The closure and partial separation of a metallic contact

THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT*By ALAN FAIRWEATHER, M.Sc, Ph.D., Associate Member, f

{The paper was first received 9th March, 1944, and in revised form Ylth April, 1945.)

SUMMARYThe problems associated with contacts between nominally clean

metallic surfaces approaching and separating normally (as distinctfrom continuously sliding) may be divided into two groups accordingto whether the path between the surfaces is metallic or gaseous. Thepaper is concerned with the first of these groups. The field of interestmay be further sub-divided, as it includes both the phenomenaassociated with nominally static contacts and those relevant toseparating contacts up to the instant when the metallic path betweenthe contacts ceases to exist.

The first part of the paper is, in some respects, an extension anddevelopment of Holm's work, although originally done with little orno reference to the earlier results. All the effects encountered in thechange of resistance with current and mechanical pressure are shownto be predictable on the basis of the existence of contact spots, andnew contributions are made in several directions. The extents of re-sistance changes are directly related to the mechanical pressure. Afresh technique is described, by means of which the existence of thespots may be demonstrated and a lower limit assigned to their number.The influence of the rate of current loading is examined, and furtherverification of the plastic character of the yielding process is furnished.The measurements described relate to one particular contact material,a platinum-iridium alloy, and to one surface finish. They covermuch wider ranges of pressures and voltages than are encountered inpractice, and permit identification of all the significant events ob-servable in a normal laboratory atmosphere, i.e. without the employ-ment of vacua or special surface-cleaning techniques. This range ofobservations is bounded only by limits at which the effects cease to bethose relevant to a clean metallic contact. One limit, attributable tosurface films, not necessarily due to tarnishing, is encountered at verysmall pressures and voltages: the other appears at higher voltageswhich, if exceeded, result ultimately in glowing and fusion of thecontact surfaces.

The second part of the paper is concerned with the unequal wear ofthe two members of a contact pair ("selective erosion" or "unbalancederosion"): this is frequently accompanied by a gain of material by onemember at the expense of the other ("material transfer" or "transfer").In severe cases one member may develop a large pip while the otherproduces a corresponding crater: the contacts may then lock together.Hitherto, experience has suggested that such pips and craters occurin a random manner and that neither seems to be associated with aparticular contact polarity. The work described presents a new andsimplified approach to the problem. It is suggested that, in generaland perhaps more especially when quenching is permissible, un-balanced erosion results from, or can be made to result from, two maincauses: first the molten metallic bridge joining the contacts when onlypartly separated, and secondly the arc. The sense of arc erosion isalways the same, independent of the metal, whereas that of bridgeerosion depends on the sign of the Thomson coefficient of the metal nearits boiling point. Thus metals for which the senses of the bridge andarc erosion are the same can only exhibit one sense of erosion: butthose for which they are opposite, can exhibit both senses, or evennone at all, depending on which effect predominates due to appro-priate circuit conditions. This leads to the idea of alloys so designedas to possess a zero Thomson coefficient near their boiling point, whichwould therefore give equal bridge erosion of both contact members.Progress has been made in the development of such alloys. The re-maining unbalanced arc erosion would then be reduced as far aspossible by the use of an appropriate quench. Such alloys would, ofcourse, have to satisfy all the conventional requirements for contactmaterials and, if possible, one more: even with a quench, the possi-

* Measurements Section paper. f Post Office Engineering Research Station.

bility of slight residual arcing cannot be neglected, so that it would bedesirable, when selecting metals for the development of balancedbridge erosion ("B.B.E.") alloys, to do so from those which do notreadily support an arc.

(1) METALLIC CONTACT RESISTANCE: ITS DEPENDENCEUPON CURRENT AND MECHANICAL PRESSURE

(1.1) Configuration of a Contact Interface and the Dependenceof Contact Resistance Thereon

The finish of a material surface is characterized by two mainforms of departure from the ideal. First, there are deviationsfrom the nominal surface geometry: these take the form of ageneral waviness about the ideal, produced by inaccuracies in the"large-scale" shaping process. Secondly, the contour of thisundulating approximation to the ideal is not perfectly smooth:it is corrugated in a manner dependent on the various polishingprocesses which have been employed. The form and extent ofsuch corrugations need not, in general, be related to the geo-metrical inaccuracies. In contact work, uncertainties regardingthe region of contact, introduced by the large-scale inaccuracies,can be obviated only by the use of surfaces having dimensionswhich are small compared with those involved in the large-scaleinaccuracies: the small-scale roughness still remains.

Thus, there are two main types of contact: first, those which,by their geometry, may be supposed to have only one mainregion of contact, e.g. hemisphere-on-plane, two hemispheres,crossed rods: secondly, those which, for the same reason, havean indefinite number of such regions, e.g. two nominally parallelor flat surfaces. It is, of course, well known that, in the lattercircumstances, the total area of the main contacting regions isonly a very small fraction of the total available area. With thesimpler structures, however, where the dimensions of the singlemain contacting region can be ascertained—as they can be,microscopically, at high enough pressures—the contact resistancemay be predicted with reasonable accuracy. But, at lowerpressures especially, other effects are encountered in contactbehaviour where such simple considerations are inadequate, andit becomes necessary to consider conditions within a main con-tacting region, i.e. the effect of the small-scale roughness.Clearly, the result is contact at a number of spots as in Fig. 1 :

VOL. 92, PART I.

the properties of such a structure form the subject of the work tobe described. The relation between such contact spots and maincontacting regions is similar to that between main contactingregions and nominal contact areas. Tf the contact materials areof low resistivity, as is generally the case with metals, currentflow will be confined almost entirely to the spots, since theportion carried across the gaps by processes analogous to cold,or more probably thermionic, emission will be negligibly small.Tt is required to predict the manner in which the resistance ofsuch a structure varies with current, mechanical pressure, and

[301 ] 17

302 FAIRWEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT

surface finish. The situation which arises when the materials ofone or both of the electrodes are of high resistivity and the gapcurrent is, therefore, of major importance, has been discussedelsewhere.1

No historical survey of the subject is necessary, as this hasbeen made adequately by Holm.2 The most important earlierpapers from the present point of view are one by Holm,3 asecond by Holm in collaboration with his wife,3 a third by Holmwith the co-operation of Stormer,4 and a fourth by Holm alone.5

The first of these papers deals with the general problem of con-tact resistance from the theoretical standpoint, and the secondwith measurements. In the third and fourth papers a return ismade to the effect of mechanical pressure and the question ofelastic or plastic yielding. Measurements similar to these haverecently been described by Bowden and Tabor,6 with particularreference to conditions of interest to the mechanical engineer.

For any small area of sensibly perfect contact, the bulk of thecontact resistance is produced by the constriction of the currentstreamlines towards the contact area: it is not, in general, de-pendent to any appreciable extent upon the height of the raisedarea, which is usually negligible. Thus, when carrying current,although the temperature of the areas is greater than that of thebulk electrodes, and their resistivity also correspondingly greater,the relevant resistivity is more nearly that of the bulk electrodesthan of the spot itself. This is a simplification, since the spottemperature is, in general, indeterminate.

With a few small regions, widely spaced, the resistance may becalculated approximately by supposing that the conditions ap-proximate to those of current streamlines entering an infiniteconductor via a finite area: the solution of this has been given byMaxwell,7-8 and is well known. If the radius of a supposedlycircular contact region is a, and the resistivity of the contactmaterial is p, then the resistance r of a region is given byr - p/(2a). But if the spreading of the current streamlines isrestricted, this result is inapplicable and the resistance of eachregion tends to that of a rod of cross-section equal to the area ofthe region, and of length equal to the depth of the electrode.For any specified nominal contact area, the same voltage isapplied to all the areas of perfect contact ("regions or spots) andthe distribution of current amongst the areas is governed bytheir individual resistances. For small regions widely spaced,the mean current densities in all areas cannot be the same unlessthe areas are identical. Thus, if the current through the area is/, it follows that / varies as a. The corresponding current densityis proportional to i/a2, whence i/a2 oc I/a, and increases, there-fore, as the area decreases. Furthermore, under such conditionsthe current distribution will not even be uniform throughout agiven area.

(1.2) The Process of Contact(1.2.1) Variation of Contact Resistance with Current: The "Collapse

Ratio."Let the electrodes be supposed initially separated and not con-

nected to a battery, and then let them be brought together at aspecified load. As the surfaces approach, the most prominentof the opposing raised spots touch, and, in general, the areawhich they then present is quite inadequate to support the load:the spots are stressed beyond the elastic limit and commence toyield plastically. This crushing process continues until the totalspot area is just that which is capable of supporting the load:the spot material is then on the verge of plastic flow, and is there-fore stressed just to the "flow pressure." This condition isfundamental in contact theory: for stability at any time in thesubsequent history of the structure, this situation must hold.Now let the battery be connected and the current through thecontact increased. Tt will further be supposed that the currentis varied very slowly so that the contact structure is at all times

in complete thermal equilibrium. The significance of thisproviso will emerge more fully later. As the current is increased,spot temperature and resistivity increase, with a resulting rise incontact resistance. Since the current distribution is not uniform,one or more of the spots will become hotter than the others.Eventually these will soften and perhaps melt, and will becomeincapable of supporting their share of the load. Accordingly, theremaining spots will be stressed beyond the flow pressure, andwill collapse until the total solid area is once more just thatcapable of supporting the load at the flow pressure. To achievethis, a fresh solid area is introduced, either by an increase in thearea of existing spots or by the introduction of new ones, whichis just equal to that rendered ineffective by softening. Thus thecollapsing process proceeds in a series of steps until a current isreached at which all the spots have completely collapsed andcoalesced into one region. This would seem to be the limit mostrelevant to normal circumstances. Further increase of currentresults at first in a more or less uniform heating of the wholecontact interface, with an accompanying rise in resistance. Thisis followed by melting of the whole interface and, eventually, bymelting of the bulk electrodes.

