J o u r n a l o f

The Pranklin Inslilule D e v o t e d t o S c i e n c e a n d t h e M e c h a n i c A r t s

Vol. 208 DECEMBER, 1929 No. 6

THREE MECHANISMS OF BREAKDOWN OBTAINED ON GLASS BY ELIMINATION OF EDGE EFFECT.

BY

P. H. MOON AND A. S. NORCROSS,

Massachusetts Institute of Technology.

THE development of our present theories of breakdown of solid dielectrics is not wi thout interest. In the earlier days electric breakdown was thought to be somewhat analogous to the failure of materials by mechanical stress, and every substance was believed to have a definite breakdown gradient at which failure occurred. Experience soon proved this idea to be untenable; and further tests were so complicated by the effect of factors such as edge breakdown, variation in rate of voltage application, imperfect contact with the dielectric, and variation of electrode area that the subject remained in a state of almost complete chaos until 1922.

At tha t t ime K. W. Wagner presented his epochal paper on breakdown as a process of thermal instability, which contri- bution aroused the dormant interest in the subject and resulted in marked progress on both theoretical and experi- mental sides. Papers by Kfirmfin, Rogowski, Fock and others revised the thermal theory and placed it on a firmer basis; while the experimental work of Inge and Walther on glass, rock salt, and porcelain verified the principal predictions of the theory.

I t was soon realized, however, tha t the thermal theory could not offer a complete explanation of breakdown.* In

* See, for instance, Bibl iography 3.

VOL. 208, No. 1248--49 705

706 P. ~-I. MOON AND A. S. NORCROSS. [J. F. I.

fact, the experiments of Inge and Walther 2 showed that at low temperatures the thermal theory ceased to apply and breakdown voltage became independent of temperature. Attempts to explain these low-temperature breakdowns lead to the ionization-by-collision theory of Joff6 and the molecular disruption theory of Rogowski.

The experimental results of Inge and Walther, however, were open to the objection that at low temperatures the punctures occurred at the electrode edge in a field of unknown strength. Quantitatively, then, the tests were of doubtful value. Thus, the next step of these investigators was to repeat the tests with improved methods which eliminated "edge effect" and caused failu're to occur in a uniform field. In I9O4 Mogcicki 4 eliminated edge breakdown by blowing thin portions in glass tubes. His method, somewhat modified, was used by Inge and Walther 1 in I928. They also elimi- nated edge effect by immersing the specimen and electrodes in a bath of correct resistivity. The great increase in appar- ent breakdown gradient caused by the elimination of edge effect is shown in Fig. I. Here the lower curve (I) was obtained in the ordinary manner, the breakdowns for the horizontal portion being at the electrode edge. Curve I I was obtained with edge effect eliminated and gives at room temperature voltages five times as great as those previously obtained, notwithstanding the fact that the thickness of the specimens used for II was only half that of the samples for I. Thus by eliminating edge effect, Inge and Walther raised the breakdown gradient to ten times its former value. Similar ratios will be found by comparing their gradient of 3000 kv./cm, with tabulated values such as those in the Smithsonian Physical Tables.

In the older tests shown by Curve I of Fig. I, the region to the right was proved to be thermal breakdown while the horizontal curve represented a different mechanism which might be called "disruptive." In Curve II, however, it will be noted that the sharp break between the two mechanisms has entirely disappeared and there is an intermediate region of uncertain character. Inge and Walther believed this to be a combination of thermal and disruptive breakdown--a region of "thermo-electric" breakdown.

1)ec., [92o,1 T H R E E ~[ECI IAN: [ , c , S Ig OI;' B R E A I , . D ( } W N . 7o7

Valuable as the Inge and Walther results are, the five points they give are not sufficient to determine the shape of the voltage-temperature curve to any precision. The purpose of this investigation, then, was to s tudy the intermediate

F i ( ; . I .

4O

-,,xz

20 oQ

I0 L

0 0 20 ° 4 0 °

\ 60°C 80 °

Temperature

i

]

I

] I I

I00 ~ /20 ° 140 °

1,5

_~ t.o

0.5

v

I . {

375 35 32.5 30 X t0 -÷

\ 27.5 25 22.5

! R e c i p r o c o l o f A b s Temp T

Breakdown Voltage of Glass

I. Inge and Walther, zoo # Object Glass without elimination of edge effect. IL Inge and Walther, Ioo u Cover Glass in $emieonducting Bath.

III . Same data as II, but curve drawn with s lopes obtained for G-i glass.

