Interfacial aspects of glycothermally synthesized alpha alumina

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Interfacial aspects of glycothermally synthesized alpha alumina
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INTERFACIAL ASPECTS OF GLYCOTHERMALLY SYNTHESIZED
ALPHA ALUMINA












By

NELSON S. BELL


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1997















ACKNOWLEDGMENTS


I would like to thank my advisor Dr. James H. Adair for his tutelage and

encouragement of my development as a colloid and surface chemist. I would also like to

thank Dr. Robert DeHoff, Dr. Michael Sacks, and Dr. David Clark from the Department

of Materials Science and Engineering and Dr. Daniel Talham from the Department of

Chemistry for serving on my committee. I am very grateful to Dr. Ellis Verink for his

support and encouragement during my studies at the University of Florida.

I am indebted to my fellow group members at the University of Florida, with

special thanks to Dr. Robert Chodelka, Dr. Seung-Boem Cho, Craig Habeger, Jeff

Kerchner, Paul Demkowicz, Dave Mitchell, Henrik Krarup, Robert Simpson and Dr.

Melanie Carraso. I appreciate the help of my fellow graduate students during my

education, specifically Mike Zamora, Jesse Arnold, Drew Amery and James Merotta. I

would like to thank the staff of the Major Analytical Instrumentation Center, and Dr.

Stanley Bates, Dr. Augusto Morrone, and Wayne Acree who all proved to be of

exceptional assistance in sample analysis. Thanks are due to David Powell and staff for

performing and analyzing gas chromotography data in the Spectroscopic Services

Laboratory in the UF Department of Chemistry.

My heartfelt thanks go to my extended family for their pride and support of my

career path, and most strongly to my parents Joseph H. Bell and Eunice S. Bell for their

unwavering faith, encouragement and belief in my ability.















TABLE OF CONTENTS




ACKN OW LED GEM ENTS ................................................................................................ ii

LIST OF TABLES ......................................................................................................... vi

LIST OF FIGURES ........................................................................................................... vii

ABSTRA CT ........................................................................................................................ x

CHAPTER 1 ........................................................................................................................ 1
INTRODU CTION ............................................................................................................ 1

CHAPTER 2 ........................................................................................................................ 6
SURFACE ENERGETICS AND INTERFACIAL PROPERTIES AFFECTING THE
MORPHOLOGY OF oc-ALUMINA DURING LIQUID PHASE PRECIPITATION ..... 6
Introduction ........................................................................................................... 6
Properties of Alum ina ............................................................................................... 7
Phase Stability ..................................................................................................... 7
Solubility of Alum ina .......................................................................................... 9
Hydrotherm al Synthesis of cx-Alum ina ............................................................ 10
Glycotherm al Synthesis ..................................................................................... 12
Glycol Chem istry ............................................................................................... 15
Surface Chem istry of Alum ina .......................................................................... 16
Surface Energy of Alum ina .............................................................................. 17
Colloidal Properties .............................................................................................. 18
Developm ent of Surface Charge ....................................................................... 19
The Double Layer M odel .................................................................................. 21
Zeta Potential ..................................................................................................... 25
M orphological Control of Precipitates ................................................................... 25
Equilibrium Shape ............................................................................................ 26
Com positional Variation of Surface Energy .............................................. 27
Electrical Variation of Surface Energy ........................................................ 28
Crystal Structure Theory .................................................................................. 31
Growth M orphology .......................................................................................... 32
Nucleation ............................................................................................................. 32
Hom ogeneous Nucleation .......................................................................... 34









Heterogeneous Nucleation ......................................................................... 36
Growth Rates ..................................................................................................... 37
Surface Integration M odels .......................................................................... 38
Screw Dislocation Growth .......................................................................... 39
Surface Reaction Theory ................................................................................... 40
M orphological Forms Resulting from Growth Rates ........................................ 41
The Effect Of Solvent ............................................................................................ 42
Surface Energy Reduction via Solvent Interactions .......................................... 46
The Jackson (x Factor ....................................................................................... 46
Interfacial Cell M odel ....................................................................................... 48
The Effect of Adsorbates ....................................................................................... 49
S u m m ary .................................................................................................................... 5 1

C H A P T E R 3 ...................................................................................................................... 54
DERIVATION OF THE EQUILIBRIUM SHAPE OF AN ALUMINA PARTICLE
W ITHIN A SOLVENT .............................................................................................. 54
In tro d u ctio n ................................................................................................................ 54
Conditions for Equilibrium ................................................................................... 55
M orphological Variation with Surface Charge ...................................................... 61

C H A P T E R 4 ...................................................................................................................... 6 9
ADDITIVE EFFECTS ON PARTICLE MORPHOLOGY ....................................... 69
In tro d u ction ................................................................................................................ 6 9
B ack g ro u n d ................................................................................................................ 7 0
M aterials and M ethods ......................................................................................... 73
Results and Discussion .......................................................................................... 75
Investigation of Solvent Degradation ............................................................... 76
Phase Purity of Precipitate ................................................................................ 80
Effect of Adsorption by Solvent and Alcohols ................................................ 80
Effect of Adsorption by Carboxylate Groups ................................................... 84
Effect of Adsorption by Nitrogen Compounds ................................................ 85
Surface Characterization of Precipitates .................................. 88
Purity of Solvent ............................................................................................... 92
S u m m ary .................................................................................................................... 9 5

C H A P T E R 5 ...................................................................................................................... 9 7
SURFACE CHARGING PROPERTIES OF ox-ALUMINA PARTICLES AS A
FUNCTION OF HISTORY AND PARTICLE MORPHOLOGY ............................. 97
In tro d u c tio n ................................................................................................................ 9 7
B ack g ro u n d ................................................................................................................ 9 8
E x p erim en tal ............................................................................................................ 10 6
R e su lts ...................................................................................................................... 10 9
D iscu ssio n ................................................................................................................ 1 1 1
Structural Examination of Glycothermally Synthesized Alumina Surface ......... 111
Surface Charging Behavior of M orphological Forms ......................................... 116









Sum m ary .................................................................................................................. 124

CH A PTER 6 .................................................................................................................... 126
MORPHOLOGICAL CHANGES IN GLYCOTHERMALLY SYNTHESIZED
ANISOTROPIC c-ALUMINA PARTICLES DURING SINTERING ........................ 126
Introduction .............................................................................................................. 126
Experim ental ............................................................................................................ 131
Results and D iscussion ............................................................................................ 132
M orphological Evolution .................................................................................... 132
Surface Energy Calculations ............................................................................... 141
Conclusions .............................................................................................................. 144

CH A PTER 7 .................................................................................................................... 145
CON CLU SION S A N D FU TU RE W ORK ................................................................... 145

A PPEN D IX A ................................................................................................................. 148

A PPEN D IX B .................................................................................................................. 152

LIST OF REFEREN CES ................................................................................................ 156

BIO GRA PH ICAL SK ETCH ........................................................................................... 168




























v















LIST OF TABLES


Table pa4ge

2-1. Mineralogical overview of the phases of alumina (Git70) ...................................... 8

2-2. Formation constants for the hydroxylation of A13' aqueous species (Bae86) ...... 10

2-3. Point of Zero Charge of Aluminum Oxide Phases (Git70) ................................... 18

2-4. Intermolecular and surface forces in vacuum. (Adapted from Isr92) ................. 45

3-1. Illustrative examples of the assumed surface energy and surface charge constants for
three planes of a.-alum ina ..................................................................................... 64

5-1. Electron dispersive backscattering results for the presence of adsorbed carbon
groups on the surface of glycothermally synthesized platelets ................................ 117

5-2. Concentration of A13, sites as a function of habit plane ......................................... 120

6-1. Immersion density values for samples sintered at varying temperatures ................ 140

6-2. Calculation of a-alumina surface energy as a function of crystallographic habit from
data at 1850'C (D eU 93) .......................................................................................... 142

6-3. Surface area values of the facets as a function of morphology ............................... 143















LIST OF FIGURES


Figure papge

2-1. Thermal transformation characteristics of Alumina (Git70) ................................... 8

2-2. Solubility of ox-A1203 calculated from speciation constants (OPALQ97) ............. 11

2-3. Hydrothermal stability diagram for the Alumina-Water system (Git70) ............... 13

2-4. Morphodrome of particle morphologies formed in the 1,4-butanediol alumina
system as a function of solids loading, shear rate, and reaction time (Cho96) ..... 15

2-5. Electrical double layer interface indicating strong cation adsorption at the interface
and diffuse anion cloud decreasing with distance from the surface (Hun87) ...... 22

2-6. Flat, stepped and kinked faces in the periodic bond chain model for a cubic crystal
structure (R in96) ................................................................................................. . 33

3-1. Surface potential and fraction of charge surface groups, U, for the hypothetical habit
planes given in Table 3-1. Surface potential increases away from the point of zero
charge as a result of the development of charge from the protonation or
deprotonation of surface hydroxyl groups ............................................................ 65

3-2. Calculated surface energy curves for each habit plane as a function of pH and
surface charging from the assumed surface energy and charge constants. As each
habit plane experiences the development of surface charge, surface energy is
d ecre a se d .................................................................................................................... 6 6

3-3. Particle morphologies as a function of pH. A. pH = 2. B. pH = 7. C. pH = 12.. 67

4-1. Gas Chromotrogaphy evaluation of solvent degradation during glycothermal
synthesis. GC thermal schedule was 1 minute at 30'C, heating at 10C/minute to
250'C. A. Vacuum distilled solvent. B. Post synthesis without discoloration. C.
Post synthesis w ith discoloration .......................................................................... 77

4-2. Infrared spectroscopy of solvent degradation ....................................................... 79

4-3. X-ray diffraction pattern of glycothermally produced 0-alumina as a function of the
adsorbate additions. A. As synthesized. B. Tetrahydrofuran. C. Methanol. D.









Acetic acid. E. Nitric Acid. F. Ammonium hydroxide. G. Pyridine H.
Tetraethylammonium hydroxide (TEAOH) .......................................................... 81

4-4. Effect of Hydroxyl groups on morphology. A. As synthesized. B. Tetrahydrofuran
(12.5 Volume %). C. Methanol (13.6 volume %). D. Sec-butoxide .................... 83

4-5. Morphological changes induced by the addition of Acetic Acid. The synthesis was
performed in the 600 ml hydrothermal vessel. 588 gl of glacial acetic acid was added
to 200 ml of 1,4 butanediol with 8 g of gibbsite. The solution pH was adjusted from
8 to 5.1 by the addition. The stirring rate used was 460 rpm ............................... 85

4-6. Effect of nitrogen compounds on morphology. A. Nitric acid. B. Ammonium
Hydroxide. C. Pyridine. D. Tetraethylammonium Hydroxide .......................... 87

4-7. DRIFTS spectra of adsorbate particle surface structure. A. Pure Solvent B.
Methanol (15 Volume %). C. Tetrahydrofuran (12.5 volume %). D. 2-Butanol. E.
Acetic Acid (pH 5.1). F. Nitric Acid (pH 5.1). G. Ammonium Hydroxide (pH 10.9).
H. Pyridine (5 Volume %). I. Tetraethylammonium Hydroxide (pH 12.2) ...... 89

4-8. Gas Chromatography of solvent samples after the synthesis reaction. The gas
chromatography heating schedule is 5 minutes at 30'C, heating at 10C per minute to
250'C, and hold at final temperature for 5 minutes. A. Tetrahydrofuran. B.
Methanol. C. 2-Butanol. D. Acetic Acid. E. Nitric Acid. F. Ammonium
Hydroxide. G. Pyridine. H. Tetraethylammonium Hydroxide ............................ 93

5-1. Scanning electron microscopy of particle morphologies. A. Platelet B. Prism C.
B ipyram id D P olyhedron ...................................................................................... 102

5-2. ATOMS Structure of primary planes. A. Basal Plane (0001). B. Hexagonal prism
(11 20). C. Bipyramid (11 2 12). D. Decahedral (10 2) ....................................... 103

5-3. Aluminum-water speciation diagram generated using the OPAL program .......... 107

5-4. Scanning electron micrograph of the seeded platelet morphology used for surface
stru ctu re an aly sis ...................................................................................................... 10 9

5-5A. Aging effects on zeta potential of the platelet morphology after aging in water for
71 and 105 days. Error bars are the 95% confidence interval ................................. 111

5-5B. Aging effects on zeta potential of the prism morphology after aging in water for 44
days. Error bars are the 95% confidence interval ................................................... 112

5-5C. Aging effects on zeta potential of the bipyramid morphology after aging in water
for 17 and 54 days. Error bars are the 95% confidence interval ............................. 113









5-6A. Zeta potential of the platelet morphology after acid wash as a function of pH and
ionic strength. Error bars are the 95% confidence interval ..................................... 114

5-6B. Zeta potential of the prism morphology after acid wash as a function of pH and
ionic strength. Error bars are the 95% confidence interval ..................................... 115

5-6C. Zeta potential of the bipyramid morphology after acid wash as a function of pH
and ionic strength. Error bars are the 95% confidence interval .............................. 116

5-6D. Zeta potential of the polyhedron morphology after acid wash as a function of pH
and ionic strength. Error bars are the 95% confidence interval .............................. 117

5-7. Diffuse reflectance infrared spectroscopy of as synthesized platelets and the platelets
after boiling in deionized water for 3 hours. The average powder particle size is 0.5
m ic ro n s ................................................................................................................... 1 1 8

5-8. Gas chromatography/ mass spectroscopy of the supernatant of the 0.5 micron
platelet particles after pH 4 acid w ash ..................................................................... 119

5-9. Comparison with the Healy-White model of surface charge generation. ApK = 8 and
iso electric p o in t is 6 ................................................................................................. 12 2

6-1. ATOMS plane representation of the basal plane (0001) of ct-alumina. (Input: space
group Rb3c, a = 4.758, c = 12.991A. A13, ionic radius = 0.39A, 02- ionic radius =
0 .9 0 A .) ..................................................................................................................... 12 9

6-2. SEM photomicrographs of the fracture surface of the slipcast ca-Al203 pellet before
sin te rin g .................................................................................................................. 13 3

6-3. SEM photomicrographs of the fracture surface of the slipcast c-A1203 pellet at
1 100C for three hours. (A) Randomly oriented particles. (B) Domain structure. 135

6-4. SEM photomicrographs of the fracture surface of the slipcast c-A1203 pellet after
sintering for three hours in air at (A) 1300 'C, (B) 1400 'C, (C) 1500 'C, and (D)
16 0 0 C .................................................................................................................... 13 7

6-5. Theoretical equilibrium shape for x-A1203 (from Cho97). With respect to the basal
plane (0001), surface energy ratios follow: I(T-012) = 1.05, -(1210) = 1.12, 7( 1123)
= 1.06, and y (10- 1 ) = 1.07 ..................................................................................... 142

A. Assembly of vacuum distillation equipm ent ........................................................... 150















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

INTERFACIAL ASPECTS OF GLYCOTHERMALLY SYNTHESIZED
ALPHA ALUMINA

By

Nelson S. Bell

December 1997

Chairman: Dr. James H. Adair
Major Department: Materials Science and Engineering

A thermodynamic derivation for the equilibrium shape of a crystal precipitated in

liquid solution has been developed. The conditions for equilibrium incorporate the effect

of a reactive interface between the solvated components and the crystal components.