Thus the resistance/current (or voltage) relationship will ex-hibit a marked minimum indicating the conclusion of the spot-by-spot collapsing process. The completed process will betermed the "major collapse" to distinguish it from its constituent"minor collapses" and any subsequent changes. The contactresistance falls, therefore, by an amount which is directly relatedto the extent of the collapse of the contact spots. Now the extentto which the spots are able to yield as a result of the applicationof current depends on the extent to which they have alreadyyielded under the influence of mechanical pressure. In otherwords, the area of a main contacting region associated with aspecified total spot area becomes proportionately less as thepressure increases. Thus the fractional resistance drop accom-panying the major collapse depends on the load. In view ofthe importance which this conception will be fourtd to have incontact theory, it is desirable to introduce a new parameterspecifying the extent of the major collapse. The significantmagnitudes are, clearly, the maximum resistance achieved priorto the collapse, and the minimum resistance fallen to at the endof the collapse. The ratio between these two resistances will betermed the "collapse ratio."

It is of interest to note that the preceding discussion dependslargely on the imperfect thermal conductivity of the contactstructure. Tf it were perfect, a slight increase in the total areaof the spots would suffice to reduce the current density, andtherefore the temperature, to a value sufficient to ensure freezing.Further, two effects have so far been neglected: first, thermalexpansion resulting from the heating of the electrodes, and,secondly, the contribution to the mechanical pressure providedby electrostatic attraction due to the very steep potential gradientswhich exist across the non-contacting regions, even at very smallcurrents, as a consequence of the very small separations involved.The results of both are, in general, to reduce the contact re-sistance in the usual way by increasing the area of existing spotsand introducing new ones.

As a result of these two effects, therefore, one or two smallminima might be apparent in the resistance/voltage charac-teristic, in addition to the major and subsequent collapses.Since they will be negligible in comparison with the major col-lapse, they will occur, if they are to appear at all, in the initialpart of the characteristic. It does not, however, seem possibleadequately to theorize regarding the magnitude of the thermaland electrostatic effects. A point is, however, worth noting inpassing: from the aspect of contact resistance, the net effects ofcurrent, mechanical pressure, electrostatic attraction and thermal

FAIRWEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT 303

expansion are much the same. Each results in reduction in re-sistance due to increase in the area of existing spots and theintroduction of fresh ones. Thus, the application of a certainmechanical pressure results in less current being required to re-duce the resistance to a specified value, and conversely. Currentand mechanical pressure especially, as well as the other less im-portant quantities, are therefore'largely interchangeable, since itis immaterial whether yielding is brought about mechanically orthermally.

Experiments.The above view was amply confirmed and extended by the

results of experiment with a hemisphere-on-plane structure, usinga platinum-iridium alloy containing 25% iridium. A platinousmaterial was employed in order to secure reasonable freedomfrom the effects of films and burning, and the alloy adoptedhappened to be the most convenient. The dimensions of thestructure were: hemisphere, 3-2 mm diameter; plane, 3-5 mmdiameter, 0-75 mm thick. The electrodes were brazed to ap-propriate threaded mounts. Their surfaces were carefullycleaned before each test by rubbing with a new piece of No. 0000blue-back emery paper. Every effort was made to avoid givingthe surfaces any "grain," and to secure a sensibly random finish.The contact was not subjected to any stabilizing process of thekind employed by some workers before commencing observa-tions, e.g. vibrating with a tuning fork, or tapping. Such a pro-cedure would only interfere with the surface structure underinvestigation. Known mechanical pressures were applied bymeans of a simple lever mechanism, suitable for pressures notless than about 0- 5 g. Considerable care was necessary to avoiddisturbance due to vibration. In order to cover the desired rangeof behaviour, currents of the order of 200 amp, with a corre-sponding contact voltage of less than 0 5 volt, were required.

Five points arising from the experience gained in making thesemeasurements are worthy of special emphasis:

(a) The whole contact structure and associated lever mechanismmust be in complete thermal equilibrium before measurementsare commenced, as well as at all times during them. In par-ticular, a run must not be started too soon after its predecessor:ample time must be allowed for the structure to cool down toroom temperature. Neglect to observe this precaution results invery unstable behaviour which might at first be somewhat puzzling.

(/>) Failure to show any collapse of the order anticipated maygenerally be attributed to particles of grit from the polishingprocess embedded in the surface. The remedy is to remove alayer from the surface with the aid of a lathe, and then polishas before.

(o) All changes are normally quite smooth and quite stablewhen completed. Oscillation of the millivoltmeter pointer, oralternate increase and decrease of the voltage with increasingcurrent, indicates the upper instability limit.

(cl) Abnormally high resistance at low mechanical pressures, ofthe order of 0 • 5 g, may be attributed to surface films. There isno remedy for this in a normal atmosphere.

(e) All changes must be carried out slowly and in small steps.The results obtained are summarized diagrammatically in

Fig. 2. From a qualitative aspect, there is no reason to supposethat they will differ very much for most metals, but any specificfigures quoted will, of course, apply only to the particular alloy•employed. Experiment showed that, for any pressure, there arein general six distinct change-points A . . . F in the re-sistance/voltage characteristic, located between two limiting in-stability regions A and F. The first of these, A, is attributableto films, though not necessarily to tarnishing, and is encountereda t very small voltages, of the order of 30 mV, and especially atvery small pressures, of the order of 0-5 g. The other region,

<I/?

3

p

C

\N

COLLAPSE

0

RAJIO QLPB

r

VOLTAGE:Fig. 2

F, appears at a higher voltage, about 360 mV, and marks theinception of glowing and ultimate fusion of the contact surfaces.B defines a maximum value of resistance, C the commencementof the major collapse, D the commencement of flattening out,and E the minimum. The resistance ordinate relevant to Edivided by that relevant to B gives the collapse ratio. B, C, Dand F always seem to occur at voltages which are roughly of thesame order, namely 40, 80, 140 and 360 mV respectively (seeTable 1). One or more of them may not always be obvious,

Table 1

Load(grammes)

0-5

1 0

2

468

91015

20

30

40

80120160

200

240

280

320360

Test No.

121212311212

T314514121112121231211

Probable value . .

Critical voltage for significant events in behaviour of

Maximum

(B)

93466155317065476535463732

N O .944343331636666436

N.O.86583263

114N.O.

4456

N.O.74

40

resistance (millivolts)

Inceptionof fall

(C)

10470

11583807098806583863732

N.O.947880

N.O.93

12410871

104N.O.

119585090

114N.O.

9478

150112

80

Inceptionof

flattening(D)

1158790

145140228139160

N.R.126144125134145120 '145109140127186124149124124140116135

N.O.140

N.O.152113138158

140

Minimum

(E)

280275206331

N.R.370191171

N.R.152

N.R.126134241200150303233149264124303291124150240224227238

N.O.202286142220

N.O.

Instability

IF)

348375342364

N.R.370360

N.R.N.R.

374N.R.N.R.N.R.

360N.R.N.R.

337259354330

N.R.380

N.R.N.R.

339N.R.N.R.

227360349374350370360

360

N.O. = not observable; N.R. — not recorded.

but they rarely disappear completely. Thus, B will not appearif A, B and C happen to be in a smooth curve. Similarly Cand D; and DF may be so flat that E is not apparent. Funda-mentally, all the change points—in particular C and D—arepoints of maximum rate of change of slope. There is no specificand obvious reason why, for instance, C and B should not beeither coincident or at the same value of resistance. Their


separation is attributed to the effects of thermal expansion andelectrostatic attraction referred to earlier.

The results of a series of tests performed at different pressuresare summarized in Table 1, and a few representative completecharacteristics are shown in Fig. 3. The six change-points areindicated by the relevant letter in accordance with Fig. 2. Forconvenience, the currents relevant to the change-points in Fig. 3have been listed in Table 2.

Five points are of interest:(a) The curves have been plotted by joining successive observa-

tions by straight lines: no attempt has been made at smoothingor the drawing of a mean curve. Since the phenomena are not

015

Table 2

010

005

1

T

1 L

D

\

(a)1/2

Load(grammes)

0-51 0248

1530

120360

Test No.

222321411

Critical current for significant events in bens

Maximum

(B)

0-280-441-31 01-31-51-35-5

17

resistance (amperes)

Inceptionof fall

(C)

0-800-701-31-63-41-59-5

1727

Inceptionof

flattening(D)

3 03 08 04-28 0

14152247

Minimum

(E)

2013188

1014186669

iviour of

Instability

(F)

2616183030

N.R.43

N.R.104

0200

20 40 60 80 100 120 140 160 180 200300 400

MILLIVOLTS

006

004

002

0

A

—-~_

— """

" ~>

-̂

—1— i - — T r —

E/F

2/ZX .

0 Z0 40 60 80 100 120 140 160 180 200200 300 400

MILLIVOLTS

007006

004

002

0

(c)4/3

N.R. = not recorded.

smooth, such a process would have been invalid. Neither hasthe obvious artifice of employing a logarithmic voltage scalebeen adopted, although the maximum and minimum are muchmore readily apparent if this is done. Such a representation,

0015

s: 0010o

00050 20 40 60 W 100 120 140 160 180 200

200 300 400MILLIVOLTS

0-007

0-006

0004

200

—•>—-~

— - * — • ' — ^ r' oi

-30/4-

20 40 60 80 100 120 140 160 180 200300 400

MILLIVOLTS

0 ~ 20 40 60 80 100 120 140 160 180 200 £200 300 400

MILLIVOLTS

0-0050004

0200

20 40 60 80 100 120 140 160 180 200300 400

MILLIVOLTS

003

002

001

° 0-00210

200

0-6

0-5

0-4

0-3

0-2

01

20 40 60 80 100 120 140 160 180300300

MILLIVOLTS400

\

\

\

A\\ r

L

RESt*—.! ^—.

STANCEi i " SCAL I x l O

f

100300

MILLIVOLTS

0200

20 40 60 80 100 120300

MILLIVOLTS

140 160 180 200400

Fig. 3nvenience each curve has been divided into 2 parts: the lower horizontal scale is thus a continuation of the upper one.nditions relevant to each curve are specified by marking of the form p/q under the serial letter: p is the load in grammes and

For coThe condit

experiments at this load.q identifies one out of a number of


however, gives an entirely false impression of the relative im-oortance of the various regions between the change-points.

(b) Sometimes marked voltage changes of the kind referred toin (c) appear in the vicinity of change-points. Examples of thisare to be found in Fig. 3 (a), (e) and (g), and especially in (e).

