TEEE Transacticns on Eletci l Ins-i+ in V-ol. I-21 No .5,, 0 ' -Q36

ACOUSTIC THEORY APPLIED To THE PHYSICSOF ELECTRICAL BREAKDOWN IN DIELECTRICS

R. T. Harrold

Dielectrics and Insulation DepartmentWestinghouse R&,D Center

Pittsburgh, PA

ABSTRACT

In order to stimulate further thought and research withinthe science of dielectrics, this paper discusses the remark-able correlation between acoustic theory and the physics ofelectrical breakdown in dielectrics. Following a brief, simpli-fied review of acoustic theory and the propagation and atten-uation of soundwaves in gases, liquids and solids, three areasin dielectrics are addressed in which the breakdown mechanismsrequire further clarification. These are the relative electricalstrengths of gases and mixtures; streamer initiation in liquidhydrocarbons; and the incubation period before treeing or break-down occurs within solid dielectrics. Acoustic analysis of gasbreakdown clearly shows that the relative electrical strengthsof gases and mixtures vary as the inverse square of soundvelocity, and consequently, are closely related to both themolecular weight and specific heat ratio of the gas or mixture.For liquid hydrocarbons, an analysis of acoustic emission levelsfrom partial discharges combined with acoustic cavitation theory,supports the hypothesis that cavitation (collapse) of micro-bubbles attached to dust particles may provide the conditionsfor streamer initiation.

Finally, attention is drawn to the relationship between thevelocity of sound within solid dielectrics and Young's modulus,Poisson's ratio and density, which suggests a potential appli-cation of acoustics for assessing the mechanical strength ofdielectrics as they age. Thus, simple acoustic measurementsperformed on solid dielectrics may provide some information onthe structural condition Qf these dielectrics before treeingand subsequent breakdown occurs.

1. INTRODUCTIONIn order to stimulate further thought and research

within the science of dielectrics, this paper is direct-ed toward introducing the reader to the remarkablecorrelation between acoustic theory and the physics ofelectrical breakdown in dielectrics. The experience ofthe author leads him to conclude that the measurementand analysis of acoustic wave velocity and attenuationwithin dielectrics can increase the understanding oftheir molecular structure and also provide a fresh lookinto failure mechanisms which require further clarifi-cation.Of all the techniques used to determine the structure

and properties of gases, liquids and solids, acoustics

has unique features in that a medium is required forwave transmission, and the waves do not in generalharm, or permanently change, the medium. This is incontrast to other forms of radiation such as electro-magnetic waves, x-rays and light waves, which do notrequire a transmitting medium, but can sometimes af-fect the properties of the medium being examined.Study of acoustic wave propagation through a dielectricoffers a safe and non-destructive means of obtaininginformation in regard to such properties as molecularvelocity and packing. For example, in gases theacoustic wave velocity is close to the mean molecularvelocity and will obviously change with temperature asthe molecules speed up or slow down; and, in liquidhydrocarbons, the wave velocity is very sensitive to

Jr C

On l 8-9367 /86/ 1 OfDO-O-7c-3 1- -:It: r-ii- .00, ", 9.3 -' Z, EPE

the degree of molecular packing. Apart from learningabout the state and structure of dielectrics by acous-tic wave interrogation and analysis, acoustics alsoallows analysis in the listening mode, i.e., the sens-ing of acoustic emissions or pressure waves frommicrocracks, partial discharges and other events whichcan occur within dielectrics.

Although a vast body of literature exists relative toacoustic theory and the analysis of gases, liquids andsolids, only a few selected papers will be listed.However, it should be noted that the Journals of theAcoustical Society of America represent a storehouse ofknowledge. In addition, Philip M. Morse [1] presentedan invited paper, "Acoustics and Basic Physics", at theTwenty-Fifth Anniversary Celebration of the AcousticalSociety in 1954, which described several areas in phys-ics where basic progress was made by application ofacoustic theory, analogy and observation. These areasinclude, for example; (a) much of the wave theory oflight being worked out by analogy with sound; (b)Einstein's work on the analysis of atmospheric temper-ature fluctuations into their component plane waves ofsound before he computed the light scattering of eachcomponent wave; and (c) heat transferring throughhelium II (liquid helium close to absolute zero) movinglike waves, with a wave velocity and relation betweenheat flow and temperature like that between volume flowand pressure in an ordinary sound wave.

A major similarity between acoustic wave propagationand electrical breakdown processes is that they bothrequire a medium. If no molecules are present, noacoustic waves can propagate and also no electricalbreakdown can occur (with the exception of surface-emitted electrons bridging a gap). Electrical break-down processes, whether of the form of streamers ingases and liquids, or surface tracking or treeing with-in solids, require a medium for propagation. Even thebest vacuum insulation has about 10 molecules per cm3(-10-8 Pa), and "vacuum" breakdown processes can beinitiated or supplemented by surface outgassing (addingto the medium) and electron emission. So, a "vacuum"condition can provide a medium for breakdown.

density (p in kg/mi3) of the material and the velocity(c in m/s) of sound in that material and is expressedas pc in kg/m2s.

2.2 Transmission of Acoustic Waves at the Interfacebetween Media of Different Acoustic Impedance

In order for ultrasound to pass without loss from onemedium to another, it is necessary for the character-istic impedances of the media to be identical. Obvious-ly, the more two media, 1 and 2, are acoustically mis-matched, the greater the reflection of ultrasonic wavesat the media interface, and this effect is described bythe reflection coefficient,

(1)RO = (PlCl-P2C2)/(PlC1 + P2c2)2. 3 Acoustic Wave VeZocity

In gases

c /Pp/Pwhere y is the ratio of principal specific heats, and Pthe pressure. As p=m/V, where m is mass and V is volumeand PV=mkfT, where R is a gas constant, it follows that cis proportional to VT, where T is the absolutetemperature.

Where incompressible liquids are concerned

e = V21-p (3)where K is the bulk modulus. For liquids which are com-pressible, ethyl ether for example

e = ryK/P (4)In solids

c = Y/pY(l-b) (5)where Y is Young's modulus and b=2o2(1-oj), where o isPoisson's ratio.

(2)

It is the author's intent in this paper to includesufficient theory for credibility and to stimulate in-terest, but not to become complex unnecessarily; how-ever, acoustic theory can be extremely complex and be-come a mathematician's delight if the reader is soinclined.