Surface charge variation with solution pH has been related to surface energy, and the

variation of equilibrium shape with solution pH has been demonstrated as an illustrative

example.

The control of particle shape has been investigated in the 1,4-butanediol-alpha

alumina system. Morphological effects of the solvent and the use of specific adsorbates

have been investigated. Specific adsorbates investigated for their effect on morphology

were tetrahydrofuran (THF), methanol, 2-butanol, acetic acid, nitric acid, pyridine,

ammonium hydroxide, and tetraethylammonium hydroxide (TEAOH). Both ammonium

hydroxide and TEAOH promote a platelet morphology, which is believed to relate to









surface charging effects. Pyridine promotes a platelet morphology but was found to

inhibit growth of uniform particles. The use of Al tri(sec)butoxide as a precursor

introduces 2-butanol to the solution, and the resultant morphology is plate-like and

dominated by { 11 2 12} facets. Tetrahydrofuran, methanol, and nitric acid had no effect

on the growth morphology. Acetic acid promoted the formation of new habit planes and

reproducibly forms a roughly acicular shape.

The development of surface potential for glycothermally synthesized alpha-

alumina has been investigated as a function of particle habit and aging effects. The

adsorption of 1,4-butanediol on the surface of the particles creates aging effects on the

isoelectric point. The final isoelectric point correlates with the number of metal cation

sites on the dominant habit plane through the configuration of ligand anions. It is

believed that differences in surface charge and isoelectric point result from the speciation

of A131 sites with OH ions from solution.

Sintering studies were performed on glycothermally synthesized a-A1203

hexagonal platelets to determine the effects of anisotropy upon the evolution of both an

equilibrium particle morphology and particle consolidation. Evidence of sintering and

densification are apparent in the morphology of the particles, but densification on the

macroscopic level was inhibited by porosity. Transformation to an equiaxed morphology

occurs with bulk densification.















CHAPTER 1


INTRODUCTION

The mineral alumina (A1203) is a major component of many products produced by

the ceramic industry (Mad97). The manufacture of alumina in 1995 was approximately 5

million metric tons, and projections for growth are nearly 4% per year. New alumina

products are requiring higher performance to satisfy needs in such applications as

refractories, abrasives, and ceramics. Refractory applications for alumina involve several

industries including ferrous material production, nonferrous ceramics, glass and cement

manufacture, and chemical production. High performance refractories are especially

demanded in steel production. Abrasives are an application that consumes approximately

80% of fused alumina production and desired properties in abrasive production are purity

and durability. High purity, durable abrasives are currently being produced using sol gel

technology. Alumina particles are also being applied to the next generation of aluminum

and magnesium metal matrix composites as automotive components. Applications as

drive shafts, brake systems, piston heads and cylinder liners are being considered.

Alumina has been applied as exhaust port liners in Porsche engines. Electronic

applications like circuit board substrates and catalytic converter supports also require

greater material performance. Advanced ceramic applications have created a need for

fine, high purity alumina with controlled and reproducible properties.









Solution synthesis techniques have the potential to satisfy many of the industrial

needs for alumina products. The key advantages of solution synthesis are the production

of high purity, monodisperse, unagglomerated powders of controlled shape (Daw89,

Hir87, Mat87, Mat92). Additionally, cost reductions result from elimination of the need

for milling to reduce particle size. Hydrothermal synthesis has successfully developed

wide application in the production of metal oxides (Kat87, Som87, Som89). The use of

water as a solvent under elevated heat and pressure is to reduce the melting point of the

material being synthesized (Lau73). This allows growth at lower temperatures than the

alternative calcination process. The use of a solvent does have disadvantages in that the

growth of the material cannot be directly observed, and high pressure equipment is

required.

The hydrothermal synthesis of alumina was investigated in the mid-twentieth

century by several investigators (Erv5 1, Ken59, Kuz64, Kuz65, Kuz7 1, Lau43, Mat67).

Hydrothermal techniques are widely used to produce gibbsite through the Bayer process,

and boehmite is a popular phase used in the production of catalyst supports (Git70). The

stability of the alpha phase, desired as the most thermodynamically stable phase, was

found to require temperatures in excess of 400'C and reaction times ranging from days to

weeks. Growth rates were measured by Kuznetsov at 600'C and highly basic conditions

(Kuz64). These extreme conditions limit application of hydrothermal synthesis to the

production of c-alumina, because the synthesis temperatures are above the critical point

of water, and the synthesis pressures are extreme.

The utilization of non-aqueous solvents has recently demonstrated that the

prohibitive high pressures of hydrothermal synthesis need not forestall low temperature









synthesis of ct-alumina (Be197, Cho95, Cho96, Ino89). Glycols have been applied as an

alternative solvent, and have demonstrated the capability to form both desired crystal

phases and novel phases that have not been produced in aqueous synthesis (Bib85, Fan86,

Ino89, Ino9l, Ino95, Ino97, Kai94, Kai95). Cho and Adair have developed the

glycothermal synthesis technology of ox-alumina for the control of particle shape (Cho95).

The use of 1,4-butanediol has been applied to synthesize (x-alumina at 270'C, and

reaction times have been found to occur as quickly as 12 hours. Control of stirring rate

was reported as the dominant variable in control of the morphological form of the

precipitate (Cho96). High shear rates develop a platelet morphology, and low shear rates

produced a polyhedral morphology. The local growth environment during growth will

dictate the final particle morphology.

The capability to control the shape of a particle creates the opportunity for custom

developed tx-alumina powders to be fabricated for a desired application. Highly

anisotropic particles can be applied to composite reinforcement as platelets or needles,

and platelets can be used as nuclei to orient layers of alumina film. The effect of particle

shape on a powder's effectiveness as an abrasive has not previously been investigated.

Thermal barriers for refractive applications can benefit from the construction of

controlled pore structures.

The synthesis and application of particles of controlled shape requires an

understanding of the effect of interfacial properties. The free energy of each facet in the

synthesis of particles is a function of the solvent environment, whereas growth rates are

dictated by the fluid dynamics during precipitation. Particle shape is thus affected by the

properties of the fluid interacting with the crystal during growth. Organic solvents add









concern for the stability of the solvent. Solvent degradation will provide new chemicals

to interact with the surface and affect growth rates or the thermodynamic stability of

facets. Chemical interactions between the solvent and crystal which alter surface energy

are factors in the development of morphology, and the interactions of an additive which

changes morphology must supersede the effect of solvent.

Particles with habit planes will exhibit differing surface electrical properties based

on the prevalence of the habit planes. Colloidal dispersion is a key element in most

forming technologies, and the stability of a suspension is critical to processes like tape

casting or slip casting. Abrasive applications also require unagglomerated dispersions,

and the electrical charging properties of a powder are critical for the design and

application of successful dispersions. Faceted, anisometric particles provide an

opportunity for developing an understanding of the effect of each habit plane on surface

potential.

Sintering of faceted particles is based on the reduction of surface free energy. The

final particle shape is determined by the equilibrium shape. The presence of defined habit

planes during sintering will affect the development of fully dense products, and affects

the driving force for sintering through the reduction of surface energy. Knowledge of the

equilibrium shape allows the determination of the driving force for sintering a particle

morphology.

The objective of this work is to examine the interfacial characteristics of faceted

particles formed in glycothermal synthesis, and relate these characteristics to interfacial

properties during synthesis. The effect of each habit plane on interfacial properties

generates an opportunity for both a fundamental and practical understanding of the









influence of surface energy on interfacial phenomena. This dissertation is divided into

six major sections. Chapter 2 presents a background on the properties of alumina,

colloidal stability, surface charge, and the effect of the interface on particle morphology.

Chapter 3 gives a theoretical treatment of the conditions for equilibrium of a particle that

grows from the solution phase, and illustrates the effect of surface charging on surface

free energy and the resultant equilibrium shape. Chapter 4 surveys the use of specific

adsorbates to control particle shape in the precipitation of alpha alumina in 1,4-

butanediol. Chapter 5 describes the effect of morphology on aqueous surface charging

properties, and the consideration of particle history on surface potential. Chapter 6 gives

observations on the sintering of platelets and their morphological development. Finally,

Chapter 7 describes conclusions and future work in this system that will be beneficial to

the community.















CHAPTER 2


SURFACE ENERGETICS AND INTERFACIAL PROPERTIES AFFECTING THE
MORPHOLOGY OF a-ALUMINA DURING LIQUID PHASE PRECIPITATION




Introduction


oa-Alumina is one of the most important technological ceramics used in industry.

Its hardness, high temperature resistance and electrical properties place alumina as a key

structural ceramic, refractory material, and insulator (Dor84, Mun97). Suspensions of

fine particles of c-A1203 are used both as an abrasive and as a forming technique for

making bulk products. When considering powder properties such as packing and

rheology, the morphology of the individual particles becomes an influencing factor

(Suy9 1). Equiaxed and anisotropic particles fulfill different roles. Structural ceramics

require equiaxed particles to gain high packing densities and composites can benefit from

either plate-like or needle-like morphologies. Particle morphology and the colloidal

properties of varying morphologies are therefore an area of research that can affect the

suitability of a powder for a particular application.

Liquid phase precipitation methods often produce powders of controlled

morphology (Cho96, Mat92). The advantages of this class of methods lie in the

production of unagglomerated, uniform particles, which are often faceted. Liquid









precipitation requires an understanding of thermodynamic, interfacial, and colloidal

properties to the control synthesis. This chapter reviews the thermodynamics and

interfacial factors necessary to understand the control of particles morphology.

Properties of Alumina


Phase Stability

In order to utilize liquid solution precipitation, the thermodynamic conditions

must favor the production of the desired phase. Alumina forms several hydrated phases,

as well as doped phases useful for their electronic properties. The various structures of

hydrated and anhydrous aluminas are succinctly summarized by Gitzen (Git70) and Table

2-1 provides an overview. Of all the forms, o-alumina (corundum) is the most

thermodynamically stable, and all other phases (excluding impure aluminas) will

transform to alpha above -1200'C in air, as shown by Figure 2- 1. Hydrated phases of

aluminum oxides begin with the nominal formula AI(OH)3, and transition through the

alumina monohydrate formula A1OOH to anhydrous A1203. Many of the variations in

crystal structure of the anhydrous crystals are the result of chemical inhomogeneity. 3-

Alumina results from the presence of alkali or alkaline earth atoms, and the foreign cation

is commonly incorporated as part of the name.

The focus of this work is the anhydrous a-A1203 phase. The crystallographic

information for this phase can be found in the JCPDS files of x-ray diffraction data

(Alu96). u-Alumina is often described as face-centered array of oxygen ions with two

thirds of the octahedral sites occupied by aluminum ions. The crystal structure of a-

A1203 is rhombohedral (hex) in space group Rb3C with Wyckoff positions "c" for the






8


Table 2-1. Mineralogical overview of the phases of alumina (Git70).
Space
Phase Density Hardness Crystal System Group Angle Unit Cell Parameters
Gibbsite 2.42 2.5-3.5 monoclinic C5h 85026' 8.641 5.07 9.72
Bayerite 2.53 monoclinic C2h 90007' 4.716 8.679 5.06
Boehmite 3.01 3.5-4.0 orthorhombic D17h 9200, 2,868 12.227 3.70
Diaspore 3.44 6.5-7.0 orthorhombic D6 h 4.396 9.426 2.844
Chi 3.0 Cubic 7.95
Eta 2.5-3.6 cubic (spinel) o7 7.9
Gamma 3.2 tetragonal 7.95 7.95 7.79
Delta 3.2 tetragonal 7.967 7.967 23.47
Iota 3.71 orthorhombic 7.73 7,78 2.92
Theta 3.56 monoclinic C2h 103042 5.63 2.95 11.86

Kappa 3.3 orthorhombic 8.49 12,73 13.39
a-A1203 3.98 9.0 rhombohedral D6d 4.758 12.99
2 1
hexagonal R-3c 4.758 12.99
1
AIO-AI203 3.84 cubic (spinel) 07 7.915


Gibbsita Chi .


Boehmite ..... GammaI
... ." ...... .... b


D iaspor


I I I !

Kappa Alpha


Delta j Theta j Alpha

Theta Alpha


IAlpha Alumina


Figure 2-1. Thermal transformation characteristics of Alumina (Git70).


0 100 200 300 400 500 600 700 800 90 1000 1100


I I I I I I I I I I I I









A131 ions and "e" for the 02- ions. The Wyckoff letter indicates the coordinate

transformations needed to represent the atomic positions for the symmetry of the

structure. For the A13+ on the "c" coordinate, the variable z has a value of 0.3523 A and

the "e" coordinate for the 02- has an x variable of 0.3064 A. The ionic radius of A131 is

0.39 A, and the ionic radius of 02. is 1.40 A.



Solubility of Alumina

Precipitation of a desired phase from solution requires an understanding of the

equilibrium solubility of the crystal components in solution. The solubility of a

crystalline phase in aqueous solution can be calculated from thermodynamic properties

and knowledge of the aqueous species. The solution of metal oxides proceed by the

formation of aqueous metal ions or ion hydroxide complexes. For alumina, the aqueous

species are [A13+], [A1OH'+], [AI(OH)2+], [AI(OH)3], and [AI(OH)4-]. Each ionic species

is predominant in select pH regimes. Baes and Mesmer provide formation constants for

the hydroxlation of each species by the following reaction (Bae86).

Al3+ + xOH- AI(OH)x3x (2-1)

Formation constants are given in Table 2-2. Polynuclear ions are excluded from the

determination. Polynuclear ions are only appreciable at pH values less than 3 (Bae86).

The free energy of a reaction can be determined from the formation constant using

the following equation (DeH93).


AG = -RTlnKeq


(2-2)












Table 2-2. Formation constants for the hydroxylation of A13' aqueous species (Bae86).
Hydroxylated Species Formation Constant (Log Q)

A1OH2+ -4.97 0.02

AI(OH)2+ -9.9 (0.1 M NaCI04)

AI(OH)3 -15.6 (0.1 M NaC04)

AI(OH)4- -23.0 0.3


AG is the Gibbs free energy of formation, T is absolute temperature, and Kq is the

equilibrium constant for the reaction. The free energy values can be determined for the

solvation reactions described in equation 2-1 from the speciation constants. By inputting

the Gibbs free energy of formation of the oxide and the ionic species, the OPAL

program generates speciation equations which can be used to generate the concentration

of each ion in solution (Ada97). The sum of these ionic concentrations gives the

solubility of the oxide as a function of pH. The solubility of alpha aluminum oxide is

given by this method in Figure 2-2.

Hydrothermal Synthesis of c-Alumina

Hydrothermal synthesis is a material fabrication technique referring to the

processing of materials in heated aqueous solution at autogeneous pressures. The high

solvent power of the aqueous environment serves to synthesize low temperature






11


6





-2



0-

-2


-4


-6


-8

pH



Figure 2-2. Solubility of ox-A1203 in water at 25C as calculated from speciation
constants (OPAL97).





polymorphs of refractory materials (Lau73). Additionally, seed materials can be used to

increase yield or control nucleation, and scaling to industrial use is not problematic

(Hir87, Klu93, Lau73, Mat92,).

The stability field of the alumina-water system was investigated in the mid

twentieth century by several investigators (Erv51, Ken59, Kuz64, Kuz65, Kuz71, Lau43,

Mat67). The reaction equation for the formation of (x-alumina from a hydrated precursor

is as follows.


