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ho IE~ ECTRIC BRE,AKDO~M :By E. J. Nurphy Be:l ~ Telephone [~.bc~ra-tor..es ~,larr`ay T1:~l, No J. A digest of the papers on dielectric breal~-do~.'n published in 194~-3 is given in Volume X of this series under the subtitle ''High Voltage Phe:~omenati . At a symposium on dielectrics held in 1946 at Br~stc>] IJniversi.ty by the Faraday Society, Prcf. A. Ron Hippel contributed a paper st~mmar.zing the resets cot previ- ous work on dielectric breakdown in solids, and indicating the nature of exiling prctlems2. The following paragraphs are concerned essentially with the cont~ribu- t~'ons to this subject published ire 1947, but it Bill be convenient to describe the background very briefly. Solids __ _ a the orb of breakdown; Which went intc Consider an electron mooring in a or'~stal having ~ given set of thermal vibrations. The electron can achieve a speed such thaws it gives up energy to the crystal lattice less rapidly than it acquires it from the field. This conclusion is based on the general form of the function giving the dependence of the probe- bility of quantum mechanical transitions on the speed. of the electron this function has a maximum. The existence of this maximum, though not its position, is independent of the nature of the c~iy-sta]. The existence of this maximum nosy be regarded as the core of three of the present theories Qua tre~k~o~no ~t WBS first proposed by A. Ron Hippel :in 1932. This theory enabled him to Bed ate break- do~n strength to the Reststrahien frequencie.s~of the alkali halides, ire first quantitative success in the theory of breakdo~n24. In 1937 H. Frthlich published much more detail With regain to the motion of electrons in a crystal under the influence of an applied field . It yielded the same general result as the von H;.ppel theory in the sense that it sh`::wed that above a certain [held strength the electron could not dissipate its energy' to the lattice as rapidly as it acquired it from the f~e3.d,o for field st,rengt'r~s higher than this the electron Is speed Would increase indefinitely. Later on <?. Smith theory of breakdown W25 derived very simply by Speger and Teller Without the 'ase of quantum mechanics in any essential connection . A fourth theory of breakdowns in which watre mechanics plays the important roles was F~ODOS=] lD 1939 by Frarz, . The first three of these theories have & central region in r~hic'n they are similar and an outer one in Which they differ' or in which ibey have not been equally de- veloped. The nature of the differences between them has been discussed in articles in the Physical Review and elsewhere in the past fe,.r, years. The most significant aspect of these differences seems to be that the Frohlich theory depends upon hiB energy e~'ectrons9 While the Seoger and Teller and von Fippe] theories depend upon comparatively Ir°~_ energy electrons. This difference is not trivia in its imp~ic.~,tions in fact the thing papers by Fr~hlich 'Rich wall now be discussed are strongly concerned With Be question as to whether the electrons which initiate breakdown are of high or of comparatively low energy.
~1 The objection has been raised against Frohlich's theory that tile high energy electrons upon Which it depends word not be found ire a crystal, i.e., that there are processes Which would prevent electrons from attaining these energies2. An adequate derivation of the function g:~vir~g the number of electrons as a function of energy in a crystal With an external field applied Would answer this question. ._. , Aim_ it, - _ ~ This is attempted by Frohlich in the pacer "Energy distribution and stabllit;y of electrons in electric fields). ,; Starting With the Bloc h theory of electronic conduction in crystals, Prohlich arrives at a distribution function for the energies of the electrons which, for low energies, reduces to the Max~ell-Boltzmann distribution but for large energies approaches as;7mptotical~y a finite value instead. of zero. An infinite supply of electrons would be required to satisfy this condition. Therefore no physically satisfactory solution is possible in a system depending only on the exchange of energy With thermal vibrations in the lattice tr: take away the energy of the electrons. The same concision can 'ce reached by a non-mathematical argument. An electron gains energy from the field and ~ie]~.s it to the lattice at rates such that after a certain speed has been exceeded it should continue to gain energy indefinitely in ~ system in Which