20

r s 708 P . H . ~fOON AND A. S. NORCROS.. [J, F. I .

region in more detail by varying the temperature through a wider range and obtaining a larger number of points. The tests were made in the Electrical Research Laboratories of the Massachusetts Institute of Technology.

APPARATUS.

The form of glass samples is shown in Fig. 2. Glass tubing was sealed off at one end which was heated and blown into a

FIG. 2.

5reel Rod

"~ / G l a s s Tube /Vercur 9 E/ectrode5 f

' !

\ ~ ,,X(X : ' .

J Form of Glass Sphere used for Breakdown Tests.

sphere as shown. It will be noted that there is a com- paratively large area of uniform thickness and that the change from the thickness of the tube to the thickness of the sphere is very gradual so that there is no appreciable concentration of stress at any point. Various thicknesses were obtained by blowing different diameter bubbles and by using various sizes of tubing. Thickness was measured after puncture had occurred by breaking away portions of the glass in the vicinity of the failure and measuring the thickness with a micrometer.

Mercury electrodes were used in most of the tests, although other materials were used in some cases.* Contact to the

* See page 719.

Dec., 1920.] TttREE ,~IECH:\N]SMS 01: I~REAKDO\VN. 7OtJ

inner electrode was made by a steel rod which was so hung tha t it would not rest on the bo t tom of the sphere. The mercury for the outer electrode was held in a well about 3.8 cm. in d iameter which was bored in a piece of steel shaft ing I5 cm. in d iameter and I5 cm. long. This large steel cyl inder was well insulated thermal ly and proved to be very effective in keeping the t empera tu re uniform.

For testing flat sheets, brass electrodes were used, the d iameter of the flat port ion being 15.9 mm. and the radius of the rounded edge being 3.2 mm. These were immersed in a liquid having the proper resistivity to prevent edge break- down.

All tests were made with direct potential obtained ei ther from a loo-kv, kenotron set or from a 4ooo-volt motor- genera tor set. Voltage was measured with a 2o-kv. volt- meter of the D'Arsonval type or with a I o o - k v . electrostat ic meter.

Wi th the kenotron set, voltage was brought up slowly by the use of an induct ion regulator in the pr imary of the trans- former. In some of the tests a motor-dr iven rheosta t was also used. At low tempera tu res the rate of voltage rise had little if any effect, but at higher t empera tu res it was found necessary to use a much lower rate of voltage application. A uniform rise giving breakdown in about ten minutes was found satisfactory.

EXPERIMENTAL RESULTS.

Tests on G-± Glass.

The first tests were made on G-I glass (a lead glass made by the Corning Glass Works). The points of Fig. 3 represent the results obtained at room tempera ture . Here, as in all subsequent curves, each point indicates one breakdown measurement . The unit of voltage is taken as the kilovolt, and the unit of thickness is the micron. (I/~ = o.ooI ram.) The curve was taken from Inge and Wal ther ' s tests on two different kinds of glass, and will be seen to agree closely with the tests on G-I glass. Inge and Wal the r obtained an average breakdown gradient of 3000 kv./cm., while our average was 3IOO kv./cm. This check was considered a sufficiently good indication tha t edge effect was eliminated, and accordingly the work was extended to higher temperatures .

7IO P . H . Moon AND A. S. NORCROSS. IJ. F. I.

The results of all tests on G-I glass are shown in Fig. 4. where breakdown voltage is plot ted against thickness. Several striking facts are at once evident.

I. For low temperatures and small values of thickness a linear relation holds, as shown by the curve for o deg. cent.

FIG. 3.

60

50

~ 40,

0

aa20

7 IO

o/ 0

/ O / . . . . . .

50 I00 150 200~ Thichness in microns

Breakdown Voltage of Glass at 20 deg.cent.

The s traight line was obtained by Inge and Walther 1 on the following: i . Cover glass in xylene, 50 cycles, peak values. 2. Lime glass spheres, 5o cycles, peak values. 3. Lime glass spheres, direct potential. Curves for these three conditions coincide. The points were obtained by" Moon and Noreross for G-x glass on direct potential.

The voltage gradient for this condition is constant at the high value of 3IOO kv./cm, and is independent of both thick- ness and temperature .

Dec., I929 .] TI tREE ~{ECHANISMS OF BREAK1)OWN. 71 I

2. For higher t empera tu re and greater thickness, the b reakdown voltage is no longer independen t of tempera ture , but decreases as the t empera tu re is raised.

60

5O

o o IOO

FIG. 4-

J

o ~o u o 9 *

200 Thichness 300 microns 400

Breakdown Voltage of Lead Glass Spheres (G-t glass).

