3-d raman spectroscopy measurments of the symmetry of residual stress fields in plastically deformed...

7/30/2019 3-d Raman Spectroscopy Measurments of the Symmetry of Residual Stress Fields in Plastically Deformed Sapphir

1/9

3-D Raman spectroscopy measurements of the symmetry ofresidual stress fields in plastically deformed sapphire crystals

Thomas Wermelinger, Cesare Borgia, Christian Solenthaler, Ralph Spolenak *

Laboratory for Nanometallurgy, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland

Received 19 February 2007; received in revised form 10 April 2007; accepted 13 April 2007Available online 12 June 2007

Abstract

The development of methods to characterize materials in three dimensions, such as tomography by X-rays, focused ion beam andelectrons, has led to progress in the understanding of materials properties. Recently, even stress and deformation tensors could be mea-sured in three dimensions. Specifically the stress fields around indents in metals were studied by three-dimensional (3-D) X-ray stressmicroscopy. In this paper, we investigate the 3-D residual stress field around a microindent using confocal Raman microscopy with alateral resolution of 300 nm and a depth resolution of 600 nm. The model system investigated was single crystalline sapphire, whichwas indented normal to its basal c(00 0 1) plane. A cross-section of the indent was studied by transmission electron microscopy to visu-alize the deformed microstructure. The major result is that the geometry of the indenter has no direct influence on the symmetry of theresulting residual stress field. Residual stresses directly depend on the crystal symmetry and the defect structures formed during inden-tation. Confocal Raman microscopy is a powerful method for analyzing 3-D stress fields and the corresponding defect structures (bypeak width analysis) with a resolution in the submicron range. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Raman spectroscopy; Residual stress; Phase transformation; Microindentation; Ceramics

1. Introduction

Novel applications in the microelectronics industry haveintensified interest in sapphire as a substrate [1]. Varioussapphire-based devices, such as fast neutron filters andhigh-pressure magnetic resonance cells, have been devel-oped. Specifically, the high strength and heat resistanceof sapphire attracts a lot of attention. Therefore a pro-

found knowledge of the mechanical properties is required.In this context, the deformation of sapphire has beenextensively studied by several groups [112]. As a result,the deformation and fracture mechanisms of the sapphiresingle crystal are well known. In contrast, magnitude anddistribution of residual internal stresses after plastic defor-mation, i.e. the properties of residual stress fields, still

remain unclear. Since these stresses may cause failure,and hence affect the lifetime of devices, it is important tomeasure and to visualize them, ideally in three dimensions(3-D). At the moment, only a few methods are known toperform 3-D measurements with a resolution at or belowthe micrometer range.

One method is 3-D X-ray diffraction microscopy, whichhas a resolution in the micrometer range [13]. Another is X-

ray microbeam diffraction, which is an experimental optionto measure the strain tensor with a submicrometer resolu-tion [1416] in three dimensions. The 3-D distribution ofthe local crystalline phase, the texture and the elastic straintensor can all be measured with a resolution below 1 lm.These instruments combine ultraintense synchrotron X-ray sources and advanced X-ray optics to probe crystallinematerials. Only a few such systems are available worldwide, and until now only a few such experiments have beenperformed to date. Consequently, alternative methods onthe laboratory scale are needed.

1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.actamat.2007.04.036

* Corresponding author.E-mail address: [email protected] (R. Spolenak).

www.elsevier.com/locate/actamat

Acta Materialia 55 (2007) 46574665
mailto:[email protected]:[email protected]


2/9

This paper demonstrates that another accurate methodfor the 3-D measurement of stresses is micro-Raman spec-troscopy. The method is based on the well known effectthat Raman signals (phonon energies) are affected by inter-nal stresses. In a Raman spectrum of deformed material,peak positions are shifted relative to the peak positions

obtained from the stress free material. Quantifying thisshift allows determining sign and magnitude of internalstress. As already proven in many 2-D studies [1721],Raman microscopy can successfully be applied in the anal-ysis of stresses in silicon devices and other Raman activematerials, such as polymers, semiconductors and ceramics.In transparent Raman active materials the method couldalso be used for the 3-D case provided a confocal micro-scope is available that provides precise positioning of thefocus spot. Such measurements at a microindent in a sap-phire single crystal are reported and discussed below.

