Cryogenic Acoustic Microscopy 1980

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    Cryogenic acoustic microscopyJ. Heiserman, D. Rugar, and C. F. QuateEdward L. Ginzton Laboratory, Stanford Uniuersity, Stanford, Califurnia 94305(Received 17 October 1979; accepted lor publication 8 February 1980)Resolution in the scanning acoustic microscope is determined by wavelength which is in turn limited byattenuation in the acoustic medium. In order to make use of the 1ow attenuation found in cryogenicliquids we have developed an acoustic microscope suited for use at low temperatures. In this paper wepresent images taken in liquid argon held at 85'K and in superfluid helium at 1.95'K. In liquid argon,wavelengths as short as 0.43 ,um were achieved while in preliminary work with superfluid helium awavelength of 0.36 prm was used. In order to operate in liquid helium, it was necessary to improve thepower transfer from the acoustic lens to liquid helium by using double quarter-wave matching layers.Techniques of fabricating and testing these layers are described. Finally, prospects for operating at stillshorter wavelengths in superfluid helium held at temperatures below 0.5'K are discussed.PACS numbers : 43.35.Lq, 43.35.Ns, 43.35.Yb, 43.35.Sx

    INTRODUCTIONSince the introduction of the scanning acoustic micro-scope by Lemons and Quate in 19?4,1 the resolution hasbeen increased to the point where wavelengths com-parable to those of visible light are employed.2 Pro-

    gress to shorter warrelengths is hampered by losses inthe coupling fluid which limit the maximum frequency ofoperation and hence the warrelength. Through the use ofcryogenic liquids we haye extended the limit on minimumwavelengthbeyond what is presently possible at room tem-perature. We expect as we develop this techniquefurther, wavelengths much shorter than those of visiblelight and hence resolution substantially better than theoptical microscope will be within reach.Fult descriptions of transmission and reflection modescanning acoustic microscopes are given elsewhere.sHere we wil.I simply summarize the operations of thereflection mode as shown in Fig. 1. A collimated beamof acoustic pulses is generated by a zinc oxide thin filmtransducer deposited on a sapphire rod. At the frontend of the rod a small spherical depression in contactwith the coupling liquid (usually water in the room tem-perature instrument) serves as a lens. Because of thelarge velocity difference between sapphire and water(a factor of 7.4) acoustic power incident on the inter-face is focused to a spot in the liquid. The object tobe examined is placed at or near the focus. Sound re-flected by the object is collected, recollimated by theIens and detected by the transducer which is sensitiyeto both the phase and the amplitude of the returningacoustic wave. The detected signal is used to modulatethe brightness of an oscilloscope dispLay or is stored in

    an analog scan converter. The object is then scanned ina raster pattern and the motion is synchronized with thex and y Etxes of the display. The image obtained in thisway can be recorded on photographic film.The key to the acoustic microscope lies in the spheri-cal interfacebetweenthe sapphire andthe liquid. There,the velocity ratio is large and the spherical aberra-tions-proportional to the square of this ratio3-arenegligible. The acoustic beam is focused to a spotwhose diameter is limited only by diffraction. It isnot possible to construct an analogous aberration-freesingle surface optical lens since optical index of re-

    fraction ratios are Limited to about two.Although large velocity differences are beneficial,large acoustic impedance differences limit the powertransfer to the coupling liquid and are undesirable.Power transfer efficiency is improved by using one ormore quarter wave matching layers, In the sapphire-vr'ater case a single glass quarter-wave matching layeris used.Resolution in the scanning acoustic microscope im-proves as wavelength in the coupling tiquid is reduced,In most liquids at high frequencies attenuation increas-es as frequency squared and this factor limits themaximum operating f requency. This limitation can beoff set by reducing the liquid path by making lenses ofsmaller radius. Current versions of the acousticmicroscope use a lens with a radius of about 30 prm.For maximum operating frequency one must choose acoupling liquid with low attenuation and low acoustic

    uelocity. In order to assess the usefulness of variousfluids as a working medium for the acoustic micro-scope, a coefficient of merit has been defined whichcompares each fluid to water.a This coefficient is de-fined as follows:M =\./x. (1)

