Ultrasonic measurements in fine powders using aphotoacoustic pulse-generation technique

Wayne Imaino and Andrew C. Tam

In this paper, we demonstrate the applicability of PA pulse generation for the monitoring of ultrasonic prop-erties of powders, for example, uncured carbon-loaded epoxy resin powders, whose average particle diameteris -15 gim. The acoustic pulse is generated by a short laser pulse (10-nsec or 1-Asec duration) of 1-10-mJenergy and is detected by a piezoelectric detector (polyvinylidene difluoride foil or commercial lead zircon-ate titanate transducer). This allows ultrasonic measurements over a broad range of porosity and pressureconditions, from loose unconsolidated powers to heat- and pressure-sintered pellets. For loose powders atatmospheric pressures (with a porosity of -50%), the acoustic velocity is remarkably small (typically 3 X 103cm/sec), and attenuation and dispersion are large. This appears to be the first demonstration of the use ofa PA technique to measure ultrasonic properties in powders.

1. Introduction

An understanding of the interparticle interaction inpowders is essential to the solution of a wide range ofproblems associated with the handling of finely dividedmaterials, such as soils, sands, grains, fibers, and xero-graphic toners. Much of our current understanding ofthe properties of unconsolidated materials comes fromthe extensive research in acoustic propagation throughsediments, rocks, and sands' in connection with variousgeophysical applications; the theories due to Wood,2Biot,3 Gassman, 4 Deresiewicz, 5 and others 6 have beensuccessful in calculating the acoustic propagationproperties from a knowledge of the material parametersand interactions in the composite material consistingof a porous powder and a permeating fluid. These au-thors have studied the dependence of the extremelyslow acoustic velocities on porosity, depth, pressure,interparticle bonding, and other parameters. Muchrecent interest in the acoustic propagation throughpowders have been induced by Plona, 7 who discoveredexperimentally the "slow" compressional wave pre-dicted theoretically by Biot3 in 1956; furthermore,Johnson8 had recently shown that Biot's theory3 is ap-plicable to the problem of the propagation of the fourthsound in liquid helium.

The authors are with IBM Research Laboratory, 5600 Cottle Road,San Jose, California 95193.

Received 13 January 1983.0003-6935/83/121875-04$02.00/0.© 1983 Optical Society of America.

Our present work is directed toward an under-standing of the particle-particle interactions in xero-graphic toner powders. Acoustic pulse velocity, at-tenuation, and dispersion are measured using thetechnique of PA pulse generation instead of the con-ventional method of contact transducer generation.1The advantages of PA generation in powders include thefollowing: (a) Acoustic pulses can be produced on a freesurface. (b) Complexities due to the properties of thegenerating transducer (rise time, ringing etc.) areeliminated. (c) The serious impedance mismatch be-tween the generating transducer and the powder iseliminated. (d) A wide range of acoustic signals can beproduced by varying the temporal or spatial profiles ofthe laser beam. To our knowledge, the present work isthe first demonstration of a PA technique for acousticmeasurements in powders.

11. Experimental Apparatus

The present work is mainly concerned with carbon-loaded epoxy powders which are commercially availablemonocomponent xerographic toners9 with a mediandiameter of 15 ,gm. These irregularly shaped particlesare composed of a solid state suspension of particulatesof Fe3O4 (0.5-ttm diam) and carbon black (0.1-gm diam)in an uncured epoxy matrix. We have also made lim-ited measurements on finely divided copper pow-ders. 10

A schematic diagram of the apparatus used to mea-sure the acoustic properties of loose powders at atmo-spheric pressure is shown in Fig. 1. The optical sourceis a flashlamp pumped dye laser'" producing laser pulsesof 10-mJ energy and 1-psec duration at a -6000-A

15 June 1983 / Vol. 22, No. 12 / APPLIED OPTICS 1875

Fig. 1. Schematics of the apparatus to measure acoustic propaga-tions in loose uncompressed powders in air using PA pulse generation

and piezoelectric detection.

glass scopepowder / window\X t ~PVF2 H

c ill o c ososcope

Fig. 2. Schematics of the apparatus to study effect of high appliedpressure. The powder (dotted) is in contact with a transparentwindow at the top and with a PVF2 piezoelectric foil at the bottom.

wavelength. The laser pulse is directed onto the freesurface of the powder contained in a steel cylinder of 4cm diam; the depth of the powder can be accuratelycontrolled by a micrometer, which is adjusted so thatthe powder column always extends to the top of the steelcylinder to avoid any air column resonance effects. Theweight of the powder used for each height is measured,and the porosity is calculated from the apparent powderdensity (powder weight/column volume) and the neatsolid density, i.e.,

porosity = n = - apparent densityneat density

A lead zirconate titanate (PZT) transducer12 is used todetect the acoustic pulse transmitted through thepowder column; its output signal is amplified13 and fedinto a waveform averaging oscilloscope.14

