Alumina : sintering and optical properties

Citation for published version (APA): Peelen, J. G. J. (1977). Alumina : sintering and optical properties. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR4212

DOI: 10.6100/IR4212

Document status and date: Published: 01/01/1977

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Download date: 26. Sep. 2021 ALUMINA: SINTERING AND OPTICAL PROPERTIES

PROEFSCHRIFT

TER VERKRlJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. DR. P. VAN DER LEEDEN, VQOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPEN· BAAR TE VERDEDIGEN OP DINSDAG 17 MEl 1977 TE 16.00 UUR

DOOR

JAN GERARD JACOB PEELEN

GEBOREN TE RENKUM Dl1' PROEPSCHRlFT IS GOEDGEKEURD DOOR DE PROMOTOREN PROF. JR. A.L. STUIJTS EN DR. R. METSELAAR Alln Beitsche Aan Evelien, Marc en Janine Aan mijn oudas DANKWOORD

lIe! onderzoek beschreven in dit procfschrift is uitgevoerd op hct Natuurkundig Laboratorium van de N.Y. Philips' Gioeibmpenfabrieken te Eindhoven. lk ben de dirccti.;; van dit iabocatoriul1l erkentelijk voor de mij geboden gelegcnhcid om het onder7.oek in dele vorm te publiceren,

Gaarne wil ik mijn dank betuigen aan allen, die bij de uitvocring van de experimcn­ ten betrokken zijn geweest en aan de lotstandkoming van dit procfschrift hebben bijgcdragcn, Ecn belangrijk deel van het ondcrzock is geda~n in samenwcrking met Dr. R. Metselaar. Yoor dCl.e samenwe!'king ben ik hem vcc1 dank verschuldigd. MijI\ dank gaat verder uit naar mijn coHcga's, die het manuscript van dlt proefschrift krilisch hcbbcn doorgelezen. CONTENTS

I. INTRODUCTION 1.1 Properties of alumina ...... 1.2 Application of alumina as a lamp envelope 2 1.3 The present investigation 2 REFERENCES ...... 4

2. SINrERJNG OF ALUMlNA AND THE lNFLUENCE OF DOPES 5 2.1 Short introduction to the sintering process . 5 .2.2 Sintering of alumina, Review of the literature 8 2.2.1 lnfluence of impurities...... 8 2.2.2 Influence of grain boundaries. . 'I 2.2.3 Influence of additives on sintering. Defect structure. 11 2.2.4 Influence of additives on the microstructure. , . 12 2.2.5 Conclusion ...... 14 2,3 Influence of MgO on the evolution of the microstructure 14 2.3.1 Introduction . . . . 14 2.3.2 Experimental prooedures ...... 16 2.3.3 ReSults . . . , . . . . , . . , 18 2.3.3.1 Influence of MgO on the dens.ity 18 2.3.3.2 lnfIuence of MgO on the grain size 19 2.3.3.3 lnl1uence of extra addition ofeaO and Y103 24 23.3.4 Auger spectroscopy 26 2.3.4 Discussion . 29 2.3,5 Conclusion. 31 REFERENCES . . . 32

3. HOT PRESSING OF ALUMINA 37 3.1 Introduction to hot pressing 37 3.2 Continuous hot pressing 38 3.3 Results and discussion 40 3.3.1 Influence of the atmosphere 41 3.3.2 Influence of the hot-pressing parameters 43 3.3.3 Influence of powder properties . . . 45 3.3.4 The mic\"ostructure of hot-pressed alumina 46 3.3.5 Crystallographic texture of the grains 49 3.4 Conclusion. 52 REFERENCES ...... 53

4. OPTICAL PROPERTIES OF ALUMINA 55 4.1 General introduction . . . . 55 4.1.1 Review of the literature 56 4.1.2 Factors contributing to transmission losses 57 4.2 The in-ljne trans)ni~siQn 59 4.2.1 Scattering theory. 59 4.2.2 Calculation of the in-line tf

4.2.3.3 Int1uence of extra addition of CaO and Y1 0 3 77 4.2.4 Dekrminalion of microstructural paramotcrs [rom the measured transmission spectra. 78 4.2.5 Conclusion. 83 4.3 Transparent and lranslucent alumina 83 4.}.1 Introduction , 8} 4.3.2 Theoretical c()nsiderations 85 433 Experimental part 86 4.3.4 Rc~ults and disC\lssion 89 4.3.S Conclusion, 92 REFERENCES 94

SUMMARY 97 SAMENV ATTlN(~ 99 L INTRODUCTION

1.1 Properties of alumina

In ceramic literature the term "alumina" is used rather loosely to denote L aluminous material of all types taken collectively; 2. the anhydrous and hydrous aluminium oxides taken indiscriminately; 3. the calcined or substantially water-free aluminium oxides, without distinguishing the phases present, and 4. corundum Dr alpha alumina, specifically. Gitzen I) in his standard review on alumina uses the term in the sense of the second definition. In the present work we wHl use the term in the SenSe of the fourth defini· tion. Many other phases like gamma, delta, cIa, kappa, chi, rho, theta alumina, all corresponding to the molecular formula Al2 0 3 , are described in the literature. They are all transition phases and some of them are of doubtful existence or the differences are mainly baSed on somewhat subtle X-ray diffraction differences. Beta alumina is not a monotropic form but it is a mixed oxide containing alkali or alkaline earth atoms. More information on these compounds can be found in the literature 1,2).

Alpha alumina, the only thermally stable oxide of aluminium, has the corundum structure. This structure may be described as a slightly distorted hexagonal close­ packing of oxygen ions. The aluminium ions occupy two-thirds of the octahedral inlerstices, while one third is empty. This structure is extremely stable. The formation energy of alumina is about 400 kcal/mol, only exceeded by the oxides of some rarc earth metals, like La. Consequences are an extremely low vapour pressure and a high melting point (2045 °C). The deviation from the stoichiometric composition of alumina at normal atmospheric conditi(ms is < 5 x 10'$ even at 1600 °c ~).

Alumina has a unique combination of useful electrical, mechanical and chemical jJroperties. Electrically it possesses high resistivity (around 10 17 nem at room temperature), good dielectric strength and a low dielectriC loSS factor at high frequencies. These electrical pr

Mechanically, alumina possesses great hardness, resistan~e to abrasive wear and dimensional stability. The strength properties of ~i!1tered alumina are strongly influenced by the microstructure: porosity, grain size, pore size, second phases. In the application of alumina as cutting tools use is made of its special mechanical properties.

Finally, alumina i~ inert against attack from most chcmicals and can be used in severe 2 environments. Even sodium does not provoke any appreciable reaction. Alumina maintains these characteristics to high temperatures: the working temperature can be \lP to 1500 °c.

I.! Application of alumina as a lamp envelope

The combination of the above·mentioned properties makes sintered alumina a very suitable material to be used as a lamp envelope in the high·pressure sodium lamp. This lamp is based on the phenomenon that the n{)[mally narrow spectrum of sodium light can be broadened to cover most of the visible spectrum, if the sodium pressure and temperature inside the lamp are increased 4).The lamp produces a golden.white light with a very high efficiency. The material of the discharge tube has to resist the ,mack from ~odium vapour at 1250 QC, and of course the light loss in the visible part of the spectrum should be as low as possible.

To meet the latter requirement a material of very low porosity has to be used. In the fifties t.he problem in sintcring alumina waS the effect. of discontinuous grain growth. The somewhat larger grains with more strongly curved boundaries tend to grow very fast, so that pores become enclosed in the grains and are unable to diffuse out. In 1960 Coble and Burke ., ,6) slIcceeded in suppressing discontinuous grain growth by adding 0.25 wt % MgO to the alumina. This drastically reduces the numbet of pores that Me trapped inside the grains and prolonged Sinterlng then produces a material that transmits light. reasonably wdl, thoush very diffusely. The material is oalled LucaloJ( (derived from translucent aluminium oxide) or DGA (derived from "door­ schijncnd gasdicht aluminiumoxidc") and has found wide application. The lamp envelopes made with it proved to be capable of withstanding attack from the hot sodium vapour for more than 20000 hours.

1.3 The present investigation

After this important. practical result a number of fundamental questions remained. How MgO could suppress the discontinuous grain growth in alumina W

Another unanswered question waS how the transmission of light through sintcrod alumina is related \.0 tbe mi;;;rostrllcture. The material Lucalox was introdl\Ced as an essentially pore-free material due to the action of MgO 7). A high density and a large grain size were thought to be necessary for a high light transmission, while the influence of the pore sile was not noticed. The lack of transparency of sintered 3 alumina was ascribed to guin boundary scattering and the intrinsic birefringence of alumina. Some recent developments point in another direction. It proved to be possible by continuous hot pressing at a relatively low temperature to produce a transparent material with a 25 times lower grain size than the normally sintered alumina 8). This indicate~ that not the size of the grains but the size of the often neglected pores determines the optical properties of dense alumina. Moreover, application of the theory of light scattering showed that the transmission of poly crystalline alumina could be described very well with the parameters pore size, number of pOres and spread in the pore size distribu tion 9).

This thesis is the result of an investigation to answer the above-mentioned funda­ mental q\lestions. Dense alumina samples with micrustructures widely varying in grain size and pore size have been prep;ned by normal sinteting and hot pressing. nle~e samples have been used to verify the statement that pores mainly determine the transmission of light through polycrystalline alumina 8,9). The in t1ucn~e of MgO on the sintering behaviour of alumina was investigated by studying the evolution of the microstructure for samples with increasing amounts of additive 10 ).

Chapter 2 of this thesis gives a survey of the intluence of impurities and additives on the sintering behaviour of alumina. It also describes the influence of MgO on the evolution of the microstructure of alumina.

Chapter 3 deals with the hot pressing of alumina powder. The microstructures of normally Sinlercd and hot-pressed alumina are compared.

Chaptet 4 deals with the uptical properties of polycrystalline, dense alumina. Jt gives relations between the light transmission and the microstructure of materials sintered in the normal way as described in chapter 2, Or hot-pressed as described in chapter 3. The questi(Jn whether a material should be called transparent Or trans· lucent is also treated in chapter 4. 4

REFERENCES

I) W.H. Gitzen, AhLrnina as a Ceramic Material, Am. Ceram- Soc., 1970.

2) B.C. Lippens, Structure and Texture of Aluminas, Thesis, Delft, 1961.

3) R,W. Vest, citeda~privatecommunlcaticmin JJ. Mills, J.Phys.Chem_ Solids 31, 2577 (1970).

4) L.B. Beijer, H _1.1 _ van Boort and M. Ko~dam, Ughting Design & Application, 4,15 (July 1974).

5) R.L Coble and I.E. Burke, Proc_4th Int. Symp. on the Rw;tivity of Solids, Eds 1.11. de Boer et aI., Elsevier Pub!. Co., Amsterdam, 1961, p_38.

6) RL- Coble, 1. App!. Phys. 32, 793 (1961).

7) C.L brochure on Lucalox, Lamp Glass Department, General Flectri(; Co .. Cleveland, Ohio, J 970_

8) 1 _G _1. Peden, Science of Ceramics 6, XVH (1973).

9) 1 _G.J. Peden and R- Metselaar, 1. App!. Phys_ 45,216 (1974).

10) J.C.J. Peelen, Mat. Sci. Res. to,443 (1975)- 5

2. SINTERING OF ALUMINA AND THE INFLUENCE OF DOPES

2.1 Short introduction to the sintering process

The process to convert powder compacts into dense products is called ~intering. It can be described as the thermally activated proce~s of densification of compacts at temperatures below the melting point. During sintering many changes ()CCUL The essential characteristics are tho increase in strength of the powder compact caused by the formation of bonds between the particles and the shrinkage of the compact as the void spaces between the particles decrease in size and are ultimately almost completely eliminatcd.·Another characteristic is the increase in average grain size. Sometimes very large grains can develop during sintering. This complex process of sintcring is influenced by a variety of factors: the nature of the powder, impurities, intentional additions, pressing conditions, sintering temperature, time and atmo· sphere. Because of the complexities involved, it is impossible to fit the sintering process in onc model.

Looking closer at the process of sintering, we can distinguish three different stages of sintering: 1. DUring the initial stage particles begin to adhere together and necks grow between the particles. At the end of this stage grain boundaries are established and grain growth begin~ to occur. Shrinkage is only a few percent. 2. During the intermediate stage grain growth continues. Continuous pore channels are formed along the grain edge~. The cross·section of these channels dCcreascs gradually until at the end of this stage, at a relative density of about 95%, the channels are pinched. 3. In the final stage dosed pores are formed at the grain boundaries and grain COrnerS. This final stage m~y lead to an almost completely dense material by removal of these pores, or, alternatively, the pores may be trapped inside the grains when the boundaries break aWilY from them: the problem of pore·grain boundary interaction becomes dominant. P(lre growth will occur as well.

Figure 2.1 illustrates the initial stage of the sintering of alumina. It shows the original powder particles and the necks growing between them.

Sintcring requires displacement of atoms, of cations and anions, and this process is determined by diffusion. Several mass transport mechanisms have been proposed as contributing to sintering, some processes producing shrinkage and others producing no shrinkage, In all cases matter flows into the neck between the powder particles. The six mechanisms for this flow of matter, as ccmsidered by Ashby I), have been Collected in table 2.1. In figure 2.2, which is a plane section through an assembly of three spheres, the possible diffUSion paths are shown. 6

Fig. 2.1. Scanning electronmicrograph of the initial stage of sintering process, showing neck growth between the particles. White bar is 1 lim.

GRAIN \'BOUNDARY

Fig. 2.2. Three-sphere model showing the six transport paths from table 2.1 (page 7). In all cases neck growth occurs, but only path 4 to 6 lead to densification (from ref. 1). 7

Table 2.1

Mechanism No. Transport path Source of matter Sink of matter I Surface diffusion Surface Neck 2 Lattice diffusion Surface Neck 3 Vapour transport Surface Neck 4 Boundary diffusion Grain boundary Neck 5 Lattice diffusion Grain boundary Neck 6 Lattice diffusion Dislocations Neck

Mechanisms only leading to rounding off of the pores without shrinkage include evaporation of matter from the convex surface of the particles and condensation in the neck between the particles. It is doubtful whether this method of mass trans­ port is very important in the sintering of an oxide with a low vapour preSSure such as aiumina. Another mechanism by which matter can be transported without shrinkage is surface diffusion. This can be a competitive process with other processes that produce Shrinkage, especially at low sintering temperature.

The shrinkage of alumina can best be explained by assuming atomic diffusion along two different paths of diffusion. Volume diffusion or lattice diffusion involves the transport of material from the grain boundary tluough the lattice int(1 the neck between the particles, while in grain boundary diffusion the grain boundary itself might be the path along which the atoms move. Both transport mechanisms will contribute simultaneollsly to the sintering process. Johnson ~) has proposed sintering rate equations for conCUHent volume, grain boundary and even surface diffusion.

The driving force for sintering is the excess free energy of a powder compared with that of a dense material. The decrease in free energy occurring on sintering a powder of 1 pm particle size is about 1 cal/g. Part of the initial surface energy is used to form grain boundaries. This grain boundary energy delivers the driving force for grain growth.

The sintering process cannot be treated in all details here. Suffice it to remark that it is a great step from a two or three particles model to the kinetics of densification of real powders having a particle size distribution, no spherical shape, etc, Therefore, discrepancies between theory and practice are often found. In ionic compounds effects from a difference in diffusivity of cations and anions have to be considered. This has often been underestimated in the ceramic literature. Ready 3) and Reynen ~) have pointed to the effect of non "stoichiometry on sintering, which sometimes can be very large. Review papers on sintering are included in the list of references S-s). Some aspects of importance to an understanding of the sintering behaviour of alumina are treated in the next section, These aspects include the influence of impurities and grain boundaries on sintering, the defect structure of alumina and the 8 inl1ucncc of additives on the Il1icro~tructurc of alumina_ Section 23 is devoted mainly to the ini1uence of magnesia on the ev()luti()n of the microstructl1[e of alurnina.

2_2 Sintering of alumina. Review of the literature

2.2.1 In/luencro oIimpuritfes

Since sintcdng is dependent on diffusion processes, it is important to know what kind of point defects are present in alumina and in what concentration, In the caSe of intrinsic diffu~ion the fraction of point defects is determined only by the temperature and the energy, hj; it costs to create the defects. Compared with NaCl, for instance, alumina is a rather unknown material. In the case of alumina there is still doubt as to whether a Schottky or a Frenkel type defect structure is present (see sec- 2_2_3) and the energy for defect formation is unknown. Oishi and Kingery 9) measured jS 0 diffusion both in poly crystalline arid in monocrystalline Alz 0 3 , It can be deduced from their results that it costs an energy of 20.5 eV to create 2 Al vacancies ~nd 3 0 vacancies. Fryer 10,1 t ) analyses his results on pressure sinlcring of undoped alumina in a different way _He believes that the activation energy he observes can be ascribed to intrinsic diffusioIl arid he arrives at a Schottky formation energy of 10 eV_ His analysis taken over by others 12), however, is very doubtfuL It is unlikely that his starting powder, Linde A, permits intrinsic behaviour at temperatures as low as 1200 - 1400 or- In a recent publication Dienes et aL 13) give a calculated value of 28.5 eV necessary to create a Schottky quintuplet or 20 eV to Create a Frenkel pair in the Allatlice_ B()(h values arc very high compared with ii/= 2.3 eV for NaC!. As a conScqllcrlcc, tho concentration of intrinsic vacancies will be extremely low, even at high temperatures. With the value of 20.5 eV the fraction of vacant calion sites at 1600 °c can be estimated as 10- 10 , 1'his is much lower than the impurity level of the purest alumina!

It is dear from this that only extrinsic diffusion behaviour carl b~ expected: the vacancy conccntJ'ation will be controlled by the number and nature of impurities present. ~nd will be independent of tempel'ature. Add to this that many impurities have a very limited wlubilily in alumina Blld thet'efore, they will be present as a dispersed second phase. The presence of these impurities in not well characterized starting materials may explain the many contradictory reslllts, which typify the investigations of diffusion in alumina, such as sintcring behaviour, electrical conductivity etc, (see figure 23). As a consequence, alumina is by no meanS a suitable model material for sintcring research 8,14). Anion impurities can be as effective as cation impurities 15), although they have usually been neglected. 2000 lOOQ 200

4 5 10 15 <0 10'{7'rK)

Fig. 2 .3. R~po,td lit¢,at"," data fOr tho electrical cunciuctivity of alumina (f,om ref. 16).

2.2.2 Influence oigrain boundaries

Sintering requires displacement of both cations and anions by diffusion. The main diffusion paths lie in the volume of the grains and in the grain boundaries. The relative effectiveness of both will be affected by the microstructure. It is very difficult to assign an exact grain boundary width. Mistler and Coble 17), analysing grain growth and sintering data, give a value of about 100 A.

At a grain boundary the atoms are less densely packed and this may result in a lower activation energy for boundary diffusion and a greater atomic mobility. Oishi and Kingery 9) demonstrated that the oxygen ion self-diffusion coefficient is enhanced by the presence of grain boundaries. Paladino and Kingery 18) measured the diffusion of 26 AI onJy in polycrystalline alumina and they state that diffusion of AI is not influenced by the presence of grain boundaries. The combined results are given in figure 2.4. Based on these results and on an analysis of the apparent diffu~ion coefficient in sintering and creep experiments, Paladino and Coble 19) conclude that volume diffusion of Al is the rate-controlling process in the sintcring of fine.grained alumina, while 0 diffuses more rapidly along grain bound­ aries. For grain sizes larger than 20 p,m they expect the diffusion of oxygen to be rate·controlling. In a later analysis Mistler and ~oble 20) expect the change-over from Al to 0 rate control to take place at a grain size of 5 .urn. It is very difficult to deduce the 10

Ternll"!"t'11.'r'$II.';' 19~O le.SCl liM 1650 I~~O 1450 13!:£1 1~'5O

Fig. 2.4. Combined ,osul" of the oxygen diffusion measurements of Oishi and Kin~ry·) and [he aluminium diffusion measurements of Pa.Lldino and Kingt;;:t'y 11').

kinetics from calculated values of the diffUSion coefficient or activation energies for a process such as sintering, because the values of Do and DAI are S() similar. This may explain why the sintering mcchanism has been ascribed to volume diffusion and grain-boundary diffusion 21). Enhanced oxygen diffusion along grain boundaries has also been reported for other oxides, like MgO 2~), Fe203 23) and CoO 24). Enhanced cation diffusion has been reported for U02 2S).

Grain boundaries may int1ucnce the diffusion ofions in another way. It has been shown 26 ,l7) lhat the concentration of defects near vacancy sources and sinks like grain boundaries differs from the bulk concentration. The reasOn is that the energies needed to creat~ anion and cation vacancies or, in the case of a Frenkel defect strllcture, vacancies and interstitials, are different. The consequence is that the grain boundary may carry an electric charge resulting from the presence of excess ions of one sign. This charge is compcnsated by a spacc- charge cloud of the opposite sign adjacent to the boundary. The distance the space charge region extends in to the crystal is assumed to be 20 to 100 A. The sign and the magnitude of the electrostatic potential at the boundary are determincd by both the solute concentration, if present, and the temperature 2~). This will be true especially for alumina with its low concentration of thermally indl1ccd lattice defccts. 11

lGngery 28) ha~ demon~trated the existence of a boundary charge in a number of oxides by observing the bowing of grain boundaries in an electric field at 1650 °C. He observed a positive sign of the boundary charge in an alumina sample containing about 1000 ppm MgO. The charge of the grain boundaries may possibly explain the preference for grain boundary diffusion of only oxygen 29) . However, as the con· cent ration and valence of impurities affects the charge of the boundaries, one has to be very careful with conclusions. There is hardly any knowledge of these effects on grain-boundary diffusion.