The crystal structure of sapphire is hexagonal rhombo-hedral, space group D63d, with two molecular Al2O3 groups

per unit cell [22,23]. This structure involves seven Ramanactive phonon modes: 2A1g + 5Eg. According to Louden[24], the Raman tensors of the active optical vibrations ofsapphire are

A1g

a 0 0

0 a 0

0 0 b

; Eg

c c d

c c d

d d o

1

The Raman frequencies (given in relative wavenumbers)of stress free sapphire are 417 and 646 cm1 for the A1gmodes and 380, 432, 451, 578 and 751 cm1 for the Egmodes [22]. The shift of these modes as a function ofapplied stress has been characterized by several groups[25,26]. Watson et al. applied uniaxial pressure up to1 GPa on macroscopic sapphire pillars and measured thecorresponding peak shifts [23]. The results of these experi-ments are listed in Table 1. The same experiment but onsapphire fibers with a diameter in the micrometer rangeshowed slightly different results [27]. Here, the shifts werefound to be about 1.8 and 1.1 cm1 GPa1 for the peaksat 417 and 380 cm1, respectively. Gallas et al. [26] useda diamond anvil high-pressure cell for the calibration ofthe Raman effect in sapphire. They received similar resultsfor the peak at 380 cm1; however, for the peak at a rela-

tive wavelength of 417 cm1 they found a pressure depen-dence of 2.2 cm1 GPa1. Shin and Raccah reported theeffect of uniaxial stress on the Raman frequencies in sap-phire [28]. Recently, a confocal Raman microscope wasused to perform an in-depth analysis of residual stressesin polycrystalline alumina coating [29].

2. Experimental

A sapphire single crystal (size 10 10 1 mm) was plas-tically deformed by microindentation. The indent wasplaced on the basal (0001) plane with a Vickers microind-enter at room temperature. A maximal indentation force of0.4 N at ambient pressure was applied under constant loadrate of 0.05 N s1. The radius of the indenter tip variedfrom one direction to the other from 0.16 to 1.1 lm. Theshape of the indent was determined using an atomic forcemicroscope (AFM) (CRAFM 200, WITec GmbH,

Germany).The residual stress field around the indent was measuredwith a confocal Raman microscope (CRM 200, WITecGmbH, Germany) equipped with a heliumcadmium laserwith a wavelength k of 442 nm. The microscope was oper-ated in the backscattering mode with a 100 objective anda numerical aperture NA of 0.9. According to the Rayleighequation

d 1:22 kLaser

2 NA2

the lateral resolution d of the microscope is about 300 nm,while the depth resolution is on the order of 600 nm. As the

microscope is confocal only information from the focalspot is collected. Confocality combined with the possibilityof a precise positioning of the focus spot in the x-, y- and z-directions allows for measuring stress fields in threedimensions.

Starting from the surface of the sapphire crystal, a stackof planar Raman scans parallel to the basal (0001) planewas recorded. Measurements were made always withinthe same x- and y-coordinates but changing z-position.The distance between two planar scans was 0.4 lm. Intotal, 19 scans were recorded down to depth of 7.6 lm.Each planar scan was 12 12 lm and consisted of48 48 spectra. As the Raman signal of sapphire was weakcompared with signals from silicon, an integration time of5 s per spectrum was chosen to obtain a sufficiently largesignal-to-noise ratio.

In order to gain some direct information on the defor-mation structure, a cross-section trough the indent wasexamined by means of transmission electron microscopy(TEM). For this purpose a TEM lamella was cut perpen-dicular to the (0001) basal plane through the center ofthe indent (Fig. 2a) with a FEI Nano Lab 600 focusedion beam microscope (FIB). The TEM lamella was about2.5 15 lm in-plane and 100150 nm deep; it was exam-ined with a FEI Tecnai G2 F20X-Twin TEM operating

at 200 kV.