To study acoustic propagation in compressed pow-ders (or in sintered powder pellets), an acoustic detectorwith faster rise time than that of the above lead zir-conate titanate transducer (1 sec) is needed becauseof the faster velocity. A polyvinylidene difluoride(PVF2) foil'5 with a rise time of -10 nsec is used. The

apparatus is schematically shown in Fig. 2; for thecompression study, a thick-walled rubber annulus of6-mm height is used to contain the powder. It is suffi-ciently leaky so that the air pressure in the pores of thepowder remains at atmospheric pressure, while thepowder is subjected to high-compression pressure byusing a jackscrew arrangement. The laser source is stillthe flashlamp pumped dye laser. For the sinteredpellet study, a shorter laser pulse is needed, because thevelocity is even higher; in this case, we use a nitrogenlaser' 6 producing near-UV laser pulses (3371 A) of 1-mJenergy and 10-nsec duration.

A typical PA signal observed on the oscilloscope isshown in Fig. 3.

Ill. Results and Discussions

Figure 4 shows a plot of the arrival time t vs theacoustic path length x for a loose uncompressed tonerpowder at a porosity of 49%. This porosity value rep-resents the natural porosity of the powder as pouredfrom its container and (after some initial settling) isstable over many days. This rather high value of po-rosity (much higher than the theoretical value of 38%

Fig. 3. Observed PA pulse signal for a compressed toner powdersample. The compression pressure is 7000 psi, and the acoustic path

length is 5.5 mm.

0.5

0.4

R

Ea)E

0.3 I

0.2 I

0.1 l

0.0 L)o 0.5 1.0 1.5

distance (cm)

2.0 2.5

Fig. 4. Dependence of the propagation time on the path length (i.e.,depth) of a loose uncompressed toner powder (Hitachi HMT 208) in

air.

1876 APPLIED OPTICS / Vol. 22, No. 12 / 15 June 1983

HMT 208 ez'n=49%

.X v=4700 cm/sec

,"6

l l fi

I

for close packing of identical spheres) is due to bridgingeffects17 which occur partly because of the attractiveforces between particles. The most striking feature ofFig. 4 is the very low acoustic propagation velocity in theloose powder, much lower than that in air or that in theneat solid material of the powder. This behavior canbe interpreted by a theory due to Biot, 3 which at lowfrequencies reduces to a modified version of Wood'sequation according to Gassman.4 In Gassman's treat-ment, the (longitudinal) acoustic velocity is given by

V = (K/p)l/2

5.5

5.0 -

00)

0

4.5 _

4.0 _

(1)

where

K Km[(Kb + Q)I(Km + Q)],

Q = (Kj(Km - Kb))/I[n(Km - Kf)],

p = npf + (1 -n)pm.

Here K, Kf, and Kb are the bulk moduli of the solid,interstitial fluid (air), and particle matrix (skeleton),respectively, pf and pm are the densities of the inter-stitial fluid and of the neat solid material of the parti-cles. In the limit of a very fine loose powder with thecondition Kb << Kf << Km being satisfied, we have ap-proximately

V - (Kf1 p)112, (2)

suggesting a simplified acoustic propagation model forthe powder where the elastic modulus is that of the airand the density is that of the powder. The approximateEq. (2) very simply explains the exceedingly lowacoustic propagation velocity through loose unconsol-idated and uncompressed powders. However, it onlyprovides a rough estimate; more precisely, the bulkmodulus of the power is due to two origins: the inter-stitial air, and the particle-particle interactions asrepresented by Kb, which is sometimes called the framemodulus. We may use Eq. (1) to calculate Kb from themeasured acoustic velocity; the data of Fig. 4 correspondto a value of Kb = 9.75 X 107 dyn/cm 2 . When thesample is repeatedly tapped to cause settling of thepowders, the porosity asymptotically approaches 32%,which is lower than the theoretical limit 6f 38% foridentical spheres, since the sample is composed of var-ious sizes. At this more densely packed state (porositybeing 32%), the longitudinal acoustic velocity becomes7 X 103 cm/sec, indicating a larger frame bulk modulus,Kb = 2.92 X 108 dyn/cm 2 .

