Effects of couplant massloading on the acoustic signature V(z) AbdellazizDoghmane, a)Zahia Hadjoub, a)KarimAlami,Jean-MarcSaurel, and Jacques Attal Laboratoire deMicroacoustique, Universit• desSciences et Technique duLanguedoc, PlaceE. Bataillon, 34095MontpellierCedex-05,France (Received6 August1991;accepted forpublication11May 1992) Nondestructive investigations of elasticpropertiesof materialsvia acousticmaterialsignature, usingreflectionacousticmicroscopy systems, arebecomingmoreandmoreattractive.The necessity of usingcouplingliquidsin suchsystems leadsto the generationof generalized surfaceleakywavessuchasRayleighwaves.The V(z) response andhencethe postionof its Fouriertransformpeakschangeaccording to theliquidimpedance dueto a fundamental phenomenon knownasmassloading.Thiseffect,neglected up till now,hasbeenstudiedin detailson severalmaterials(tungsten,stainless steel,and SiO2)with water,mercury,andother couplingliquidshavingdifferentdensities assuming the samevelocity.For example,it is found that skimmingshearvelocitycanbe determined with a betterprecision whenheavycoupling liquidsare used.However,skimminglongitudinalvelocityseemsto be independent of the couplingliquiddensity,whereasits efficiency getslargerwith higherliquiddensities. PACS numbers:43.35.Pt, 43.35.Sx, 43.35.Zc INTRODUCTION Recently,therehasbeena growinginterestin thefieldof acousticmicroscopy. •-3 It is a nondestructive evaluation technique thatisevolving veryquicklydueto itsimportant roleintoindustrialareas.The acoustic microscope canbe used to characterize surfaces and subsurfacesof materials via acousticimagingand/or quantitativemeasurements. The so-calledacousticmaterialsignature,alsoknownas V(z), measures moredirectlyelasticpropertiesof solids. Thissignature isobtained byrecording thereflected acoustic signalvariations asa functionofthesample defocus z, when the latteris movedalongthe axisfrom the focalplane towardstheacoustic lens.Thissignalresponse isdueto the interference between a narrowbundleof axialspecular reflectedwavesand manyotherleakysurfacewaves. 4'5However,onlythemostefficient modes wouldappearin the V(z) curves. Nowadays,wideaperture(40ø-50ø) acousticlensesare mostlyusedwithwaterasa coupling liquid.Theuseofmercury,despiteits chemicalreactivity,is becoming morefre- quent; 6'7it hasa velocity of 1450m/s,close tothatofwater, but a density13.6timeslarger.This latter assigns to the liquidahigherloadingandanimpedance comparable tothat of mostsolids,thusensuringa bettertransmission of waves into objects.Furthermore,mercuryis fourtimeslessabsor- wavesare, in principle,definedon the boundaryof solids with vacuum.However, if the vacuumboundingplane is replacedby a liquid,asfor acousticmicroscopes, theexisting wavesare rather known as "genealizedRayleigh waves," which are mostlyleaky waveswith a characteristicvelocity VR, differentfrom RayleighvelocityVR. Up till now, only a smallvariationwasreported in a limitedstudyofliquids. 8In this work, we investigateexperimentallytwo very different liquids,waterand mercury,representing the usualpractical liquid and liquid metal, respectively.Then, this investigation, whereonly the liquid densityhasbeenchanged,canbe extendedtheoreticallyto includeintermediateliquidsdensitiesandevenhigher.The phenomenaof loadingeffects,associatedwith differentmodes,are socomplicatedthat we only concentrateon Rayleighand longitudinalskimmingwave modesdue to their greatimportancein the determinationof elasticpropertiesof solids.To includea largerangeof materials, tungsten,stainlesssteel,and SiO2,whosedensitiesare 19.3, 8.0, and 2.2, respectively,are considered.As far as skimming longitudinalmodesare concerned,the experimental V(z) analysiswith waterhasbeenrecentlyexplained usingthe ray representationmodel as done with Rayleigh modesusingthe polesand the zerosextractedfrom the reflectance