Table 1Pressure dependence of Raman frequencies in sapphire

Frequency(cm1)

Peak shift (cm1/GPa)

Shin et al.[27]

Watson et al.[22]

Gallas et al.[25]

Jia and Yen[26]

380 2.3 0.2 1.37 0.06 1.10 0.10 1.10417 1.7 0.1 2.11 0.06 2.20 0.07 1.80432 1.8 0.1 2.95 0.08 1.16451 1.0 0.2 1.66 0.10 578 2.7 0.3 2.77 0.12 0.55646 5.0 0.4 0.00

751 2.5 0.3 4.80 0.20 1.70

4658 T. Wermelinger et al. / Acta Materialia 55 (2007) 46574665


3/9

3. Results

Fig. 1 shows the Raman effect of undeformed sapphirefor two different crystal orientations and correspondingdifferent polarization of the incoming laser light. The blackspectrum (rectangular symbols) was measured with an inci-

dent laser beam polarized perpendicular to the c(0001)axis and features six major lines at the wavenumbers 378,417, 428, 447, 575 and 748 cm1. The gray spectrum (trian-gular symbols) was recorded with an incident laser beampolarized parallel to the c(0001) axis and features threeprominent lines at 378, 417, 645 cm1, plus a faint peakat 748 cm1. These measurements with the actual experi-mental set-up are in agreement with literature [22]. Thepeak at 378 cm1 gets stronger, compared with the otherpeaks, with increasing numerical aperture of the objective.Therefore, this particular vibration must have a strongerin-plane component than the other phonons due to the factthat a parallel laser beam only interacts with out-of-plane

phonons.Fig. 2a shows an AFM map of the topography of the

Vickers microindent on the c(0001) plane of the sapphiresingle crystal. The indent has a diameter of about 4.55 lm. No pile-ups are visible at the edges of the indent.Though there are some slightly asymmetric features, suchas the tip radius, the shape of the plastically deformed areacorresponds to the fourfold symmetry of the indenter tip. Across-section through the middle of the indent shows thatthe indent has a depth of about 0.5 lm (see Fig. 2b).

All measured Raman peaks from the indented area areshifted due to residual stresses. Fig. 3ad shows the shift

of four different peaks measured 0.4 lm below the surfaceof the sample. While a shift to higher wavenumbers indi-cates compressive stresses, shifts to lower wavenumbersare due to tensile stresses relative to the direction of thephonon probed. The map in Fig. 3a contains a mixture

between in-plane and out-of-plane stresses; the other mapsin Fig. 3 represent out-of-plane stresses only. All peaksshow a similar threefold stress distribution. The clarity ofthe pattern is obviously affected by the signal-to-noise ratioof the different peaks. The peak at the wavenumber at417 cm1 has the best signal-to-noise ratio and is thereforeselected for the further investigations.

Fig. 4 shows the stress distribution over the indent area interms of the shift of the peak near 417 cm1 for increasingdepth, starting form the surface of the crystal down to3.6 lm. Bright colors correspond to compressive stresseswhile dark colors correspond to tensile stresses in the out-of-plane direction. Threefold symmetry is apparent in allscans. The measurements were made down to 7.6 lm butthe threefold symmetry disappears 3.6 lm below the surface.

Image processing tools such as ImageG allow the calcu-

lation of a 3-D image from a stack of 2-D maps. Fig. 5

Fig. 1. Raman spectrum of sapphire for different polarization of theincoming light. Black spectrum (rectangular): polarization perpendicularto c(00 0 1) axis; gray spectrum (triangular): polarization parallel to

c(00 01) axis. Objective 100 magnification, numerical aperture 0.9.

Fig. 2. (a) AFM image of the Vickers microindent in the basal (00 01)plane of the sapphire single crystal. The indent has a diameter of about4.55 lm and clearly shows a fourfold symmetry. The trace T marks theposition of the TEM sample. (b) Cross-section through the middle of theindent which has a depth of approximately 0.5 lm.