J / IOO°

/ jzso

F; ~ / 5o °

~_00 °

~_50 ° 30~

~50 o

50O

3. Above 15o deg. the spacing between the curves shows a sudden increase, indicat ing an augmented effect of tem- perature. I t will be shown later t ha t the transi t ion to thermal breakdown occurs in this region.

The curves branching off from the s traight line are of the form V = a d '~ where a and n were chosen to fit the major i ty of the points. I t is t rue tha t the points at very great thick- ness appear to be slightly low, bu t it was not t hough t tha t the accuracy of the da t a war ran ted a more complicated ex- pression than the above.

The same results are plot ted in Fig. 5 where logari thmic scales are used so tha t all curves will plot as s t raight lines. The s t ra ight line on the left is for disruptive breakdown and has the slope (n = I.OO). The group of lines on the upper par t of the d iagram were at first d rawn with slightly different slopes with n vary ing from about o. 7 to about o.6. However, the points seemed to be fitted a little bet ter if all these lines were drawn parallel; and when this was done, n was found

712 P . H . M o o n AND A. S. NORCROSS. [J. F. [ .

to be .2//33. In the lower part of the figure, the lines are evi- dently of quite different slope. The simplest result is ob- tained by drawing these parallel with a slope of 1~. Fig. 5

FIG. 5.

T h i c k n e s s in Mic rons o ° /00 lo 50 100 /50 200 zso ~ ~ ~ z ' ~ . . . . . . . 200

4o i 30

io o

, , . J.oo"

o i

j L - ° o 0.050

a~c 025

/ 0.00 11.25 1.50 1.75 Z.O0 Z.Z5 ?.50 Z.75

19 d Breakdown Voltage of Lead Glass Spheres (G-I glass).

o

thus indicates three mechanisms of breakdown--disruptive breakdown shown by the straight line with unit slope, thermal breakdown shown by the lower lines with slope 1~, and another mechanism indicated by the group of parallel lines with slope 2.4,~.

These are shown to better advantage in Fig. 6 where the same curves are plotted against the reciprocal of the absolute temperature. For simplicity, all experimental points have been omitted, the values used for these curves being taken directly from the curves of Fig. 5- On the left the breakdown voltage is seen to be independent of temperature (disruptive

Dec., i929 .] T H R E E ~¢{ECHANISMS OF B R E A K D O W N . 713

breakdown).* On the right the voltage decreases very rapidly as tempera ture increases. The slope of these curves

FIG. 6.

Temperature I00 O° 20° 50° 750 /O0°C 150° 200° 2500 300° 2.00

I " ~ . ~ . ~ 1.75 50 " " ~ " - 2 "-402"-2~:a.,

" * ~ ~ , , " ,,N,.L'--.. ~ , 30 - - - - - /50

~20 1.25

, - .% -~ I0 X 1.00 "~

'

~ ~ 075 ,, "~

3 0.50

2 025

X ooo 1375 35 32.5 30 ZZ5 25 XlO -~ 22.51 20 IZ5

Reciprocal of Abs. Temp. -~ Breakdown Voltage o/Lead Glass Spheres (G-I glass).

is approximately that predicted by the thermal theories. Between these two regions is a third one, distinct from the other two and, to the best of the authors ' knowledge, here described for the first time.

Resul t s on L i m e Glass.

To make sure that the intermediate region was not due to some peculiarity of the glass, further tests were made on ordinary laboratory glass tubing (sodium-lime glass). Spheres were blown as before. As shown in Figs. 7 and 8, the curves are similar to the previous ones.

* F u r t h e r t e s t s a t -- 60 deg. gave t he s a m e resu l t s as those ob ta ined a t o deg. VOL. 208, No. 1248- -5o

7I 4 P . H . MOON AND A. S. NORCROSS. IJ. F. I.

Tests on Flat Sheets.

Tests were then made on microscope cover glass of German manufacture. The sheets were about 4 cm. square and had

FIG. 7-

T h i c k n e s s sn Microns 20 50 I00 200 300 iO0, I00;

50

40

30 >>f J ~ / ~ '~

-

9.75 0.5 _ . ~ ~ - - - -

0.35 9.50 t25 /5 /.75 2.0 2,Z5 2.5 2.75

Ig d

Breakdown Voltage of Lime Glass ,S'pheres.

1.50

an average thickness of 200 microns. The electrodes and sample were immersed in a mixture of aniline and xylene, the aniline being added gradually until tests showed tha t edge effect was eliminated. For temperatures above IOO deg. cent., a heavy lubricating oil (Mobiloil " E " ) was used.