2A1(OH)3 A1203 + 3H20


(2-3)









The pressure temperature diagram for the formation of alumina phases is given in Figure

2-3 (Git70). This diagram presents the thermodynamically stable phases of diaspore and

cc-alumina, but several metastable phases such as boehmite and gibbsite are produced in

practice. Gibbsite is formed at all pressures below -l35C, and boehmite between 135C

and 375C, with diaspore formed at higher pressures and temperature greater than 300'C.

cc-Alumina (corundum) is formed at temperatures greater than 400'C. Hydrothermal

synthesis of corundum has not been developed for commercial application, as the reaction

temperature is greater than the critical point of water (374.1 C), and the autogeneous

pressure is approximately 40 MPa.

The dehydration of a precursor like gibbsite or diaspore is inhibited by the

presence of water, due to the development of water as a reaction product. The use of an

aqueous solvent inhibits the formation of the anhydrous phase. Investigation into

nonaqueous solvents for the liquid phase synthesis of alumina has been more promising.

Glycothermal Synthesis

The principles of hydrothermal synthesis are not restricted to aqueous solutions.

Several solvents with satisfactory properties can be used in a synthesis reaction. The

choice of an effective solvent for the formation of a desired phase must satisfy the

following requirements (Dem73).

1. Congruence of the dissolution of the test compounds.

2. A satisfactorily sharp change in the solubility of the compounds with changing

temperature or pressure.

3. A specific quantitative value of the absolute solubility of the compound being

crystallized.








4. The formation of readily-soluble mobile complexes in the solution.

5. A specific redox potential of the medium, ensuring the existence of ions of the

required valence.










I
10000 Diaspore





II
S-A1203










I
'y-A1203




CLl
100










100 200 300 400 500

Temperature C


Figure 2-3. Hydrothermal stability diagram for the Alumina-Water system (Git7O).









Use of a nonaqueous solvent changes the thermodynamic environment of

synthesis. The stability of phases can be changed to produce novel compounds (Bib85,

Ino97). Alcohols are commonly used, as well as carbon tetrachloride (Dem73). Inoue's

group has performed much of the pioneering work in glycothermal synthesis. Use of

glycols as solvent has been successful for producing a pseudo-boehmite alumina (Ino89),

o-alumina (Be197, Cho95, Cho96, Ino89, Kai94), yttrium aluminum garnet (Ino91),

BaTiO3 and TiO2 (Kai95), gadolinium aluminum garnet (Ino95), and rare earth ferrites

(Ino97). The hydroxyl groups complex with ionic species to provide transport, and in a

non-oxidizing environment the glycols exhibit adequate thermal stability.

Inoue determined that pseudo-boehmite like phases of alumina could be formed in

1,6 hexandiol and that oc-alumina was formed by the 1,4-butanediol solvent (Ino89). Cho

investigated the use of the solvent 1,4 butanediol for the synthesis of (x-alumina, and

found that the dehydration reaction temperature has a lower limit of 270'C, and that

synthesis could be performed in reaction times as low as 12 hours (Cho95, Cho96).

Cho determined that particle morphology could be controlled by choice of

reaction conditions (Cho95). Variables influencing morphology include stirring rate,

solids loading of precursor, and reaction time. Through control of process conditions,

morphologies ranging from hexagonal platelets to fourteen-sided polyhedra could be

formed. Figure 2-4 presents a morphodrome of reaction conditions in the 1,4 butanediol

system.












12.0 mI I I 240
120 N ~ NZ2-3urn 3-4urn


5.0 3-4um 130

3u-4uu



3-4um 3-4um 4u3
0.7 364u



1-2um NA
0.0 1-2um 0

5 10 20 30
Solids Loading (grams/250 ml)


Figure 2-4. Morphodrome of particle morphologies formed in the 1,4-butanediol alumina
system as a function of solids loading, shear rate, and reaction time (Cho96).




Glycol Chemistry

The use of a non-aqueous solvent requires that the solvent is understood both for

solvent properties as well as chemical stability. Glycols coordinate with ionic species

through the hydroxl groups. Inoue investigated the performance of glycol as a solvent as

a function of the number of carbon atoms in the backbone. 1,4-butanediol performed best

compared to two, three, and six carbon chain glycols due to the intramolecular

participation of the hydroxyl group in cleavage of the HO(CH2)n-O-Al< bond formed by

the alkoxyl exchange reaction (Ino9l).









However, glycols are susceptible to oxidation by strong acids or high oxidation

state transition metals. Secondary glycols oxidize to become ketones and primary

alcohols form carboxylates (Atk90). Glycols specifically react to form esters, ethers, and

acetals. Dehydration of 1,4-butanediol produces either butadiene or tetrahydrofuran. In

the temperature range 250'C to 350'C and with a suitable catalyst, tetrahydrofuran is the

principle product. Nitric acid is used with 1,4-butanediol to form succinic acid.

Butadiene is produced in the presence of cuprous oxide or sodium dihydrogen phosphate.

In the presence of alumina, 1,4-butanediol and ammonia at 400'C produces pyrrolidine.

With hydrogen sulfide in place of ammonia at the same conditions, tetrahydrothiophene is

produced (Cur52). The stability of the glycol solvent in the presence of additives will

certainly affect the success of the glycothermal synthesis, and consideration of the

catalytic properties of reaction components should be factored into their use in

glycothermal synthesis.

Surface Chemistry of Alumina

Alumina is an amphoteric oxide. Crystallographic alpha alumina is known to be

unstable in an aqueous environment compared to the hydrated phases. Alumina tends to

react with the water present in the atmosphere to develop a surface terminated by

hydroxyl groups (Git70, Isr92). It can have either negative or positive surface charge as a

result of the surface dissociation of these hydroxyl groups. Potential determining ions are

assumed to be H' and OH. Heat treatments are known to dehydrate the surface of alpha

alumina, and render the surface hydrophobic. Exposure to water either as liquid or vapor

causes the surface to age and redevelop hydroxyl groups.









Gitzen provides a review of colloidal behavior of aluminum oxide phases (Git70).

The point of zero charge (pzc) of the phases of alumina are given in Table 2-3.

Corundum and the aluminum hydroxides have a particularly wide range of pzc values.

Possible reasons include different measurement techniques (electroosmosis,

microelectrophoresis, pH of lowest solubility), variations in surface hydration, or the

presence of impurities. The point of zero charge of alpha alumina is particularly

dependent on the calcination history. It is believed that the surface structure of the

hydroxide groups have a significant effect on the charging behavior. Disordered surfaces

(perhaps induced by grinding) may form AI(OH)3 surface groups, and more ordered

surfaces may exhibit AlO OH surface groups. Finally, surface curvature will affect

surface structure.

Surface charge can also be developed in non-aqueous solvents. The colloidal

properties in ethanol were investigated by Wernet and Wernet (Wer94) who found by

titration experiments that the point of zero charge in ethanol is pH 9.5.

Surface Energy of Alumina

Material surface energy values are applied in precipitation, contact angle

measurements, and sintering to understand processing phenomena. The surface energy of

c-alumina is anisotropic as a result of the hexagonal crystal structure. Surface energy

measurements are environmentally specific, and techniques for measurement differ

accordingly. Solid-vapor energies are usually measured near the melting point of the

material where some degree of fluid flow is present. Surface energy between the solid-

vapor interface for cc-Alumina has been measured at 1850'C (DeH93) to give a value of

905 mJ/m2. This value is an average and is not specific to a crystallographic direction.









Table 2-3. Point of Zero Charge of Aluminum Oxide Phases (Git70).
Phase Point of Zero Charge (pH)

Gamma Alumina 9.0

Amorphous AI(OH)3 9.4

Gibbsite 9.20

Boehmite 9.40-9.45

Corundum 6.7 9.4

Aluminum Hydroxides 5.1 9.4


At room temperature, the solid-liquid interface surface energy of the basal plane

of alumina in deionized water has been measured by Ducker using the atomic force

microscope (Duc94). Through force of adhesion measurements, a value of 75 mJ/m2 was

determined. If solvent adsorption does not relate to the crystal structure, this value can be

used to relate surface energies of various habit planes via the Gibbs-Wulff construction.


Colloidal Properties


The stability of particle suspensions is a function of the attractive and repulsive

forces between particles. Central to the stability of the particle dispersion is the

development of surface charge which forms an energy barrier to particle agglomeration.

Electrical forces are approximately one thousand times stronger than Brownian motion

(Rin96). The surface charge is measured by the zeta potential of the colloid, which in

turn is a function of the electrical properties of the interface. An explanation of

fundamental surface charge and electrical double layer structure is needed for









interpretation of experimental results. The governing equations for colloidal interface

structure are covered in a variety of sources (Ada90, Isr92, Ros88) and detailed

information is available in Hunter (Hun87).

Development of Surface Charge

Colloids in suspension develop surface electrical charges by reaction with the

surroundings. The four mechanisms that cause the surface of a colloid to develop charge

are the presence of defect structures or polarization of surface ions in the lattice, dominant

ion surface composition, ion adsorption or ionic exchange and, dissociation of surface

groups (Hun87). The presence of defect structures cause charge imbalance in an ionic

crystal, and lead to electrical fields. Such defects can occur by ion exchange between

material ions and an aqueous species, where the replacement is of different charge. Space

charge can also be generated by vacancies within the crystal, which manifest as surface

charge (Kli65a, Kli65b). The crystal structure of a salt can favor the presence of one ion

over the other on the surface to give a surface charge dependent on the concentration of

the ions in solution. A colloid can be composed of surface molecules which exhibit acid-

base behavior. Last, ions or ionic molecules can be adsorbed on the surface to such an

extent that charge is generated. Those ions which adsorb on the surface to control the

surface charge are termed the potential determining ions.

Metal oxides are believed to form surfaces of hydroxide groups which dissociate

amphoterically by the following equations (Git70, Hun87).

AH2+ AH + H+ (2-4)

AH A- + H+ (2-5)









The electric charge at the surface attracts ions of opposite charge and repels like-charged

ions. The metal oxide layer is made more complex because the activity of the potential

determining ions on the surface is related to the potential of the surface. Oxides are

known to generate much higher charge magnitudes as a function of pH than sparingly

soluble salts (Hun87).

The modeling of the acid-base character of amphoteric oxides was developed by

Healy and White (Hea78, Hea80) to represent the development of surface charge as a

function of pH. The ratio of the concentration of surface species are controlled by the

following surface dissociation constants.

[AH][H+],
[ AHf+ (2-6)


K [A-][H+], (2-7)
[-AH]

The net surface charge density of the interface, G, is related to the number of

surface groups per unit area, N, by the following relationship.

[AH ]- [A-]
a=eN, --- A +- = eNa (2-8)
[AH + [AH+ I +[A-]

The fraction a has a range of plus to minus one, and the quantity relates the net number of

charge sites to the total number of dissociation sites. The surface concentration of

potential determining ions [H+], is related to the bulk concentration [H+] by the

Boltzmann factor.


[H ], = [H+]exp(-eTo/kT)


(2-9)









In a combined expression, the surface charge and the surface potential IO, are

related by the dissociation constants K, and K.


eN (H'/ K+) exp(-eP./ kT)-(K / H+)exp(e, /kT)
a=e.1 + (H' / K+) exp(-ell / kT) + K_/H+) exp(eT, / kT) (-0


The Double Layer Model

The presence of electric charge on a particle in aqueous solution causes oppositely

charged ions to be attracted to the charged surface. The counter charge may be either a

diffuse layer, or an adsorbed layer and a diffuse layer. This model is called the double

layer to reflect the two layers: the adsorbed surface layer or Stern layer and the diffuse

layer of counter ions near the surface. The diffuse or Gouy-Chapman layer can extend a

appreciable distance from the surface of a particle (Hun87).

The structure of the double layer describes the distribution of ions near the particle

surface, as shown in Figure 2-5 (Ada90). The surface exhibits a surface potential o.

The surface potential arises through various mechanisms dependent upon the colloid and

environment. The Stern or Helmholtz layer is composed of adsorbed ions which may be

transient. The adsorbed ions can only approach as closely as their hydrated radius for

cations, or ion radius for anions. As no species exist between the surface and the

adsorbed ions, the potential difference between the surface and the Stern layer Ts, is

linear. The adsorption of ions in the Stern layer is related by an adsorption function

similar to the Langmuir expression (Ada90).

S- = Cexp kT (2-11)


E) is the fraction of the surface covered by adsorbed ions, C is a constant and (D refers to












--1

STERN LAYER

uLJ
I-
0O
GOUY-CHAPMAN LAYER
0



I-
o,, 0 )Ee


DISTANCE FROM SURFACE



Figure 2-5. Electrical double layer interface indicating strong cation adsorption at the
interface and diffuse anion cloud decreasing with distance from the surface (Hun87).





the chemical contribution to the adsorption energy of the ions in the Stern layer to the

surface.

In the Gouy-Chapman layer, counter ions are attracted to the surface charge, and

like ions are repelled. Thermal motion keeps the ions in the diffuse layer from becoming

attached to the surface. The electrical potential in the diffuse layer decays by the

Boltzman equation from the Stern potential to zero.


n z nkO exp-Zie(x) (2-12)









nkO is the concentration in the bulk of the solution of ion k, k is the Boltzmann constant,

and T is the absolute temperature. The charge density of the solution, p, is the sum of the

ionic charges per unit volume.

(ZkeiF (2-13)
p =X zkenk = Zkenko expy kT (


The relation of the charge density to the electrical potential (D is given by the

Poisson equation.

V2 = -p / eE0 (2-14)

e is the dielectric constant of the liquid phase, eo is the permittivity of free space, and V2

is the LaPlacian operator. The negative sign is used in the equation because as the

surface is assumed positively charged, and thus the potential in the solution is negatively

charged. By incorporating the Boltzmann charge density expression into the Poisson

equation, the Poisson-Boltzmann equation is derived, to relate the potential as a function

of distance from the interface.


V2 D = l I.zi enio exp z ) (2-15)


A universal, exact analytical solution for this equation does not exist, and several

simplifying assumptions have been used for special cases (Hun87).

Surface charge density is determined by integrating the net charge of the double

layer from the surface to infinity, and reversing the sign of the charge. Therefore it has

the same sign as the potential.

a=J-pdr= fEEoV24dr (2-16)









Although the Poisson-Boltzman equation must be solved for specific boundary

conditions, analytical solutions for simplified cases allow predictions for the probability

of agglomeration to be derived. A common simplification used in colloid science is the

Debye-Huckel approximation, in which the surface potential is assumed to be relatively

small (-25 mV). Under these conditions, the expression for the Poisson-Boltzman

equation for a flat plate is as follows.
8m72 e"2
V2 _8n0z e = _22 t (2-17)
eeokT


where K is the Debye length and 1/K is considered to be the ion atmosphere radius. K2 can

be calculated from the expression:


K 4e2 niz (2-18)

The summation term divided by two is the ionic strength of the solution, and ni and zi are

the concentration and valence of the ions in solution. Highly concentrated ionic


solutions, or the presence of highly charged ions can cause the ion atmosphere radius to

collapse. This allows particles to approach very closely and aggregation can occur due to

van der Waals forces. The distribution of ions as a result of the surface potential in the

Gouy-Chapman layer is determined from the solution by the simplified Poisson-

Boltzmann equation (Ada9O).
zie
'-P(r) = exp(-io) (2-19)
E E"









Zeta Potential

Zeta potential is the potential at the "slipping plane" between the moving and

stationary phases, where the potential in the bulk of the liquid phase is considered to be

zero. It cannot correspond to the potential nearer to the solid phase than the plane of

closest approach of fully hydrated counter ions.