Following a brief, simplified, review of acoustictheory and the propagation and attenuation of soundwaves in gases, liquids, and solids, three areas indielectrics are addressed in which there is no generalagreement on the conditions prior to breakdown or onthe mechanisms initiating certain critical phenomena.These are the relative electrical strength of gases andmixtures; streamer initiation in liquid hydrocarbons;and the incubation period before treeing or breakdownoccurs within solid dielectrics. It is shown that inthese areas acoustic theory, analogy and reasoning canprovide a fresh look at these problems and perhaps givea new interpretation of the actual events occurring.

2. SIMPLIFIED ACOUSTIC THEORY APPLIEDTO GASES, LIQUIDS AND SOLIDS

2.1 Acoustic Imrpedance

The characteristic impedance or specific acoustic im-pedance of a material depends on the product of the

2. 4 Acoustic Wave Attenuation

Acoustic wave attenuation or losses in gases, liquidsand solids are very complex and depend on molecular ab-sorption, viscosity and heat conduction. Theory and ex-perimental results do not agree well [3]; however,Stokes and Kirchoff [3] have considered the absorptionof sound through a medium due to heat conduction and in-ternal friction and developed the following equation:

42a=_ 4 (y-1)Absorption 2a =- 3 2[- j+ Ppk] (6)

where 2a is the intensity absorption coefficient of aplane wave, p is the coefficient of viscosity, f thefrequency, po the mean density, c the velocity of soundin the medium, y the ratio of the specific heats, Cp thespecific heat at constant pressure, and k the thermalconductivity. Apart from the attenuation trends predict-ed by this equation, the attenuation of acoustic wavesversus frequency is generally approximately proportionalto f for solids. Eq. (6) does predict a direct effectof viscosity on the acoustic wave attenuation, an inverseeffect of density (note pc is acoustic impedence) and aninverse cubic effect of sound velocity.

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H-srrol d: A-coustic: theory appl iedi to the py-,yi cs of ele- tri-cal bre-akdo-w'n in dielectr-is

3. AN ACOUSTIC INSIGHT INTO THEELECTRICAL BREAKDOWN

STRENGTH OF GASES AND MIXTURES

Paschen's law states that the breakdown voltage, Vd,of a gas in a uniform electric field is a simple func-tion of the product, pd, of the pressure, p, and thespacing, d. This applies only at a constant tempera-ture, and at atmospheric pressure and a temperature of20 or 250C, at which copious measurement data are avail-able. The breakdown voltage is, therefore, a simplefunction of p and the spacing d, where p is the gasdensity. As gas breakdown data have accumulated overyears of research, it has gradually become clear thatthe relative electrical strengths of different gasesand mixtures generally depend upon their densities ormolecular weights. For example, Camilli [2] demonstrat-ed the correlation between electric strength and themolecular weight of fluorogases. Olivier, Gervais andMukhedkar [3] showed that ac or dc uniform-field volt-age breakdown in gases can be described by the equation,U=pGdst, where p is the gas density, d the gap lengthand G, s, and t are constants. Cooke and Cookson [4]have shown that the high molecular weight SF6 and verylow molecular weight He, have similar electricalstrengths at similar densities; Pelletier, Gervais andMukhedkar [5] have successfully applied the above equa-tion to the data obtained from the electrical breakdownof gas mixtures.

A simplified view of electrical breakdown in gases isan electron avalanche followed by a primary streamer andsecondary streamers to complete the process. With elec-tronegative gases, breakdown should not occur if therate of electron attachment to neutral molecules isgreater than the ionization rate, or rate of release, ofelectrons. The influence of the gas molecular weight onthese processes has been described by Camilli [2]: "Thecharacter of gas molecules determines both the ionizationand electron attachment. Large molecules are obviouslymore easily hit and will cause more collisions which re-duce the average electron velocity. Thus, a gas ofhigher molecular weight would ionize at higher voltageand will exhibit a greater electron attachment than oneof lower molecular weight".

The analogy between acoustics and these factors con-trolling the electrical breakdown in gases is thatacoustic waves propagate in gases by molecular collisionand the molecular weights of the gases influence thepenetration and velocity of the acoustic waves. A wayin which this analogy can be critically examined is tocompare the acoustic wave velocities in gases and mix-tures with a large amount of uniform field gas breakdowndata. Fortunately, Vijh [6], in examining the corre-lation between the relative electrical strength and mo-lecular weights of gases, accumulated and normalized alarge amount of data. These data are relative to thedielectric strength of N2 as unity and are for atmos-pheric pressure and, presumably, mostly at room tempera-ture. In addition, Wootton [7] has examined the elec-trical strength of mixtures of SF6 and He, and Pelletier[5] the strength of N2-He mixtures. This author [8] hasmeasured the acoustic wave velocities in SF6-He andother mixtures, Table 1. There are, therefore, about100 electrical breakdown data points available coveringthe range of 0.1 to 10, relative to N2; with measuredacoustic wave velocities ranging from -140 m/s (SF6) to-960 m/s (He).

These data are plotted in Fig. 1, and a very clear re-lationship is observed between the relative electricalstrength (RES) and acoustic wave velocity c, i.e. the

RES is inversely proportional to c2. From Eq. (2)where c2=p/yP, the RES at one atmosphere is then pro-portional to p/y, where p is the gas density and y isthe ratio of the principal specific heats.

Table I

Measurements of the Velocityof Sound in Gas Mixtures [8]

(Atmosphere Pressure & loom Temperature, 88 kms)Bound Sound Sound

GCs Mixture Velocity Gas Mixture Velocity Gas mixture Velocity-8 -2 rn/sec H- a/sec SF8 - a/sec100% 0 135 100% 0 136 100% 0 135

90% 10 143 90% 10 142 9l 10 13880% 20 149 80% 20 150 60% 20 14370% 30 156 70% 30 161 70% 30 14960%

50%

40%

40

60

80

168

180

198

80% 40 177 60% 40 155

50% 60 198 60% 60 161

40% 60 217 40% 80 168

30% 70 213 30% 70 260 30% 7020%

10%

0

80

go

100%

247

274

345

178

20% 80 308 20% 80 18710% 90 444 10% 90 2040 100% 061 0 100% 217

ct11* 751673-11U

:5

8

,; 6

= 3

O 200 400 00 oD 10 1200I Cl Sound Velocity In Gas or Mixture IMeters/ Seondl1

Fig. 1: Relative eZectricaZ strength (RES) of gasesand mixtures versus sound veZocity (C).