Dec., n)29.1 " I ' I t R E F . . ~ ' I E C I I . \ N 1 S M S r.)F I-~REAKI)OWN. 7 1 5

\Vithin the tempera ture range of 100 deg. to 200 deg. this had a satisfactory resistivity wi thout the addit ion of any adul terant . At temperatures above 2o0 deg. molten paraffin

FIG. 8.

Temper,2ldr#' /e ~ 20" 50" 75 ° -00 ° 50"C 200" 25l.'" 300" ~i!O

±

. : b

c~3

75

50

25

O0

)25

)00

P75

3.50 35 32.5 30 ?Z5X/O -425 ?25 20 175

Reciprocal o£ Abs. Temp ~ Breakdown Voltage qf Lime Glass Sphere,.

was employed while at 312 deg. tests were made in air. There seemed to be very little difficulty in eliminating edge effect at high temperatures, but the difficulty increased rapidly as the tempera ture was lowered and the voltage raised.

The results of the tests on cover glass are given in Table I. and are plotted in Fig. 9 which also gives curves for G-I and lime-glass spheres.

It will be noted tha t all three curves are of the same shape and show the intermediate as well as the thermal mechanism. If the tempera ture had been reduced sufficiently on the cover glass and lime glass it is highly probable tha t these would

716 P . H . MOON AND A. S. NORCROSS. [J. F. I.

also show a region independent of t empera ture as did the G-I glass.

I00

50 40 30

~5 t~

2

1.0

0.5

Fie,. 9. T e m p e r a t u r e 20°C 50 ° 750 I00 °

, , ]

G-I C/~eas s ~ h e r o s S

150" ZOO ° Z50 ° 350 °

Z.O

15

a5

~ 0 0

\ 36 34 32 30 Z8 Z6 Z4XlO -4 Z2 20 18 1694

Reciprocal o{ Abs. Temp. 'IT

Breakdown Voltage of various glasses 2o0 ~ thick.

To get a quant i ta t ive idea of the degree of edge breakdown elimination, the electrode face was considered to be divided into the ten concentric rings of equal area which were num- bered from the center outward. With a very large number of tests, one would expect approximately the same number of punctures to occur in each ring if edge effect is entirely el iminated; while if edge effect is only partially eliminated there should be a distinct preponderance of punctures around Ring IO. The actual results are shown in Table I I, which indicates tha t there was little if any concentrat ion at the edge.

Effect of Electrolytic Polarization.

I t is a well-known fact tha t glass conducts electrolytically, the sodium ion being chiefly responsible for the conduction. 8 Before the application of a voltage, the ions are distr ibuted

Dec., 1929.] T H R E E ) ~ { E C H A N I S M S OF B R E A K D O W N . 7I 7

at random throughout the glass. If a direct voltage be now applied to electrodes which are insoluble in the glass, the ions drift under the action of the outer field and gradually produce poorly-conducting layers near the electrodes. Thus the apparent resistivity of the glass decreases with time; its

TABLE I.

B r e a k d o w n Tests on Cover Glass.

Cent.). Distance Sample d 0 V i lg V.* from Edge No. (microns). (deg. (kv.). l= ' (ram.).

In xy lene + anil ine.

i 2 3 4 5 6 7 8 9

IO I I i2

16o 205 i6o 230 175 235 228 224 242 i85 240 17o

87.0 lO4.O lO4.5 lOO.5

8o.o 69.o 64.o 53.0 32.5 29.0 33.o 37.o

14.8 14.8 12.3 14.5 18.o 21.o 20.5 31.o 38.O 32 .,5 44.0 25.0

27.7 X I0 -4 26.5 26.4 26.8 28.3 29.2 29.6 30.6 32.6 33.1 32.6 32.2

1.234 I . i62 1.I54 I.I2O 1.293 1.275 1.273 1.457 1.524 1.542 1.587 1.444

+ 3 . I 2. 3

- - I .O + 2 . 2

1.5 - -1 . 5 + 0 . 5

3.9 2.I 3.5 0.6

--0.2

In Mobiloil " E . "

13 14 15 I6 17 18

I9O I9O 230 2o0 230 212

I39.o I34.o 157.o 184.o I95.o 2OI .0

8.3 10.5 8.2 5.5 4.30 4.65

24.2 24.6 23.2 21.8 2I. 4 2I . I

0.934 i .o35 0.873 0.740 0.603 0.655

+4 .1 6.0 1.3 4.2 6.2 3.5

In paraffin.