Unfortunately function near all the theoscillations critical vlaues. present s in the experi- mental V(z) curvescannotbe totally in agreementwith this Despitetheexistence of several wavemodes,onlyRay- conceptandforeignpeaksin the FFT domainarenot clearly explainedyet. Their efficiencyare significantand the correleigh waveshave recievedconsiderableattention in view of their usefulness for not onlythe detectionof surfacedefects spondingchangeof the reflectancefunctionisnot soevident, in ultrasonic nondestructive testingofmaterials, butin man- especiallywhen high-densityliquidsare used. In orderto takecareof thesephenomena alsopresentin ufacturing electromechanical devices aswell.PureRayleigh the V(z) simulation,comparisonbetweentheoreticaland a)Present address: Laboratoire desSemiconducteurs, Institut dePhysique experimentV(z) havebeendoneall alongthis paper,based BP 12,Universit•deAnnaba23000,Algeria. on the loadingeffecton Rayleighand skimmingwaves. bent than water. 1545 J. Acoust. Soc.Am.92 (3),September 1992 0001-4966/92/091545-06500.80 ¸ 1992Acoustical Society ofAmerica 1545 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 134.71.135.191 On: Tue, 25 Nov 2014 11:15:03 I. OBSERVATIONS - OF LOADING EFFECTS I (8) A. Y(z) and R (0) analysis In microanalysis, the interpretationof resultsis based onthevariationof thesignalintensity(V) withthesample defocus (z). Hencethe V(z) response isthemostimportant methodfor accuratelydetermining materialssurfacevelocities.Thestudyof the V(z) functionisdirectlyrelatedto the "acoustic reflectivity" of thematerial,givenby9']ø I ß Wster-Tungsten 0 lens = 50ø ....... o .•z....... +H '• , o o o L , 0.5 0 o o o o R(O)P2(O)e"•'zcøsø sin0 cos0 dO, ( 1) Jo 0 I ß (b) where0 is the anglebetweena wavevector(k) andthe lens axis (z), P(0) is the pupilfunctionof the lens,andR (0) is the reflectance functionof the specimen. This latter func- ß Mercury-Tungsten 0 lens = 50ø 1.0 . I I tion,foracoustic waves, canbefoundbysolving theacoustic i Fresnel equation. ]] It depends onthecoupling liquid-iso- • tropicsolidboundary conditions (impedance Z, density,incidenceangle 0, and velocity of different wave modes). Therefore,R (0) shouldprovidevaluableinformationabout criticalanglesat whicheachleakymodecanbeexcitedat its own characteristic velocity. For a betterillustration of theeffects of coupling liquid loading,we calculateR (0) for tungsten, asa high-density material,with waterandmercuryascouplingliquidsthat .•_ o o 0.5 0T OL o -H 0 0 10 20 30 40 50 Angle of incidence [deg.] can be verifiedexperimentally.In the evaluationof the re- flectioncoefficient, a computerprogramwasdeveloped to carry out the necessary numericalcalculationsfor different liquid-solid combinations. In Fig. 1(a), the typical reflectioncoefficient,modulus FIG. 1. Reflectioncoefficientamplitude( .... ) and phase(•) as a functionof incidenceanglefor: (a) water-tungsten and (b) mercury-tungsten interfaces. (dashed curve),andphase(solidcurve)at thewater-tungsteninterfaceisshownasa functionof incidence angle;the modulus isreferredto theleft handside,whereas thephase to the fight-handside.As 0 increases, we canidentifythe firstsmallchanges in bothamplitude andphaseat 0 - 17.1ø, B. Experimental results corresponding to the criticalangle0L for longitudinal(or All experimentswere carried out usingan acousticmicompressional) wave excitationin tungsten.Above the croscopeworkingin reflectionmodeat 145MHz with a halfshear(or transverse) wavecriticalangleOr all theenergyis angleof the lensof 50ø.Tungsten,stainlesssteel,and SiO2 reflected,dueto the absenceof transmission in the solid,and were investigatedwith water and mercuryas couplingli- themodulusof thereflectance functiongoesto unity.Howquids.Comparablebehaviorsand resultsare obtainedin all ever,the mostdominantfluctuationin phaseoccursa few cases;theftore, we