2.2.1 Influence of additives on sintering. Defect strncture

Many investigators have studied the initial stage of sintering of deliberately and un· intentionally doped alumina to see, what defect model might explain the sintering data. Not only the sintering behaviour has been studied, also the steady state creep behaviour, thermal grooving and electrical conductivity, which are all diffusion­ controlled processes. Failure to recogni~e the importance of purity, concentration of additives, tho presence of second phases, the intemlation b"tween ~int"ring and grain growth, and different sintering mechanisms like grain boundary and volume diffusion, led to great confusion in the literature (see e.g. fig. 23).

Until 1971 the basis of every explanation was a Schottky defect structure, i.e. with AI and 0 vacancies as the main native defects. Addition of 4+ or 5+ cations would create AI vacandes, addition of 2+ cations 0 va~ancies. In 1970 Bagleyet a!. 30)

found an increase of the sintering rate of alumina, when doped with Ti02 • In 1972 McAllister and Cutler 31) reported that addition of both MnO and Ti01 to alumina increased the rate of thermal grooving. In 1973 Rao and Cutler 32) also found that addition of FeO increased the sintering rate of alumina. These observations are difficult to explain with a Schottky type defect structure, since the assumption of Schottky pairs as the predominant defects leads to the conclusion that the sintering rate of Fe.dopcd alumina is controlled by the diffusion of 0 vacancies, whereas the sintering rate of Ti-doped alumina is controlled by the diffusion of A1 vacancies. It is diffucult to understand such a cnange in the rate· controlling species. If a rapid diffusion path for the oxygen ions is assumed to explain the sintcring data for Ti"doped alumina, it is difficult to explain why the sintering rate of alumina is enhanced by the presence of divalent cations.

In 1971 Brook, Vee and Kroger Ja), in an investigation of the electrical conductivity of doped and undored alumina, were the first to suggest the existence of a Frenkel· type defect structure, that is to say AI interstitials and Al vacancies as the main native defects. An A1 interstitial is a possible defect in view of the octahedral holes in the oxygen sublattice, one third of which are empty. Rao and Cutler 32) tried to verify this by measuring the power by which the volume diffusion coefficient depends on the total Fe content. With the same intention Hollenberg and Gordon "") studied to what power the creep rate of Fe-doped alumina depends on the oxygen 12

partial pressure. They all found that the scatter in their data did not enable them to determine the rate-controlling species Al j .. or Vo _The calculations of Dienes et a1. I') of the formation energy of defects in alumina favour the idea of a Schottky defect structure. In another calculation thc formatioll energy or Schottky defects is estimated t() be greater than that of Fre)l kel defects 35) The rapid ratc of reduction of Mg-doped alumina compared with that of Ti-dopcd alumina led Cox 36) to ~uggest the presence of the very mobile interstitial cation in Mg-doped samples. Recently Dutt and Kroger }1) concluded fr<)m the oxygen pressure depen­ dence of the electrical condl1ctivity of Fc-doped alumina that AJ i --must be the majodty defect ~pecies_

The assumption of Frenkel defects is attractive, because it makes the sintcring and creep data consistent. The sintering rate of Fe-doped alumina can then be explained as being due to diffusion of Al by an interstitialcy medlanism. whereas the sintering rate of Ti-dop~d alumina is controlled by the diffusion of Al through a vacancy mechanism. ThllS in either case the sintering rate is contrulled by the djffu~ion of Al ions with no chang~ in tbe rate-controlling species. For MO the incorporation reaction becomes:

(2.1) and hr MOz:

3(MO z)s ,., 3M Ai + V Ai' + 600 (2_2)

2.2.4 Injluem:f! o/addiliv&s all the microstmcture

Apart from the theoretical considerations of the previous section, another goal of additives is to lower the sintering temperature or to produce a desired microstructure by controlling the relative rates of the competitive reactions, which occur during the h~ating of a powder compact. The critical stage during Sinlering is the final stage. Sint~ril1g may thm lcadto an almost completely deme material, if the pores remain on the grnin boundaries and are able to migrate with the grain boundaries_ Alternatively, grain boundary migration may proceed too rapidly, trapping the pores inside the grains. This will never re~ult in a very dense materiaL This so called discontinuous grain growth (fig. 2.5) occurs when undopcd alllInina is sintered at high temperatures.

The migration rate of grain boundaries is strongly influenced by the number, size, geometry, and mobility of the pores, which exert a drag on the boundaries. A gimilar drag can be exerted by impurities or additives, and the presence of a sotid or liquid phase ',t the boundaries has also a strong inf1llence ()O the grain boundary mobility. A basis for an understanding of the conditions, which determine pore migration and grain boundary impurity drag was bid by Brook 38) and extended recently by Carpay 39)_ 13 , .' " .. .. . ,. : . .: - . ;,. ! ' .. ," .:,' , , .... "

' ... .. :~~ -: '.. , '. , I .,

. . . . ' . : ~". ' - ', . , , . ~ , : " " .' . -... ', ..: ' ...... , '. , ...' : . ~ . ': ......

Fig. 2.5. Undoped alumina sintered for 10 h at 1850 ° C, showing discontinuous grain growth.

The effect of many additives, such as oxides, fluorides, metals, has been investigated to overcome the discontinuous grain growth in alumina. A summing up can be found in ref. 40). In a very recent paper Kovatschev 41) describes the influence of 16 dif­ ferent additives. Cahoon and Christensen 42) and Coble and Burke 43,44) were the first to demonstrate that discontinuous grain growth could be inhibited by adding 0.25 wt % MgO to the alumina powder, reSUlting in a densely sintered product. Warman and Budworth 4S) even published criteria for the selection of additives to enable the sintering of alumina to proceed to full density. Their two criteria are: volatility of the additive to get a uniform distribution on the grain boundaries and insolubility of the additive in alumina for it to remain on the grain boundaries. They found that ZnO, NiO, CoO and Sn02 gave the same result as MgO.

Rossi 46) and Rossi and Burke 47), reporting their work on finding additives other than MgO that would permit sintering of alumina to full density, were unable to confirm earlier work, except for NiO . They observed that many additives like CaO, SrO, BaO, Y203 and Zr02 when sintered at high temperatures, yielded a micro­ structure similar to that shown in figure 2.6. This microstructure is characterized by clusters of fine pores at the centre of about 150 11m large grains. Surrounding each fine pore cluster is a region which is free of fine pores, but it may contain very coarse pores, 10 - 20 11m in diameter. The struc­ ture also shows an intergranular phase which is presumed to have been liquid at the sintering temperature. All these additives form eutectic compositions melting below the sintering temperature. The authors make this structure plausible, proposing a sequence of events leading to three generations of grains. 14

Fig. 2.6. Alumina doped with 0.3 wt % Y 20, sintered for 3 hat 1900 °e, showing pore clusters in grain centres and pore-free regions with occasional large pores (from ref. 47).

The above illustrates the strong influence of the presence of a solid or liquid phase at the grain boundaries on the evolution of the microstructure. Less work has been done on the influence which powder characteristics have on the occurrence of dis­ continuous grain growth in alumina. Agglomerates in the powder and density fluctuations in the powder compact can strongly influence the microstructure 48 -51).

2.2.5 Conclusion

Densification and grain growth during sintering of alumina are influenced by a complexity of factors. Contradictory results reported in the literature are often caused by using poorly characterized starting powders. The diffusion during sintering is impurity-controlled. The kinetics of the sintering process are strongly influenced by the presence and the charge of the grain boundaries. Sintering experiments with deliberately doped alumina can be explained consistently, if a Frenkel type defect structure is assumed. Impurities or additives play the leading part in the evolution of the microstructure.

2.3 Influence of MgO on the evolution of the microstructure

2.3.1 Introduction

Without doubt MgO is the most intensively studied of the additives that promote the sintering of alumina to high densities. The great improvement in the optical and mechanical properties of the sintered material justifies all these investigations. Ryshkewitch 52) was the first to suggest MgO as the ideal additive for the sintering 15

of alumina, this system having a eutectic point at 1925 °C, well above the practical sintering temperature of alumina. His explanation is that a dispersed phase will form a system of barriers between the oxide particles,inhibiting their mutual contact and coalescence_ Coble 4~,44) demonstrated that alumina could be sintered with the aid of 0.25 wt % MgO to a nearly pore-free condition. Other necessary conditions are the Use of a carefully selected powder and sintering in an atmosphere of a gas that can readily diffuse out of closed pores in the partially sintered compact 53). Coble's result marked thc first achievement of a nearly pore· free mlltedaL Since that time other materials have been developed with extremely low porosities, e.g. MgO 54), La­ doped Ph (Zr .Ti)03 for opto-eiectronic devices '5), (Ni,Z)) )Fe~ 0 4 for recording heads 56), garnets for magneto-optical applications 57), Th-doped Y Z 0 3 for poly­ crystalline laser rods ,8), MgAl2 0 4 ,9).

MgO is often said to play the role of grain growth inhibilor. However. it does not inhibit normal grain growth, as will be shown in sec. 2.3-4, but it only inhibits the discontinuous grain growth. The result is that pores are nOt trapped inside the grains, but can disappear by diffusion of vacancies_ Several theories have been put forward to explain the role of MgO, Ryshkewitch 52) mentioned the physical separation of the alumina grains. The action of second-phase particles of spinel located preferen­ tially at grain boundaries in pinning these boundaries and decreasing the mobility has generally been realized 60-63). Jorgensen and Westbrook

The goal of the investigation to be described in this chapter was to study the evolution of the microstructure of alumina with increasing amounts of MgO, ~tarting far below the solubility limit. This WOrk is only possible if the available alumina powder has an impurity content in the ppm range. Up to now no work with such low impurities has been published_ However, only then it is possible and significant to use MgO as an additive in concentrations as small as 50 ppm. The density and grain size of the sintered alumina will be given as a function of the MgO content.

Auger electwn spectroscopy (AES) is a very sensitive technique to see whether different concentrations of additive are present in the boundary and bulk regions. Marcus and Fine 66) in 1972, who were the tlrst to apply this technique to look for an enrichment of MgO at the grain boundarie:j>, could not detect any MgO at all, but to their surprise they found a strong Ca cnrichmenL Before them Tong and Williams 67) 16

reported an increased Mg concentration at the grain boundaries_ They used the technique of spark source mass spectrometry, which makes craters about 0.3 J.lm deep at the (;;rain boundaries. Analyses of the data of ref. 66 yielded a rather high detection limit for Mg, so it seemed worth while to repeat their experiments. During this work Tayl(Jr et al. 68) reported that they found an enrichment of Mg at the grain boundaries by a factor of Z- They used the technique of X-ray photo­ electron spectroscopy (XPS), which has a somewhat greater sensitivity than AES-

23.2 Experimental procedures

All experiments described in this chapter were carried out with an alumina powder, obtained from Rubis SyntMtique des Alpes, code A 15 RZ. This powder, made by

calcination of alum, consists of 85% Ct-AI 2 0" with a mean particle si7.e of 0_3 pm and 15% r-Ab 0 3 with a mean particle sir.e of 0_02 /lill. The decon1p()~iti()n reaction during calcination is accompanied by sintering, in which process luge agglomerates can grow_ Since these agglomerate~ can have an unfavourable influence on the sintering process, we used a p()wder deagglomerated by the manu factureI', which reduces the mean sizo of the ag(;;lomerates from 15 pm to 4 ).Im- Figure 2.7 is an eiect.ronphot.omicrograph of this powder, showing the particles of Ct- and r- AI2 0 3 - The specific surface of the powder determined by the BET adsorption method is 15 m2 (g. The impurity content was analysed spectrochemically except for the impurities Na, K and Ca, for which the spectrochemical method is wther insensitive_ Their cuncentration was determined by atomic absorption analysis. The results can be summarized as follows: Fe 5, Ga 4, Mg 0.8, Si 30, Na 10, K 30, Ca .;;; IO ppm.

The additive MgO was added as a solution of Mg acetate- 4 H1 0 (Merck, reagent grade) in absolute alcohol to a suspension of the alumina powder in the S'lme alcohoL This suspension was dried while continuously stirring. After further drying the powder was sioved and prepressed in a plexiglass die to avoid CQntamirl3tion into pellet.s 20 mm in diameter and 10 mm thick. These pellets were then isost.atically pressed at 100 MNhn 2 and preheated in oxygen at 700°C to decompose the acetate to oxide. The sinr.ering took place in a high-purity ahlmina tube heated in a molybdenum resistance furnace.

Great care was taken to measure the apparent densities of the sintered spc(;imcns because of the small difference with the theoretical density of alumina. The X-ray density was calculated frum our experiment;llly determinod lattice parameters 3 a'" 4_7585 ± 0.0002 A and c = 12_9942;1; 0.0005 A to be 3_9859 j; 0.0005 g/cm • The density was determined by the method of Prokic 69), which takes into aCl;()Unt the counterbalancing force of the air. The density of the sarnple at temperature r, D1, can be calculated from

M t Di - Do (2.3) M~ ~M;- v-l-=- Do 17

"t

;, 0 '

... .

O.llJm

Fig, 2 ,7 . Elec[ronpho[omicrograph of alumina powder used in [he sinrering experimenrs, showing panicles ot 0,- and ,),-Al. 0 3 ' 18 where MI is the weighl of the sample in air, M2 is the wm of the weight of the sample in air and the weight of .a thin nylon thread fixed to a hook of the balance and submerged in distilled and boiled·out water of density DJ . M,ds the weight of the sample tied to the nylon thread and submerged in the water, Do is the density of the air, dependent on temperature, barometric pressure and relative air humidity­ The density of water was checked using the density of a highly perfect silicon single crystal as a reference 10). An accuracy in the apparent density of ± 0_0005 gfcm' 4 can be achieved. This means an inaccuracy in the pOf()sity of ± 2.5 x 10. .

The microstructure of the sintered samples was studied by microscopic observation of polished and etched samples. Polishing was done on a vibratory poliShing machine with diamond paste_ Etching was carried out by heating the polished samples at 1450 °c for 1.5 h (thermal etching). The mean grain size was calculated using the relation 11): G"' 1.5 T, where Tis the mean grain intercept of random lines Dn photo­ graphs of the polished and etched cfoss-sections- The value obtained in this way is a good approximation if the size distribution of the grains is not too wide, i_e_ if no discontinuous grain growth has occurred_

For ttie Auger experiments a commercial Auger spCdrometer was used, consisting of a Physical Electronics Cylindrical Mirror Analy:.:er and a standard Auger ultra­ high vacuum system (VItek-Perkin Elmer). To prevent charging effects ()n alumina we used the grazing inddcncc electron gun, the diameter of the electron beam being about 50 Mm- In-depth profiles could be measured by means ofaXe·ion gun. Rods 2 mm in diameter were prepared from the sample and fractured in a specially constructed break apparatus under ultra-high vacuum (10'10 Iorr). The fresh sllrfacc was then analysed with the Auger spectron1eler.

2.3.3 Results

2.3,3.1 Influence of MgO on the density

Sintering experiments were carried out on alumina powder compacts with increasing amounts of MgO dope, starting with the undoped alumina fOf comparison_ Figure 2.8, Cllrve A, gives the density of the specimens after sintering at 1630"C for 1.5 h in a humid H2 atmosphere (dew point 20 ·C) to prevent yolatilization of MgO. It is seen that doping with 50 ppm MgO is already sufficient to increase the density of alumina substantially_ The density reaches a maximum at 300 ppm dope level; at larger dope concentrations a deCrease in density is found, Second.phase particles can be detected in the specimens with 300 ppm MgO and more with the optical microscope_ This is in agreement with the solubility data of 2 Roy and Coble 7 ), They found for the solubility of MgO in alumina in vacuum:

In X .. 8.1 - 30 706fT, (2.4) 19 where Xis the atomic fraction Mg/Al and Tthe absolute temperature. According to this equation the solubility of MgO in alumina at 1630 °c is 250 ppm. The highest density is thu~ obtained when the amount of MgO corresponds to the solubility limit in alumina. With electron microprobe analysis Mg and Al could be detected in the second-phase particles. The MgfAl ratio in the spinel phase was about 20 % lower than in stoichiometric spinel. This corresponds to the high solubility of Al103 in MgAl 2 0 4 at high temperatures 73). ,...... ';j; c L.OO -.::J'" 3.96

196

3.94

lS2 A: 1.5h 1630'C B: 1.S h 1630'C 3.90 +'0 h ,850'C

o 50 100 300 1000 3000 ppm MgO fig. 2.8 lnflu~no. of MgO content on the density of .inteNd alumina.

All specimens underwent a second heat treatment at 1850 °c for 10 h, This resulted in an increase in the density of all samples; see figure 2.8, curve B. There is no distinct peak now because all samples with a MgO content between )00 and 1000 ppm reach nearly full density. Higher MgO contents result in a decrease of the density, This decrease is greater than can be ex:plained by the slight decrease in theoretical density due to the presence of the second phase. According to eq. (2.4) the solubility limit at 1850 °c is 1350 ppm MgO,

2,3.3,2 Influence of MgO on the grain size

The microstructure of the speciJ1len~ was evaluated and the mean grain size deter­ mined for the various amounts of MgO dope. Figure 2.9 gives the result after the sintering treatment at 1630 °c for 1,5 h, It appears that MgO promotes grain growth until the solubility limit is reached. The mean grain siu decreases when more MgO is present, probably because of the dragging effect of the second phase particles on the grain boundaries. In the single-phase region we observe a distinct increase in grain size with the MgO content together with an increase in density. 20 E 2,8

Il!)

QJ N 7 ';jj / c /. nI 6 I- l!) 5 ./ t. 1.5 h 1630 ·C

~o,r' --~~~--~------50 100 300 1000 3000 ppm MgO

Fig. 2.9. Influence of MgO content on the mean grain size of alumina sintered for 1.S h at 1630°C.

Pores lying on a grain boundary obviously influence grain growth more or less like a second phase . The fewer the pores, the more freely the grain boundaries can move.

Fig. 2.10. Undoped alumina sintered for 1.S h at 1630 °c.

Figure 2.10 is a photomicrograph of the microstructure of undoped alumina specimen. No discontinuous grain growth has occurred at the temperature of 1630 °C, although some pores lie inside the grains. 21

Fig. 2.11. Alumina doped with 300 ppm MgO sintered for 1.5 h at 1630 °e.

Figure 2.11 shows the microstructure of the sample doped with 300 ppm MgO, while figure 2.12 gives the microstructure of the sample doped with 3000 ppm MgO. This last picture shows the many second-phase particles present, mostly at the corners of the grains.

Fig. 2.12. Alumina doped with 3000 ppm MgO sintered for 1.5 hat 1630 0c.

During the second sintering period at 1850 °c for 10 h discontinuous grain growth occurs in the undoped alumina sample. This is illustrated in figure 2.13. 22

.. ' . . ' , ...... ", " .. / .. •. / . ... .: . .' . ,. , . . ". • ' 0", ~,;.: ; ' . ~ / o • ' ,', ' 0 ' . .' .. ' : ~ . (. :' = /' '. •

:', ' .. ..

. . ' "0 • ~. O • • ' ...... , ...... " .

Fig. 2.13. Undoped alumina sintered for 10 h at 1850 cc.

The microstructure contains many large grains of 100,um and more, while most of the pores are trapped inside the grains. The specimen doped with 50 ppm MgO contains cracks and shows a non·uniform microstructure: many very large grains, even larger than 100 ,urn, are visible within a matrix of much smaller grains. Grain growth occurs in a stage at which most pores have disappeared . The large grains now are essentially pore-free, in contrast to the case of undoped alumina. Large pores are found between the large and the small grains. The same holds, but to a much lesser extent, for the sample with 100 ppm MgO. This sample contains no cracks, however. The non-uniform microstructure is illustrated in figure 2.14.

, " " I , . '\.. • . . J ~. \ . : r -~ '. .. t'j: " . \ ,. ) / >-.... t • • -' . , -" .r, ':. .n 1 " . . ~~~ - "~' ',1•. / '( , .( " -: . ~ .: ... ~ \ { .~ 50pm . ~ . .... " ~ /.....-: .. /1 :-/\(' .... r" .J . • ".1; ...... r~

Fig. 2.14. Alumina doped with 100 ppm MgO sintered for 10 h at 1850 cc, showing non­ uniform grain growth. 23

All samples with more MgO show a very regular distribution of grain sizes. Illustra­ tions are given in figure 2.15, which shows the microstructure of the sample with 300 ppm MgO, containing occasionally a second-phase particle, and in figure 2.16, which shows the microstructure of the sample with 3000 ppm MgO, containing large coarsened spinel particles.

Fig. 2.15. Alumina doped with 300 ppm MgO sintered for 10 h at 1850 °C.

Fig. 2.16. Alumina doped with 3000 ppm MgO sintered for 10 hat 1850 °C. 24

The mean grain size of these samples is given in figure 2.17. Essentially the Same dependence on the MgO content is found as in the previous case after sintering at 1630 °C; increasing grain size in the singlo-phase region, decreasing grain size in the second-phase region .

.------. E 2:- I~

N 25 III .§c: 20 (!)

15

15 h 1630·C 10 -10 h 18S0 'C

0 50 100 300 1000 3000 ppm MgO

fig. 2.17. Influence of MgO come", on th~ mo

Although parI of the second phase can originate from precipitation during cooling, the solubility rate of the spinel particles, present at lho grain corners, is apparently very low.

