Journal of the European Ceramic Society 25 (2005) 1313–1324

High temperature elasticity measurements on oxides by Brillouinspectroscopy with resistive and IR laser heating

Stanislav V. Sinogeikina, ∗, Dmitry L. Lakshtanova, Jason D. Nicholasa, b, 1,Jennifer M. Jacksona, Jay D. Bassa, b

a Department of Geology, University of Illinois, 245 HNB 1301 W Green St., Urbana, IL 61801, USAb Department of Materials Science, University of Illinois, 245 HNB 1304 W Green St., Urbana, IL 61801, USA

Available online 5 February 2005

Abstract

Knowledge of single crystal and aggregate elastic moduli of materials at high temperature is important in the development of high-temperature structural ceramics as well as for other areas of material sciences. Sound velocities, and hence elastic moduli, can be readilymeasured on micro-crystals, polycrystalline aggregates and amorphous materials using Brillouin scattering. We have developed techniquesfor determining the elastic moduli at high temperatures, using both electric resistive heating (to 1800 K) and COlaser heating (toT> 2500 K).To f a variety ofc mbination ofB aching them exceeding2 -a ings©

K

1

fpchattt

R

en-ysicalted.igh-ctorys notn beara-per-asticr

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2

he full set of elastic constants of transparent oxides at high temperatures can be measured on samples with dimensions of 100× 100× 20�mr even smaller. Compact resistance heaters of our design were used to study the temperature dependence of the elastic moduli orystalline oxides and glasses, and can be used to observe high-temperature phase transitions involving elastic softening. The corillouin scattering with CO2 laser heating allows measurements of the elastic moduli of oxides at even higher temperatures, approelting points of refractory materials. The acoustic velocities of single-crystal MgO were measured to a maximum temperature500± 100 K. Both Brillouin and Raman measurements were performed on CO2 laser-heated samples of single-crystal�-Al 2O3 to tempertures exceeding 2000± 100 K. Our results show that Brillouin scattering coupled with CO2 laser heating is a viable means of performound velocity measurements at temperatures significantly higher than those readily made using resistance heating.2005 Published by Elsevier Ltd.

eywords: Spectroscopy; Mechanical properties; High-temperature elasticity measurements by Brillouin scattering

. Introduction

Knowledge of the high-temperature elastic properties isundamental for understanding the mechanical behavior anderformance of structural ceramics under high temperatureonditions. In particular, it is highly desirable to understandow properties such as elastic stiffness, fracture toughness,nd anisotropy in mechanical behavior of composite ma-

erials depend upon the single-crystal elastic properties ofhe individual constituents. Such information would be ex-remely valuable in the design and development of high tem-

∗ Corresponding author. Tel.: +1 217 333 6379; fax: +1 217 244 4996.E-mail address:sinogeik@uiuc.edu (S.V. Sinogeikin).

1 Present address: Lawrence Berkeley National Laboratory, 1 Cyclotrond, MS 62-203, Berkeley, CA 94720, USA.

perature composites with superior properties.11 In addition,the temperature derivatives of elastic moduli allow dimsional changes and stresses due to heating under phconstraints, as well as acoustic excitations to be calcula2

Brillouin scattering provides a means of studying the htemperature elastic properties of oxides and other reframaterials. It is an optical spectroscopy method that doerequire any mechanical contact with the sample, and caperformed on very small samples with dimensions compble to the size of a focused laser beam. From Brillouin eximents one can easily obtain the entire single-crystal elmodulus tensor,Cijkl (orCij in the reduced Voigt notation) fomaterials of arbitrary symmetry, and from this the aggreelastic moduli (such as the bulk modulus, Young’s moduPoisson’s ratio, etc.) can be calculated via suitable aving schemes. Brillouin spectroscopy can be used to s

955-2219/$ – see front matter © 2005 Published by Elsevier Ltd.oi:10.1016/j.jeurceramsoc.2005.01.001

1314 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

other properties at high-temperature such as the refractiveindex,3,4 photoelastic properties,5 hypersonic attenuation,6

and the mechanisms of phase transitions.4,6–12

The considerable potential of the Brillouin scattering tech-nique for characterizing material properties at high temper-atures has only begun to be exploited. Of the relatively fewhigh-temperature Brillouin scattering experiments reportedin the literature, most have used large samples with dimen-sions that typically exceed several millimeters. Although thisdoes not present a problem for work with common materi-als, many novel materials of interest cannot be synthesized aslarge single crystals. Therefore, one emphasis in our labora-tory program has been to employ methods that are suitable forexperiments on microscopic-sized single crystals, and to ex-tend Brillouin scattering studies to polycrystalline samples.Measuring the elastic properties on such samples by moreconventional methods such as ultrasonic interferometry is of-ten problematic or not possible, especially for single-crystalsamples of low crystallographic symmetry.

In this paper we review both resistance and laser-heatingmethods developed in our laboratory that allow measure-ments of the full elastic modulus tensor on small samples(≤100�m) to extremely high temperatures, approaching themelting points of refractory materials. We further describethe advantages and limitations of each heating method.

2

g ofi sticp ghts pectt thev

V

ws -l ,n -t ands

uireso n bem in as ure-m alsoh aturem aksi alc con-t ctives t thato t flex-

ibility in furnace design. Third, for transparent oxide crystalsthe thermal emissivities are generally extremely low (ordersof magnitude lower than those of metals),14 which results in alow background from thermal emission and allows measure-ments to be performed at temperatures exceeding 2000 K.3,15

It can be seen from Eq.(1) that Brillouin scatteringis geometry-sensitive. The scattering angle, and phonondirection must be carefully controlled in any experiment.In general, one must know the orientation of the samplecrystallographic axes, crystal faces, and optical indicatrix todetermine the acoustic velocity and corresponding phonondirection. For practical purposes it is more convenient touse a special symmetrical geometry16 in which a plate-likesample with two flat parallel faces is oriented symmetricallywith respect to the incident and scattered light directions(Fig. 1). In this geometry the phonon direction,q, is in theplane of the sample. As seen inFig. 1, for the case of an op-tically isotropic material, Snell’s law allows the replacementof nsin(θ/2) with n0 sin(θ* /2) in Eq. (1), whereθ* is thepredefined external scattering angle, andn0 is the refractiveindex of air, which for practical purposes is set equal to 1. Themain advantage of this “platelet symmetric geometry” is thatvelocities are measured independent of the sample refractiveindex, (which changes appreciably with temperature, pres-sure, and across phase transitions) so long as two principala telet( ry ise side ah cell.

