. However, during surface relax-

ation these atoms move toward a layer of oxygen

atoms and hide among them. This must be the

main source of the drop in the surface energy of

the B-layer due to relaxation. From the density

profiles, it can be concluded that on the (00 1)

surface of y-alumina, oxygen and aluminum atoms

are located mainly on the same level, with some

I I

cl I

Fig. 8. Density profiles for various terminations of the (00 1)

surface of y-alumina and for the bulk crystal in this direction.


9/12


oxygen atoms placed a little above the surface of

the A-layer.

Fig. 9 shows atom configurations of the simu-

lated surfaces and compares them with that of

the idealized ones. In the idealized case, no va-

cancies are included in the crystal structure,

whereas they are included in the simulated sys-

tem. The configurations of the idealized and sim-

ulated A-layers are very similar, however, vacan-

cies are present at some positions of the tetrahe-

drally coordinated aluminum atoms located

slightly below the surface. Due to these vacancies

and the lack of the attracting cations, some pairs

of two-coordinated oxygen atoms rotate above

the surface. This is a major difference from the

idealized A surface, which only consists of three-

coordinated oxygens. Because atoms do not

change their coordinations during the simula-

tions, only surface relaxation takes place for the

A-layer. For the B-layer, there is clearly a surface

reconstruction instead of relaxation. All the two-

coordinated aluminum atoms, which at the begin-

ning of the simulation were located above the

surface, change their coordination as they move

toward oxygen atoms and form new bonds with

them. Mainly four- and five-coordinated Al atoms

appear on the surface, with some three-fold Al

Idealized

0 10

20

Fig.

9.

Atom configurations for the terminations of the (00 1)

surface for the idealized and simulated models of y-alumina.

Al

-0

I :

271

0

Fig. 10. Density profiles for various terminations of the (1 10)


atoms also present due to defects in the structure

of the surface. Additionally, there are more alu-

minum atoms on the simulated surface then on

the idealized one because some Al atoms from

the lower level move toward the surface during

the reconstruction. There is also a difference in

coordinations of the oxygen atoms present on the

surface. There are fewer tetrahedrally coordi-

nated oxygens on the simulated surface than on

the idealized one. The oxygen atoms are mainly

three-fold, but two-coordinated oxygens also oc-

cur. The difference may be very important be-

cause the lower surface energy of the B-layer

makes it the most probable termination on the

(00 1) surface of y-alumina.

5.2.

110) surface

There are also two possible terminations for

the (110) surface. Fig. 10 shows density profiles

of the sample surfaces compared with that of the

bulk crystal. Fig. 11 shows atom configurations of

the respective surfaces. Configurations of the

simulated surfaces are also compared in this fig-

ure with that of the idealized ones.

For the A-termination, surface relaxation en-

compasses three layers of atoms. Oxygen atoms,

which are located above the cation vacancies,


10/12

272


rotate slightly above the surface. They are bonded

to only one aluminum atom each. Thus, the sur-

face of the A-layer consists not only of the two-

and three-coordinated oxygens, but also of NBOs.

Coordination of the aluminum atoms does not

change during the relaxation, but the density

profile shows that some of them slightly follow

the NBOs in the move upward. In spite of differ-

ences in surface energy, the configurations of all

of the (110) A-layers studied here are very simi-

lar to each other. They differ in the number of

NBOs on the surface, due to the different va-

cancy distributions in each simulation, but the

surface energy does not seem to be correlated to

that number.

There is also a difference in the surface energy

among the B-terminations. Decrease in the sur-

face energy is accompanied by the disorder ap-

pearing on the surface. The B-surface shown in

fig. 11 is the one with the moderate surface

energy and with the moderate number of defects

on the surface. The two top atom layers are

involved in the surface reconstruction with even

some oxygen atoms from the second layer moving

to the surface. As a result, five coordinated alu-

minum atoms appear on the surface, in addition

to the three- and four-fold ones. The oxygen

dealized

Simulated

I.. . . . . . . /

I

AsA A.A A.A A:

r..