This suggests that apart from density p, the specificheat ratio y is also an important factor which influencesthe electrical breakdown strength of a gas or mixture.The specific heat ratios vary with the type of gas orvapor and some published [9] values are listed in Table2.

Data Relative to N as Unity andMainly tor Atmospheric PressureRoom Temperature. Quasi-UniformFields and Eectrode Spaings In5 to 2Q mm Region-l e* Data Compiled by Vijh ( 6)O SF6- He I Wotton 17) 1* N2 - He I Peiletler. Gervais and Mukhfedar I 5 )

o SF6-C02t. .... .

RES. 1C2

SFsf6.fH

H~~~~~~~~~~~~~~~~~~~~

Ir

-

- E an4a .% -.. . f, l= X tE lk- .n- 1.L X4 si *n V -.i '1N.;

Table II

Specific Heat Ratio (y) of Gases

Gas Te

Monatomic GasesHelium 0Argon 0

Diatomic GasesAirHydrogenOxygen

Triatomic GasesCarbon DioxideSulphur DioxideNitrous Oxide

Polyatomic GasesBenzene (C6H6)

Trichloroethylene (CM4)Sulphur Hexafluoride (SF6)

0-174-175-14

4-1116-34

20

20

perfect monatomic gas with three degrees of freedom hasy=1.67, a perfect diatomic gas with five degress offreedom has y=1.4, and a triatomic gas having threetranslational and three rotational degrees of freedom,a y=1.33. In general, y=1+2/n, where n is the total

2 number of degrees of freedom. Exact measurements ofthe specific heat ratio of a gas depend upon its purity,and small quantities of moisture, for example, canchange the specific heat ratio [10]. It is interesting

1.630 to note that many of these characteristics of gases, in-1.667 cluding the effects of impurities which can also be ex-

plored by acoustic analysis, can influence the RES ofgases.

1.401121.407/81.400

1.3001.2601.324

The analogy between acoustic theory and electricalbreakdown in gases becomes more credible by consideringthe data for measured and calculated values of the lim-iting breakdown voltage for SF6-He mixtures, versus SF6concentration, published by Kline, Davies, Chen andChantry [11], with much of the data attributed toMoruzzi and Craggs [12]. These data generally followan inverse sound velocity squared relationship, Fig. 2,as can be readily checked. In addition, Nonken, in a

CUFve 751934-A

4 xlO1

1.40 3

1.1301.2

(Calc. fromsonic wavevelocity)

It is interesting to note that the specific heat ratioof a gas is usually determined [9] by some method in-volving an adiabatic expansion, such as the determinat-ion of the velocity of sound in the gas. The actualsound velocities measured in gas mixtures of SF6-He andSF6-N2 were used in the Fig. 1 curve, while the remain-der of the sound velocity data were calculated. Itshould be noted that the SF6-He data fit the curve verywell which tends to confirm the importance of the effectof the specific heat ratio on the RES of a gas or mix-ture, because the measurement of the sound velocity doesrepresent a measurement of y.

Hydrogen is the one gas which does not seem to fit onthe RES curve of Fig. 1, as its RES is clearly much high-er than predicted (assuming that the published RES valuesare actually for pure H2). However, if an acoustic anal-ogy is pursued, then hydrogen could be considered a"transition dielectric". In other words, most of the gas-es and mixtures (Fig.l) have decreasing RES with increas-ing sound velocity, with the clear exception of hydrogen,which has a sound velocity close to that of liquid hydro-carbons and begins the transition to the higher RES ofliquid dielectrics.

As the specific heat ratio of a gas or mixture appearsto be an important factor associated with the RES, it isworth considering its implication. The specific heatratio of a gas is the ratio of specific heat at constantpressure to that at constant volume and depends upon thetype of gas molecules and their associated degrees of

Ev

-

2

I

U I0.1

Fig. 2:valuesSF6-HeKZine,

I% SF6

Comparison of measured and calculatedof the Zimiting breakdown voltage formixtures vs. SF6 concentration (AfterDavies, Chen and Chantry [11]).

translational, rotational, and vibrational freedom. Adiscussion of a Camilli [13] paper, draws attention tothe decrease in breakdown strength of nonuniform fieldgaps with increasing gas pressure and the relationshipof this phenomenon to the rate of diffusion of spacecharge of the positive ions. He also notes that iondiffusion is inversely proportional to the square rootof molecular weight, which of course is a measure ofsound velocity because c=lyP/p. Also, it should bementioned that the mean free path between molecularcollisions in a gas is inversely proportional to the gasdensity.

The author believes that sufficient data and evidencehave been presented to justify the claim that acoustic

Theory--- With Ionizaion"d SF by He

+ + ~~~6SF6, He+ onlyExperiment

J L Pack, Glow Dischargev JLMoruzzi Ij

& J D Craggs Spatial Current GrowthO LI Kline, etal.J

J LMoruzzi, Breakdown Voltage& J D Craggs

Relative Values* Based on Acoustk

Wave Velocty

10 100

r- I

.,n-

Harrold: AcO-&tij t-heory appl ied to the p-ys_i of electrical bre,k;dow- in dielectric-7

theory can help in understanding and predicting- elec-trical breakdown phenomena in gases. In any event, itis clear that simply by making laboratory measurementsof soundwave velocity in gases and mixtures, good esti-mates can be made of their relative electricalstrengths.

4. ACOUSTIC CAVITATION AND THEINITIATION OF ELECTRICAL

BREAKDOWN IN LIQUID DIELECTRICS(INCLUDING THE DEGREE OF

MOLECULAR PACKING)Electrical breakdown in liquid dielectrics is very

susceptible to impurities, such as moisture and parti-cles, to the electrode surface condition, and to thevolume of liquid under electrical stress. For thesereasons, there are insufficient reliable published dataavailable for attempting to correlate the breakdownvalues with acoustic wave velocity in order to yieldinformation similar to that found for gases. It ispossible that this may be achievable in the future byusing point-to-plane breakdown data which are believedto be insensitive to liquid impurities; however, onearea in liquid breakdown which is not well agreed uponis the mechanism by which a streamer initiates at anelectrode surface. Many authors [14-17] have proposedthat breakdown begins with a cavitation process at theelectrode surface, and, as this is an area related toacoustic theory, it is worth some examination.