T. Wermelinger et al. / Acta Materialia 55 (2007) 46574665 4659


4/9

shows the 3-D stress field around the Vickers indent calcu-lated from the stack of images in Fig. 4. Only out-of-plane

stresses are shown. As every color represents a certain

stress, image processing makes it possible to calculate thevolume of different stress components. In principle, the vol-

ume of phase-transformed regions could also be deter-

Fig. 3. Stress maps (12 12 lm) at the indent 0.4 lm below the surface, for the peaks at wavenumbers (a) 378 cm1, (b) 417 cm1, (c) 575 cm1 and (d)748 cm1. In maps (b)(d) bright colors correspond to compressive stresses while dark colors correspond to tensile stresses in the out-of-plane direction.Map (a) contains an in-plane as well as an out-of-plane component.

Fig. 4. Shift of the peak at 417 cm1 wavenumbers around the indent. High wavenumbers correspond to compressive stress while low wavenumberscorrespond to tensile stress. The map distance is 0.4 lm.



5/9

mined. However, in the current case the volume in the par-ticular area was found to be too small for quantification.

As a further result of the stack of images, one canextract single line depth scans. Fig. 6 visualizes the stressdistribution of three different line scans in z-direction.These scans show the variation of the peak shift withincreasing depth. Scans were taken (i) far away from theindent (Fig. 3, arrow I) as well as (ii) within the indentedarea dominated by tensile stresses (Fig. 3, arrow II) and(iii) within the indent dominated by compressive stresses(Fig. 3e, arrow III). The peak position was determined byfitting the measured intensity to a Gaussian function; errorbars in Fig. 6 refer to the standard deviation of the fittedcurve. At a depth of about 2 lm the differences of the peakposition between the three lines nearly vanish. But down to4 lm the values from the tensile region are slightly below

the other two curves. With increasing depth the values of

the line scan far away from the indent are slightly shiftedto lower wavenumbers.

Fig. 6b shows the variation of the peak width for thesame line scans. As before the major differences are visibledown to a depth of about 2 lm. Although the absolutevalue of the peak shifts for the tensile and the compressivestress are comparable, there are significant differences inpeak width. As the peak width is influenced not only bythe stress but also by the defect density, it can be deducedthat regions of compressive stress exhibit higher defectdensities.

At the side walls of the indent pronounced and strongchanges are observed in the Raman spectrum (Fig. 7).The peaks are broadening and their position is shifted tohigher wavenumbers. For example, the peak at 748 cm1

is shifted to 773 cm1. This property is found locally justbeneath the side walls of the indent and disappears at a

depth of about 1.0 lm below the sample surface.

Fig. 5. (a) The calculated 3-D stress field (20 20 2 lm) around themicroindent. Dark colors refer to tensile stresses, bright colors tocompressive stresses. (b) The tensile stresses above a certain thresholdare transparent. Only areas with neutral or compressive stresses are visiblein this volume (12 12 4 lm).

Fig. 6. (a) Peak position of three different line scans in the z-direction.Measured in the unstressed part of the sample (see Fig. 3, arrow I), in themiddle of the indent where tensile stresses are dominating (Fig. 3, arrowII) and in the middle of the indent where compressive stresses areprominent (Fig. 3, arrow III). (b) The peak width instead of the position.



6/9

The TEM contrast image Fig. 8 gives an overview overthe very complex deformation structure of the indentedarea and of the transition region towards the un-deformedmaterial. The sample is a thin lamella cut out through themiddle of the indent (trace T in Fig. 2) by means of FIB.Arrow a marks the center of the indent. Dark bands balong the sample surface are platinum layers deposited forsample preparation in order to provide for the requiredmechanical stability of the lamella. Obviously, thedeformed zone is wide and deep and the defect density is

high. At least three morphologically different areas areobserved: (i) an area of intersecting elongated cells oblique

to the c-axis and not parallel to the slopes of the indent(area c); (ii) an area of elongated cells perpendicular tothe c-axis, almost without any intersection (area d);and (iii) an almost contrast-free area just below one ofthe slopes of the indent (area e). From this phenomeno-logical picture only a few general but important conclu-

sions can be drawn as follows. The complex stressdistribution seems to activate simultaneously both slipand twinning as competing deformation mechanisms.Directly beneath the indent, both mechanisms seem tobecome activated with similar probability: interaction ofall activated deformation systems leads to the observedintersecting cell structures. More distant from the indentcenter, deformation is essentially concentrated on the basalplane. Again, the mechanism seems to be a combination ofboth slip and twinning. The process shears material awayfrom the indent so that a stack of horizontal, parallelcells is formed. The width of these cells increases with thedistance from the surface. The tip of the arrow d points