will only presentresultson tungsten,as degreesbeyondOr; this is centeredaround0R -- 34.7ø,at the mostdensematerial.Figure 2 (a) and (b) showthe typiwhichwavesin theliquidcancoupleintogeneralized leaky cal V(z) curvesand its fast Fourier transform(FFT) specRayleighwaveonthesolid.Thephasechanges byalmost2•r trum for the water-tungsteninterface. Only generalized overa fairly smallchangeof 0. leaky Rayleighmodesappearwith the characteristicvelocThe reflection coefficient versus incidence angleat the ity VR, which can be preciselydeterminedfrom the sharp mercury-tungsten interfaceis shownin Fig. 1(b). The fluc- principalray in the FFT spectrumand is found to be 2640 m/s. tuationsin amplitude andphaseoccurat criticalangles0L The resultsof the mercury-tungstencombinationare and0R,andaremoreenhanced at longitudinal waveangle, comparedto water-tungstencombination(this will be plottedin Fig. 2 (c) and (d), leadingto thevelocitieslistedin furtherinvestigated in Sec.III). We alsonoticethat, around Table I. The main discrepancies of resultsbetweenwaterand 0R,theextension ofthephasevariations islarger.Themain mercuryare better observedin the FFT spectraand can be featuresof bothreflection coefficients in Fig. 1(a) and (b) summarizedin the following:(i) a shift of the principalray canbegroupedintotwoparts:at thegeneralized leakyRay[ in Fig. 3 (d) ] from whichgeneralizedleakyRayleighvelocleighandat theskimming longitudinal angles. To putthese ity is determined,(ii) the appearanceof severalother peaks, featuresinto evidence,experimentalV(z) curvesare to be and (iii) the skimming modesmuch more enhancedwith studied. 1546 mercury. Thesefeatureswill be further developed. J. Acoust.Soc.Am.,Vol.92, No.3, September1992 Doghmaneeta/.' Couplantmassloadingeffects 1546 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 134.71.135.191 On: Tue, 25 Nov 2014 11:15:03 0 160 320 480 640 800 z[•m] 0 20 40 60 RaysNbr FIG. 2. ExperimentalV(z) curve(a) anditsFFT spectrum(b) forwater-tungsten interfaceandfor mercury-tungsten interface(c) and(d). The opening angleof the lensis 50*. II. LOADING RAYLEIGH A. Phase EFFECTS ON GENERALIZED but determinesthe efficiencyof surfacewavescoupling on LEAKY the specimen. •3 The increaseof the gradientof the phase WAVES curve betweenOr and 0R is indicativeof a velocityvariation. distortion To investigatethe influenceof couplingliquidsdensity on surfacewavesin the vicinity of the generalizedleakyRayleigh angle, we calculatedR(O) for different solids with manyotherfictiveliquidshavingdifferentintermediatedensitieslaying betweenthoseof water and mercury, and beyond. A samevelocityof 1500 m/s, similar to that of water or mercurywas taken in all calculations.Figure 3 summarizesthe phasevariationswith 0, near 0R, for tungsten.It is obviousthat as the liquid densityincreases, the curvesshift away from 0R leading to the appearanceof a kink. Sharp variationsbetweenthis kink and the peak of the •r phase transitionareobservedfor eachcouplingliquid.The slopeof the curvesintervenesin the V(z) responseand this in veloc- ity calculations. • This gradientnot only accounts for the differencesin the V(z) responeof differentmaterialswith similar acousticvelocitiessuchas Aluminium and steel,•2 B. Velocity variations In order to calculatethe generalizedleaky Rayleighvelocities,we havecomputedthe V(z) responsefor the above solidsusingthe sameconditionsasbefore.Numericalcalculations were carried out at an operatingfrequencyof 145 MHz for a lensopeningangleof 50ø.Generalizedleaky Rayleighvelocitieswerethen preciselydeducedfrom FFT spectra of V(z) curvesfor different valuesof liquid densities. Figure 4 showsa setof thesespectrafor tungsten;it can be noticedthat, around0R, a very sharppeakis obtainedwith water, but as the liquid densityincreasesthe peaknot only broadensbut slightly shifts from its initial position [Fig. 4 (b) and (c) ] towards relatively higher velocities.However,for d> 10.25, any increasein the couplingliquid density would lead to a larger shift of the principal ray and a TABLE I. Experimental andcalculated velocities of tungsten deduced from V(z) curvesvia FFT technique. The openingangleof the lensis 50*. Computed V(z) ExperimentalV(z) Couplingliquid VR' (m/s) V•. (m/s) VR' (m/s) Water 2640 not measurable 2630 not determinable Mercury 2829 2835 5218 1547 J. Acoust.Soc. Am., Vol. 92, No. 3, September1992 5229 VL (m/s) Doghmaneet al.: Couplantmass loadingeffects 1547 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 134.71.135.191 On: Tue, 25 Nov 2014 11:15:03 Coupling liquids/Tungsten VR. = VR (a)I VL Liquids density dl= 1.0 d2= 4.0 d3= 8.0 d4=13.6 d s=20.0 • ....... ...... ........ OR Angle of incidence FIG. 3. Phaseof reflectioncoefficient,near 0R, as a functionof incidence anglefor many liquidscouplingtungsteninterfaces. splittingof thepeak [ Fig. 4 (d) and (e) ]. This novelsplitting phenomenonis not only obtainedtheoreticallybut is obeservedexperimentallyas well (Fig. 2). Its existencewill be discussedin a next paper. To betterillustratetheseobservationswe haveplottedin Fig. 5, the resultsof the computationof generalizedleaky RayleighvelocitiesVR' (solidcurve) asa functionof liquid densityfor a tungstensample.The curvecanbedividedinto threeregions:(i) a veryslowincreasein VR' for smalldensities (d < 8); (ii) a transitionregioninto which a transferof energycouldbehappeningbetweendifferentmodes,leading jl• VR'=VT to a sharpincreasein VR'; and (iii) a saturationregionfor which VR' = 2835 m/s, a value closeto the shearvelocity VT, whenthe liquid densityapproachesthat of the solid. To put thesetheoretical predictionsinto evidencewe haveplotted,in Fig. 5, experimentalvelocities(solidpoints) measuredwith mercuryand water (Table I); the agreement with the calculatedcurveis quitegood.This velocitychange, 0 150 3 ,0 5•;0 as a consequence of the phasevariation in a range of few Rays Nbr. degreesbetweenOTand 0R, may well inducea high coupling betweenthe liquid and the shearlateral mode in the solid. This phenomenoncan obscurethe Rayleigh wave effect. FIG. 4. FFT spectra of V(z) curvesfor tungsten obtained withdifferent liquidsdensities: 1.0(a), 4.0 (b), 10.25(c), 10.3(d), and20.0 Hence, the use of heavierliquids makesthe effectof shear coupling (e). critical angle much more significantthan that of Rayleigh angle. Therefore, the saturationsituationin Fig. 5 correspondsto VT; whereasthe lower velocityvalueapproaches that of the Rayleighvelocity VR. Theseresultsare in agree- C. Efficiency The efficiency of a givenmodeis takento bethe amplimentwith the predictionsof the generalizedRayleighveloc- ity <secular < equation •4'•5from which one finds that•5 1548 J.Acoust. Soc.Am.,Vol.92,No.3, September 1992 tudeof the corresponding ray in the FFT spectrum,from whichthevelocityof suchmodeisdetermined. FromFig.4, Doghmane eta/.'Couplant massloading effects 1548 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 134.71.135.191 On: Tue, 25 Nov 2014 11:15:03 2900 I principalray, whichgivesV•, remainspracticallyunshifted in all casesfor a givensolid,thusleadingto a constantvalue of longitudinalvelocity:for example,for tungsten,V• was foundto be 5218m/s, in goodagreementwith that obtained experimentally(Table I). Region I I I .... VT=2835 m/s ........ I I 2800 I C. Efficiency I In Fig. 4, wecanseethat theamplitudeof theFFT peaks corresponding to skimminglongitudinalmodesvarieswith liquid density.Thesevariationsare indicativeof the solidliquidcouplingandare responsible for efficiencyconversion I I I 2700 .......... I of thesewavesaswell asfor their contributionto V(z) mech- I anisms.The skimmingFFT amplitudeis plottedin Fig. 6, for a half-openingangleof 18ø,againstliquidsdensity.At FI I I 2600 0 first,therei• anincrease ofthecurveasthecoupling liquid • ..... v_=2630m/s I 0 10 I . 