it c`an only lose energy by exchange With crystal vibrations. In this system an electron Lehigh achieves ~ high energy w~11 rearer lose it and there Bill be an indefinitely continued increase in the popu~at on of high energy electrons - an impossible condition. The fai.luxe of this system to give ~ physically satisfactory solution implies that £~ditiona]. means of di mi nishing the energy cuff the electrons need to be sought Ionizing collisions (i.e., collisions -which put electrons in the conduc- tion band) 2nd also collisions bet`-Tee;~ electrons may be necessary in order for a stationary distribution to exist. The theory for ~ s`-sten~ In Which ionizing co]lis~ons contribute to the distribution has not been reorked out. But by consider- ation of the conditi.or~s under Which ~ stationary distribution is not obtained, FrahI~ch gives a basis for his assumption that. Then an external field is ailed there may be many electrons smith energy near the ionization level. Ties analysis of the energy distribution when ~ field is applied to ~ crystal many lead to further interesting consequences when it is worked out more fully. This paper also helps to explain the basis of the cr~tericr~ (or condition) for breakdown assumed by Froh:lich in his first paper, namely9 that break6G~n commences Then the applied field attains a value such that electrons Faith energy equal to or less than the ionization energy vial be accelerated indefinitely. The reason for this choice of the condition for breakdown has not been entire].`r clear from Previous capers. The present pacer makes the basis for it more evident by slowing that there may be a considerable number of electrons in the cryst,&l with energy near the ionization energy. The title of the other paper by Froh1ich is: "On the theory of dielectric breakdown in solids', It refers mainly to the temperature dependence of break`3o,.~n strength in the higher temperature range. It has been estab].ished that in the lover range of temperatures the breakdown strength increases with temperature. This is explained by the earlier Frohlich theory on the basis of the change of relaxation
42 time With temperature. But at higher temperatures the sign of the temperature co- efficient is reimmersed, the breakdo~-,tn s~rength.decreades ~,irith increasing temperature. At first this Ivan attributed to thermal brea,;dovFn. B-ut it s now claimed that this does not account for it's The extens~ori of Frohlich's theory described In this paper i s designed to- accc>~t for the negative slope of the brea,kdov!n strength-tam, erasure curve at high temperatures. The earlier theory involved the assumption that in dielectrics the pop,'- ~ation c.f electrons in the;conduct~on [eve's is too small for e]ectron-.-e]..ectron . collisions ,t,o;be important:. the interaction of movi~ng electrons ~h the thermal vibrations of,the. lattice has the whole basis of.the absorption of~the e2.ectron's ener.gy,by,the.lattice. In this.pa.pe.r the possibility is examined 'that break6..o~;,n could,~c,cur,after the,ele.c.tron density in the conduction band becomes great enough that electron-electron collisions account for a subs-tan- part of '~he energy less of,a,ny,..elec.tro,n.. The concent,ration.of e.~.=ectrons 'is such that an e].ect-.~onic temper- ature can be defined for the conduction electrons when the field is alp.'''... ''A smsIl~.temperatuxe difference exists between the niow ng electrons and the lattice. This is the way energy is lost by thee set of conduction electrons. 'TIle mathematical analysis shows that breakdown could occur in such ~ systems that there exists a temperature To below which the temperature coe.ffic~ent is cos;'ive4v,!n~e ab<.:ve it is ne,gative, Ad that at this temperature the' energy acquired. from Isle Bleed by the electron between two Jarge-ang~e collisions Is equal to kT. The vc^'u~- of the breakdown Strength is not calcu:~.tedl,, the t'neor,~r succeeds one y on ~,rec~ct~ng the existence of ~ maximum in the breakdown strength a=. a function of temperature. In the cal.c~.at~..on 'of the energy gain and e..:ergy loss oil the electron ac-count,.i~ taken.of the fact that there ~,.s a s,.~'ust,an+~al~co~ent.~-ation of ,'i..so:l.ated levels." due to lattice imperfections at the higher ter;~.`,era,,~;~,'.~< FJect~cns can ne' trapped6.in,the isolated levels. Me crapped niece.;., moire ~;~~~.~- very slowly lit the applied field. There~ore.the ele~t-rons, AS ~ set, gall en£:g;,~ On t,he't~eld mainly in,the con,duct~ion.leve].s aria lose it to the 'later, m=''..n:'; -~re.