to a small horizontal crack. The low-contrast area e fea-tures no clear traces from any deformation structure, nei-ther from c nor from d. Therefore, deformationmust here involve an additional mechanism, such as, forexample, phase transformation (see the following section).Near the surface of the sample a thin layer of high disloca-tion density is observed (area f) which is obviously notdue to the indentation experiment. It is well known thatpolishing sapphire may induce such a thin layers of defects[2].

4. Discussion

4.1. Mechanical aspects of indenting sapphire

In the previous section it is demonstrated that 3-DRaman measurements of the residual stress field at a Vick-ers microindent clearly reveal a threefold stress distribu-tion, though the geometrical shape of the indent is ofcourse fourfold symmetrical. This result is surprising andinteresting. It can be explained with the crystallographicanisotropy of plastic deformation in hexagonal crystalsand the probability Tc for activating the different deforma-tion systems as follows.

Several groups investigated the room temperature plas-ticity of sapphire [37,9,10]. Nowak et al. used a sphericalmicroindenter for the analysis of plastic deformation.According to their work, the probability Tc of activatingthe cth slip or twinning system depends on the shear stressvalue sc acting on the particular slip or twinning plane, aconstraint factor Kc, denoting the orientation of theindented crystal surface, and the critical shear stress sCRc[1,5]. It is given by

Tc sc

sCRcKc 3

Table 2 lists the available deformation systems and crit-

ical shear stresses for sapphire with a c/a axis ratio of 2.73.

Fig. 7. Raman spectra of sapphire taken parallel to the c(0001) axis. Thegray spectrum (triangles) is taken from the unstressed part of the crystal.

The black spectrum (squares) is taken form the middle of the indent.

Fig. 8. TEM image of the FIB lamella which was cut out through theindent. (a) Center of the indent. (b) Platinum layer. (c) Elongated cells. (d)Cell structure perpendicular to the c-axis. (e) Almost contrast-free area. (f)

Thin layer of dislocations originating from polishing.



7/9

For a spherical indentation with an opening angle a of130 (180 2 * w, with w = 25), which is comparable tothe opening angle of a Vickers indent (a = 136), the prob-ability Tc is shown in Fig. 9 for an indentation on thec(0001) plane and a force of 0.218 N. Rhombohedral twin-

ning (see Table 2, mechanism 1) has the highest probabili-ties. This mechanism has six equivalent glide systems, threeof which are favored at this opening angle a. The same istrue for mechanism 3 (rhombohedral glide), which alsoshows a preference for three of its six glide systems, thoughat a lower probability level. The opening angle a has astrong influence on the symmetry of deformation and isthe main reasons for the appearance of a threefold symme-try in the residual stress field. A flat punch indent, forexample, should activate different deformation systemsand will probably lead to a sixfold symmetry of the residualstress field.

The TEM image Fig. 8 shows that in the actual experi-

mental set-up rhombohedral twinning and rhombohedralslip are the dominating deformation mechanism. Thisbehavior must be due to the very complex stress distribu-tion beneath the indent. According to Fig. 9, the dominat-

ing deformation systems involve threefold symmetry.Therefore it is reasonable to assume that the same propertyis to be expected for the residual stress field.

The strong changes of the Raman spectra observeddirectly below the indent cannot be explained with slipand twinning mechanisms alone. However, they might well

be due to a phase transformation. Colomban and Havelfound similar peak shifts in their work [30]. They statedthat, in molecular approximation, the 417 cm1 band orig-inates from an AlO stretching mode of the AlO4 tetrahe-dron. The shift of this peak to higher wavenumbersindicates a compressed structure. As already explained, thisproperty is detectable down to 1.0 lm. The TEM imageshows a bright zone directly under the indent, where thecontrast of the image is different from the other deformedareas. It highlights that this zone is only visible on one sideof the indent. The zone is about 0.5 lm deep. The focusspot has in z-direction a diameter of about 0.6 lm. If onecompares the cut out direction of the lamella and the stress

distribution, one sees that the asymmetry of the deforma-tion structures is also visible in the stress maps. Thus itseems possible to measure a small signal of the phase-trans-formed area even if the microscope is focused 1 lm belowthe surface, which corresponds to the findings of themeasurement.