tureeo teredlt n oft S ge-o aces

F te di-r .φ lef ndθ

. Brillouin scattering

Brillouin scattering arises from the inelastic scatterinncident light (photons) from thermally generated acouhonons in the sample. The Brillouin portion of the licattered by the sample is shifted in frequency with reso the incident light by a factor that is proportional toelocity of the acoustic waves:

=(

�ω

ω

) (c

2n sin(θ/2)

)= �ωλ

2n sin(θ/2)(1)

hereV is the velocity of an acoustic wave,�ω is frequencyhift of scattered light,ω is the frequency andλ is the wave

ength of the incident light,c is the speed of light in vacuumis the index of refraction of the sample, andθ is the scat

ering angle, or the angle between the incident laser raycattered ray inside the sample.

Among the advantages of this technique are that it reqnly very small samples, and that acoustic velocities caeasured along numerous crystallographic directions

ingle sample, which makes it highly suitable for measents on low-symmetry crystals. Brillouin spectroscopyas several noteworthy characteristics for high-tempereasurements. First, the intensity of the Brillouin pe

ncreases with sample temperature.13 Second, no physicontact with the sample is needed, thus reducing sampleamination problems and allowing measurements on reaamples in a controlled atmosphere. Moreover, the facne only needs optical access to the sample allows grea

xes of the optical indicatix are within the plane of the plaa condition that is usually easy to satisfy). This geometspecially advantageous when the sample is mounted inigh-pressure diamond anvil cell, or a high-temperature

Another geometry commonly used in high-temperaxperiments is back-scattering (BS) geometry.3,17 In this ge-metry the incident laser light is focused and the scat

ight is collected through the same lens (θ = θ* = 180), andhe sampling phonon direction is identical to the directiohe incident/scattered light inside the sample. Because Bmetry requires optical access in only one direction, it pl

ig. 1. Platelet, or symmetric, scattering geometry. Solid lines indicaections of the incident and scattered beams in the sample (rectangle)α andare the angles between the incident (i) and scattered (s) beams and samp

ace normals.q is the phonon direction.θ is the actual scattering angle, a* is the external scattering angle.

S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324 1315

minimal restrictions on the design of high-temperature cells.In general, heaters designed to be used with Brillouin scat-tering in a BS geometry can achieve higher temperatureswith better thermal stability (lower temperature gradients).The major disadvantages of BS geometry is that normallyonly longitudinal acoustic modes are observed, and that themeasured Brillouin shift is proportional to the product of theacoustic velocity and the refractive index (�ω = 2nV/λ). Al-though obtaining single crystal elastic moduli is somewhatproblematic with BS geometry, it has proved useful in stud-ies of phase transitions.12 Also, the combination of plateletand back-scattering geometry can provide information on therefractive index of the sample.3,17

The velocities of acoustic phonons are related to theadiabatic elastic moduli and density of a material throughChristoffel’s equation:18

|Cijklqjql − ρV 2δik| = 0 (2)

whereV is phonon velocity,qj andql are unit vectors in thephonon propagation direction,Cijkl is the elasticity tensor forthe material,ρ is the density, andδik is the Kr̈onecker deltafunction. Using Eq.(2), the measured acoustic velocities inknown crystallographic directions can be inverted to obtainthe single crystal elastic moduli using, for example, a lin-earized general least-squares inversion procedure.19

inw com-p owers ystale O,Y od-u ersea ns,w las-t sixd

3

uinmoB st rizeri andi tedo var-i nge.Ts thes andtl ensm em-

Fig. 2. Schematic diagram of the Brillouin spectrometer with six-pass Fabry-Perot interferometer. Abbreviations: BS, beam splitter; FL, focusing lens;CL, collecting lens; L, lens; M, mirror; SF, spatial filter; R, retroreflector;PR, prism; PMT/SSD, photomultiplier tube or solid-state detector; FPC,Fabry-Perot interferometer control unit.

perature cells, and increases the sharpness of Brillouin peaks.The scattered light is directed to either a Raman spectrom-eter, or to a piezoelectrically scanned plane-parallel tandemFabry-Perot interferometer,13 used in six-pass configuration.The tandem interferometer suppresses neighboring orders ofscattered light. A combination of a dispersing prism and aspatial filter after the Fabry-Perot interferometer serves as aninterference filter, removing any fluorescence and most of thethermal radiation generated by the sample so that it does notshow as a high background in Brillouin spectra.

4. Resistance heating

4.1. High-temperature cells

4.1.1. Symmetric (Brillouin) high-temperature cellWe have designed a high-temperature cell for use

with symmetric scattering geometry Brillouin experiments(Figs. 3 and 4) to temperatures in excess of 1500 K.22 Thecell is compact (about 5 cm in maximum dimension), andeasily fits onto a standard three- or four-circle goniometer,allowing a number of additional applications such as X-rayscattering. Because the cell mounts on a goniometer, one ob-tains very good control of the scattering geometry, and anyphonon direction within a plane of the platelet can be eas-i i-n .g.,1

roma )d pro-

The minimum number of crystallographic directionshich the velocities need to be measured to obtain thelete elasticity tensor depends on the crystal class. Lymmetry materials have more independent single-crlastic moduli.20 For example, cubic materials (e.g., MgAG) are characterized by three independent elastic mli and require measurements of longitudinal and transvcoustic velocities in two distinct crystallographic directiohereas orthorhombic crystals with nine single-crystal e

ic moduli generally require velocity measurements inirections.

