Kappaalumina Phd

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Metastable Alumina from Theory:Bulk, Surface, andGrowth of -Al2O3

CARLO RUBERTO

Akademisk avhandling som for avlaggande av teknologiedoktorsexamen i fysik vid Chalmers tekniska hogskola forsvaras

vid offentlig disputation den 11 juni 2001, klockan 13.15i Gustaf Dahlen-salen, Origovagen 1, Chalmers, Goteborg.

Avhandlingen forsvaras pa engelska.Fakultetsopponent ar professor Claudine Noguera,

Laboratoire de Physique des Solides, Paris, Frankrike.

Huvudhandledare ar professor Bengt I. Lundqvist

Avdelningen for tillampad fysikChalmers tekniska hogskola och Goteborgs universitet

Goteborg, 2001


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THESIS FOR THE DEGREE OF DOCTOR OF PHILOSPOHY

Metastable Alumina from Theory:Bulk, Surface, andGrowth of -Al2O3

CARLO RUBERTO

Department of Applied PhysicsChalmers University of Technology and

Goteborg University

Goteborg, Sweden 2001


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Metastable Alumina from Theory:Bulk, Surface, and Growth of -Al2O3CARLO RUBERTOISBN 91-7291-054-2

c CARLO RUBERTO, 2001

Doktorsavhandlingar vid Chalmers tekniska hogskola

Ny serie nr 1738ISSN 0346-718X

Applied Physics Report 0125

Department of Applied PhysicsChalmers University of TechnologySE-412 96 GoteborgSweden

Telephone +46 (0)31-772 3199

Cover:

The combination of density-functional theory and high-performance computing(background) is the basis for the theoretical investigation conducted in this

Thesis on the metastable phase of alumina. The inset figures illustrate theapplicability of theoretical methods for technological applications. From bottomleft: (i) CVD-coated cemented-carbide cutting-tool inserts; (ii) a scanning-electron micrograph of a coated insert, showing, from bottom to top, theWC/Co substrate, layers of TiC, Al2O3, and TiN; and (iii) the atomic structureof -Al2O3, as determined from the present work.

Chalmersbibliotekets reproserviceGoteborg, Sweden 2001


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Metastable Alumina from Theory:

Bulk, Surface, andGrowth of -Al2O3

CARLO RUBERTO

Department of Applied PhysicsChalmers University of Technology and

Goteborg University

ABSTRACTAluminas are materials of high technological importance that show a fascinatingstructural flexibility, with a large amount of different phases (, , , , , , . . . )and phase transitions at relatively high temperatures. This variety provides the dif-ferent alumina phases with a wide range of properties but at the same time makesexperimental and theoretical investigations on them difficult to perform. In partic-ular, a fundamental understanding at the atomistic level is lacking for metastablealuminas, for most of which not even the atomic structure is well known.

In the present Thesis, I report on first-principles theoretical investigations at the

quantum-mechanical level, based on the density-functional theory (DFT), to studythe stability and bonding of the metastable -Al2O3. The motivation for this isthree-fold. First, the use of-Al2O3 as a wear-resistant coating on cemented-carbidecutting tools, deposited with chemical-vapor deposition (CVD), provides a hightechnological interest for this material. Second, basic understanding of the stabilityof a metastable alumina yields general insights into metastable-alumina properties.Third, the study of a relatively complex ionic crystal like -Al2O3 can be used toinvestigate the general problem of ion-crystal stability.

The work is performed in three parts: (i) The atomic and electronic bulk struc-

tures of -Al2O3 are determined; (ii) The structure and stability of the (001) and(001) surfaces are understood; (iii) The thermodynamics of the Al2O3 nucleationon TiC(111) is investigated. The results yield fundamental knowledge on the CVDgrowth process of-Al2O3, on the stability of metastable aluminas, and on the cohe-sion of low-symmetry ionic crystals in general. The limited validity of point-chargemodels for ion-crystal stability is discussed. A surprising prediction of a 1D electrongas at the -Al2O3(001) surface is furthermore revealed.

Keywords: density-functional theory, DFT, plane waves, pseudopotentials, first principles,ceramic materials, ionic crystals, cutting tools, stability, structure, Paulings rules, Taskers

rules, surface states, one-dimensional electron gas, TiC, adsorption, bonding, polar surfaces


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LIST OF PUBLICATIONS

This thesis consists of an introductory part and the following papers, referred toby Roman numerals in the text:

I. First-Principles Calculations on the Atomic and Electronic Structureof -Al2O3Y. Yourdshahyan, C. Ruberto, L. Bengtsson, and B. I. LundqvistPhysical Review B 56, 8553 (1997).

II. Theoretical Structure Determination of a Complex Material: -Al2O3Y. Yourdshahyan, C. Ruberto, M. Halvarsson, L. Bengtsson, V. Langer,

B. I. Lundqvist, S. Ruppi, and U. RolanderJournal of the American Ceramic Society 82, 1365 (1999).

III. Stability of Polar Flexible Ion-Crystal Surface: Metastable Aluminaand 1D Surface MetallicityC. Ruberto, Y. Yourdshahyan, and B. I. LundqvistApplied Physics Report 01-22, submitted to Physical Review Letters.

IV. Surface Properties of Metastable Metal Oxides: A Comparative CaseStudy of - and -Al2O3C. Ruberto, Y. Yourdshahyan, and B. I. LundqvistApplied Physics Report 01-23.

V. Energetics and Bonding of Alumina Nucleation on TiC(111)C. RubertoApplied Physics Report 01-24.

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My contributions to the publications are the following:

I. I participated in the final analysis of the found structures, performing theband-structure and effective-mass calculations. I also participated activelyin the writing of the manuscript and in the discussions surrounding theanalysis of the results.

II. I participated actively, together with YY, in the setting up of the sixtystructural configurations of -Al2O3 and in the calculations on them. Mypart in this work was 50-50 with YY. I did not participate in the executionof the experimental part of the work. The analysis part was performedjointly among the authors, but especially by YY, me, and MH. Most part

of the manuscript was written by YY and me, with contributions from MHand BL and comments from the other authors. Sections VII, IX, and allexperimental parts were not written by me.

III. The project idea originated from YY with whom I performed the initialcalculations. I performed most part of the calculations, with help from YY,and wrote most of the manuscript in a dialogue with the other authors.Most of the analysis was performed by me, with suggestions and commentsfrom the other authors.

IV. Same as above. However, YY provided essential groundwork for the man-

uscript work.

V. I performed all of the calculations, as well as the analysis and writing ofthe manuscript. However, useful and inspiring discussions with Mats Hal-varsson and Bengt Lundqvist are acknowledged.

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Contents

1 Introduction 1

2 Alumina 5

2.1 Alpha Alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.1 Bulk Structure . . . . . . . . . . . . . . . . . . . . . . . . 112.1.2 Electronic Structure . . . . . . . . . . . . . . . . . . . . . 132.1.3 Surface Structure . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Metastable Aluminas . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.1 Bulk Structures . . . . . . . . . . . . . . . . . . . . . . . . 242.2.2 Electronic Structure . . . . . . . . . . . . . . . . . . . . . 282.2.3 Surface Investigations . . . . . . . . . . . . . . . . . . . . . 29

2.3 CVD of Alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.3.1 TiC(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Stability of Ionic Crystals 43

3.1 Bulk Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.1 Quantum-Mechanical Description . . . . . . . . . . . . . . 473.1.2 Classical Model . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 Surface Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4 Theoretical Method 59

4.1 Density-Functional Theory . . . . . . . . . . . . . . . . . . . . . . 61

4.1.1 The Hohenberg-Kohn Theorems . . . . . . . . . . . . . . . 614.1.2 The Kohn-Sham Equations . . . . . . . . . . . . . . . . . 644.1.3 Interpretation ofExc . . . . . . . . . . . . . . . . . . . . . 664.1.4 Approximations for Exc . . . . . . . . . . . . . . . . . . . . 68

4.2 Plane-Wave Pseudopotential Method . . . . . . . . . . . . . . . . 704.2.1 Periodic Supercells . . . . . . . . . . . . . . . . . . . . . . 704.2.2 Plane-Wave Expansion . . . . . . . . . . . . . . . . . . . . 714.2.3 k-Point Sampling . . . . . . . . . . . . . . . . . . . . . . . 724.2.4 Pseudopotentials . . . . . . . . . . . . . . . . . . . . . . . 73

4.3 Results from DFT Calculations . . . . . . . . . . . . . . . . . . . 75

4.3.1 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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viii Carlo Ruberto, Metastable Alumina from Theory

4.3.2 Electronic Structure . . . . . . . . . . . . . . . . . . . . . 784.3.3 Surface Calculations . . . . . . . . . . . . . . . . . . . . . 80

5 Results and Conclusions 83

Acknowledgements 87

Bibliography 88


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Il mondo esisteva prima delluomo ed esistera

dopo, e luomo e solo unoccasione che il mondo

ha per organizzare alcune informazioni su sestesso.

Italo Calvino


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CHAPTER 1

Introduction

This Thesis deals with a series of theoretical investigations, based on com-putational techniques, aimed at obtaining a fundamental understandingof the structure properties of a metastable alumina phase, -Al2O3. The

theoretical method used investigates the properties of solid materials from aquantum-mechanical, first-principles, point of view. In other words, it uses ap-proximation methods to solve the Schrodinger equation (SE), which is the equa-tion governing the microscopic world (atoms and electrons), for the many-particlesystem of valence electrons in a material. This is done without resorting to any

input information other than the atomic numbers of the atoms and their posi-tions in space. The method used is the density-functional theory (DFT), whichhas shown an impressively good accuracy and predictive power over the last thirtyyears.