4.2. 3-D Raman microscopy

The lateral resolution of the microscope is restrictedby the wavelength of the laser and the numerical aper-ture. Even in the case for deep blue lasers and oil immer-

sion objectives, which have the highest numericalaperture, the lateral resolution is in the order of 150200 nm. In comparison with a 3-D X-ray crystal micro-scope [14], which also has a resolution in the submicrom-eter range, the lateral resolution of an optimized confocalRaman microscope is slightly better. Other advantages ofthe confocal Raman microscope are the straightforwardsample preparation, the fast measuring method and thegood accessibility.

Another feature is the direct measurement of severalcomponents of the stress tensor. As the different peaksbelong to different phonon vibrations of the crystal, it ispossible to relate different peaks to particular crystallo-graphic directions. Therefore it is also possible to assigndifferent peak shifts to different directions. However, somerestrictions also have to be taken into account. Everycrystal class features different Raman active phononvibrations; thus it is not possible to predict in generalhow many components of the stress tensor are accessible.Silicon, for example, exhibits a single Raman peak whichbelongs to triply degenerated optical phonons [31]. Byexamining the polarization and the direction of the scat-tered light, all components of the stress tensor can beobtained [32]. For sapphire analyzed in the actual exper-imental set-up, it is possible to measure an out-of-plane

component from the peaks at 417, 578 and 751 cm

1

Table 2Possible twinning and slip systems of sapphire crystal [5]

Symbol Twinning or slipsystem

Description Critical shear stress(GPa)

1 h0 11 1iK1f0 1 1 2g Rhombohedraltwinning

0.111

2 h11 0 0iK10 0 0 1 Basal twinning 0.148

3 h211 0if011 2g Rombohedral slip 34 h211 0i0 0 0 1 Basal slip 175 h1 01 0if1 21 0g Prismatic slip 1.2

h1 01 0if1 1 0 1g6 h1 01 0if1 0 1 2g Pyramidal slip 18

h1 01 0if11 2 3g

Fig. 9. Probability for activating a slip or twinning system for alldirections l around a spherical indent [33]. Numbers 13 correspond to

symbols in Table 2.



8/9

and a mixed out-of-plane and in-plane component fromthe peak at 380 cm1. Therefore only the out-of-planecomponent could be measured directly.

As not all components of the stress tensor could be mea-sured, it was crucial make certain assumptions about thestress state in order to calculate stresses. While the surfacewas assumed to be stress free, below the indent the stresscan be assumed to be hydrostatic. The following figure(Fig. 10) shows the calculated stresses in the center of theindent at different depth levels based on the results of Wat-son et al. [23]. This calculation was chosen due to the factthat all three peaks, which belong to out-of-plane stresses,show similar stress values, as to be expected.

At the surface of the sapphire the assumption of hydro-static pressure is not valid. As expected, the out-of-plane

stress, which can be estimated from the shift of the peaksat 417, 578 and 751 cm1, is almost zero. In contrast, thepeak at the wavenumber 380 cm1, which also has an in-plane component, exhibits a strong compressive stress ofabout 1.7 GPa. Below the surface, where the pressure isassumingly hydrostatic, the out-of-plane stress seems tobe in the tensile regime. The peak at 380 cm1 shows nosignificant shift, which means that the tensile stress of theout-of-plane component is compensated by the in-planestress.

Only transparent and Raman active materials are suit-able for 3-D stress measurements. These are ceramics, dia-mond and most polymers. This is a drawback incomparison with the 3-D X-ray stress microscope, whichcan be used for any crystalline material. In the case ofceramics, single crystal samples are preferred because poly-crystalline samples involve peak broadening, which makesan accurate determination of the peak position more diffi-cult. Fully amorphous samples are still Raman active, butpeaks are in general too broad to allow for an accuratedetermination of the peak position.