. Brillouin system

Descriptions of the instrumentation used in our Brilloeasurements are given in Ref.21. A schematic diagramf the Brillouin system currently in use is shown inFig. 2.riefly, light from an Ar-ion laser (λ = 514.5 nm) passe

hrough a polarization rotator and Glan-Thompson polan series, which allows control of both the polarizationntensity of the incident light. Samples are typically mounn an Eulerian Cradle so that their orientation can be

ed and phonon directions probed over a wide angular rahe incidence angle is typically 40◦ or 45◦ (80◦–90◦ plateletymmetric scattering geometry). The light is focused onample with a lens with focal distance of 25–50 mm,he scattered light is collected by a smallf-number (∼3.4)ens. A vertical aperture mask in front of the collection l

inimizes astigmatism caused by the windows in high t

ly sampled by changing theχ-angle of the goniometer. Fally, the cell is easily used with very small samples (e00× 100× 20�m or smaller).23–25

The main body of the original cell can be constructed fmachinable alumina silicate ceramic22 or metal (Inconel

epending on temperature requirements. A metal cell

1316 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

Fig. 3. Schematic diagram of Brillouin scattering in the high-temperaturesymmetric Brillouin cell. TC: thermocouples, HW: heating wires.

vides better mechanical stability and is easier to handle, butthe high thermal conductivity of the metal body limits themaximum temperature to about 1300–1400 K if a Pt–Rh heat-ing element is used. With a ceramic symmetric cell up tothis point we were able to achieve temperatures exceeding1600 K.

For windows we used a variety of refractory transparentmaterials. Fused silica windows are adequate to 1500 K, butcan lose optical quality or soften at higher temperatures. Sil-ica can also react with other cell materials, such as high-temperature cements, at high temperature. As alternative win-dow materials we have used single-crystal sapphire and cubiczirconia, both of which have higher temperature stability andlower chemical reactivity. The disadvantage of these win-dows is that their higher refractive indices introduce moreastigmatism that diminishes the quality of the Brillouin peaksand increases collection times. As a heating element we typi-cally use Platinum or Platinum70Rhodium30 wire, wound onboth sides of a threaded ceramic core. We use the largest pos

F dow.T lishedpi

sible ratio of heater length-to-inner diameter of the heater tominimize temperature gradients. It was found that the double-coil design of the heater (the heating wire wound inside andoutside of the heater core) produces more stable temperaturesand smaller temperature gradients in the sample chamber.

The temperature is measured directly by two or morethermocouples (K or R type) through a computer data ac-quisition board. The thermocouples are attached with high-temperature cement to a window or embedded into a platinumsample holder (Fig. 4).23,26The thermal mass of a relativelylarge Pt sample holder helps to damp out any temperaturefluctuations in the cell. At the highest temperatures, the tem-perature fluctuations usually do not exceed 2◦ over severalhours of operation.

Samples can be cemented directly onto the window,22,25

or embedded into a thin platinum foil24 that is cemented to thecell window, with thermocouples placed around the sample(e.g.,Fig. 5in Ref.22). In later experiments we used 250�mthick platinum foil as a sample holder to provide thermalmass. The sample is either cemented into the holder, or toavoid reaction with a cement it can be placed in a recess andheld with a platinum cap (Fig. 4).

4.1.2. Axial (synchrotron) high-temperature cellWe have designed an alternative ceramic heating cell with

l n

F Bril-louin, Raman, and synchrotron X-ray measurements. (1) Thermocouple con-nector; (2) ceramic thermocouple/sample holder; (3) sample holder withsample and thermocouple; (4) heating elements; (5) silica glass/MgO win-dow; (6) insulating ceramic fiber tape; (7) ceramic furnace body; (8) pins;(9) ceramic base; (10) through holes in ceramic base to minimize its thermalconductivity; and (11) metal base for mounting the furnace.

ig. 4. Top-view (A) and cross-section (B) of sample mounting on a winhis setup shows a small sample embedded into platinum foil and polane-parallel together with the foil. If a sample is large enough (>300�m)

t can be inserted into platinum holder without using the foil.

-

imited optical access (Fig. 5) for backscattering Brilloui

ig. 5. High-temperature axial ceramic furnace for back-scattering

S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324 1317

measurements or for synchrotron X-ray measurements ofthermal expansion.27 This cell also fits easily onto a stan-dard X-ray goniometer and is compatible with our Brillouinsystem. The advantages of this cell over the cell for symmet-ric scattering experiments are higher thermal stability, lowerthermal gradients (due to the aspect ratio of the furnace andbetter thermal insulation), and higher temperatures (up to1800 K with Pt70Rh30 heating elements).

The limited optical access provided by this cell allows itto be used only in back-scattering or near-forward scatteringgeometries. While such measurements do not provide acous-tic velocities and elastic moduli directly without the knowl-edge of the refractive index, they can be extremely useful instudying phase transitions.12 In addition to X-ray diffractionand Brillouin experiments, this cell has been used for otherhigh-temperature applications such as measurements of therefractive index and Raman scattering.28

4.2. Results using resistance heating

4.2.1. Single crystalsThe symmetric high-temperature cell has been used to

measure the elastic properties of single crystal MgO, which isan important ceramic and is used in a variety of applications.Because the elastic properties of MgO have been investigatedi ntm eatingt

era-t oomt tho -m alityw -pw ions( or

F h-t d peak– thes

Fig. 7. Acoustic velocities in MgO as a function of crystallographic direction(χ-angle) at room temperature (solid symbols) and 1510 K (open symbols).Lines show acoustic velocities calculated from the best-fit elastic moduli atroom temperature (solid) and 1510 K (dashed).

both the crystallographic orientation of the sample and single-crystal elastic moduli.31 The results of the joint inversionsyield sample orientations at the three different temperatures(that are within one crystallographic degree), which we ap-plied to the data at all temperatures to calculate phonon direc-tions. At other temperatures the data were usually collectedin 6–7 directions, which provides redundancy in calculationof the three independent Cij ’s for cubic MgO. Note that mea-surements in only 3–4 crystallographic directions would besufficient to obtain orientation and elastic moduli of such cu-bic phases, providing that the normal to the sample plane isknown. Such a dense dataset was used to assess the internalconsistency of the measurements.