One way in which acoustic theory could perhaps con-tribute to the hypothesis that cavitation processesinitiate streamers in liquid dielectrics can be under-stood by first considering the levels of acoustic emis-sions associated with different magnitudes of electricaldischarges in liquids. The data illustrated in Fig. 3

Point b Plane

;: ID ~~~Comns Discharges in O li

IC ~ ~ ~ ~ ~ ~ ~

Z~ ~~\

100Ee rcll tn

Fig. 3: Graph of acoustic signaZ (P) versuselectricaZ puLse charge (QJ for corona dis-charges in oil [18].

indicat'e the range of relative acous-tic emission levelsmeasured 100 cm from electrical discharges ( ~~~SeriesInsulation

,-- Point Discharge,.' 8 kV I Ogihara (20)-

For 1 pC the Estimatei| Discharge Energy Is - a 002 pj,, i ,,1,,lii ,,1,,i ,,1,,al,, I I,

-76.

i -t- 'i-s._e-t- o i_ -ct-%' 'tT-- o l -t i . >- Nc, -, OC obe- 1986

PD, an energy of -4Xl0-2 iJ. These values are for thetotal discharge energy which is dissipatedforms, i.e., heat, light, electromagnetic, and acoustic.In order to learn whether the cavitation hypothesis hasany credibility, it is first necessary to estimate thequantity of PD energy which is dissipated acoustically.

The acoustic energy of a PD can be estimated from thepressure level measured near the source. Based on ex-tensive studies [19] by this author of the 30 to 90 kHzacoustic emission levels from ac point discharges inmineral oil, and on similar measurements by Ogihara[20] in the 100 to 300 kHz range, the pressure level 10cm from a 1 pC discharge is estimated to be 0.2 Pa-2 pbar)and from a 10 pC discharge 0.6 Pa. Based onthese pressure levels, the acoustic energy WA associatedwith 1 and 10 pC discharges can be calculated from thefollowing formula [22]:

Table III

Phenomenon

Acoustic Emissions From1 to 10 pC PD inMineral Oil

Cavitation (Collapse) of10 5 to 10 4 cm [0.1 to hPm]Radius Gas Bubbles inMineral Oil

Estimated Acoustic Energy

2 to 6 x 10 7 UJ

20 to 2000 x 10-7 #J

4Trr2P:atWA= 2 P 10-7 (7)

where P is the peak pressure level in Pa (dynes/cm2), tis the time in s during which the sensor responds tothe acoustic emissions, p is the density of the soundtransmitting medium in gm/cm3 (kg/m3), c is the velocityof the ultrasound in cm/s (m/s), and r is the distancein cm (m) between the ultrasound source and sensor.

From Eq. (7), the calculated acoustic energy associat-ed with a 1 pC PD is _2X10-7 ,uJ and, from a 10 pC PD,-6X10-7 ,J.

Note, these are the approximate values of the acousticemission levels expected from these partial dischargemagnitudes. The next step is to estimate the energyassociated with a likely form of cavitation which couldoccur in a mineral oil insulation system.

It has been shown [22] that, in all liquids, micro-scopic dust particles are present that entrain gas inthe form of extremely small bubbles (10-5 to 10-4 cmradius) that are stabilized and kept from going intosolution. These bubbles represent potential cavitationsites, and, under certain conditions and forces, thesebubbles will collapse or implode. From cavitation stud-ies [22] of liquids, it has been demonstrated that thesestable bubbles are cavitation sites and that, at 25 kHzin mineral oil, the power required for cavitation isabout 14 W/cm2, for a 100 ps pulse. Using these pulsedata, it can be calculated that, for bubbles of 10-5 to10-4 cm radius, the acoustic energy to cause cavitation(or collapse) of these bubbles ranges from 20X10-7 to2000x10-7 pJ

.

The data for the estimated acoustic energy from 1 to10 pC PD in mineral oil, as well as the estimated energyfor initiating cavitation (collapse) of microbubbles inmineral oil, are summarized in Table 3.

Clearly then, the acoustic energy associated withcavitation conditions in mineral oil, which cause thecollapse of microbubbles, is much larger than theacoustic energy estimated to be associated with 1 to 10pC PD. In addition, the measurements of acoustic emis-sions from actual 5 to 20 pC PD in mineral oil indicatemuch larger values than expected. These facts givecredibility to the hypothesis [23] that electrical dis-charges in mineral oil can begin with the cavitation(collapse) of microbubbles attached to dust particlesand that the smallest actual discharge in mineral oilhas a value in the -5 pC range.

It should be pointed out that the cavitation forcesare assumed to be caused by high-intensity electricfields, due to nonuniformities at electrode and particlesurfaces. In addition, the effect of cavitation isassumed to be the collapse of microscopic bubbles, al-though other cavitation effects are degassing or theformation of gas bubbles (proposed by other proponentsof the cavitation hypothesis) and bubble resonance.Finally, during observations [24] of cavitation (bubblecollapse) in oil and benzene, small explosive ruptureswere seen in dark field illumination. Conditions ofthis nature would seem likely to initiate a positivestreamer under suitable electric field conditions.

4.1 The Influence of the Degree of MoZecuZar Packingof Liquid Hydrocarbons on Sound VeZocity

Another area within the subject of liquid dielectricsis worth drawing attention to, i.e., the relationshipbetween sound velocity and the molecular packing ofliquid hydrocarbons. Heuter and Bolt [24], who give adetailed account of the molecular structure and packingof liquids, also describe a simple model of a liquidcomposed of rigid balls of matter packed in a character-istic way. They explain that the time required for thetransfer of momentum from molecule to molecule in asoundwave is directly proportional to the mass of themolecules and the distance between the molecules, andis inversely proportional to the molecular volume.Further, they note that measurements of sound velocityversus temperature will furnish information on theamount of association (electrical binding forces betweenmolecules) present in a liquid as well as the boilingpoint, critical point, and index of refraction; all ofwhich are related to the cohesion forces between mole-cules and the degree of their packing. Heuter and Bolt[24] also give an example of the sound velocity reveal-ing a large influence of the length or shape of themolecules on the degree of their packing: "For instance,if in the benzene ring (C6H6), one H atom is replacedby N02, giving nitrobenzene, the effective volume isincreased, which causes an increase in sound velocityfrom 1326 to 1473 m/s at 200C."