~.~?~ Ted in' the ' isolated levels. It is sho~.thar On. a.su~ffi~ienCi,~r Ok. ~i.e'~o'stre~gth the elect tropic temperature A.. grow in~=f-2~ite~y, i.e.9 ttle orysta' bill break domes' ' ' Ti'ith thins extension the :~QU]ich, theory- now corers brea'~dowll by high eneeiegjJ\ra°n0Sby low energy- ~,~'l1el~a2~.-ere.rgy).el'ectrons. The high et~-cgy el.ectrons are responsible for bres2~ow,~ at the loper tempe-ratures, the Jo;"er energy electrons (electrons with them energies.) produce breakdown at. tilde h:.~her +,e.~oera..tu~es. The high e're~'gy.(lo'~ tem-perature) theory a+'+rib~tes ti.-le e].~.;at~on of' breakdown st~e.hath in m=~d ~.-f733.aLs lo a prece~s'anal~ogous tic :r,~-u Which explains th.e.fa:ct that t'ne resinate of an 'Troy _s '-,ig~^'ar than that ~ the pure metals. The presence of ~imp,~r~'f,i.es o`- a~i7.~ii~YLu~;es In a C'''`rS~..\ Wi97.. S3..8G S7~..~= t the position of To to lower tem~eratuL es 'by increasing the number 'of isol acted ~ e:, elsO Cn this theory the addition of impurit;ies would increase t~'b-i?eak~o~~;~n .s~reng~J~ of-some di- el.ectrics While it wc.~:ld diminish that of others, depending fin ~i.~e',~,er room temnera- t~re lies<on one side or the other of the temce~at,.Lre;l'c~~ct'-t~e sut.s~ance in question.' A parallel statement copied be made a'~ou'~'p-'ir'i'~ic.ation'. T'n-us the theory9 though quali.tative, makes interesting predictions whith call Restudied ex~erlmen tally. ' ~
43 A brief paper on breakdown has been published 'oy Halo. and Seitz7. They franc'. that the breakdown strength of K~)r is independent of temperat~?.re over a con- side~al'1e range. They propose that the breakdown of solids depends upon the release of electrons from excitonS 9 -that is, Strom excited (electron-positive hoJe)~pa~rs. This Mold Scoot i'or the smallness of the temperature coefficient. Froblichts high-~nerature theory includes some aspects similar to this. An experimental StU63J of the temperature dependence of the orientation of breakdown paths in crystals was made by i. W. Dav~-sson4. This type of investigation may prove useful? in the study of bile motion of high energy electrons in a crystal lattice. One of the interesting questions which appears in connection with these theories arid experiments is whether the directions taken by the breakdown paths are determined by high energy electrons which initiate breakdown (an implication of the I'roh~i.ch theory' presumably) or whether flower energy electrons initiate the breakdown, but the observed paths are those followed by high energy electrons developed Wafter the offset of breakdown. There is evidence in favor of the Batter vied. von Fippel and Davison found, a fen years ago9 a peculiar result. the break- do~n strength of NaCl crystals is -independent of direction, but the breakdown paths are in (130) directions En the field is applied along a (100N direction. This can be explained if the breakdown is triggered. off-by the Boa energy (long r.'ave) electrons which are not mucks influenced by tt,e sym~.etry of the crystal, while the - breakdown paths are produced by high energy (short Wave length) electrons developed after breakdown s initiated. which aloe ~'nf7..uenced by the crystal. s~pmmetries2. Frohlichis expression for the breakdown strength contains the ionization energy of the crystal (the energy required. to take an electron from the ground level to some level in the conduction bandy in 'the denominator. The other theories do not involve the ionization energy. Tt is.introduced by Frohlich's criterion for bran. It may be that this criterion is unnecessarily strong. in any case, this is a notable difference between the several theories' and it is avail able for experimental investigation. Studies of the breakdown of so]~ids divide themselves naturally into a few significant sub-~nvestigations9 for example, the relation of breakdown strength to characteristic frequencies9 such as the Res~st~-ah'en frequencies, the sign of the t,em~erat~re dependence and the st,ee~ne~s of its slopes the i.nf~uence of ~mpuri:ties ; car adm~.xtures9 and the orientation of breakdown paths O The caters contributed in 194C' refer mainly to the te~i~cerature dependence. , The theories discussed or mentioned above refer to instantaneous break do~,,:!n. In many practical situations voltages are ar!r:]ied for a long time and the For example g i r1 the case of paper i.nsu lated cables it mat' occur by the e].ectrochemica~ process described by the Writer in 719,~,622 actual brea'<~,vn may occur in other ways.