,. AA AA AA AA;

. . . . . . . .

A+A A.A A&A A;

AA AA AA AA;

k

90 A GQ I

O.O*A,A A.A

layer B

o1...

. . . .

.L ,

&A&,

-

10

2

0 18 20

Fig.

11.

Atom configurations for the terminations of the (1 10)


1

Fig. 12. Density profiles for various terminations of the

(I

1 1)


atoms are no longer three-fold only, but some of

them are rather two-coordinated. Large defects

occurring on the surface additionally expose the

second layer of atoms, therefore, it is difficult to

estimate the number of atoms on the surface.

5.3. Cl I 1) surf ce

There are several possible terminations of this

surface, however only two of the ones which

expose aluminum atoms above the level of oxy-

gens were simulated (see fig. 121. Those termina-

tions have been usually considered as the A- and

B-layers of the (1 1 I> surface [3]. Surface energies

of both terminations are high, but different, be-

fore reconstruction; after the reconstruction the

average energies are equal. The energy is usually

lower for layers with the larger number of the

cation vacancies present near the surface. For all

of the (1 11) surfaces studied, the reconstruction

is extensive and the surfaces become amorphous

or at least significantly distorted. Fig. 13 shows

that the regular patterns of the idealized termina-

tions vanish during the simulations. A driving

force of the reconstruction is a tendency to in-

crease coordination of the aluminum atoms. As a

result, the number of three-coordinated Al atoms

is much lower on the simulated surfaces than on


11/12


273

Idealized

Fig. 13. Atom configurations for the terminations of the (111)


the idealized ones. One-coordinated Al atoms,

initially present in the A-layer, also bind to addi-

tional oxygens during reconstruction. Because of

this, disorder is much broader on the A-layers

than on the B-layers. It is clearly shown by figs.

12 and 13 which present examples of both A and

B terminations of the (111) surface with the

similar surface energies which are also close to

the average values.

6.

Conclusions

The simulations show that surfaces of the alu-

mina crystals can be terminated by different lay-

ers of atoms. Although some terminations seem

to be unfavorable when the unrelaxed crystal

surfaces are considered, they become more prob-

able after surface relaxation or reconstruction

during the simulations. For basal surface of (Y-

alumina, the termination C which was usually

considered in earlier theoretical studies has the

lowest surface energy in the present simulations.

In addition, the simulations show that another

termination (B) has the energy only slightly higher

then C and looks exactly the same as C. This is in

agreement with experimental observations of two

terminating layers on the (0 0 0 1) surfaces. Simu-

lation results cannot be compared with experi-

mental observations of the (1 i 00) and (1 120)

surfaces, because such data are not yet available.

However, regularity of the surfaces suggests that

they might be an object of studies on the atomic

level, e.g. by atomic force microscopy.

Surfaces of y-alumina obtained from the simu-

lations differ greatly from idealized surfaces which

have been considered so far in previous studies.

One reason for the difference is the presence of

cation vacancies in the current simulations. Al-

though the presence of vacancies in the crystal

structure of -y-alumina has been recognized for a

long time, the vacancies were usually ignored in

previous models of the surfaces. Differences are

also caused by the occurrence of surface relax-

ation or reconstruction. Atoms with various coor-

dinations, not expected from the idealized mod-

els, appear on the surfaces as a result. Some

surfaces are often disordered, but their energy is

significantly lower than the lowest one for (Y-

alumina. This may explain the experimental dif-

ference in surface area between these two forms

of alumina.

Acknowledgement

The authors acknowledge support from the

Center for Ceramic Research at Rutgers Univer-

sity.

References

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Surface Science Volume 295 issue 1-2 1993 [doi 10.1016%2F0039-6028%2893%2990202-u] S. Blonski; S.H....

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