Measurements [24] by Schaaff's of the sound velocityin 92 different aliphatic hydrocarbon compounds con-taining C, H, 0, N, and Cl atoms are shown in Fig. 5.A remarkable correlation is seen between the product ofsound velocity and molar volume, and the product ofmolecular volume and Avogadro's number. These smalldifferences between liquid hydrocarbons which can bedetected from sound velocity measurements, not onlydemonstrate the potential of acoustics for the analysisof liquid molecular structures and for detecting low

Harrold;: ACOUStif- theory ppIied to t r,-s ph.yic s. of leetri aI breek'-c-n ii- die1et-r:c7s

levels of impurities; but also for an acoustic exam-ination of the RES of liquids when reliable breakdowndata are available.

Curve 751894-A

3 xlo8

I-

EuI.)

u

Vm , (cm3)

Fig. 5: The dependence of sound veZocity onmolecular packing for 92 hydrocarbon Liquids(W. Schaaffs). The product of sound velocityc and molar volume V is pZotted versus theproduct of molecuZar voZume Vm (as determinedfrom the atomic constituents) and Avogadro 'snumber N; note that VmN=sV. (After Heuterand Bolt [24]).

s. THE RELATIONSHIP BETWEEN ACOUSTICWAVE VELOCITY AND THE STRUCTURALPROPERTIES OF SOLID DIELECTRICS

Reliable and agreed upon breakdown data for soliddielectrics are even more scarce than that for liquids,which in turn does not approach the copious data avail-able for gases. This is not surprising, because solidshave more impurities and abnormalities than liquids,and also the breakdown values are susceptible to speci-men thicknesses and conditions at the interface betweenthe dielectric and electrodes. Obviously, with gases,it is reasonable easy to obtain volume purity in the99.9% range, but with liquids, 103 particle impuritiesper cubic centimeter are not uncommon under the best oflaboratory filtering conditions [25]. For solids thesituation is even more difficult. Consequently, thereare insufficient data for an acoustic analysis likethat carried out for gases, Fig. 1, although it is sus-pected that for solids, a continuation of the Fig. 1curve would yield progressively higher electrical break-down strengths with increasing sonic wave velocity be-cause of increasing values of the material bulk modulus.However, one unknown area in solid dielectric failuremechanisms is worth exploring acoustically, i.e., whatis happening within a dielectric during the incubationperiod prior to an electrical tree occurring; an eventoften followed by electrical breakdown?

In this context, one area that needs to be criticallyexamined is that of acoustic emissions (AE) from possi-ble microcracks and other events, which may occur insolid dielectrics under service conditions of cyclicalmechanical stresses due to electrical and other forces.Provided these emissions can be separated from externalnoises, they may provide an early warning of a treeingevent which in itself would likely have a larger acous-tic emission signal at initiation; however, thesetypes of data, although of value, would probably notyield the answers to the questions as to why the em-missions occurred, and what changes are taking placewithin the dielectric structure during the incubation

period? An acoustic approach, which can yield informa-tion regarding the structure and composition of a di-electric, is a simple measurement of the sound velocityand attenuation in the dielectric.

As discussed earlier, the velocity of sound in asolid depends upon its density, Young's modulus andPoisson's ratio, and can be expressed as:

p-(-b) (8)where Y is Young's modulus, p is the density of thesolid and b=2o2/(j-o), where a is Poisson's ratio.Thus, any changes in the acoustic wave velocity (c),in a dielectric with time, could indicate a change inthe ratio, tensile str-ess/tensile strain (X), or theratio, fractional lateral contraction/fractional longi-tudinal extension (6), or density (p). If, for example(Y) reduced, then c would fall and if (6) increased invalue c would also fall. Consequently, a fallingacoustic wave velocity with the age of dielectricscould be an indication of changing mechanical propettieswhich may contribute to sudden electrical failure.Before pursuing this thought further, it is worth ex-amining the spread of measured acoustic wave velocitiesfor a large number of plastics, many of which are com-mon dielectrics. Fortunately, Zacharias, Zachariasand Parnell [26], who developed a very accurate soundvelocity measurement system for solids, based on thevelocity difference in a constant-temperature liquidwith and without an immersed specimen, measured thesound velocity in 53 different plastic materials atboth 25 and 500C. These are valuable, hard to finddata, not only because of the measurement comparison onthe same system, but also because of the accuracy(0.01%) of the measurement system. These data are re-produced in Table 4. All the materials exhibit afalling sound velocity with increasing temperature (thereverse of the situation for gases), ranging from -2to -10 m/s/OC. Also, these data include the materialdensity values as well as the abiabatic bulk modulusB, calculated from B=pc2. The values of B are plottedagainst sound velocity in Fig. 6 and the relationshipwith c2 is clear; however, the scatter in the dataseems larger than that which can be attributed to thedifferent values of material density. This infers,bearing in mind that the sound velocity data are veryaccurate, that the materials examined are not pure,and contain impurities or suffer from density varia-tions which influence the velocities of sound withinthem.

Although various mechanical tests can be employed toestimate the strength of a dielectric, a measurementbased on acoustic wave velocity is attractive becauseit can often be performed without destroying or damag-ing a specimen. In addition, it may be possible tomeasure the wave velocity within an insulator or cabledielectric in situ and gain information with regard toremaining life. It is intriguing to consider that asmaterials age the acoustic wave velocity within themmay change. To examine this hypothesis, different agematerials of similar constituents and manufactured undersimilar conditions are required. This author has ex-amined the sound velocity within polyethylene of dif-ferent age from RF coaxial cables, but before reportingthese results, it should be mentioned that a briefsearch of the literature has revealed that this is nota new idea. As far back as 1962, Goldman [27] in hisbook on "Ultrasonic Technology" discussed the conceptof sound velocity and attenuation measurements in