For a system of cohesionless particles, the framemodulus may be estimated as6

Kb = 1.5[Em/(l - r2)2/5R2/5p3/, (3)

where E is the Young's modulus of the bulk neat solid,m is the average number of contacts made per sphereper unit displacement, r is the Poisson ratio, R is theeffective radius of the particles, and Po is the pressureapplied onto the particles. This equation predicts thatthe frame modulus averaged for a powder column depthx goes as x3/5 if Po is due to the weight of the particlesonly. This implies a nonlinear relationship betweenpropagation time t vs depth x, whereas Fig. 4 indicates

. 52.5 3.0 3.5

log1 0 pressun

1.8

I1.3 U_

00

0.8

4.0 4.5

Fig. 5. Observed data for the acoustic properties of a toner powder(Hitachi HMT 208) depending on the applied pressure in psi. Theunit for the velocity is cm/sec, and for the FWHM of the acoustic pulse

is gsec.

a linear relationship. This can be explained as follows:due to the bridging effect'7 in the toner powders, pres-sure is not transmitted hydrostatically; e.g., the flow rateof the powder through an orifice is nearly independentof the height of the powder above it; the external pres-sure Po in the toner powder is composed of two terms-alarger term due to the effect of interparticle forces anda smaller term due to the head pressure (i.e., depth -density gravitational acceleration). In comparison,the t vs x plot for copper powders is found to be no-ticeably nonlinear, with velocity increasing with depth.This suggests that in copper powders, Po is mainly dueto the weight of the particles in contrast to the situationfor the polymeric particles.

To explore Eq. (3) further, we plot the observedacoustic velocity V as a function of pressure Po appliedon the toner powder by using ajackscrew. This log-logplot is shown in Fig. 5. Equation (3) implies that V goesas pl 3; this is indeed observed at high pressures in Fig.5. At low pressures, the dependence is different. Pil-beam and Vaisnys6 have suggested that the above ex-ponent should be larger than 0.3 when the deformationdue to pressure is large. The maximum deformationin our case may be large, because the volume decreaseis as much as 15% in our compression data. Also plottedin Fig. 5 is the variation of the width of the acousticpulse with Po. This indicates a large dispersion at lowPo and a lower dispersion at high Po.

IV. Conclusions

The usefulness of the PA technique for the study ofthe acoustic properties of a powder under various po-rosity and pressure conditions has been demonstrated.We find that the acoustic velocity measurement pro-vides an effective probe of the frame bulk modulus Kb,which sensitively depends on the interparticle forces.By monitoring the acoustic velocity, we have shown thatKb depends both on porosity and on applied pressureand that a large increase in Kb can be achieved byapplying high pressures to the powder system, (e.g.,many kilobars).

15 June 1983 / Vol. 22, No. 12 / APPLIED OPTICS 1877

I I I

HMT 208

0

0

0

I 0an

We are indebted to Hans Coufal of IBM ResearchLaboratory, Phil Marston of Washington State Uni-versity, Bill Pong of University of Hawaii, and David L.Johnson and T. J. Plona of Schlumberger-Doll Researchfor valuable help, suggestions, and information.

References1. For a recent review, see A. L. Anderson and L. D. Hampton, J.

Acoust. Soc. Am. 67, 1865 (1980).2. A. B. Wood, A Textbook of Sound (Bell, London, 1941), pp.

361-362.3. M. A. Biot, J. Acoust. Soc. Am. 28, 168, 179 (1955).4. F. Gassman, Geophysics 16, 673 (1951).5. H. Deresiewicz, Adv. Appl. Mech. 5, 233 (1958).6. See, for example, C. C. Pilbeam and J. R. Vaisnys, J. Geophys.

Res. 78, 810 (1973) and references therein.7. T. J. Plona, Appl. Phys. Lett. 36, 259 (1980).

8. D. L. Johnson and P. N. Sen, Phys. Rev. B 24, 2486 (1981).9. Toners available from Hitachi Metal of America, 1 Red Oak Lane,

White Plains, N.Y. 10604.10. Copper powder, 140 mesh, available from Sargent-Welch Scien-

tific Co., 7300 N. Linda Ave., Skokie, Ill. 60077.11. Laser model LFDL-1, Candela Corp., 96 South Ave., Natick,

Mass. 01760.12. Transducer model V306, Panametrics, 221 Crescent St., Waltham,

Mass. 02154.13. Preamplifier model 1201, Ithaco, Inc., 735 W. Clinton St., Ithaca,

N.Y. 14850.14. Oscilloscope model 7854, Tektronix Inc., P.O. Box 500, Beaverton,

Ore. 97077.15. PVF2 foil model Kynar 5412-144A-2, Pennwalt Corp., 900 First

Ave., P.O. Box C, King of Prussia, Pa. 19406.16. Laser model UV12, Molectron Corp., 177 N. Wolfe Rd., Sunny-

vale, Calif. 94086.17. K. Kendall, Contemp. Phys. 21, 277 (1980).

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