Zeta potential measurements determine the potential away from the surface

beyond which the ordered solvent layers are no longer bound to the surface. This is

affected by ionic strength of the solvent (i.e. the concentration of ions in the solvent).

The Stern assumption is that the zeta potential is measured at the inner Helmholtz plane

where the centers of the adsorbed ions lie on the surface. Alternatively, the zeta potential

can be assumed to lie at the outer Helmholtz plane; the distance of closest approach of

fully hydrated ions in solution. Specifically adsorbed ions will likely be dehydrated and

thus closer to the surface as opposed to the distance of approach of fully hydrated ions.


Morphological Control of Precipitates


The morphology of a precipitate dictates processing behavior of a material, and is

of fundamental interest in synthesis. Shape is influenced by internal crystal structure,

environment and temperature. An amorphous precipitate will generally be spherical as

the surface energy is isotropic, but a crystalline product will develop facets corresponding

to low energy habit planes. External conditions that affect morphology include pH,

temperature, reactant concentration and proportion, the presence of additives, solvent

interactions and agitation.









The crystal morphology relates to either the equilibrium shape determined by the

surface energy of the interface, or to growth shapes dependent on the formation

mechanism. Surface energy is a function of both the solvent or additive adsorption on the

interface and the material crystal structure. Growth rates of crystal habit planes depend

on the mechanism of addition of solute to the precipitate and the supersaturation. The

effect of adsorbates is to either reduce habit plane surface energy or slow their growth so

that they are not eliminated. By considering the effects of the variables involved in

crystal growth, control of the desired particle shape can be realized.

Equilibrium Shape

The derivation of the equilibrium shape of a crystal was first developed by Wulff

(WulO 1). Assuming that a crystal will minimize the sum of the products of surface

energy and area, a crystal with anisotropic surface energy will develop facets to reduce

the surface energy component of the system (Cur85). The surface energy properties of a

crystal are modeled by the Wulff plot, which is a three dimensional vector representation

of the surface energy of the crystal. Each crystal orientation is represented by a vector

centered at the origin of magnitude equal to the surface energy. Faceted crystals exhibit

pointed minima or cusps corresponding to facets with lower values of surface energy.

By considering the condition of mechanical equilibrium for such a crystal

(DeH93), the surface energy of a plane {hkl} divided by its perpendicular distance from

the center of mass of the particle to the facet, 2khkl is equal to a constant.

Y"hkl _kT p
In = constant (2-20)
Ahkj 2V.. po









Vm is molecular volume and p and po are the actual and equilibrium vapor pressure of

components. Liquid phase growth assumes concentration terms in place of pressure.

This constant is equal for all facets, { hkl 1. The central distance k1hkl is, therefore,

proportional to the surface energy of the face. An equilibrium shaped crystal will be

dominated by those facets which have the lowest free energy according to the condition

that XYdhklAhkI is minimized, where Ahkl is the area of facet {hkl}.
hkl

This derivation was performed for the solid-vapor interface, and does not consider

the complications present in growth from solution. Surface energy is highly dependent

upon the environment in which the crystal exists. The presence of solvent molecules can

significantly reduce surface energy by interacting with the surface, and the presence of

ions can modify pH or surface structure via adsorption. An explanation of the variation

of surface energy with environmental effects is needed to understand the effect of

solution conditions on the equilibrium shape.

Compositional Variation of Surface Energy

Surface energy is an interfacial property of thermodynamics, and texts on the

subject should be consulted for in depth discussions (Def66, DeH93, Lup83, Sut95). It

utilizes surface excess properties, which describe the difference between the energy in the

real system and the energy computed from the hypothetical Gibbs model interface

(DeH93). All excess properties like surface energy are defined per area of interface.

Adsorption for example is a surface excess of one of the components in the system.

The thermodynamic property of surface energy has been defined in several ways

by different authors. DeHoff describes the surface energy as the change in internal energy









of a two phase system with a change in internal area (DeH93). Adamson defines surface

energy as the reversible work needed to increase the surface area of a phase (Ada90). In

terms of specific surface excess properties, the definition of surface energy, 7, is given by

DeHoff (DeH93).

=U1 TS" -Xf _krFk (2-21)
k

In this definition, Us and SS are the internal energy and entropy, .tk is the chemical

potential of each component k and Fk is the specific adsorption of each component.

Surface energy is usually reported in terms of mJ/m2 and is dependent upon the

environment of measurement and crystallographic orientation.

Surface energy variation with composition is given by the Gibbs adsorption

equation. The change in surface energy for uncharged components at constant

temperature and pressure is given by the Gibbs adsorption isotherm over all components,

k (Ros88).


dny + SW kd, (2-22)
A

Fk = nk / A {moles/m-2} (2-23)

Electrical Variation of Surface Energy

Ionic materials like most ceramics require additional terms to represent their

electrochemical behavior. The surface of ceramics develop charge and exhibit

polarization. The presence of an external field causes the potential of charged

components to vary with position within that field. The saturated components in the

liquid phase are affected as a result, and the effect of the field necessitates the use of









electrochemical potential. The electrochemical potential, 77', is defined by the following

relation (Ada90, Gra47, Haa69, DeH93).

771 = l.k' + zkeT (2-24)

where Zk is the valence of the ion including sign, e is the electron charge and T is the

electrical potential. The condition for equilibrium in an electrostatic field requires that

the electrochemical potential gradient is zero (DeH93, Haa69). The gradient in chemical

potential and thus composition depends on the sign of the ion, zk.

The presence of surface charge at the interface affects the particle's equilibrium

shape through the effect of electrical charge on surface energy (Gra42). A direct

substitution of electrochemical potential for chemical potential in the Gibbs adsorption

equation is not strictly accurate as charge components are related through the condition of

electroneutrality. One component must be dependent to maintain charge balance (Gra42).

Electrocapillarity theory requires a model of the behavior of the electrode or

surface in order to relate electrical properties to observable phenomena. The ideal

polarized electrode (IPE) is applicable to the ceramic interface. The IPE has the property

that no continuous current is allowed to flow as the potential difference is altered slightly

from the ideal state. In the case of a ceramic surface, the ideal electrode can be assumed

as long as there is no dissolution of the surface. For intermediate pH's, this assumption is

sufficient. The variation of surface energy with the potential at the interface is given by

Grahame and Whitney (Ada90).


c fd c
dy + S~dT = -YFidy~i FjFizjd((D D) __ F,zjdd,,p (2-25)









F is the Faraday which is equal to Avagadro's number of electrons (96,490 Coulombs),

and Ifk is the specific adsorption of components of valence Zk. As the condition of

electroneutrality requires that charge cannot be varied independently, one component of

the system must be made dependent. The Gibbs adsorption equation uses a substitution

for chemical potential of the components that reflects the dependent component.

-k : 77k + Zk Tde,, (2-26)

This substitution gives the relationship between components. If we assume that

[H+] is the dependent component, the electrochemical potential of [H+] becomes related

to the potential of all other components. As a result, the expression for the change in free

energy of the electrochemical interface is written as follows.


dc + S"dT = -E.d(DP Oc)- I Fd(r/k + Z d,,) (2-27)
k

Here the number of components, c' is equal to c-1.

The quantity F-p is a thermodynamic quantity proposed to be equivalent to the

surface charge density.

P
eP = FXI-kzk =( (2-28)


However, this term for excess surface charge is only strictly valid for a completely

polarized surface (Ada90). The presence of ions on either side of the surface makes the

choice of the dividing surface a variable for the determination of the value of the specific

surface adsorption of the surface components.

For a constant composition, the electrocapillarity equation reduces to the

Lippmann equation (Ada90).










-(2-29)

Crystal Structure Theory

Early theories of morphology were based on aspects of crystal structure. Donnay

and Harker proposed a theory that linear growth velocity of a habit plane is inversely

proportional to interplanar spacing (Don37). Observed crystal faces are those with the

highest "reticular densities", and the degree of density determines the prominence of the

form. Reticular density is related to the packing arrangement of the surface ions or

molecules.

Surface energy was incorporated by Hartman and Perdok (Har55) by

consideration of periodic bond chains (PBC). A PBC is an uninterrupted chain of strong

bonds within the crystal lattice (Har55, Har73). Crystal faces are described by the

number of periodic bond chains parallel to the facet. A flat face (F) has at least two

PBC's parallel to the surface, stepped faces (S) have one PBC parallel to the surface, and

kinked faces (K) have no PBC's. Kink sites can form the most bonds with growing

components. Linear growth is assumed to be fastest in those directions in which

attachment energy is greatest. That is, kinked faces have the greatest linear growth rate,

G, and therefore are eliminated quickly. The flat faces are the slowest growing and

therefore dominate at low supersaturations. Figure 2-6 shows the formation of F, S, and

K faces for a cubic structure.

Hartman and Bennema (Har8O) describe the attachment energy, Eatt, as a habit

controlling factor. An expression is derived for the specific surface energy of a face

{hkl } based on the interaction energy per mole of a slice dhkI with the ith underlying site.










Y = (fZd,,, I iEi ) / 2V,, (2-30)

In this equation,f is a conversion factor, Z is the number of molecules in the

primitive unit cell, dhkl is the interplanar distance of face {hkl }, and Vuc is the volume of

the primitive unit cell. The attachment energy is defined as the bond energy released

when one building unit is attached to the surface of a crystal face. Increasing attachment

energy increases relative growth velocity. The attachment energy model only considers

bond energies, which is incorrect for cases other than vapor phase synthesis.

Growth Morphology

The shape of a precipitate grown from a supersaturated liquor depends less on

surface energies than the growth rates of the characteristic facets (Soh92, Wa179, Klu93,

Mat92). The growth mechanisms of crystals are understandably necessary to understand

the rate of habit movement. The BCF theory describe the stability of a face with respect

to the crystal structure, but the mechanism of nucleation and growth cannot be dismissed

in a discussion of morphology.

Nucleation

The driving force for nucleation lies in the degree of supersaturation of the solute

expressed as the difference in chemical potential. All materials have some degree of

solubility within a solvent. If the level of concentration of the material components are in

excess of equilibrium, then precipitation will occur in order to restore equilibrium

chemical potential. The difference in chemical potential, AYI, of a component is related to

the equilibrium concentration c0 and the actual supersaturation, c.





































Figure 2-6. Flat, stepped and kinked faces in the periodic bond chain model for a cubic
crystal structure (Rin96).





Ay = kTlnIc) (2-31)


The supersaturation can be represented by several expressions such as S = c/c0, cY = (c-

co)/cO or c co (Boi88). Relative supersaturation is given by a = (c-cO)/co = S 1.

The formation of a crystal from homogeneous solution requires the development

of a stable nuclei. Nuclei formation is broadly classified as either homogeneous or

heterogeneous. Homogeneous nucleation occurs without the interaction of an interface

with another phase and requires high supersaturation levels. A more common occurrence









is heterogeneous nucleation in which an impurity phase assists in the formation of a

nuclei (Soh92).

Homogeneous Nucleation

Classical approaches determine the critical size for a homogeneous nucleus as a

balance between the decrease in Gibbs free energy from the formation of the bulk phase

and the increase in energy through the formation of the interface. For a spherical cluster

of radius r, the formation energy is expressed as

4
AG'f = 4 '-AG + 41rr y (2-32)
3

AG, is the bulk free energy of the bulk volume. The balance of the volume energy

decrease and the increase in energy due to the surface creates a critical size for a stable

nucleus. Nuclei that exceed this size are thermodynamically stable for increasing growth.

The Gibbs-Thomson equation can be used to relate the volume free energy to

supersaturation.

Au p
AG = = RTln S (2-33)
V, M

p is the density of the solid phase, M is the molecular weight, and V,, is the molecular

volume. The critical size for a stable nuclei, r*, is found from the derivative of the free

energy of formation as follows.

2__ 2yV ,1
r* 2 AG, (2-34)
AG, kT In S


The free energy of formation is thus:










AG*- 167ry V(
3(kTln S)2 (2-35)

The rate of nucleation is generally assumed to follow an Arrhenius form like that

of chemical reaction kinetics. The rate of nucleation, J, is given by the expression:

Kexp 167ry3V2 (2-36)
J )Kexp- kT' 3k 3T3 (I nS)2 (


The constant K relates the diffusional energy barrier to the jump frequency. Above a

critical supersaturation, an exponential burst of precipitation occurs. Increases in

supersaturation increase nucleation rate, as does a decrease in surface energy.

The kinetic equations for determining the activation energy for nuclei formation

do not consider the formation of a surface energy, but rather the interaction of a molecule

and a cluster (Ruc90). The formation of a nucleus is modeled as the aggregation of

components resulting from collisions or aggregation. The collisions of multiple clusters

is not considered as the probability of this event will be rare compared to that of

individual collisions. A stable cluster exists at some number of components N. Dynamic

equilibrium in the system gives expressions for the nucleation and growth of a nucleus.

Nucleation AN + A, AN+I

Growth AN+I + A, AN+2

The expression for the critical radius of a nuclei, R., is complicated and requires a

numerical solution. Comparison with the classical theory shows greatest difference at

high supersaturation, but general trends and phenomena agree with classical results

(Ruc90). The nucleation model states that nucleation rate is proportional to the ion









concentration as a power law expression, with an exponential, p, between 2 and 6

(Wa179).

J = k cp (2-48)

The specific differences due to the nucleation of ionic species were addressed by

Chiang et al. (Chi88a) and Chiang and Donohue (Chi88b, Chi88c). According to this

theory, addition of material to a cluster of ions requires the formation of neutral ions on

the surface before integration into the lattice can occur. Nucleation rate is related to

growth rate by a power law with an exponential which depends on the particular

mechanism of material addition.

Heterogeneous Nucleation

Heterogeneous nucleation involves the use of another solid phase as a template to

reduce the activation energy needed for the formation of a stable nucleus. The lattice

mismatch between dissimilar materials will create dislocations and/or surface stress

(Wa179). Nucleation is distorted by this mismatch, and the solid-solid interface modifies

the surface energy requirements. Liquid phase precipitation models have been applied to

solid-solid interface precipitation (Soh92).

-g72V2f(O) ,
AGhet = 2 = AGomf(0) (2-38)


/3g is a geometric factor relating volume to surface area, v is the number of ions in a

neutral molecule, cD is the affinity defined by the change in chemical potential due to

precipitation, andj(1) depends on the wetting angle of the solid phase by the liquid.

f(E) = (2- 3cosO +cos3 e)/4 (2-39)









The functionfl(O) in the case of solid-solid interface relates the nucleation effect of the

substrate without carrying a physical meaning, and may have a different expression.

When the free energy of the precipitate-solution interface is greater than the difference

between the precipitate-substrate interface and the substrate-solution interface, the

activation energy for heterogeneous nucleation is less than that of homogeneous

nucleation.

Growth Rates

Solvents affect growth rates by the transport of supersaturated solute through a

quiescent layer of solvent and absorbed solute at the solid-solution interface. The steps of

integration of material at the solid solution interface involve diffusion from the bulk to

the surface, surface adsorption, surface diffusion to a high energy site, desolvation, and

integration into the lattice. The released solvent must then counter diffuse from the

surface into the bulk (Nan87). The slowest of these processes becomes rate limiting.