However, such a method would not be applicable to large-scale and complexsystems like real, technologically important, materials without the help of ad-vanced computational resources. Even with the powerful help of the DFT, thesolution of the SE for as large a system as the 1023 electrons per cm3 of a realmaterial still requires an impressive computational power. This is available to-day thanks to the combination of increasingly sophisticated algorithms with the

perfomance of massively parallelized supercomputers. As a comparison of theincredibly fast advances in this field, it can be considered that the calculationsperformed in Paper I and II of this Thesis needed of the order of half a year tobe carried out at the time of those investigations. Today, the same project wouldbe achievable in a couple of months, under normal computer-usage conditions.At the same time, the investigations performed in Papers IIIV would have beenunthinkable of at that time.

Therefore, one aim of this Thesis is the demonstration of todays applicabilityof DFT-based methods for complex and technologically relevant materials.

A second aim is the investigation of the -Al2O3 structure from an atomistic

point of view. There are mainly two motivations for this. The first one is to

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2 Carlo Ruberto, Metastable Alumina from Theory

gain a deeper and more detailed understanding of this material, used as wear-resistant coating on cemented-carbide cutting tools. This aim actually originatedthe project, thanks to the contact with one of the industrial partners of our Ma-terials Research Consortium, Sandvik Coromant AB. This application of-Al2O3is described in more detail in Sec. 2.3. Although -Al2O3 had been used for overtwenty years as a chemical-vapor deposited (CVD) coating for wear-resistant cut-ting applications, all knowledge was based on empirical studies. These, however,were hampered by the difficulty in probing the atomic structure of the material,due to its poor crystallinity, its metastability, and the difficulty in producing suf-ficient amounts of pure-phase samples. Therefore, the exact atomic structure ofthe material was unknown, even though a large number of experimental attemptshad been performed. Thus, the goal was to (i) determine the atomic structure of

-Al2O3 and (ii) to use that information to gain more knowledge on the propertiesof this alumina phase, especially of those relevant for the cutting-tool application.In particular, a better understanding of the mechanisms lying behind the CVDgrowth of -Al2O3 would provide useful information for the cutting-tool manu-facturers, most notably Sandvik Coromant AB and Seco Tools AB, two Swedishcompanies that are world leading in the production of cemented-carbide cuttingtools. The aim is to optimize the production process of these coatings and toincrease their reliability. In the appended Papers I and II, we solve the questionof the atomic structure of -Al2O3 through a combination of DFT-based com-putational methods and experiments. Thereafter, Papers III and IV deal with

the investigation of the surface structure and properties of the (001) and (001)faces, believed to be the preferred growth directions of CVD -Al2O3. Finally, inPaper V, a study is performed on the thermodynamics of the first stages of thenucleation of -Al2O3 on a TiC(111) surface, known to be a preferred surface forCVD -Al2O3 nucleation.

The second motivation for studying -Al2O3 is provided by the general interestin alumina, from both a technological and a fundamental point of view. Techno-logically, the aluminas are highly important materials. As ceramics, they have awide range of applications wherever extreme mechanical, thermal, and chemicalstabilities are required. They are wide-band-gap materials, making then excel-

lent as substrates in electrical and elctronic applications. At the same time, theincredible structural flexibility of alumina provides a large variety of differentphases, with individual properties. For example, the metastable and phasesare characterized by high porosity and surface activity, making them good cat-alysts and catalyst supports in, for instance, catalytic converters in our cars.However, like for -Al2O3, very little is known on these metastable phases at theatomic level, mainly due to the lack of uncontroversial information about theiratomic structures. At the same time, from a more fundamental point of view, thealuminas are fascinating materials that provide high challenges for experimentaland theoretical studies and puzzle because of their incredible structural flexibility.

It is believed that the presence of tetrahedrally coordinated Al atoms in the


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Chap. 1: Introduction 3

atomic structures, as well as a high ionic bond character, are common to mostmetastable alumina phases. Thus, a study on the stability of a metastable alu-mina like -Al2O3 can yield general insight into the stability effects of tetrahedralAl ions for the alumina structures. A large part of the emphasis in this Thesisis put on stability comparisons between different structural configurations andcandidates for the -Al2O3 systems. Throughout the investigations, extensiveuse is made of intuitively appealing models for describing the bulk, surface, andgrowth stability of a highly ionic crystal like -Al2O3. In this way, the extent ofthe applicability of such models for an efficient description of the stability of thismaterial is put to the test.

The third major aim of the Thesis is the general investigation of the factorsaffecting the stability of bulk, surface, and growth of ionic crystals. Being a

highly ionic material with relatively low symmetry and complex atomic structure,-Al2O3 works excellently as a prototype for probing the structural properties ofmore complex ionic crystals. In particular, the validity of intuitive stability ruleslike Paulings rules (for bulk stability) and Taskers rules (for surface stability)are examined and put to the test. In general, we found that the lower symmetryof more complex structures like -Al2O3, having a mixture of different cation andanion coordinations, makes simple point-charge models insufficient in describingthe effects arising from the asymmetry in charge distributions.

The Thesis is organized as follows. In Chap. 2 the alumina phases are de-scribed, starting from a historical background of the vast human interest in these

materials, giving a summary of their variety of applications, and then describingin more detail the known information on bulk and surface structures of the stablephase of alumina, -Al2O3, followed by a similar description for the metastablealuminas. Finally, a section describing the application of alumina as a CVDcoating on cutting tools is included, providing the technological background formy work. In this section, an introduction to the TiC bulk and (111) surfacestructures is also given, as a preliminary to Paper V.

In Chap. 3 a review of the theoretical picture of bonding in ionic crystals isgiven. The emphasis is on the more empirical, classical, rules for bulk and surfacestability formulated by Pauling and Tasker, respectively, since these are widelyreferred to in the appended Papers.

Chapter 4 gives a somewhat detailed description and explanation of the DFT-based method used to study -Al2O3. First, the groundwork of the DFT ispresented and derived. Thereafter, the implementation of the DFT used here,the plane-wave-pseudopotential method, is explained. Finally, some explanationsare given on how the results obtained from the DFT calculations are used andanalyzed to obtain the desired information on atomic and electronic structures.The aim of Chap. 4 is to provide even the non-expert physicist with a grasp ofwhat DFT is about and on how it can be succsfully applied. Finally, Chap. 5sums up the results from the five appended Papers, giving the general conclusionsobtained from this work.


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CHAPTER 2

Alumina

Aluminum oxide and its hydrates present a variety of amaz-ing contrasts. From the hardness of the sapphire to a soft-

ness similar to that of talc, from an apparent density of over200 pounds to one of about 5 pounds per cubic foot, fromhigh insolubility and inertness to ready solubility in acidsor alkalies and marked activity, the properties can be var-ied over wide limits. Some forms flow and filter like sand;

others are viscous, thick, unfilterable, or even thixotropic.Crystals may be of any size down to a fraction of a micronin diameter, with various allotropic forms, and there are also

amorphous forms. Some varieties have a very high adsorp-tive power, others none at all. Some are catalytically active,others inactive. But they are all converted into-alumina(corundum) if heated hot enough and long enough.

Francis C. Frary, Director of Alcoa Research Laboratories,in Adventures with Alumina (1946) [1]

Aluminas are ceramic materials of extremely high technological importancethroughout the history of humankind. Various aluminous minerals com-monly found in nature are known and used since ancient times: for exam-

ple, the Bible mentions a stone called shamir that was probably emery (-Al2O

3mixed with iron oxides and other minerals), a natural abrasive still in use today;people in Mesopotamia were making fine pottery from a clay consisting largelyof an aluminum compound already before 5000 B.C.; sapphire (-Al2O3 conta-minated with iron and titanium) and ruby (-Al2O3 with chromium) have beenhighly prized as gemstones since about 800 B.C. [2].

The earliest known reference to an aluminum compound is from 425 B.C.,when alumen (latin, plural form: alumina) is mentioned by Herodotus. TheRomans used the word for materials with a styptic or astringent taste, whichprobably consisted of impure forms of alum and aluminum sulfate. Pliny gave

A colorless soluble hydrated double sulphate of aluminium and potassium used in the

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descriptions of alum and of its use as a mordant for dyes in about A.D. 80. In1786, de Morveau [4] suggested the name alumine for the base of alum, which inEngland was anglicized to alumina [5]. In 1799, Greville [6] described a mineralfrom India with the composition Al2O3 and named it corundum, believing itto be the native name of the stone. From alumina, the word aluminum wascoined by the English chemist Humphry Davy in 1807 after he had verified thatalumina has a metallic base, which was successfully produced first in 1825 by theDane Hans Christian rsted, however. The word was kept in the United Statesbut modified to aluminium in many other countries [2, 7, 8].

Today the word alumina is used rather indefinitely and can in the literaturebe found to denote anything from the group of all aluminous materials takentogether to the particular group of aluminum-oxide phases, sometimes including

also aluminum hydroxides, or only the specific -Al2O3 [5]. In order to avoidmisinterpretations, I reserve here the term alumina for only compounds usuallyattributed the chemical formula Al2O3, even though, as described below, it is notentirely certain that all of them are anhydrous.

One of the reasons for the vast technological importance of alumina is theabundancy of aluminum (Al), making up 8.1% of the earths crust. Only oxygenand silicon are more abundant [2]. Also, aluminas are believed to have relativelylow bioreactivity: Aluminas are usually poorly absorbed in the human body afteroral ingestion, and inhalation of alumina particles has been shown to have littlelung damage at the doses usually occurring in normal human activity [9].