(c) Some experience and discretion are required occasionallyin locating the maximum, B, when the low-voltage instabilityregion, A, is extensive. Fig. 3(7), for 0-5 g, has been includedto show how important this becomes at low pressures.

(d) Cases where all the change-points are not separatelyapparent are given in Fig. 3 (6) and (e).

(e) Information regarding the plastic and therefore non-reversible character of the yielding, and also regarding the partplayed by thermal expansion may be obtained from the reversecharacteristic. Here there are two situations of major im-portance, depending on whether the upper instability limit isexceeded before the return journey is made. If it is, then fusionof the surfaces results, the resistance falls and no recovery ispossible on reducing the voltage. This is shown in Fig. 3(/) bythe dotted curve following the arrow. If it is not, then somerecovery is possible on cooling, but the recovery will be farmore rapid than the collapse, because the partings of the spotsbrought together by plastic yielding will be sensibly simultaneousand instantaneous. This is because negligible elastic recoveryis possible, and a comparatively small drop in temperature willbe required to effect parting. This is shown in Fig. 3(/) wherethe upper instability limit was just reached. The extent of therecovery is such that a value corresponding to the original maxi-mum is returned to. Thermal expansion is therefore by no meansa negligible factor.

(1.2.2) Variation of Collapse Ratio with Mechanical Pressure.At very low pressures, for normal surface finishes, the spot area

will in general be much greater than that necessary just to supportthe pressure. Thus, as the pressure tends to zero, the spot areatends to a' finite quantity dependent only upon the overall con-tact area and the surface finish. At very low pressures, there-fore, no collapse occurs and the collapse ratio tends to be unity.The transition between this condition and that of normal plasticyielding at higher pressures is effected via an intermediate con-dition of elastic yielding.

Similarly, at very high pressures, once the contact membershave been pressed together so tightly that the contact spots havespread and coalesced into a few large spots of contact, and theinterfacial structure is approaching more nearly that of a solidblock of metal, collapse is again impossible, and the collapseratio tends once more to be unity.

The subsequent history of the contact is of little interest, butit may be noted that, once the solid-block structure has beenachieved, the only collapse which can occur is that correspondingto complete fusion of the contact members; the collapse ratiomight then be considered as eventually falling to 0. The anti-cipated variation of collapse ratio with mechanical pressure thusappears as in Fig. 4.

Experiments.Related values of collapse ratio and mechanical pressure, ex-

tracted from the results of the same tests which furnished Table 1and Fig. 3, are plotted in Fig. 5. The portion of the collapse-

10

08o

§=0-6

3X

o

^ o]

o

o

0o

o ——n°0

r°—

5 10GRAMMES

Fig. 5

50 100

PRESSURE

Fig 4

ratio/pressure characteristic for pressures greater than that cor-responding to the minimum value of the collapse ratio is thusamply verified; the technique employed was not sufficientlyrefined to explore the region 0-0 • 5 g. There is no doubt thatsmoother data could have been obtained by performing manymore runs at each pressure and averaging the results, but theamount of work and time involved would have been very great,since each of the 20 points might quite easily take a week toobtain.

(1.2.3) Effect of Rate of Application of Current.For a constant mechanical pressure, the duration and extent of

the collapsing process resulting from the passage of current aregoverned by the time for which the spots remain in a plasticcondition. This depends on the temperatures of the spots andof their environment, and therefore on the rates at which heat isgenerated in, and conducted away from, the spots. The stableresistance at a given current is thus determined largely by therelation which has existed amongst these quantities, and there-fore in particular on the rate at which the current has been in-creased and on the thermal conductivity and flow properties ofthe material. It is difficult to predict the course of events for allpossible situations, but it is worth while to record some experi-mental results which may, in general, be accounted for on thelines suggested above.

Experiments.An ideal experimental investigation would be carried out by

taking a set of identical contact structures, and ascertaining themanner in which the resistance varied as the current or voltagechanged smoothly at different rates with respect to time. Such aprocedure is not, however, practicable.

Experiment shows that a specific contact resistance for acertain current and mechanical pressure is not readily repro-ducible. If, however, sufficient exploratory measurements aremade, it is possible to ascertain the most likely value, and, bydint of repeated trials involving repolishing, it is possible toobtain contacts whose resistances agree within 1 %. But identityof resistance at one particular current for a given pressure doesnot ensure that contacts are identical: their subsequent behaviourmay be vastly different, and if the matching process is refinedeven further and identity of behaviour at, say, three points isspecified, the contacts may still be different: for instance, theresistance may rise or fall as the voltage is increased beyond the


last of the three points. For experimental purposes, therefore,some compromise is necessary: the one adopted was arrived atin the following manner. Preliminary work led to the conclusionthat the resistance might be specified to have values quoted inTable 3, and that the contacts might be segregated quite

Table

Current

Specified values

Type

Resistancedecreasing

Resistanceincreasing

Attack ratio

1-21-6 —Test No. 2

1-9

1-41-6 —Test No. 1

3-0

3

10 mA

Re0-00400

0-004000-004000-00400

0004000-00410000400

20 mA

sistance (ohn000510

0005100-00508000510

0-005000-005020-00504

1A

is)0-00600

0006180-006200-00620

0006150006150-00619

arbitrarily into those whose resistance initially increased andthose whose resistance initially decreased. The closeness of thevalues employed to the nominal values is apparent from theremainder of the data in the Table. A pressure of 240 g wasused, with a target current of 60 amp selected to ensure that theresistance minimum was passed.

Smooth variation of current with time was also not readilyachievable: instead, it was thought adequate to cover the rangeof 1-60 amp in a number of specified steps, each step beingmade as rapidly as possible, but sufficient time being allowed toelapse to ensure stability before the next step. The significantfactor is obviously the ratio between successive current magni-tudes, rather than the difference between them: this ratio hasbeen termed the "attack ratio." Fig. 6 shows the resultsobtained for each type of contact.

0-007

0-006

0-005

0-006

xo

0'005

Vz

\\

\

\

5 10AMPERES

20 50

Fig. 6

(1.2.4) Variation of Contact Resistance with Mechanical Pressure.It may readily be shown—see, for instance, Bowden and

Tabor6—that if the contact surfaces yield plastically, their re-

sistance R is related to the mechanical pressure P by a law ofthe form R1 oc 1/P, but that, if they yield elastically, R} oc \/P.The slope of the resistance/pressure characteristics when plottedin logarithmic co-ordinates may thus be taken as a convenientcriterion of the relevant process.

Since the measurement of contact resistance necessitates thepassage of some current, it is apparent that the ideal test pro-cedure would be to select a current in a region of the resis-tance/voltage characteristic such that, thioughout the range ofpressure to be employed, the resistance was independent of thecurrent. But from the results already described it is clear that,except perhaps at very high pressures, there is no region wherethe resistance is not, or has not been, influenced by the current.Hence a less direct method of approach must be adopted: thevariation of contact resistance with mechanical pressure mightbe determined for a range of currents, whence it might be possibleto infer the mode of variation as the current tended to zero.For conditions prior to the inception of the major collapse, thepassage of current tends to make the contact resistance moremarkedly dependent on mechanical pressure. Thus, if R isplotted as a function of P for various currents, the mean slopeof the resulting curves should become less steep as the current isreduced, tending finally to the desired value at small currents.As the pressure approaches values for which the collapse ratiois approaching unity, say, for pressures of the order of 400 g, theeffect of the current becomes less and the curves converge: theideal resistance/pressure characteristic for zero current wouldpass through the intersection region without change of slope.

Tt may be of interest to note in passing that, if the only re-quirement for a certain type of contact were that it should havethe least possible resistance for a given mechanical pressure, thebest material would be that for which the ratio XIVp wasgreatest, where X and p are the electrical conductivity and flow-pressure of the material.

Experiments.

Since the avoidance of impact effects during pressure changingwas of first importance, the pressure was applied electromagneti-cally. The lever mechanism was employed as before, but theweights were replaced by an iron plunger operated by a current-carrying solenoid.

The results are shown in Fig. 7 (a) and (b). The region ofconvergence of the curves is indicated by the dotted rectangle,and the slopes of the curves by the relevant dotted lines: theseslopes are summarized in Table 4, whence the limiting valueappears to be nearer 2 than 3 and does not differ greatly fromthe corresponding figure obtained by Bowden and Tabor.6

Table 4

Current (mA)

Slope

200

0-74

100

1-30

50

1-66

20

1-63

10

1-57

6

2-28

It would therefore seem that plastic yielding occurs for pressuresas low as 10 g. It was anticipated that for very low pressuresa transition to elastic yielding, with an associated change of slopefrom 2 to 3, might have occurred. But other effects, previouslyreferred to, associated with low pressures, masked any sucheffect which might have been present.

(1.2.5) Further Consideration of the Contacting Process and a Methodof Estimating the Probable Number of Spots.

Six points are worthy of special emphasis:(a) The process of collapse is not smooth, but proceeds inter-

FAERWEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT 307

0-1

CO

io-oi

0001

(a)

10 100 1000GRAMMES

0-01

0-001

5b-xjoo\ NN

5 0 \ J ^ T ^ O N

\\2OO

\\ \ \

\ (b)

\vs.

10 100 1000GRAMMESFig. 7

not—neglecting of course any smoothing ofthe transition via space currents, which willbe negligible—and the collapse of existingspots is a slow process, since experimentshows that stability may not be attained untiltimes of the order of half an hour or morehave elapsed. Suppose, then, that some kindof instrument is used to record the voltagechanges, with the object of ascertaining theprobable number of spots. If the instrumentdetects every change, no matter how slow,then, since in any particular minor collapseall the spots, both old and new, participate,the final number of spots will be given bythe number of changes taking place within thefinal minor collapse interval. Alternatively,if, as is most likely, the instrument respondsonly to sensibly instantaneous changes, thenonly the introduction of new spots is recorded.The total number of changes therefore givesa lower limit to the number of new spotsintroduced as a result of the application of thecurrent.