Based on diffusion, the rate of mass transport, dn/dt, relates to the supersaturation by the

following equation.

dm D (2-40)


A is the interfacial area, c is the supersaturated concentration and 3 is the thickness of the

laminar film of adsorbed solvent. By increasing shear rate in the solution (agitation), the

film thickness is reduced and the growth rate increased.

Modifications to the diffusion transport theory were made by considering the

incorporation of components into the crystal as a rate limiting mechanism. Reaction for

the diffusion and the surface reaction are represented by separate equations (Nyv85).









dm/dt = k, A(c- c.) (2-41)




where kd and kr are the mass transfer coefficients for the diffusion and the surface

reaction. These equations can be combined through an overall coefficient K defined as

follows.

1 1 1
+ (2-43)
K kd k,

The diffusion mass transfer coefficient is related to the laminar thickness of the solvent

layer and the diffusion coefficient by kd = D/8. If the surface reaction is fast, the

coefficient due to diffusion is rate limiting. By increasing the agitation, the growth rate

increases due to compression of the solvent layer until a maximum rate is achieved at

which point the growth of a crystal layer is controlled by surface integration mechanisms

(Nyv85, Soh92, Wa179).

The overall growth rate in terms of characteristic dimension G is given by the

following expression.

dL
G=-dt K,(c-c,)=K1S (2-44)
dt

K is a constant, and S is the supersaturation. Each habit plane will have a

different rate constant. The final morphology will depend on the relative growth rates of

each habit plane (Boi88).

Surface Integration Models

The mechanism through which new material joins the crystal depends on the

nature of the interface. For a perfectly smooth interface with no defects, growth of a new









surface layer is modeled via the adsorption of solute components and their coalescence to

form a stable nucleus. The rate at which the nucleus spreads to cover the entire surface

determines the type of growth. Mononuclear growth occurs when the spread of the

nucleus is fast, such as in the case of a small crystal where there is not much area needed

for growth. At the opposite extreme is polynuclear growth in which nuclei form on

growing nuclei before an entire surface layer is covered. In the birth and spread model,

nuclei are considered to spread at a constant rate independent of size. The overall growth

rate is given as follows.

dL =2 1[InIn S (2-45)
G d- K (S 1)Y[in S]Y exp -lnS 1


K2 and K3 are constants. The formation of two dimensional nuclei is the rate limiting

step of this mechanism. In this case, bulk diffusion and the surface reaction are ignored.

However, this model fails to explain growth at low supersaturation.

Screw Dislocation Growth

Burton, Cabrerra and Frank (Bur5 1) proposed that the activation energy for

growth of a plane surface would be reduced by the presence of a screw dislocation. The

dislocation would provide edge sites for the addition of components which would

eliminate the need for the formation of two dimensional nuclei.

The growth rate is expressed differently for cases of low supersaturation and high

supersaturation. For the limiting cases, the growth rate is expressed as follows.


Low supersaturation G = K4(Sy,) (2-46)


High supersaturation


G =K1sS


(2-47)









Here K4, K5, and S, are constants. At low supersaturation, the growth rate is

parabolic but growth becomes linear at high supersaturation. According to this theory,

growth is controlled by surface diffusion and the distance between kinks or surface steps

which is itself a function of supersaturation and crystal size. This derivation assumes

vapor phase growth.

Chernov modified the BCF theory by considering the bulk mass transfer

limitations between vapor and liquid phase growth (Mye93). Vapor growth is not limited

by mass transfer due to its rapid speed. The presence of solvent limits the rate of material

transfer to the crystal surface, creating bulk diffusion control of growth. The parabolic

dependence at low supersaturation is also predicted. The importance of hydrodynamic

conditions in crystal formation is therefore satisfied.

Surface Reaction Theory

Nielson (Nie83) and Estrin (Est93) describe the kinetics and mechanisms for ionic

crystal growth from solution involving less soluble solutes. Models assume that the rate

limiting step for the growth rate is the surface reaction.

G = K6 (S 1)q (2-48)

K6 is a constant, and q is the order of the reaction. Parabolic growth has a reaction order

of two, and is dominant for sparingly soluble salts such as BaSO4, CaCO3, and

CaC2O4,H20.

A chemical consideration of growth has been developed by Chiang and Donohue

which considers the electrical double layer interface of colloids (Chi88b, Chi88c). In

ionic crystals, surface lattice sites are treated as reactant species, and growth is considered

to proceed via chemical reaction with adsorbed ions. By consideration of the linear









adsorption isotherm from the electrical double layer, second order dependence of growth

rate on supersaturation is derived. Ionic crystals are represented by either the surface

reaction/molecular integration model (Mechanism 1) or sequential ionic integration

(Mechanism 2). In Mechanism 1, component ions A and B adsorb separately to the

surface, and must diffuse until they react to form an adsorbed surface species AB. This

surface species AB then migrates until it can be integrated at a lattice site. In Mechanism

2, component ions adsorb and integrate into the crystal separately.

Those methods controlled by bulk diffusion have growth rate expression similar

to equation 2-45, with separate rate constants for each ion, and equilibrium concentration

equal to the cation or anion concentration at the interface. The growth rates of cation and

anion are equal in order to satisfy electroneutrality (Soh92).

Morphological Forms Resulting from Growth Rates

As can be seen, facet growth rates are limited either by component diffusion to the

interface or by the integration mechanism into the lattice. Lattice integration has been

modeled for rate limiting mechanisms of integration. Addition may be direct for kink or

step facets, but flat faces require the birth of two dimensional nuclei. Growth of the

surface nuclei can become the rate limiting step of facet growth. The mechanism of

component addition can require the formation of neutral surface species before

integration with the lattice. Surfaces which support direct integration will have faster

growth rates.

Habit plane growth rates are considered as functions of supersaturation levels.

Near equilibrium, growth rates are proportional to surface energy. Low supersaturation

levels promote compact shapes with habit planes corresponding to faces in the BCF









theory. The surface is largely composed of flat facets as these surfaces have the lowest

surface energy. Side and kink facets provide more sites for component addition, and

therefore have higher surface energy. Integration of components will be swift, and thus

these facets will have growth rates that are diffusion controlled. Lower diffusion rates

will increase the amount of surface area of S and K faces on the crystal. As

supersaturation increases, the particle morphology deviates from equilibrium. Diffusion

of components is increased, and component adsorption on the surface and integration

with the lattice likewise increase. The particle surface will become dominated by facets

which are interface controlled. Increases in stirring rate or temperature increase diffusion

rates.

Dendrites are formed under conditions in which there are concentration gradients

in the adsorbed layer of solvent. This is a function of fast growth rates (Wa179).

Hydrodynamic forces reduce the thickness of the diffuse solvent layer near sharp edges

faster than in the center of planes (Soh92). The higher concentration near the edge either

creates a higher driving force for precipitation or permits faster rates of mass transport,

and this creates protrusions. If the supersaturation is high enough, growth will continue

and form elongated structures. Whisker formation is generally associated with the screw

dislocation model of Burton Cabrerra, and Frank (Bur51). Impurity adsorption on a

specific family of habit planes can also promote this type of growth.

The Effect Of Solvent


Solvents affect the morphology of precipitates both by influencing surface energy

and by modifying growth rates via transport properties. The interaction of the solvent









with the crystal structure establishes a solvent specific Wulff plot for the system. The

supersaturation and growth rate of the crystal dictate the growth form.

The nature of the solvent will influence the stability of a growing interface by the

types of intermolecular bonding mechanisms that the solvent supports. The role of the

periodic bond model with respect to solvent properties states that the solvent will adsorb

to the interface structure of the habit plane. Faces with more PBC's are expected to

adsorb more strongly, and therefore reduce surface energy to a greater degree. It is likely

that solvent will order at the interface, and the order may create PBC's that are not related

to the crystal structure (Boi88). The solvent characteristics can affect the type of

interfaces stabilized in the crystal. The interaction of a polar solvent like water with

oxygen ions in a crystal can lead to the promotion of specific habit planes (San97).

Compounds containing polar molecules like -OH or -NH2 have habit planes that are

stabilized by solvents which can exhibit hydrogen bonding (Wa179).

Growth of an interface is specifically affected by the solvent's transport

properties. The viscosity, density, mass transport, heat transport and diffusivity of the

solvent at temperature will affect growth rates (Klu93). Viscous forces arise from solute-

solvent and solvent-solvent interactions. Solvation forces will dictate the structure of the

solvent near the solid-solution interface, and prediction of solvation effects on viscosity

remain under investigation (Isr92, Man96).

Electrolyte solutions have been modeled by Myerson et al. for the effect of

electrolyte concentration on viscosity and diffusivity (Mye97). Ions in electrolyte

solutions affect the thermodynamics of the solvent as a result of the electrostatic forces

between them. In supersaturated solution, the solvent diffusivity is strongly decreased as









supersaturation increases. Solvent viscosity is less dependent upon solute concentration.

The difference in behavior reflects the formation of ion pairs which diffuse at slower rates

than individual ions, and supersaturated solutions will have higher concentrations of ion

pairs or aggregates (i.e. unstable nuclei).

Solvation of the surface will affect crystal growth. Growth requires the addition

of growth units, whether individual ions or surface ion pairs. These units are generally

solvated, and after integration into the solid, the liberated solvent must diffuse to the bulk.

The diffusivity of the solvent can contribute to the growth rate of a facet. Complexes can

form in solution that "capture" components. The additional bonds must be broken before

integration can occur, and this increases the activation energy for growth. A lower rate

results. Higher adsorption energy of solvent stabilizes surface energy and lowers growth

rate (Klu93).

The effect of hydrogen bonding on surface energy is hard to quantify, as the

structure of hydrogen bonds is not well characterized. It is known that the interaction

energy is proportional to the inverse second power of distance (Isr92), and that highly

polar molecules like water can form discrete layers of polarized molecules (Hor90). The

arrangement of these molecules produces an oscillatory force close to the surface as

measured by atomic force microscopy (Duc94). Hydrogen bonding should be highly

dependent on the arrangement of surface ions and the surface charge.

Surface Energy Reduction via Solvent Interactions

The solute-solvent interface controls the energetic stability of a habit plane during

precipitation. Solvent molecules interact with the surface through intermolecular

potentials. Table 2-4 gives the intermolecular potentials typical of ionic solids (Isr92).













Table 2-4. Intermolecular and surface forces in vacuum. (Adapted from Isr92).
Type of Interaction Interaction Energy w(r)

Charge-Charge (Coulomb energy) Q Q2
4;reor

Charge-Dipole (fixed) Qu cos E)
4 wEO r 2

Q2U2

6(47re0)2 kTr4
Charge-Dipole (freely rotating)

Dipole-Dipole (fixed) u1u,[2cosE1) cosE)2 sin1 sin2 cosc(]
47rVe or'
2U2
3(4 .0) 2kTr6 [Kessom energy]


Dipole-Dipole (freely rotating)

Charge-nonopolar Q2cx
/ 2(4 ire )2 2r4


Dipole-non-dipolar (fixed) u2cx(1 + 3cos2 E)
2(4rEo )2 r6

U 6 [Debye energy]
(4re 0)2 r- 6
(freely rotating)

Hydrogen Bonding proportional to -1/r2

complicated, short range









Interaction energies can be divided according to the type of interaction, of which

dispersive, polarization, and hydrogen bonding are usually considered for ionic solids.

The interaction energy, or pair potential between atoms or molecules w(r), must

accommodate both the effects of the solvent as well as the solute.

In practical terms, a solvent that has an appreciable dipole moment will become ordered

at an electrically charged interface. The degree of ordering will scale with the magnitude

of the dipole moment. The change of entropy due to solvent polarization can be

measured through the heat of immersion, AHimm. The heat of immersion relates the

change in surface energy between the solid-vapor and solid-liquid interface, but cannot

provide information on the absolute values of the interfacial energy in either state. The

heat of immersion will depend on the various components of intermolecular interaction:

dispersive forces, polarization, hydrogen bonding, and habit plane effects. The total heat

of immersion can thus be considered to be the sum of these interactions.

AHI,,72 = AHd -i-AH." + AHH-bond + hiabit (-1
im /71 nm +AHimint (2-61)


Predictions of the components due to dispersive interactions have been

investigated by Fowkes (Fow63), but qualitative predictions of the components of free

energy related to molecular forces have not been well developed. Attempts to understand

the role of solvent on surface energy employ models relying of predicting interactions

between individual components of the solid and liquid.

The Jackson c Factor

An expression to relate the effect of the solvent molecules near the solid-solution

interface was derived by Jackson in 1958 (Klu93). By a consideration of the number of









extra molecules on the surface, the change in free energy of a planar surface can be

related to the fractional coverage of the surface, 0.


= a = (I-)O+OlnO)+(1-0)ln(1-0) (2-49)
nkT

(/fJdd''Olt1i"O / RT)EE (2-50)

odlvenl'tifl is the heat of dissolution. x is a "surface entropy factor" and it measures the
solvent th ofi enrpadte

degree of smoothness of the crystal face at the atomic level. E is the fraction of the total

binding energy that binds a molecule to other molecules at the solid-liquid interface. E is

equal to ns/nb, where n, and nb are the number of nearest neighbors on the surface and in

the bulk. Low index plane have T values between 0.5 and 1.

The regular solution model has been applied to the x factor for solvents that do

not significantly interact with the surface. Such solvents avoid hydrogen bonding,

solvation or complex ion formation. Qualitatively satisfactory results were found by

assuming the heat of dissolution to be equal to the heat of vaporization plus the heat of

mixing. Using an ideal expression for the entropy of mixing, the x factor is expressed as

FHJ~ IT AC,
=In X iq-t f "I, ~
a= RT,, n q +R T T dT] (2-52)


X is the solubility of the material at temperature T. AHfUS is the heat of fusion at the

melting point. Solvent interaction increases the solubility of the solute and gives a

negative heat of mixing. A lower a factor increases the growth rate indicating that higher

solubilities promote rapid crystallization (Klu93).

The ax factor qualitatively expresses the various growth mechanisms. If oa is lower

than 3, fast growth occurs with linear relationship to supersaturation. For an ax factor









between 3 and 5, step limited growth occurs, and the growth rate is typical of the birth

and spread type. For cx above 5, growth is dislocation controlled, and a parabolic

dependence of supersaturation like that of the BCF model prevails.

Interfacial Cell Model

Liu has developed a model for the interface structure that has shown promise in

the prediction of crystal morphologies (Liu97). The model employs an inhomogeneous

cell model in which solute composition and concentration, solvent, and impurities are

explicitly incorporated. Thermodynamic differences are described by the surface scaling

factor, C*(hkl).

A Hdlss x
A(hkl) A(hkl) 0j
C, hkl) -- Alli,. In (2-53)
A In XA (D (

A~is [ ISsi
Hdia(hkl) is the enthalpy of dissolution at the crystal surface (face specific), and AH-I s


the enthalpy of dissolution in the bulk. XA(hk) and XA are the mole fraction of solute at the

crystal faces {hkl} and in the bulk. 'pj is the change in bond energy per structural unit in

direction j at the surface and (Ij is the corresponding energy in the bulk. Calculations of

XA(hkl) can be performed using computer analysis, and the effect of solvent at the interface
is largely characterized by C*hkl) (Liu97).