20 30 Coupling liquids density FIG.5.Generalized leakyRayleigh velocity asafunction ofcoupling liquid density fortungsten: calculated curve(•) andexperimental points getsheavierdue to an increasein efficiencyof suchmodes. Then, asthe liquidsdensitybecomeslarger,the curvetends towards a saturation value. Hence, it can be concluded that the efficiencyof the conversionandre-radiationof longitudinal modes becomes better when the impedancesare matched. (•). IV. CONCLUSIONS it isobvious thatasliquiddensityincreases from1to 10.25, In this article, the results of numerical calculations of theefficiency of generalized Rayleighwavemodesdecreases reflectioncoefficients at liquid-solidinterfacesarepresented [Fig.4(a), (b), and(c) ]. Howevertheappearance of the for differentsolids,usingvariouscouplingliquidswith difsplitting effectleadsto aninitialincrease [Fig.4(d) ] thena ferent densitiesand same velocities.The changesin both decrease[ Fig. 4 (e) ] for d - 20. III. LOADING EFFECTS ON SKIMMING WAVE MODES A. Phase curve distortion Thedifficultyin observing skimming wavescomes from notonlyRayleighwavesthatcoverthemby morethanone orderofmagnitude, butalsofromthelargeimpedance ratio between solids andliquids.Therefore,. to remedy thisprob- lem,onewouldeithermatch,to a highdegree, theimpedances of thecoupling liquidsandtheobjects, or reducethe openingangleof thelensin sucha wayto justincludethe longitudinal criticalangle. •6In thepresent study,wecombinebothapproaches. Bycomparing Fig. 1(a) and(b), nearlongitudinal criti- calangles, wenoticethatthefluctuation ismoresignificant for themercury-tungsten interface. However, unlikeRayleighwavemodes, in thevicinityof 0L thephase curvedoes notexhibitlargevariations overanextended angular range. It increases verysharply at 0L thendecreases lessrapidly, amplitudeandphaseat criticalangles0• and 0R are studied in detail.For generalizedleakyRayleighwaves,whosemodulusof R (0) goesto unity, the kink of phasechangeis related to generalizedRayleigh velocity. Hence VR, increases from V• - 2630 m/s to Vr = 2835 m/s for tungstenasthe impedanceratio approachesunity due to a high coupling betweenliquidsand shearwaves.Experimentalresultsobtainedon tungstenwith water and mercury,well agreewith theoreticalpredictions. The couplingliquidshaveno loadingeffecton longitudinal velocities,but they changethe efficiencyof skimming modesgeneration.This efficiencyis more enhancedwhen the impedances of liquidsand solidsare matchedand when smallaperturelensesare used. 12 dueto theonsetof Rayleighmodeinfluence; in thatcaseone wouldexpect nosignificant longitudinal velocity change. B. Velocity variation In thecalculation of V(z) curves, representing longitudinalwavemodes,similarstepswerefollowedasin Sec.IIB for thesamesolids,liquids,andconditions. However,care mustbetakenin choosing thelensopening anglein sucha way to avoidmultiplecriticalangleswhichwouldconfuse V(z) response.Therefore, /9lens was chosensuch that 0•ens -- (0• -t- 1ø)-- 18øinordertogetthebestgeneration of skimming modes. •5The importantobservation is that the 1549 J. Acoust.Soc.Am.,Vol.92, No. 3, September1992 0 10 20 30 40 Liquids density FIG. 6. Efficiencyof longitudinalskimmingmodesasa functionof coupling liquidsdensityfor tungsten.The openingangleof the lensis setat 18ø. Doghmaneeta/.' Couplantmassloadingeffects 1549 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 134.71.135.191 On: Tue, 25 Nov 2014 11:15:03 ACKNOWLEDGMENT Thisworkwascarriedout under"l'a½½ord programme Franco-Alg•rien No. 90 MDU 152." 7j. Attal, "AcousticMicroscopy ImagingMicroelectronic Circuitswith LiquidMetals,"in Scanned ImageMicroscopy, editedby E. A. Ash (Academic,New York, 1980), pp. 97-118. 8j. Kushibiki, T. 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