Acoustic velocities were inverted for the elastic moduliusing a linearized inversion procedure described by Weidnerand Carleton.19 The density of MgO at high-temperature wascalculated from the thermal expansion data from Refs.32,33. The resulting single-crystal elastic moduli are shown inFig. 8and listed inTable 1, along with the previous ultrasonicresults of Sumino et al.30 and Isaak et al.29 Our Brillouin re-sults are in agreement with previous measurements, and nosystematic deviations from the trend of the ultrasonic resultswere observed. Further descriptions of these results are givenby Sinogeikin et al.22 The excellent agreement between ourresults and independent measurements at lower temperaturesd usedt ticitym in ex-c

suret mod-u ep n nu-c r-f callyi oly-

n several previous studies,17,29,30it also provides an excelleeans of assessing the accuracy of our resistance h

echniques.The acoustic velocities in MgO as a function of temp

ure and crystallographic direction were measured from remperature to 1510± 10 K with 100–200 K intervals, bon increasing and decreasing temperature.22 Up to the maxium temperature the Brillouin spectra were of superb quith negligible thermal background (Fig. 6). At three temeratures (295± 1 K, 1073± 5 K, and 1510± 10 K) the dataere collected in more than 10 crystallographic direct

Fig. 7) which allowed us to perform a “joint inversion” f

ig. 6. Brillouin spectra of MgO in [1 1 0] direction in symmetric higemperature cell. Unshaded peaks – room temperature spectra, shadespectra at 1510± 10 K. The intensities of the peaks are scaled to fit on

ame plot.

s

emonstrates that our experimental techniques can beo obtain accurate high-temperature single-crystal elaseasurements on very small crystals to temperatures

ess of 1500 K.The symmetric high-temperature cell was used to mea

he temperature dependence of the single-crystal elasticli to 1473 K of Yttria (Y2O3), which, in the form of densolycrystalline ceramics, has been considered for use ilear applications and infrared optics.2 We have further peormed single-crystal studies on a number of geophysimportant silicate minerals, including the high-pressure p

1318 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

Fig. 8. Single-crystal elastic constants of MgO as a function of tempera-ture. Open symbols (circles and squares) represent two different runs fromthis study. Diamonds and crosses show ultrasonic data of Isaak et al.29 andSumino et al.30 for comparison. The size of the symbols is bigger than theexperimental uncertainty.

morphs of olivine (�-Mg2SiO4 and �-(Mg,Fe)2SiO4),24,25

lawsonite (CaAl2(Si2O7)(OH)2·H2O),26 and magnesium-aluminum garnet—pyrope (Mg3Al2Si3O12).23

4.2.2. Polycrystalline aggregatesThe synthesis of crystals large enough for single-crystal

elasticity measurements can be a significant experimentalchallenge, and the ability to measure elastic properties us-ing polycrystalline aggregates is essential in this case. Themain restriction for measurements on polycrystals is that thesamples need to be well sintered, so that they are transparenand do not produce a lot of elastically scattered light. Elas-tic Rayleigh scattering of light from the sample generallyproduces a very broad central elastic peak and increases thebackground in these types of experiments.

Table 1Polynomial representation of single-crystal and aggregate elastic moduli ofMgO

Modulus/coefficient This study,to 1510 K

Sumino et al.30

300–1300 KIsaak et al.29

300–1600 K

C11 a 315.5 315.2 317.9b −0.058 −0.062 −0.062c −1.703 0.692 0.283

C44 a 158.9 160.7 161.4b −0.010 −0.014 −0.013

C

K

µ

Ac

The high-temperature elastic moduli were measured onfibers of mullite (∼2.5Al2O3·SiO2), a common ceramic ma-terial, to 1475 K.1,34 Even though the samples consisted ofhighly-textured polycrystalline fibers,35with crystallites hav-ing different rotation about theirc axis by up to 5◦, it waspossible to extract all nine single crystal elastic constants(orthorhombic symmetry). That study34 revealed substan-tial differences between bulk elastic properties calculatedfrom “single crystal” measurements and the properties re-ported in the literature for polycrystalline-sintered mullite. Itwas shown that factors, such as microstructure, intergran-ular silicate glassy phases, and composition have signifi-cant effect on the elasticity of mullite ceramics, especiallyat hightemperatures.

We also performed high-temperature elasticity measure-ments on a range of polycrystalline garnet-structured com-pounds (Mg4Si4O12–Mg3Al2Si3O12solid solutions), that arestable at high pressure and are geologically important phasesin the deep Earth.23 The measurements were performed onextremely small samples (

S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324 1319

supercooled liquid state is easily seen in Brillouin scatteringmeasurements.7,15,38,39In addition to obtaining the elasticproperties by measuring the magnitude of the Brillouin shift,analysis of the widths of the Brillouin peaks gives informa-tion on relaxation and viscoelastic properties of glasses andmelts. This information can in turn be related to the mobilitiesof atomic species in these materials.40

5. IR laser heated measurements

Conventional high-temperature Brillouin scattering,which employs resistance heaters, can be routinely per-formed to temperatures of about 1500 K.2,12,22,34There area few examples of Brillouin measurements performed tohigher temperatures.3,17 The highest temperature measure-ments performed by Brillouin scattering with resistive heat-ing thus far are those by Vo-Thanh et al.15 who measuredthe product of the compressional acoustic velocity (VP) andrefractive index of silicate melts up to 2350 K. In theory itis possible to make resistance furnaces which will be able toachieve higher temperatures, but there are a number of lim-itations that make these cells impractical for Brillouin mea-surements.

One limitation is a high thermal background in high-t be-l atere amicc tem-p y re-a rnacee terio-rt era-t 00 K,e ciento here-f atingm fullye ing.

ce-r gthi elyum nsa ly ath chc byt ing,d ons.T eri-m fromt ityo nol sioni ser,

exciting Brillouin scattering, is significantly higher than theintensity of Brillouin peaks, that is when Brillouin peaks cannot be distinguished from thermal background. Opticallytransparent samples (especially well polished single crystals)have extremely low emissivity in the visible, usually ordersof magnitude lower than metals. This allows relatively lowthermal emission and the possibility of performing Brillouinscattering to temperatures exceeding 2000–2500 K.