    Here ),, is the minimum achievable wavelength in waterTNPUT rf-ffUfllrH'

    OUTPUTCIRCULATOR

    TO OUTPUTELECTRONICSANO OISPLAYELECTRICALMATCHINGNETWORK r TRANSDUcER

    LENS

    ANTI-

    MECHANICALLY SCANNEDFIG. 1. Schematic of a reflection mode scanning acoustic mi-croscope.

    1 629 J. Acoust. Soc. Am. 67(5), May 1980 000 1 -4966/80/05 1 629-09$00.80 @ 1980 Acoustical Society of America 1629

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    TABLE I. Properties of various cryogenic liquids compared to water.Temp a/1zx1gtt P Cx10-5 ZxlO4Liquid "K d:i s2,/cm g/cms cmls g/ cmz s M Refs'

    Hzoo2N2H2XeArNeHe

    25"C60'c907720

    16687274.21.950.4

    1919586L2049

    191L322011966

    610154

    1.01.0L.140.800.072,9t.41.2o.t470.1460.145

    1.51.50.900.851.190.630.840.600.1830.2270.238

    1.51.51.00.680.081.8L,20.720.o270.0330.035

    1.0 6t.4 62.5 6-82.2 6-92.3 62.4 62.2 102.4 62.5 6,113.7 Lt,lz23 t3,t4aAs described in the ted, at this temperature a scales as /. This value is from the data of Ref. 14extrapolated to 1 GHz.and tr is the achievable wavelength in the given liquid.We can express M in terms of the absorption coeffi-ciert (a/72) and the velocity of sound C. We will makeour comparison with water at 25"C, where d./f2,, eqvals191 x 10-1? dB s2/cm and C*= 1.5 x1O5 cm/s. We takeaL, lhe total attenuation through the liquid cell, and1., the acoustic path length in the liquid, to be con-stanL We can then write

    x, =Z=911 r. etJ" dL T'In ptace of Eq. (1) we can now writeM=I-=%.(%,UJ\'''. (B)I C\d/f'/For those liquids where the attenuation scales as fre-quency squared we let f.=f. For other liquids we mustspecify the frequency used in the comparison. Sincewe want Liquids with large values ol M we look for thoseliquids with a low value for both the velocity C and theattenuation o. Several fluids of potential interest arelisted in Tabte I. There we find that values lor M bet-ween 2 and 4 can be realized for a number of cryogenicfLuids. For the special case of helium very large valuesmay be possible.

    A number of factors can contribute to contrast in thescanning acoustic microscope. Specular and diffusescattering occur at the liquid-object interface. Somepower is converted to longitudinal and shear waves inthe sample which can be scattered by boundaries orinternal imperfections or absorbed. Some power maybe converted to surface waves at the liquid-sampleinterface. This "Leaks" back into the liquid with itsphase shifted and may be detected by the transducer.This tast mechanism is very sensitive to the lens toobject spacing and leads to great sensitivity to heightchanges and material differences.sI. CRYOGENIC APPARATUS

    The mechanical apparatus used in the room tempera-ture acoustic microscope is not well suited to use withcryogenic fluids. It is necessary to use a design inwhich the complete microscope assembly is immersed

    directly in a cryogenic bath. It is desirable, however,to adjust the alignment with water at room temperaturebefore cooling down to cryogenic temperatures. Thusstrict thermal compensation is needed to ensure thatthe lens to object spacing does not change between roomtemperature and the cryogenic temperatures, i.e.,during a change of up to 300'K.A diagram of the assembly used is shown in Fig, 2.Coarse adjustment of the focal distance is made witha pushrod that is controlled by a differential micro-meter head at the top o[ the assembly. The pushrod isspring loaded by two diaphragms in the cryogenic liquid

    and thus has negligible backlash. Fine focus is achievedby a piezoeLectric positioning element (BurleighInstruments PZT aLigner-transtator) located in theOIFFERENTIAL MICROMETER