Aluminas are most often produced through thermal treatment of aluminumhydroxides, which are commonly found in nature. The most important aluminumore, containing mainly aluminum hydroxides, was discovered in 1821 near LesBaux in southern France and later named bauxite. Large deposits of bauxiteare today known in almost all parts of the world and can supply the world withaluminum and aluminum oxides for hundreds of years at present production lev-els [2]. However, -Al2O3 can also be found directly in nature in the form ofcorundum, emery, or sapphire. Furthermore, alumina can be produced directlywith various other techniques, for example, amorphous alumina by anodizationof aluminum in acid solution [10] and alumina coatings of varying phase composi-

tion by industrial chemical-vapor deposition (CVD) or physical-vapor deposition(PVD) [11, 12, 13, 14, 82, 96] (See Sec. 2.3). On the other hand, direct oxida-tion of aluminum yields only a very thin layer of aluminum oxide, which actuallyprotects aluminum metal from further oxidation, preventing its corrosion.

Confusion exists regarding the terminology for the aluminum hydroxides, re-flecting the long history of human interest in them and the relatively recentattempts at categorization. For instance, different chemical nomenclatures havebeen defined. In the following, I give the Alcoa nomenclature (generally used in

manufacture of mordants and pigments, in dressing leather and sizing paper, and in medicine asa styptic and astringent. Formula: K2SO4Al2(SO4)3 24H2O. (Collins English Dictionary[3])


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Chap. 2: Alumina 7

Al O3 2Al(OH)3Al O3 2 Al O3 2

Gibbsite

Al O3 2 Al O3 2Al O3 2Al O3 2Boehmite AlOOH

Al O3 2Al O3 2 Al O3 2

Al O3 2 Al O3 2

Al O3 2

Al O3 2

AlOOH Al O3 2

2 3Al O2.25Al O H O3 Al O3 2Al O3 2

Al O3 2Al O

3

2Al O /

3

2Al O

3

2

Al O3 2Al O3 2

Al(OH)3/

o500 C o1000 C

Diaspore

BayeriteAl(OH)3

(fast

Tohdite

Amorphous/Melt

dehydration)

Al O32 /

CVD

PVD/CVD?

Figure 2.1: Commonly accepted transition sequences of the aluminas from the hy-droxides to corundum (-Al2O3) during thermal treatment. Enclosed areas indicatetemperature range of stability. Temperatures are approximate and depend, as well as

the sequences, on degree of crystallinity, heating rates, impurities, moisture, alkalinity,thermal history of the material, etc. Data collected from Refs. [8, 10].

America), followed by the Haber (commonly used in Europe) nomenclature. Fora fuller description, see Ref. [5]. The two most common aluminum trihydroxidesare gibbsite (or hydrargillite) (-Al2O3 3H2O or -Al(OH)3) and bayerite(-Al2O3 3H2O or -Al(OH)3). Gibbsite is commonly found in nature, mainlyobtained from bauxite by the Bayer process. Bayerite is only rarely found in na-ture, but can be prepared synthetically in a number of ways. The most commonaluminum monohydroxides are boehmite (-Al2O3H2O or -AlOOH) and di-aspore (-Al2O3H2O or -AlOOH), both found in nature as major constituentsof bauxite deposits around the world. Boehmite can also be easily produced in

the laboratory. Yet another hydroxide, which is obtained synthetically, is to-hdite (chemical formula 5Al2O3H2O, no Alcoa or Haber nomenclature exists forit), first described in 1951 by Houben [15], and later confirmed by Torkar andKrischner [16] and Yamaguchi et al. in 1964 [17].

Dehydration of the aluminum hydroxides by thermal treatment produces aseries of transition aluminas, designated as oxides, although it is not certainthat all are anhydrous. The term transition rather than metastable reflectsthe fact that the phase transition between them is irreversible and occurs onlyon increasing the temperature. The name activated aluminas is also found inthe literature, reflecting the higher chemical activity of these forms. The final

product of the dehydration (calcined alumina), independently of start product,


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is always -Al2O3, in more or less (99.099.99%) pure form. The phase is stablefrom 0 K temperature up to its melting point at 2040C. Figure 2.1 summarizesgraphically the transition sequences that are generally accepted. Note, however,that the transition sequences and temperatures depend strongly on degree ofcrystallinity, heating rates, impurities, moisture, alkalinity, the thermal historyof the material, etc. A review of transition sequences can be found in Chap. 5 ofRef. [8].

The use of greek letters to denote the different phases of alumina and alu-minum hydroxide was introduced by Haber in 1925 for the phases then known[18]. The letter was used for corundum, while -Al2O3, originally introducedrather vaguely by Ulrich in 1925 [19], was generally used to denote any transitionphase obtained at low temperatures or in the oxidation of aluminum. In 1935

Hagg and Soderholm [20], and Verwey [21] applied the name to the spinel struc-ture of alumina. The Alcoa system of nomenclature was introduced by Frary,who in 1946 [1], and later Stumpf et al. in 1950 [22], examined the X-ray diffrac-tion patterns obtained during the dehydration processes, identifying five differentalumina phases, which they called , , , , and . Also, Stumpf gave a moreprecise definition for -Al2O3. Since then, several more alumina phases have beenreported: and [23], [24], [25], [26], [27], [28], and [29].

In addition, the designation -Al2O3, assigned by Rankin and Merwin in1916 [30], has been preserved, although it was subsequently shown [31] that -Al2O3 in reality contains alkali or alkaline earth atoms, and should therefore not

be considered an alumina phase. Also, the designation -Al2O3 can be found,although its actual chemical composition is Li2O5Al2O3. Two reduced forms ofalumina are also known, Al2O and AlO, but they have no special designation.For a more thorough account of the history of alumina nomenclatures, as well asof preparation processes, see, e.g., the classic review by Gitzen [5], or the morerecent reviews by Misra [8] and Hart [32].

Thanks to this impressive structural flexibility, the number of applicationsof alumina is enormous and steadily growing. Aluminum oxides and hydroxidescan be found literally everywhere in our everyday life: in toothpaste, porcelainbathtubs, spark plugs, catalytic converters in our cars, condensers and microchips

of our TV sets, in microwave ovens, dental and bone implants, in the paper ofbooks and magazines, in gemstones, glass, whiteware, and fine china, only tomention some. In particular, the stable phase has an extremely high hard-ness (closest to diamond among the naturally occuring abrasives), high meltingpoint, high electrical resistivity, low chemical activity, and special optical prop-erties, making it, for instance, an excellent inert substrate (for, e.g., integratedcircuits and catalysts), protective coating (on, e.g., refractories, cutting tools,space ships), abrasive (in, e.g., polishing compounds), ceramic (in, e.g., white-ware, fine china, porcelain insulators, spark plugs, glass), bioceramic (in boneand dental implants), gemstone (in sapphire and ruby). A thorough review of

the many applications of (or calcined) alumina can be found in Ref. [32].


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Chap. 2: Alumina 9

The transition aluminas are characterized by a relatively high thermal sta-bility, a high surface area and porosity, and varying degrees of chemical activity.They are therefore widely used as adsorbents (gas or liquid drying, water pu-rification, desiccants), catalysts (alcohol dehydration, Claus catalysis), catalystsupports with an active role in the catalysis process (dehydrogenation, hydrore-fining, automobile catalytic converters). See Refs. [8, 7] for a more thoroughreview. Also, recently the discovery of techniques for growing layers of differ-ent alumina phases by CVD on cemented-carbide cutting tools has opened up amajor new field of application. Especially -Al2O3 coatings can be favored over-Al2O3 in some cutting-tool applications, despite the metastability, because ofsmaller grain size, epitaxial growth, and lower density of pores. Last but notleast, alumina is the starting point in the production of metal aluminum.

Yet, basic knowledge of the aluminas is limited. In particular, knowledge ofmost transition-alumina structures is still lacking. To date, only the stable phase and the metastable and structures are well-established. The reason forthis is mainly in the relatively complex structural arrangements, together withtheir large variety. Several transition aluminas, for example, are reported to havea disordered Al-sublattice structure (, , , ). For others (, ), even theform of the crystal unit-cell is controversial. Also, the presence of hydrogen inthe structure has not been inequivocally ruled out for all unknown structures:for instance, for -Al2O3 there have even been a large number of contradictoryresults published over the years [33].

This lack of knowledge renders accurate and predictive theoretical studieson the properties of the transition aluminas difficult to perform. At the sametime, experimental investigations are difficult to perform due to the metastabil-ity, the difficulty of producing sufficient amounts of pure-phase samples, the lowcrystallinity of the samples, and their high surface area.

Theoretically, reliable calculations on the aluminas are made difficult by theinability of simple semi-empirical methods to treat the small energy differencesoften occuring between the many and similar structural possibilities. For in-stance, it has been shown that without the inclusion of quadrupole effects noteven the right lowest-energy structure is predicted for alumina, with a never-

observed bixbyite structure being energetically more favored than the corundumstructure [34]. Due to this fact, accurate and fundamentally sound methods areneeded in order to obtain the information necessary to make reliable studies. For-tunately, today first-principles methods are available to give full account of theversatility of the ion-electron system. However, the relatively low symmetry ofthe transition aluminas, having unit cells with a large number of atoms, has fora long time made first-principles methods on the aluminas computer-demanding

Oxidation of H2S to sulfur and water, aimed at removing the emission of sulfur compoundsfrom natural-gas plants and petroleum refineries.