5.1. Experimental methods

The CO2 laser-heating system used with Brillouin scat-tering measurements is shown schematically inFig. 9. It isbased on a conventional Brillouin system (Fig. 2) with theaddition of a 100 W CO2 (λ = 10.6�m) pseudo-CW laseroperating in TEM00 mode, a broadband spectrometer, andoptical components to deliver the CO2 laser beam to a sam-ple and analyze Raman and incandescence spectra. The CO2laser is equipped with a built-in power stabilization systemwhich provides a nominal power stability of±0.5% (afterwarm-up). In all experiments we used an unfocused laserbeam with a near-Gaussian beam profile and a full widthat half maximum (FWHM) of∼2 mm. All Brillouin/Ramanmeasurements were performed in a platelet symmetric scat-tering geometry. A detailed description of the system ande 28

5

5nts

o mum

F sure-m irror;B ter;V en inF

emperature Brillouin spectra which, at temperaturesow 2000 K, is usually related to the radiation from helements (e.g., heating wires and polycrystalline ceromponents), rather than a sample itself. The maximumerature of elasticity measurements is also limited by anctions which can take place between a sample and fulements or a ceramic cement, usually resulting in a deation of the sample at extreme temperatures.3,17 In addition,here are practical limitations to the construction and opion of resistance furnaces for temperatures far above 15specially for ones which are compact and have suffiptical access for accurate Brillouin measurements. T

ore, it is desirable to use non-resistive, or contactless heethods in order to achieve maximum temperatures and

xploit the benefits of high-temperature Brillouin scatterThe most effective contactless method for heating

amic (oxide) materials is irradiation by longer-wavelennfrared lasers (λ∼10�m). Such techniques are routinsed for thermal processing of silicates and oxides41,42 andaterial synthesis,35 as well as for studying phase relationd physical properties of such materials, especialigh pressures.43–45 The maximum temperature whian be obtained with IR laser-heating is limited onlyhe maximum temperature of sample stability (meltecomposition, deterioration) rather than heater limitatihe maximum temperature in Brillouin scattering expents is also determined by the thermal background

he sample (which is directly proportional to emissivf the sample). The collection of Brillouin spectra is

onger possible when the intensity of thermal emisn the region corresponding to the frequency of the la

xperimental setup is given in Sinogeikin et al.

.2. Results from laser-heating measurements

.2.1. Brillouin scattering on MgOThe feasibility of performing Brillouin measureme

n laser-heated samples (temperature stability, maxi

ig. 9. Schematic diagram of the laser-heating system for Brillouin meaents. Abbreviations are: AM, aperture mask; BSt, beam stop; M, mS/FM, beam splitter or flipping mirror; NF, notch filter; PM, powermeC, video camera. The details of the Brillouin spectrometer are givig. 3.

1320 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

experimental temperatures, thermal gradients) was firstdemonstrated on single crystals of MgO in the (1 0 0)orientation polished plane-parallel to∼50�m thickness.The Brillouin measurements were performed in the [1 0 0]and [1 1 0] crystallographic directions. Below 1900 K thethermal background in the Brillouin spectra was negligibleand became significant only above 2100 K. At high temper-ature the Brillouin peaks remained sharp and well defined toa temperature of∼2400 K (Fig. 10). At higher temperaturesthe quality of the spectra degraded due to an extremely highthermal background, and significantly longer collectiontimes were necessary to obtain a reasonable signal-to-noiseratio (note that the intensity of the Brillouin peaks increaseslinearly with temperature,13 whereas the intensity ofthermal radiation is proportional toT4). Temperatures inthe laser-heating experiments were obtained by comparingmeasured velocities of MgO with previous measurements to1500 K with a resistance heater22 and extrapolated to highertemperatures. The acoustic velocities in this experimentserved as an internal thermometer, and the temperaturescalculated separately fromVP andVS peak positions werewithin 80 K. We calculated that the highest temperatures ofour Brillouin measurements were 2300± 100 K in the [1 0 0]direction and 2520± 100 K in the [1 1 0] direction. Webelieve that optimization of the system (e.g., using a shorterw se thet

erea eateds com-p eatedu ngt serb ients

Fh

are not a serious concern in the present experiments becausewe used a broad unfocused CO2 laser with FWHM∼ 2 mm,while the spectra were collected from an axial area of40–60�m.

The axial thermal gradients were estimated based on thewidth of the MgO Brillouin peaks as compared to measure-ments in resistively-heated cell with practically nonexistentgradients. The acoustic velocities in MgO decrease rapidlywith temperature (especiallyVP[100] andVS[110])22 thus thepresence of temperature gradients in a sampling volumewould increase the width of Brillouin peaks. Analysis of theBrillouin peaks obtained using laser-heating indicated thatthe axial thermal gradients across the samples at the highesttemperatures do not exceed 50 K (which is within the uncer-tainty of temperature determination). The further details aregiven in Sinogeikin et al.28

5.2.2. Brillouin and Raman scattering on Al2O3One of the drawbacks of laser heating (especially for

transparent samples) is that the temperature cannot be mea-sured with a thermocouple, and can only be characterized bythermal emission above 1200–1500 K in the best of cases dueto extremely low emissivities of transparent oxide materials.An inability to characterize moderate sample temperatureswould significantly limit the applicability of CO2 laserh ents.T froma ringt

ayo K,t ea-s easur-a onalf xper-i ans ,i pec-t spot( notp ture-s tokesi olutep

fort sm okesi maybon ea-s s withi ft

havee hich

avelength phonon probe, such as 488 nm) can increaemperature limit by several hundreds of degrees.

The Brillouin measurements on laser-heated MgO wlso used to access the thermal gradients in the laser-hpot. Laser heating is a localized heating method asared to resistive heating where the entire sample is hniformly. Therefore, it is important to consider axial (alo

he axis of CO2 beam) and radial (perpendicular to the laeam) temperature gradients. The radial thermal grad

ig. 10. Brillouin spectra of MgO in the [1 1 0] direction with CO2 lasereating at 1920± 100 K and 2520± 100 K.

eating for high-temperature elasticity measuremherefore, to characterize temperature in the rangembient to 1500–2000 K, alternative ways of measu

emperature are needed.Even though the thermal radiation is the primary w

f measuring and calibrating temperatures above 120046

here exist a variety of alternative ways of temperature murements based on the temperature dependence of mble physical properties of materials, for example vibrati

requencies obtained from Raman spectroscopy. Our emental setup allows the collection of Brillouin and Rampectra from the same spot on the sample (Fig. 9). Thereforet is possible to use information contained in Raman sra to characterize the temperature in the laser-heatedexcept for some cubic crystals, such as MgO, which doroduce any first-order Raman spectra). The temperaensitive properties of Raman spectra are anti-Stokes/Sntensity ratio, the widths of Raman peaks, and the absositions of Raman peaks.