19 15o 23I.O 2.15 19.8 0.394 - -0 .2 20 240 254.0 2.00 I9.O o.261 + 3 . 4 21 2IO 271.o 1.7o 18. 3 o.2I 9

In air.

225 312.o [ 1.17 17.1 [ 0.042 22 6.5 I I

V is ac tua l b r eakdown vol tage , lg V * is corrected to a c o m m o n base of 200 th ickness .

718 P . H . MOON AXD A. S. XORCROSS. IJ F. I.

conductivity may finally reach a value thousands of times greater than it had originally. The thickness of these layers is also a function of the applied voltage, causing the apparent resistivity to decrease as the applied voltage is increased. Thus these two familiar characteristics of glass are explained. at least to some extent, by electrolytic polarization.

T A B L E I I .

F r e q u e n c y D i s t r i b u t i o n .for P u n c t u r e s o f Cover Glass .

R i n g N u m b e r . N u m b e r o f P u n c t o r o s .

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . o

6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

i i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

I 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

1 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

U n k n o w n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

T o t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2

For many years it has been known that all, or most, of the polarization in glass can be eliminated by using an anode which will supply the glass with sodium ions as fast as they are withdrawn from the anode layer by the action of the field. The sodium ions will then pass completely through the glass from anode to cathode and the distribution of potential through the thickness of the specimen will be practically linear. Such non-polarizing electrodes have been used to some extent in conductivity measurements; but as far as the writers can find, have not been applied to breakdown experi- ments.

One of the purposes of these tests was to find if electro- lytic polarization had a marked effect on breakdown voltage, and to make sure that the intermediate region was not in any way due to such phenomena. Glass bubbles were used as

Dec., ]929.] "['ltREE MECttANISMS OP I~REAKDOWN. 719

before. The first tests were made at about 370 deg. wi th molten NaNO3 electrodes. Polarization appeared to be eliminated: absolutely no change of current with time could be detected, and Ohm's law applied. Moreover, the current was greatly increased over its value with ordinary electrodes, a bubble of 3o~ thickness and 2 cm. diameter having a resistance of only 65 ohms. As would be expected, this greatly increased current caused greater heating and lower breakdown voltage.

At lower temperatures, electrodes of sodium amalgam and of an aqueous solution of Na2S()4 were used. Various thick-

• i

k _ i

i 34

FIG. 1o.

I i

i , ~.-... [

i N i % I

32 30

\ x

\ \

! I b

28 Z6 Z4 X IO-* ZZ Reciprocal o£ Abs. Temp.

I ! \ ] a

L ZO 18 16

Effect of Electrolytic Polarization on breakdown of lime glass zoo ~ thick. O N a a m a l g a m e lec t rodes . • N a a m a l g a m , a l so Na2SO4 so lu t ion . ~x M o l t e n N a N O a . D o t t e d c u r v e o b t a i n e d w i th H g e lec t rodes .

15

I.O

0.5 2~

0.O

9.5

~.0

05

nesses of glass were tested and curves similar to Figs. 5 and 6 were obtained. Only the IOO ~ curve is reproduced here. (Fig. IO.) It will be noted that in the intermediate region the breakdown voltage is practically unchanged by the elimination of polarization, while in the thermal region the

720 P . H . Moon AND A. S. NORCROSS. [J. F. I.

voltage is greatly reduced. This serves as another indication tha t the intermediate mechanism is not a combination of the other two but is a distinct entity.

A few tests with Pyrex and G-I glass showed a similar reduction in breakdown voltage. A I62 # sample of G-I which would normally fail at IOOO volts, broke down at 400 volts with non-polarizing electrodes. Pyrex of 230 ~ and 295 ~ punctured at 400 and 450 volts, respectively. This would indicate tha t the sodium ion is largely responsible for the conduction in these glasses as well as in lime glass.

Other electrode materials, such as Wood's metal and ordinary solder at high temperatures and dilute HCI at low temperatures, gave results in agreement with those obtained with mercury electrodes. The effect of electrode area was also investigated roughly and found to have no noticeable effect. By using tubing ranging from 4 mm. to I8 mm. bore, bubbles could be blown having diameters from IO mm. to 37 mm. but with the same thickness. The results were identical within the limits of experimental error.

Resistivity Tests Measurements of direct-current resistivity were made on

the various glasses used in these experiments, the readings being taken after sufficient t ime had elapsed so tha t a s teady state was reached.

Table I I I summarizes the resistivity constants of all the glasses. Here A and B are constants from Poole's equation:

l g p = A - - B X ,

where p is the resistivity in ohm-cm, and X is the gradient in millions of volts per cm.