2.3.3.3 Influence of extra addition of CaO and Y 2 O~

Many combinations of MgO and some other oxide as additive have been tried to ~ee whdher the pwpertics of sintered alumina could be improved. The patenlliterature in particular gives many examples of such investigations. Most attention has been paid to the combinations MgO + CaO 14) and MgO + Y 203 75), To see whether the

extra addition of CaO or Y2 0] could enhance the transmission of alumina sintered at relatively low temporatures, we carried out $inlcring experiments starting with the alumina powder already doped with 300 ppm MgO, To this powder 0.1 wt % Y2 0, was added as an emulsion of very pure Y1 O~ in absQlute alcohol. The SO ppm extra CaO was added by immersion of a compact in a solution of Ca acetate. These pellets were already isostatically pressed and presintercd at 1250 °c in oxygen. This treatment increases the relative density tll 56 % and gives the necessary mechanical strength, Knowing the constant amount of water these compacts 25 absorb, one can calculate the required concentration of the Ca acetate solution to add 50 ppm CaO.

Comparing the microstructure of the samples with and without Y2 0 3 , it can be concluded that Y 203 has an inhibiting effect on grain growth. But also the density is lower after the same sintering treatment. The spread in grain size distribution is larger without the occurrence of discontinuous grain growth. Electron microprobe analysis reveals solid phases of two types: a phase containing only Mg and Al, often in the form of needles, and a phase containing only Y and Al, probably Y 3 Als 0 12 particles with a diameter of 1· to 2 pm, lying on the grain boundaries. This phase must be responsible for the decrease in grain size compared with the samples without the extra Y2 0 3 dope.

Addition of extra CaO causes a much more irregular microstructure (Figure 2.18). Although the mean grain size is not much larger, the grain size distribution is very wide. The same is true of the pore size distribution. The density is equal or stays a little behind. The phase diagram of the system Al2 0 3 -- CaO predicts low melting eutectics. The straight grain boundaries in the microstructure point indeed to the presence of a liquid phase 76). With electron microprobe analysis two phases can again be distinguished: the well-known spinel phase with extra Alz 0 3 in solid solution, and a more irregularly occurring phase containing Mg, Ca and AI, presumably CaO . 6 AI2 0 3 with part of the Ca atoms substituted for Mg atoms. Both phases are clearly distinguishable by the different colour of the luminescence,

'. \ . /

, /"

."

~- \

Fig. 2.18. Alumina doped with 300 ppm MgO and 50 ppm CaO sintered for 10 h at 1850 °c, showing a rather irregular microstructure. 26 which occurs when the sample is irradiated with a broad defocussed electron beam (figure 2.19). The colour of the spinel phase is green, that of the Ca-containing phase is black, while the main phase is violet-blue.

The results of the transmission measurements on these samples and on the samples containing only MgO are given in section 4.2.3.

Fig. 2.19. Luminescence of the same sample as in fig. 2.18 in the electron microprobe. The colour of the spinel phase is green, that of the Ca-containing phase is black.

2.3.3 .4 Auger spectroscopy

Auger spectroscopy was used to investigate the possible grain boundary segregation of MgO and CaO in alumina. Samples containing 1000 ppm MgO and 45 ppm CaO were used for these experi­ ments. The bulk concentrations were verified by atomic absorption analysis. The powder compacts were sintered at 1630 °c for 1.5 hand 1850 °c for 10 h in a humid H2 atmosphere. Rods 2 mm in diameter were prepared from the sample. Figure 2.20 is a scanning electronmicrograph of a fracture surface, which shows that the fracture is mainly intergranular.

Other rods were fractured under high vacuum. The Auger spectrum of the fresh fracture surface is shown in fig. 2.21. Besides the peaks of Al and 0, the Ca peak at 292 eV is very clear in the spectrum. The Ca concentration at the surface could be fixed 77) at about 6 at %. This means an enrichtment of the surface by a factor of 1000.

Signal averaging techniques were used to decrease the detection limit for Mg. A part of the resulting spectrum is shown in figure 2.22. 27

Fig. 2.20. Scanning electronmicrograph of a fracture surface of an alumina sample with 1000 ppm MgO and 45 ppm CaO, showing mainly intergranular fracture. White bar is 10 /-1m.

Auger signal

i -3x

Cal2921 AI

AI o _ Energy I eV I

! I I I , o 200 400 600 800 1000 1200 1400 1600

Fig. 2.21. Auger electron spectrum of a fresh fracture surface of the sample in fig. 2.20.

Quantization of the Mg peak yields a Mg concentration of about 0.1 at %. This agrees with the analysis of the original powder. No grain boundary enrichment could thus be established. It should be remarked that the accuracy of the Auger analysis is a factor of 2. A further remark should be that part of the MgO may have evaporated during the sintering treatment. In fact, analysis of the sintered piece showed that the MgO content had decreased by 20 %. A minor enrich­ ment of Mg at the grain boundaries is therefore still possible . 28

II ~

Port Cit tne group of hnliJs, of AbO) ~ at ~ 1350 .v _E~ergy I.vl 1040 1200 13S0

Fig. 2.22. Part of the A1)g~r el~c[rOIl spectrum of the ~<1.lYIplt!" in figure 2.20, obtl:iined by means of .ign.l .v

By simultaneous sputtering of the fracture ~urfacc with Xe iom and measuring the Auger spectra, the profile normal to the surface was investigated. The remlt, of

~ 5 sec sputter line ..".,.., 30 -Iv- 1 min 1 ~

~ ~ 10 .. ~ 40 C

Fig_ 2_23_ Behaviuur of the Auger 'ignal of <:. a. a functiOn of spYl!cring time_ 29 these experiments are shown in figure 2.23. The figure indicates that Ca is concen­ trated in a region nea, the intergranular f,acture surface. One has to be very careful in translating the sputter time into a depth measured in Angstroms. The intergranular surface is very rough and the Xe ion beam hit the surface at grazing incidence. The sputtering of the surface can therefore be expected to be non-uniform.

2.3.4 Discussion

The results of sees 2.3.3 and 2.3.4 demonstrate that MgO influences both the densification kinetics and grain growth of alumina in the same way. This suggests that densification and grain growth are governed by the same mechanism. This could also be concluded from intermediate stage sintering data of CoO ll).

Very small amounts of MgO promote the sintering of alumina. A second phase of spinel is obviously not necessary. The experiments with Auger spectroscopy do not point to an important grain boundary segregatiun uf MgO or tu its presence as a mOl around the grains, which would decrease the grain boundary mobility. This is contrary to the conclusion arrived at by Jorgensen and Westbrook (>l) and Budworth 65). Our conclusions are supported by the work of Johnson and Stein 78). With broad beam AES they observed Mg peaks representing not more than twice the bulk level. With scanning Auger microprobe they were able to determine that most of the Mg detected on the fracture surface is confined to discrete particles and that the overall coverage between the particles corresponds to the bulk level in the alumina. The overall increased concentration of Mg at the grain boundaries found by Taylor et aI. 68, n) must be the result of precipitation rather than segregation. It should be realized that the results of grain boundary analysis will be influenced by the cooling rate after sintering. During slow cooling segregation and precipitation may strongly increase.

Our eJ\periments and the eady eJ\perilnents of Marcus and Fine 66) show that ell is a pronounced segregant. Since the size misfit for the Ca ion in alumina is large, it may be that elastic strain energy makes an important contribution to its tendency to segregate. The ionic radius of Ca is about 0.99 A, significantly larger than that of Al, which is about 0.50 A and Mg, which is about 0.65 A. 1n spite of its strong tendency to segregate, CaO as the only additive to alumina is not effective in pre­ venting discontinuous grain growth in alumina 45). Nor did the combination of MgO and CaO in our experiments improve the density of the samples or their transmission properties (section 4.2.3). The same holds for the combination MgO and Y,O).-.

111ere is still another reasun for rejecting the idea of solute segregation of Mg. Figure 2.9 (page 20) shows that in the single-phase region the grain size increases with the MgO content. In the case of segregation of Mg to the grain boundaries one would expect the reverse to occur. This reverse effect has been found in Y 203 containing various amounts of Th02 , and was ascribed to segregation of III 30). 30

Coble 44) already observed that addition of MgO to alumina did not irlhibit the rate of normal grain growth, and Coble and Burke $) listed possiblo reasons for this. However, they added 0.25 wt % MgO, which far e)(cecds the solubility limit. Our results indicate that MgO even promotes normal grain growth as long as the solubility limit has not bem reached.

II sCCms that the average grain growth rate is completely controlled by the volume fraction and si

We must conclude that the inhibition of discontinous grain growth by MgO is not caused by a considerable red\lction in grain boundary mobility due to ci ther a soltltc segregation mechanism or to the presence of spinel a~ second-phase particle~. More important is the enhancement of the sint.ering rate or rale of pON removal, which averts the condilion for the occurrence of discontinu()l[s grain growth. A second effect of MgO may be an increase of the pore mobility, so that the pore can f·oUow the grain boundary more easily. Possibly both mechanisms contribllte to the inhibition of discontinuous grain growth by MgO. The additive might also change the poro geometry, i.e. the grain boundary angle of a pore situated on a grain boundalY. This dihedral angle is determintd by the fa tio of the grain boundary energy and the SIIrface energy. Jorgensen 51 ), trying to detect pos~ible solute segregation, states that addition of 0.1 wt % MgO inGreases the angle by a faGtor of 2. However, we were unable to observe this large increase in our samples.

Above the solubility limit scc()nd'phase particles are present and this changes the situalion completely. The second·phase inclusions lie on grain edges and at grain corners and influence the grain growth process, An increase irl the MgO content corresponds to an increase in the average number of second·phase part.icles per grain boundary and/or iln increase in their average size. This results in an increasing drag on the grain bOllndaI'ies and e)(plains the decreasing mean grain size found experimentally. MocelUn and Kingery ~2), who have annealed samples of MgO-doped al\lmina, als(l find that second-phase draggjng probably con· troIs the grain growth kinetics.

Another aspect of an increasing amount of second-phase particles is the decrease ill sintering rate, which is expressed in lower densities (figure 2.S, page 19). The same phenomenon has beon found in other systems. Rcijncn 4) has put forward the 31

hypothesis that grain boundary sliding is essential for fast sintering, and suggests that a dispersed second phase would suppress this grain boundary sliding for purely geo­ metrical reasons. If this hypothesis holds in this case, longer sintering times should give higher densities. This has indeed been confirmed. Another explanation involves an overall decrease of mobility in the boundary when the boundary is 'blocked' by a dispersed phase.

Finally a remark on the non-uniform microstructure in the samples with 100 ppm MgO and less, as illustrated in fig. 2.14 (page 22). It is possible that this is caused by a non-uniform distribution of MgO. Locally mare MgO may be present and this would then result in a higher rate of pore removal and more rapid grain growth. These large grains oan then grow at the expense of others. This might explain why the large grains are nearly pore-free (in contrast with the large grains in the case of undoped alumina) and why large pores are often found between large and small grains. A similar phenomenon has been found by Groscovkh 83) in the ThO~ "doped

YZ 0 3 system.

2.3.5 Conclusion

The addition of MgO promotes both the densification and grain growth of alumina as long as the solubility limit has not been reached. The most effectIve dope level corresponds to the amount that can be brought into solid solution. Auger spectro­ scopy shows no important enrichment of the grain boundary area with MgO. These results do not support the theory of grain boundary segregation. The essential action of MgO seems to be enhancement of the pore removal rate. At higher dope levels, when seccmd·phase particles are present, grain growth is slowed down and the densification is also negatively influenced. 32

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25) D.K. Reim ann and T.S. Lundy, J. Am. Ceram. Soc. 52,511 (1969).

26) J. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford, 1946.

27) K.L. Klieuwer and 1.S. Koehler, Phys. Rev. A., 140, 1226 (1965).

28) W.D. Kingery, l.Am. Ceram. Soc. 57, I (1974).

29) W .D. Kingery, J. Am. Ceram. Soc. 57, 74 (1974).

30) R.D. Bagley, LB. Cutler and D.L. Johuon, J. Am. Ceram. SaG. 53, 136 (I 970).

31) P. McAllister and LB. Cutler, 1. Am. Ceram. SOG. 55,351 (1972).

32) W.R.Rao and I.B.Cutler,J.Am.Ceram.Soc.56,S88(i973).

33) R.J. Brook, 1. Yee and F .A. Kroger, J. Am. Ceram. Soc. 54,444 (J 971).

34) G.W. Hollenberg and R.S. Gordon, J. Am. Ceram. Soc. 56,140 (1973).

35) R.R. Oils, Ph.D. Thesis, Stanford University, 1965, cited in K. Kitazawa and R.L. Coble, J. Am. Ceram. Soc. 57, 245 (1974).

36) R.T. Cox, J. de Phys. Colloquc C9, 34, 333 (!973).

37) B.V. Dutt an d F .A. Kr()ger, J. Am. Ceram. Soc. 58,474 (1975).

38) RJ. Brook, J. Am. Cenl.m. Soc. 52,56(1969).

39) F.M.A. Carray, 1. Am. Ccram. Soc. 60, (1977), in press.

40) W.H. Gitzen, Alumina as a Ceramic Material, Am. Ceram. Soc., 1970, p.13!. 34

41) LT. Kovatschev, B"r. Dtsch. Keram. Ges. 53,223 (1976).

42) B.P. Cahoon and C.1. Christensen, J. Am. Ceram. Soc. 39,337 (1956).

43) R.L.Coble and J.E.Burke, Pwc.4th InL Symp.on the Reactivity of Solids, Eds .I.B. de Boer et aI., Elsevier, Amsterdam, \961, p. 38.

44) R,L, Coble, J. Appl. Phys. 32, 793 (1961).

45) M.O. Warman and D.W. Budworth, Trans. Brit.Ceram. Soc. 66, 253 (1967).

46) G. Rossi, Phys. ofSintering 5, 75 (}973).

47) G. Rossi and J.E. Surke,J.Am.Ceram.Soc.56,654(1973).

48) A.L. Stuijts and C. Kooy, Sci. Ceram. 2,231 (1965).

49) R.E. Mistler and R.L. Coble, J. Am. Ceram. Soc. 51,237 (1968).

50) L. Berrin, D,W. Johnson and 0.1. Nitti, Bull. Am. Ceram. Soc. 51, 840,896 (1972).

51) R,T. Tremper and R.S. Gordon, Proc. Conf. Ceramic Processing before Firing, Eds G.Y. Onoda and L.L. Hench, Wiley & Sons, New YMk, 1977, p.23!.

52) E. Ryshkewitch, Sprechsaal 88,436,472 (l955),

53) R.L. Coble, 1. Am. Ceram. Soc. 45,123 (1962)

54) G.D. Miles, R.A. Sambell, 1. Rutherford and G.W. Stephnson, Trans. Brit. Ceram. Soc. 66, 319 (1967),

55) C .S. Snow, J. Am. Ceram. Soc. 56,479 (l973).

56) A.L. Stuijts, Proe. Brit, Ceram. S()c. 2,73 (1964).

57) R. M dselaa r, P.J. Rijnic rsc and U. Ell z, Ber. DISch. KOrarn. Ces, 47, 663 (1970).

58) C. Grescovich and J.P, Chernock, J AppL Phys. 45, 4495 (1974).

59} R.J. Bratton, J, Am. Ceram. S()c. 57,283 (1974).

60) W, Dawihl and E. Dorre, Ber.Dtseh.Kerarn.Ges,4l, 85 (l964). 35

61) EV. Degtyareva, Inorg.Mat.l,25S(1965).

62) LD. Prendergast, D.W. 8udworth and N.H. Brett, Trans. J. Brit. Ceram. Soc. 71, 31 (1972).

63) N.A.Haroun and D.W.Budworth, Trans. BriL Ceram. Soc. 69,73 (1970).

64) P J. Jorgensen and LH. Westb rook, J. Am. Ceram. Soc. 47, 332 (I 964).

65) D.W. Budw orth, Min. Mag. 37,833 (1970).

66) H.L. Marcus and M.E. Fine, J. Am. Ceram. Soc. 55,568 (1972).

67) S.S.C. Tong and J.P. Williams, J. Am. Ceram. Soc. 53, 58 (1970).

68) R.l. Taylor, J.P. Coad and R.]. Brook, J. Am. Ceram. Soc. 57,539 (1974)

69) D. Prokie, J. Phys. D(Appl. Phys.)7, 1873 (1974).

70) 1. Henins, J. Res. National Bureau of Standards 68A, 529 (1964).

71) M.r. Mendelson, J. Am. Ceram. Soc. 52,443 (1969).

72) S.K. Roy and R.L. Coble, J. Am. Ceram. Soc. 51, I (1968).

73) D.M.Roy and E.F. Osb()(ne, Am. J. Sci 25I,337 (I953).

74) B.J _ Hunting et aI., U.S. patent 3 846146.

75) Hitachi Ltd., Dutch patent No. 6912533.

76) c. Kooy, Sci. Ceram. 1,21 (1962).

77) P.W. Palm berg et aI., Handbook of Auger Electron Spectroscopy, ed. 1972.

78) W.C. Johnson and D.P. Stein, J. Am. Ceram. Soc. 58,485 (1975)

79) R.I. Taylor, J.P. Coad and A.E. Hughes, J. Am. Ceram. Soc. 59,374 (1976).

80) P.J. Jorgensen. Defects and Transport in Oxides, Eds M.S. Seltzer and RI. Jaffe, Plenum Press, New York, 1974, p. 379. 36

81) P.J. Jorgensen, Grain Boundaries in Engineering Materials, cds 1.L. Walter, J.H. Westbrook and D.A. Woodford, Claitor's Publishing Division, Baton Rouge, 1975, p. 205.

82) A.Mocellin and W.D.Kingery, J.Am. CeralTI.Soc. 56,309 (1973).

83) C. Grescovich, private communication. 37

3. HOT PRESSING OF ALUMINA

3.1 Introduction to hot pressing

Hot pressing Or pressure sintering is an alternative meanS of densifying a powder compact. The process differs from sintering in that heat and pressure are applied at the Same time. The additional pressure delivers an extra driving force for the dcnsification process. Therefore, densification OCCurS al a much lower temperature than in the normal sintering process. This low temperature and the relatively short time cycle of the hot-pressing process make it possible to fabricate very fine-grained alumina. If only sintering temperature and time can be varied a relationship exists between density and grain size of the compact 1,2). This makes it practically im­ possible in normal sintering to combine a low POf()sity with a small grain si;[e. The application of pressure enables extremely low porosities to be obtained combined with a grain size below I Jll11, without the use of $intering additives. Hot pressing is therefore an attractive method to obtain unusual microstructures possessing such features as low porosities, very small grain sizes and very small pore sizes. The method is applied mort in materials research than in industrial practice b CcauSC of its high cost and poor shaping possibilities.

In spite of the importance of the hot-pressing process, fundamental knowledge concerning the factors that affect the process is limited. The extra variable of pressure leads t,) process mechanisms that are mOre complex than those occurring in pressureless sintering. Just as in normal sintering, it has been recognized thar generally several mechanisms contribute jointly to the densiflcation process 3,4). During the early stages of densification particle rearrangement by particle sliding, aided by fragmentation and possibly plastic flow, is an important mechanism, especially at high pressure and lower temperatures. There is general agreement that the final stage of deosiHcation of alumina occu,S by enh.anced diffusion under the influence of stress or by Nabarro-Herring diffusional creep $-8). The measured activiation energy agrees with that for the final stage of normal sintcring and for the self-diffusion of Al ions in alumina 7,S). It should be noticed, that these experiments were performed in graphite dies, which only allow pressures up to 2 70 MN/m • At higher pressures plastic flow may be another important mechanism­ The recognition that several mechanisms contribute jointly to densification has led to the development of pressure sintering maps, which visualize the mechanism contributing mostly to densification under given conditions 9,10)_

As in normal sintering, impurities play an important roie in hot pressing, Gaseous impurities are especially important because they do not get enough time to diffuse Ollt and are trapped in the pores. These gaseous impurities may come from the atmosphere or from gases adsorbed 00 the powder or from chemically bonded anions, like H2 0, CO 2 and S 11,12). These impurities may inhibit further shrinkage of the pores, they may discolour the alumina and they may have a negative influence 38

011 the physical and mechanical properties. On annealing they may cause bloating of the hot-pressed alumina 13). Rossi and Fulrath 7) estimate that a monolayer of Hz 0 is still covering 15 % of the surface of alumina at 1250 "c. Outgassing and vacuum hOI-pressing helps, but not always suffjciently.

Additives have been used to enhance the dcnsification of alumina. Rice 11) reports that LiP is successful, while MgO gives no significant difference. Use has been made of the transition of 1'-AI 2 0 3 to o:-A1203 14), called reactive hot pressing. This was only successful when high healing rates were used IS),

Although hot pressing is a costly procI>SS, it has great practical value in Ihat it permits the densification of materials thaI show an intdnsic poor sinterability. Moreover, there are special applications where c(lSI is not of primary importance. Examples of materials where hot pressing has been successfully applied are~ optically transparent materials, MgO 16), Yz 0 3 17) and Sc~ 0 3 IS); low-loss microwave ferrites 19); transparent piezoelectrics for electro-optical devices iO): piewe1ectrics lor application at high frequencies 21). Rhodes et a!. 30) report that they h

Much attention has been paid to the practical development of hot-pressing techniques Some of these developments have recently been reviewed 22). Many aspects of h!)t­ pressing, which could not be dealt with i.1l. this short introduction, call. be f()und in a review by Spriggs 23).