The anti-Stokes/Stokes intensity ratio is widely usedemperature measurements.47–49The theoretical limit of thiethod is about 1200 K, above which the anti-Stokes/St

ntensity ratio approaches unity. In practice this methode accurate only at temperature below∼750 K.47 The widthsf Raman peaks increases with temperature.48,50 Unfortu-ately, the quality (and therefore the accuracy of width murements) of the Raman peaks progressively degradencreasing temperature51 thereby limiting the applicability ohis technique.

In our experiments as an internal thermometer, wexplored the use of temperature-induced Raman shift, w

S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324 1321

seems to be the most accurate spectroscopic method ofmeasuring moderate temperatures.47 The Raman shift isgeometry (scattering angle) independent, and can be readilycalibrated in any geometry with a variety of high-temperaturedevices.51,52

Brillouin and Raman spectra were measured on a laser-heated sample of�-Al2O3 (sapphire). This material was cho-sen because of its importance as a ceramic, and it has beencharacterized by a variety of experimental techniques. Sap-phire has a high melting temperature (2326± 3 K) and doesnot undergo any high-temperature phase transitions. Its singlecrystal elasticity at high temperature was previously mea-sured by rectangular parallelepiped resonance to 1825 K53

and by Brillouin spectroscopy to 2100 K.3

The calibration high-temperature Raman measurementswere performed in an axial resistive heating furnace (Fig. 5)in a near-forward scattering geometry. An argon-ion laser(λ = 514.5 nm) was used as an excitation source. Both Stokesand anti-Stokes Raman shifts were measured to 1500 K.Above that temperature the thermal emission by the plat-inum holder, heater, and ceramic parts produces extremelyhigh thermal background which significantly degraded thequality of the Raman peaks, and did not allow us to preciselydetermine their positions. The temperature shifts of the Ra-man peaks were fitted by quadratic functions.48 The sharpa −1 o-s thep om3 uredb

per-f lec to5 tra

Fig. 11. Frequency shift of the most intense line (417 cm−1) in the Ramanspectrum of sapphire as a function of temperature measured by thermocou-ples in an externally—heated cell. The solid line is the quadratic least-squaresbest fit (�ν = 4.95− 0.0157× T− 3.4556× 10−6 × T2). Data above 1400 Kwere not used in the fit. The uncertainty in temperature and peak positionsis smaller than the size of the symbols.

were collected in the [1 0 0] and [0 1 0] crystallographicdirections up to 2000± 100 K. Up to the highest temper-ature, the quality of Brillouin spectra was excellent. Thethermal background in Brillouin spectra was observed onlyabove 1900 K, but remained negligible up to the maximumtemperature. Raman spectra were collected during each runbefore and after the Brillouin measurement and were furtherused to calculate sample temperature (note that the Ramanand Brillouin spectra were collected from exactly the samevolumes of the sample, where the light from Argon ion laserpasses through the sample). Unfortunately, the Raman peaks

F mples,( study. ency sht ) mea

nd intense peak at 417 cmgave the most consistent pitions (Fig. 11). The temperatures, as calculated fromosition of this peak and a fitted function in the interval fr00 to 1400 K, were within 10 K of temperatures measy thermocouples.

The laser-heating Brillouin measurements wereormed in a 80◦ symmetric platelet geometry on singrystals cut into∼1 mm× 4 mm slabs and polished0–60�m thickness. High-temperature Brillouin spec

ig. 12. Acoustic velocities in�-Al2O3, measured on laser-heated sa[0 1 0]) (plate B). Diamonds and circles are measurements from thishe 417 cm−1 Raman peak (seeFig. 11). Open squares—ultrasonic (RPR

as a function of temperature ina-direction ([1 0 0]) (plate A) andb-directionThe temperature was calculated from the temperature-induced frequift ofsurements of Goto et al.53

1322 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

Fig. 13. Selected single-crystal elastic moduli of�-Al2O3, measured onlaser-heated samples, as a function of temperature (solid symbols). Opensymbols are from ultrasonic measurements of Goto et al.53.

were not distinguishable from the thermal background above2000 K, which prevented us from performing measurementsat higher temperatures.

The measured acoustic velocities in the [1 0 0] direction asa function of calculated temperature are shown inFig. 12A.Fig. 12B shows the velocities measured in two distinct orien-tations corresponding to the [0 1 0] crystallographic direction.Also shown are the velocities calculated from single-crystalelastic moduli reported in Goto et al.53 (Fig. 12A and B,open squares). From our measured velocities the single crys-tal moduli C11, C66 and C12 were calculated (Fig. 13 andTable 2) using the thermal expansion data of Goto et al.53

Table 2Selected single-crystal elastic moduli of Al2O3 at high temperatures

T (K) C11 (GPa) T (K) C66 (GPa) C12 (GPa)

297 498 296.9 167.5 162.5518 488 296.9 167.0 163.5518 486 503 164.0 160.3798 473 805.2 157.5 159.4979 468 1008.3 152.7 159.1

1173 456 1213.7 148.8 156.81417 444 1456.5 142.9 155.81648 432 1701.6 136.8 155.01805 423 1826.3 133.5 154.71980 414 1967 128.7 156.212

T ,a

The good agreement between our results and those measuredby ultrasonic techniques demonstrates the viability of usingBrillouin scattering of laser-heated samples in combinationwith Raman spectroscopy to obtain reliable elasticity infor-mation at moderate temperatures where the application ofthermoradiometry is not possible.

6. Summary

We have developed techniques for measuring the elas-tic moduli of ceramic materials at high temperatures, us-ing both external heating (to 1800 K) and laser heating (toT> 2500 K) of samples. The full set of elastic constants oftransparent oxides (even possessing low symmetry) at hightemperatures can be measured on samples with dimensionsof 100× 100× 20�m or even smaller, which is not readilyachieved by other techniques.

We have designed compact resistance heaters which wereused to study temperature dependence of the elastic moduli ofa variety of single-crystal and polycrystalline oxide materialsand glasses, and were used to observe high-temperature phasetransitions involving elastic softening and glass transitions invarious materials.