TABLE I I I .

Resistivity of Various Glasses.

U,me gl,a,~s No. 19 20.

,, ,, ,, 23 . .

7~-I glass No. 8 Pyrex No. IO. Cover glass No. 22.

(measured by Poole).

Temp.

27.6 deg. 27.8 30.0

24.5 24.0 29.0 29.0

A.

11.55 11.35 I 1.63

14.86 I3.8o 12.71 12.82

B.

1.37 1.41 1.37

1.20 1.60 1.23 1.33

Dec., 1929 .] THREE ~/[ECHANISMS OF BREAKI~OWN. 721

I t is seen tha t the values of B are all very nearly the same and are in agreement with values obtained by Poole : The values of A (A = lg p at zero gradient) are lowest for lime glass, somewhat higher for cover glass, and very much higher for G-I. Other samples of G-~ gave approximately the same resistivity which is over a thousand times as high as tha t of lime glass.

S u m m a r y of Resul ts .

For each region, the breakdown voltage is given by a relation of the form:

V = K i d r" (IO) ~'/r,

where d is the thickness in microns, T is the absolute temper- ature, and K¢, n¢ and be are constants of the material, different for each region. A tabulat ion follows:

T A B L E I V

Material.

G- I glass

Lime glass. Lime glass (non-polarizing

electrodes). Cover glass. Pyrex.

D i s r u p t i v e Breakdown.

K1.

31oo kv./cm.

48oo

nl.

I .OO

I .OO

In te rmedia te .

b~. n2. b2.

o 0.66 470

0.63 735

0.63 735 687

o 0.70 715

T he r ma l Breakdown.

0.25

o.I85

0.45

b3,

154o

I9IO

153o 1500

Apparent ly there is no connection between resistivity and breakdown in the disruptive region. Glasses of widely dif- ferent resistivities may puncture at the same gradient, as would be expected if this is a process of molecular disruption. However, a comparison of Fig. 9 and Table I I[ shows in the intermediate and thermal regions a direct correlation between resistivity and breakdown voltage. G-I glass which has the highest resistivity has also the greatest breakdown strength, while the other glasses are progressively lower as their resistivities are lower.

Table IV offers a possible explanation of the discrepancies

722 P . H . MOON AN[) A. S. NORCROSS. [J. F. I.

obtained in the past in regard to the effect of thickness. Some investigators have found tha t breakdown voltage varies as the first power of the thickness, others are equally sure tha t the 2~ power is the correct one, while others favor the square root of thickness. Of course, tests made without edge effect elimination are of questionable value. Neverthe- less, it is possible tha t those tests which have an exponent of uni ty were disruptive breakdowns, those tha t gave 2/~ were intermediate breakdowns, while those tha t gave l~ or lower were themal breakdowns.

T H E T H R E E M E C H A N I S M S .

Fur ther reference to Fig. I shows, in addit ion to the Inge and Walther curves I and I I, a curve I II which has been drawn to fit their five points using the slopes obtained for G-I glass. I t will be noted tha t the broken curve fits their points at least as well as their smooth curve. Thus the only experimental results with which the present tests can be compared tend to verify them rather than otherwise. Ap- parently other investigators have not found this intermediate region because edge breakdown has prevented them from obtaining the high gradients of III .

The phenomena may be visualized as shown in Fig. II . Here the heavy curve represents the breakdown voltage of glass at various temperatures, I being disruptive, III thermal, and II the intermediate mechanism. It is probable tha t if some means could be devised to suppress II and III , all breakdowns would be disruptive as shown by the dot ted line I. On the other hand, if mechanism I could be suppressed at low temperatures, the higher voltages of II or I I I might be realized. The heavy llne is obtained actually because that mechanism is selected which results in the lowest breakdown voltage. For some other material it is possible tha t the three curves might be as represented in Fig. I Ib . Here I I cannot be obtained experimentally unless some means is found for suppressing either I or III . In general, however, it seems likely tha t three mechanisms will be present in other uniform materials. Such a supposition can be verified only by a great number of careful experiments on different materials with edge effect eliminated, aided as much as possible by theories of the three mechanisms.

Dec., t929.1 THREE ~,[EC[t:kNISM,'q OF ];{RE;\KiJO\VN. 1" ,~

F | G . l l ( l .

• \ / / /

/ "\,

.___L T

FIG. Itb.