    TOPPLATE

    HE ATSHIELDS

    VACUUM FEEDTHROUGH

    SUPPORT ROD

    1630

    RF CABLE

    MAG NE T

    PZT ALIGNER /TRAN SLATORLENSSAMPLE SUPPORTPEOE S TA LCOIL SUPPORT

    FIG. 2. Schematic of the assembly used in cryogenic liquids.J. Acoust. Soc. Am., Vol.67, No.5, May 1980 Heiserman ef a/.: Cryogenic acoustic microscopy 1630

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    ACOUSTICOBJECT

    CRT OISPLAY

    L ENS,30 nsrt PULSE CIRCULATOR

    t60 MH Z

    cryogen and acting in series with the coarse adjust.The fine adjust altows 1 prm total mosement (at 2'X)and about 100A position resolution. Electrical con-nections are made to feedthroughs in the top plate toallow for thermometry and control and monitoring sig-nals for the PZT positioner and scanning stage. Therf drive and signal pulses are carried through the topplate on a stainless steel semirigid coax. Details oftypical rf and control electronics are shown in Fig. 3.

    An important part of the scanning acoustic micro-scope is the mechanism that mechanically translatesthe object through the acoustic beam in a raster pattern.A cross section of the mechanism used at cryogenictemperatures is shown schematically in Fig. 4. Thesample is mounted horizontally in a sample holder ontop of a flexible pillar made of a 9-cm length of smalldiameter aluminum tubing, Mounted below the sampleholder are four small coils of wire spaced at rightangles in a plane normal to the pillar; only two of thefour coils are shown in Fig. 4. Situated about each coilis a set of stationary cobalt-samarium magnets. Twoof the coiis, an orthogonal pair, are used to drive thetop of the flexibLe pilLar and sample holder in the twofree dimensions. The other two coils are used to detectthe velocity of the sample holder. The velocity signalsare used in a servo loop to improve the mechanicalresponse of the system and to reduce the effect of anyexternal vibrations coupled into the scanner. VelocitysignaLs are also integrated to give the position of thesample. External vibrations might couple into themechanical system of the scanner, but with this systemthe true position of the sample is always accurately

    known. This position information is used to control theelectron beam of the CRT display (or scan converter)so that the position of the beam is synchronized with theposition of the sample. The fast axis of the rasterscan is usually driven at a 30-Hz rate. The time re-quired to scan one frame varies from 10 to 30 s.The top of the flexible pillar travels in an arc ratherthan a plane and as a result the lens to sample spacingchanges as the sample is scanned. The effect is small,however, because the pillar is relatively long and thescanned field is generally Iess than 250 pm on a side.The piezoelectric positioning element is sometimes

    rqrLL_-____

    FIG. 3. Block diagram oftypical electronic compo-nents used in the cryogenicscanning acoustic micro-scope.MIC ROSCOP EVIOE OIN FORMAT ION

    SENSECOI L

    MOTION

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    used to control the focal position of the lens to com-pensate for nonplanar motion of the sample'Tests in liquid argon indicate that for our presentLevels of external vibration the scanner can execute araster scan to within 0.2 pm of an ideal raster pattern'Furthermore, when the scan deviates f rom the idealpattern, the position of the sample is at aII times knownwith an uncertainty of Iess than 0.1 pm. In liquidhelium vibrations from the vacuum pump used to main-tain the helium bath at 1.95 "K degrade the scanner per-formance and image quality to some extent. We expectto be able to correct this in the future by further isola-tion of pump vibrations, increasing the stiffness of theflexibte pillar, and improving the scanner electronics'