We have combined Brillouin and Raman scattering withC lasticm res,a uins gw tt ea-sB ades pera-t ocitym gO),o odes(

ledw ings antlyh ating.W ina s foro tem-p notp

A

forr earchw EARE Sci-e

928 415 1939 130.1 155.1083 407 296.9 168.1 161.3

296.9 168.1 161.3296.9 167.7 162.1484 164.6 160.0752.2 158.6 159.7957.7 154.3 158.5

1136.6 151.0 156.21398 145.1 154.6

he uncertainty in temperature is

S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324 1323

References

1. Kriven, W. M., Palko, J. W., Sinogeikin, S., Bass, J. D., Sayir, A.,Brunauer, G.et al., High temperature single crystal properties ofmullite. J. Eur. Ceram. Soc., 1999,19, 2529–2541.

2. Palko, J. W., Kriven, W. M., Sinogeikin, S. V., Bass, J. D. and Sayir,A., Elastic constants of yttria (Y2O3) monocrystals to high tempera-tures.J. Appl. Phys., 2001,89, 7791–7796.

3. Zouboulis, E. S. and Grimsditch, M., Refractive index and elasticproperties of single-crystal corundum (�-Al2O3) up to 2100 K. J.Appl. Phys., 1991,70, 772–776.

4. Askarpour, V., Manghnani, M. H., Fassbender, S. and Yoneda, A.,Elasticity of single-crystal MgAl2O4 spinel up to 1273 K by Brillouinspectroscopy.Phys. Chem. Miner., 1993,19, 511–519.

5. Bucaro, J. A. and Dardy, H. D., High-temperature Brillouin scatteringin fused quartz.J. Appl. Phys., 1974,45, 5324–5329.

6. Pelous, J. and Vacher, R., Thermal Brillouin scattering in crystallineand fused quartz from 20 to 1000◦C. Solid State Commun., 1976,18, 657–661.

7. Masnik, J. E., Kieffer, J. and Bass, J. D., Structural relaxations inalkali silicate systems by Brillouin light scattering.J. Am. Ceram.Soc., 1993,76, 3073–3080.

8. Ngoepe, P. E. and Comins, J. D., Brillouin scattering investigationsof cerium fluoride at high temperature: a diffuse superionic transition.Phys. Rev. Lett., 1988,61, 978–981.

9. Ngoepe, P. E. and Comins, J. D., Brillouin scattering investigation ofthe rare-earth fluorides at high temperatures.J. Less Common Metals,1989,148, 375–380.

10. Botha, P. J., Chiang, J. C. H., Comins, J. D., Mjwara, P. M. andNgoepe, P. E., Behavior of elastic constants, refractive index, and lat-

1 f sta-

1 s, J.

1 lts982,

1tureion,

1 icatet.

1 i ofcell.

1 elas-

1 ity

1 .

2 ,

2 and

2 ass,ea-

23. Sinogeikin, S. V. and Bass, J. D., Elasticity of pyrope and majorite-pyrope solid solutions to high temperatures.Earth Planet. Sci. Lett.,2002,203, 549–555.

24. Sinogeikin, S. V., Bass, J. D. and Katsura, T., Single-crystal elasticityof �-(Mg0.91Fe0.09)2SiO4 to high pressures and to high temperatures.Geophys. Res. Lett., 2001,28, 4335–4338.

25. Jackson, J. M., Sinogeikin, S. V., Bass, J. D. and Weidner, D. J.,Sound velocities and elastic properties of�-Mg2SiO4 to 873 K byBrillouin spectroscopy.Am. Miner., 2000,85, 296–303.

26. Schilling, F. R., Sinogeikin, S. V. and Bass, J. D., Single-crystalelastic properties of lawsonite and their variation with temperature.Phys. Earth Planet Inter., 2003,136, 107–118.

27. Jackson, J. M., Palko, J. W., Andrault, D., Sinogeikin, S. V., Laksh-tanov, D. L., Wang, J.et al., Thermal expansion of natural orthoen-statite to 1473 K.Eur. J. Miner., 2003,15, 469–473.

28. Sinogeikin, S. V., Lakshtanov, D. L., Nicholas, J. D. and Bass, J. D.,Sound velocity measurements on laser-heated MgO and Al2O3. Phys.Earth Planet. Inter., 2004,143–144, 575–586.

29. Isaak, D. G., Anderson, O. L. and Goto, T., Measured elastic moduliof single-crystal MgO up to 1800 K.Phys. Chem. Miner., 1989,16,704–713.

30. Sumino, Y., Anderson, O. L. and Suzuki, I., Temperature coefficientsof elastic constants of single crystal MgO between 80 and 1300 K.Phys. Chem. Miner., 1983,9, 38–47.

31. Zha, C.-S., Duffy, T. S., Downs, R. T., Mao, H.-K. and Hemley, R.J., Sound velocity and elasticity of single-crystal forsterite to 16 GPa.J. Geophys. Res., 1996,101, 17,535–17,545.

32. Suzuki, I., Thermal expansion of periclase and olivine and their un-harmonic properties.J. Phys. Earth, 1975,23, 145–159.

33. Dubrovinsky, L. S. and Saxena, S. K., Thermal expansion of periclase.

3 ass,

3 ers.

3 s to

3 e.

3 es ofscat-.

3 lastictures.

4 igh-es.

4 .,g-

4 s at

4 earthto

ni.

4 ating

4 -ray

tice parameter of cubic zirconia at high temperatures.J. Appl. Phys.,1993,73, 7268–7274.

1. Ngoepe, P. E. and Comins, J. D., Brillouin scattering studies obilized zirconias at high temperature.J. Phys. C: Solid State, 1987,20, 2983–2994.

2. Jackson, J. M., Sinogeikin, S. V., Carpenter, M. A. and BasD., Novel phase transition in orthoenstatite.Am. Miner., 2004, 89,239–244.

3. Sandercock, J. R., InLight Scattering in Solids III: Recent Resu,ed. M. Cardona and G. Guntherodt. Springer-Verlag, New York, 1pp. 173–206.

4. Mao, H. K., Shen, G., Hemley, R. J. and Duffy, T. S., InPropertiesof Earth and Planetary Materials at High Pressure and Tempera,ed. M. H. Manghnani and T. Yagi. American Geophysical UnWashington, 1998, pp. 27–34.

5. Vo-Thanh, D., Polian, A. and Richet, P., Elastic properties of silmelts up to 2350 K from Brillouin scattering.Geophys. Res. Let,1996,23, 423–426.