The present investigation describes the hot pressing of alumina by the technique of continuous hot pressing, This technique was developed in our laboratory 24) and will be described briefly in 8ec.3.2. The goal of the work reported in sec, 3.3 was to eliminate lhe porosity as far as possible and to keep the remaining pores as small as p()ssible, We hoped that this cumbination of properties would result in really transparent alumina. Sin!ering of alumina powder in the normal way always results in translucent alumina, The question of transparent versus translucent alumina is discussed in sec" 4"3" The microstructure of hot-pressed alumina is described in sec. 3.3.

3.2 Continuous hot pressing

The process of continuous hot pressing, as opposed to the l1()fmal single piece process, allows the fabrication of solid rods of, in principle, infinite length. As the cyclic heating and cooling uf tho die in the single-piece process is avoided, the die Ufe is lung. Figure 3,1 gives a schematic view of the die during operation. The cylindrical die D is heated by a resistance wire W, wound in a groove in the die, The kmpcratIJre ls measured at different heights in the die by means of a number 39

Fig. 3.1. S~hematic repro.ontation of tbe COn!inUOus hot-prossing process. Solid arrow,; indicate pr~s5ure~, open arrows the: direction of motIon.

of thermocouples placed in small holes bored radially into the die as far as 1 to 2 mm from the inner surface of the die. The powder P is compacted between an upper punch U and a lower punch 1. The lower punch is continuously lowered by a spindle mechanism. The upper pinch, which is watereooled, exerts a constant force on the powder. In this way the matedal is pushed through the die, and while the upper part P is still in powder form the lower part S is already a sintered rod an d can be considered as an extension of the lower punch L.

When the upper punch reaches a preset lowest level, it is lifted to make rOOm for the next batch of powder to be fed in, Careful choice of this level, with water-cooling of the upper punch, allows this new batch of powder to be fed in before the top of the powder layer starts to sinter. If the pressing conditions have been chosen properly, the individual batches cannot be detected later in the hot-pressed rod. The sintering takes place in the middle of the die in a zone of highest temperature of about I em. The sintering powder mass passes through the hot zone by means of an audible slip' stick mechanism. The velocity can be chosen between 5.0 mmlh and 1.5 mlh, which means that the sintering timc can vary between 2 hours and 0.5 minute.

The die consists of fine-grained, dense alumina. To overcome the high tensile stresseS which build up during pressing., the die is mQunted under a permanent compressive stress. The compressive streSS is applied by pressing support blocks from six sides 40

against the die, which for this reason has the shape of a hexagonal prism (see figure 3.2). The practical advantage of this design is that the performance of the die remains excellent even if the die is cracked due to thermal or mechanical shocks.

Fig.3.Z. Details of the die assembly.

The hot-press allows high temperatures and pressures to be attained. A maximum pressure on the upper punch of 200 MN/m2 is possible. The maximum temperature is higher than 1500 0c. Pressing rate, pressure and temperature are the parameters that determine the hot-pressing process. It is remarkable that hot pressing of alumina powder is possible in an alumina die without the powder sticking to the die wall. The rods obtained have an extremely good finish, with shiny surfaces, as if the rods had been polished after hot-pressing.

3.3 Results and discussion

Most experiments described in this section were carried out with a-Al2 0 3 powder obtained from Rubis Synthetique des Alpes, code A6. The specific surface of this powder, determined by BET-analysis, is 6.3 m2/g. The impurity content was analysed spectrochemically with the following semiquantitative result: Si 200, Fe 100, Na";;; 100, Ga 20, Pb 3, Mg 7 ppm. The average particle size of the powder is about 0.3 /-lm , but the powder contains many large agglomerates of particles. The average size of the agglomerates is 20 /-lm. For a comparison with the powder used in the sintering experiments, see sec. 2.3.2. The difference in hot-pressing behaviour between these powders is discussed in sec. 3.3 .3. Section 3.3.1 deals with the influence of the atmosphere on hot pressing, while sec. 3.3.2 is devoted to the influence of the process parameters temperature, 41

pressure and transit rate. In section 33_4 the microstructure of hot-pressed alumina will be described and compared with the microstructure of normally sintered alumina. Finally, section 33_5 discusses a possible crystallographic texture of the grains.

3.3.1 Influence o/the atmosphere

The atmosphere in normal sintering experiments will influence their results. According to Coble 2,) the gas molecules must be soluble in the solid; if not, they exert an inhibiting effect on pore closure during the final stage of densification. This is the case with nitrogen, argon and helium. The hot press is provided with gas-tight seals, allowing hot preSSing to be cauied out in all kinds of atmosphere, including vacuum. In this case 'vacuum' means a pressure of about O. I - 0.5 Torr. This way of hot preSSing has been extended with an outgassing step by installing an adjustable time switch: after the die has been fed with a new charge of powder, the upper punch remains in the lifted position during an adjusted time allowing gaseous impurities to diffuse out. We carried out a series of experiments in different atmospheres but at the same temperature of 1440 Dc, the same pressure of 120 MN/m2 and the same transit rate of 25 mm/h. The results are given in table 3, I.

Table 3_1

Influence of the atmosphere -'" Atmo sphere Density (g/cm 3 ) Colour m _ _... " --- 3.980 white 3.979 grty 3.980 white 3.980 white vacuu m 3.982 grey id T I min. outgassing 3983 white -"-'."-- -..>."..., ...... --. The table shows that the differences in density are slight. In all listed atmospheres a 3 high density can be achieved (the theoretical density is 3.986 g/cm ). There arc slight variations of the density along a hot-pressed rod- The values indicated in the table are the lowest measured values. The density of the last pressed part of the rod is often Significantly higher than the average density. The reason for this phenomenon is not completely clear but may be related to the somewhat conical outlet of the die-

The outgassing step results in a slight improvement of the density. The colour change from grey to white is striking. This may be caused by gaseous impurities which get 42

the opportunity to disappear. As the powder is made by calcining AlNH4 (S04)2 , sulphate impurity may be responsible for this effect. A chemical analysis indeed showed the presence of 365 ppm S04 in the powder. Above 1100 °c in a reducing atmosphere the expected Al2 S3 is a liquid and this may lead to some liquid-phase sintering. This may very well explain the large grains that can be found in the microstructure of vacuum hot-pressed alumina (figure 3.3).

Fig. 3.3. Undoped alumina hot pressed in vacuum at 1440 DC, 120 MN/m2 and 25 mm/ h showing large elongated grains.

The influence of gaseous impurities is also apparent from the behaviour of hot­ pressed rods on annealing. The dense hot-pressed bodies always undergo a decrease in density. The decrease depends on the atmosphere during hot pressing. This may be illustrated by the results of the following experiments:

d = 3.970 vac. h .p. d = 3.982 } 120 h 1050 °c 1 d = 3.981 } 2 h 1400 DC

_ O2 _ O2 O2 h.p. d - 3.982 d - 3.980 d = 3.959

The decrease in density of the body hot pressed in O2 (A = 0.53%) is about twice the decrease in density of the body hot pressed in vacuum (A = 0.27%). Annealing experiments were also carried out under an isostatic gas pressure : vac. h .p. d: 3.981} 20 h 1360° d =3.978; .1=0.08% H2 h.p. d - 3.980 92 0 ~ d =3.975; .1=0.13 % atm 2 O2 h.p. d = 3.983 d = 3.976 ; .1= 0.18 % 43

We again find a decrease in density, even for the body hot pressed in vacuum. Assum· ing that 1 % of the surface of the alumina powder is still covered with gas molecules at 1440 °c (e.g. H~O molecules) and that this gas will be trapped inside the pores during hot pressing, a gas pressure of 400 aim can be estimated in the pores. The microstructure after annealing shows that considerable pore growth has taken place without a large increase in grain sb:e. Very typical are also the many fissures and broad grain boundaries, possibly formed by merging of small grain boundary pores_ This su pports the hypothesis that the decrease in density after annealing is caused by bloating due to the high gas pressure inside the pores. Bloating of hot "pressed alumina on annealing has also been described by Rice 11). The same phenomenon has been found for hot"pressed Fe2 O~ Z6).

3.3.2 Influence of the hot'pressing parameters

The density of the hot-pressed products can be directly influenced by the parameters transit rate, preSsure and temperature. Some experiment~ were carried out to estimate the importance of each of these parameterS. Figure 3.4 gives the influence of the transit rate on the density, the other parameters being held constant (temperature 2 1440 °Cand pres~u[e 120 MN/m ).

4.00

S Il 50 m vlmm/hl

Fig_ ~-4- Influence of the transit rat" during hot pr.ssing on the d"n.ity of alumina. Temperature 1440 ·C, pressure 120 MN/m' iUld atmosphere 0,.

The atmosphere in all experiments was O2 , The hot zone in the die being about 1 em, the transit rate can be transformed immediately in a sintering time. Under the chosen conditions of temperature and pressure the optimum velocity is apparen tiy about 25 mm/h_ A transit rate of 5 mm/h proves to be too low: samples pressed under 44 these conditions show discontinuous grain growth (figure 3.5). This very low transit rate requires much lower temperatures. Indeed, at 1300 °c the density was again 3.980 g/cm3 and in vacuum at 1280 °c and a transit rate of 5 mm/n a rod could be 3 pressed to a density of 3.984 g/cm .

Fig. 3.5 . Undoped alumina hot pressed in 0, at 1440 cc, 120 MN/m 2 and 5 mm/h showing discontinuous grain growth.

The influence of temperature and pressure appears from figure 3.6. All experiments were performed with a transit rate of 25 mm/h and an O2 atmosphere. It can be seen that a combination of high pressure and high temperature is not always favourable. '00

196

194

150 200 -P[MN/m'l

Fig. 3.6. Influence of temperature and pressure during hot pressing on the density of alumina. Transit rate 25 mm/ h, atmosphere 0,. 45

There are optimum conditions above which the density decreases again due to dis­ continuQus grain growth.

3J3 Influence of powder propertles

Some hot pressings were carried out with the same alumina powder as used for the sintcring experiments and characteri~ed in sec. 2.3.2. The main differences between this powder AIS RZ and the powder A6 with which all other hot-pressing experi­ ments were carried out ate: a higher specific surface, smaller average size of the agglomerates and a higher I?urity. The conditions chosen for these experiments were: 1 transit rate 25 mm/h, pressure 120 MN/rn and an O2 atmosphere. Figure 3.7 gives the influence of the teml?erature on the density. Although the attainable densities do not differ much from these shown in figure 3.4 and figure 3.6, the optimum temperature is seen to be almost 100 6 C lower. The A15RZ powder can be considered to be more reactive; this results in a higher densification rate but also in a higher grain growth rate. Comparison of the microstructure confirms that the discontinuous grain growth starts at a lower temperature. This results in trapping of the pores inside the grains and a lower density at the temperature where the powder A6 attains maximum density.

1/;00 '500 '300 rfel

Fig. 3.7. I"'fh,e ... ~e of temp.rat~r. during hot pro.. ing on the densit), of A15RZ alumina. P(e~~"N 120 MNfm' , Iran.it rate 25 mm/h and atmo'phere 0,.

Limited trials of hot pressing alumina powder with 0.05 wt % and 0.2 wt % MgO indicate no significant differences compared wlth the undoped alumina. The distribution of grain sizes may be somewhat more hom(lgeneous and the average grain size somewhat lower (figure 3.8). 46

Fig. 3.8. Alumina doped with 0.2 wt % MgO hot pressed in 0, at 1440 °e, 120 MN/ m 2 and 25 mm/h.

3.3.4 The microstructure of hot-pressed alumina

When we compare the microstructure of dense, hot-pressed alumina with that of dense, but normaHy sintered alumina, we find a number of characteristic differences. Due to the much lower densification temperature (1400 ue instead of 1850 °e in normal sintering) we may expect a small average grain size. Figure 3.9 is a scanning electron micrograph ofa dense sample, that was hot pressed at 1350 °e. lt shows a uniform microstructure wi th an average grain size jj = 1.4 11m (obtained by multiplying the average grain intercept by the geometrical factor 1.5 27). This is still a factor of 5 larger than the average size of the particles in the starting powder. Figure 3.l0 is also a scanning electronmicrograph of a sample that was hot pressed at 1440 0c. It shows a less uniform microstructure with an average grain size jj = 1.8 11m. These values are typical of hot-pressed alumina. All values measured on hot-pressed samples lie between 1.0 and 2.0 11m.

In view of these small grain sizes we can also expect small pore sizes. Figures 3.9 and 3.10 show that most pores are between 0.1 and 0.2 11m. These pores, which cannot be detected with the optical microscope, are much smaller than those usually found in normally sintered alumina. Grain growth is always accompanied by pore growth, because pores may coalesce when small grains disappear 28). A typical value for the average pore size in sintered alumina is 0.5 to 1.0 11m. Another difference between the pores in hot-pressed and normally sintered alumina is their position: in hot­ pressed alumina all pores lie on the grain boundaries, while in sintered alumina most pores lie inside the grains. This agrees with the much lower grain boundary mobility at the hot-pressing temperature. 47

Fig. 3.9 . Scanning electronmicrograph of alumina hot pressed at 13 50 0c.

Fig. 3.10. Scanning elecuonmicrograph of alumina hot pressed at 1440 c c. 48

The differences in microstructure and fabrication parameters are summarized in table 3.2.

Table 3.2

Preparation conditions and microstructure of hot-pressed and sintered alumina

hot-pressed alumina sintered alumina

temperature 1400 °C 1850°C time 0.5 h lOh pressure 125 MN/m2 0.1 MN/m2 atmosphere not critical H2 additive - MgO mean grain size 1.5 11m 25 11m mean pore size 0.2 pm 1.0 11m density ;;. 99.9 % ;;. 99.9 % position of the pores in tergranular intragranular I

Most hot-pressing experiments were carried out with a common, agglomerated alumina powder. These agglomerates can be found again in the hot-pressed product. Figure 3.11 is a dark field picture of the agglomerates, focussed 25 pm beneath the surface. It shows that the agglomerates, which can be many tens of a micron, are still intact after hot pressing.

Fig. 3.11. Agglomerates in hot-pressed alumina seen under dark field illumination and focussed 2S /-Lm beneath the surface. 49

5 j.lm

Fig. 3.12. Transmission photomicrograph of an agglomerate in hot-pressed alumina.

Figure 3.12, taken in transmitted light, shows an agglomerate in higher magnification. It demonstrates that a significant part of the end porosity after hot pressing is caused by the presence of these agglomerates in the starting powder. These agglomerates, often appearing as white spots and containing more impurities than the bulk, have sometimes been called the measles in alumina.

3.3.5 Crystallographic texture of the grains

A preferred orientation of the grains may be expected if plastic flow contributes considerably to densification during hot pressing 3). A strong texture could influence the optical properties of hot-pressed alumina (sec. 4.3.4). Therefore we investigated the possible crystallographic texture by looking at polished and etched sections perpendicular and parallel to the pressing direction and by using X-ray diffraction techniques. Investigation with the optical microscope and with the scanning electronmicroscope gave no indication of any preferred orientation of the grains, nor did we find any such indication in the case of the large elongated grains in figure 3.3.

The degree of crystallographic texture is best determined by X-ray diffraction. Table 3.3 lists the intensities of a great number of reflections for samples parallel and perpendicular to the pressing direction and for a normally sintered sample, the grains of which are randomly oriented. The reflections from the basal plane viz. (0006) and (000.12) are only weak. More suitable for investigation are the strong reflections (10 1.l 0) and (1129), which are very close to (0001) and nearly in­ distinguishable. The angle between (101.10) and (0001) is only 15°, the angle 50

between (1129) and (0001) is ISo. The reflection~ (0330) and (1120) correspond to prism planes.

Table 3.3 r------.. _-,,_ .. ~~ X·ray refleclion intensities from indicated planes in hot-pri;'ssed and normally sintered alumina

angle sample and orientation with plane (0001 ) in sintered h.p. alumina h_p_ alumina degree~ alumina 1 h.p_ direction II h.p.direction

(0112) 57_6 22.5 23 24 (1014) 38.2 49.S 58 20 (1120) 90 18 11.5 32.5 (0006) 0 0.5 I 0 int. x 10 7 11 2.5 (l1~3) 61.2 6l.S 39 49 (0224) 45 2L5 19 19 (II ~6) 80 43.5 55 23 (1232) 76.5 3 7 3 (1234) 30 15 14_5 20 (0330) 50 8 15.5 43 (000.12) 0 0.8 2 0.5 int. x 10 8 24 5_5 (I Q1_10) I (1129) 17.5 6 15 2 , ...... """ ...._-_. -_._".'"'",', ... ,'-.....

Table 3.3 shows that most reflection intensities are dependent on the pressing direc­ tion. Ret1cctions from the basal planes are increased in sections perpendicular to the pressing direction, and reflections of the prism planes are increased in sections parallel to the pressing direction. The ret1ectians of the planes in normally sintcrcd alumina are often in between the two others. These results lead to the qualitative cunclusion that hot pressing introduces a certain preferred orientation uf the crystallites.

A more quantitative indication of the distribution of the ('-axes can be obtained by rotating the specimen about the normal to the plane of the incident and reo tlected beam. The X-ray counter is fixed in position to receive a chosen reflection. BCC3llSC the (0006) and the (000.12) relkctions aro both vcry weak, we choose the (I 0 1_"10) or (ll 29) reflection, which makes only a small angle with th~ c-axis. In the case of a perfect alignment of the grains we expect two peaks at :18 0 (l1gure 3_13A), in the case of a random distribution we expect the rotation to have 51 no influence (figure 3.13B). In the intermediate case we expect two overlapping peaks or one broad peak. The result for a section perpendicula, to the hot­ presSing direction is given in figure 3.13C. The ordinate gives the ratio of the intensities of the hot.pressed sample and alumina powder. According to the figure, the volume of material with ,,·axes (or better the normal on the (101.10) planes) in the direction of the pressing direction is increased by a factor of 1_66 compared with the random distribution of a powder. This means that there is only a slight preferred orientation of the grains in hot-pressed alumina_ It con· firms the result of the previously mentioned investigation with the scanning electronmicroscope.

1Id9Q.~ "I)ri9ntt;l.lon

-so om;I o.m; I "90 e r

-~ i .!1 -~ ¢ ~ .90 0 .90 (lnglo from ba$Ol pig""

Fig. 3.13. Intensity of the (101.10) rdlection in hot.pressed alumina as a function of the angle with the b • .al plane_ (A) In the "as. of • perfect orientation. (8) in the C's< of a random distribution. (e) measured for a sample pe~peJ)di(oula~ to the hot-p~essing direction.

Hamano ct aI. 29) report on alumina hot pressed at much higher temperatu,es: 1600 °c to 1900 °e. They find an orientation 3 to 5 times normal with the coaxes tending to parallel the compression direction. Rhodes et aI. 30) have studied the hot forging of dense alumina samples at 1750 °e to 1950 °c. They find a strong cry~tallographic {OOOI ~ texture normal to the pressing direotion. The texture was attributed to the dominance of basal slip during deformation: the basal planes rotate into a stable position normal to the compressive force. They 31) alSo determined the ratio of the relative intensity of the (0006) reflection for two samples 52 and obtained values of II and 17 respectively. Compared with (,I1.lr value of 1,66 it means that hot pressing causes a much lower degree of preferred orientation than hot forging.

3.4 Conclusion

Continuous hot pressing allows alumina to be densificd to nearly full density. This hot-pressed alumina is further chiHacteri~cd by a very small size of the grains and the pores. The optim\lm processing parameters arc strongly infl\lenced by the powder characteristics. Gaseo\ls impurities and agglomerates in the powder determine the rest porosity. C~mtinuous hot pressing (,Inly causes a slight degrc0 of preferred orientation of the grains. 53

REFERENCES

I) G.C. Kuczynski, Mat. Sci. Res. 6,217 (1973).

2) T.K. Gupta, J. Am. Ceram. Soc. 55,276 (1972).

3) R.M. Spriggs and L. Atteraas, Ceramic Microstructures, Eds R.M. Fulrath and J .A. Pask, J. Wiley & Sons, New York, 1968, p. 70 I.

4) R.M. Spriggs and S.K. Dutta, Mat. Sci. Res. 6,369 {l973).

5) R.L.Coble and J.S.Ellis, J.Am.Ccram.Soc.46,438(1963).

6) T. Vasilos and R.M. Spriggs, J. Am. Ceram. Soc. 46, 493 (1963).

7) R.C. Rossi and R.M. Fulrath,J.Am.Ceram.Soc.48,558(1965).

8) R.C. Rossi, J.D. Buch and R.M. Fultath, J. Am. Ceram. Soc. 53,629 (l970).

9) D.S. Wilkinson and M.F. Ashby, Mat. Sci. Res. 10,473 (1975).

to) M.R Notis, R.B, Smoak and V. Krishnamachari, Mat. Sci. Res. 10, 493 (1975).

II) R.W. Rice, Fabdcation and Characterization of Hot-Pressed AI~ 0;), Naval Research Lab., Washington, D.C., AD 709 556, 1970.

12) M .H. Leipold and C.M. Kapadia, J. Am. Ceram. Soc. 56,200 (1973).

13) R.W. Rice, Proc. Brit. Ceram. Soc. n, 99 (1969).

14) DJ. Matkin, W. Munro and T.M. Valentine, J. Mat. Sci. 6,974(1971).

15) C.J.P. Steiner, R.M. Spriggs and D.P.H. Hasselman, J. Am. Ceram. Soc. 55, 115 (1972).

16) R.W. Rice, Am. Ceram. Soc. Bull. 41, 271,586 (1962).