    II. OPERATION IN LIOUID ARGON AND NITROGENA benchmark in our efforts to operate the acousticmicroscope at cryogenic temperatures was establishedwith liquid argon held at about 85 1K. This liquid waschosen based on its inertness, high figure of merit, andrelatively large acoustic impedance. This last feature

    altowed us to use the same sapphire lenses as we haveused in water. A single quarter-wave matching layer ofglass provided a good power match. In tiquid argon thecryogenic microscope was operated at 2 GHz where thewavelength was 0.43 pm, equal to wavelengths in theviolet part of the optical spectrum. The high resolutionof the argon microscope is demonstrated in Fig. 5.Here a comparison is made between acoustic, scan-ning electron, and optical micrographs of a photoresistgrating.ts The grating was made by exposing a 0.15-pm layer of photoresist on a silicon wafer using twointerfering optical beams. The photoresist lines are0.2 pm wide and the center-to-center spacing between

    Iines is 0.4 prm. The acoustic microscope clearly re-solves the lines with a considerable amount of detail onthe line edges. The contrast is excellent. After viewingacoustically the sample was coated for viewing in thescanning electron microscope [sBu, fig. 5(b)]. Theresolution is far better in the SEM image, butneverthe-Less the acoustic image shows a surprising amount ofsurface detail when compared to the SEM image. Figure5(c) shows the same object viewed with an opticalmicroscope fitted with a high power, dry objective.The change in the index of refraction between air andphotoresist is smaII and it was also necessary to en-hance the optical contrast by coating the sample witha metallic fi[m.We have examined several other objects in the argonmicroscope chosen from materials, integrated circuits,and biology. We were able to produce excellent imagesof a spread of human metaphase chromosomes whichare natural objects with submicron structures.r6 Con-trast in these objects was high and resolution was atleast as good as high quality oil immersion opticalmicrographs. Figure 6 was chosen to illustrate theimaging performance with integrated circuits. Theobject here is a microwaye dual gate field effecttransistor (FET)1? and the two linear features arethe gate electrodes which are 1 pm wide. Figures6(a) and 6(b) are acoustic micrographs taken at two

    (b)

    (c )FIG. 5. Images of a photoresist grating: (a) acoustic micro-graph in liquid argon, (b) scanning electron micrograph, and(c) optical micrograph using high power, dry objective. Lineperiod is 0.4 pm. Images show different areas of the sample.

    different focuses. Figure 6(c) is an optical image ofthe same device using a high power oit immersion ob-j ective.

    We have also operated the microscope in liquid nitro-gen at 77 "K using a drive frequency of 1.9 GHz. Re-duction of frequency compared to argon was necessarydue to the lower acoustic impedance of Iiquid nitrogen.As predicted in TabIe I, results were very similar toargon at a comparable frequency. Since liquid nitrogenis less expensive and more readily available thanliquid argon, we will continue our investigations withthis liquid.

    W(o)

    t

    1632 J. Acoust. Soc. Am., Vol.67, No.5, May 1980 Heiserman et al.: Cryogenic acoustic microscopy 1632

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    (o)4.

    FIG. 6. Images of a high frequency field effect transistor.Parallel, horizontal Iines are gate electrodes and are 1 trtmwide: (a) and (b) acoustic micrographs at two different focuses,(c) oil immersion optical micrograph,III. LIOUID HELIUM

    Liquid helium is the most promising cryogen for usein acoustic microscopy and so we have designed ourapparatus to be suitable for use in helium at tempera-tures down to about 1.1oI{.The velocity of sound in Iiquid helium is nearly con-stant f rom ahsolute zeto to temperatures near thetambda temperature, Tt=2.17 1(, but the attenuationvaries considerably in this range. The attenuation o isplotted against 7' in Fi.g. 7. The data is from measure-ments by Imai and Rudnickri at 1 GHz and Abrahamet al.,\a extrapolated from 208 MHz. Above 2.5 T( thevariation is understood in terms of classical mecha-

    t04

    to3

    to2

    O.l t Tr lOT (.K )