The procedure envisaged in (/) does not,however, take account of those spots whichexisted prior to the application of the cur-rent. In order to estimate the probable totalnumber of spots, it is necessary to know therelation between the contact resistance andthe number of spots. Since each successivegroup of spots is subject to less squeezing-out than its predecessor, the spots will notbe all of the same size, and the desired rela-tion is not likely to be linear. If no otherlimiting factor were encountered, it might beexpected to be roughly logarithmic. Butsuch a limit is imposed by the fact that thepossible number of spots is finite, dependingon the surface finish, and this limit may bereached before the relatively slow collapse ofexisting spots is completed. The resistancewould then continue to fall without a corre-sponding increase in the number of spots:such behaviour is illustrated in Fig. 8. Theapparent variation of the number of spots with

mittently, corresponding to the collapse of existing spots and theintroduction of new ones.

(6) These small collapses occur in groups of increasing sizebecause the surfaces move closer together as a result of eachminor collapse.

(c) The number of collapses is directly related to the numberof contact spots.

(d) The collapse of each existing spot, and the introductionof each new one, causes a change in resistance and, therefore, involtage. Thus a supposedly "static" current-carrying contact,i.e. one free from any kind of extraneous disturbance, is apotential source of noise of the "click" variety throughout theperiod of time required for it to attain thermal and mechanicalequilibrium.

(e) All the spots, except those introduced during the last minorcollapse, collapse more than once.

(/) No matter at what rate the collapse of existing spots takesplace, the introduction of new ones is sensibly instantaneous,since the relevant portions of the surfaces either touch or they do

"ANC

E

cO

RES

-—LIMIT -

jID

VAL

>-Q

STE

NUMBER OF SPOTSFig. 8


time depends upon whether or not the current applied is sufficientto take the contact condition as far as the second instability limit.If not, then the incidence of spots decreases uniformly with timeas in curve A in Fig. 9. If it does, then a second period of rapidapparent incidence is encountered prior to the ultimate flattening-off: the result would then be as in curve B in the same Figure.

Experiments.Since the contact voltage may be of the order of 300 mV,

whereas the change to be looked for is probably between 0 • 1and 0-001 mV, it was apparent that some means of isolating thechange was required. Accordingly, the contact voltage wasdifferentiated by means of a transformer, the output of which wasconnected to a conventional a.f. amplifier feeding a peak volt-meter and associated galvanometer. The overall sensitivity ofthe apparatus was such that a nominally instantaneous change of1 mV at the primary terminals of the transformer produced agalvanometer deflection of about 8 cm. The results of the testsare given in Figs. 10 and 11. The actual incidence of the spotsis apparent from the curve for 40 g and 5 amp in Fig. 10, wherethe observation points are shown. These orders of pressure andcurrent were used in order to show the points effectively, as thenumber of spots involved is comparatively small and they occur

fairly slowly. For the same reason these data were employed inFig. 11. The two curves at 10 g, for 5 amp and 40 amp respectively,demonstrate the single and double regions of activity predicted.

It may be noted that, with existing technique, the clicks are nota potential source of noise in communication equipment.

(2) MOLTEN BRIDGES BETWEEN SEPARATING CONTACTS:THEIR PROPERTIES AND INFLUENCE UPON EROSION

AND TRANSFER(2.1) Outline of Erosion and Transfer Phenomena

The separation of two contacting, current-carrying electrodesproceeds in two steps: first, a period during which the electrodesare bridged by a drop of molten metal held in place by surfacetension; secondly, one during which current-flow is maintainedby some form of gaseous discharge. Earlier studies of erosionand transfer, such as those of Holm9 and others, were confinedmainly to the second step. Since the present paper is concernedwith the pre-gaseous regime, discussion of this work will belimited to a brief mention of certain aspects only. For furtherinformation, reference may be made to the original literatureand to the books by Loeb10 and Thomson.11

At least three significant discharge processes have been identi-fied: these are the arc, the spark and the so-called glow dischargeoccurring at very small electrode separations of the order of10~4 cm. The duration of any particular discharge process, andthe extent of the associated erosion or transfer, are governedlargely by the duration of the appropriate transient current andvoltage condition. This in turn depends on the circuit para-meters, particularly at radio frequency: the importance of thisaspect is frequently overlooked. Thus, an alteration in the dis-position or length of leads associated with the contacts, whilstinsignificant in normal operation, may radically alter the dis-charge processes. The phenomena involved have been examinedin much detail by Curtis12 and, less comprehensively and withparticular attention to automobile coil-ignition systems, byHartzell13 and McCarty.14 Reference may also be made to

0-125

0-120

0-115

0110

0-105

0-100

k\n\° 40g- 5 A

\

10 50 100SECONDS

Fig. 10

500 100020

CLICKS

Fig. 11

30 40


related work by Watson.15-16 Since practical contacts arealways finite, their nominal separation cannot always be sup-posed identical with the length of the path taken by the dis-charge, so that the phenomena associated with very small separa-tions may perhaps be less relevant to practical contacts than iscommonly supposed. Furthermore, in view of the very largedifferences in the orders of the currents involved in these threeprocesses, it seems reasonable to expect that arcing will be ofgreatest importance. Thus erosion associated with gaseous dis-charge would show, in general, a predominant loss of the positiveelectrode.

The bridging process has, in comparison, received little atten-tion. The temperature of an ultimate "hot spot" has been con-sidered by Slepian,17 and indirectly by Holm.2>3 The propertiesof the bridge itself have received some notice from Betteridgeand Laird,18 who reported that a bridge formed between electrodeshaving a fixed nominal separation has a current/voltage charac-teristic similar to that of an arc, i.e. of the form VI — constant.No explanation could be found for this, and none appears tohave emerged since. These workers also realized that unequalheating of the electrodes might result from Thomson effect,* butunfortunately they generalized this supposition to account forall negative transfer in all contacts. Since the magnitude andsign of the Thomson coefficient are not the same for all metals, orfor a particular metal at all temperatures, this generalization isobviously invalid. For the metals tested by Betteridge andLaird, namely a platinum-iridium alloy with 25 % iridium, andtungsten, the sense of bridge erosion is that corresponding to apredominant positive loss and a negative gain. The sense ofthis is, of course, the same as for arcing.

As a result of the Thomson effect the point of maximum tem-perature in the bridge will be located nearer to one end than theother, and fracture will occur at this spot. The ultimate breakagemight be expected to occur under one of two conditions: eitherwhen the temperature of the hottest spot reaches the boilingpoint of the metal; or, more likely, when, at a temperature justbelow the boiling point, the surface tension has become negligible,and the axial electromagnetic forces resulting from the waistedform of the bridge (see, for example, Hague,19 and the referencesthere cited) are adequate to part the bridge. The second condi-tion probably degenerates into the first, and it is likely that bothconditions obtain almost simultaneously. Fracture is thereforeunsymmetrical: more material is burnt off, or vaporized from,one contact than the other, and one may even gain material atthe expense of the other. Tf, for temperatures in the vicinity ofthe boiling-point of the metal, the Thomson coefficient is positive,the positive contact pips: if it is negative, the negative contactpips. This process continues, and, owing to the configuration,the temperature maximum may move below the surface of onecontact, resulting in the familiar pip and crater formation de-picted in Fig. 12, and perhaps in failure to separate the contacts.

Clearly, then, a desirable requirement for a metal to be used asa contact to interrupt currents of the order of amperes is that itsThomson coefficient shall be zero at temperatures in the vicinity ofthe boiling point of the metal. So far as is known, no pure metalsatisfies this requirement. Tt should, however, be possible toprepare alloys having this property, but there is no method ofpredicting the composition of such alloys. Even for singlemetals the situation is complicated by the fact that the sign ofthe coefficient may reverse more than once within a particularrange of temperature. For instance, those of copper and gold

• Current flow in an unequally heated conductor results in heat transfer in eitherthe same, or the opposite, direction to the current. The effect is known as Thomson

effect, and the Thomson coefficient, a, is'defined by the relation Q — o-j.-It, where Qal

is the heat carried by a current/ in time t through a conductor having a temperaturegradient dQ/dl. a may be measured in microcalories/coulomb/deg C or, in electricalunits, microvolts/deg C.

Fig. 12

do so twice in the range 20-300° K. Tt is to be expected, there-fore, that for any particular combination of metals, whateverthe behaviour of their individual coefficients, there may beseveral compositions satisfying the above requirement, some ofwhich may be useful and others not. For experimental purposes,a start may perhaps most easily be made by alloying metalshaving coefficients of opposite sign at temperatures near theirboiling points. This does not imply that the desired alloyscannot be obtained from metals whose coefficients are of thesame sign at such temperatures. It merely assumes tentativelythat the behaviour of an alloy at its boiling point is that whichmight be expected from a simple mixture of the constituents ifeach were supposed at its boiling point. Only experiment candecide whether such a simple view is adequate. If it is foundnot to be, then the fundamental concept of an alloy having azero Thomson coefficient at temperatures near its boiling point isin no way invalidated, but the search for such an alloy will becorrespondingly more laborious.

The conventional requirement for a contact, as regards lowcontact-resistance, freedom from corrosion and burning, hardnessand durability, seem to limit the choice so that at least one ofthe metals must be a noble one and, most probably, platinum.But the possibility of achieving the desired result by the use ofbase metals, either entirely or very largely, must not be over-looked. Indeed, such alloys would probably be of greatesteconomic value when containing a large proportion of poor con-tact material and in circumstances where the individual con-stituents would be unsatisfactory alone. They might also havea useful application under conditions of such severity that evenotherwise good materials would show bad unbalanced erosion.

Evidently two major problems require solution, namely(a) To ascertain why the current/voltage characteristic of the

molten bridge has the approximate form VI — constant, andwhether this relation is fundamental, because, if so, it might beimportant in contact theory.

(b) To discover what erosion or transfer phenomena, if any,are associated with the bridge, and, if they exist, how they maybest be mitigated.

An exact analysis of these problems demands a knowledge ofthe variation of the thermal and electrical conductivities, andof the Thomson coefficient, of metals, throughout a range of tem-perature extending from the melting-point to the boiling-point.

1-5

10

0-5

10AMPERES

Fig. 13.—Platinum.

10AMPERES

Fig. 14.—Palladium.

\ \

\RO/

\90/20

sWO/20

~ ~ — .

15

10

o

0-5

\ \

\ \ x

\55/ll

X30/H ^ ^

^165/11\I59/ZI

^^191/18

——

— —

10AMPERES

Fig. 15.—Iridium.