17) S.K. Dutta and G.E. Gazza, Mat. Res. Bull.4, 791 (1969).

18) G.E. Gazza, D. Roderick and B. Levine, J. Mat. Sci. 6, 1137 (1971).

19) J.G.M. de Lau, Proc. Brit. Ceram. Soc. 10,275 (1968). 54

20) C.H. Haertling and C.E. Land, J. Am. Ceram. Soc. 54, 1 (1971).

21) D. Pcrdllijn, R.R.P. Varekamp and H.C. Vorjans, PrOG. Brit. Ceram. Soc. 18,239 (1970).

22) A.L. Stuijrs and J.G.M. de Lau, to be published in Ceramurgia Int.

23) R.M. Spriggs, High Temperature Oxides, part Ill, Ed. A.M. Alper, Academic Press, New York, 1970, p. 183.

24) G.1- Oudemans, Proc. Brit. Ceram. Soc. 12,83 (1969).

25) R.L. Coble, J. Am, Ceram. Soc. 45.123 (1962).

26) A.C. Crouch and R.T. Pascoe, Proc. Brit_ Ceram. Soc, 20,189 (1972).

27) M.r. Mendelson, J. Am. Cefam, Soc 52,443 (1969),

28) W _D. Kingery and E. Francois, Proe. 2nd Conf. on Sintering and Related Phenomena, Eds C. KLlczynski et aL, Gordon and Breach, New York, 1967, p,471.

29) y, Hamano, M_ Kinoshita and Y.Oishi, YogyoKyokaiShi70,165 (1962), cited by R.M. Spriggs and L. Attoraas, ref- 3.

30) W,H, Rhodes, DJ. Sellers, A.H_ Heuer and T. Vasilos, Development

and evaluation of transparent A12 0 3 , AVCO Corporation, Lowell, Ma., AD 661487,1967.

31) W.H. Rhodes, D.L Sellers and T. Vasnos, J. Am. Ceram. Soc. 58,31 (1975), 55

4. OPTICAL PROPERTIES OF ALUMINA

4.1 General introduction

Interest in the optical properties of alumina will depend on the different applications. Once alumina has been chosen for use as a lamp envelope material, its optical proper· ties are of the utmost importance, since they then belong to the primary function of the material. In this chapter we will mainly be concerned with those optical properties which are influenced by the ceramic microstructme and the chemical composition, and so. indirectly by the fabrication process of the material. The function of a lamp envelope is to transmit the light prOduced by the gas discharge. For this application only the total transmission is of importance. However, the in,line transmission (the light transmitted in the direction of the incident light, see figure 4.1) is a much more sensitive property to study the relation with the microstructure. incident light

in -line transmission

Fig.4.1. When a narrow beam of light pass.. tl)rough a slice of porous polycrystallille alumina, tho/;; tran.smlssion in the jncid~nt direoction is r~duc;-~d and a diffuse reflection and a diffusoe trans­ mission ar,= gc-neratc:d.

In sec. 4.2 we will describe how the in·line transmission can be calculated and how thi$ property depends on the microstructure. In sec. 4_3 we will consider the diffusivity of the transmitted light- The main reason for this investigation is the striking difference between polycrystalline alumina sintered in the normal way, as described in chapter 2, and hot-pressed alumina, described in chapter 3. In common parlance hot-pressed alumina can be described as 'transparent', while normally sintered alumina is, at best, 'translucent'. 56

This introductory section gives a short historical review of the literature on the optical properties of alurnina (sec. 4.1.1), followed by a discussion of the various factors responsible for the loss of light, like refloction, absorption, birefringence and scattering (sec. 4.1.2)_

4_1_1 ReJ!iew of the literature

Various f~ctors arC responsible for the loss of light when a narrow beam of light passes through a plane-parallel slice of a ceramic material. The situation is shown in figure 4.1 _At each change of refractive index a certain amount of scattering occurs. Moreover the passing light is attenuated by the intrinsic absorption of the materiaL Inhomogcneilies in the refractive index inside the material include grain boundaries, second-phase particles and pores. 'The intrinsic birefringence of alumina also in­ fluences the transmission of light.

No quantitative theory exists that. describes the influence of all microstructural parameters. The interest in the ()ptical properties of polycrystalline materials like alumina, magnesia etc_ can be related to the progress made in sintering technology. In 1960 Coble and Burke)) announced the sintering of alumina to a high density (Lucal(lx)_ At the same time Lee and Kingery 1) reported on the infrared tranS­ mission properties of polycrystallinc alumina- They conduded that scattering by pores was the major factor limiting infrared transmission, because the wavelength dependence of the transmission resembled the transmission curves of fine particle suspensions.

Bowever, in later publications 3,4) the influence of grain boundaries was pointed Ollt as welL The manufacturer of Lucalox S) states that a high density and large grains are necessary due LO the strong dependence of in-line transmission on the density and grain size. The lack of transparency of Lucalox is stated to be another consequence of the presence of grain boundaries- For the question of translucent or transparent alumina, ~ee section 4_3_ The overemphasis given in the literature on the role of grain boundaries can be traced back til the missing of a quantitative theory describing the influence of the different microstructural parametMs. It also results from the belief that aU pores are eliminated in the magnesia-doped, high temperature"fired alumina. However, the material is to be described as essentially pore-free. A material with a relat.ive dlm~ity of99.9 % and uniform 3 pores of 0_5 pm diameter, still contains 10 10 pores per cm , too many to simply neglect!

Budwort.h 6) considers Lhe scattering of light by both pores and grain boundaries. Bis conclusion is that the limited transparency of sintered alumina is due to residual porosity and grain growth control addit.ive rather than to optical anistllropy. Be introduces a grain boundary scattering coefficient to describe the inl1ucllce of the grain si:cc. According to him it is probable that l'esidual additive at the grain bound­ aries is responsible for a grain size effcct. 57

Kahan et al. 7) describe a completely different scattering modeL The parameters in their model are grain size, birefringence and porosity, not the pore size. For a given birefringence and ~ero porosity the model predicts a rapid decrease of transmission as the grain size increases. This is hardly to understand. The int1uence of porosity is greatly underemphasi~ed in their model.

Bondar et al. 8) have studied the effect of annealing of polycrystallinc hot"pressed magnesia. They found a decrease in IR transmission. This was ascribed to pore growth during heat treatment by pore coalescence.

Crimm et al. 9) presented empirical relations between the IR transmittance of poly­ crystalline alumina and density, grain size, sample thickness and surface finish. They found that variations in density were the major contributors to the variations in transmission. The relative contribution of grain size was of minOr signiflcance in the grain size region of 20 to 60 11m. However, this minor contribution can also be explained by minor variations in the density of the samples. They consider the effect of grain size as a result of the birefringence of alumina and estimated that the fraction of light deviating from its original path for a thickness of SO grains is only 2.5 x 10'3.

In contradiction with this estimation of the effect of birefringence Rhodes et al. 10,11) ascribe the improved transmission of hot-forged alumina to reduction of the optical anisotropy and birefringent scattering due to the presence of a strong crystallographic texture (see sec· 3.3.5).

4.1.2 Factors contributing t(J transmission losses

We will now discuss successively the factors influencing the transmission of light through a slice of polycrystalline alumina. These factors !He, as already mentioned in the prevjous section, absorption, reflection at the surface, birefringence and scattering by inhomogeneities inside the material like grain boundaries, second.phase particles resulting from sjntering aids or impurities and pores.

Due to the high value of its electronic energy gap AI:. OJ is transparent in a wide rang~ of wavelengths. Between 0.2 and 7 11m the transmission of a :2 mm thick sample of sapphire exceeds 10 % lZ). At short wavelengths the transmission is terminated by electronic transitions, at long wavelengths the ela~tic vibration of ions is responsible for absorption. The intrinsic absorption of alumina in the visible and near IR range is negligible. However, absorption losses may increase due to the presence of impurities, especially transition metal ions.

Inevitable is the light loss due to reflection at the surface of the material. Provided there is no absorption, the fraction of light reflected at normal incidence is given by Fresnel's formula: 58

(4.1) where n is the refractive index of the rna terial.

The reflection losses are higher because multiple reflection occurs at the front and back of the slice- Therefore the total reflection loss!?'t is 13) 2R (4,2) Rt = 1+1<-

In the region of visible light alumina has a refractive index of 1.77, which means that the reflection loss is 14 %, at normal incidence and for perfectly polished surfaces_ The importance of a good surface finish appears from the wOrk of 9 Grimm et aL )_ The dispersion of the refractive index of synthetic sapphire between 0.26 and S.6/.!m has been determined by Malitson 14)

All inhomogeneities inside the material wnt give rise to scattering of light. The grain boundaries come into the picture for two reasons: firstly, alumina has a hexagonal crystal stwcture and possesses an optical anisotropy; secondly, the grain boundary itself may be considered as an inhomogeneity _Jeppcsen 15) has measured the birefringence: at 5890 fJ... he finds for the ordinary ray flO = 1.768 and for the extra­ ordinary ray fle '" 1.760. The extent to which the transrnission is affected by this birefringence at the grain interfaces will depend on the value of 6.n '" flo - fie and the number of interfaces, thus on the grain size, An exact calculation of the int1uence of the birefringence is difficult. A model has been proposed by Dalisa and Seymour 1~) tor ferroelectric ceramics, but this model gives too high values for polycrystaJline alumina. (The modd predicts a width of the 0 scattering profile of 4 for .::l.n = 0,008 and 500 grain interfaces, whereas the experimental value is less than 0,8°; see section 4.3). Budworth 6) and Johnson 17) both give an estimation of the birefringence contribution. They me eg_ (4.1) and assume that all grains arc perfectly misoriented, which. means that at all boundaries the relative refractive index m = 1_760/1_768.

For a sample thickness of 0.5 mm and a mean grain size of 25 I1Il1 (20 grains) the fraction oflighl deviating from its original path is then 10'4, for a mean grain sile 3 of I J-lm al the same sample thickness (500 grains) this fraction is 2.5 x 10- , This simple estimation points to a negligible contribution of the birefringence to the light IOS5, except for very small grain sizes, e,g. less than 0.1 /1m. Besides these theoretical considerations ther~ are two experimental justifications for neglecting the birefringence, First, hot.presscd alumina with its very small grain size of I /-1m can be made transparent (see sec. 3.3 and 4.3); second, the in·line transmission of hOI.prcssed alumina approximates to the transmission of sapphire in the infrared region of the spectrum (see sec- 4_2), 59

The other reason why we have to consider the role of grain boundaries in scattering i~ that impurities or additives can precipitate or segregate at the boundarie~_ Clean boundaries represent regions of atomic disorder only some tens of A wide 18). This is too small to hinder the light appreciably in passing the grain boundary. Indeed, no difference in transmission has been found in poly crystalline and single crystaJljne alkali halides 19). Fmm an optical point of view a polycrystalline material without birefringence and without pores or precipitates can be considered as a single crystal. To be sure that the effect of grain boundaries can be neglected one has to use starting powders of high purity and to minimize the amount of additive.

This leaves us with the pores as the principal scattering centres. Pores are very efficient scatterers because of the great difference in refractive index, At a porosity of 0.5 % pOlycrystalHne alumina is still completely opaque. Scattering of light results in the generation of a diffuse transmission and also of a diffuse reflection due to ba~kward scattering (figure 4.1, page 54).

4.2 The in-line transmission

The in-line transmission, defined as the fraction of the original intensity that emerges from the material in the direction of incidence, is very sensitive to changes in the microstructure, much more than the total transmission, which also includes the diffuse transmission, The relevant parameters in the micro~tructure are the porosity, the pore size and the pore size distribution, In this section we will first outline the general scattering theory (section 4.2.1), which we need to calculate the in-line tranS­ mission as a function of the above mentioned parameters (section 4_2,2). Then we will present our measurements of the in-line transmission of samples with different microstructures (section 4.2_3). Finally we will show how the same microstructural parameters can be calculated from the measured transmission spectra (section 4.2.4).

4.2.1 Scattering theory

Studies of light scattering go back to Tyndall's experiments with aerosols (1869) followed by the theoretical contributions of Lord Rayleigh (from 1871)_ The problem generally is to relate the properties of the scatterers - shape, size, size distribution and refractive index - to the unperturbed, transmitted light or the angular distribution of the scattered light_ Scattering theory is widely used by astronomers and metercologists. but also by chemists and phySicists in the study of colloidal solutions, supcnsions, glasses and polymers. The feature common to these problems is that the scatterers have a larger refractive index than the medium. Pores in a ceramic material represent an example of scatterers with a (much) smaller refractive index than the medium.

The complexity of scattering problems depends on the ratio of the si7.e of the scatterer to the wavelength. The Rayleigh scattering theory is applicable to particles, 60 that are no larger than one tenth of the wavelength. This implies that we may consider the particle to be placed in a homogeneous electric field of the light wave. This Held will induce a synchronously oscillating dipole that radiates in all. directions. Rayleigh sca!!ering is characterized by the fact that the scattered intensity is inversel: proportional to the fourth power of the wavelength and the fact that the ilngular distribution of the scattered light is symmetric with respect to the axis of the in­ cident light and to an axis normal 10 this direction.

If the scattering centres are much larger. the lighl scatlered from one portion of a particle may be out of phase with thaI coming from another portion. The scattering intensity in a given direction is now the result of a superposition of contribution$ C(lming fr(lm different p(lints of the particle. With incI'easing particle sb::e the scattered light becomes more concentrated in the forward direction and the sco.ttering lnten~jty becomes less and less dependent on wavelength. In 1908 Mic 10) gave the full solution of the problem of the scattering of light by a homo· geneous sphere of arbitrary sil.e. It can be shown 22) that Mie's theory C(lntains Rayleigh scattel'ing as a special case. For increasing particle sizes the calculations become increasingly complex, and require the LIse of a high·speed computer-

The scattering treatment for very large particles (particle size larger than ten times the wavelength) can be greatly simplifIed by the theory of diffraction. The diffracted light is spread over a small angular zone.

In oU!' treatment of the scattering of light by pores in a Geramic material we have t.o use the rig(l(()US Mie theory _Theref(lre, a brief outline will be given of that part (If the Mie theory that we need to calculate the scattered light intensity. The complete theory can be found in the standard books on scattering by Van de Hulst 21) or by Kerker 22).

The scattering in any direction is described by a complex amplitude fundion S (0, '-PJ which gives the amplitllde and phase of the ~cattered wave. 0 is the anglc between the forward and the scattered direction Or scattering angle and I{J is an a7,imuth angle. 111c general formulation involves four amplitude functiom S I - S4. but in the ease of homogeneous spherical particles S3 and S4 ar., ~_ef(l_ Fw scattering in the forward direction also holds SI (0,0) = S, (0,0)-

The scattered wave is calculated frum Maxwell's equations by requiring that the wave al the surface of the sphere satisfies certain boundary condltiol1$- The soil! lion contains the wavelength A in the medium surrounding the sphere, the normaliz-ed radius, x = 27rr/A, and the relativc refractive index, ttl = II~Pb~r

~ 2n+1 { } fi(n+TJ "/j1l/j(coSO)+b/j1/j(COSO) , n=1 (4.3)

The components SI and S2 are perpendicular and parallel, respectively, to the scattering plane. This plane contains the incident direction and the direction of the scattered wave (0,

The coefficients a/j and bn are given by 1/I n (m;x;) -.JJn(x) - m I#n (mx) 1#;" (x) an '" I#n (mx) tn(x) - m -.JJn(mx) ~rdx) (4.4) m-.JJ';(mx) I#n(x) - I/In(mx) I/In.(x) bn ;; m-.JJ'lmx) t/j(x) - I#n(mx) tnjx) where I#n and t n are Riccati-Bessel functions.

The addition of a prime to the functions denotes diffe,entiation with respect to their arguments. The Riccati-Bessel functions are defined as

'/Inft) = Z in(z) , (4.5) In(z) = Z {infz) - iYn(z)} , where in andYn are spherical)3essel functions of the first anq second kind :13).

1n cq. (4.3) the coefficients an and b n are multiplied by the angular functions 7fn (cos e) and 1n(eos e), which express the direction dependence of the solution. These functions can be exprEssed in the Legendre polynomial Pn(cos (}) by dPn (cos e) 11n (cos /J)= --d·co-sir·~

The intensity of the scattered radiation is given by the intensity functions i! and i~ defined as 62

(4.7) i~ = IS~ F , where i 1 is again the component polarized perpendicular to the scattering plane and i~ the component polarized parallel to this plane. If natural light of intensity 10 is incident on a sphere the intensity of the scattered light at the distance d in any direction is

(4.8) with k .. 21T/A .

To be able to cakul!ite the in-line transmission, we consider the total energy abstracted from the beam of light by a particle. When we neglect absorp lion by the particle, the total extinction cross·secti()fi Cext equals the scattering cross-section Csca . This is the total energy scattered by a particle in all directions. Each particle forms a geometric obstacle of cross·section G '" Tft2 • However, its capability for scattering differs from its geometric cross-section by a factor Q. The scattering cross-section is therefore defined as

(4.9) where Qsca is called the efficiency factor for scattoring.

Mit's evaluation led to expressions for CSCQ and Cext. For Csca the expression reads

A2 GO Csca = 21f L (2n+l) {ianl~ + Ibnl~}. (4.10) n"'l

The efficiency factor fQ( ~catt.,dng can be found by dividing by Tfr2, So that

') 2 Qsca '" 71: (2n+1) jlanl" + IbnI }. (4.11) n=l

The dimensionless quantity Qsca depends on m and x, thus on the relative refractive index, the wavelength and the size of the spheres.

In a medium containing Nindependent particles per unit vQlume the intensity of a pT()ceeding beam decreases in a distance [by the fraction e·rl r is the cx tinction coefficient or scattering coefficient if absorption is absent. It is computed from r;;; Nnr2 Qsca (4.12) independently of the state of polarization of the incid'~nt light. 63

A final remark: the A used in scattering theory is the wavelength in the suspending medium. This means that Ar= Ao/nmedium where AO is the wavelength in vacuum and nmedium in our case is the refractive index of the ceramic containing the pores.

4.2.2 Calculation of the in-line tr(lnsmission

4.2.2.1 Pores with a fixed radius

After this introduction to scattering theory we can calculate the in-line transmission of light passing through a slice of polycrystalline alumina. As a first approximation we assume that the pores are homogeneously distributed and can be thought of as spheres with a fixed radius r. The refractive index of the gas in the pores is set equal to 1. The refractive index of alumina has been determined for the complete rangc of transparency by Malitson 14). He found the following dispersion equation:

I 1.023798 A~ 1.058264 Ag 5.280792 ;>"5 ) lh (4.13) n "" ( +;>"3 - 0.00377588 ... A~ + 0,0122544 + "At - 321.3616' where AO is the wavelength in vacuum. This equation gives us the relative refractive index m .. 1in as a function of the wavelength. Figure 4.2 gives a graphical repre­ sentation of eq, (4,13).

&55 100 o.~

~~, 1.7'>

().~

1:J!l 0.59

0.60 \ll!j 0.61

062 1~O M~

0.2

Fig. 4.2. Ordinary refractive inde~ n and relative refractive i!>dex m = Un as a function of wave· length A. according to mea.uroment. repotted by M.lit.an I.) On sapphire at 24 • c. The main problem of calculating the in-line transmission is the calculation of the scattering coefficient Qsca as a function of m and x. According to eq. (4.11) Qsca is 64

a SIJnlluation of terms containing the coefficients an and bn. These coefficients contain spherical Bessel functions with complex argument The number of terms required for evaluating thc series is proportional to,x. Hence, reliable Mie scattering computations for large spheres arc tedious and time consuming. Tables have been published wich give Qsca for many values of m and x. However most values of Qsca have been computed fm m > I. Exceptions are the tables given by Boll et aJ. 24, 2S) for m" 0.60, 0.70,0.80 and 0.90 and Chimey 26) for m =0.50 and 0.75. Inter­ polation of these data for the desired values of m is dangerous because of the complex character of Qsca.

fo'or the exact calculation of Qsca we used the numerical procedure outlined by Dave 27) and the recurrence rdations he gives for the Bessel functions. To test the reliability of the calculations we compared the value of these Bessel functions with tho~e tabulated in the Handbook of Mathematical Functions ~;)). This showed an increasing deviation for the higher order functions due to aooumulated rounding errors. Therefore we changed the forward reourrence relation for a backward recurrence (sec Ross 18). The improved program has been tested for very large values of x. Ref. 21 gives a ~imple formula for m '" 1.342 and x > 5 :

2 3 Q = 2.0-7.680 X-I sirl (0.684 x) T 1.84 X- / + 'ripple' . (4.14)

The result of the test is given in table 4.1 which gives the calculated value of Q, the value of Q obtained from this formula, and the number of calculated Bessel functions N

Table 4.1

x Q (calc) Q (form) N

5011 2.0305 2.0345 168 10071 2.0180 2.0165 326 20011 2.0198 2.0178 647 30071 2.0240 2.0239 959

The table shows good agreement, even for extreme values of x. Therefore, the calculation procedure can be considered to be reliable.

The calculated efficiency factor can be represented in several ways. Figure 4.3 gives Qsca as a function of the pore radius r for three different values of the wavelength. A generali,.ed representation of QSCIl is given in figure 4.4, where this quantity is plotted against the function p defined by

41TY P '" 2x I m-l I = },,~- II-/! I . (4.15) 65

(The physical meaning of p is the difference between the phase shift which a central light ray experiences upon travelling thwugh the sphere and that obtained in the absence of the particle).

if".(U, I m. 0,56 ~.1.0, ... 0.57 btl:), mz 0.'58

OJ.