For instance, production of butadiene, used for synthetic rubber, from n-butadiene.

Hydrodesulfurization, denitrogenation, demetallation.


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and thus of limited applicability. Even for alumina, having only ten atoms in itsunit cell, reliable comprehensive studies on surface effects have long been at theedge of state-of-the-art methods and computational possibilities. Long-rangingeffects and deep relaxations make cluster models insufficient for accurate investi-gations. Even slab calculations need supercells of at least nine atomic layers toyield a complete description of surface effects [35].

Our work on the bulk-structure determination of-Al2O3 (Papers I and II) isthe first determination of a transition-alumina structure by first-principles the-oretical methods. The use of first-principles methods to study the metastablealuminas has in fact only in recent years reached the level of computational powerneeded to perform such tasks, thanks to the combination of efficient theory, im-provement of computer power, including parallelization, and development of more

efficient algorithms.In the remainder of this Chapter, I review the existing information on the

stable and the metastable alumina phases, relevant for our investigations on bulkand surface structure and stability of the metastable -Al2O3. In Sec. 2.1, thebulk and surface atomic and electronic structures of -Al2O3 are described, bothfrom the existing literature and from our DFT calculations. An introductionto the existing work on the clean and unreconstructed -Al2O3(0001) surfaceis provided, as an introductory background to our work on the more complex,but somewhat similar structurally, -Al2O3(001) and (001) surfaces. In Sec. 2.2,the same is done for metastable aluminas: the known information on their bulk

structure is reviewed, with emphasis on the technologically important -Al2O3.Some considerations on how our results on -Al2O3 are generally relevant formetastable phases are made. Finally, in Sec. 2.3, an introduction to the use ofalumina as a CVD coating on cutting tools is given, providing the background andtechnological motivation for our focus on -Al2O3 and our work on the growth ofalumina on TiC(111). A review of existing information on the clean and oxygen-covered TiC(111) is also included, in order to give the background material neededfor our growth investigation.


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Chap. 2: Alumina 11

SECTION 2.1

Alpha Alumina

The only alumina phase for which atomistic knowledge was well developed priorto our study is the stable phase. As for all aluminas, the interest in -Al2O3 hasbeen high, due to the large variety of applications. Compared to the metastablealuminas, however, the phase is more easily studied, thanks to its high stabil-ity, spontaneous occurrence in nature, good crystalllinity, and relatively simpleatomic structure.

In this Section, the known information on atomic and electronic bulk andsurface structures of -Al2O3, relevant for our work, is reviewed and compared

to our DFT calculations on -Al2O3.

2.1.1

Bulk Structure

The crystal structure of -Al2O3 was determined in 1925 by Linus Pauling andSterling Hendricks [36], only eight years after the X-ray powder diffraction methodfor structure determination was introduced by the Braggs. The unit cell is rhom-bohedral, composed of two Al2O3 molecular units (i.e., 10 atoms). The structureis more easily visualized, however, with a trigonal unit cell, that is, a hexagonal

coordinate system, composed of six molecular units (30 atoms). A summary of itscrystallographic specifications is given in Table 2.1, where the experimental struc-tural parameters are compared with those obtained by our DFT-LDA and GGAoptimization of the bulk structure (with the method described in Sec. 4.3.1). Itcan be seen that both methods are very accurate. However, the well-known ten-dency of the LDA to overbind is noticed, with lattice parameters approximately1% lower than experiments. On the other hand, the GGA (PW91) yields resultsslightly higher (1%) than the experimental ones.

The structure (see Fig. 2.2) is easiest described as an almost close-packedABAB stacking of oxygen ions in planes that are perpendicular to the [0001]

direction (the c axis of the hexagonal coordinate system). The smaller aluminumions occupy 2/3 of the six-foldly coordinated interstital sites present between theoxygen layers. A six-foldly coordinated site (i.e., one having six nearest-neighbor(NN) O ions) is also called an octahedral site, reflecting the fact that the NN Oions form the vertices of an octahedron that surrounds the Al ion. In each layerthe Al ions arrange themselves in one of three types of hexagonal network, whichdiffer in the position of the vacant octahedral site (, , or in Fig. 2.2). Thehexagonal networks in successive Al layers are shifted laterally by one octahedralsite, such that their stacking sequence along [0001] is . If the romanletters A and B denote the stacking type of the oxygen layers, a layer of octahedral

sites between a double AB oxygen layer is denoted by the stacking letter C (in


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Chap. 2: Alumina 13

a hexagonal close packing there are three different stacking possibilities: A, B,and C). To differentiate between O and Al planes, capital letters are used for Oand lower-case ones for Al [39]. Hence, all Al layers are in stacking type c, andI adopt the convention of using superscripts, , , or , to denote the vacancyposition in each layer. With this notation, the -Al2O3 structure of one trigonalunit cell can be described by the stacking sequence AcBcAcBcAcBc along[0001].

The Al ions in each layer are in reality slightly displaced along [0001] relativeto one another, so that each Al layer is actually composed of two Al sublayers.This is due to the high ionic character (see Sec. 2.1.2) of the material, whichgives rise to an electrostatic repulsion between the positively charged Al ions inneighboring layers. As can be seen in Fig. 2.2, due to the hexagonal arrangement,

every Al ion has one NN Al directly above (or below) in one of the two neighboringlayers, and a vacant site in the opposite layer. Since the Al ions are in octahedralcoordination, they have no O ions directly above or below that can screen theirpositive charge from the Al ion in the neighboring layer. Another way to describethe same thing is to say that the coordination octahedra of the two Al ions haveone face in common (the O triangle in the O layer in-between). Whenever sucha face sharing between cation polyhedra occurs, the overall stability of the ioniccrystal is lowered, due to the increased electrostatic repulsion between the cations.This is in fact part of the content of Paulings third rule for ion-crystal stability, asdescribed in Sec. 3.1.2. In the case of-Al2O3 this destablization gives rise to two

different AlO distances: 1.89 (1.87) A in the direction toward the neighboringAl vacancy and 1.93 (1.99) A in the direction toward the neighboring Al ion.The numbers are those given by Wyckoff [40], while the values in parenthesesare those obtained by our DFT-GGA optimization of the bulk structure. Also,the AlAl repulsion distorts the octahedra, shortening the edges of the sharedoctahedra faces to approximately 2.50 A, in contrast to the ideal OO distanceof 2.80 A predicted by Paulings [41] and Shannons [84] empirical ionic radii.

2.1.2

Electronic Structure

The electronic structure of bulk -Al2O3 has been amply studied, both experi-mentally [43, 44, 45] and theoretically [43, 46, 47, 48, 49, 50, 51, 52, 53]. Figure 2.3shows the local density of states (LDOS), projected onto atomic s and p orbitals,for the valence-electron states, as obtained from our first-principles DFT-GGAcalculations (see Sec. 4.3.2).

The LDOS shows the existence of a very large band gap between the filledupper valence band, dominated by O 2p orbitals, and the empty conduction band,dominated by Al 3s and 3p orbitals. As discussed in Sec. 3.1.1, this shows thebonding in bulk -Al2O3 to be highly ionic, with only little covalent character.

This can also be seen from the calculated DFT charge densities. Use of the


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20 10 0 100

2

4

6

8

10O

EEF [eV]

DOS[states/(eVc

ell)]

sp

20 10 0 100

0.2

0.4

0.6

0.8

1Al

EEF [eV]

Figure 2.3: Local density of states (LDOS) for bulk -Al2O3, as obtained from ourDFT-GGA calculations, projected on atomic s and p valence orbitals for O and Al.

Note the different scales for O and Al LDOS.

25.0

20.0

15.0

10.0

5.0

0.0

5.0

10.0

25.0

20.0

15.0

10.0

5.0

0.0

5.0

10.0

Z L FQB Y

zk

Q

ky

F

B

L

kx

Y

Q

F

ZB

Figure 2.4: Valence band structure, as ob-tained from our DFT-LDA calculations, forbulk-Al2O3. The Bruillouin zone for the

rhombohedral unit cell is shown above. Thelabeling of symmetry lines and points follows

the notation of Ref. [42].


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Chap. 2: Alumina 15

method described in Sec. 4.3.2 to integrate the DFT-GGA charge density aroundeach atom yields high ionicities, with valencies of +2.78 and

1.85 for Al and O,

respectively. This is in good agreement with a previous theoretical estimate byChing and Xu [51], yielding +2.75 and 1.83, respectively.

Figure 2.4 shows the band structure obtained from our DFT-LDA calculationon -Al2O3. As can be seen, the band gap is almost direct, only slightly shiftedfrom the point, in good agreement with the experimental result of French[43]. However, it is a well-known fact that DFT in LDA and GGA consistentlyunderestimates the magnitude of the band gap. The experimental value for -Al2O3 is, in fact, 8.8 eV [43], while our LDA value is 6.6 eV.

Figure 2.4 shows that the top of the valence band is flat, meaning that thevalence electrons are very tightly bound to the oxygen ions and have very high

effective masses. On the other hand, the conduction bands show a large curvature,especially at the point, indicating a good mobility for electrons if they only couldbe excited across the wide band gap. The calculations of Xu and Ching [48] yield,in fact, effective electron masses as low as 0.16 me.

2.1.3

Surface Structure

The surface properties of the alumina phases are essential for their high techno-logical applicability. In particular, -Al2O3 is often used as substrate material,

catalyst support, or corrosion- and wear-resistant coating. More generally, be-cause of its relative simplicity, -Al2O3 has been chosen as a prototype materialfor understanding the surface properties of complex oxides with high ionic char-acter. Also, study on -Al2O3 has been considered to be the first step towardestablishing an understanding of the surface properties of aluminas in general.