44 Liqui_ Gases ~ - No papers Here' found on the break'!dov~n strength of liquids. A review of the breakdown of gases '~as given by ProfO JUNO 3. octet as the 38th Kelvin Lecture before the Institute of Eieetrica'l`Engir~eers in London on. April. 24j 1947. ,It is reprinted in Sciencel°. Professor toed revier~s'-the histor:~- of the subject, explains the present theories, and'ir~dicates' proL3e~.~.s for fu-~re study. A bibliobrap'ny of 90 papers is given A cti,sc~a,ssio:~ of 'icicle Spark T?~scha.~geti was also held at a meeting of the Physical Society in Condor. Qua April 239 197trio This discussion is re~7ier!ecl. in Nature9. The Townsend theory of breakdowns as Iodized by holists attributes break- dor,tn to the ejection of electrons from the cathode' boy- tile 'action of positive ion:, radiatior~ en cl ~neta-stabJe atoms. These' are''gene'rated in the gas blat the electrons moving in the applied' field. ~hen-these 'products 'just suffice to generate one free electron at the.cathode for each ' primary e~ectron'in- tine gas ttie condit~on~for brea~d,'c~n''ex~sts. This theory has prc~ed;, satisfactory When applied to gases at reduced pressure.' ' ' ' . . '.' ' 2 '' . . . . . . . . . .. .. ' At Pressures near'atmospher'ic and for long gap lengths it,has .not,been sufficient 'to explain observations. A theory of the long spark at atmospheric' . pressure has been proposed by Loeb and Meek and indere~dentl-)~ by Raether which depends upon photoionization of the gas by' radiation coming from. prec,.eding parts of the disc] arge. : This' is sometimes referred to as ti.:e'st',eamer" me~chan:-sm of breakdown. This is clearly a significant develor~ment, because breakdown processes at atmospheric pressure should be studied In a different way where photcioniza~icn of the air (or other gas mixcure) is important than where.it is got important,. they c 'pressure: ; The foll.oring papers' have a 'bearing cn the sludgy of the spark `?+ atmos Zingerman and Nikaevkaia33 have investigated the mechanism of discharges in long gaps by means of photographs of incomplete breakdowns. They show that the d~scharge'channel'is not formed by the progress of one avalanche from cath;ode,to anode but' consists of separate stre~c,hes Which grow together into a Coleman channel. L. H. Fisher]1 attempted to verify the theory of Jong,-sparks of Loot and Meek but encountered experimental difficulties which are of interact In connec~..on . . . . ,.~th the design of such experiments. Loebl3 has-investigated the mechanism of -the negative point corona at ~ atmospheric pressure in relation 'to the second Tc~nsend c,oef~icient. i, D. Craggs 7 has studied the loca].ized after-gIc~ observed with long sparks in ~:ar~'ous gases. 5raggs and Fo,~ood25 have studied the after-glor~ following start sparks 1~. hydrogen at one atmosphere pressures They show that recombination of electrons and ions is apparently the cause of the light em7t-'-ed in the alter-~lo~ ard ca].cu].=Ge t~ereircrn a coefficient of recombination. They also show that ion concentrations in the hydrogen spar' channels may be found by observing the Stark broadening of Balmer lines.