The process to characterize morphology with this model requires use of an

interracial structure analysis using computer models. Calculation techniques include

Monte Carlo or molecular dynamics techniques, the application of density-functional

theory calculation or self-consistent field lattice theory.









The scaling factor is employed in the determination of relative growth rate of a

face by the following relationship.
n "dX., C*1 h410)
r rel "lk1 dhk K A expr- A / nhklkT] (2-54)
xhk Cl-(hkl) hk'I(hkl)' hkl dss/


In this expression, dhkl is the interplanar distance for orientation { hkl }, nhkl is the number

of non-coplanar PBC's in crystal slice { hkl 1, hkl is the orientation factor equal to
sliced Ecr where E ,,ic is the 2D latttice energy. XA, AH d and T are all experimentally


measurable. The calculation of the scaling factor is the most elusive parameter. In this

model, development of an accurate computational model is needed in order to have

successful prediction of morphology.

The Effect of Adsorbates


Adsorbates in crystal growth are used in order to control various characteristics of

the growth process. Adsorbates have four primary effects: crystal habit modification,

growth rate modification, crystallographic modification, and phase transformation

control. Crystal habit modification obviously affects the morphology by specific

adsorption of an adsorbate on a specific habit plane or planes. The growth of the

adsorbed surfaces is retarded to give that habit plane more dominance over the crystal

shape. Examples include the modification of NaCl crystals by urea (Wa179), CaSO4 habit

modification by organic derivatives of phosphoric acid (Soh92), and modification of

protein crystals by chemically similar proteins (Hir97). The effect of adsorption has been

found to increase with increased concentration, but optimum levels of coverage exist.

Part of the effect of adsorbates can be attributed to solvent extrusion. By exclusion of









solvent from the interface, the transport of growth units is inhibited. The desolvation of

the surface creates an additional activation energy barrier to the integration process.

The behavior of adsorbates can be considered from two extremes. An adsorbate

can exist as a strongly bound molecule that is effectively immobile. Adsorbates will

preferentially fill kink sites as these sites provide the highest attachment energy. Low

concentrations of additive can saturate kink sites quickly. Step sites and face adsorption

follow. These three types of adsorption sites were observed experimentally by Boistelle

in 1974 (Klu93). Immobile adsorbates can become incorporated into the crystal, and are

expected to have greater effects on crystal growth rate. The adsorbate can also interact

with the surface structure to generate a "surface phase" that interacts laterally to create a

new surface tension.

The reduction in growth rate of a moving step has been related to the presence of

strong, immobile adsorbates. The adsorbates pin the growth front, and passage of the

growth front creates curvature. The movement of a growth step is postulated to cease

when the distance between impurities is less than twice the radius of curvature of the

growing interface, Pc.


VA = V P1 2pdAYV (2-55)

d"12 is the average density of impurities ahead of the step, VA and vp are the velocities of

the adsorbed and pure surfaces. When impurity concentration pins the growth front,

growth will cease. A critical two dimensional nuclei size can be related to impurity

adsorption on the surface by the following expression.









2A7'
2pc- kTS (2-56)


A is the lattice constant, and S is supersaturation. A critical nucleus depends inversely

with the supersaturation. Low concentrations of adsorbate do not affect growth

significantly so that classical derivations hold, but higher adsorbate concentrations require

greater supersaturations for growth.

The adsorbate can otherwise be considered to be mobile and diffuse two

dimensionally through the surface. Mobile adsorbates are expected to be "swept away"

by a growth front, and incorporation into the lattice is less common. Retardation of

growth rates is also less severe (Klu93).

Habit modification results from the specific adsorption of an additive on only one

type of habit plane. Such adsorption relates to the arrangement of components on that

face, as well as the solution chemistry during the reaction. By its presence on the habit

plane, growth rates are slowed, and the adsorbed face becomes more dominant on the

surface structure (Hir97).


Summary


At the crystal interface, bulk properties of interaction energy are interrupted, and

surface ions must compensate either via the transfer of electrons (valence transfer) or by

rearrangement of ions to create polarization. Both mechanisms generate surface charge.

The presence of the liquid interface provides a reduction of surface energy via the

interaction of the solvent molecules. The solvent can interact with the surface by

chemical bonding, hydrogen or hydrophobic bonding, dispersive forces, and polarization

due to surface potential (Wa179, Par83). The degree of interaction is highly dependent on









the arrangement of ions on each surface, and obviously will differ between habit planes.

The composition of the surface in turn will depend on the crystallographic habit plane,

potential determining ions in solution, presence of defects in the lattice structure, and the

presence of specific adsorbates.

The solvent and method of precipitation affect the resulting morphology of the

precipitate. The solvent affects the equilibrium shape by preferentially interacting with

crystal facets to reduce surface energy and by influencing the transfer of solvated

components to the surface. The stable morphology is a result of a combination of

reaction conditions including stirring rate and supersaturation. Growth shapes are

transitional shapes in the achievement of the equilibrium shape and are dependent on

kinetic and environmental factors (Boi88). Supersaturation and the rate of

supersaturation generation are important factors for supply of components for crystal

growth, and the incorporation of components into the precipitate can be limited by several

mechanisms. These mechanisms include the diffusion of components from the bulk,

desolvation of the surface, adsorption of growth units (ions), surface transport of growth

units to low energy sites, and the incorporation of components into the lattice, as well as

the reverse process of dissolution (Nan87). The stirring rate can affect the rate limiting

mechanism for particle growth by influencing the hydration layer of the particle surface,

or increasing diffusional transport rates between the bulk solution and the particle surface.

Stirring rate and solids loading will control the growth shape of a precipitate as it

develops the equilibrium morphology, but the equilibrium shape is not necessarily

realized under conditions of growth. Equilibrium morphology will be attained after






53


annealing at constant solubility product, where material on high energy facets is dissolved

and precipitated on low energy facets.















CHAPTER 3


DERIVATION OF THE EQUILIBRIUM SHAPE OF AN ALUMINA PARTICLE
WITHIN A SOLVENT


Introduction


Curie first proposed the concept that at equilibrium, a faceted particle will have

minimum surface energy by achieving the lowest summation of the products of facet area

and surface energy (Cur85). The thermodynamic derivation of the equilibrium shape of a

particle has been performed by Wulff (Wul0l) and contributions using this derivation

have arisen from many authors (Bra75, Cah74, Def66, Her50, Her5l, Hof72, Sea94,

Sto92). The results of this work indicate that there exists a simple relationship between

the pressure in each phase and the distance from the center of mass of the particle. The

condition for mechanical equilibrium is as follows.


Pc=P"+2 (j= ,2, ...,F) (3-1)

Pc and pv are the pressure within the crystal and vapor respectively, y, is the surface


energy, and Aj is the central distance for each facet j. F is the total number of facets for

the crystal. The central distance is the perpendicular distance from the center of mass to

the surface of the facet. This relationship is the basis for the Gibbs-Wulff construction

which states that the ratio of the surface energy to the perpendicular distance is a constant

for all facets (DeH93).










% constant (3-2)

This relationship results if the pressure in the vapor (or liquid) phase is identical

for all facets. The equilibrium shape is modified by several additional factors resulting

from the solid-liquid interface. Surface charge is commonly developed within a solvent

(Soh92). The surface charge will affect the fluid pressure near the surface according to

the field strength (Ada90). Additionally, the solid-vapor interface does not consider

chemical reactions in the transition from one phase to another, and common components

are considered to be present in both phases. Solution growth can involve chemical

transformation from solution components in the formation of crystal components. The

effect of electrically charged species (ions and/or electrons) add the requirement that

electroneutrality is maintained within the system. Ceramic oxides require consideration

of the above factors in the derivation of equilibrium shape.

Conditions for Equilibrium


This derivation assumes Gibb's model of the interface. The system is assumed to

consist of a faceted particle of o-alumina in equilibrium with a liquid solvent which

supports ionic species. The components of the u. phase are A13+(o) and 02(X) ions. No

explicit defect structures are considered in this work. The liquid phase is considered to

support AI3+(1), O-f(l), and H+(1). The number of species is kept to a minimum for ease

of discussion, but additional components could be included in a generalized derivation.

The expression for the total entropy of the hypothetical system is as follows.

d S)S d'a+dS 1,1+S dA (3-3)









The superscripts c and I refer to the alpha and liquid phases, and the prime states

that these are extensive thermodynamic properties. S' is the specific superficial excess

entropy of the interface. The use of charged components (ions) requires a consideration

of the electrical effects in the derivation. The expression for internal energy can be

separated into chemical and electrical components to give the following expression

(Ada90).

dU'+dEot = dU' +dU +U sdA + dEpot (3-4)

U' is the internal energy of each phase (alpha and liquid), Us is the specific superficial

internal energy of the surface, and dEpot is the electrical potential resulting from the phase

transition. The change in electrical potential of a species during a phase transition is

related to the change in the number of moles by the following equations (Ada9O).

pot = =zF(D -,F)dna F((J'c- )dn (3-5)
k k

(D is the electrical potential in the bulk of each phase and zk is the ion valence for each

ion,k,. Therefore the expression for the change in internal energy can be expressed as

follows (Ada90, DeH93).
dU'a = TadSlapa dV'a +l. Ynk k
d'a a + V zkF(a V)dno (3-6)
k=1 k

The summation expressions can be combined into the statement recognized as the

definition of electrochemical potential, 77k, where F is Faraday's constant.

77k = .t + ZkFAk (3-7)









where /k is the chemical potential, and A(Dk is the change in electrical potential between

phases. Grahame claims that/.tk is not the ordinary chemical potential, as it depends on

temperature, local concentration of components and the local electrical field (Gra47).

The expression for the internal energy of the alpha phase is therefore given by the

usual expression with the use of electrochemical potential terms instead of chemical

potential (DeH93).

C'
d ,p= TadSa-Pa dVa+flkdna (3-8)
k=1

This expression can be rearranged to give the differential for entropy of the cx

phase.


dSa hp = dU'- 1 +--dVa dn (3-9)
a Tax k=T d

Corresponding expressions apply to the liquid phase. Using expression 3-3, the

entropy of the system can be expressed as follows.

1 Pa I C
dS',s... z-_ TdU+--dV T-- rl dn- +
~Z.,
Ta T T k1 (3-10)
P1 1 C
dU"a + dVar Y.,rl7kan' +S 'dA
T1 T- F k=l

The isolation constraints in the system are constant internal energy, constant

volume, and conservation of atoms.

dU'= 0 = dU"a +dU'+U"dA (3-1 la)

dV'= 0 = dV'O +dV'+V"dA (3-1 lb)

dMk = 0 (3-1 ic)

The following relationships result.









dU' = -dUlUsdA (3-12a)

dVWa = -dV'" (3-12b)

There is no specific superficial volume as it is defined to be zero. In addition, the

relationship between volume and facet area for a polyhedron is given by a geometrical

expression (DeH93). The volume of the crystal is thus proportional to the surface area of

the facets and the central distance, 4j.

1 F
dVc= vc/Aj (3-13)


The expression for the entropy of the system with internal energy and volume

constraints now appears as follows.

c/S a (1 ji~a F
so Ta T Ta ) 2 (3-14)

~{~f~ ~7n~+ s ~dA


Reactions of the crystal with the solvent (i.e. dissolution and precipitation) will

now be considered separately and inserted into the derivation upon completion. The

conservation of atoms statements are as follows.

dmA =0= dnA13+() + dnA3+(l) (3-15a)

dr0 =0 = dn02() + dnoH_() + FOH dA (3-15b)

dm- 0 dn+() + dno11_() + FoHM)A + F"H+dA (3-15c)

F is the specific superficial excess concentration of the components. The expression for

the electrochemical potentials can be written:









I 77A3+(a)dnA3+(x) + T7"2-()dl 2-(O() +77A13+(I)dnA3+(l) (3-16)
T (+ oH_(dflnoH_ 1) + 7H+(I)dnH+(I)

Substituting for the conservation of atoms,


I (7A/3+a) -77A13+(1) )dflAl3+(.) + (TIOH (I) 7702-(a) 7H+(1) )dn'OH (I) ( -7
T (772-(a) 77H+(l) )I-OH1dA + ( -7Ff+(/) (3-17)

The first two terms give the following reaction equations.

o01(l) --Q'(a) + H+(l)

Al3 +(a) Al3+(l)

Where chemical (or electrochemical) reactions can be written, the thermodynamic

property of Affinity is applied to represent the reaction. Therefore, for a reactive interface

the following relationships prove useful.

dnk = v,krd (3-18)


where the variable r designates the different independent chemical reactions possible in

the system, vk,- are the stoichiometric coefficients for the components of the reactions, and

d ,. is a property called the extent of reaction. The extent of reaction is the difference

between an initial amount of each component, no, and the component amounts at

equilibrium, n,: The extent of reaction determines the number of molecules of each kind

in the phase, as well as the electrical charge on each phase. The relative positions and

charge magnitude determine the electrical field in the system, thereby determining the

electrical energy of the system (Def66).

The affinity of each reaction is given by A,..









A,. = k (3-19)
k

Thus the expression for the entropy of the isolated system is as follows.


dIS'SS,iso Iy I jdU'a+( ra - _,d.jd Ao2 d o
-AA3+dA3+ +-' + () + j (3-20)

---+( T+ (7702_(a)+7+l+(a))Fo_ + (nH+ )F+dA


If we define surface energy to be

y -U) -TSs I 77mF,j (3-21)
/1

and let the total surface area, dA, be represented as

F
dA = XdA, (3-22)
j=1

then the expression for the entropy of the system results.


d = (dI I 1 I - -__ Ad4,, (3-23)
Sssi- rT l j-1 T' T' -2 jj dc 2=


The equilibrium conditions are found from setting the argument of each

differential equal to zero. The equilibrium conditions become clear.

Thermal Equilibrium: T7 =

Reactive Equilibrium: A,.= 0


Mechanical Equilibrium: P' = P1.. --2


The expression for thermal equilibrium agrees with previous derivations involving

multiple phases (Ada90, Def66, DeH93). The reactive condition assumes that

electrochemical potentials are used in the expression. The expression for the reactive









equilibrium satisfies the requirement that the exchange of material across the interface is

not independent of the species, for in the exchange of charged particles electroneutrality

must be maintained (Gra47). The inclusion of a reactive surface is a solution to the

generation of charge at the interface. The extent of reaction allows for equilibrium to be

attained and accounts for the generation of surface charge. Grahame utilized the chemical

potential of electrons in his derivation to account for the generation of charge (Gra47).

Such an inclusion in an ionic material would be inappropriate.

Morphological Variation with Surface Charge


The conditions of precipitation have shown that differences in morphology can be

controlled as a function of solution conditions such as stirring rate, solids loading, pH,

additive concentration and reaction time (Nyv85, Soh92). The equilibrium shape also is

dependent on solution conditions through changes in surface energy. Surface energy has

been related to the charge on colloidal particles through the electrocapillarity studies of

Grahame and Whitney (Gra42, Gra47). Reductions in surface energy occur as the

electrical charge on the particle surface differs from the point of zero charge. The

relationship between particle charge and surface energy is given by the Lippmann

equation which states that the change in surface energy is equal to the negative of the

surface charge density times the change in potential.