Thus, many studies have been conducted on the different -Al2O3 surfaces,both by theory and experiment. The three most important corundum surfacesare the basal (0001) plane, the pyramidal (1012) plane, and the prism-diagonal (1120) plane. Most often, the corundum planes are denoted withthe hexagonal basis vectors. For a list of other corundum planes as well asmineralogical and trigonal-cell notations see, for example, Ref. [54].

Most theoretical investigations have concentrated on the basal plane, (0001).Although not a natural cleavage plane, this surface can be produced by cutting,polishing, and annealing. It is the easiest surface to visualize, the cut occurringparallel to the close-packed Al and O planes. Depending on annealing tempera-ture, LEED patterns for -Al2O3(0001) have been observed in a variety of differ-ent reconstructions. In ultrahigh vacuum, they include (1 1), (3 3)R30,(2

3 23)R30, (33 33)R30, (31 31)R9, in order of increasingannealing temperature [55, 56, 57].

Equivalent to (0112) and (1102).

Equivalent to (1210) and (2110).


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AluminumOxygen

A

B

A

B

A

B

A

[0001]

[110]

[0001]

AlAl

O OO

AlAl

O O O

AlAl

O O O

Al

O

(0.85 )

(0.84 )(0.51 )(0.84 )

(0.86 )

O

(0.89 )

(1.02 )(0.27 )(0.88 )(0.12 )85%

+0.2%

AlO

0.7%

+3.0%0.8%

+1.3%7.1%+4.8%

+20%45%+3.2%

(0.46 )

Al

O O OAl

Al

O O O

AlAl

OOO

AlAl

O O O

Al

(0.85 )

(0.85 )(0.49 )(0.85 )

(0.85 )(0.49 )(0.85 )

(0.85 )(0.49 )(0.85 )

(0.85 )

repeat

unit

Unrelaxed: Relaxed:

Figure 2.5: Non-polar surface structure of unreconstructed-Al2O3(0001), before and

after relaxation, according to our DFT-GGA calculations. The atomic layers perpendic-ular to [0001] are shown, together with interlayer distances. The relaxation magnitudeis given in percentages. The non-polar repeat unit for building the surface is shown.

The pyramidal (1012) surface is the usually observed cleavage plane of crystalswith corundum structure, presumably because of the fact that it intersects severalof the vacant cation positions, thus requiring fewer bonds to be broken. However,while Cr2O3, Ti2O3, and V2O3 all cleave excellently along (1012), this is not thecase for -Al2O3 or -Fe2O3. Polished -Al2O3(1012) surfaces can be preparedeasily by annealing in air or vacuum. The prism-diagonal (1120) surface has

received less attention, even though it has been used as a substrate for silicon,due to its close epitaxial match with Si(111).

Here, I will focus on the unreconstructued (0001)(1 1) surface, which hasbeen the subject of most theoretical and experimental studies. It is the surfacemost close to -Al2O3(001), which is the preferred growth direction of -Al2O3during CVD.

The (0001)(1 1) surface is reported to be stable up to at least 1000C [57].Although it has been the subject of theoretical studies for at least 15 years,only very recently has a clear consistent picture, in agreement with experiments,started to appear. A number of different terminations are possible, all of which

have exclusively O or Al atoms in the outermost layer, as can easily be seen bylooking at Fig. 2.2. Due to the high ionicity, this implies that all terminations arenominally polar (see Sec. 3.2), except for the one obtained by cutting the bulkstructure in-between two Al sublayers. According to Taskers rules [61], onlynon-polar surface terminations are stable. The surface obtained by a cut in the amiddle of an Al layer corresponds to a Tasker-type-II termination, which is nonpolar thanks to the symmetrical distribution of charges in the repeat unit (seeFig. 2.5). Of course, this assumes a fully ionic, point-charge, situation, wherethe ions have full charges, Al3+ and O2. This cut leaves half an Al layer on topof both (0001) and (0001), which are thus equivalent, thanks also to the (0001)

mirror symmetry of bulk -Al2O3.


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Chap. 2: Alumina 17

Early theoretical attempts on the unreconstructed (0001) surface were per-formed with semi-empirical methods [47, 58, 59, 60]. Both Tasker (1984) [61]and Mackrodt et al. (1987) [59, 60] compared the energies of different, unrecon-structed, -Al2O3 surfaces, before and after relaxation. They only considerednon-polar surface terminations. While Mackrodt et al. conclude that (0001) haslowest energy after relaxation, Taskers results show the lowest-energy relaxedsurface to be the pyramidal (1012). Both point out the importance of relaxationeffects, which considerably lower the surface-energy values, in some cases by morethan 50%. Mackrodt et al. comment on the remarkably large surface relaxationof (0001), with changes of59% (AlO), +2% (OAl), 49% (AlAl), +26%(AlO), +8% (OAl), and 4% (AlAl) for the top interlayer distances. Tasker,on the other hand, sees only modest structural changes, involving mainly small

perpendicular relaxation.Subsequently, the Hartree-Fock calculations of Causa et al. (1989) [62] and

Mackrodt (1992) [60] yielded similar inward surface relaxations (53% and 49%,respectively) for the top (0001) AlO layers as the semi-empirical result of Mack-rodt et al. However, the relaxed surface energy of Causa et al. (5.32 J/m2)disagrees considerably with that of Tasker (2.97 J/m2), which is in some agree-ment with both the semi-empirical (2.03 J/m2) and the Hartree-Fock (2.00 J/m2)results of Mackrodt et al. On the other hand, the unrelaxed surface energy is ingood agreement (6.53 J/m2 for Tasker, 5.95 J/m2 for Mackrodts semi-empirical,and 6.72 J/m2 for Causa), except for Mackrodts Hartree-Fock, yielding 3.20

J/m2. Causa et al. also studied the prism (1010) surface, which obtainedslightly higher relaxed energy than (0001), in contrast to Taskers result, andconsiderable structure relaxation.

The possibility of a different surface termination than the one predicted byTaskers rules was first addressed by Guo et al. (1992) [63] in a first-principlescluster investigation. They calculate the (0001) energies of separation (that is,the sum of the energies of the two (0001) and (0001) surfaces obtained afterbulk-structure cut, see Sec. 4.3.3) for cleavage in-between the Al sublayers (A)and between an O and an Al plane (B). However, they do not consider thepossibility of a surface terminated with a partially filled O layer nor do they

include relaxation effects. They obtain values of 7.4 J/m2

for termination type Aand 14.0 J/m2 for type B, in agreement with Taskers rules. They also examinethe pyramidal (1102) surface in the same way, obtaining a value for the energyof separation of 5.9 J/m2 for the unrelaxed lowest-energy termination, again inagreement with Taskers rules.

In another study, Blonski and Garofalini (1993) [64] use molecular-dynamicssimulations to compare the surface energies of different terminations of the basal(0001), of the prism-diagonal (1120), and of the prism (1100) faces, includingrelaxation. Also these results are in agreement with Taskers rules. After relax-ation, the obtained surface-energy values are 2.04 or 2.19 J/m2 for the most-stable

(0001) termination, depending on the position of the surface Al atoms. This is


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lower than the values that they obtain for the (1120) (2.27 J/m2) and the (1100)(2.35 J/m2) faces, indicating a higher stability for the (0001) surface. Again,however, the possibility of a (0001) surface terminated with a partially filled Olayer is not considered.

In 1993, the first DFT slab investigation, by Manassidis et al., appeared, firston only (0001) [65] and later on the rhombohedral (1011), pyramidal (1012),prism (1010), and prism-diagonal (1120) planes as well [66]. Their results show alowest relaxed energy for the prism (1010) surface (1.40 J/m2), with (0001) onlyslightly higher (1.76 J/m2). However, due to computational limitations, only twooxygen layers are used for the (1010) slab, while three oxygen layers are deemedsufficient for the (0001) slab. Only the terminations predicted by Taskers rulesare considered. The (0001) and (1010) surfaces are also the only ones to show

a considerable structure relaxation. For (0001), the top interlayer relaxationsare 86% (AlO), +3% (OAl), 54% (AlAl), and +25% (AlO). The (0001)surface energy decreases from 3.77 to 1.76 J/m2 during relaxation. Also, theDFT charge-density plots show a high ionicity of the surface region of the slab,comparable to that of the middle atomic layer.

At the same time, Godin and LaFemina (1994) [67] used a non-self-consistenttight-binding method to investigate the effects of relaxation on atomic and elec-tronic structures of the (0001) surface with half-Al-layer termination. Their topinterlayer relaxations are approximately 88% (AlO), 0% (OAl), +20% (AlAl), and 0% (AlO). A slab of six O layers is used. The electronic structure for

the unrelaxed surface shows the presence of an empty band-gap surface state, ap-proximately 1 eV below the bottom of the conduction band and of Al 3pz and 3scharacter, and of a filled surface state 1 eV below the top of the valence band,of O 2p character. After relaxation, the authors argue, the surface Al atoms,becoming almost coplanar with the surface O, rehybridize into sp2 arrangements,causing the two surface states to mix. This pushes the empty state up into theconduction band and lowers the energy of the filled one. Also, a deeply lying O 2ssurface state mixes with orbitals on the subsurface Al atoms, lowering its energy.In addition, the authors argue that the large inward relaxation is made possibleby the open character of the -Al2O3(0001) surface, which allows the surface Al

atoms to become coplanar with the O atoms while approximately conservingnear-neighbor bond lengths.

