Molecular dynamics simulations of α-alumina and γ-alumina surfaces

......t.:.:.: .i....... :.:.:;.: ./....... :,:,:.> ............:.:,:.> ,:.:_,., ““l’......... . . . . . . p::~:l:~::::::~:l:“.:.............’.’.’.

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‘i.

::::.

. .. . . . . . .. . . . . . .>;:,~,:z:i

li::::z:‘:‘.‘

Surface Science North-Holland

295 (1993) 263-274

surface

Molecular dynamics simulations of a-alumina S. Blonski

science

and y-alumina surfaces

1 and S.H. Garofalini

Department of Ceramics and Interfacial Molecular Science Laboratory, Institute for Engineered Materials, Rutgers Unioersity, P.O. Box 909, Piscataway, 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 technological applications. While a-alumina is mainly seen as a structural, optical and electronic material, y-alumina is usually used as a catalytic support. Because surface properties of the crystals affect the successful application of these aluminas, the surfaces have been an object of a number of theoretical and experimental studies. For (Yalumina, only one possibility of surface termination 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 simulations of a-alumina surfaces with different terminating layers of atoms were performed. Conversely, for y-alumina, the concept of different terminations has been known and examined previously. However, theoretical models of y-alumina surfaces are usually based on an idealized structure of the crystal, with an excess of aluminum atoms [3]. In this study, an extended approach for

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. Therefore, 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 Newton’s 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 interactions. The two-body part is a modified BornMayer-Huggins form, given as Qij =Aij exp( -rij/pij)

’ On leave from the Department of Applied cal University of Gdansk, Poland.

0039-6028/93/$06.00

0 1993 - Elsevier

Physics,

Science

Techni-

Publishers

+(

4i4je2/rij)

B.V. All rights reserved

erfc(

‘ij/Pij)

>

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

264

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 complementary 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

A ,_,,=0.2490 fJ,

/3O_A, = 2.34 A,

A *,_*, = 0.0500 fJ,

P/,_A, = 2.35 A.

= 2.34 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,,_,, parameter, 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, because 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 coordinations so as to test ideas regarding glass properties [51. The three-body interactions imposed on all of the Al-O-Al and O-Al-O triplets have the following functional form: qjilk

=

exP[

‘jik

Yij/(‘i,

+Yik/tTik

if rij <

-

Rrj)

-Rzk)]ajik,

Rij and

rik <

Rik;

Pjik = 0, if rrl 2

Rtj or

with the angular

rik 2 R,k ; part, fljik, given by

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

ejik + l/3)

for AI-O-Al; sin 19,~~cos tijik]*,

for O-Al-O; where ejik is an angle formed by the ions j, i, and k with the ion i placed at the vertex. The angular

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 paramchave the following values: ters, hjrk, Yi,, and R,j, A/,_o_/,,

= 0.001 fJ,

yo_*, = 2.0 A, R omA, = 2.6 A,

A,~,,_,

= 0.024 fJ,

y&-o = 2.8 A, R,,_o

= 3.0 A.

The same values of the three-body parameters were used in the previous studies of glasses. The simulations were run for 50000 time steps each with the initial 5000 steps being used for temperature equilibration. All the reported simulations have been performed at 300 K. After the bulk crystals were simulated, the desired surfaces were exposed and surface simulations were performed in the way described by Garofalini [4l. A surface was created by removing periodic boundaries in one dimension, while keeping them in the other two dimensions. Simultaneously, atoms in the layers most apart from the surface were immobilized, 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 movement 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 functions (RDFs) of the atomic positions. The partial radial distribution functions were calculated for each pair of ion types from the formula [71: gi,tr)

=Wj(r)/No(r)7

where N,,(r) denotes the number of ions of type j in a shell between r - Ar/2 and r + Ar/2 around

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

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)

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

= (%/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 perpendicular to a surface were calculated by counting the number of ions in slabs parallel to that surface. The slabs have the thickness of about 0.1 w each depending on the size of the simulation cell.

3. Structures of bulk crystals The initial structure of a-alumina was defined according to Wyckoff [8], with the lattice parameters 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

r

4

simulation diffraction

3 C xl 2 1 0 0

2

4

6 8 10 r [Al 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].