QO~~~~~------~~~----~t~5~----~W~------~~~ rlJ.lml_

Fig. 4.3. The t:!:f:fici~n(:y f,actot for S~Qttt'tin~ by pores in alumina as a function of th~ pore radius" (or thr¢~ "alu~s of the wavelength A•.

fig. 4.4. ·rh. effi(;ien.:l' fa(;tor for scattering as a function of p" 2"x I »1-1 I willi m - 0.S65. 66

The curve in figure 4.4 is calculated for m '" 0.565. All curves have in common a rapid increase to Qsca ~ 2.16 and then a damped oscillation about the limiting value Qsca = 2. Superimposed upon this main oscillation is a ripple structure which is not shown he,e and which can only be found ifvery small increments of x are selected in computing Qsca. The limiting value Qsca'" 2 follows from the theory of diffraction by a circular disk.

For comparison with the experimentally determined transmiss\(m curves a plot of the transmission T against the wavelength 71.(1 is more suited. For a sample thickness t we have

(4.16) where R t takes into account the tolal reflection losses as defined in eq. (4.2), and 'Y is the ~cattering coefficient defined in eq. (4.12). The notation of Tin cq. (4.16) implies that the scattering is due to independent ~cattering cclltres and that we exclude mult1ple SC;lttering_ The exponential thickness dependence of the trans­ mission in alumina has been experimentally verified by Grimm et al. 9). The total geometrical cross-section G = Nrrr2 can be expressed in the experimentally more accessible quantity Vp, the volume fraction of porosity, by G' = 3 Vp/4 r. This gives fm the scattering coefi1cient 3Vp Qsca 'Y '" --4r- . (4.17)

Wilh equations (4.16) and (4.17) the in-line transmission can be calculated. {n tlgure 4_5 results arc shown for three different values of the pore radius r, with a porosity Vp '" 0_002 and a ~ample thickness t =0.5 mm. The great influence of the pore si~-e is very clear: at short wavelengths large pores 3rc necessary for a high transmission, at longer wavelengths the reverse is true.

60

r=l0f-lm 40

20

°O~~~~----~----~----~4------.5~

"ol~rnl- Fig. 4.5. Cakulatc::u tranS.I'lliSSlOn c.:llI:'V("S;)8;.1. function of wavelength for n fix.~d I)(ll'( raulu:!i r. P",o,ity V f' = 0,002, ;ample ,hickn ..' t = 0_5 mm, 67

The pronounced influence of the pore size can also be seen in figure 4.6, which gives the transmission as a function of pore size for two wavelengths, Ao '" 0.5 Mm and A¢ = 2 pm, porosity Vp" 0.001. and thickness t .. 0.5 mm.

100

80

o~ ''; '~ 60 <= i'.. :E" i:.

20

3.0 pore di~meter (Mm)

Fig. 4.6. Calculated ttal1lmissj')n as a f\lnction of the pore radius r for twO v.lues of the wave- 1~IlgJ;h ).. •. porosiw Vp ~ 0.001, sample ~bickness t = 0.5 mm. No corro~tion has b.on mad. for 'et1ec~io~ lm~~'.

In figure 4.6 the reflection losses have not been taken into account for simplicity. It follows from figure 4.6 that the curves have their minimum value if 2r/'t.. '" 0.73; then the interaction between light and pores is strongest. Fot smaller pores the scattering behaviour goes into the direction of Rayleigh scattering, revealing a very strong dependence on wavelength and pore size. FOr pores larger than the critical size the tnlnsmi$sion increases with size, but less drastically, and the transmission hardly depends on wavelength.

The oscillations in Qsca of figure 4.3 and figure 4.4 are also present in figure 4.5. The fact that we never observe such oscillations in experimental transmission curves suggests that the assumption of uniform pore size is not realistic. In fact Van de Hulst 21) has shown for the limiting case of Rayleigh-Gans scattering (lm-l HI), that the amplitude of the osdllations in Qsca deCreases if we no longer assume the 68 presence of scattering centres with a fixed radius, but instead introduce a site distribution.

4.2.2.2 Pore sh::e distribution

The assumption of uniform pore size is not realistic in actual ceramic materials; there is always a spread in pore size, just as there is always a spread in grain size. Determination of the pore size distribution is very laborious: many measurements of generally very small pOres are necessary to estimate the distribution with any accuracy. It is understandable from this argument that hardly any results on pore size distribution have been published. Moreover, the derivation of the true si;-:e distribution from the observed distribution in a polished section is a complex problem 29). An approximate method for this conversion, valid for spherical pores, has been givGn by Tornandl 30).

For grain size and powder particle size distributions a logarithmic Gallssian distri­ bution is often assumed 3l). This lognormal distribution applies exactly for quantities that are the result of a process involving steps where the probability of a change is proportional to the instantaneous value of the quantity. Many growth and breakdown processes belong lo this category :12). We do not know of any data published on the nature of pore size distribution functions. Only few measurements of pore size distribution~ have been reported in literature. However, figures shown by Oel 33) can be fitted reasonably well with a lognormal distribution.

We have tested in two differenl ways the assumption of a lognormal pore site distribution in several highly sintered ailunina specimens with large pores. One method was to determine pore sizes with a planimeter from photographs of a polished section. The other method made use of an image analyser 34): the picture of a TV camera was converted into sixtoen grey levels; the black spots from a certain grey level (the pores) could then be counted automalically. Neithct method is very accurate and the tesults proved \0 bo very sensitive to sample pr~para!ion and sample magnification. The resulting two-dimensional distribution was then converted into a three-dimensional one ~o). A lognormal distribution fitted the experimental distributions reasonably welL St.andard deviations were found with a bet.ween 0.25 and 0.35.

For the representatiOl\ of the logarithmic distribution we used the so·called ZOLD function (zeroth order logarithmic distribution function), described by Espenscheid ct aL ~$, 22). This function is given by f(t} = (2~fi~-~~e~·p(f-;;2) cxp [~(ln r 2~}n-~Ill)~-J (4.18) dei1ned by two parameters rm , which is the modal value of r (the value of the rtidills r for which the functionf(r) reaches its maximum value) and u, which is a measure 69 of the width and also of the skewness of the distribution (the skewness of the dis­ tribution increases with its width). A property of this ZOLD function is that the mOdal value of r remains constant as the value of 0 is varied. The relation between rm and i, the mean pore radius, is r'" f r f(r) dr"" rm exp dol). (4.19) o

The pre"exponential factor in (4.18) is the normalizing factor to ensure ff(r)dr"'l. (4.20) o

4.2.2.3 In fluence of pore size distribu lion on the scattering coefficien t

Afte, the introduction of a pore size distributionj{r} we have to reformulate the expressions of section 4.2.2.). For convenience we introduce the dimensionless parameter U "" rlrm. If r is normalized with respect to rm, then f(u) does not widen with time, but remains COnstant during normal growth 36).

We define an effective porc radius reffas the radius that identical pores should have to cause the same light scattering as the whole of lognormally distributed pores. For each sphere holds: volume/geOmetric cro$s-$ection;;; 4r13. The effective pore radius may now be written: "'" f u3 f(u} du 3 total volume '" r 0 (4.21) reff=- "4 total geom. cross-section m 00 f u2 f(uj du o

Substituting eq. (4.18) we have reff"" rm exp (fOl j. (4.22)

Thi$ expression already indicates the importance of the width of the pore size distri· bubon. Table 4.2 gives some values:

Table 4.2

a reff/rm 0 I 0.2 1.15 0.4 1.75 0.6 3.53 0.8 9.39 70

We further define an effective efficlency factor for scattering Qeffby

. . j Qsca (u) f(uJ u~ du total scattenng cross-sectIOn _ 0 Qeff (4.23) = total geometrical cross7eciion- - jf(u) u 2 du o With eg. (4.18):

"'" 2 J Qsca (u) f(u} u du I) (4.24) 0"(21l-)~ exp (~)-)-

Finally we introduce the generalized parameter Pelf­ With eg. (4.15) and eg. (4.22) we can write:

41frm 2 Pefr ----x;- (n-I) cxp (#;O" ;. (4.25)

Using the ZOLD distribution eg_ (4.18) with parameters a and rm and using the Mic expressions to calculate Qsca (u), we can numerically integrate eg. (4.24) to obtain Qeif The results of the calculation of Oef! as a function of Peff are shown in figure 4.7 for m '" 0.565. The figure indicates that the oscillations in Qeffare damped out with increasing values of the parameter u. For u> 0.3 no oscillations are observed.

lS

1.0

10 1, p ~j I ------Fig. 4.7. The df~ct;v~ dfici~ncy fa"Wt for s~atlering by porcs in .lumina with a lognormal pore ~i.c .;I;.tribution as a function of Peff = 4tr'eff Im--·ll/11. with m = 0.565. The width of the disr;::ribt..l'don jt')c;-rea~es. with incr~a5in8 0 values, 71

The influence of the spread in pore sizes on the transmission is illustrated in figure 4.8, where the calculated in-line transmission is given as a function of wavelength. T.1tI%] r 80

60

0" 40 06

05 20 Q4 03

0 02 0 2 3 5 Aol!.Im)-" Fig. 4.8. Calculated transmission cutv.s for .lumin. with a lognormal pore size distributiOn as. function of wavelength. The width of the distribution inc~ ••s¢s with inc~easing u valuos. Th. maximum <;If tll. distribution rm " 0.5 I'm, porosity Vp ~ 0,002, and sampl~ thii;kness t =0.5 mm_

The transmission Teffis obtained from eq, (4.16) after substitution of _ 3Vp Qeff _ 3Vp Qeff "1------' (4.26) 2 4reff 4rm exp (tcr )

The curves in figure 4,8 have been calculated for'm =0_5 Mm, Vp =0,002 and t = 0.5 mm. The figure shows that with increasing values of a the curves are flattened out more and more, while the over-ali transmission increases in the visible part of the spectrum and decreases at longer wavelengths, The influence of a on the in-line transmission is expressed by Qeffand reff Eq. (4.26) shows that with the assumptions made the in-line transmission of polycrystaIline alumina is a function of three parameters of the micro ~tructure: the value of the pore radius where the distribution function assumes its maximum, 'm; the width of this distribution, 0-; and the porosity, Vp_ For each set of these parameters it is possible to calculate the transmission as a function of wavelength.

4.23 Measurements 0/ the in "line tmnsmission

All samples used for the transmission measurementS were plane-parallel slices with a thickness of 0,5 ± 0.01 mm. These slices were made from the sintered pellets (chapter 2) Or the hot-pressed rods (chapter 3) by sawing, grinding and polishing. The grinding of hot-pressed alumina proved to be much more time-consuming than 72 the grinding of sintered alumina. The slices were given a final polishing on both sides with 0 - 2 I_UTI diamond paste to obtain a good surface finish. The importance of surface finish on transmittance has been demonstrated by Grimm et a1. 0:>). Scratches and so on will greatly affect the back.scattering of light.

Transmission measurements were carried out in the wavelength range from 0..4 . 2.5 11m with a Beckman DK 2 spectrophotometer. This apparatus could be oquipped with an integrating sphero to measure the total transmission, I.e. the sum of the diffuse transmission and in·line transmission. For measurements of the in-line trans­ [11ission the apparatus could be provided with a special transmission unit with the detector situated 25 em behind the sample ({) minimi;1;e the measurement of 1 scattered light. As the light.sensitive surface area of the detector waS 7.2 mm , only light scattered in a <;:(me of a half-angle less than 0-0 I rad (about 0.5°) could inter­ fere with the transmission measurement. This means that only a small <;:onection has to be applied to the measured SC < t " Dol A

~~f

C

Fig. 4.9. Pos.ition of thl:: Sctr):~pk in the BcckIno,o !'.pcctrQphct0m~~a uscd for me~l,.~\.J.rcment of the in-line n.n.mi»io'l (A), enrol transmission (B) and tot "I r~t1oction (C).

The transmitt;mce m~aSll(ements at higher wavelengths (2.5· 7 pm) were !llade using a Hit.achi double-beam Speet(ophotometer. The position of the sample irl this apparatus is shown schematically in figure 4.10. Much mure scattered Ught will be 0 measured. The aperture angle of the Hitachi can be calculated and is about 4 • This )11eanS that the transmission at 2,5 I.UTI measured with th~ Beckman will differ from that measured with the Hitachi. 73

t ---- ~G': ------,.. -/ .,,\

I ~,.. I " , ~

s

Fig. 4.10. Posi[jon of the sample;n the Hitachi spectrophotometer.

4.2.3.1 Influence of the pore size

The two techniques for fabricating dense, polycrystalline alumina, vb;_ normal Mntcring described in chapter 2 and hot pressing described in chapter 3, provide materials with very diverse microstructures. A comparison of the microstructure of hot-pressed alumina and sintered alumina has already been made in chapter 3. At about equal porosities the mean grain size differs by a factor of twenty and the mean pore sb;e by a factor of five. We expect therefore a ~reat influence on the optical properties. Figure 4.1 I gives the in-line tranSmission of a hot-pressed sample and a sintered sample, both dcnsified to about the same relative density of 99.95 % 4 (porosity Vp = 5 x 10- ). The transmission of sapphire is also shown for comparison. 100r------,

'-Sapphira 80

0.4 0.6 O,S 1.0 2.0 -- ,--_ W.volongth ~ [urn]

Fig, 4.11. Measured in-line transmission of a sample of hot-pressed alumina (KG 15 3-HU) and norm.lly Sintcrcd .lumin. (0176-S6) meaSured with the Beckman spectrophotometer. 4 Porosity V -p .. 5 X 10- , sample thickness t ~ 0.$ mm for both samples_ The figure .lso shows [he m~nsmlssion of sapphire. 74

As can be seen, the in-line tranSmission of the hot-pressed sample is strongly dependent on wavelength: it is very low at the shorter wavelengths but approximates to the transmission of sapphire in the infrared_ This is in agreement with a Rayleigh type of scattering and points indeed to the presence ofvery small pores_ It also provides experimental evidence of the minor importance of the birefringence, The value of ton is 8,5 x 10-3 at Ao "0.4 !.1m 1,) and i'in is 7.5 x 10"3 at Ao = 1.0 !.1m 14), In spite ()f this small change in the birefriIlgcnce there is a very significant change in the in-line transmission. Normally sintered alumina has a higher in-line trans­ mission at the shorter wavelengths, but the dependence on wavelength is weak, Thi$ is in agreement with a Mie type of scattering and points to larger pore sizes, The increase in transmission is continuous without oscillations, indicating a spread in the pore sile distribution of (};.. 0.3 (see section 4.2,2.3)_

The complete transmission curve is shown in figure 4.12.

T,r._,,"'~ 80

70

60

60

.0

JO zo

10

Fig. 4.12. Complete tt"",smi;;i"" curve. of tho ~an\e samp! .. a; in figure 4,11, HI' means hot· pr~!i~d alumina f S meuns n.ormally sintert:d alumina,

The discontinuity at Ao '" 2.5 11m is the result of the difference in aperture between the two spectrophotometers, reflecting the fact that the Hitachi is not a suitable apparatus to measure the in-line transmission. The decrease in transmission above 4.5 Mn1 is probably due to true absorption ~7) and not to scattering. The figure shows that the influence of light scattering by the pores in hot-pressed alumina at the longer wavelengths is greatly reduced, This ()pens the possibility of using hot­ pressed alumina as an LR. window.

Figure 4.13 gives the total transmission and the total reflection (normal reflection + diffuse ret1ection) of the same samples as measured with the Beckman spectro· photometer, Although the in-line transmission of hot-pressed and sintered alumina 75

90 ~ppni~ Tmtol eo ::::===== l!;,;r~1 Mh::tl tl"Cll""I5mi5~ion ';11 60 ~ 50

<0

:ll 20 ~ toto.l rtH.~;i(Jr. "'0

O~ DB O~ I, .S 2 '.[~ml

FiS.4.13. Total transmission and total rcfl~ctk>n of tbe same samples as in fi(1ure 4.11 measured with th~ B~ckman sp~ctrophotometer. are very different (figure 4.12), the total transmission does not differ very much. AI the shorter wavelengths the total transmission of sintered alumina is even higher. At these wavelengths hot-pressed alumina is seen to have a strong diffuse reflection. This is to be expected when the scattering behaviour more and more resembles Rayleigh scattering.

From figure 4.6 we have seen that transmission is lowest for some critical pore size, this pore size being of the same order of magnitude as the wavelength used. At smaller pore sizes pore growth will have a detrimental effect on the transmission and this can be demonstrated by annealing hot-pressed alumina samples. At larger pore sizes pore growth will enhance transmission. This is illustrated in figure 4.14. It gives the in-line transmission and total transmissiOn of two identical samples, one sintered for 2 hours at 1800 °c, the other sintered for 24 hours at 1800 °c. At this high temperature there is hardly any inCrease in density by prolonging the sintering time from 2 to 24 hours. However, there is a considerable increase in mean grain size from 17 pm to 32 pm and this is accompanied by a conSiderable increase in pore size. The mean pore size as determined with the method outlined by Fullman 3S) has increased from 0.33 pm to 0.46 pm.

4.2.3.2 Influ ence of the M gO con ten t

In chapter 2 we have described the influence of the amount of MgO On the evolution of the microstructure. As both the porosity and the pore size are affected the amount of MgO Can be expected to have a great influence on the in-line transmission. 76

0.5 to 2(1 2.5 WAVel."NGTH ",,,,I fig. 4.14. M!;':.j\$u .. ~d 1;t'.&flsmission curves of two samples of alumina $intlt:I'~d ;).[ 1800 ~ C fur 2. h and 24 h [esp~c(iv~Jy. I'O(oample thickness t ~ 0.5 mm for both "'''plcs.

The same samples 1I~ de~cribed in section 2.3.3 and d(lped with 50 ppm to 3000 ppm MgO as a ~intering aid were used for the transmission measurements. All samples received the same sintering treatment: first, l.S hours at 1630 °c and second, 10 hours at 1850 °e. The microstructures and the densities (If these specimens can be found in section 2.3.3. From the sample with 50 ppm MgO containing some cracks no sljce~ for the transmission measu)'em~nts Gould be prepared. Results for the other specimens are given in table 4.3. The trammissiml values have been taken from the transmission spectra at the wavelength of 0.5 pm.

Table 4.3

Measured in-line transmission and MgO content

ppm MgO transmission (%)

100 29 200 25 300 18 1000 12 3000 4

The data of the table can be understood 4ualitatively a, follows. The samples with 300 ppm MgO and more contain an increasing amounl of second-phase pllrtidcs. These particles result from the undissolved additive or result from precipitation during cooling, 01' both. These particles act as scattering centres; lhe: rcrractly~ index of stoichiometric spinel MgAl;l 0 4 is 1.72 at th~ wavelength of 0.5 Prll. The low transmission of the last sample is of course also cau~ed by its lower density (fig.2.8). 77

Although the samples with 100 and 200 ppm MgO have about the same total volume fraction of pores, the former has the highest transmission. The reaSon must be the larger mean pore size which is found in this s

The composition with 300 ppm MgO was chosen to investigate the influence of the sintcring temperature on the in·line transmission, bdng very sensitive to differences in pore density and pore size. All samples were sintered for 10 hours at the temperature indicated in table 4.4, except the last two samples, which were sintered for 24 hOurS. Transmission values are again those at 0.5 ,urn wavelength.

'fable 4.4

Influence of sintering temperatur~ on in·line transmission

temp. ("C) transmission (%)

~-- 1850 19 1800 21 1750 21 1700 12 1650 13 1600 iO

The table shows that the sintering temperature can be lowered to 1750 0 C without any significant change taking place in the in-line transmission. Samples sintered at lower temperatures have lower transmission values, not only because of their higher porosity but also because of their smaller mean pore size.

4,2.3-3 Influence of extra addition of Y203 and CaO

Sintering experiments were carried out to see if small additions of Y 20; or CaO could enhance the transmission of alumina sintered at relatively low t~mperatures. These experiments and the influence of the additives on the micro~tructUIe were described in section 2.3.3.3. Here we only give the results of the in-line transmission measurements. Only one composition with extra Y1 0 3 and one with extra CaO was studied: 300 ppm MgO + 1000 ppm YlO~ and 300 ppm MgO + 50 ppm CaO. Table 4.5 gives again the transmission at 0.5 Mm of samples sintered for 10 hours at the indicated temperature. An exception is again the sample sintered at 1650 °c, which was sintered for 24 hours.

From the data of this table it Can be concluded that addition of extra Y 203 has an adverse effect on the in-line transmission. The effect of addition of extra CaO on the in-line transmission is negligible. 78

Table 4.5

Inf1uence of sintering temperature on in-line transmission .,,' ... .. _. Temp. (C) transmission (%) transmission (%) transmission (%) MgO only ,. extra Y20J + extra CaD ...... _----- 1800 21 - 22 1750 21 II 20 1700 12 9 12 1650 13 6 13 ,...