5. Summary and conclusions

The residual stress distribution around a Vickers indent

in sapphire was analyzed with a confocal Raman micro-

scope. Interestingly, the residual stress field is not directlyinfluenced by the geometry of the indent. Although theindent shape had a fourfold symmetry, the residual stressfield was found to be of threefold symmetry. This resultcan be explained by the property of sapphire. Sapphirehas a hexagonal crystal structure and therefore shows an

anisotropic deformation. The probability for activating acertain slip or twinning system is strongly orientationdependent. The dominating slip and twinning systems,namely rhombohedral twinning and slip, exhibit a clearthreefold symmetry. This symmetry leads to a threefoldsymmetry of the residual stresses. Moreover, experimentalevidence for a phase transformation at the side walls of theindent was found. The exact structure of this proposedphase was not investigated and must be determined infuture research.

It is shown that confocal Raman microscopy is apowerful tool for analyzing 3-D stress fields with a spa-tial resolution in the submicrometer range. Depending on

the Raman tensors, it is possible to get access to severalcomponents of the stress tensor. In the case of sapphire,only an out-of-plane component was measurable due tothe fact that the experimental set-up only allowed toanalyze out-of-plane vibrating phonons or phononswhich had an out-of-plane as well as an in-plane compo-nent. In principle, the method can be applied for allRaman active transparent materials at modest expensesand short timescales compared with synchrotron basedtechniques.

Acknowledgements

The authors thank Kyburz AG for donating us a singlecrystal sapphire, and Dr. Steve Reyntjens and Dr. ErwanSoutry from FEI Application Research Lab., Eindhoven,for the preparation of the TEM lamella as well as theTEM analysis. This work was supported by ETH ResearchGrant TH -39/05-1.

References

[1] Nowak R, Manninen T, Li CL, Heiskanen K, Hannula SP, LindroosV, et al. Anomalous surface deformation of sapphire clarified by 3-DFEM simulation of the nanoindentation. Jsme Int J Ser ASolid

Mech Mater Eng 2003;46:265.[2] Hirayama TSaT. Lattice strain and dislocations in polished surfaces

on sapphire. J Am Ceram Soc 2005;88:2277.[3] Pirouz P, Lawlor BF, Geipel T, BildeSorensen JB, Heuer AH,

Lagerlof KPD. On basal slip and basal twinning in sapphire (alpha-Al2O3). 2. A new model of basal twinning. Acta Mater 1996;44:2153.

[4] Nowak R, Sakai M. The anisotropy of surface deformation ofsapphire continuous indentation of triangular indenter. Acta MetallMater 1994;42:2879.

[5] Nowak R, Sekino T, Niihara K. Surface deformation of sapphirecrystal. Philos Mag A 1996;74:171.

[6] Nowak R, Sekino T, Niihara K. Non-linear surface deformation ofthe (10(1)over-bar-0) plane of sapphire: identification of the linearfeatures around spherical impressions. Acta Mater 1999;47:4329.

[7] Inkson BJ. Dislocations and twinning activated by the abrasion of

Al2O3. Acta Mater 2000;48:1883.

Fig. 10. Stresses in the middle of the indent at different depth levels.



9/9

[8] BildeSorensen JB, Lawlor BF, Geipel T, Pirouz P, Heuer AH,Lagerlof KPD. On basal slip and basal twinning in sapphire (alpha-Al2O3). 1. Basal slip revisited. Acta Mater 1996;44:2145.

[9] Tymiak NI, Daugela A, Wyrobek TJ, Warren OL. Acoustic emissionmonitoring of the earliest stages of contact-induced plasticity insapphire. Acta Mater 2004;52:553.

[10] Page TF, Oliver WC, McHargue CJ. The deformation-behavior ofceramic crystals subjected to very low load (nano)indentations. JMater Res 1992;7:450.

[11] Lloyd SJ, Molina-Aldareguia JM, Clegg WJ. Deformation undernanoindents in sapphire, spinel and magnesia examined usingtransmission electron microscopy. Philos Mag A 2002;82:1963.