15 10AMPERES

Fig. 16.—Platinum-iridium 25%.

15

inoO•

3

The curves in Figs. 13-16 are identified by marking of the type rjs, where r is the starting diameter (cm x 10-s) and i is the starting current (amp).


Such information is almost non-existent. As regards the thermaland electrical conductivities, for most metals, with certain ex-ceptions such as bismuth, gallium and antimony, the electricalresistivity in the liquid state just above the melting point is abouttwice as great as that of the solid just below the melting point.A theoretical analysis, based on the hypothesis that the changein resistivity for normal metals is due to the change in atomicfrequency,* has been given by Mott:20 good agreement withexperiment was found. The thermal conductivity is then esti-mated on the assumption that the Wiedemann-Franz-Lorenz lawis relevant to the liquid metal, i.e. that if A, X and u denote thethermal conductivity, the electrical conductivity and the absolutetemperature respectively, the ratio X/Xu, generally known as theLorenz constant, is indeed constant. Thus, numericallyX/X ------ u x 2-4 x 10~8 (volts/degrees)2approximately. Concern-ing the Thomson coefficient, there seems to be no adequatetheoretical or experimental guidance. A general survey of presentknowledge regarding the effect of temperature on the propertiesof metals has been given by Hume-Rothery;21 reference mayalso be made to the book by Bridgeman.22

(2.2) Current/Voltage and Temperature/Voltage Characteristicsof Molten Metallic Bridges

(2.2.1) Preliminary Experiments: Inadequacy of Simple ThermalTheory.

Experiment was directed first to a study of the current/voltagecharacteristics of six metals, platinum, iridium, palladium, gold,silver, and a platinum-iridium alloy with 25% iridium, in anormal laboratory atmosphere. The alloy was included becauseit had received some attention from earlier workers. It soonappeared that neither gold nor silver would support a stablebridge, and attention was therefore confined to the remainingfour.

The results are shown in Figs. 13-16. With platinum, byappropriate increase of current, the bridge may readily be ob-tained in the non-luminous condition and its behaviour observedthroughout the successive main stages of red glow, incandescence,melting and final explosion. The melting process takes placealong the step in the characteristic: the portions of the charac-teristic both above and below the step are very roughly hyper-bolic. With palladium, Fig. 14, the upper liquid region is notrealizable and decrease of current below the point at whichmelting occurs results in freezing and degeneration to simpleohmic behaviour. No explanation is advanced for the failureof palladium to sustain a stable liquid bridge, but it is pointedout that the melting and boiling temperatures are closer togetherthan with platinum. With iridium, however, the liquid regionis the only one readily obtainable, and the characteristic is relevantto the hquid phase only and shows no discontinuity. Withplatinum-iridium, the absence of the step is due to the fact thatthe melting of an alloy is a much less sharply defined processthan it is with a pure metal.

Tests showed that, in general, bridges of a given materialalways explode at about the same voltage independently of theirsize. Typical values are given in Table 5, which relates to 12bridges for each metal.

The experimental results outlined so far are summarized inFig. 17. Since, with increasing current, the bridge steadilycools, it is theoretically possible for there to be some point A atwhich the behaviour of the bridge is just ohmic. The magnitudeof this ohmic resistance is defined by the slope of the line OA.It is immaterial whether the point A is obtainable in practice:

• The atoms in a solid vibrate about mean positions which are fixed in the solid:those in a liquid are considered to vibrate about mean positions wMch are not fixed,but which move slowly compared with the velocity of vibration. The frequency ofvibration is known as the "atomic frequency" and is not the same in the solid andliquid states.

Metal

Explosion voltage <rMeanMax.

^Min.

Table 5

pt

1-291-321-22

111

Ir

•44•47•42

75%Pt-25%lr

1-371-391-32

O CURRENTFig. 17

in general, it is not. With decreasing current, the bridge heatsup and the working point traverses the portion AB of thecharacteristic. In the vicinity of B the bridge glows, rapidlysoftens and melts, and becomes liquid at C. Further reductionof current may result in one of several effects:

(a) The bridge may continue to heat up, the working pointtraversing the region CE with final explosion at E.

CURRENTFig. 18


(b) Alternatively, at C or any point D inCE, the bridge may rapidly cool and resumeits ohmic condition at some, point in the lineOA, say at P or Q.

(c) Or again, if the bridge has either gainedor lost material, it may resume its ohmicbehaviour with a resistance different fromthat corresponding to OA, e.g. at R or S, orR' or S'.

If the melting region is ignored, and atten-tion confined either to the wholly solid or tothe wholly liquid regimes, Fig. 17 may be re-placed by Fig. 18. Such a characteristic mayconveniently be represented by the equationR = V/I - A + BV2, where A and B are con-stants. For small V, A — ohmic resistance.For large V, l/B -- limiting value of VI -—asymptotic power. The location of the pointA, defining the transition from ohmic toconstant-power operation, is readily obtainedby determining the maximum value of thecurrent by differentiation. The change occurswhen VI --- 1/2/?, i.e. as soon as the powerbecomes half its asymptotic value.

The functional form of the current/voltagecharacteristic is not, however, a sufficient basisfor analysis. A knowledge of the relationbetween temperature and voltage or betweentemperature and current, is necessary. Thiswas examined experimentally, a few resultsbeing shown in Figs. 19-22. It is apparentthat the temperature/voltage relation may,over appropriate ranges, be approximated toby a simple power law of the form T oc V".For platinum /; is usually of the order of1 • 5, whereas for platinum-iridium it is morefrequently about unity.

Having established experimentally the formsof the voltage-dependence of current andtemperature, it was desirable to ascertainwhether such behaviour is consistent withthe simple concept of a bridge of fixed dimen-sions. The results of such an investigationare outlined in the Appendix, whence itemerges that the observed phenomena arenot in accord with such a simple theory.Thus the possibility that the bridge dimensionsare not constant presented itself. This wouldmean that the current/voltage characteristicsfor supposedly fixed separations are, in fact,characteristics for constantly changing separa-tions.

(2.2.2) Further Experiments: Effect of ElectrodeExpansion.

Careful microscopic examination revealedthat the contact surfaces did appear to ex-pand and contract with increase and decreaseof current, thus altering the length and dia-meter of the bridge. This was particularly inevidence with palladium where with certainvalues of current, the surfaces moved to-gether to such an extent that the glowingbridge vanished and the whole structurerapidly cooled and gave the ohmic behaviournoted earlier. In favourable circumstances,this cooling was followed by separation of

15

£10

so-—

llb/ZZ

1000

15

1500 2000'TEMPERATURE

3000 °C 6 9 10


225/22

15AMPERES

Z0

250/2? 250/22

1000

15

1500 2000TEMPERATURE

3000 X 8 9 10 15AMPERES


200/20

/

;

11

\

200/20

\

to

1000 1500 2000 3000X 8 9 10 15TEMPERATURE AMPERES

Fig. 21.—Platinum-iridium 25%.

20

1500 2000 3000 °CTEMPERATURE

Fig. 22.—Platinum-iridium 25%.AMPERES


the surfaces with subsequent reappearance of the glow, and theinception of a state of oscillation in which the contact surfacesalternately heated up and cooled down. Such an oscillatingregime could be maintained for periods of the order of an hour.

A careful quantitative study was made of the variations ofbridge length and diameter, and of resistance, with current for

10 ' 15AMPERES

Fig. 23.—Platinum./. and D are in arbitrary units—1 unit = 1 •88 X 10—5 cm.

D

800

700

600

500

400

300

200

100

0

L

50

xlO

500

ROHMS

0-15

0-10

0-05

-A

—

w

<• * • —

V\\

D—- X.N

the metals already employed. Some results are shown inFigs. 23-26, from which it will be seen that, in general, withdecreasing current, the length increases and the diameter de-creases, in roughly a constant-volume relationship—to within50%—for resistance changes of the order of 10 : 1. Great carewas needed in measuring the diameter of the bridge so as toavoid confusing the diameter of the glow surrounding the bridge

LD

150

100

50

LDZ

xlO3

300

200

100

ROHMS

0-15

0-10

005

\

" \

— •

/

/

Loy^ ^

v Ji-~-—

15AMPERES


20

LD

I C A

on

50

n

xiO3

300

200

*

100

ROHMS

015

o-io

0-05

\

\

\

\

\

<^ \

• —

LD* '

\

\ n

\

\

/

//

— — - _ _

^

8 10 12AMPERES

Fig. 24.—Iridium.

7 10 15AMPERES

Fig. 26.—Platinum-iridium 25 %.


with the true diameter of the bridge itself, which appears as abright core within a less intense glow. Comparison of the orderof the measuqed and calculated values of the bridge (plus spread-ing) resistance is a useful guide in this respect. The observeddimensional changes, together with the known variations of re-sistivity with temperature, are quite adequate to explain the formof the current/voltage characteristics: a more detailed discussionof this follows. Quantitative measurements were also made onthe palladium oscillation effect: the results are shown in Fig. 27.

relatively so cool, that the electrode surfaces commence to absorban appreciable amount of heat from the bridge. As a conse-quence, the surfaces expand and their separation decreases, thuscompressing and cooling the bridge. If this decrease in separa-tion is sufficiently great, the thermal and electrical resistances ofthe bridge may be so rapidly reduced that the whole structurefreezes in the new position, and the behaviour may rapidlybecome ohmic. Alternatively, since the system possessesthermal capacitance as well as thermal resistance, it may oscillate.

0 7

0-6—/-

0 5 -

0-4-

0-3

0-2

/

/

I

1/

I

7

t

10 20 30MINUTES


4-0 5 0

The apparent bridge resistance consists of two components:first, the resistance of the bridge itself, and, secondly, the sum ofthe two spreading resistances located at the junction of each endof the bridge with each bulk electrode. As a result of currentflow, heat is generated in these resistances, the bridge being, ingeneral, much the hottest. The rate of heat dissipation in thespreading resistances, due only to current flow in the spreadingresistances, increases rapidly as the junction with the bridge isapproached. Thus, regions in the surfaces of the bulk electrodeswhich are not far removed from the bridge junctions are heatedby two sources: first, by current flow, and, secondly, by thermalconduction from the bridge. Consider, then, the effect of varyingthe magnitude of the current whilst the nominal separation ofthe electrode supports remains unchanged.