4.2.4 Determinl1tion of microstlUctural parameters from the measured trans­ mission spectra

In this section we shall compare the calculated results and the experimental results for in-line tranSmission. Wilh the assumptions made in section 4.2.2 we have seen that the in-line transmission of polycrystaIline alumina is a function of three para­ meters of the microstructure: tht porosity Vp. the spread in the pore size distri­ bution (} and the value of the pore radius, where this distribution is maximum rm· Generally we must treat Vp as a free parameter and not as a known quantity. It is derived as a small value from a difference, which makes it relatively uncertain at very high densities. With much CarC it is possible to determine the density with an ~ccuracy of ± 0.0005 g/tm3 (sec section 2.3.2). This means an inaccuracy in the porosity of ± 0.25 x IO-~. For each parameter set (rm, 0, Vp ) it. i~ possible to calculate the transmission a~ a function of wavelength. Conversely, we can try to determine these parameters from the measured tranSmission curve. In fig\lfe~ 4.15, 4..J 6,4.17 and 4.18 the calculated effective transmission, corrected for rcl1ection losses. has been plotted against the pore radius rm at three different wavelengths. 0.5,2 and S 11m. The parameter a has the values 0.3, 0.4, 0.5 and 0.6 and the parameter Vp has the values 0.0005, 0.001,0.002 and 0.003.

It is advantageolls, when trying to determine the parameters rm. 0, Vp from the measured transmission, to plot the scattering coefficient 'r instead of the trans­ mission against the wavelength. According to eq. (4.19) '}' is directly proportional to the porosity Vp. Moreover, 'r is a material property, while the transmission T is a sample property.

In comparing the calculated scattering coefficient with the experimental one, we have to realiLc that Qsca is based on the total amount of light scattered by a particle in all directions. However, it is impossible to m~asure only the intenSity of the undisturbed light, with the complete exclusi(ln of light scattered in the 79

90r---~------~ 1..W.l V.=01l00S 60

70

o 0.1 0.2 o.J O~ as -----400 r,....I..I.i m]

Fig. 4.15. C,..lc"'at~d. transmission cQrrecteo for reflection 10515~5 35 a function of th~ modal value of 1;h~ por~ radius 'Ym for different vah,Ics of the width of the distribution a and th~ wavelength ),.. ' Porosi~y Vp = $ II 10" , sample thicknoss t .. 0,5 moo.

Hg. 4.16. The Same as in figure 4,15, Vp = 10" forward direction. Therefore Qsca must be corrected for the light scattered in a cone of half. angle 8 determined by the detector in the spectrophotometer. Gurnprecht and Sliepcevich ~9) define a correction factor F as

(4.27) 80 where Qa stands for the actual scattering coefficient and Qt for total ~cattering co· efficient. it and i2 are the intensity functions of the scattered wave introduced in eq. (4.7).

~o T.,.I%I \.:.'5 ~rr. ~o

'ro

50

50

'U

W

20

1D

O~ 06 0" as O~ ;0 -r.. [)Jrrl ]

Fig. 4.17. Th~ same as in fih'ure 4.15, VP = 2 )( 10".

':II)

eo 02 u:l 7(1 0,a'. i-'5)JrT1 ~5 -:i 50

,0

,0

01 07 O~ Og ;0

Fig. 4.18. The .ame as in figure 4.15, Vp = 3 " 10-'. 81

Assuming that i = (il + i1.)/2 is independent of e for small values of e, eq. (4.27) reduces to

(4.28)

The value of i can be approximated in several ways. Gumprecht 39) demonstrates that for large spheres (x ~ 20) and small angles (8 .;;; 1.5") the exact value of I is in good agreement with the value calculated from the much simpler diffraction theory. Penndorf 40) proves that for x > 5 the value of i can be approximated by (Y4X 2 Qt)2 . We tlnd that F decreases with the size parameter x. In our experiments the highest value of x is about 20. This gives I - F = 3.9 x 10'3 according to the method of Gumprecht and I _. F'" 4.3 X 10-' according to the method proposed by Penndorf. The agreement is very satisfactory and it means that the correction upon Qsca is only 0.4 %. For smaller values of;x this correction is even less, for which reason we have neglected it in the following.

We return now to the tlgures 4.15 to 4.18. These curves also give the scattering co­ efficient at a given wavelength as a function of pore radius 'm , with 0 and Vp as parameters. Comparison with the experimentally obtained,), at some discrete wave­ lengths gives generally a number ofpossib1c combinations of 'm , r:J and Vp. For each of these combinations we can calculate the scatterin(l coefficient as a function of wavelength. By repeated comparison with the experimentally determined scatterin(l coefficient at twelve wavelengths one can find the parameter set that gjves the best fit Over the whole wavelength region.

This procedure was applied to normally sintered and hot-pressed alumina. As an example figure 4.19 gives a plot or the experimental and calculated 'Y versus \0 of a sintcrcd alumina. The curve shown was obtained by using a least-squares opti­ mization in the choice of rm, r:J and Vp " The points were obtained from the trans­ mission measurements. The measured density of the sample i~ 3.978 g/cm~, which 3 gives Vp -- (2 ± 0.25) x 10- . The best tit with the experimental trammission was 3 obtained with the parameters Vp "' 1.9 x 10- , (J '" OA and rm " 0.34 Mm "for the mean pore radius (this gives r "0.43 Mm). The va.lue found for the porosity in this way is in good agreement with the experimental Vp. The values of (] and rm are also very reasonable.

The same calculations Wl>fl> made for samples of hot-prossed alumina. Figure 4.20 is an example and gives the experimental and calculated scattering coefficient of a hot-pressed specimen. The measured denSity of this transparent material is ),984 g/cm', which means a pc)rosity Vp =(5 ± 2.5) x 10"4. For several values of (J a combination of Vp and 'm can be found that (lives a reasonable agreement between calculated and measured transmission curveS. In figure 4.20 the calculated 4 curve belongs to the set (] =OJ, Vp '" 4.9 X 10- and rm = 0.11 pm. However, the standard deviation of a least-squares fit for this curve is only slightly lower than the 82

50 r 30

0.5 to 1.5 2.0 Aol jJm ]

Fig, 4,19. Scattering coefficients a. a function of wavelength. Dot., measured on a oormally sintcrcd s.ample of alumina. Solid line; calculated as::iuming a lognormal pOt{!' si;!.e di').J;:rtbllJ;:ion with 'm = 0.34 1'''', <, m 0.4 ond Vp < 1.9 x 10".

20

15

10

o~~~~~~~~~~~~L-L-~~ 05 10 1.5 2,0 'ol\Jm!-

Fig. 4.20. Scattering co

Tm = 0.11 I'm, <"1 g 0.3 and Vp = 4.9 X 10"'. 83

4 standard deviation for a curve with the parameter set (J '" 0.6, Vp " 6.6 x 10- and 'm '" 0.03 Ilffi· A comparison of these values of'm with the value estimated from the micrstructure shows that the value of'm " 0.11 /-1m is to be preferred. The porosity is again in good agreement with the experimentally found porosity.

4.2.5 Conclusion

The light transmission of polycrystalline alumina is governed by the scattering of light by the residual porosity. The Mie theory allows a calculation of the trans­ mission losses due to scattering by pores. The experimental data can only be described by this theory, if we assume a spread in pore size. We have calculated transmission spectra for alumina with a given value of the po\Osity Vp , assuming a lognormal pore size distribution with a modal value of the pore radius rm and width of the distribution u. The measured in-line transmission spectra of normally sintered and hot·pressed alumina samples with widely differing micro­ structures can be well described by this theory. We have determined the micro­ structural parameters Vp, rm and (J from the measured transmission spectra. Very reasonable values for rm and (I are obtained, while the calculated and experimental values of Vp are in good agreement. This good agreement supports our assumption that in this approximation we can neglect the influence of birefringence on the transmission loss in alumina.

4.3 TranSp!lfent !lnd t~!ln$lucent alumina

4.3.1 Introduction

In chapter 3 we mentioned a striking difference between hot-pressed and normally sintered alumina. Even after alumina has been sintered to nearly theoretical density at high temperatures, the material is translucent. It looks, at best, like ground glass. A slice of hot-pressed alumina, on the other hand, can be seen through very well, and in common parlance this material would be described as transparent. The difference is j)Iustrated in figure 4.21, which shows two discs of alumina held 10 em above a printed page. The text remains readable only in the case of hot­ pressed alumina, although there is considerable loss in contrast.

There is much confusion in the literature in descriptions of a densely sintered ceramic material. Words like 'transparent', 'nearly transparent' and 'translucent' are often used inaccurately. The definition of the word transparent given in Webster's dictionary 41) is: 'having the property of transmitting light without appreciable scattering so that bodies lying beyond are entirely visible'. In this sense sintered alumina is not transparent. This definition also indicates that the difference between translucency and transparency is rather subjective: it leaves the judgement to the human eye. We shall return to this point in the next section. 84

grain size of about

Th~ pores are inside the grains. The m

specimen shows a ~ess h magnesia present) of about

.•. " 1 j and h' redomi

HOT-PRESSED DENSE SINTERED ALUMINA ALUMINA 0)'.-

TRANSPARENT TRANSLUCENT

Fig. 4.21. Photograph showing twO di~c~ of polycry'talline alumina "hour 10

The lack of tr~nsparency of ~intcrcd alumina has been ascribed to grain boundary ~catteriIlg and birefringence s, 10, II). This underestimates the infhlence of porosity and pore size. Because of its v~ry small grain size (Jess than I }.lIn is pussible) it is precisely the hot-pressed alumina that should suffer frum a relatively high contributiun of grain boundary scattering and double refractiun. Nevertheles~, this material is the more transparent one.

In the following the dtfferenc~ between transparent and translucent alumina is described in terms of the width of the forward lobe in the angular s(anel'ing dia­ gram and in terms of the blur both rnateJ'iais cause in imaging a test object. A di~cussi()n is also devoted to the relationship between these properties and the microstructure of the material and its preparatioll method. 85

4.3.2 Theoretical considerations

In section 4.2 we focussed OUr attention on the in-line tra.nsmissiOn. This quantity could be calculated with the three parameten: pore size, spread in the pore size and porosity. The same three parameters determine the angular distribution of the scattered light. This distribution can be calculated from eq. (4.3), which gives the amplitude functions of the scattered wave as a function of the scattering angle (). The variation of the angular scattering with the size of the scatterers and with the scattering angle is quite complicated ::). For particles an order of magnitude smaller than the wavelength the scattering diagram is calculable from the Rayleigh scattering. The diagram is characterized by the symmetric forward and backward scattering. With increasing particle size forward scattering dominates more and more (the Mie effect), very complex oscillations with the scattering angle develop and the forward scattering lobe becomes increaSingly narrow. FOr large particles nearly all the scattered light is concentrated in a very small angular zone (diffraction). The width of the forward scattering lobe and the position of the maxima and minima can be used to determine the particle size in a monodispe)"se or nearly mono disperse system 42). However, no oscillations are found in the scattering profiles of our alumina samples (figure 4.22),

100

0,010 10 ;;0 3(l 40 so 60 70 60 90 scattoring angle B

Fig. 4.22. Angular disrribucion of tile scattered light intensiry on a logoarithmic scale (),.o = 0_546 I'm), mcasur~d on a sinr~red and hot-prossed samp!. of alumina. 86

The extent to which a sample of densely sintered alumina is translucent, or possibly transparent, can be characteri7eed by the width at half height of the small scattering profile. The light respoP$ible fDr this scattering profile consists of two parts. The first part is the transmitted beam, which is unperturbed by the presence of the scattering centres. Sinoe its phase is solely determined by the optical path through the medium, this beam is coherent with the incident light. This light contributes to the image formation. Tho second part consists of the radiation, which is scattered in the forward direction and very close to that direction. This light has suffered a phase delay due to the scattering process and is not coherent with the incident light. Its contribution to the image formation will strongly depend on the distance bClwecn the ceramic slice and the object we are looking at. At sufficiently high density of the ceramic the contribution of the unperturbed light to the total trans­ mitted light will be relatively large and in that case we can expect transparent alumina.

Although the mea~urement of the width of the diffusely transmitted light gives information about the degree of translucency of II oeramic sample, it does not give a definite answer to the question whether a ~pecimen is really transparent. The reason is the difficulty of measuring the light intensity at very smail scattering angles. A more adequate method is to measure the distortion of the image that arises when we look through a slice of alumina at a test object at a certain distance behind the alumina. Then we have to give a better definition of the concept of transparency. For II material to be transparent we now require that the distortion of the image does not affect the limit of resolution of the eye- This definition corresponds very well with that given by Webster (previous section), but it is also more quantitative. The limit of resolution of the human eye is about I minute of arc 43). Thi~ means that the eye resolves details of 1 mm at 3.5 m. For imaging pictures it is more customary to express the resolution in the number of lines per miJIimetre that can be resolved. At a distance 0[25 em the eye resolve~ about 18 lines or 9 black and white line-pairs per millimetre.

A photographic technique can be used to measure the resolution by photographing a test chart through a slice of alumina. Generally, the diffusely transmitted light will caUSE image blur. This blur is a convolution of the scattering profile and the light source. The distortion of the image is proportional to the distance between object and ceramic, and to the width of the forward scattering lobe. In the case of transparency the distortion must be so slight that at a distance of about 25 em from the test chart 18 lines per mm can be resolved, irrespective of the distanoe between te~t object and ceramic.

4.3.3 Experimental part

The same samples whose in-line transmission was measured were used for the measurements of the angular distribution of forward scattered light and the photo" 87 graphic measurements. All these samples had a thickness of 0.5 mm. The measure· ment of the angular distribution was carried out with a modified Zeiss Gonio· photometer GP2. A schematic representation of the experimental set·up is given in figure 4.23.

L

Iv= 0.54 jJm

s

Fig. 4.23. Sch

The light source was a mercury lamp. A parallel beam of monochromatic light wilh a wavelength of 0.546 /.1m was used. The aperture of the photomultiplier was 0.25°. Measurement without a sample of the beam width at half intensity w, gave w =0.65°.

The microscopy resolution test chart of the National Bureau of Standards (figure 4.24) was used to determine the resolution a$ a function of the distance between the object and the alumina platelets. Photographs were made with a Leitz Aristophot for photomacrography equipped with a 120 mm lens. The position of the lens and the image plane could be adjusted $0 that the magnification of the test chart was exactly one (see figure 4.25). The sample could be moved up and down between the test chart and the Ions. The number of lines per mm resolved at a certain distance could be determined visually or with a densitometer. 88

111;l,i IIIII~ IIIF5 111111.0 W..l.2 ~ ::~: 11111,U L""'~ IIIII~ 111111.1 I L8 2 111111. 5 IIIII \. 4 111111. 6

MICROCOPY P[SOWTlON TEST CHAlrr

NfiYlONAL BU~E.AU OF :;IANLlIII~D'3-196J-A

Fig. 4.24. Micro;copy r<

image

I",ns f=120mm

240 mm

----'----'---'-- test chart t t t light ~aurce

Fig. 4.25. Schematic rcprC5~ntati"n of the po,ition of the s.mpl. in the oct·up for (h. phOlD· graphic me.~iU~n'lMtS. The sample can be mov~d between test chart ~nd lens over a di~tancc of 24 em. 89

4.3.4 Results and discussion

The angular distribution of transmitted light measured On the same representative specimens for sintered and hot-pressed alumina as in the figures 4.11 to 4.13 is given in figure 4.26. The intensity of light at 0° has been put at 100 % for both samples. As expected, hot -pressed alumina has a very sh~rp peak round the in· line 0 transmission, The width at half height, w, for the best samples is 0_8 , only little more than is measured for the blank. There is little spread in the measured values of w for hot-pressed specimens with small differences in density and pore size. All values lie between O.S" and 15°. From one hot"pressed sample slices were made perperulicular and parallel to the pressing direction (sample KG 153-HIS), 0 The measured values of ware: w1 '" 1_0° and wIi = 1.5 • The difference has to be attributed to the slight crystallographic texture accomplished by the hot-pressing technique_ This point has already been discussed in section 3.3.5. Rhodes et al. II ), who have a pronounced texture in their hot-forged alumina, also find a difference in transmission for specimens taken parallel and perpendicular to the forging direction_

100

80

i': 60

20

4 16 scatleri n9 angle e

Fig_ 4.26. Scattering profile of tran.mitted light 0,. = 0.546 I'm) measured on a normally Sintcrcd and a hOI-pressed sample of alumina. The rdative light intenSity is plotlod as a function of the scattering anglo e_ l'h~ imensity in th. direction of incideoco is arbitrarily assumed to be 100 in both cases_ 90

The normally sintered alumina specimens all have a much broader peak at half height. Values between 4° and 8° are found. This confirms that light passes through sintered alumina much more diffusely. The degree of translucency is determined by the number and size of the pores and the presence of second-phase particles. The data of some specimens have been collected in table 4.6 (which will be discussed below), together with the preparation conditions, the measured in-line transmission at the same wavelength (0.546 11m), T, and the sharpness of the image at a distance of 3 mm expressed as the number of lines per mm resolved at that distance, N.

The difference in width of the scattering profile found for hot-pressed and normally sintered alumina (figure 4.26) results in a sharp difference in the optical resolution. Figure 4.27 shows the test chart seen through the same slices of hot-pressed and sintered alumina at a distance of 3 mm above the test chart.

Fig. 4 .27. Test chart seen through the same alumina samples as in figure 4 .26 at ad istance of 3 mm between test chart and ceramic. 5 line pairs per mm can be resolved through the normally sintered sample, 18 line pairs per mm throught the hot-pressed sample. Magnification 4x.

In the former case there is no visible loss in sharpness at this distance: the 18 black and white lines per mm are clearly distinguishable. On the contrary in the case of sintered alumina the diffusely transmitted light already causes at this small distance considerable blurring of the image . The limit of what can be resolved at 3 mm is five line pairs per mm.

The data of five sintered samples and two hot-pressed samples are summarized in table 4 .6. 91

Table 4.6

Relation between preparation conditions, microstructure and optical properties

.-~, ... ,'-,'., ...... - MgO sintering Vp T w Nom'" Sample cont. I Nw conditions (%) (%) (") (mm- ) (ppm)

a 500 2h1800°C 0.1 8.4 5.3 4.0 21.1 b 500 24 h 1800 °c 0.1 22.0 4.1 5.6 23.0 c 100 10 h 1850 °c 0.025 29_5 3_6 63 22.7 d 200 to h 1850 °c 0.025 25.0 4.0 5.6 22.4 e 300 10 h 1850 °c 0_025 18.5 4.9 4.5 22.1 f 0 25m 1440 °c 0.05 7.7 1.0 tranS· - p= l20MPa parent g 0 40m 1440 °c 0.025 18.1 0.8 trans· - p", 120MPa parent ------.. . " ... -

The sample~ a to e are all translucent but to a different degree. The first two samples do not differ in porosity, but they differ considerably in mean pore size_ Due to the long sintering time considerable grain growth and pore growth has occurred in ~ample b. The mean pore size as determined with the method outlined by Fullman 3$) has increased from 0.33 pm to 0.46 Jlm (see also section 4.2.3.1). This larger mean pore size is respon~jble for a much higher transmission, 1; a smaller half·height width of the scattering profile, w, and a better resolution limit at the test distance of 3 mm, N

The samples c, d and e differ in MgO content. Thi~ has only a minor influence on the density after the indicated ~intering treatment, but it certainly influences the concentration of second-phase particles and the pore size. As already discussed in section 2_3_4 non-uniform grain growth occurs in the sample with 100 ppm MgO, due to an irregular distribution of MgO- This results in a large mean pore sh;e and thus in a high transmission and small half.height width. The sample with 300 ppm MgO contains second.phase particles, which are extra scattering centres.

For small distances between ceramic and test chart the limit of resolution defined as the number of lines per mm that can just be resolved, N, should be proportional to the reciprocal of the product of this distance and the width of the scattering profile, w. This means that at a constant distance the product N w must be a constant too. This is shown in the last column of table 4.6.

The samples f and g listed in table 4.6 were prepared by hot pressing without addition of MgO. They differ mainly in porosity due to the longer hot pressing time of the last sample. This results in a higher in-line transmission, but the 92 difference in width of the scattering profile is smaiL In contraSl with the samples a to e it turns out thal the sharpness of the image of the test chart is independent of the distanoe for both samples. Even at the largest possible distance of 24 om (see figure 4.25) the 18 black and white lines are cleady resolved. This resolutjon corresponds with the resolving power of the eye. The hot-pressed samples with a thickness of 0.5 mm thus behave in accordance with the definition of transparency given above and they can be called transparent. This is illustrated in figure 4.28.

6 3 .··IIIII~ ·11111&i 11111 . '! 7 I I 7.1 Ill II '~J~C 1111171; 'I 7.1 8 0 11111~ IIIII~ 1111~ 11111 . 9.0 9 0 lllll~ IIIII~ 1 11111 . .IIIII~·: •IIIII"!£' 1.Iit- IIIII~ 'i~I.:.·,· ....I,i IIIII~ t;J;. . ~ I.:&. IIIII~ I~~ :111~n~'.~ IOO~ I~I~ 1,,:.<;. l:i.i ~ ~ III!~ III~ II~

Fig. 4.28. To« ohart seen through a ,lice of hot-pr~ss~d ~l"mi"a at distance, of 8. 16 and 24 ~m. The last picture tak~n without the ceramic lllusct'.a.tes tl)(" equality in sharpness but thte lQ~!l. of contrast, Magnification 4 x.

It shows the test chart seen through sample g at distances of 8, 16 and 24 em, followed by a picture of the test chart without the ceramic slice at 24 em. With increasing distance only the contrast decreases. This is more serious for samples with a low in-line transmission, where the intensity of the unperturbed radiation is low 44). The hot-pressed sample will ultimately loose its transparency, if the in·line transmission decreases further due to a too large number of small pores.

4.3.5 Conclusion

The striking difference in transparency betwccn hot-pressed and normally sintered alumina can be described in terms of the width of the diffusoly transmitted light.