A self-consistent tight-binding study was later performed by Gautier-Soyeret al. (1996) [68], aimed at better comparing the surface electronic structure of(0001) before and after relaxation. It shows that at the unrelaxed surface thereis an enhancement of AlO charge transfer, compared to the bulk, that is, theAlO bond is more ionic than in the bulk. This is shown to lead to a decreaseof the surface band gap through the appearance of a surface state 2 eV belowthe conduction-band minimum, of mainly Al 3s character with participation ofAl 3p and O 2p and 2s. After relaxation, the band gap at the surface Al/O layer

is restored to the bulk value, through a decrease of surface AlO charge transfer.


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20 10 0 100

0.1

0.2

Unrelaxed

20 10 0 100

5

20 10 0 100

5

20 10 0 100

5

20 10 0 100

5

20 10 0 100

0.5

20 10 0 100

0.5

20 10 0 100

0.5

20 10 0 100

0.5

[0001]

p

z

E E [eV]F E E [eV]F

p

O s

DOS[states/(eVc

ell)]

layerone

layertwo

layerthree

layerfour

surface Al

Al

pxy

Figure 2.6: Local density of states (LDOS) from our DFT-GGA calculation on the

unrelaxed-Al2O3(0001) surface. The LDOS for the top four surface layers (repeatunits) are shown, projected onto atomic s and p valence orbitals. The picture in theupper right corner shows the LDOS for only the surface Al atoms, projected ontovalencepxy andpz orbitals.

to obtain a good description of the relaxation effects.Figures 2.6 and 2.7 show the surface LDOS, before and after relaxation, re-

spectively, obtained from our DFT-GGA calculations. For the unrelaxed (UR)surface (Fig. 2.6), a surface state (SS) can be seen just above the Fermi energy(EF), of Al s, Al pz (as shown in the inset), and O pz (not shown) character. Thedistance between the peak of this SS and the bottom of the conduction band isapproximately 2.8 eV, to be compared with the 1 eV of Godin and LaFemina andthe 2 eV of Gautier-Soyer et al. However, it must be remembered that our calcu-lated bulk band gap is 25% lower than the experimental one. It is instructiveto look at a three-dimensional plot of the wavefunction corresponding to this SS,

shown in Fig. 2.8. The dangling-bond character of the SS is clearly visible, lyingpredominantly on the surface Al atom but also on the surface O atoms.

Calculations of the surface-atoms ionicities, from our DFT-GGA charge den-sities, yield that before relaxation the surface Al atom has an ionicity of +2 .67,that is, an excess of approximately 0.1 electrons compared to the bulk situation,while the surface O atoms have lost the same amount. After relaxation, the bulkionicity is re-established. Thus, at the unrelaxed surface there is a larger chargetransfer between surface O and Al atoms, in agreement with the results fromthe analysis of Gautier-Soyer et al. [68] discussed above. Our calculations showthis charge transfer to arise from the O valence bands crossing EF and from the

presence of a partly filled SS band of dangling-bond character on the surface Al


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Chap. 2: Alumina 21

20 10 0 100

0.1

0.2

[0001]

20 10 0 100

5

20 10 0 100

5

20 10 0 100

5

20 10 0 100

5

20 10 0 100

0.5

20 10 0 100

0.5

20 10 0 100

0.5

20 10 0 100

0.5

Relaxed z

AlO

E E [eV]F E E [eV]

p

layer

three

p

one

layertwo

F

layer

four

xy

layer

sp

surface Al

DOS[states/(eVc

ell)]

Figure 2.7: Same as Fig. 2.5 but for the relaxed surface.

atoms.

In 1997, Ahn and Rabalais [69] published the results from an experimentalstudy based on time-of-flight scattering spectrometry (TOF-SARS), LEED, andclassical ion-trajectory simulations on the unreconstructed (0001) surface. They

show the surface to be terminated by half an Al layer, which relaxes inwardsby 63%. However, hydrogen atoms are found to be present at the surface, evenafter annealing to 1100C. Due to the lack of any features in the azimuthal-anglescans for the scattered H atoms, it is concluded that the hydrogen atoms resideeither in random sites or in sites above the surface Al layer. A subsequent studyby Toofan and Watson [70], using tensor LEED, argues that domains with half-Al-layer termination and with O-layer termination can both be found. In bothdomains, an outward relaxation of the topmost layer is observed (+0.20 A forthe 1/2-Al termination and +0.12 A for the O termination), accompanied bysome twisting and relief of buckling in deeper layers. It is argued that the strong

disagreement with theory arises from the use of unrealistic, idealized, surfaces intheoretical investigations. However, a grazing incidence X-ray scattering (GIXS)investigation by Renaud (1998) [71] can clearly rule out O and full-Al layer ter-minations, and shows that the topmost interlayer relaxations are 51%, +16%,29%, and +20%, qualitatively in agreement with the theoretical results, withbest agreement for the deeper layers. Of these three experimental studies, onlythe last one reports to have annealed the samples at as high a temperature as1500C, for three hours, yielding a surface with wide, atomically flat terraces,and a good near-surface crystalline quality.

In 1999, four papers [72, 73, 74, 75] were submitted at almost the same time,

theoretically studying the effect of the environment on the surface stability of


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Figure 2.8: Modulus squared ofthe calculated KS wavefunctions cor-

responding to the states having en-ergy 0.5 eV above EF, for the un-relaxed -Al2O3(0001) surface. Large

bright balls are O atoms, small darkones are Al atoms. Only the parts of

the wavefunctions lying inside the unitcell (shown with bright thin lines) are

shown.

the unreconstructed (0001). All four employ DFT calculations to compute theground-state total energies of-Al2O3 slabs having different terminations: full Allayer, half Al layer, full O layer, and partially full O layers (2/3 and 1/3). Theseare then used in a thermodynamic approach to study how the equilibrium totalenergy varies as a function of O or Al chemical potential, or O partial pressure. Inthis way, a picture is obtained on how a realistic situation, in which the surfaceis in contact with an O environment, can affect the surface termination. Theresults show that the non-polar termination (with half an Al layer) is remarkablystable, even at very high O pressures. The O-terminated surface is found to havea very large work function, characteristic of a high dipole moment, and a partially

empty O valence band, which crosses the Fermi level. However, this terminationis found to be stabilized by the addition of hydrogen to the surface. In fact,adding an H atom to each surface O makes the O-terminated surface the moststable one, at all O partial pressures. Wang et al. [74] show that the clean 1/2-Al surface undergoes a 86% first-layer relaxation, in agreement with previousDFT studies. However, addition of H on this surface lowers the relaxation toapproximately 69%, in very good agreement with the experimental result ofAhn and Rabalais. Also, at the H-covered O-termination surface, the outwardO layer relaxes outwards, by 0.11 A for 1/3 H coverage, and 0.19 A for full Hcoverage, in very close agreement with the result of Toofan and Watson, who

thus, Wang et al. conclude, most probably had H present on their surface.


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Chap. 2: Alumina 23

SECTION 2.2

Metastable Aluminas

Despite their metastability, the transition aluminas [10] have received an im-pressive technological attention, thanks to their high stability, with transitiontemperatures above 500C, and their special properties. While retaining goodthermomechanical and electrical resistances, they are also characterized by highsurface area, fine particle size, and/or catalytic activity. Due to these facts,they are often used as adsorbents, catalysts, catalyst supports, coatings, and softabrasives. Also, interest in the transformation mechanism between the differentalumina phases has developed due to the application of -Al2O3 as a protec-

tive oxide scale on the surface of high-temperature metals and alloys. A stablescale formation is promoted by heat treatment of the oxide and an understandingof the intermediate metastable aluminas occurring during the heat treatment istherefore essential. Also, sintering of nanosized Al2O3 powders relies on the phasetransformation of the powders from to alumina and thus on the propertiesof the phase.

A large amount of research has been devoted to the transition aluminas, aimedat characterizing their dehydroxylation and transformation mechanisms, porosityand specific surface area, surface structure and chemical reactivity, and crystalstructure. However, due to metastability, poorly developed crystallinity, diffi-culty in obtaining pure-phase samples, and possible surface-energy stabilization,use of advanced experimental techniques has been difficult. Single-crystal X-raydiffractometry (XRD) is not feasible, thus leaving as main tools of analysis pow-der XRD and selected-area electron diffraction (SAD). Still, the similarity andflexibility of the crystal structures and the continuous nature of the transfor-mations during heating, which causes the coexistence of several phases in thesamples, make even these techniques difficult to apply. Also, different phasesshow different symmetries, which are impossible to extract from polycrystallineXRD, which averages the structure over many crystals. Transmission-electronmicroscopy (TEM) can provide some information, but, unfortunately, not at theatomic resolution needed for determination of crystal structures. On the other

hand, high-resolution electron microscopy can yield information on atomic struc-tures, especially when combined with theoretical investigations. However, suchstudies have so far been few.

As a result, structural information on almost all metastable alumina phasesis still lacking or controversial, and phase-transformation mechanisms are poorlyunderstood. In this Section, the existing information on atomic and electronicbulk and surface structures of the metastable aluminas is reviewed.


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Oxygen Tetrahedral Al

Octahedral AlA

BC

Figure 2.9: Bulk ideal-spinel structure. Three subsequent oxygen (111) layers withAl overlayer are shown. The O layers are stacked in an ABC sequence along [111],

while there are two different Al layers: (i) with only octahedrally coordinated Al and(ii) with mixed octahedrally and tetrahedrally coordinated Al. These two Al layersalternate along [111]. Solid lines in each layer mark the smallest 2D unit cell for the

(111) surface.