265

off is also shown. The excellent agreement between crystallographic data and simulation results 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 yalumina. 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 suggest 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 vacancies are located on tetrahedral sites. Recently published results of other molecular dynamics studies of bulk y-alumina support such an assumption [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 positions. 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 energy 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-

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

266 2,

I

o-o

tion could have been omitted the crystallographic structure

in the generation of y-alumina.

of

1

~~~ 0

I,:

,,

:

~ ~\

‘I /’

‘,

,: \ \

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 reported in the literature (7.91 A> [ll]. Fig. 2 shows partial radial distribution functions (PDFs) for the relaxed structures obtained from the simulations of the crystals with both lattice constants. Although the expansion is clearly visible, the shapes of the PDFs are unchanged. The simulated 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 simulation; 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-

4. Surfaces of cu-alumina Three surfaces of a-alumina were simulated: (000 l), (11 001, and (1 120). These are the surfaces which frequently occur in natural and artificial corundum crystals and have been the subject of several experimental studies [14-161. From density profiles of the crystals with different orientation, 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-dimensional periodicity on the surfaces were simulated. Surface energies obtained from our simulations 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

Surface

energies Surface This work

Unrelaxed surfaces 12.77 (0001) A B 12.85 5.04 C (1120)

(iioo)

CliOO)

energy (J m-*) Ref.

Ref.

Ref.

[I71

[I81

[211

_

_

_

6.53 _

5.95 _

5.17 _

4.37 _

6.72 _ _ _

A B C

14.32 3.49 14.41

A

5.56

6.87

6.46

5.65

8.04 2.19 2.04

_ _

_ _

_ _

2.97 _

2.03 _

5.32

2.65 -

2.50 _

_ _

2.89

2.23

5.59

Relaxed surfaces (0001) A B C (1120)

of cu-alumina

A B C

8.39 2.21 4.17

A

2.35

267

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

E, = 8.04 J m-z

d

$

3 I

I

E, = 2.19 J m-* m

I

E

2

I

I

E, = 2.04 J mz

Height

[A]

1

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 crystals. 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. Surfaces B and C are surprisingly similar, considering the difference between the initial configurations 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

CBA

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 crystal 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 experimental value of surface entropy, which describes the temperature dependence of the surface energy, 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.

layerA

layerB

4.1, (0001)surface Three possible terminations of the (0 0 0 1) surface 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 significantly lower than the third one (A), which is terminated by a layer of oxygen atoms. The sur-

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.

26X

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina 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 aluminum 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 unbalanced 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, therefore, there should be 60 Al atoms in each aluminum 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 surfaces, the simulations show that only two different 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 experiments performed under different resonance conditions. Contrast reversals suggest that the atomic configurations in the regions are different, very possibly due to the surfaces terminated at different 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-’

3 Height

[A]

CBA

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. Surprisingly, it is achieved with only modest relaxation of the surface. The surface profile remains very similar 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 reconstruction of the surface occurs. The depth involved in the reconstruction has a thickness of about 7 A. Despite the reconstruction, the surface energy of this termination is high. As a result of the reconstruction, there is a layer of nonbridging oxygen (NBO) atoms at the top of the surface. The NBOs and aluminum atoms bonded to them also form a regular pattern on the surface (see fig. 6). This layer of NBOs might result in strong reactivity of the surface. For the terminating 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.

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of LX-and y-alumina surfaces

00;

layerA

269

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

a-A&O, (11 TO) layer

Fig. 6. Atom configurations surface

for the terminations of a-alumina.

c

of the (1120)

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 disordered. From the results, it is believed that longer simulations are needed to form an entirely periodic surface. Additionally, it should be noted that, although there are only octahedrally coordinated aluminum atoms in bulk a-alumina crystals, the surface Al atoms are often four- or five-coordinated, as indicated in fig. 6. 4.3.

(1700)

The crystal structure of -y-alumina is much more complicated than the structure of cyalumina. In a-alumina, Al atoms have only octahedral coordination, but in y-alumina, aluminum atoms are coordinated octahedrally as well as tetrahedrally. Occurrence of vacancies at some

(a> 20

k-

a-AI,O,

10

(iioo) layer A

0

I

lox

”

(b) ‘,’

” I

”

E, = 2.35 J me2 4

surface

There is only one possible termination of the (1iOO) surface. After splitting the crystal at that level, the surface undergoes significant reconstruction. In the most external layer, two-coordinated oxygens move slightly above the surface formed by three-coordinated oxygens and fourcoordinated aluminum atoms. Other changes also

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.

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

270

Table 2 Calculated surface energies for y-alumina (letters in parentheses show notation of surfaces used by other authors [3])

particular surfaces of y-alumina are discussed more detail in the following subsections.

Surface

5.1.

(001) (110) (111)

Surface

A B A B A B

(EJ (F) (D) (Cl (A) (B)

energy (J rn-‘)

Unrelaxed surfaces

Relaxed surfaces

3.24 3.37 4.62 4.62 9.45 14.08