    FIG. 7. Attenuation of sound in superfluid helium at 1 GHz asa function of temperature. High temperature (solid line) datafrom Ref. 11, low temperature (dashed line) data extrapolatedfrom the data of Ref . 14 at 208 MHz.nisms; viscosity and thermal conductivity contributeto this loss. Attenuation in this regime scales as fre-quency squared. The sharp peak at ?, where heliumbecomes a superfluid is due to the presence of a second-order (lambda) phase transition at this temperature.The broad peak at 1.4 "I( followedby a rapid falloff inattenuation at lower 7 is somewhat surprising. Tounderstand these effects, we recall the behavior ofthe mean tree path of thermal phonons in the liquid atthese temperatures.

    At temperatures near the peak, the phonon mean freepath is determined mainly by scattering between pho-nons and rotons, the high momentum thermal excita-tion found in superfluid helium. Figure 8 shows thetemperature dependence of the phonon mean free pathcharacterizing viscosity from a calculation by Landau

    t04roo

    I

    Nr9oEoID!t,

    o.t

    (c)

    ?3IF(LlrJlrJErzlrJz o.o lo.6 t.o r.4 r.8 2.oT (.K)FIG. 8. The viscous mean free path of phonons in superfluidhelium as a function of temperature. From data of Ref. 18.

    .lr rul l*4' :": .

    1 633 J. Acoust. Soc. Am., Vol.67, No. 5, May 1980 Heiserman et al.: Cryogenic acoustic microscopy 1633

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    and l(halatnikov.ls From this it is evident that at thepeak in attenuation the viscosity mean free path is ap-proximately equal to the acoustic wavelength. At 1GHz this is about 0.2 pm. The peak itself results f roma relaxation process between the equiLibrium popula-tions of rotons and phonons.tn Well above this tempera-ture (the thermodynamic regime) we can assign valuesof pressure and temperature to regions small comparedto an acoustic wavelength and thermodynamic argu-ments apply. Howerrer at very low temperatures (betow0.6'K) the mean free path is large compared to anacoustic wavelength and the thermal phonons are notable to establish equilibrium during one acoustic period.We can no longer resort to an equilibrium thermody-namic description of the system. In this limit, knownas the collisionless regime, we must consider thestatistics of scattering of acoustical phonons by the gasof thermal phonons. From consideration of a three-phonon process a new dependence for the absorption atlow temperatures can be obtained where (for hf

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    tooF

    o.80 0.90 l.o r.r 1.2t/tofIG. 10. Calculated transmission coefficient from sapphireto liquid helium using the gold glass quarter-wave matchinglayers of Fig. 9.pedance equal to the geometric mean of the values forthe solid and the liquid helium. For fused quartz thisideal val.ue is O.? x lO5 g/cm2 s. For sapphire it is1.2 x 10s g/cm2 s. Unfortunately few solids possess sucha low value of acoustic impedance.

    It is possible, however, to add a second quarter-wavematching layer and improve the match at the expense

    of bandwidth. The first layer is chosen to have a veryhigh acoustic impedance. This effectively increases theimpedance of the lens material and makes it possible tochoose as a second layer a material of relatively highimpedance and still produce a reasonable match intoIiquid helium. We can compare the different combina-tions with the following expression for the transmissioncoefficient. It is written in terms of the impedances ofthe lens material (2"), the first and second layers (2,and Zrl and the hel.ium (Zr") (see Ref. 20):r=(-*#"/=z?:\. (5)' '\(zzz"/zl+ z4), f 'This expression is vatid for lossless isotropic mediaat thequarter-wave resonant frequency of the layers.For a single layet Zr= Zr". ln Tabte tI we list a varietyof possibte matching schemes and compare theirtransmission efficiencies. We have experimented withseveral of these schemes and for our initial effortshave chosen a double layer composed of gol.d and glasson sapphire.