2.2.1

Bulk Structures

The metastable-alumina structures can be divided into two major groups, de-pending on the stacking of their O anions [10]: face-centered cubic (fcc) packing(, , , , , , and ) and hexagonal close packing (hcp) (, , ). It should

be noted that the stable phase falls into the hcp category.The two alumina phases most often used in catalytic applications are and

. This is due to their high surface area and chemical activity. They have bothbeen described as defect cubic-spinel structures, with lattice parameter a 7.9A [10], although with some distortion (the reported c : a ratios are 0.9830.987for and 0.9850.993 for [77]).

In the ideal spinel structure, AB2O4, the O sublattice can be viewed as a2 2 2 array of fcc unit cells. The A cations occupy tetrahedral sites, whilethe B cations sit in octahedral sites. In Wyckoff notation, the O atoms occupythe 32e sites, the A cations the 8a sites, and the B cations the 16d sites of the

F d3m space group [37]. The structure can thus be viewed as an ABC close-packed stacking of O layers along [111], with cations in the interstitial sites (seeFig. 2.9). Like in -Al2O3, thus, the O and Al layers alternate along [111].However, in the spinel structure there are two different types of Al layers, whichalternate along [111]: layers composed of only octahedral cations, and mixedlayers containing both octahedral and tetrahedral cations. There are two types oftetrahedral cations in the mixed layers: upward pointing and downward pointing,equally distributed within each mixed layer. It should be noted that the cationdistribution follows Paulings third rule (see Sec. 3.1.2): no face sharing betweenthe cation coordination polyhedra occurs. This is made possible by the presence

of tetrahedral coordination, where the top O atoms can screen the charge of a


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Chap. 2: Alumina 25

tetrahedral cation from one of the two neighboring cation layers. In the case of-Al2O3, for instance, where all Al atoms are in octahedral sites, face sharing isunavoidable.

Due to the stoichiometry, not all cation sites can be occupied by Al atoms inan Al2O3 compound having spinel structure. The commonly accepted models for- and -Al2O3 have all O atoms in the 32e positions, leaving, then, 2/3 32 =211

3Al atoms to fill the cation sites. The structural uncertainty thus resides in

the occupancy of the cation sites, including the relative distribution of the Albetween the tetrahedral and octahedral sites. In the ideal spinel, 33.3% of thecations are tetrahedral and 66.7% octahedral. In the Al2O3 stoichiometry, thiscan theoretically vary from 25% tetrahedral and 75% octahedral, if all octahedralsites are filled, to 37.5% tetrahedral and 62.5% octahedral, if all tetrahedral sites

are filled [33].There is a large confusion regarding this distribution (see Ref. [33] and ref-

erencies therein). Many studies show a preference for tetrahedral sites. Othersprovide evidence for the opposite, with a preference for occupation of octahedralsites. In addition, many authors suggest that there is a significant portion ofAl atoms occupying non-ideal spinel sites, that is, sites allowed by the F d3mspace group, but which are not occupied in the normal spinel structure. Non-idealspinel cation sites that have been reported to be occupied by Al atoms are quasi-trihedral 32e, quasi-octahedral 32e, tetrahedral 48f, and octahedral 16c sites.Additional source of complexity is provided by the uncertain role of hydrogen,

with the possibility of many hydroxyl groups being present on the large surfacearea and several reports on presence of hydrogen in the bulk of -Al2O3. On theother hand, studies ruling out the presence of bulk hydrogen are also reported.

Zhou and Snyder [76] suggest that the presence of the abnormally coordinatedAl ions (quasi-octahedral and quasi-trihedral) are related to the high surface areaand that these ions are mainly located in the surface layer. They support thisby comparing the percentage of quasi-trihedral Al in -Al2O3 with the statisticalpercentage of atoms lying in the surface layer estimated from the value of thespecific surface area. The majority of the new surfaces created during the dehy-droxylation of the aluminum hydroxides creating the and aluminas are (111)

faces. The large presence of abnormally coordinated Al atoms could therefore berelated to strong relaxation effects of the atomic (111) layers at this surface. In-deed, as shown below, our DFT calculations on the close-packed (001) and (001)surfaces of -Al2O3 indicate that a more open Al-sublattice structure allows amuch larger relaxation of the surface atomic layers than in -Al2O3. In -Al2O3,the more open structure is caused by the lack of Al face sharing, made possibleby the presence of tetrahedrally coordinated Al atoms.

A recent DFT-GGA calculation by Wolverton and Hass [33] shows a preferencefor the Al atoms to occupy the tetrahedral spinel sites, and thus create vacanciesin the octahedral sites. Indeed, the cation sites are more closely packed together

in the octahedral cation layers than in the mixed layers. Within a highly ionic


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Oxygen Tetrahedral Al

Octahedral AlA

BC

Figure 2.10: Bulk structure of -Al2O3. Three subsequent oxygen (201) layers withAl overlayer are shown. The O layers are stacked in an ABC sequence along [201],

while there are two different Al layers: (i) with only octahedrally coordinated Al and(ii) with only tetrahedrally coordinated Al. These two Al layers alternate along [201].Solid lines in each layer mark the smallest 2D unit cell for the (201) surface.

picture, it is expected that the cations tend to maximize their mutual distanceas much as possible. This is confirmed by the result of Wolverton and Hass thatthe cation vacancies also tend to order and maximize their separation. Therefore,it could be expected that the and aluminas have a rather open Al-sublatticestructure as well, again thanks to the presence of tetrahedral Al atoms, whichincreases the possibility of avoided face sharing.

It can easily be seen in Fig. 2.9 that removal of any cation in an octahedrallayer leaves a large vacancy region for a tetrahedral Al ion of the layer above, thathas been exposed at a (111) surface, to relax into. Thus, the observed abnormal Alatoms could in reality be deeply relaxed surface atoms that in the bulk structureoccupied tetrahedral sites. It is interesting to notice that in both the - andthe -alumina structures, as reported by Zhou and Snyder, the tetrahedral andthe abnormal Al atoms make up together approximately 50% of all Al atoms(51% and 43% for and , respectively). This is very close to the fraction oftetrahedral Al in bulk -Al2O3, into which both phases transform upon heating.The alumina also has an ABC O stacking, and a 50%50% share of tetrahedral

and octahedral Al atoms (see Fig. 2.10). As pointed out by Zhou and Snyder,the cation-site distribution in the three phases is similar, suggesting a displacivestructural change, rather than a reconstructive one, during the phase transition.Again, this would support the idea of the abnormal Al ions in and beingstrongly-relaxed tetrahedral Al ions rather than displaced octahedral ones.

The structure of-Al2O3 has also been described as based on the spinel struc-ture (see the review of Levin and Brandon [10] for a full list of references). How-ever, it is believed to be a superlattice of the spinel structure, composed of atripled unit cell of spinel with 160 atoms per unit cell. Two different unit cellshave been proposed, based on XRD and SAD: tetragonal with lattice parameters

a = b = a and c = 3a and orthorhombic with a = a, b = 1.5a, and c = 2a.


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Chap. 2: Alumina 27

Some reports point toward the true unit cell being orthorhombic, and explain theoccurrence of results pointing toward the tetragonal unit cell as being caused bydata misinterpretation or from the coexistence of and . The orthorhombic-Al2O3 seems to have space group P212121 or P21212. In a study by Levin etal. [29], orthorhombic with lattice parameters a = 2a, b = a, and c = 1.5a,and space group P212121 is observed. Apparently, this structure is still largelycontroversial.

All cubic alumina phases (, , and ) transform eventually to -Al2O3 asthe last step before the stable phase. The phase is the only well-determinedmetastable-alumina structure [76, 10], apart from the structure. It has a mono-clinic unit cell, with space group C2/m. It contains 20 atoms (four Al2O3 units),with the Al atoms equally distributed between octahedral and tetrahedral sites.

The lattice parameters are: a 1.5a, b = 2/4a, c = 2/2a, and = 104.The ABC stacking of the O sublattice is along the [201] direction of the unitcell. Like in the spinel structure, there are two different cation layers, alternatingalong [201]: one layer with only octahedral cations, and one with only tetrahe-dral cations, as shown in Fig. 2.10. Again, as can be seen in Fig. 2.10, no facesharings occur between the Al coordination polyhedra, causing the presence ofwide vacancy lines in the octahedral layers.

It is believed that the phase transformations from , , and to conservethe ABC stacking of the O sublattice, and consist only of redistributions of thecation positions [10, 76]. This is accompanied by a reduction of surface area and

porosity, which possibly causes the many abnormally coordinated surface atomsto diffuse into more-ordered bulk sites. As discussed above, the tetrahedral andabnormal Al atoms in and make together up for approximately 50% of allAl atoms, and can therefore be the ones making up the 50% of tetrahedral Alin -Al2O3 after transformation. Zhou and Snyder [76] show that during heatingthe cubic spinel structure gradually collapses, possibly due to the surface-areareduction and ordering of the tetrahedral-Al sublattice, so that in the early stagesof the transformation it exhibits tetragonal character before finally settling intothe monoclinic -Al2O3. Thereafter, the tranformation proceeds reconstructivelyto -Al2O3, where the O stacking has to change from cubic ABC to hexagonal

ABAB.Recently, three more cubic alumina phases have been detected by Levin etal., [28], [27], and [29]. The cation positions have not been identified, butspace groups, lattice parameters, number of cations per unit cell, and orientationrelationships relative to -Al2O3 have been reported [10].