-u (3-24)
dcI

Surface charge generation in ceramic colloids has been described by Healy and

White assuming that the surface is composed of terminating hydroxyl groups (Hea78,

Hea80). These hydroxyl groups regulate surface charge through the addition or loss of a









proton, and therefore relate to the solution pH. The electrocapillarity curve for a ceramic

surface can thus be generated by manipulation of the surface charging relationship for

ionizable surface groups, and the effect of pH on surface energy can be estimated. If the

various planes of a particle are characterized by different charge constants and point of

zero charge, the pH of the solution can be related to the equilibrium morphology.

The surface potential, 'IF, for the Healy-White model is found from the solution to

the equality

sinh(eYo / 2kT) Usinh( e UN e'P0
___ ___ ___kT kT )
='{'N e'P (3-25)
o + 6cosh( U U0
kT -kT


where yion and 6 are terms concerning the solution ionic strength and surface charging

characteristics respectively, and WN is the Nernst potential. The fraction of ionized

groups, (xio, is given by the right hand side of the equality. Surface charge is determined

from the number of active sites and the fraction of ionized groups by the following

relationship.

co = eNs ,.o, (3-26)

e is the charge on an electron and N, is the number of surface sites per unit area. Surface

energy can be related to the surface charge by graphically integrating the cY vs. pH curve

(Stu92). The resulting data requires an integration constant K which is the surface energy

at the point of zero charge. The relationship is written as follows.


-=- J odpH + K (3-27)









For considerations of the equilibrium shape, the Gibbs-Wulff construction

depends on the value of surface energy, and it is obvious that equilibrium shape will

differ as surface charge is modified. For instructive purposes, the effect of pH on shape

can be estimated by characterizing the surface charging behavior of a material as a

function of the specific habit plane. Surface energy at the point of zero charge must be

determined. As an illustration, the surface energy and surface charging characteristics of

alumina will be estimated and related to morphology. Table 3-1 gives the assumed

surface energy and surface charge characteristics for three habit planes of o-alumina. The

site density is taken from the number of aluminum sites present on each surface, where it

is assumed that the reaction of a hydroxyl ion from solution with the A13 ion provides all

the sites on the surface. The basal plane has been found to have the lowest surface energy

at the solid-vapor interface (Cho97) and this is reflected in the choice of lowest surface

energy at the point of zero charge which was estimated from information presented by

Ducker et al. (Duc94).

The surface potential for each habit plane was calculated from equality 3-25 using

the assumed values for acid dissociation constants, and is presented with the fraction of

dissociated surface groups in Figure 3-1. The solution to equality 3-25 was performed

using Mathcad Version 7 (Mat97), and surface charge was calculated from the potential

using equation 3-26. An ionic strength of 10-4 M background of 1:1 electrolyte was

assumed for all calculations. The surface charge was related to the surface energy by

determining the slope between data points, and the differences were summed from the

point of zero charge to give the electrocapillarity curve for each habit plane. The surface









Table 3-1. Illustrative examples of the assumed surface energy and surface charge
constants for three planes of (x-alumina.
Habit Plane Site Density Point of Zero pKal pKa2 yPZC

(sites/nm2) Charge

{0001} 1.25 3 -1 7 75

{11201 1.1 7.5 5 9 120

{10121 0.85 10 6 14 135


energy constant for each plane was added to give a curve for the surface energy for each

habit plane presented in Figure 3-2. Solution pH values of 2, 7 and 12 were used to

evaluate the theoretical equilibrium morphology. These theoretical morphologies are

presented in Figure 3-3.

As each habit plane reaches it's point of zero charge, it's surface energy is

maximized and therefore the plane becomes less prominent over the equilibrium shape.

At pH 2, the basal plane is near its isoelectric point, and surface energy is relatively high.

In contrast at pH 12, surface charge has lowered the surface energy and the basal plane

has become more dominant. This relationship correlates with observations of growth

rates of corundum under alkaline conditions (Kuz65). The basal plane grows slowly

under alkaline conditions, suggesting that surface energy is low. Likewise the decahedral

plane is prominent at pH 2 due to the reduction of its surface energy. The hexagonal

prism plane does not experience significant reduction in surface energy and is least

prominent at pH 7 near its isoelectric point.







65








0,3

Basal Plane (0001)
0.2 -.. ...... Hexagonal Prism (1120)
"'" ". -- Decahedron (10T2)


E 0.1 -



0.0



-0.1



-0.2



-0.3

0.6 2 4 6 8 10 12
0.4
0.2 --.
0.0 - - -
-0.2
-0.4
-0.6
2 4 6 8 10 12

pH






Figure 3-1. Surface potential and fraction of charge surface groups, oX, for the
hypothetical habit planes given in Table 3-1. Surface potential increases away from the
point of zero charge as a result of the development of charge from the protonation or
deprotonation of surface hydroxyl groups.







In order to employ these types of relationships, the surface energy and surface


charge characteristics for a material must be determined as a function of habit plane.















140


120


100


80


60


Figure 3-2. Calculated surface energy curves for each habit plane as a function of pH and
surface charging from the assumed surface energy and charge constants. As each habit
plane experiences the development of surface charge, surface energy is decreased.



Information of this type is becoming available for alumina through several investigations

using the atomic force microscope (Duc94, Lar97).

Assumptions used in this derivation require that the solution to the equality 3-25

is performed with a monovalent background electrolyte, which will not be the case during

precipitation of ceramic oxides due to the presence of higher valence cations.

Additionally, the concentration of background electrolyte will vary with the solubility of

the oxide in solution. Precipitation is assumed to occur near equilibrium levels in order


- Basal Plane (0001)
...... Hexagonal Prism (1] 0)
- Decahedron (0OT2)


--- ----------
.. . . . .I. . . . .. . . . . . . . .






67















A















B















C

Figure 3-3. Particle morphologies as a function of pH. A. pH = 2. B. pH = 7. C. pH =
12.






68


for surface energy to influence the morphology. A complete description requires an

inclusive program that involves aspects of colloidal chemistry and solubility.















CHAPTER 4


ADDITIVE EFFECTS ON PARTICLE MORPHOLOGY


Introduction


Precipitation techniques for the manufacture of ceramic powders have the primary

advantage of removal of the need for milling to eliminate agglomerates. Additional

benefits of using precipitation methods for material synthesis lie in reducing the cost of

fabrication, control of particle size distribution, or control of particle morphology. The

control of morphology creates an opportunity for designing powders with specific

properties. If particle properties are tailored to the needs of an application, the final

properties of objects made using those particles are superior. Control of the shape results

from well defined synthesis conditions, and the degree of quality control necessary can be

a factor in determining the usefulness of the technique. A robust method for control of

powder properties is needed in order to apply a precipitation technique to large scale

production. This chapter presents investigation into the use of adsorbates for the specific

modification of the morphology of ax-alumina, and characterizes the condition of the

solvent during the reaction for its effect on morphology.









Background


Facets develop in liquid phase precipitation through solvent-precipitate

interactions that stabilize a low energy configuration of the surface. Different solvents

stabilize different facets as a result of either the conformation of the solvent molecule

adsorbed on the surface or the molecular forces between the solvent and the precipitate

surface. The particle morphology in liquid phase precipitation is a function of the growth

rates of the habit planes formed during synthesis. Factors that influence particle

morphology include the degree of supersaturation, the fluid flow dynamics, the reaction

time and the effect of specific adsorbates. The interaction of the solvent and precipitates

determines the lowest energy facets, and the kinetic conditions of growth affect the

development of the facets to influence the shape of the crystal.

The stability of o-Alumina habit planes during hydrothermal synthesis has been

investigated by Kuznetsov (Kuz64, Kuz65, Kuz71). This work utilized alkali

mineralizers (NaOH, KOH, Na2CO3, NaHCO3, etc.) and high temperatures (6000C) to

measure growth rates in corundum. Under these reaction conditions, the growth rates of

crystallographic faces were found to relate as (81 96) scalenohedron > (10- 1)

rhombohedron > (22 4 3) hexagonal dipyramid > (11 20) hexagonal prism >> (0001)

basal. Facets that appeared on a sphere were the (0001) basal, (10 1 1) rhombohedron,

(11 20) hexagonal prism, and (22 4 3) hexagonal dipyramid, which eventually reduced to

the stable basal and hexagonal prism facets. The most stable habit planes are the basal

plane and the hexagonal prism facets under hydrothermal conditions and basic pH.

Kuznetsov proposed that rate limiting steps are connected to the surface chemical









structure, so that adsorption kinetics and the dehydration of crystal faces dominate the

growth process.

The glycothermal technique for the synthesis of c-alumina has shown that several

particle morphologies can be formed dependent upon reaction conditions (Cho95). These

shapes range from platelets which are dominated by the (0001) basal plane and the

(11 2 0) hexagonal prism facets, to polyhedra dominated by the (10 12) habit planes.

Control of the formation of the dominant habit plane was found to be a function of

stirring rate, solids loading, and reaction time (Cho95). However, the influence of

specific adsorbates in glycothermal synthesis has not been investigated. In order for a

chemical additive to be effective in changing the morphology, it must have an affinity for

the surface of the precipitate. Additionally, the additive must not catalyze solvent

degradation, or itself suffer degradation under synthesis conditions. Finally, additives

must not alter the thermodynamic conditions to change the development of a desired

phase.

In order to serve as a specific adsorbate, the additive used must have a chemical

interaction with the surface. In adsorption on ionic solids, the presence of charged ions,

dipolar molecules, or available bonding orbitals will promote adsorption. The effect of

surfactants on the stability of alumina suspensions provide a broad basis for categorizing

the compounds that adsorb at the interface (Big95, Esu95, Hua95, Koo95, Lee88), and

alumina is often used as a substrate for infrared examination of adsorption (Kis75,

Mor80).

An additional concern in the evaluation of non-aqueous synthesis techniques is

the specific adsorption of the solvent itself. Alcohols are known to interact chemically









with alumina at elevated temperatures (Gre62, Kag67). Alumina is known to have a

catalytic effect for the production of some organic chemicals (Pin87), and the effect of

solvent degradation on morphology and glycothermal synthesis has not been investigated

to date. Additives will change the solution speciation of components, and may promote

the formation of new chemicals in the reaction system. Solvent degradation must be

considered as a factor will influence the thermodynamic stability of the system,

supersaturation levels, and flow dynamics via viscosity changes. The 1,4-butanediol used

in this study is sensitive to oxidation. In order to maintain the solvent, oxidizing

additives must not be employed, and sources of oxidation should be avoided as much as

possible.

The influence of adsorbates on the surface energy of the various habit planes can

be used to promote controlled growth and therefore control morphology. The

morphology of crystals grown in solution is determined by the habit plane with the

slowest growth rates. In situations where the supersaturation is low and the surface

energy influences the growth of habit planes, the equilibrium form can be related to the

effect of adsorbates on surface energy. When adsorbates do not interact, the stable habit

planes are believed to be those with close packed ions, as these planes are believed to

have lower surface energy. Adsorbates which interact to form stable film structures can

stabilize non-closely packed planes. However, adsorption can be so strong that growth

rates of the particle can be reduced.









Materials and Methods


Alpha alumina is synthesized in 1,4-butanediol by reaction of gibbsite powder1 at

300'C tor 36 hours under a stirring rate of 460 rpm and autogeneous pressures. A 600 ml

stainless steel hydrothermal reaction vessel was used for the reaction2. The solvent purity

was assured by vacuum distillation of the solvent prior to each synthesis run.

Gibbsite powder was ground in an alumina mortar and pestle with methanol to

provide dispersion. The suspension of gibbsite in methanol was added to 150 ml of

vacuum distilled 1,4-butanediol. The suspension was placed under agitation and 60'C for

12 hours to remove the methanol carrier. The suspension of gibbsite in 1,4-butanediol

was loaded into the 600 ml vessel, and the container was rinsed with 50 ml of 1,4-

butanediol. The solution pH was measured using a solid-state pH meter3 both before and

following the addition of the desired amount of additive. The vessel was placed under

vacuum for 10 minutes to remove entrapped air in the solvent. The interior of the vessel

was then purged with nitrogen gas for 10 minutes. The heating schedule used a three

hour ramp from room temperature to 300'C, a hold period at temperature for 36 hours,

and a one hour ramp to room temperature. The autogeneous pressure due to 1,4-

butanediol remained below 29 kPa (200 psi), but vessel pressures could ascend to 100

kPa.






1 Spacerite S- 11, ALCOA, Pittsburgh, PA.
2 Parr Autoclave Model, Parr Instrument Company, Moline, IL.
3 Sentron 1001 pH System, SENTRON Inc., Federal Way, WA.









Following synthesis, the solvent was measured for pH and a sample was taken for

analysis. Gas chromatography4 and infrared spectroscopy5 were performed on the

solvent. The precipitate was collected and washed by five cycles of centrifugation and

dispersion in methanol. The precipitate was characterized by scanning electron

microscopy6, x-ray diffraction7, and diffuse reflectance infrared spectroscopy8.

Scanning electron microscopy samples were prepared by allowing a suspension of the

precipitate in methanol to dry on a sample mount, followed by 5 minutes sputter coating

with Au-Pd.9 X-ray samples were prepared by placing a drop from a suspension of the

precipitate in methanol on a dry glass slide, and allowing the methanol to evaporate.

Scans were run from 10 to 70 degrees 20, with a 0.05 degree step size. IR samples were

prepared by mixing dry precipitate with dry KBr in a 1:100 ratio by weight. The

materials were ground by hand in an agate mortar and pestle and dried at 115'C for 1

hour before measurement. The heating rate for gas chromotography was an initial

temperature of 30'C, a heating rate of 10C/minute, and a five minute hold at 2500C.

One synthesis run was performed by the reaction of Al-tri(sec)butoxide with water

in 1,4-butanediol. A volume of 17 ml of Al-tri(sec)butoxide were added to 200 ml of

solvent in a 1000 ml vessel. The Al-tri(sec)butoxide reacted with water present due to


4 Gas Chromatography, Hewlett Packard 5890A.
5 Infrared Spectroscopy, 20SXB FT-IR spectrometer, Nicolet Analytical Instruments,
Madison, WI.
6 Scanning Electron Microscope, JSM 6400, JEOL, Boston, MA.
7 X-ray Diffractometer, APD 3720, Cu-Ka, Fine Tube, 40 kV, 20mA, Phillips
Electronics, Mahwah, NJ.
8 Infrared Spectroscopy, 20SXB FT-IR spectrometer, Nicolet Analytical Instruments,
Madison, WI.









condensation from the atmosphere to form a hydrous gel and 2-butanol. The reaction was

performed at 130 rpm and 300'C for 24 hours.

Results and Discussion


An attempt to characterize the full spectrum of adsorbate effects is beyond the

scope of this study. To couple the reaction variables of solids loading, stirring rate and

reaction time to the effect of a specific adsorbate would be a tedious study requiring

excessive material and time. This survey is designed to identify those adsorbates which

will adsorb strongly to form new habit planes or inhibit growth such that morphology is

modified. To that end, one experimental condition was chosen as a reference point for

study of the effect of adsorbates. The synthesis conditions are 300'C for a period of 36

hours under a stirring rate of 460 rpm, which is expected from experience with this vessel

to be a medium level of agitation. The expected morphology for this reaction condition is

a columnar shape with height approximately equal to the dimension of the basal plane.

The surface is bound by the basal plane (0001) and the hexagonal prism planes { 11 20).