45 The fol.lo~ing papers are also of interest in connection With the break- do~n of gases. If. Drakarev~4 shovels that, because an electron released by ioniza- tion gives up its energy during ~ 'arge umber of collisions, the mean-energy of the electron. is, under certain conditions, larger than the thermal energy of the re- ~ai~;ng gas. The conditions under which the notion of temperature can be applied to the electron gas are considered and a formula for the electron temperature is derived. 1.. Sena355 considering that the charge exchange is the basic process of interaction boatmen ion and atom' shoes that a proportionality exists between mean velocity of drift Of ions in the field anc! square root of fief 6-strength over pressure. The distribution of velocities of the ices is of a sharply anisotropic nature and cannot be associated with the concert of temperature. Jacobs and I,&RocOIue36~37 have investigated the ~.inimum sparking ~oten- tia~s of barium-, magnesium and alun~.num. in argon and in helium. They find that the Ado of electrons emitted from the cathode per bombarding Positive ion (Vm) is 0.1499 O.O8S and. C.045 respectively in argon. }~,Iinimum sparking potentials ~n lielium are 146 ~ 29 161 ~ 1, and lg7 ~ 2 volts. in general they are higher {lean argon. ~ graphical method is proposed for ~,redicti.n~, sparl~in=~ potentials for metals based upon the values of Vm or the work function. Bo M. Gokhterg38 has made measurements on the first Townsend cceffic:ient (~) for a number of gases of widely varying dielectric strengths. He `'inds that the brea''do~7n fields are those for ;.Thich. (a) reaches 0.0235 ~ -the Pressure in men Hg. The practical applications of gaffes smith high breakdown strengths are discussed. Troop and van der Oraff20 have -estimate the insulation of high voltages ~n vacuum. They find that t',~e gradient at the electrodes When breakdown occurs is, for high. voltages (lOQ-700 kV), far beloT.-~? the value for fi.elcl emission. They suggest cumulative release of secondary e1..ectrons9 positive Ions and photons as the mechanism. E. JO Sandbergl9 has studied the breakdown strength of gases and ioniza- tion coefficients. Hale and H!uxford2 discuss the estimation of ~.inimum sparking potential from the cathode work func-tio7l0 I. I. t.evintov23 has investigated the excitati.or~ te~.~erat~re~=, in the ch=nne] of the ;mc~.~lse discharge at atmospheric pressure. E. Elenbeas~7 leas st~..died the excitation temperature, the gas te~pera- ture and the electron temperature in the high pressure ~,ercury discharge. Elec- trodless discharges are discussed by G. I. Labati~9. F. A. ~,nglish30 has studied corona from-<2ine POSi~iVO poirt,s. Tord Rayleigh32 has considered the surprising amount of energy vehicle can 'ce collected after the electric discharge has passed. Fo JO [lev,rellyn ~ di.scusses the incendiary' action of sharks in relation to their physical routes. The stupor of brea'<do~r7n at microwave frequencies is, of con~i-derabJe intere~,tO ~ paper on this Subject has been !r~,ublisted bit R. 500pe-1OO
~6 An interesting d.irection of ~.nvest~.gation is that of the influence of certain gases ~h pclyatomic monocles (such as the ~reons) on c.,rc;~a and br~ak- dov.~n in air 4 The capture of electrons to form negative Cons is improbable unless there is some wale of disposing of the energy They collisions would accomplish these but they are rare. Pol~ratomi~ molecules of suitable types may do this by dissociating the excess energy is carried Amy as kinetic energy- of tie products 0. 15 In interesting paper on this subject has been :;ub'.~.sced by fJeleler and bobs . Their investigation was made in terms of the r~.ega.tlve corona in air. They measure the corona current arid also eke visua.' observ~ticusO The effect of freon is to reduce the current in Ache corona at ~ given voltages It also introduces ~ lag or "hysteresis" in the value of voltage at which a portico or type of corona starts. A second paper gives the results of a study of the positive corona 5~. The visual characterist,ics of the corona changed markedly with change in the perk centage of freon in the air9 as did also the c,~rrc:~ts and onset potentials. Mo V. Blanc28 has studied the ignition of explosi ve gas mixtures by electric sparks. This. includes minimum ignition energies a:~d quenching d~st=~.~ces of mixtures of methane, oxygen and inert gas c s. , ;., it. ., . , .