1 .R17

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Table IV

Sound Velocity and Bulk Modulus of Plastics

(E. M. Zacharias, Jr., M. W. Zacharias, and R. A. Parnell, Modern Plastics, May 1974) [26]

g/CccSound Velocity,m/sec Temp. Coeff. Density Modulus,10 psi

Item No. and Description At 25*C At 50*C (per 'C) (25"C) Adiabatic Bulk

1) Bettle cellulose-filled UFa 2983 2870 -4.56 1.46 18.92) Cymel 1077 cellulose-filled IWa 3044 2983 -2.46 1.49 20.13) Polyester casting resilno 2475 2353 -4.88 1.23 11.04) AM1000 ABSb 2148 2091 -2.31 1.05 7.025) CIT-31336 ABSb 2143 2045 -3.93 1.08 7.276) DH-10OO ABSb 2214 2152 -2.48 1.05 7.527) KA10 ABSb 2032 1954 -3.14 1.19 7.188) LE-1000 ABSb 1991 1926 -2.60 1.02 5.899) TD-1001 ABSb 2091 2030 -2.43 1.04 -6.63

10) X7-1000 ABSb 2141 2078 -2.55 1.04 6.9511) X17-1000 ABSb 2196 2119 -3.09 1.06 7.4312) X27-1000 ABSb 2208 2146 -2.50 1.06 7.5213) 800-1000 ABSb 2228 2156 -2.90 1.39 10.014) Polyester GRPc 2618 2401 -8.68 1.80 18.215) 25053 HDPEd 2269 2096 -6.95 0.93 7.0516) 35063 IIDPEd 2313 2176 -5.52 0.96 7.5017) Styron 475 high-impact PSd 2122 2048 -2.95 1.04 6.8018) Styron 678 general-purpose PSd 2264 2195 -2.78 1.05 7.8419) LDPE type 950d 1988 1777 -8.47 0.92 5.3620) LDPB type XlP-4212.35d 1968 1745 -8.93 0.91 5.2121) DC 306 siliconee 2606 2448 -6.30 1.86 18.522) Silastic 4505 filled silicone 977 911 -2.66 1.74 2.44

rubbere23) XRi 90504 siliconee (discont.) 1866 1706 -6.41 1.15 5.8724) Vespel SP-1 polyimide 2507 2314 -7.75 1.42 13.125) Vespel SP-21 polyimidef 2594 2349 -9.86 1.57 15.626) Surlyn 1650 ionomer resin 1887 1741 -5.87 0.95 4.9827) Surlyn 1652 ionomer GRP 2053 1852 -8.07 1.09 6.7528) Teflon FEP resinf 1258 1164 -3.77 2.15 4.9929) Teflon TFE resins 1456 1331 -5.00 2.21 6.8730) Tefzel ETFE fluoropolymer 1610 1504 -4.23 1.71 3.8031) B995 phenolic with wood flour 2941 2824 -4.72 1.35 17.0

and cotton flock filr32) Nylafil G-1/30 6/6 nylon with 2517 2348 -6.75 1.36 12.6

30% long glass fibersh33) Nylafil G-10/40 6/6 nylon with 2594 2422 -6.88 1.48 14.6

40% long glass fibersh34) Nylafil G-12/40 6/10 nylon with 2422 2269 -6.16 1.42 12.2

40% long glass fibersh

Harrold: Ac:o_ tic thec,y ar-lied ti th-- p.hysics Of eieCtric 1--'-makt-doi, - nr d e1 etr

35) Valox 310, thermoplastic 2284 2137 -6.26 1.31 10.0polyester GRPi

36) Valox 310-SED, thermoplastic 2215 2091 -4.98 1.40 10.1polyester GRPil

37) Valox 420, thermoplastic 2368 2206 -6.52 1.52 12.5polyester GRPi

38) Valox 420-SED, thermoplastic 2377 2240 -5.51 1.62 13.4polyester GrP'

39) Lexan grade MR4004-112, 2173 2101 -2.89 1.20 8.23MIL:500 PCi

40) Lexan grade 9034-112, 2176 2093 -3.34 1.20 8.29Mfl:250 PCi

41) Lexan grade 9034-112, 2180 2094 -3.43 1.20 8.32MIL:375 PCi

42) Polypenco nylon 101k 2582 2451 -5.27 1.15 11.243) Polypenco nylon 901k 2615 2389 -9.05 1.16 11.744) Plexiglas acrylic (sample #1)1 2647 2552 -3.79 1.19 12.145) Plexiglas acrylic (sample #2)1 2651 2554 -3.90 1.19 12.246) MX-1430, paper-base phenolic 2401 2205 -7.85 1.37 11.6

laminatem47) CEF, fine-weave-canvas phenolic 2613 2493 -4.81 1.32 13.2

laminatem48) MX-1403 grade CE, medium-weave- 2509 2387 -4.87 1.39 12.7

canvas phenolic laminate with1/32-in. Buna S centerm

49) Astrel 360,polyarylsulfone 2148 2081 -2.70 1.36 9.15thermoplasticn

50) Kel-F 81 type 60600 1816 1715 -4.06 2.12 10.251) Polysufono 2221 2171 -2.01 1.24 8.9252) Nylon-6/6 2313 2116 -7.89 0.94 7.4153) PVC 2252 2173 -3.16 1.39 10.354) 2024 aluminum 5930 5900 -1.15 2.77 14155) 6061 aluminum 5965 5900 -2.54 2.68 13956) 7075 aluminum 5840 5790 -2.02 2.79 13857) Ti6A14V titanium 5730 5695 -1.36 4.40 21058) Brass 4120 4100 -0.88 8.40 20759) 303 stainless steel 5360 5305 -2.22 7.76 32460) 316 stainless steel 5310 5275 -1.34 7.92 32461) Cold-rolled steel 5520 5470 -1.88 7.79 344

a--American Cyanamid f--Du Pont Co. l--Rohm and Haas Co.b--Borg-Warner g--Durez Div., Hooker Chemical m--Synthane-Taylorc--Cincinnati Milacron h--Fiberfil Div., Dart Ind. n--3M Co.d--Dow Chemical i--General Electric o--Union Carbide Corp.e--Dow Corning k--Polymer Corp.