These habit planes have previously been observed as the most stable facets of (X-alumina

in hydrothermal growth (Kuz64). Using this shape as a reference allows the effect of an

adsorbate to be seen qualitatively in the promotion of new particle morphologies, or in the

modification of habit growth rates to promote rod-like or plate-like morphologies. Batch

nucleation in the vessel creates a near monosized particle size distribution. Deviations in

the size distribution can also be attributed to adsorbate effects.


9 Sputter Coater, Hummer II, Technics, Inc., Alexandria, VA.









Investigation of Solvent Degradation

The importance of solvent purity in crystal growth is highly stressed in the

literature (Buc51, Nan87, Nyv88, Soh92). Unlike hydrothermal techniques, the purity of

the non-aqueous solvents must be evaluated to characterize the effect on morphology.

Figure 4-1 shows gas chromatography (GC) results for three samples of 1,4 butanediol.

Figure 4-1A is the result of a vacuum distillation of 1,4 butanediol, used to purify the

solvent before use. The single, strong peak beginning at 16 minutes, 40 seconds is

characteristic of 1,4 butanediol. Four small peaks are present at later times resulting from

column bleed and polysiloxanes from the injection port. This data indicates that the

vacuum distillation procedure (Appendix A) is satisfactory for providing pure, initial

solvent. Figure 4-1B is a GC scan showing the chemical components after glycothermal

synthesis at 300'C for 36 hours. The 1,4 butanediol peak dominates, but two new peaks

are present. The smallest peak results from water, produced as a by-product of the

synthesis reaction and as adsorbed from the atmosphere during sample preparation. The

second peak at 8 minutes has been characterized as tetrahydrofuran by mass spectroscopy

performed with the gas chromatography. 10

The tetrahydrofuran (THF) is produced by dehydration of the solvent.

Dehydration of 1,4-butanediol produces either butadiene or tetrahydrofuran. In the

temperature range 250'C to 350'C and with a suitable catalyst, tetrahydrofuran is the

principle product. The pure solvent was held at 300'C for 48 hours and found to form

THF without the presence of reactant precursors. Thus, alumina does not participate in


10 GC/Mass Spectroscopy, Model 4500, Finnigan MAT, San Jose, CA.




















(f


Figure 4-1. Gas Chromotrogaphy evaluation of solvent degradation during glycothermal
synthesis. GC thermal schedule was 1 minute at 30'C, heating at 10C/minute to 250'C.
A. Vacuum distilled solvent. B. Post synthesis without discoloration. C. Post synthesis
with discoloration.





the formation of THF at 300'C. Some proportion of the water peak is therefore the result

of the solvent degradation. In the usual synthesis reaction, there is no discoloration of the

solvent. Sample 4-1 C is of solvent which has been greatly degraded and has changed

color from a transparent liquid to an orange color. The GC data indicates that no 1,4


I I I I









butanediol is present, all having been transformed to tetrahydrofuran. The characteristic

peak due to water is also present.

The production of THF does not alter the color of the solvent, and the vacuum

applied to the solvent prior to synthesis effectively prevents discoloration. If the vacuum

is not applied or if the integrity of the vessel is compromised, the solvent can degrade and

change the color to a yellow hue (or orange). Varying degrees of discoloration have been

noticed. Figure 4-2 presents transmission infrared spectroscopy of the vacuum distilled

solvent and three solvents that experience either no discoloration, light yellow color, or

strong yellow color. The broad peak between 3400 and 3300 cm1 indicates hydrogen

bonding between hydroxyl groups. The pair of peaks at 2940 and 2872 cm-1 are

characteristic of -CH2 vibrations. The peaks below 1600 cm1 are the "fingerprint" region

of 1,4-butanediol and are indicative of various modes of -CH2 and C-O-H symmetric and

asymmetric vibrations (Pin87).

The clear solvent contains 1,4-butanediol, tetrahydrofuran, and water. The

presence of water creates the broad low peak near 2200 cm-1, and the cyclic ether bond of

the THF appears at 1776 cm-'. Other than the new peaks at -2200 and 1776 cm"1, there

are no peaks indicating the presence of new molecular groups. That is to say, no

oxidation of the solvent is occurring. Oxidation of the solvent should produce

carboxylate groups from each primary alcohol. The characteristic infrared vibration of

The carboxylate group occurs between 1725 and 1695 cm-1. Hydrogen bonding

between carboxylate groups creates to a broad unusual peak between 3100-2200 cm-.

These vibrations are not evident in the spectra of any of the solvent degradation samples.

The lightly discolored solvent shows a similar profile to the clear solvent, with a slight














150



..125



~100


'-75

0


...Vacuum Distilled
H





"25 ,No Discoloration
Light Discoloration
Strong Discoloration
0 I I I I I I
4000 3600 3200 2800 2400 2000 1600 1200 800 400

Wavenumber (cm"1)




Figure 4-2. Infrared spectroscopy of solvent degradation.






shift in the hydrogen bonding peak from 3343 to 3353 cm-1. No solvent oxidation to

produce carboxylate is evident.

The strongly discolored solvent shows a shift in the hydrogen bonding peak from

3330 in the distilled solvent to 3413 cm-1, and the peak is no longer symmetric, being

skewed to the higher wavenumber. This indicates that the degree of hydrogen bonding in

the material has been reduced. The peaks at 2979 and 2877 cm4 are reduced in intensity

with respect to the -OH hydrogen bonding peak. This reduction is also seen in the peaks









between 1550 and 1350 cm1. The C-O-C peak at 1776 cm-1 has increased in intensity

suggesting that many more ether groups are present. No strong, broad peak between 3600

and 2500 cmf typical of carboxylate groups is evident. The absence of carboxylate

groups suggests that the source of discoloration of the solvent is not oxidization but rather

polymerization. The mechanism of polymerization is not known, and may be changed by

the additives in the system. Use of the vacuum to remove trapped gases in the solvent

prior to synthesis effectively prevents discoloration.

Phase Purity of Precipitate

The thermodynamic phase stability of the system must not be affected by the use

of a specific adsorbate in order for the precipitation of the desired phase to occur. X-ray

diffraction (XRD) was used to determine the phase purity of the precipitate formed in the

synthesis reaction. Figure 4-3 shows the XRD results for the pure solvent condition as

well as the phase purity for the use of each adsorbate. In each case, the characteristic

peaks of c-alumina are sharp and well defined. Differences in peak magnitude between

samples is an effect of sample preparation. Differences in peak proportion results from

preferred orientation of the particles. Particles of high aspect ratio can align so that

certain crystallographic planes are proportionally over-represented. This can affect the

magnitude of peak height. However, in all the scans, high intensity peaks remain strong,

and low intensity peaks are weak, in qualitative agreement with literature values.

Effect of Adsorption by Solvent and Alcohols

The characterization of the effect of adsorption by the various components can be

related to the chemical reactive sites of the additive. Glycols and alcohols are

characterized by the presence of hydroxyl groups which bond chemically through the







81








32000



28000 A



24000 B



20000

C
U DA
16000



12000 E



F
8000



4000





10 20 30 40 50 60 70

2e




Figure 4-3. X-ray diffraction pattern of glycothermally produced o-alumina as a function
of the adsorbate additions. A. As synthesized. B. Tetrahydrofuran. C. Methanol. D.
Acetic acid. E. Nitric Acid. F. Ammonium hydroxide. G. Pyridine H.
Tetraethylarnmonium hydroxide (TEAOH).









deprotonation of the alcohol in conjunction with a surface oxygen (Gre62, Kag67, Kis75).

The reaction creates an alcohol group and a hydroxyl group on the surface according to

equation 4-1.

ROH + 02. w RO- + -OH (4-1)

The presence of the surface alcohol group will affect the surface energy according

to the degree of adsorption. The degree of adsorption should be affected by the size of

the steric group of the molecule, and the nature of the alcohol (primary, secondary, or

tertiary). Theoretically, glycols can react at two sites.

In the absence of specific adsorbates, the surface of the precipitate must be

dominated by the adsorption of the solvent. The morphology resulting from the

glycothermal synthesis without the use of adsorbates is shown in Figure 4-4A. The shape

is as expected from the reaction conditions, and the particle is bounded by the basal plane

(0001) and the { 11 20} habit planes. The kinetic factors affecting growth promote a

columnar shape in which the length perpendicular to the c-axis is approximately equal to

the length parallel to the c-axis. This aspect ratio of the parallel to perpendicular length

c/a can be used to characterize changes in growth morphology. The presence of

tetrahydrofuran formed during the synthesis may well affect the final morphology of the

particles. Examination of the effect of THF on the morphology was examined by adding

it as an initial component at two levels; 5 and 12.5 volume percent. The final particle

morphology for the 12.5% addition is shown in Figure 4-4B. The morphology of the 5%

addition is indistinguishable from the higher level. The scanning electron micrographs

show that the morphology is qualitatively unaffected by the addition of THF, as the












































Figure 4-4. Effect of Hydroxyl groups on morphology. A. As synthesized. B. Tetrahydrofuran (12.5 Volume %). C. Methanol (13.6
volume %). D. Sec-butoxide.









aspect ratio c/a is still approximately 1. Tetrahydrofuran does not show evidence of

specific adsorption.

Figure 4-4C indicates the effect of the addition of methanol. A volume of 30 ml

of methanol was added to the reaction vessel (15 vol%). Methanol has been observed to

specifically adsorb on the { 1 121 habit planes to promote a platelet morphology

(Cho95). The presence of the steric methoxy group on the surface is believed to stabilize

the high angle facet so that its surface energy is lower than the basal plane. The

development of the high angle { 11 2 12) facets by adsorption of methanol were not

observed in these experiments. The morphology resembles the expected morphology

with no new habit planes evident in the particles. Growth rates of the facets are also

unaffected as no change in aspect ratio is evident.

Figure 4-4D shows the resultant morphology when Al-tri(sec)butoxide was used

as a precursor material in place of gibbsite. The resulting morphology is plate-like and

exhibits the high angle { 11 2 12} planes expected from prior research (Cho95). The

particle size distribution is broader than the pure solvent case, with particles between 1

and 4 microns. This suggests that particle nucleation is affected.

Effect of Adsorption by Carboxylate Groups

Carboxylate groups are expected to adsorb through a dissociated hydroxyl, but the

proximity of the double bonded oxygen will affect the strength of the adsorbate bond and

can stabilize a new surface structure by its presence. 588 gl of glacial acetic acid was

added to serve as a specific adsorbate. The pH of the suspension was changed from -8.0

to 5.1 by this addition. The morphology produced is shown in Figure 4-5. These





























Figure 4-5. Morphological changes induced by the addition of Acetic Acid. The synthesis
was performed in the 600 ml hydrothermal vessel. 588 gl of glacial acetic acid was added
to 200 ml of 1,4 butanediol with 8 g of gibbsite. The solution pH was adjusted from 8 to
5.1 by the addition. The stirring rate used was 460 rpm.





particles show that the specific adsorption of acetic acid stabilizes the (11 22) habit

planes in place of the basal plane. The resulting morphology is acicular and uniform with

an aspect ratio of -2.5. This indicates that the presence of acetic acid does not bond so

strongly that the nucleation rates are disturbed.

Effect of Adsorption by Nitrogen Compounds

Nitrogen atoms within a molecule will adsorb via the unbonded electron orbital.

The nitrogen compounds that were investigated include nitric acid, ammonium

hydroxide, pyridine, and tetraethylammonium hydroxide. Use of these compounds adds

additional complexity as each of these ions has acid or base properties, and various steric

effects.









The effect of nitric acid is shown in Figure 4-6A. The additive synthesis was

performed using 400 pl of 1.0 M HNO3. The pH was altered from pH 8.4 to pH 4.8 by

the addition of the nitric acid. The morphology is approximately equivalent to the case of

no adsorbate addition. Particle surface is not as well characterized by the { 1120} planes,

but a general short column-like morphology is dominant. In addition, some small particle

aggregates can be seen of approximately 1/100th the size of the large particles. This

indicates that some specific adsorption may have occurred to affect the nucleation rates of

the reaction. Solution pH changes during the synthesis may have contributed to the

bimodal size distribution.

The effect of ammonium hydroxide is shown in Figure 4-6B. The additive

synthesis was performed using 3 ml of 1.0 M NH4OH. This addition altered the pH from

pH 8 to pH 10. The particle morphology has assumed a more plate-like configuration

with an aspect ratio of 0.5. The particles are approximately monosized, indicating that the

adsorption does not affect the nucleation kinetics of the synthesis. There are additional

particles present that are approximately 1/100th the size of the faceted particles that are of

irregular shape.

The effect of pyridine is shown in Figure 4-6C. The additive synthesis was

performed using 10 ml of pyridine. The change in pH was not measured. The change in

morphology is striking for the case of the pyridine addition. Plate-like particles with well

defined habit planes are obvious and the aspect ratio is -0.2. The facets dominating the

surface are the basal plane (0001), the { 11 20} and { 11 22} habit planes but the growth

rates of the facets vary, so that a single characteristic shape is not defined. Pyridine

adsorbs through the unbonded orbital of the nitrogen atom, and the predominance of the













































Figure 4-6. Effect of nitrogen compounds on morphology. A. Nitric acid. B. Ammonium Hydroxide. C. Pyridine. D.
Tetraethylammonium Hydroxide.









basal plane indicates that pyridine adsorbs most uniformly on that plane.

In addition, the particle size distribution of the particles has been profoundly

affected. In place of the approximately monosized distribution at one micron effective

diameter, the particles range in size from 0.5 micron to 7 microns. This indicates that the

specific adsorption of pyridine has affected nucleation kinetics. Fewer nuclei are formed

initially, and as a result the initial nuclei grow very large. The nuclei formed during the

latter stages of precipitation have less material available for growth, and are smaller. If

the vessel were held at reaction temperature for long periods of time, the smaller particles

would become dissolved to precipitate on the larger particles.

The effect of tetraethylammonium hydroxide is shown in Figure 4-6D. The

additive synthesis was performed using 350 jil of 1.0 M TEAOH which altered the

suspension from pH 8 to pH 12.2. The particles formed are more plate-like than

expected, with an aspect ratio of -0.5. This morphology echoes the previous effect of

ammonium hydroxide. The steric groups of TEAOH have not affected adsorption and

modification of growth rates. The similarity of habit modification to the effect of

ammonium hydroxide suggests that the presence of base has modified the surface energy

of the facets, to promote the platelet morphology.

Surface Characterization of Precipitates

Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS) was used

to characterize the surface structure of each precipitate formed with the use of adsorbates.

Figure 4-7 presents the % transmittance of infrared radiation. Due to a power spike in the

instrument, there is an erroneous spike at 1350 cm-1. The infrared spectra of corundum is

described by Gadsden (Gad75). There is a broad shoulder expected at 800









89









600


iA

550.

B


500 .




450




400




M 350




300




250

I-
S G
200




150




100




50





4000 3600 3200 2800 2400 2000 1600 1200 800 400


Wavenumber (cm-1)



Figure 4-7. DRIFTS spectra of adsorbate particle surface structure. A. Pure Solvent B.

Methanol (15 Volume %). C. Tetrahydrofuran (12.5 volume %). D. 2-Butanol. E.

Acetic Acid (pH 5.1). F. Nitric Acid (pH 5.1). G. Ammonium Hydroxide (pH 10.9). H.

Pyridine (5 Volume %). I. Tetraethylammonium Hydroxide (pH 12.2).