Apart from -Al2O3, the common alumina phases based on an hcp packingof the O layers are - and -Al2O3. The existence of a transient phase, formedform dehydrating tohdite, has also been reported [26]. Three different unit cellsare reported for -Al2O3: cubic (not spinel), with lattice parameter a = 7.95 A[22]; hexagonal with lattice parameters a = 5.56 A and c = 13.44 A and space

group P6/mm or P63/mcm [78]; and hexagonal with lattice parameters a = 5.57


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Phases E [eV/Al2O3]

Our calculations Wolverton and Hass [33] Exp. [80]DFT-LDA DFT-GGA DFT-LDA DFT-GGA

0.15 0.09 0.21 0.08 0.16

0.25 0.04 < 0.12

Table 2.3: Calculated and experimental values of the energy differences between bulk- and-Al2O3, respectively, and the stable-Al2O3, per Al2O3 unit. The experimentalvalue for is actually the enthalpy difference between and . However, since transforms to before, the value can be used as an upper bound for the value.

A and c = 8.64 A [79]. It has been suggested to have a layered structure with Al

in octahedral sites, but with a strongly disordered stacking along the c direction.It is not clear whether all three structures exist or whether the differences areonly a matter of interpretation. The phase has been described as having arandom distribution of Al over both tetrahedral and octahedral positions [26].

Finally, the structure of the phase has only recently been completely de-termined by our combination of theory and experiment. A review of the manyattempts at determining this structure experimentally is given in Paper II, whilePapers I and II account for our work on this structure determination. For a de-scription of the atomic and electronic structures of this phase, Paper II is referredto.

Table 2.3 shows experimental and theoretical energy differences between the, , and bulk structures.

2.2.2

Electronic Structure

On the electronic structure of metastable aluminas there exists some experimentaland theoretical work in the literature. This concerns most notably the phase,for which structural information is available as a basis for theoretical work, andthe phase, due to its technological importance. In addition, we have performed

DFT calculations on the electronic structure of -Al2O3 (Paper II). All resultspoint toward the metastable aluminas as highly ionic systems, similar to -Al2O3.However, the large band gap is slightly smaller for the metastable phases (Table2.4). The theoretical value for -Al2O3 is based on a structure model in whichthree cation vacancies are located on the octahedral sites in a cubic spinel unitcell. It is interesting to note that the band gap appears to consistently decrease,when the fraction of tetrahedrally coordinated Al in the bulk structure increases,and that both experimental and theoretical studies follow this trend, despite theknown DFT underestimation of band gaps.

Calculations performed by Mo and Ching [52] with a first-principles LDA or-

thogonalized linear-combination of atomic orbitals (OLCAO) method yield Mul-


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Chap. 2: Alumina 29

Phase Band gap Amount

Exp. [82] Theory [Our calcs.] Theory [52, 83] of AlT

-Al2O3 8.75 0.05 eV 6.6 eV (direct) 6.24 eV (indirect) 0%6.26 eV (direct)

-Al2O3 7.95 0.05 eV 5.34 eV (indirect) 25%5.35 eV (direct)

-Al2O3 7.00 0.05 eV 5.13 eV 2537.5%-Al2O3 4.64 eV (indirect) 50%

4.98 eV (direct)

Table 2.4: Experimental and calculated band-gap values for the stable -Al2O3 andfor some metastable alumina phases. The percentage of Al ions that are in tetrahedral

coordination in each structure is also shown.

liken populations showing - and -Al2O3 to have very similar ionicities. Thevalence is almost the same for octahedrally coordinated Al in both structures(+1.10 and +1.05 for and , respectively), while it is higher for the tetrahedralAl in (+1.23). Also, a study of the electron-localization function (ELF) on bulk-Al2O3 [81] shows a high ionicity.

Using the modified-Voronoi approach, with the ionic radii provided by Shan-non [84], described in Sec. 4.3.2, we have estimated the valence-charge localiza-tion around the atoms in bulk -Al2O3 from our calculated DFT-LDA and GGA

charge densities. With the LDA (GGA) we obtain values of +2.79 (+2.78) and+2.92 (+2.89) for the octahedral and tetrahedral Al, respectively, while the val-ues for the O atoms vary between 1.92 (1.93) and 1.80 (1.80), dependingon whether they have tetrahedral Al neighbors or not. Again, the tetrahedral Alions show a higher ionicity or charge localization than the octahedral Al. Thevalues can be compared with the GGA ones obtained by us for -Al2O3, +2.78and 1.85 for Al and O, respectively. The ionicity of the octahedral Al is thusthe same in these two, stable and metastable, phases as well.

2.2.3

Surface Investigations

Like for the electronic structure, investigations on surface properties of metastablealuminas have concentrated on the and phases. On -Al2O3(100) and (010),a periodic Hartree-Fock calculation has been performed by Borosy et al. [81].However, due to lack of sufficient computational power, the study was limitedto thin slabs and did not allow surface relaxation. The calculated surface ener-gies (3.88 J/m2 for (100) and 4.41 J/m2 for (010)) indicate a higher stability forthe (100) surface, and a lower surface energy than the ones calculated with thesame Hartree-Fock computer code (crystal) by Causa et al. [62] for the relaxed

-Al2O3(0001) and (1010) surfaces. Mulliken-population analysis shows a slight


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electron transfer toward the surface atoms, while electron-density differences in-dicate a strong polarization of the surface O atoms, with an electron loss in theAlO bond direction.

For -Al2O3, due to the lack of structural information, implying the need toconsider large supercells and different structural configurations, mainly molecular-dynamics studies have been conducted. Blonski and Garofalini (1993) [64] com-pare the stability of different terminations of (001), (110), and (111). Differentstructural possibilities for each surface are examined. On average, after relax-ation one of the two terminations considered for (001) is found to have the lowestsurface energy (0.79 J/m2), only slightly lower than that of the two terminationsconsidered for (111) (0.87 and 0.88 J/m2). The (110) terminations have the high-est energies, 2.54 and 1.21 J/m2. The surface energies are thus lower than

those obtained for alumina, whose most stable (0001) termination is found tohave a relaxed surface energy of 2.04 J/m2. This is symptomatic of the highersurface area of alumina. During relaxation of the lowest-energy (001) termina-tion, the Al atoms initially above the surface move toward a layer of oxygen andhide among them, making this surface O terminated, with O slightly above Al.The surface energies of the considered (111) terminations, with Al at the surface,are very high before relaxation. After relaxation, they are the lowest ones andalmost equal for both termination types. The lowest surface energy is obtainedfor the terminations with the larger number of cation vacancies near the surface.The relaxation strongly distorts the atomic structure, yielding almost amorphous

surfaces. The Al coordination tends to increase, and the number of tetrahedralAl atoms is much lower after relaxation.

In another molecular-dynamics investigations, Gunji et al. (1998) [85] alsoexamined the (100), (110), and (111) surfaces. The outermost Al layers in theconsidered (100) slabs are composed of only octahedral Al, and are found tobe stable during relaxation. The tetrahedral Al, present in the next layers, arefound, however, to be unstable, and move to octahedral sites closer to the surface,increasing the Al density near the surface. At the (110) surfaces, both tetrahedraland octahedral Al atoms are exposed at the surface. During relaxation, theoctahedral Al are stable, while the tetrahedral Al move to bulk octahedral or

tetrahedral sites, thus decreasing the surface Al density. At (111), the octahedralAl exposed at the surfaces are again found to be stable, while the tetrahedral Almove to bulk octahedral sites, if their initial location is in the second surface Allayer, or remain in the surface sites, if they are exposed at the surface, makingthe coordination of surface Al to be mainly three. Also, a larger number of bulktetrahedral Al are found to migrate to bulk octahedral sites during relaxation of(111), compared to the other surfaces. Of the three surfaces, (111) is found tolower its surface energy the most during relaxation, while (110) is the most rigid.Unfortunately, no absolute surface energies are given by Gunji et al. to comparethe relative stability of the three surfaces.

The formation of micropores in -Al2O3 has also been studied. This is impor-


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Chap. 2: Alumina 31

tant for characterizing the transformation mechanism to alumina during heattreatment. Alvarez et al. (1995) [86] performed a molecular-dynamics study onthe thermal evolution of a large system exposing the (100) plane, starting fromdifferent initial bulk densities, that is, different volumes of the box of the system.It is found that on increasing the temperature there is a general tendency, inde-pendently of initial density, to expose the (110) planes. Thus, the pore formationis suggested to be caused by the coalescence of the interstitial spaces left by themigration of tetrahedral Al atoms to octahedral sites in the neighboring (110) Allayers.

In 1999, Sohlberg et al. [87] performed a DFT-GGA study on the (110) sur-face terminations, based on their recently suggested bulk structure of -Al2O3,which incorporates the presence of hydrogen in the structure [88]. It has been

subsequently argued by Wolverton and Hass [33] that this bulk structure is ac-tually thermodynamically unstable. However, the possibility that it is formedkinetically cannot be ruled out. The surface study of Sohlberg et al. was moti-vated by the observation by NMR spectroscopy that no three-foldly coordinatedAl are found at the surface. Their calculations show that the three-foldly co-ordinated Al atom exposed at the surface of the most stable (110) terminationrelaxes deeply, to a vacant octahedral site below the top O layer. Also, a largeenergy gain (2 J/m2) is associated with this relaxation. It is also shown thatafter relaxation, Paulings second rule is fulfilled for the surface ions, whereas theoriginal surface-Al position is electrostatically unfavorable. It is argued that this

lack of three-coordinated surface Al explains the observed lack of IR-spectrumbands for adsorbed OH groups on three-coordinated Al ions at the surface.

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