~7 B; .LI(~RAPEY _ ~ D:;~,(-S' Of Literature On Die1OCt1~1CS? X9 (3946-47! ~ 17 ''L. VOn Hi3?Pe~ 9 mranS. ?'ara6QY SOC., 42A (1946 SU~11eL1en1) PP 78-87 h. PrOI11iCY-, PrOC. ROY. SAC. A, I609~1937} P 230 tT. lo. Davissong [ih,RSe to 70, (19,!~6N PP 685-698 It ~rolllich, Proc. Roar. SQC. (7 Onion), 1SS, {1947) P 532 lI ~ P,rohlich g P:roc . Roy. Scc . q IS~ 9 ~ 19471 ~ 521 Malmlo~ T and Seitz, Phases O Rev., 71 ., (71.947' ~ 125 Seeger and Teller, Phys. Rc~r. hi, (1938 N P 515 10 2 3. 44 ~ 60 70 a O 9. Natures 160 (19471 JUDY 26,, PP 110-112 lGo L. 1~0 LOeb' SCienCe 9 106 (19,!47) SePL. 129 PP 229~236 110 T . 7-, FiSLer, P11_YS. ROV. ~ 729 (~.947) DC) 1~23-428 120 Re.ference deleted 1.3. T-,. P. Ioeb9 rhys. Rev. 719 (191.~7) P 712 14- o 15. DL5A. 16 0 17. l.g. 19 0 2~0 0 21. 22 0 23. FL. Ao Bak and o1:;hers' J. Tech. PLys. USS1? 179 (1947? P 1153 It'~:1~1 =~I' - 61~ 9 1 .~r/~. '~ - v · ~ ~f29 (1047J p 289 I`.~onr an~ ~eissl~,r9 T:;h~rs. RO1T. ~ ~;29 (1947) P 294 R. Coopex., 5,I.~.E49 94 Pt~. 3, (1947J PP 315~325 J. D. Craggs and others, ,T. AP7. PhYS. 189 (19471 P 919 . Franz s Z ~ f. Physik g ~ 607 ~ 1.939) E. J. Sa:~oberg, JO Tech. PLiys. g USSR9 17 (1947N P 299 Tr~rnp and van der Greaff, J. App. Phy~,. ,, iS (1947N PP 327-332 I~ale and H~uxford, <-, APCO P?1YS. ~ IS {1947) ~ 586 E. J. ~ urpi;y9 191;.6 Im-lual Report 9 Conferenco on Electrica1 Insulatio~l; 1TRG, P 11 I . I ~ I,: ~ri ntov, ~ 0 Tech. Phtys . ., (USSR) 17 ~ (1947) p 781 r.~_." -~' ~-" - ~.~ nn~h ~rh~'c! ~`T
48 24b A. von Hiprcl, 7~. f . Physi>., 75 c ( 1033) P 145 250 Cra~gs and Fopr?ood7 Proo. rhys. SocO (Tondon ~.J7` 947 p 771 .. . . 260 Craggs and F;oprocd, Prc.'cO Pl~ys. ~ocO 593~1947) p 7r5 . . . . . .. . 270 E. Elenbaas, Phillips Research Bc-cor~s, 29 (]947) F~b. pp 20-41 .. . . . ~. 2ge Fllo V ;,lanc ar~d others, I~. Cham. PhysO g :1 5g (194.7) P 753 · .. ; 290 C;. I. Babat, J. I. EcEo 9 ~.' (1947~) pp 27-37 . - · . 3o o 310 32. . 11. English5 PhysO Rev. g 71 (~.947) pp 633-639 F. J7 Ilel.!elly~l9 I.R.I. Trans.9 23, (2'947) pp 29-^,4 tord Rayleigh9 Proc. 170yO Soc. g IS99 (1947) 296 ~. . 330 Zinger~lan and Nik~e~l-~aia, J. Exp. Theorc Ph,~s. 16, (19i,.~) r' 499~509 (in 8ussian? 34. 00 Dr~arev' J. Pn~'rs. USSR lOg (1946> p 81 350 L. Sena9 u. F,l~ys. USSR 1O, <1946) p I,,rl'9,,,,` 36 0 37 0 38. TaCObS and ~ C" Rocque ~ J q .AI?P. Ph~rs O la, (~.947J r) ]. 99 ; JCCQ6S and ~a Rocquc,, Tr~!ns. ElectrocTic~n. .cc,c. 9~9 (1947N P 14 S. I~. Gok}~berg, 74Zlll. ,Acod. Sci. USSR 10, <'9461 p 425 · .;