[12] Kollenberg W. Plastic-deformation of Al2O3 single-crystals byindentation at temperatures up to 750-degrees-C. J Mater Sci1988;23:3321.

[13] Poulsen HF, Nielsen SF, Lauridsen EM, Schmidt S, Suter RM,Lienert U, et al. Three-dimensional maps of grain boundaries and thestress state of individual grains in polycrystals and powders. J ApplCryst 2001;34:751.

[14] Ice GE, Larson BC. 3-D X-ray crystal microscope. Adv Eng Mater2000;2:643.

[15] Larson BC, Yang W, Ice GE, Budai JD, Tischler JZ. Three-dimensional X-ray structural microscopy with submicrometre reso-lution. Nature 2002;415:887.

[16] Tamura N, MacDowell AA, Spolenak R, Valek BC, Bravman JC,Brown WL, et al. Scanning X-ray microdiffraction with submicrom-eter white beam for strain/stress and orientation mapping in thinfilms. J Synchrotron Radiat 2003;10:137.

[17] Loechelt GH, Cave NG, Menendez J. Polarized off-axis Ramanspectroscopy: a technique for measuring stress tensors in semicon-ductors. J Appl Phys 1999;86:6164.

[18] Dewolf I, Vanhellemont J, Romanorodriguez A, Norstrom H, MaesHE. Micro-Raman study of stress-distribution in local isolationstructures and correlation with transmission electron-microscopy. JAppl Phys 1992;71:898.

[19] De Wolf I, Jian C, van Spengen WM. The investigation ofmicrosystems using Raman spectroscopy. Opt Lasers Eng2001;36:213.

[20] Bonera E, Fanciulli M, Batchelder DN. Combining high resolutionand tensorial analysis in Raman stress measurements of silicon. JAppl Phys 2003;94:2729.

[21] Bonera E, Fanciulli M, Batchelder DN. Raman spectroscopy for amicrometric and tensorial analysis of stress in silicon. Appl Phys Lett2002;81:3377.

[22] Porto SPS, Krishnan RS. Raman effect of corundum. J Chem Phys1967;47:1009.

[23] Watson GH, Daniels WB, Wang CS. Measurements Of Ramanintensities and pressure-dependence of phonon frequencies in sap-phire. J Appl Phys 1981;52:956.

[24] Loudon R. Raman effect in crystals. Adv Phys 1964;13:423.[25] Shin SH, Pollak FH, Raccah PM. Effects of uniaxial stress on Raman

frequencies Of Ti2O3 and Al2O3. Bull Am Phys Soc 1974;19:536.[26] Gallas MR, Chu YC, Piermarini GJ. Calibration of the Raman effect

in alpha-Al2O3 ceramic for residual-stress measurements. J Mater Res1995;10:2817.

[27] Jia W, Yen WM. Raman-scattering from sapphire fibers. J RamanSpectrosc 1989;20:785.

[28] Shin FHP S, Raccah PM. Proceedings of the third internationalconference on light scattering in solids. In: Balanski RCCLaSPSP M,editor. Third international conference on light scattering in solids,1976.

[29] Ohtsuka S, Zhu W, Tochino S, Sekiguchi Y, Pezzotti G. In-depthanalysis of residual stress in an alumina coating on silicon nitridesubstrate using confocal Raman piezo-spectroscopy. Acta Mater2007;55:1129.

[30] Colomban P, Havel M. Raman imaging of stress-induced phasetransformation in transparent ZnSe ceramic and sapphire singlecrystals. J Raman Spectrosc 2002;33:789.

[31] De Wolf I. Stress measurements in Si microelectronics devices usingRaman spectroscopy. J Raman Spectrosc 1999;30:877.

[32] Loechelt GH, Cave NG, Menendez J. Measuring the tensor nature ofstress in silicon using polarized off-axis raman-spectroscopy. ApplPhys Lett 1995;66:3639.

[33] Abramof PG, Ferreira NG, Beloto AF, Ueta AY. Investigation ofnanostructured porous silicon by Raman spectroscopy and atomicforce microscopy. J Non-Cryst Solids 2004;338:139.


3-d raman spectroscopy measurments of the symmetry of residual stress fields in plastically deformed...

Documents