1.94 0.79 2.54 1.21 0.87 0.88

cation sites creates another complication to the structure. Hence, surfaces of y-alumina have a more complex structure than a-alumina. In particular, 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 simulations. Therefore, in order to find the average properties of the y-alumina crystal surfaces, 12 to 16 different samples for each of the surfaces were studied. Three y-alumina surfaces were examined: (00 l>, (1 lo), and (111). The average surface 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, simulations of bulk amorphous alumina resulted in higher energy than the crystalline y-alumina, indicating that the crystal is the more stable bulk structure and the amorphization of the surface is not an artifact. Surface disordering during simulations is accompanied by a change in coordination of aluminum 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 similar. 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

in

(001)surface

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 structure 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 relaxation 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

cl

I

I

Fig. 8. Density profiles for various terminations of the (00 1) surface of y-alumina and for the bulk crystal in this direction.

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

oxygen atoms placed a little above the surface of the A-layer. Fig. 9 shows atom configurations of the simulated surfaces and compares them with that of the idealized ones. In the idealized case, no vacancies are included in the crystal structure, whereas they are included in the simulated system. The configurations of the idealized and simulated A-layers are very similar, however, vacancies are present at some positions of the tetrahedrally 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 threecoordinated oxygens. Because atoms do not change their coordinations during the simulations, only surface relaxation takes place for the A-layer. For the B-layer, there is clearly a surface reconstruction instead of relaxation. All the twocoordinated aluminum atoms, which at the beginning 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

Al -0

I

10

Fig. 9. Atom configurations for the terminations surface for the idealized and simulated models

20

of the (00 1) of y-alumina.

:

0

Fig. 10. Density profiles for various terminations of the (1 10) surface of y-alumina and for the bulk crystal in this direction.

atoms also present due to defects in the structure of the surface. Additionally, there are more aluminum 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 coordinated oxygens on the simulated surface than on the idealized one. The oxygen atoms are mainly three-fold, but two-coordinated oxygens also occur. The difference may be very important because the lower surface energy of the B-layer makes it the most probable termination on the (00 1) surface of y-alumina. 5.2.

0

271

(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 figure with that of the idealized ones. For the A-termination, surface relaxation encompasses three layers of atoms. Oxygen atoms, which are located above the cation vacancies,

272

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces

rotate slightly above the surface. They are bonded to only one aluminum atom each. Thus, the surface of the A-layer consists not only of the twoand 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 differences in surface energy, the configurations of all of the (110) A-layers studied here are very similar to each other. They differ in the number of NBOs on the surface, due to the different vacancy 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 surface energy is accompanied by the disorder appearing 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 aluminum atoms appear on the surface, in addition to the three- and four-fold ones. The oxygen

Idealized

I..

I A

r.. ,.

.

AsA

.

.

A.A

.

Simulated

.

A.A

.’

/

A:

A’A A’A A’A A’A; . . . . . . . . A A+A A.A A&A A;

!

A’A

A’A

A’A

o1...

.

0

10

.

X

A’A; .

.

.L

20

90 k ,

0

A”$

$‘GQ

‘O.O’*A,A

A.A

I layer

B

&A&,

-

20

18 X

Fig. 11.Atom configurations for the terminations of the (1 10) surface for the idealized and simulated models of y-alumina.

1 Fig. 12. Density profiles for various terminations of the (I 1 1) surface of y-alumina and for the bulk crystal in this direction.

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) surface There are several possible terminations of this surface, however only two of the ones which expose aluminum atoms above the level of oxygens were simulated (see fig. 121. Those terminations 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, before 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 terminations vanish during the simulations. A driving force of the reconstruction is a tendency to increase coordination of the aluminum atoms. As a result, the number of three-coordinated Al atoms is much lower on the simulated surfaces than on

S. Blonski, S.H. Garofalini / Molecular dynamics simulations of a- and y-alumina surfaces Idealized

Fig. 13. Atom configurations for the terminations of the (111) surface for the idealized and simulated models of y-alumina.

the idealized ones. One-coordinated Al atoms, initially present in the A-layer, also bind to additional 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.

273

terminating layers on the (0 0 0 1) surfaces. Simulation results cannot be compared with experimental 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 simulations 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. Although 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 relaxation or reconstruction. Atoms with various coordinations, not expected from the idealized models, appear on the surfaces as a result. Some surfaces are often disordered, but their energy is significantly lower than the lowest one for (Yalumina. This may explain the experimental difference in surface area between these two forms of alumina.

Acknowledgement

The authors acknowledge support from the Center for Ceramic Research at Rutgers University.

6. Conclusions The simulations show that surfaces of the alumina crystals can be terminated by different layers of atoms. Although some terminations seem to be unfavorable when the unrelaxed crystal surfaces are considered, they become more probable after surface relaxation or reconstruction during the simulations. For basal surface of (Yalumina, 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

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