T

" D _ _ ~

I

The Three Mechanisms

I. D i s rup t ive I I . I n t e rmed ia t e

I I I . The rma l

724 P . H . MOON AND A. S. N O R C R O S S . [J. F. I.

As previously stated, two theories have been advanced to explain Region I. Joff6 considers it to be due to ionization by collision like the breakdown of ~ gas, 8 while Rogowski 7 and others favor the idea of the disruption of the molecules because of electrostatic forces. Neither theory is satisfactory at the present time, a l though several considerations lead us to believe tha t the molecular disruption theory 7 (possibly modified by the effect of sub-microscopic cracks 9) is the more probable explanation. The nature of the intermediate mechanism (II) is still a mat ter of conjecture.

Of the three mechanisms of breakdown, only the thermal can be analyzed mathemat ical ly to a satisfactory extent. Several investigators have worked out the thermal theory for the resistivity law:

- - 3 ' 0

P = P0~

but Fock 10 appears to be the only one who has used the more accurate but less tractable expression:

p = p l E ~'/~"

Also the Fock theory seems to be the only one which gives exact values for all thicknesses and temperatures. Unfor- tunately, however, the results as given by Fock do not admit of easy visualization. They are given in the form of three tables, the breakdown voltage being obtained by using all three one after another. If his parameter c is assumed to be independent of x (which is t rue to engineering accuracy*), the results can be simplified to a single set of curves, Fig. 12. Here the two Fock parameters v and c are defined by the relations:

500 V V - -

44.6Oplkl fl '

ks d [ 7 ~ - - - - •

kl 2~

* R e f e r e n c e t o T a b l e 2 of F o c k ' s p a p e r s h o w s t h a t for 0 < a < 12.5 ° , c is c h a n g e d b y less t h a n 0 . 0 1 % b y a v a r i a t i o n of x t h r o u g h t h e r a n g e z2 t o 22; w h i l e e v e n a t a = 60 °, t h e c h a n g e is o n l y 2 . 4 % .

[)ec., i929. ] THREE ~ECHANISMS OF BREAKI)OWN. 725

kl = thermal conduct iv i ty of insulation, watts /cm. /deg . Cent.

k2 = thermal conduct iv i ty of electrodes, d = thickness of insulation, cm.,

= " " electrodes, cm., V = breakdown kv.,

and/3 is obtained from the resist ivity equation:

p = p ~ ( i o ) ~ / T .

~ 0 ~ - -

J Y J

15 j / / J J

l0/J J J

05 J 8.0

F I G . I 2 .

f F

J I f

I

J -------

9:0 O0 1.0 2.0 / 9, c

Breakdown Voltage according to the Fock thermal theory.

500 V

k2 d = _ __ c kl 28

k t = thermal conduct iv i ty of insulat ion, wat t s / cm. /deg . Cent, k2 = thermal conduct iv i ty of electrodes. d = th ickness of insulation, cm.

= th ickness of electrode, cm. p = p ~ ( i o ) ~ / T

3.0

It will be noted that these curves give an excellent picture of the whole range of thermal breakdown. If resistivity, thermal conduct iv i ty , etc. are known, the breakdown voltage

726 P . H . Moon aNt~ A. S. NORCROSS. [J. F. I.

can be predicted for any tempera ture and for any thickness, provided of course tha t the breakdown is thermal. With a given material and given electrodes, the breakdown kilovolts V and the thickness d are directly proportional to v and c, respectively. Thus the curves show tha t for small thick- nesses (lg c < 9.6, approximately) the breakdown voltage varies exactly as the square root of the thickness, a conclusion which was enunciated previously by Rogowski, Kfirmfin, and others. But the curves show more than th i s - - they indicate tha t at greater thickness (lg c > 9.6) the breakdown voltage varies to less than the o.5 power of the thickness and gradually approaches a constant value as the thickness is increased.

Fro. 13.

3.5

30

15

~0

015 10

./o

!

9 8 7 E Breakdown Voltage according to the Fock thermal theor:~.

The effect of tempera ture is better shown by Fig. 13 which was obtained by replott ing Fig. 12. To the l imited accuracy

Dec., i929. ] rFHREE MECHANISMS OF ~REAKI~OWN. 727

of the graph, these lines appear to be straight with a slope

ba = o.435 ~.

|nge and Walther 2 have shown that the lines are not exactly straight, but are slightly concave upward, the slope at any point being

b3 = ~ /2 - T / 2 . 3 o .

The two expressions give values in reasonable agreement for ordinary ranges of temperature.

It is now desirable to compare the predictions of the Fock theory with the experimental results. Unfortunately, a precise quantitative check is not yet possible due to lack of data on thermal conductivities and temperature coefficients. With the present data, however, it can be stated that the results are in at least approximate agreement with the theory.