The normally sintered, translucent alumina is characterized by the blur it cauSes in imaging a test object, This blur is proportional to the distance between object and ceramic, and to the width of the angular distribution curve. The degree of trans­ lucency depends on the number and size of the pores and second·phase particles. 93

For a material to be really transj>arent we require that the distortion of the image does not affect the limit of resolution of the eye. This is realized in a material with very few and very small pores. Samples of hot.pressed alumina satisfy these con­ ditions. Transparent alumina is characterized by the fact that the sharpness of the image is independent of the distanCe between object and ceramic. Wilh increasing distance only the contrast decreases. 94

REFERENCES

I, R.L. Coble and J ,E. Burke, Proc. 4th Int. Symp, on the ReactivHy of Solids, Eds J.H. de Boer et al., Elsevier, Amstordam, 1960, p. 38.

2. D.W, Lee and W ,D, Kingery, ], Am. Ceram, SO(;, 43, 594 (1960).

3, R. Hanna, J. Am. Ceram. Soc. 48, 376 (1965).

4. II. Lange and R, Skib be, Technisch.wissenschaft.liche Abhandlungen der Osram·GesellschaJt 9, 203 (I967),

5. G.E. br(lchure on Lucalox, Lamp Glass Department, General Electric Co, Cleveland, Ohio, 1970,

(i. D.W. fludworth, Special Ceramics 5,185 (1972).

7, H,M.Kahan, D,P.Swbbs and R.V.Jones, lnt. Symp.on Optical and Acoustical Microeleclrunics, Polytechnic ln~titute of New York, 1974.

8. LA, Bondar, F.K. Volynets, L.V. Udalova and V.p. Usachcv, Inorg. Mat. 7, 553 (1971).

9, N.Grimm, G,B, Scott and LD.Sibold, Bull. Am.Ceram. Soc. SO, 962 (1971),

10. W.H, Rhodes, D.L Sellers, A.H. Heuer and 1'. Vasilos, Final Repl. for C(lntract AVSSD·0415.67 RR, Aveo Corp" Lowell, Mass., 1967.

11. W.H.Rhodes, D.J.Seller~ and T.Vasilos,J,Am.Ceram.Soc.S8,31 (1975).

12, W.D, Kingery, H,K. Bowen and D.R. Uhlmann, Introduction to ceramics, 2nd Edition, John Wiley & Sons, New York, 1976, p. 648.

13. G, Kortlim, Rcl1oxionsspektroskopie, Springer Verlag, Berlin, 1969.

14. l.B, Malitson, J. Opt. Soc. Am. 52,1377 (1962).

15. M ,A. Jeppesen, J, Opt. Soc. Am. 48, 629 (1958).

16. A.LDulisa and RJ,Scynl0uI, Proc,oftheIEEE61,981 (1973).

17. P.O. J(lhnsol1 cited as private communication in ref- 9. 95

18. W .D. Kingery, J. Am. CeraIn. Soc. 57, I (1974).

19. M.A. Ford and G.R. Wilkinson, J. ScL Instr. 3l, 338 (1954).

20. G, Mie, Ann. Physik 25, 377 (1908).

21. H.C. van de Huist, Light Scattering by Small Particles, John Wiley & Sons, New York, 1957.

22. M. Kerker, The Scattering of Light and other Electromagnetic Radiation, Academic Press, New York, 1969.

23. Handbook of Mathematical Functions, Ed. by M. Abram owitz and LA. Stegun, National Bureau of Standards, 1964.

24. R.H. Boll, R.O. Gumprecht and C.M. Sliepcevich, J. Opt. Soc. Am. 44,18 (1954).

25. R.H. Boll, LA. Leacock, G.C. Clark and S.W. Churchill, Tables of Light Scattering Functions, Univ. af Michigan Press, Ann Arbor, Michigan, 1958.

26. F.C. Chromey, J. Opt. Soc. Am. 50, 730 (1960).

27. J.V. Dave, IBM J. Res. Dev. n, 302 (1969).

28. W.D Ross, App!. Opt. U, 1919 (l972).

29. E.E. Underwood, Quantitative Microscopy, Ed. by R.T. DeHoff and F.N. Rhines, McGraw-Hill Book Co, New York, 1968, p. 149.

30. G. Tomandl, Ber. Dtsch. Keram. Ges. 48, 222 (I 97l).

31. F. Schuckher, Quantitative Microscopy (see ref. 29), p. 201.

32. 1. Aitchison and l.A.C. Brown, The Lognormal Distribution, Cambridge Univ. Press, 1957.

33. H.1. Oel, BeI. Dtsch. Keram. Gcs. 43, 624 (1966).

34. CE. Peterson, Tijdschrift v.h. Ned. Electronica· en Radiagenootschap 39,87 (1974).

35. W.F. Espenscheid, M. Kerker and E. Matijevic, J.Phys.Chem.68, 3093 (1964). 96

36, M ,I. Mendelson, J, Am, Ccram, Soc, 25, 4J3 (1969),

37, D ,A. G ryvn ak and D ,E, Burch, J, Opt, Soc, Am, 55,625 (1965),

38. R -L FuUm an, Trans. AIME J. of Metals S, 447 (1953),

39, R,O, Gumprecht and C,M, Slicpcevich, J,Phys,Chem, 57,90 (1953),

40. R.B. Penndorf, J. OpLSoc. Am. 52, 797 (I 962),

41. Webster's Third New Int. Dictionary of the English Language, Bell & Sons, London, 1966,

42, J ,R, Hodkinson, App!. Opt. 5, 839 (1966).

43, 1 ,P.C. Sou thall, Introduction to Physiotogkal Optics, bover Publications, New York, 1961.

44, KJ, Rosenbruth, Optik 16, 135 (I959). 97

SUMMARY

Ceramic materials are used in widely diverging applications. This holds for aluminium oxide Or alUmina (All 0 3 ) in particular. The field of application has brO

The transmission of light through sintered alumina is determined by the micro­ structure, bec

The properties of alumina are discussed briefly in chapter 1. The application of sintercd alumina as a lamp envelope is also treated briefly in this chapter.

Chapter 2 deals with the sintering process. In subsequent sections the influence of impurities and grain boundaries on sintering is discussed. Additions of divalent and tetravalent oxides can strongly influence the sintering rate. A survey is given of these experiments and of their interpretations which, cQmbiqed with the results of measure­ ments of the electrical conductivity, have led to the model of a Frenkel.type defect structure in the cation sublattice of alumina.

In the final stage of the sintering process of alumina very rapid grain growth generally occurs. As a result the pores, which were at first located on the grain boundaries_ become trapped inside the grains from where they can hardly disappear by diffusion. This so·called discontinuous grain growth is responsible for a relatively high residual porosity, but can be prevented by the addition of a small amount of magnesia (MgO). There is no agreement in the literature about the role of MgO. The leading opinion is that MgO segregates on the grain boundaries, thereby decreasing the mobility of the grain boundaries. The second part of chapter 2 describes the author's work directed towards elucidating the role of MgO. This work was carried out by ~tudying the evolution of the microstructure of alumina with increasing amounts of MgO. As the solubility of MgO is small (about 250 ppm at 1600 °C), very pure alumina powder has to be used if additions below the solubility limit are stilI to be significant. Auger electron spectroscopy was used to see whether indeed an important enrich­ ment of the grain boundaries with MgO occurs. This could not be detected. The experiments show that MgO in solid solution already prevents discontinuous grain growth, so that this phenomenon cannot be ascribed to a reduction of the mobility of the grain boundaries by a segregation mechanism or by the presence of a second 98

phase on the bO\lOdari~s_ A better explanation is given by the fact that MgO enhances the ratc of pore removal, resulting in a decrease in the number and Silt of the pores on the grain boundaries. MgO may also increase the mObility of the pores.

Chapter 3 deals with hot pressing of All 0 3 powder. Application of preswre delivers an extra driving force for sintcring, resulting in densificatio[] at much lower temperatures thall arC possible with normal sintering_ Due to this low temperature hot pressing gives a dense material with a much smaller grain size and pore si~e- ·A striking characteristic of hot-pressed alumina is ilS transparency, whereas normally sintered al\lmina is "only" translucent.

Chapter 4 deals with the optical properties of densely sintered alumina_ First, a survey is given of the factors that may influence the transmission of light through polycrystalline alumina_ It is concluded that it is not the intrinsic birefringence of alumina Or the presence of grain boundaries that determine the loss of light, but mainly the residual porosity.

The sec~)[]d part of chapter 4 outlines the general Mic scattering theory. A model is developed that permits calculation of the in-line transmission, deflned as the trans­ mitted light in the diredion of the incident light. This ill-line transmission, being much more sensitive to changes in the microstructure than the [Olal transmission, is determined by the volume fraction ()f porosity, the mean pore size and the spread in the pore size distribution. The measured traI18mission spectra agree very well with this model. Reason~ble values for the three microstructural parameters mentioned can be deduced from lhe expcrimen tal traI18mission spectra.

The third part of chapler 4 goes into the difference between the transparent hot­

pressed AI; O~ and the translucent sintered Al2 0 3 , This is descdbed in terms of the width of the angular distribution of the diffusely transmitted light. This light causes a certain blur in an imaged test object. To meet our transparency criterion this distortion or the image caused by thc materia! mllst not affect the limit of resolution of the eye. Samples of hot-pressed alumina satj~fy this c()[]dition for lransparency. Only the CCll1trast decreases_ 99

SAMENVA TrING

Keramische materialen worden VOOr zeer uiteenJopende toepassingen gebruikt. Oit

geldt men name ook voor aluminium oxide (Ah 0 3 ), He! toepassingsgebied werd belangrijk verruimd sinds men er in slaagde aluminium oxide zo dieht te sinteren, dat het Iichtdoorlatend werd. Seder! ruim 10 jaar wordt dit doorschijnende alumi­ nium oxide gebruikt als omhulling voor de zeer efficientc hoge druk natrium lamp. Deze toepassing is mede succesvol geworden omdat het keramische materia-al be­ stand bleek tegen de zeer agressieve natrium damp.

De lichtdoorlaatbaarheid van gesinterd A1~ 0 3 wordt bepaald door de microstructuur, Omdat de intrinsieke absorptie van zichtbaar licht verwaarloosbaar klein is. Het is daarom van belang de samenhang te kennen tussen de optische eigenschappen en de

parameters van de microstructuur. Een onderzoek naar het sintergedrag van All 0 3 isnodig om de gewenste microstructuur te kunnen realiseren. Oit zljn de twee hoofd­ lijnen van het onderzoek, dat in dit proefschrift beschreven is_

In hct inleidende hoofdstuk 1 worden de eigenschappen van AI:! 0; beknopt bespro­ ken_ Tevens wordt kort ingegaan op de toepassing van gesinterd A1.0 3 a)s lampom­ huliingsmateriaaL

Het sinterproccs word! bchande1d in hoofdstuk 2. Ingegaan wordt op de invloed die verontreinigingen en korrolgrcnzcn kunnen hebben op het sinteren_ Toevoegingen van tweewaardige en vierwaardige oxiden kunnen de sintersnelheid sterk beinvloeden_ Een overzicht wordt gcgeven hoe deze experim"nten, gecombineerd met de uitkorn­ sten van de metingen van het electrisch geleidingsvermogcn, hebben geleid tot het model van een Frenkel defect structuur in htt kationen rooster van Al~ 0 3 -

In het laatste stadium van het sinterproces van Ah 03 treedt doorgaans cen zeer snelle korrelgroei op, waardoor de porien, die aanvankclijk op de korrelgrenzen lagen, ingesloten Taken in de krista11en en niet of nauwelijks meer door diffusie kunnen VeI­ dwijnen, Deze zogenaamde discontinue korrelgroei, die verantwoordelijk is voor een betrekkelijk hoge rcstporositeit, kan voorkomen worden door het toevoegen van magnesium oxide (MgO)- In de Iiteratuur bestaat geen overeenstemming over de wer­ king van het MgO. De mening die men het meest aantreft is, dat het MgO segrcgeert op de korrelgrenzen en daardoor de mobiliteit van de korrelgrenzcn remt. In het tweede deel van hoofdstuk 2 wordt het eigen werk beschreven, dat gericht is gcwcest op he! vcrhelderen van de rol van het MgO_ Dil is gebeurd door de ontwlkkeling van de microstructuur met toenemende hoeveeiheden MgO te volgen. Doordat de oplos­ baarheid van MgO zo klein is, (ongcveer 250 ppm bij 1600 °C), moest met zeer zui­ ver Al~ 0 3 gewerkt worden om toevoegingen beneden de oplosbaarhcidsgrens nog zinvol te laten zijn. Met bchuJp van Auger electronenspectroscopie is ondcrzocht of inderdaad een belangrijke verrijking van de korrelgrenzen met MgO plaats vindt. Oit kon echter niet worden aangetoond. Vi! hel onderzoek voIgt, dat MgO in vaste 100 oplossing reeds discontinue korrelgroei voorkomt, zodat dit effect niet toegeschreven kan worden aan verlaging van de mobiliteit van de korrelgrenzen door een segregatie mechanisme of de aanwezigheid van een tweede fase op de korrelgrens. De oor~aak moet gewcht worden in het feit, dat het MgO de snelheid waarmee de porien verdwij­ n~n blijkt te verhagen, waardoor er minder paden in aantal en grootte op de korrel­ grens zitten dan zonder MgO het geval zou zijn. MogeJijk neemt ook de mobiliteit van de porien toe.

In hoofdstuk 3 word! het ondorzoek aan het hoctperscn van All 0] poeder beschre­ Yen. De bij het heetpersen toegepaste druk levert een extra drijvende Kracht voor het sinteren, waardoor verdichtjng bjj lagere ternperaturen magelijk is. Het gevolg is een dieht matcriaal met cen veel k1cincre korrelgrootte en poriegrootte dan met normaal sinteren mogelijk is. Ben opvallende karakteristiek van heetgeperst Al 2 0 3 is, dat het doorzichtig is, terwijl normaal gesinterd Ah 0 3 "Slechts" doorschij. nend is.

Hoofdstuk 4 behandelt de optische cigenschappen van dieht gesinterd AI2 0 3 , Nage~. gaan wordt eerst welke factoren de transmissie van licht door gesinterd Al~ 0" be­ invloeden. Geconcludeerd wordt dan, dat niet de intrinsieke dubbele breking van Al z 0 3 of de aanwezighcid van korrdgrcnzen in de ecrstc plaats bepalend is voor het Iichtverlies, maar dat de restporositcit hiervoor in hoofdzaak ycrantwoordelijk gesteld moet wOrden.

In het tweede dec! van hoofdstuk 4 wordt de algemene verstrooiingsthcorie van Mie uiteenge7.et. Tevens wordt een model ontwikkeld om de rechtlijnige transmissie, ge­ deflnieerd als het lieht dat doorgelaten wordt in de richting van het opvalJende licht, te kUrlnen herekenen. De~e rechtJijnige transmissie, die veel gevoeliger vOur verandc­ ringen in de mierostructmu is dan de totale transmissic, wordt bepaald door de volumefractie porositeit, de gemiddelde poriegrootte en de spreiding in de porie­ grootteverdeling. De gemeten transmissiespectra blijken goed met dit model overeen te kOmen. Zelfs kunnen redeli.lke waarden voor de drie genoemde parameters uH de experimerltc/c transmissiespectra worden afgeleid.

In het derde ded van hoofdstuk 4 wordt ingegaan op het ondcrscheid tllsscn het door~ichtige heetgeperste AI. O~ en het doorschijnende gesinterde AI. 0,. Dit haudt verband met de brecdte van de ho~kverdding van het diffuus doorgclalcnlicht. Bij het afbcelden van een te~tobject veroorzaakt dit licht een bepaalde onscherpte. Heetgeperst AI~ 0 3 blijkt te voldoen aan de eis, die men aan een transparant mated­ aal moet stdlen, nl. dat deze onsGherpte beneden het oplossend vermogen van he! oog blijft. Wcl blijkt he! contrast te verminderen. 101

LEVENSBERICHT

De schrijver van dit proefschrift werd op 16 april 1941 te Renkum geboren. Zijn middelbare schoolopleiding ontving hij aan het Christelijk Lyceum te Arnhem, waar hij in 1959 het diploma Gymnasium ~ behaaJde. In datzelfde jaar begon hij zijn Scheikunde stu die aan de Vrije Universiteit te Amsterdam. Na een afstudeer· onder1loek onder leiding van Prof. Dr. C. Maclean legde hij in mel 1967 het docto, raal examen in de Physische Chernie af. De militaire dienstplicht vervulde hij op de ontwikkelingsafdeling van de Artillerie Inrichtingen te Zaandarn. Inmiddcls in dienst getreden van de N.Y. Philips' Gloei· lampenfabrieken te Eindhoven begon hij in mei 1969 zijn werkzaarnheden als wetenschappelijk medewerker op het Natuurkundig Laboratorium in de groep onder leiding van Prof. Ir. A.L. Stuijts. STELLINGEN

J, G. J. Peclen 17 mei 1977 Bij het zoeken naar cen verklaring vOOr het verschi! ill rechtHjnige lran~mi~sie van heetgesmede preparaten van A!203 in richtingcn loodrecbt op en evenwijdig aan de smeedrichting wordt door Rhodes e.a. ten onrechte gecn rckening gehouden met de mogelijkheid, dat de porien tussen de kristallieten cen langgerektc ¥orm gekregen hebben.

W. II. Rhode., D. J, Sellers en T. Vasilos, J. Am. Cetam. So~. 51!, 31 (1975).

II Het vcrstrooiingsmodel van Kahan e.a. dal als parameters de korrelgrootte, de dubbe\e brcking en de porositeit bevat, maar niet de poricgrootte, leidl tot onrealistische rcsultaten.

H. M. Kahan, D. P. S(ubbscll R. V. JOnes, Int. Symp. on Optjc~1 and AcoustiQal Mimoelecttonics, Polytechnic ln~tjtute of New York, 1974. Dit proof.ehlift, hoofd,tuk 4.2.

III

Het door MarCus e.a. uit Augcr onderzoek aan breukvlakken van Al2 0 3 afgeleide model, waarmce zij de inboud van Ca op het sintergedrag van Al 2 0 3 willen ver­ klaren, wordt onvoldoende door de experimcnten Qnderstcund.

H. L. Marcus, J. M. Harris en F. J. :-;,.Ikuwski, Fr~clure Mechanic., of CermTlics, vol. L, f·:d, R. C. Bradt e.,., Plenum Pre", New YOlk, 1974, p.387.

IV Dc argulll<;>nten, waarnlec Jorgensen en Westbrook de segregatie van loegevoegd MgO op de korrelgrenzen van Al~03 verdedigen, zijn of specu!aticf of indirect.

1'. J. Jorgensen en J. R Westbrook, J. Am. Cemm. Suc. 47, 332 (1964). 1'. J. Jorgensen, Grain Boundaries in ~:n~nc"Ting Materials, Ed. 1. L Walter e.a., ClaitN\ Pub!. Div" Baton Rouge, 1975, p. 205. nit proefschrift., h""fd.(uk 2.3.

v De hegrippen "translucenl" en "transpanlnt" worden in de keramischc lilemt\lur onzorgvlI!dig gcbruikt.

Oil p[oefschrift, houfdstuk 4.3. VI A1s men, zoals in de engeistalige literatuur vaak gebeurt, toevoegingen "impurities" noemt, betekent dit nog niet dat er zonder toevoegingen geen "impurities" zijn.

VII Het vaststellen van concentratieprofielen d.m.v. het sputteren van een breukopper­ vlak, lOa Is dit gebruikelijk is in de Auger clektronenspectroscopie, dient met grate vOQfzichtigheid te gebeuren.

H. L. Marcus, J. M, Harri;; en F. J. Snlkowski. Fracture Me"hanic~ of Ceramics, vol. I, flds R. C. Bradt e ... " Plenum Press, New York, 1974, p.387. R. L T.ylor, 1- 1'. Coad en A. E. Hughes, 1. Am. Ccram. Soc. 59,374 (1976). VIII

De bewering van Takagi c.a., dat het sinteren van ZrO~ gestabiliseerd met CaO aanzienlijk versneld wordt door hel toevoegen van Ah03 I is in zijn algemeenheid onjuist.

H. Takagi, S. Kuwabara en H. MalSumoto, Sprechsaal107, 584 (1974). M. J. Bannister cn W. G. Garrett, Ceramurgia Irtt. 1, 127 (1975).

IX De bekende uitspraak "Meten is Weten" dient wat betreft het karakteriseren van keramische poeders met de nodige terughoudendheid te worden gehanteerd. x De regcl van Burton en Machlin om segrcgatie in het opperviak van legeringen te voofspellen m.b.v. het fasendiagram is aanvechtbaar.

J. J. Burton en E. S. Machlirt, Phys. Rev. lett"rs 37, 1433 (1976).

XI De theotie van Hench, die zegt dat een ideaal implantatie materiaai geen histo­ logische veranderingen aan het grensvlak mag verOOfzaken, is moeilijk toe te passcn op de door hem zelf ontwikkelde bioglas coatingen.

L. L. Hench en E. C. Ethridge, Adv. in Biomedical Eng. S, 36 (1975).

Xli Het verwijzen naar eigen niet gepuhliceerd werk voor essentWle informatie onder­ graaft de betrouwbaarheid van het artikel. XIII Voor het besturen van gcrneenschappen die cen bepaald doel nastreven is het principe van "one man, one vote" niet altijd het moest geschikte.

XIV Achter het verschil in visie op de toelating van kinderen tot het Avondmaal in de Protestantse Kerken ligt een verschil in beleving van het Avondmaal bij de ouderen.