    The properties of quarter-wave matching layers foruse in helium were initially evaluated using water at

    (b)

    fIG. 11. Optical [eft) and acoustic insuperfluid helium (right) images of asilicon on sapphire integrated circuit.Acoustic wavelength is 0.36 pm. Lensto object distance increases from (a) to(c). Horizontal bars are polysilicon,10 pm wide and 0.5 trm thick. Verticalbar is aluminum, 15 pm wide and 1.0pm thick.

    (c)

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    room temperature. Test "flats" were prepared bydepositing ZnO transducers on one end of a short(1 mm) sapphire rod with the c axis aligned along therod axis. The ends of the rod were accurately paratleland carefully polished. The fitms to be evaluated weredeposited on the opposite end. Acoustic pulses centeredat lrequency f were generated in the rod and theecho train produced by the multiple reflections ob-served on an oscilloscope. The amplitude of a parti-cular echo (normally the first) was measured with therod in contact with air (total reflection) and with a dropol water applied to the matching layer end. The ratioof these amplitudes squared (or the difference in deci-bels) is the reflection coefficient of the test piece-water interface at the f requency/. Measurements atseveral frequencies near the quarter-wave resonantfrequency of the layers gives the frequency dependenceof the reflection coefficient. For the case of a singlelayer the center frequency together with the measuredthickness of the layer yields a value for the longitudinalvelocity of sound in the layer (C) while the magnitudeof the reflection coefficient gives the acoustic impe-dance. For two layers of thicknesses d, and d, the ex-pected frequency dependence of the reflection coefficient/?(/) can be written in the same approximation as Eq.(5) as'"

    Rl0=lz=- z='l' , (6)lZ+Lt Iwhereo Z"Zr- Z"Zrtand, tan6, -i(Zltand>, rZrZrtan6r) ao - or,O t= (zrf / C ,)dt ,O z= (zrf / c 2)d, .For two layers the impedance and velocity of the lowimpedance, outer layer are separately evaluated. ThenEq. (6) with Zr= Zr c1n be inverted to obtai.n Zr. Fromthese measurements the expected transmission coeffi-cient into liquid helium T(f) can be calculated usingEq. (6) with Z,= Zs" lnd recalling that ?(/)=L -R(f).

    Figure 9 shows data taken on a gold glass matchingdevice evaluated using water. Figure 10 shows the pre-dicted frequency dependences of the matching section inliquid hetium. At the center frequency, the transmis-sion coefficient to helium is about 670. This can beimproved upon using different materials as indicated inTable II, but the gold-glass matching section was ade-quate for initial work at 630 MHz with the temperatureheld at 1.95 "K. At this temperature and f requency thewavelength in liquid helium is 0.36 pm.

    For our first object in liquid helium we choose asilicon on sapphire integrated circuit. Optical andacoustic micrographs are shown in Fig. 11. The verti-caI bar is aluminum and is 1,0 pm thick. Successiveacoustic micrographs were taken at slightly differentfocat positions. Figure 11(c) is the greatest lens toobject spacing and represents focus on the top of thealuminum stripe. The image of Fig. 11(b) is slightlycloser focus and that of FiS. 11(a) is closest. Depth offield and phase effects are evident in (c) where only

    the thicker aluminum is visible. Due to the imperfectmatch (even with the layers most of the acoustic poweris reflected at the sapphire-helium interface and re-mains in the crystal) the information pulse interferedwith pulses in the sapphire rod resulting in the fringesand contrast variations evident in the images. Such de-fects will be eliminated by improving the match. Evenso features with sizes in the micron range are evident,especially edge roughness apparent in Fig. 11(a).IV. CONCLUSION