The curves of Fig. 12 explain why the slopes of the lg V - lg d curves are not the same for the two glasses, and are both much smaller than the generally accepted value of 0.5. Due to the good thermal conductivity of the mercury electrodes and their excellent contact with the glass, the materials are operating on the flatter curve to the right, the G-I glass being at approximately lg c = I.o and the lime glass at I.I 4 for Ioo microns. This difference can be ex- plained by a reasonable difference in the thermal conductivity of the two glasses. Of course, this means that the straight lines of Figs. 5 and 7 should actually be slightly curved to conform to the theory. These curved lines would fit the data about as well as the present straight lines do.

In regard to the change with temperature, the experi- mental results are apparently straight lines as required by theory. The slopes are I54 o, 19IO, ~53o and I5oo for the various glasses as shown in the last colunm of "Fable IV. Division by o.435 gives 354 o, 439o, 352o and 344 ° for [5. h is well known that for all glasses ~ lies in the range from 30oo to 5000, so the slopes b:~ are in at least approximate accord with theory.

CONCLUSIONS.

The results of these tests indicate that there are three distinct mechanisms of breakdown in the range of temperature

728 P . H . MOON AND a . S. NORCROSS. [J. F. I.

and thickness usually used. Which one will be encountered in a given case depends on temperature, thickness, and constants of the material.

In the disruptive range, breakdown gradient is inde- pendent of thickness, temperature, and resistivity. I t is a constant of the material and is 31oo kv./cm, for G-I glass.

In the intermediate range, the breakdown voltage varies approximately as the 2~ power of the thickness and is an exponential function of the reciprocal of the absolute temper- ature.

In the thermal range, the breakdown voltage varies as the half or lesser power of the thickness and is also an exponential function of the reciprocal of the absolute temperature.

Thus it is possible to tabulate the characteristics of the different regions for glass as follows:

Type. Effect of Effect of Effect of Effect of Temperature. Thickness. Resistivity. Therm. Cond.

I. Disruptive V=Kld

I I. Intermediate V= K2dn2(io)b=lT

n~ = 2/3 approx. III. Thermal V=K~d"3(Io)balT

na =0.5 or less b~ =0.435 $ where B

None

Exponential

Exponential

s obtained fron

Directly )roportional

Varies as 2/3 power

Varies as half *ower (or less)

p =pl(IO) ~fT

None

Has marked effect

Has marked effect

None

?

Has marked effect

In conclusion, the authors wish to express their sincere appreciation of the help and inspiration of Dr. V. Bush. They also wish to acknowledge their indebtedness to Messrs. R. A. Swan and W. F. Bart let t for the results on Pyrex and to Messrs. W. E. Creedon and W. E. Lowery for the tests on G-I glass at - 60 deg.

BIBLIOGRAPHY.

I. Inge and Walther, Durchschlag von Glas in homogenen und nichthomogenen elektrischen Feldern. Archly f. Elek., I9, I928, p. 257.

2. Inge and Walther, Durchschlag yon Glas. Zs. f. Phys., 37, I926, P- 292. 3. Bush and Moon, A Precision Measurement of Puncture Voltage. A . I . E . E .

Trans., 46, I927, p. Io25.

Dec., i929 .] "['HREE M E C H A N I S M S OF BREAKDOWN. 729

4. J. Mo~cicki, 0ber Hochspannungs-Kondensatoren. E. T. Z., 25, I9o4, p. ,527.

5- H. H. Poole, Electrical Conductivity of Some Dielectrics. Phil. Mag., 42, I92I, p. 488.

6. Joff6, Kurchatoff and Sinjelnikoff, The Mechanism of Breakdown of Dielec- trics. Jl. of Math. and Phys., 6, 1927, p. I35. Publications of M. I. T., Vol. 62, No. I 17.

7 - W . Rogowski, Molekulare und techuische Durchschlagsfeldstarke fester elektrischer Isolatoren. Archiv f. Elek., I8, I927, p. x23.

8. Kraus and Darby, A Study of the Conduction Process in Ordinary Soda-lime Glass. Jl. Am. Chem. Soc., 44, I922, P. 2783 .

9. G. E. Horowitz, Das Griffithsche Princip und die dielektrische Durchschlags- festigkeit. Archly. f. Elek., I8, t927, p. 535-

lo. V. Fock, Zur Wtirmethorie des elektrischen Durchschlages. Archiv f. Elek., i9, i927, p. 7 r.

VOL. 2O8, No. I248--5I