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(C) Sound Velocity Meters/ Sec. 250CFig. 6: Adiabatic buZk moduZus of pZastics versus

sound veZocity (Data from Zacharias, Zacharias &ParneZZ [26]).

materials for assessing changes in their elastic con-stants and for determining the occurrence of micro-cracks and other phenomena which increase the atten-uation of ultrasound. Specific information is given ofmeasurements by Truell [28] of the ultrasound atten-uation within aluminum, subject to cylical stresses.It is postulated that during the stress cycles, micro-cracks occur, which cause an increase in ultrasoundattenuation; however, this promising work may not havebeen pursued and does not appear to have been appliedto dielectric materials. Aging of dielectric materialsis a very important subject which is experiencing in-creased interest. A recent paper by Lamarre [29] de-scribes work directed toward characterizing aged elec-trical insulating materials by viscoelastic methods.The measurements reported are mainly the dynamic mod-ulus and loss factor (tangent delta) of aged, cross-linked polyethylene and other polymers in relation totemperature. Lamarre concludes that this technique canmeasure changes occurring during aging, but interpre-tation is difficult, and temperature cycles during amaterial lifetime may "anneal out" any changes; never-the less, investigations of this nature serve to en-courage the application of acoustic techniques to mate-rials in order to measure possible changes due to age.

5.1 UZtrasound VeZocity and Attenuation Measurementsin Old and New PoZyethyZene

This author carried out some sound velocity and atten-uation experiments using old and new polyethylene of thesame density ( 0.87 gm/cm3) from RG59B/U 75 Q RF coaxialcable. The old sample was at least 10 years old and hadbeen kept in a laboratory drawer. It had apparentlyturned yellow with age. The new sample was white andfresh from a new supply in the laboratory storeroom.

The inner and outer copper conductors were removed toleave only the polyethylene. The specimens used were10 cm in length. Acoustic transducers were bonded toeach end of the polyethylene and, as pulsed acousticwavetrains (65 kHz) were transmitted through the poly-ethylene (acting as a waveguide), the wave transit time(velocity) and attenuation were measured. During thistime, the polyethylene was inside an oven with a thermo-couple bonded to its surface and was heated from -20 to-500C and allowed to cool. The heating time was ap-proximately 35 min and cooling time near 70 min.

The most striking observation from these simple ex-periments was received acoustic signal levels jitteringand cylically (every second or so) varying in magnitude.This effect was especially evident in the first two tem-perature runs of the old polyethylene, with signals in-creasingly varying from 700 to 750 pV at 250C and from50 to 150 iPV at 500C. The third temperature run, withold polyethylene, produced much less signal change, asdid the two runs with new polyethylene. At 500C, allthe experiments exhibited a substantial change in sig-nal level. Due to these signal fluctuations, the bestway to present these dat-a is to take average readingsand convert these to signal attenuation values in de-cibels, for example, 6 dB represents a signal reductionof 2:1 and 20 dB, 10:1. In Fig. 7 the signal atten-uation values are plotted against temperature for the

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heating and cooling of both the old and new polyethylene.Clearly, there is a difference between the signal atten-uation levels for the two specimens. Generally, at 250C,there is -15 dB more attenuation offered by the oldpolyethylene, and at 500C, 6 dB more attenuation. Thistype of effect could be an indication of a change incyrstallinity or the development of microcracks withinthe old polyethylene.

With regard to the measurements of acoustic wave ve-locity, these were in the range of 1100 m/s at 250C andreduced to -650 m/s at 500C. Rates of change of sonicvelocity were typically in the range of 10 to 20 m/s/OC.Due to the small signal levels transmitted along the

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polyethylene specimens, the transit time measurementswere sometimes difficult to interpret precisely, socomparisons of the wave velocities in the old and newspecimens cannot be considered precise. However, itis worth noting that, for two temperature runs on theold polyethylene, the sound velocity values were gen-erally lower (-10%) than those of the new. This resultwould be expected if the old material had a lowermodulus than the new.

It is speculated that the cylical variations in theacoustic signal levels transmitted along the polyethy-lene specimens could be due to changes in crystallinityor crystal alignment, or due to a sort of "materialflow" at -300C and above as the polyethylene softens.This latter effect can be duplicated by transmitting asonic beam through a stationary liquid in a vessel andthen rocking the vessel so that the liquid wobbles upand down in the container. Although the acoustic beamis transmitted well below the liquid surface, the re-ceived acoustic signal follows the surface motion andvaries perhaps one to three times in level.

These sonic measurements on polyethylene are includedfor interest and to demonstrate the capability ofacoustic analysis of dielectrics. The data can only beconsidered as preliminary and obviously more preciseexperiments are required using materials of known com-position and age before definite conclusions can bedrawn. In addition, the sonic velocity measurementsnear 1100 m/s are about half of the published valuesfor longitudinal waves in polyethylene, and this mayindicate that shear waves or surface waves which travelat lower velocities are actually propagated.

6- SUMMARYThe thrust of this paper has been directed toward in-

troducing the reader to the remarkable correlation'between acoustic theory and the physics of electricalbreakdown in dielectrics. Several different phenomenaassociated with electrical breakdown in gaseous, liquid,and solid dielectrics have been examined from anacoustic viewpoint. Acoustic analysis of gas breakdowndata clearly shows that the relative electricalstrengths of gases and mixtures vary as the inversesquare of sound velocity, and consequently, are closelyrelated to both the molecular weight and specific heatratio of the gas or mixture. Based on this analysis,it is anticipated that laboratory measurements ofsoundwave velocity can be used for predicting the rela-tive electrical strengths of gases and mixtures.

In the area of liquid dielectrics, the cavitationhypothesis of breakdown initiation has been addressed.Specifically, this hypothesis was examined by compari-son of the relative energies associated with bothpartial discharges and with the collapse of microbub-bles. This analysis suggests that a breakdown streamerin, for example, mineral oil, begins with electricfield-induced cavitation (collapse) of a microbubbleattached to a dust particle. Another important featureof liquid dielectrics is their degree of molecular pack-ing. It is shown that this packing correlates remark-ably well with data from sound velocity measurements.

In regard to solid dielectrics, attention has beendrawn to the relationship between acoustic wave velocityand the material age and its mechanical strength. Itis proposed that simple temperature and sound atten-uation and velocity measurements, made throughout thelifetime of a solid dielectric, may yield informationon its mechanical properties during the incubation

period before the occurrence of a tree or other eventswhich precede electrical breakdown.

It is hoped that the analyses presented in this paperwill help stimulate thought and research within thescience of dielectrics.