Let it be supposed that a bridge has been struck in the normalway and that the current is then changed. With increasingcurrent, the electrode surfaces heat up and expand, and theirseparation decreases. The bridge becomes shorter and wider,and decreases in resistance; since the current is controlledseparately, the bridge becomes cooler. With decreasing current,the electrode surfaces cool and contract, and their separationincreases. The bridge becomes larger and narrower, increases inresistance, and becomes hotter. Hence an increase of currentthrough the bridge results in a decrease of voltage across it, andconversely. Thus, if the current is steadily decreased, a valuewill be attained at which the bridge explodes. Alternatively, apoint may be reached where the bridge is so hot, and the electrodes

Thus, the surface contraction occurring on freezing may besufficient to pull out the cold bridge, which may heat up againand so repeat the cycle. This process continues indefinitelyuntil some outside influence fixes the behaviour, at one or otherof the extreme limits of oscillation by freezing or exploding thebridge, or half-way between the two.

From the contents of the preceding Sections, it is apparentthat the quasi-hyperbolic current/voltage characteristics are asubsidiary effect associated with the contraction and expansionof hitherto supposedly fixed contact surfaces, and are not ofoutstanding practical importance. No further work in thisdirection is therefore justified.

(2.3) Influence of Bridging and Arcing upon Erosion and Transfer

(2.3.1) Method of Attack.To correlate the direction of erosion and transfer with the

sign of the Thomson coefficient a threefold investigation isdesirable.

(a) To prove that the displacement of the temperature maxi-mum does exist, to show that the amount of the movement iscalculable, and to demonstrate experimentally the resulting asym-metrical temperature distribution. In particular, to determinethe sense of this for metals near boiling point.

(b) To carry out erosion and transfer trials rigorously con-trolled so that only bridges are significant, and to show that thesense of the erosion and transfer agrees with the sense of the

FAIRWEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT

temperature asymmetry determined under (a). To be of value,such trials must include some performed with metals for whichthe direction of bridge erosion and transfer is opposite to thatoccurring under purely arcing conditions.

(c) To carry out a comparative series of erosion and transfertrials, using the same metals as in (b) but so arranged that onlyarcing can occur, so as to demonstrate the constant direction ofarc erosion and transfer.

Since there are no published data regarding Thomson coeffi-cients at high temperatures, it seemed best to select, with the aidof the Tables,23. 24. 25 two metals having coefficients of oppositesign at ordinary temperatures, and also coefficients whose magni-tudes were increasing with temperature. In this way, it washoped to reduce the possibility of a sign change between ordinarytemperatures and boiling point. Furthermore, in order tominimize masking effects due to burning and corrosion, it wasdecided to employ only noble metals. The choice fell naturallyupon platinum and gold: preliminary bridge erosion tests showedthat the two metals did behave in the opposite senses hoped for,but that the signs of both their Thomson coefficients had reversed.As a matter of interest, further bridge erosion tests were carriedout on a number of other metals, with the following results.The metals are classified according to whether the sense of bridgeerosion is the same as, or opposite to, that of arc erosion.

Same as arcing: aluminium, antimony, cadmium, copper, gold,iridium, iron, nickel, palladium, silver, tin, tungsten, zinc.

Opposite to arcing: bismuth, lead, platinum.

It is worth emphasizing that tests carried out in the usualmanner, under mixed bridging and arcing conditions, are notalways of great fundamental value. They may furnish informa-tion regarding the behaviour of a certain contact material in acertain circuit, but, for the purpose of predicting the behaviourof the contact under other conditions, the knowledge thusacquired concerning the contact material is very meagre. Thus,if the resulting erosion is of opposite sense to arc erosion, thenit may be inferred that bridge erosion also is of opposite senseto arc erosion, and is the more important. But if the resultingerosion is of the same sense as arc erosion, then nothing can besaid concerning bridge erosion. It may either be of the samesense as arc erosion, but of unknown significance, or it may beof opposite sense and less-important. Reference may be madeto related work by Benedicks and Harden.26 Clearly, forspecified circuit conditions, it is possible to obtain balancedtotal erosion by the use of an alloy having a positive Thomsoncoefficient of such magnitude in the vicinity of its melting-pointthat the arc erosion is just cancelled. Such an alloy would,however, be of limited application.

(2.3.2) Theory.The fundamental equations (cf. Appendix) are now

d /^du\ dii dv

dx dx<£)' «KD + 0 • (1)

dx (2)

Practical conditions are probably best represented by the specialcase for which a ~ constant; A = constant; and X = XQJU, whereXQ — constant. Tt may be shown that the departure, 8, of thetemperature maximum from the mid-point is given by

o =••- - arc tan 0)

, . cosha///2 . „where A ~ u0 j£— and B — w0

cos ul/2

and ,,2 _ x > " where v2

sinh or///2Asin ul/2

JL

315

• (4)

. (5)

(2.3.3) Determination of the Sign of the Thomson Coefficient for Metalsnear Boiling-Point.

The sign of the Thomson coefficient may be inferred from aninvestigation of the temperature asymmetry associated with thebridge. This may be performed in either of two ways:—

(a) By direct observation of the temperature distribution inthe bridge itself: this is complicated by the small size of the bridge.

(b) By examination of the temperature distribution in the bulkelectrodes: since the temperature maximum is nearer one end ofthe bridge than the other, a marked difference of temperaturebetween similarly situated points in each electrode should bedetectable some distance away from the contact face.

In both cases, the temperature distribution of interest is thatjust before the bridge explodes.

The first of these may be attacked in two ways:(i) Visually.—One end of the bridge should be noticeably

hotter than the other. This is suitable only for low-temperatureconditions in which one end of the bridge has commenced toglow whilst the other end is still dark. Although this satis-factorily demonstrates the existence of temperature asymmetry,per se, it cannot, as pointed out earlier, necessarily be inferredthat the sense of the asymmetry so observed is identical with thesense at temperatures near the boiling point. A photographicrecord of the kind of temperature asymmetry readily observablewith platinum is shown in Fig. 28. Two pictures are given, cor-responding to both senses of battery connection, so as to showthat the effect is determined by battery polarity and not by anyspurious lack of symmetry associated with the general structureof the electrodes and their supports. In both cases the negativeend of the bridge is the hotter.

(ii) Photographically.—By locating the hottest portion of amolten bridge at the instant of fracture. The final fracture ofthe bridge resulting from the separation of the contacts producesan intense flash of light. By obtaining a photograph of thecontact surfaces, and of the flash of light, at the instant offracture, it is possible in certain circumstances to ascertain withwhich contact the final "hot spot" is associated. A typical resultfor platinum is shown in Fig. 29: two photographs are againreproduced so as to cover the effect of battery-reversal. In bothcases the final flash is associated with the negative contact.

The second of the general methods previously mentioned.(/>) above, can be tackled thermo-electrically: this can be doneonly at points where a thermocouple can conveniently be fitted,i.e. since the temperature gradients at the ends of the bridge arevery steep, at points where the temperature hus been degradedfrom the order of 103 deg C to the order of 10° deg C. Undersuch conditions, as a result of the large currents employed, thePeltier effect at the contacts between the electrode and its mount,and between the mount and the holder, becomes of importance.Consistent results can be obtained only in circumstances wherethe Thomson effect predominates, i.e. where reversal of thebattery shows that the sense of the asymmetry depends only onthe polarity of the electrodes, and is always roughly of the samemagnitude under similar conditions of current and voltage. Aset of results for platinum is given in Fig. 30. The negativeelectrode is again seen to be the hotter.

(2.3.4) Erosion and Transfer Trials.Experience shows that, except for contacts which have been

subjected to long-duration tests, visual estimation of surfacedeformation—especially in profile—is not always reliable. For


Flash Fig. 29 Flash Stage micrometer

A/18 I L= I5O,D=I58

B/18 : L= 143,0=156



quantitative work, weighing is the only satis-factory method, but care is still required. For,when pip-and-crater formation is extensive,two masking effects may occur: a portion ofthe pip may break off and fall away com-pletely, with the result that the contact whichhad been gaining weight shows a sudden loss.Alternatively, it may break off inside thecrater, thus giving the contact which had beenlosing weight a sudden gain. Microscopicexamination readily reveals such occurrences.Of these two effects, the first is the more com-mon, so that, in general, the most satisfactorypicture of contact erosion is obtained byrelating loss of the losing contact with numberof operations and current, and supporting thisby careful microscopic study of the form ofsurface deformation.

Some results are given in Figs. 31 and 32:of these the most interesting are those rele-vant to platinum, for which the senses ofbridge and arc erosion are opposite. Underbridging conditions, the negative contacterodes in agreement with the observations ofthe preceding Section, which showed it to bethe hotter. It may be that, in accordancewith expectation, the loss resulting from bothbridge and arc erosion is ultimately directlyproportional to the number of operations.The preliminary period of slower loss may beattributed to the effect of harder surfacelayers, produced by cold-work, which erodeless rapidly than the softer material under-neath. The bridging curves given for goldand palladium, and the arcing curve for gold,approach the region of direct proportionalitymore slowly. This is due to the fact that,proportionally, much more energy was dissi-pated with platinum than with the others:also, that platinum erodes much more cleanlyso that the results obtained are not affectedby pipping and cratering, or splashing (boththe gold and the palladium bridge-erosiontrials were run at 10 amp).

(2.3.5) Search for B.B.E. (Balanced BridgeErosion) Alloys.

A first series of bridge-erosion trials car-ried out at coarse (10-15%) intervals in theproportion of gold revealed that platinum-gold alloys in the range 0-10% gold bridge-erode in the same sense as platinum, and thatthose in the range 25-100% do so in thesame sense as gold. Clearly, an alloy givingbalanced bridge-erosion lay in the range10-25% gold. Further exploration, at 3%intervals in the proportion of gold, showedthat the alloy lay between 19 and 22% gold.

From the purely practical point of view,such an alloy will be far superior to gold, butit may not necessarily be much better thanplatinum, as an increase in total erosion mightresult which would nullify the benefit of theb.b.e. condition. For instance, experimentshows that platinum-gold alloys with morethan a certain proportion of platinum (even

VOL. 92, PART I.