    We have obtained preliminary results from an acous-tic microscope operated in cryogenic liquids. Refine-ment of these techniques wiII allow wavelengths wellbeyond those of visible light to be employed for acous-tic microscopy. The improved resolution thus obtainedwiII extend the range of sizes accessible to acousticmicroscopy to about 0. 1 pm. We now have a plan forconstructing a microscope for use in superfluid heliumbelow 0.5 oK. There the operating frequency can beincreased and we expect a corresponding increase in theresolving power.Apart from the increase in resoiution acousticmicroscopy at cryogenic temperatures will makepossible sorne novei observations. Potentially im-portant applications lie in the study of solids at lowtemperatures. We are particularly interested in thestudy of the intermediate and mixed states of super-conducting materials. Because the difference in acous-tic attenuation between the normal and superconductingstates is typicatty large at high frequencies and tem-peratures well below the transition temperature, itshould be possible to obtain sufficent contrast to di-rectly image the Iamellar structure of type I samplesand the vortex array found in type II materials. With

    such observations we hope to study the time and mag-netic field dependent behavior of these effects in detail.ACKNOWLEDGMENTS

    Lance Goddard deposited the thin films used in thisstudy. The authors would like to acknowledge the sup-port of the Office of Naval Research, Physics Programthrough contract N00014-77-C -0412.

    lR. A. Lemons and C, F. Quate, Appl. Phys. Lett.24, 163-1650974\.2V. Jipson and C. F. Quate, Appl. Phys, Lett. 32, 78g-7g7(1978).3R. A. Lemons and C. F. Quate in Physical Acoustics, editedby W. P. Mason (Academic, New York, 19?9), Vol. XIV.aJ. Attal and C. F. Quate, J. Acoust. Soc. Am.59,, 69-73(197 6 ).5A. Atalar, J. Appl. Phys.49, 5130-5139 (19?9).6M. Greenspan in American Institute oJ Physics Handbook(Ntccraw-Hill, New York, 1972), 3rd ed., Chap. 3e.?B. G. Dudar and S. .A.. I\{ikhailenko, Sov. Phys.-Acoust. 22,287-292 (1976).8A. Van'Itterbeck and W. Van Dael, Physica 28, 861-8?0(19 62 ).sA. Pine, J. Chem. Phys. 51, 5171-5173 (1969).10J. S. Imai, Doctoral dissertation, UCLA, 1969, Appendix B;1636 J. Acoust. Soc. Am., Vol. 67, No. 5, May 1980 Heisermaneta/.: Cryogenicacousticmicroscopy 1636

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    D. G. Naugle and C. F. Squlre, J. Chem. Phys.42, 3725(1965h D. S. Swyt, J. F. Havlice, andE. F. Carome, ibld.47, rt99-L200 (1967).rlJ. S. Imri and I. Rudnick, Phys. Rev. Lett. 22, 694-697(1969); M, A, Woolf , P. M. Platzman, and M. G. Cohen, ibiil-17,294-297 (t969\.12J. H"i"erman, J. P. Hulin, J. Maynard, and I. Rudnick,Phys. Rev. B 14, 3862-3867 (1976).l3J..wilks, LiEtiil and Soti,it Heli.um (oxford U. P., oxford,1967).1{8. M, Abraham, Y. Eckstein, J, B. Ketterson, M. Kuchnir,and J. Vignos, Phys. Rev. 181, 347-373 (1969). For a re-cent review of theoretical developments see H. Maris, Rev.Mod. Phys. 49, 341 (19771.

    tScourtesy of IBM Corporation.r6D. Rugar, J. Heiserman, and C. F. Quate, J. Micros. (Ox-ford) (in press).l?Courtgsy of Hewlett-Packard Corporation,18L. D. Landau and I. M. Khalatnikov, Sov. Phys.-JETP 19,709-730 (1949). Translation: Coll,ected Papers of L, D.Landaa, edited by D. Ter Haar (Gordon and Breach, NewYork, 1965), p. 511.10I. M, Khalatnikov and D. M. Chernikova, Sov. Phys.-JETP22, 1336-1346 (1966); 29,274-286 (1s66).20I-. Brekovskil