7. REFERENCES

[1] P. M. Morse, "Acoustics and Basic Physics",Invited Paper presented at the Twenty-FifthAnniversary Celebration of the AcousticalSociety of America on June 24, 19-54. Journalof the Acoustical Society of America, Vol. 27,pp. 213-216, 1955.

[2] G. Camilli, "Gas-Insulated Power Transformers",The Institution of Electrical Engineers, London,Paper No. 3288S, 1960.

[3] G. Olivier, Y. Gervais and D. Mukhedkar, "ANew Approach to Compute Uniform Field Breakdownof Gases", Paper 77-709-9, presented at IEEEPES Summer Meeting, Mexico City, Mexico, 1977.

[4] C. M. Cooke and A. H. Cookson, "The Nature andPractice of Gases as Electrical Insulators",IEEE Trans. on Electrical Insulation, Vol. EI-13, No. 4, pp.. 239-248, 1978.

[5] J. M. Pelletier, Y. Gervais and D. Mukhedkar,"Dielectric Strength of N2-He Mixtures andComparison with N2-SF6 and C02-SF6 Mixtures,IEEE Trans. on Power Apparatus and Systems,Vol. PAS-100, No. 8, 1981.

[6] A. K. Vijh, "On the Relative ElectricalStrengths and the Molecular Weights of Gases",IEEE Trans. on Electrical Insulation, Vol.EI-17, No. 1, pp. 84-87, 1982.

[7] R. E. Wootton, Final Report, "Gases Superiorto SF6 for Insulation and Interruption",EPRI Contract 847-1, 1979.

[8] R. T. Harrold, "Acoustical Properties ofDielectrics and Electrical Strength", NationalAcademy of Sciences, Conference on ElectricalInsulation and Dielectric Phenomena, Whitehaven,PA, pp. 256-267, 1979.

[9] G. W. C. Kaye and T. H. Laby, "Physical andChemical Constants", 11th Edition, Longsman,Green and Co., London, pp. 57-59, 1956.

[10] M. N. Saha and B. N. Srivastava, "A Treatiseon Heat", Published by the Indian Press, PrivateLtd., Allahabad, Calcutta, India, Fourth Edition,p. 94, 1958.

[11] L. E. Kline, D. K. Davies, C. L. Chen and P. J.ChanDtry, "Dielectric Properties for SF6 and SF6Mixtures Predicted from Basic Data", Journalof Applied Physics, Vol. 50, 1979.

[12] J. L. Moruzzi and J. D. Craggs, "Ionization andAttachment and Breakdown Measurements in Mixturesof SF6 with Helium, Argon and Hydrogen", Proc.of 12th International Conference on Phenomena inIonized Gases, Eindhoven, The Netherlands, p. 226,1975.

I -; X..I

~-- T t J --E rIE _trn i T r -t:v- ,l-1 -eT i . i3

[13] G. Camilli and J. J. Chapman, "Gas Insulationfor High-Voltage Apparatus", AIEE Trans., Vol.66, pp. 1463-1470, 1947.

[14] P. K. Watson and J. B. Higham, "Electric Break-down of Transformer Oil", IEEE Symp on Insulat-ing Materials, 1953.

[15] N. Klein, Y. Amariglio and E. Burstein,"Cavitation in Transformer Oil Due to ElectricFields", National Academy of Sciences, Conf. onElectrical Insulation and Dielectric Phenomena,Annual Report, pp. 5-7, 1964.

[16] W. B. Smith-White, "On the Mechanical Forces inDielectrics", Proc. Royal Society, pp. 466-478,1948.

[17] C. J. Frei and G. Rey Mermier, "Influence ofUltrasonic Excitation on Breakdown Time LagDistributions in a Liquid Dielectric", IEEEConf. Pub. 177, pp. 10-13, 1979. ThirdInternational Conf. on Dielectric Materials,Measurements and Applications, Univ. of Aston,Birmingham, 1979.

[18] R. T. Harrold, "The Relationship BetweenUltrasonic and Electrical Measurements ofUnder-Oil Corona Sources", IEEE Trans. onElectrical Insulation, Vol. EI-ll, No. 1,pp. 8-11, 1976.

[19] R. T. Harrold, "The Electro-Acoustic EnergyRelationship of Partial Discharges in MineralOil and Air", National Academy of Sciences,Conf. on Electrical Insulation and DielectricPhenomena, pp. 91-98, 1977.

[20] H. Ogihara, "Detection and Location ofCoronas in Oil Immersed Transformers withCorona Detector", Electrical Engrg., Japan,Vol. 84, pp. 12-21, 1967.

[21] E. Talvio, "Partial Discharge Carrier Currents",Sahko, 41, Vol. 2, Finland, pp. 50-53, 1968.

[22] T. F. Heuter and R. H. Bolt, "Sonics", Wiley, Sons, New York, p. 42 and pp. 225-242, 1955.

[23] R. T. Harrold, "Acoustical Techniques forDetecting and Locating Electrical Discharges",Chap. 10 of Engineering Dielectrics, Vol. I,Corona Measurement &, Interpretation, ASTM STP669, 1969.

[24] T. F. Heuter and R. H. Bolt, "Sonics", Wiley &,Sons, New York, p. 227, 1955.

[25] Y. Kako, E. Takahashi, H. Okubo, A. Kishi andT. Okamoto, "Influence of Minute Particles onBreakdown Characteristics of Insulating Oil",Paper 15-03, CIGRE, Paris, August, 1986.

[26] E. M. Zacharias, Jr., M. W. Zacharias and R. A.Parnell, Jr., "Measuring Sound Velocity andBulk Modulus of Plastics", Modern Plastics,Vol. 51, No. 5, pp. 88-90, 1974.

[27] R. Goldman, "Ultrasonic Technology", ReinholdPublishing Corp., New York, pp. 222-229, 1962.

[28] R. Truell, B. Chick, A. Picker and G. Anderson,"The Use of Ultrasonic Methods to DetermineFatigue Effects in Metals", WADC TechnicalReport, pp. 59-389, 1959.

[29] L. Lamarre, "Characterization of Aged ElectricalInsulation Materials by Viscoelastic Methods",31st International SAMPE Symposium, Las Vegas,NV, 1986.

Manuscript was received 16 May 1986, in revisedform 13 August 1986.