10000

X

!|000

o

1010 10" I05

INTERRUPTIONSFig. 31.—Bridge erosion.

10000

'Ox

1000

o

I04 ' I05

DISCHARGESFig. 32.—Arc erosion.

18

318 FAIR WEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT

with as great a preponderance as 98 % platinum) bridge-erode,in the same sense as platinum, worse than pure platinum.For alloys having less than this proportion of platinum, asteady improvement takes place with increasing proportion ofgold, until the balanced condition obtains. Gold, however,always seems to show improvement with addition of platinum.The above effect does not seem to be due to hardness, sincethe addition of gold to platinum has a hardening effect. Itmay well be that the magnitude of the Thomson coefficient isvery susceptible to small impurities, and that small additionsmay at first increase the magnitude of the bridge erosion,whilst leaving the sense unchanged.

In view of the possibility of achieving the b.b.e. compositionwith metals whose coefficients are of the same sign, a very briefexamination was made of the copper-palladium series. Itappeared that there are probably not less than two such com-positions located somewhere in the ranges 20-30% and 50-60%palladium.

(2.4) Experimental Methods

(2.4.1) Contact Structure.Hemispherical contacts were employed, of diameter •£• in, and

were hard-soldered to suitable brass mounts. Voltmeter con-nections were provided by brass soldering spills, hard-soldered tothe mounts as near as possible to the contacts. The mountedcontacts were accommodated in a suitable micrometer holderfixed to a microscope stage. A magnification of the order of40 was employed, and dimensional measurement was performedwith the aid of a micrometer eyepiece, the sensitivity being suchthat one division on the micrometer head corresponded to 2-50or 1-88 x 10~5cm, depending on the actual instrumentemployed.

(2.4.2) Bridge Temperature Measurement.As the dimensions of the bridge are of the order of 10~3 cm

it was evident that an optical method was necessary. At tem-peratures much in excess of the melting-point, the bridge is inrapid motion over the contact surfaces, moving at times to theside of the contacts opposite to that viewed, and disappearingfrom sight. Some consideration and preliminary experimentsshowed that an optical method, employing colour-matching witha compaiison source of known temperature, was probably thebest. A convenient temperature-standard exists in the tungsten-filament lamp, since it is known27 that, for any straight- or coiled-filament tungsten lamp, vacuum or gasfilled, having a uniformlyheated filament, the resistance R and temperature T are relatedby the formula RccT1 2. Thus, knowing a pair of relatedvalues of filament temperature and resistance, the temperaturecorresponding to any other value of resistance may readily becalculated. This property was invaluable, because it was re-quired to measure temperatures up to the boiling-point ofplatinum (3 910" C) with the aid of a reference standard con-sisting of an ordinary disappearing-filament optical pyrometerreading from 700° C to 1 900° C.

In conventional optical pyrometry, using a pyrometer of thedisappearing-filament type, the standard source, i.e. the glowing,electrically-heated filament, is much smaller than the body beingtested, e.g. a furnace wall. Therefore, an image of the filamentis viewed against a background formed by an image of the testbody, and the filament temperature adjusted by altering thecurrent until the image of the filament just disappears. In thepresent problem, the test body is far smaller than the standardsource, so that the normal procedure was reversed. An imageof the filament of the tungsten lamp was obtained, without changeof size, in the diametral plane of the bridge: the bridge was then

viewed through the microscope, and appeared against a back-ground of colour dependent on the lamp temperature.

The lamp temperature was so adjusted that the boundarybetween the side of the bridge and the background just vanished.This adjustment was always made in the same sense, i.e. by in-creasing the lamp temperature from a low value to that at whichthe boundary just vanished. By this means, inaccuracies due tothe dazzle which would have resulted from the converse pro-cedure were avoided. The recorded observation was always theresult of several settings.

(2.4.3) Electrode Temperature Measurement.This was done with probe thermo-junctions of the kind

illustrated in Fig. 30. They were of the copper-eureka varietyand were prepared by welding with a very small gas-blowpipeflame, calibration being performed with the aid of an oil bath.

(2.4.4) Fracture Photography Technique.The purpose of the work was to obtain a photograph of the

contact surfaces and of the flash of light at the instant of fracture.The basis of the technique was the provision of a source ofillumination for the photography of the contact-surface profiles,satisfying the following conditions:

(a) Sufficiently intense to enable a silhouette photograph to betaken through a microscope.

(b) Sufficiently instantaneous in action to permit the accuratetiming of its occurrence within time intervals of the order ofmilliseconds.

(c) Sufficiently short-lived to permit the photography of amoving-contact surface.

A conventional spark-set, of the kind employed in high-speedphotography, was used; both the duration and operating lag ofthe spark did not exceed 5 microseconds. The spark-gap andoptical system were arranged below the microscope stage, andthe contact holder above. The spark-set was triggered by thevoltage change occurring across the contacts, as a result of thefracture of the bridge. For sensibly instantaneous triggering, anappropriate valve circuit wasvused, but where time delays of theorder of milliseconds could be tolerated a high-speed electro-magnetic relay sufficed. As most of the energy of the bridgeflash lay in the infra-red range, whereas that of the spark lay inthe ultra-violet, much improved definition was obtained by theuse of a blue-green filter. No lens was employed in the camera,and Kodak Super XX film was used with the standard developingprocedure.

(2.4.5) Erosion and Transfer Trials.(2.4.5.1) General.

Since automatic-telephone equipment was readily available, itwas considered simplest to develop a detachable contact holderwhich would be equally suitable for bridging and arcing tests,and which could be fitted to a standard Post Office 3 000-typerelay. Further, in order to make changes in weight most ap-parent, it was necessary to use the smallest possible contact con-sistent with adequate mechanical strength and ease of manipula-tion. The average weight of the gold contact was about 130 mg,and of the platinum contact about 150 mg. The assembly isshown in Fig. 33, which is self-explanatory. For arcing andlight-current bridging trials, 14-mil springs with soft-solderedcups were used, whereas, with heavy-current trials, 40-mil springswith hard-soldered cups were required. Weighing was donewith a standard micro-balance with which weights could bedetermined directly to 0 1 mg and, by estimation, to 0 01 mg.Weighings were performed at roughly logarithmic intervals inthe number of operations: originally a start was made at 1 000operations, but experience showed that this might well have beendeferred until 10 000.


Fig. 33

Fig. 34

(2.4.5.2) Bridging.In order to obtain bridging devoid of arcing, the voltage

employed must be as far below 14 volts—the conventionalminimum arcing voltage—as possible, and preferably of theorder of 2 volts. Provided this condition is satisfied, and subjectto the limits imposed by batteries and automatic-telephoneequipment, an appropriate value of current may then be deter-mined with regard to one factor only. This is, to give with areasonable number of operations a loss of the losing contact

which, taking into con-sideration the limitations ofthe weighing technique, canbe specified with a knowncertainty. A loss of theorder of 0-5 mg during thefirst 10 000 operations wasregarded as suitable. Pre-liminary trials showed thatthis could be obtained withgold at a current of 10 amp,and with platinum at a cur-rent of 25 amp. Experi-ment was directed first toten contact pairs of platinumand ten of gold: at laterstages in the work, in anendeavour to secure rapiderosion with small currents,ten pairs of tin were addedbut were afterwards re-placed by ten pairs of pal-ladium. The 10-amp and25-amp test sets were runat 450 and 900 operationsper hour respectively.

(2.4.5.3) Arcing.To secure arc erosion

and transfer sensibly un-affected by splashing andthe formation of solidbridges, gaps much less than1 mil in length cannot beemployed. This necessi-tates the use of voltagesmuch in excess of the mini-mum sparking voltage forair of approximately 300volts. Such voltages weremost conveniently obtainedas multiples of the maxi-mum d.c. supply voltageavailable, i.e. 240 volts,by charging condensers inparallel and dischargingthem in series. Experimentshowed that the smallestsuitable multiple of 240 was720, which was obtained bydischarging three conden-sers in series. Having fixedthe voltage, it then remainedto decide upon a suitableamount of energy to bedissipated at each dischargeso as to avoid splashing.

This depends on the contact material and is controlled by thecapacitances of the condensers employed. As a result of sometrials, three 2-/xF condensers were found suitable for platinum,and three l-/xF condensers for gold. Since the condensers haveto be connected to the gaps by means of auxiliary contacts, it isapparent that, without adequate precaution, considerable energydissipation might take place due to discharge between thesecontacts. The only satisfactory method of minimizing this wasfound to be by the use of an electromagnetically-operated


vacuum switch of the type shown in Fig. 34. This. hadnegligible delay and, as an added precaution, was maintained indarkness.

Experiment was confined to five contact pairs of platinum andfive of gold. These were fitted in holders similar to those usedin the bridging trials (Fig. 33). The contact assembly was ac-commodated on a standard relay yoke, and the gap adjusted byan insulated screw. The same weighing procedure was adoptedas before. To permit rapid testing, automatic equipment wasemployed as before; this combined the functions of voltagemultiplication and application, and provided appropriate safe-guarding and testing facilities. The apparatus furnished 144 dis-charges per gap per hour, and a rough oscillographic examinationin the case of gold showed that the discharge lasted approximately0 03 millisec. The condenser capacitance was approximately0-3 fiF, and the voltage 750, so that the total quantity of elec-tricity involved in each discharge was roughly 0-2 x 10~3

coulomb, and the mean discharge current of the order of 6 amp.In order to reduce the statistical time-lag of the discharge, andso minimize arcing failures, which were particularly evidentwhen commencing fresh trial periods, the gaps were irradiatedwith ultra-violet light. Under extremely adverse conditions,this halved the proportion of arcing failures.

(3) BIBLIOGRAPHY(1) FAIRWEATHER, A.: "Contact Non-Linearity, with reference to

the Metal Rectifier and the Carborundum Ceramic Non-LinearResistor," Journal I.E.E., 1942, 89, Part 1, p. 499.

(2) HOLM, R.: "Uber metallische Kontaktwiderstande," Wissen-schaften Verb'ffentlichungen aus den Siemens-Konzern, 1929,7, p. 217.

(3) HOLM, R., and HOLM, E.: "Charakteristiken von Kontaktwider-standen," ibid., 1929, 7, p. 272.