6. Whitfield, C. H., Brody, E. M. and Bassett, W. A., Elastic modulNaCl by Brillouin scattering at high pressure in a diamond anvilRev. Sci. Instrum., 1976,47, 942–947.

7. Zouboulis, E. S. and Grimsditch, M., Refractive index andtic properties of MgO up to 1900 K.J. Geophys. Res., 1991, 96,4167–4170.

8. Love, A. E. H.,A Treatise on the Mathematical Theory of Elastic.Dover Publications, New York, 1944.

9. Weidner, D. J. and Carleton, H. R., Elasticity of coesite.J. GeophysRes., 1977,82, 1334–1346.

0. Nye, J. F.,Physical Properties of Crystals. Oxford University PressNew York, 1995.

1. Sinogeikin, S. V., Katsura, T. and Bass, J. D., Sound velocitieselastic properties of Fe-bearing wadsleyite and ringwoodite.J. Geo-phys. Res., 1998,103, 20,819–20,825.

2. Sinogeikin, S. V., Jackson, J. M., O’Neill, B., Palko, J. W. and BJ. D., Compact high-temperature cell for Brillouin scattering msurements.Rev. Sci. Instrum., 2000,71, 201–206.

(MgO) and tungsten (W) to melting temperatures.Phys. Chem. Miner,1997,24, 547–550.

4. Palko, J. W., Sayir, A., Sinogeikin, S. V., Kriven, W. M. and BJ. D., Complete elastic tensor for mullite (∼2.5Al2O3·SiO2) to hightemperatures measured from textured fibers.J. Am. Ceram. Soc., 2002,85, 2005–2012.

5. Sayir, A. and Farmer, S. C., Directionally solidified mullite fibMater. Res. Soc. Symp. Proc., 1995,365, 11–20.

6. Kriven, W. M., Possible alternative transformation toughenerzirconia: crystallographic aspects.J. Am. Ceram. Soc., 1988, 71,1021–1030.

7. Lee, W. E. and Heuer, A. H., On the polymorphism of enstatitJ.Am. Ceram. Soc., 1987,70, 349–360.

8. Askarpour, V., Manghnani, M. H. and Richet, P., Elastic propertidiopside, anorthite, and grossular glasses and liquids: a Brillouintering study up to 1400 K.J. Geophys. Res., 1993,98, 17,683–17,689

9. Schilling, F. R., Sinogeikin, S. V., Hauser, M. and Bass, J. D., Eproperties of model basaltic melt compositions at high temperaJ. Geophys. Res., 2003,108(B6), 2304.

0. Kieffer, J., Masnik, J. E., Reardon, B. J. and Bass, J. D., Hfrequency relaxational spectroscopy in liquid borates and silicatJ.Non-Crystal Solids, 1995,183, 51–60.

1. Belov, A. V., Bubnov, M. M., Gur’yanov, A. N., Devyatykh, G. GDianov, E. M., Prokhorov, A. M.et al., Drawing of glass-fiber waveuides using CO2 lasers.Sov. J. Quant. Electron., 1978,8, 1169.

2. Paek, U. C. and Weaver, A. L., Formation of a spherical lenoptical fiber ends with a CO2 laser.Appl. Opt., 1975,14, 294–298.

3. Yagi, T. and Susaki, J. I., High-pressure research: application toand planetary sciences. InHigh-Pressure Research: ApplicationEarth and Planetary Sciences, ed. Y. Syono and M. H. ManghnaAmer. Geophys. Union, Washington, 1992, pp. 51–54.

4. Andrault, D. and Fiquet, G., Synchrotron radiation and laser hein a diamond anvil cell.Rev. Sci. Instrum., 2001,72, 1283–1288.

5. Fiquet, G., Andrault, D., Itie, J. P., Gillet, P. and Richet, P., Xdiffraction of periclase in a laser-heated diamond-anvil cell.Phys.Earth Planet. Inter., 1996,95, 1–17.

1324 S.V. Sinogeikin et al. / Journal of the European Ceramic Society 25 (2005) 1313–1324

46. Nicholas, J. V. and White, D. R.,Traceable Temperatures: An Intro-duction to Temperature Measurement and Calibration. John Wiley &Sons, New York, 2001.

47. Cui, J. B., Amtmann, K., Ristein, J. and Ley, L., Noncontact temper-ature measurements of diamond by Raman scattering spectroscopy.J.Appl. Phys., 1998,83, 7929–7933.

48. Herchen, H. and Cappelli, M. A., First-order Raman spectrum ofdiamond at high temperatures.Phys. Rev. B, 1991, 43, 11740–11744.

49. LaPlant, F., Laurence, G. and Ben-Amotz, D., Theoretical and ex-perimental uncertainty in temperature measurement of materials byRaman spectroscopy.Appl. Spectrosc., 1996,50, 1034–1038.

50. Schmidt, C. and Ziemann, M. A., In-situ Raman spectroscopy ofquartz: a pressure sensor for hydrothermal diamond-anvil cell exper-iments at elevated temperatures.Am. Miner., 2000,85, 1725–1734.

51. Richet, P., Gillet, P., Pierre, A., Bouhifd, M. A., Daniel, I. and Fiquet,G., Raman spectroscopy, X-ray diffraction, and phase relationshipdeterminations with a versatile heating cell for measurements up to3600 K (or 2700 K in air).J. Appl. Phys., 1993,74, 5451–5456.

52. Zouboulis, E. S. and Grimsditch, M., Raman scattering in diamondup to 1900 K.Phys. Rev. B, 1991,43, 12490–12493.

53. Goto, T., Anderson, O. L., Ohno, I. and Yamamoto, S., Elasticconstants of corundum up to 1825 K.J. Geophys. Res., 1989, 94,7588–7602.

High temperature elasticity measurements on oxides by Brillouin spectroscopy with resistive and IR laser heatingIntroductionBrillouin scatteringBrillouin systemResistance heatingHigh-temperature cellsSymmetric (Brillouin) high-temperature cellAxial (synchrotron) high-temperature cell

Results using resistance heatingSingle crystalsPolycrystalline aggregatesPhase transitionsGlass transition

IR laser heated measurementsExperimental methodsResults from laser-heating measurementsBrillouin scattering on MgOBrillouin and Raman scattering on Al2O3

SummaryAcknowledgmentsReferences