(4) HOLM, R., and STORMER, R.: "Eine Kontrolle des metallischenCharakters von gereinigten Platinkontakten," ibid., 1930, 9,p. 323.

(5) HOLM, R.: "Zur Theorie der ruhenden, metallischen Kontaktemit und ohne Fremdschicht," ibid., 1931, 10, p. 1.

(6) BOWDEN, F. P., and TABOR, D.: "The Area of Contact betweenStationary and between Moving Surfaces," Proceedings of theRoyal Society, A, 1939, 169, p. 391.

(7) MAXWELL, J. C : "A Treatise on Electricity and Magnetism,"p. 432 (Clarendon Press, 1904).

(8) JEANS, J. H.: "The Mathematical Theory of Electricity andMagnetism," p. 356 (Cambridge University Press, 1927).

(9) HOLM, R.: "Die Elektrodenzerstaubung in Abhebekontakten,"Zeitschrift fur Technische Physik, 1934, 15, p. 483.

(10) LOEB, L. B.: "Fundamental Processes of Electrical Discharge inGases" (Wiley, 1939).

(11) THOMSON, J. J.: "Conduction of Electricity Through Gases"(Cambridge University Press, 1906).

(12) CURTIS, A. M.: "Contact Phenomena in Telephone SwitchingCircuits," Bell System Technical Journal, 1940, 19, p. 40: BellMono. B-1202.

(13) HARTZF.LL, H. L.: "Improvements in Coil Ignition Systems ofInternal-Combustion Engines," British Patent Specification532462—1938.

(14) MCCARTY, V. E.: "Improved Coil Ignition Apparatus forInternal-Combustion Engines," British Patent Specification532299—1938.

(15) WATSON, E. A.: "Coil Ignition Systems," JournalI.E.E., 1932, 70,p. 105.

(16) WATSON, E. A.: "The Effect of Hydrocarbon Vapour on theContact Points of Ignition Apparatus," Proceedings of theInstitution of Automobile Engineers, 1927-8, 22, p. 812.

(17) SLEPrAN, J.: "Temperature of a Contact and Related CurrentInterruption Problems," Journal of the American J.E.E., 1926,45, pp. 930 and 1308.

(18) BFTTERIIX;E, W., and LAIRD, J. A.: "The Wear of Electrical Con-tact Points," Journal I.E.E., 1938, 82, p. 625.

(19) HAGUE, B.: "Electromagnetic Problems in Electrical Engineer-ing," p. 348 (Oxford University Press, 1929).

(20) Mon, N. F.: "The Resistance of Liquid Metals," Proceedingsof the Royal Society, A, 1934, 146, p. 465.

(21) HUME-ROTHERY, W.: "The Metallic State. Electrical Propertiesand Theories" (Clarendon Press, 1931).

(22) BRUXJMAN, P. W.: "The Thermodynamics of Electrical Pheno-mena in Metals" (Macmillan, 1934).

(23) FOWLE, F. E.: "Smithsonian Physical Tables," p. 405 (Smith-sonian Institution, 1934).

(24) LANDOLT-BORNSTEIN, ROTH/SCHEEL: "Physikalisch-ChemischeTabellen," p. 680 (Springer, 1927, 5th revised edition, 1stsupplementary volume).

(25) "International Critical Tables," 1929, 6, p. 228 (McGraw-Hill).(26) BENEDICKS, C, and HARDEN, J.: "Untersuchungen uber die

Metalliiberfiihrung bei Kontakten bzw. dafiir geeigneteGoldlegierungen," Zeitschrift fur Technische Physik, 1932, 13,pp.71, 111 and 166.

(27) FORSYTHE, W. E.: "Measurement of Radiant Energy," p. 32(McGraw-Hill, 1937).

(4) ACKNOWLEDGMENTSThe research described in this paper was carried out in the

Post Office Engineering Research Station; the author's thanksare due, therefore, both to the Engineer-in-Chief of the PostOffice for permission to publish the work, and also to severalfriends and colleagues for helpful discussion and assistance.Special thanks are due to Mr. H. Kestelman, of UniversityCollege, London, for much appreciated advice and guidance onvarious mathematical topics.

(5) APPENDIX.To ascertain whether the observed current/voltage and tem-

perature/voltage characteristics are consistent with a simplethermal theory postulating a bridge of fixed dimensions.

Since the precise form of the dependence of X and A upontemperature, u, is not known, it is not possible to solve thefundamental equations of the problem for /, the current density,and u as functions of V directly and so compare theory withexperiment. The converse procedure must be adopted: we pro-ceed to ascertain in what way X and A must vary with // in orderto produce the observed variation of / and u with V. Therelevance of a thermal theory then rests on the likelihood of thevariations specified by X and A.

It will be assumed that, because of the small size of the bridge,and the large mass of the relatively cold electrodes, most of theheat is lost by conduction and a negligible amount of radiation.It will further be assumed that the main influence of the Thomsoneffect is to alter the location of the temperature maximum, andnot its magnitude. For convenience, the origin will be taken atthe centre of the bridge. Let

2/ — length of the bridge.a — cross-sectional area of the bridge.u = absolute temperature at a point x<v — voltage at a point x.

The fundamental equations are

ydv

dxT (6)

(7)

The results of experiments may be written

V = K{w - «o)* (8)

V

or

where /!' = Ala and /?'

/ —A'

= i?/a.

r BV2 ' '

V

+ B'V2 * *

- • • (9)

(10)

FAIRWEATHER: THE CLOSURE AND PARTIAL SEPARATION OF A METALLIC CONTACT

From (6), (7), (8) and (10) it may be shown that Let u{ = w0 and u2 ^> wo

X(u) =--- 2^[l + -T^11 - "o)2al • • (11)

and

321

(15)

Suppose that the bridge in question is made of platinum, andthat ul and u2 correspond to room temperature and the melting-*)l j^2 r 2' n-3/2 tnat ul ana u2 correspona to room tempera

A(«) = -r, - -O-2QL{U - wo)2*"1 1 + -77#2(" - "o)2* (12) point of the metal. From tabulated dataA o LA J

Consider two states of a particular bridge for which X(Hl) andf,.̂ are the values of X relevant to «. and w2- From (11)

-3/2

Cancelling —, and writing — K2 - c ( = ^

Xfc*) J f [1 f a»2~»o)2 a] }3 / 2

X(«a)" I t1 -r C0/J - ifo)2*] I

= 4(approx.); 770° C

and experiment shows that

a = 1-5, whence C = 0 2 6 x 10~9

(13) Experiment also shows that

1

Now

14-7; K 1680

2-82 \ 106

0726 N 10-91016

Such a value is absurd and the thermal theory must thereforebe rejected as untenable.

DISCUSSIONS AT INFORMAL MEETINGS OF THE INSTITUTION

254TH INFORMAL MEETING, 22ND JANUARY, 1945Chairman: Mr. S. H. Parsonage.Subject: "The Applications of Electricity to Water Supply" (introduced

by Mr. J. F. Shipley).Opening the discussion, Mr. Shipley, who for some years was

concerned with water supply and purification abroad, pointedout that to-day there were more than 1 000 different authoritiessupplying water in England and Wales, of whom 25 suppliedmore than 50% of the needs of the country, 125 authorities morethan 25 %, and the remaining 875 the remainder of the needs.

After referring to the recent Government White Paper, in whichit is proposed, inter alia, to make a grant of £15 000 000 inEngland and Wales and £6 375 000 in Scotland for conservingwater resources, he said there would probably be an obligationon all water suppliers, which would mean the tapping of resourcesin the smaller villages and hamlets in the country. Electricitywould play a great part in aiding the greater provision of watersupplies. The reliability of electricity supply had increased evenduring the war, and methods of control of electric motors andpumping plant were still developing.

Electricity would have to be used for pumping and might alsobe used for water purification.

An ordinary pump would be used for pumping water fromsurface level; but pumping from underground would need eithera borehole pump, or a reciprocating pump driven by an electricmotor, or a submersible pump. In his opinion submersiblepumps were not yet fully developed; they suffered from havingto satisfy extremely limited dimensions which led to very smallclearances, etc. The troubles now experienced were largelymechanical and were caused by the varying quality of the waterand its effect on the materials of construction.

Mr. Shipley mentioned purification by ozone, by electrolyticmethods producing hypochlorite, by an electrolytic process whichinjects ionic silver into the water and thus produces purification,and by ultra-violet light, which is generally used as a secondaryand not as a primary process.

In the discussion, attention was directed to the automaticpressure system, consisting of a tank, a small pump and a

pressure switch whereby the pressure in the tank was alwaysmaintained at about 60 lb/in2. When water was used and thepressure in the tank was reduced to 40 lb/in2, the motor cameinto operation automatically. This dispensed with large-capacity overhead tanks.

Referring to submersible pumps, one speaker said that suchpumps had been manufactured in this country for twelve years,and had already achieved a high degree of reliability. Somepumps of this type have been submerged for as long as six yearsand have then required practically no overhauling and servicing.In one case the insulation resistance of the windings, after thepump had been submerged for 26 000 hours, was still 15 megohms.

It was suggested that if we were to make increasing use ofriver water—and five-sixths of the Metropolitan Water Board'sintake was said to be river water—very few submersible pumpswould be required. But the extension of rural water supplieswas prominent in the minds of many of the speakers.

Details were given on the merits and de-merits of electricdrives for pumping plant. The merits mentioned were flexi-bility; the decreased commitments of a water authority in in-stalling electric pumps as compared with other types involvingprime movers; automatic control; amenities at the pumpingstations; and ability to provide the lighting and heating at thestations as well as the motive power. One of the de-merits wassaid to be the risk of failure of the electricity supply, which wasnot under the control of the water authority. A representativeof an urban supply stated that, where electrical plant wasdepended on for the main duty, a standby plant capable of thenecessary output, with a further standby to the standby, wasalways installed. But the standby could be used very effectivelyfor "peak-lopping."

Tariffs were the subject of much comment; and it was heldthat, inasmuch as the peak load for water occurred in thesummer and the peak load for electricity in the winter, thewater and electricity authorities could do much to help eachother. Another point was that local supplies of undergroundwater, which could not always be utilized economically whensteam plant was used, could easily be made economically avail-

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The closure and partial separation of a metallic contact

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