360 PHILlPS TECHNICAL REVIEW VOL. 13, No. 12

DIÈLECTRIC LOSSES IN GLASS

by J. M. STEVELS. 666.1: 537.226.3

.On~ of the many industries in which glass is used is that of electrical engineering.

A problem arising in this industry is the behaviour of the glass in an electric alternatingfield. The dielectric losses of glass form one of the factors that decide this behaviour. Extensive .investigations are still being cqrried out with a view to producing glasses having small dielectriclosses at all frequencies. These investigatiQns have not only led to an improvement of theexisting kinds of glass but they have given a better insight into the physical and chemicalstructure of glass.

Dielectric losses

Glass is a material that is much used in electricalengineering: the bulbs of incandescent lamps andof radio valves (transmitting and receiving valves)are made' from glass, that is also indispensableas an insulating material and for very many otherpurposes. It is therefore ofgreat importance to knowhow the electrical properties of glass are affected byits composition, for this enables a choice to be madeof the best kinds of glass for certain uses. Thisarticle will deal with the behaviour of glass in anelectric alternating field, attention being mainlyfocused on the dielectric losses of glass.

When a piece of glass is interposed as a dielectricbetween the plates of a capacitor and an alternatingvoltage with a frequency f is applied to thatcapacitor, if the glass were free of losses, then thecurrent flowing through the circuit would be exactlyan angle nJ2 in advance of the voltage across thecapacitor. This means that no energy would be dis-sipated in the capacitor. In practice, however, everydielectric, and thus also glass, dissipates a smalleror larger proportion of the energy applied and con-verts it into heat. The measure of this dissipationof energy (the dielectric losses) is denoted by theangle fJ by which the actual difference in phase be-tween current and voltage deviates from nJ2. Theenergy dissipation per unit of time for a small fJis approximately equal to f tan fJ; the angle fJ iscalled the loss angle.

In glass, as is the case with other materials, thedielectric losses vary strongly with the frequencyof the electric field. The "spectrum" of the lossesof glass is broadly represented by the fully drawncurves in jig. 1, which have been drawn for twotemperatures, viz. 50 OK and room temperature. Itis to be noted, however, that these diagrams haveno quantitative significance; the losses differ greatlyaccording to the kind of glass considered. The graphgives only a general impression of the lo~ses as afunction of frequency. Although the frequency

range in these diagrams extends from 1 to 1014 eJs,only measurements between the frequencies of50 cJs and 1010 cJs will be dealt with.Fig. 1 reveals that there are two maxima of the

losses, shifting in frequency as the temperature ischanged but not in the same direction. Between themaxima is a "valley" of relatively smalllosses, thedepth of this valley decreasing as the temperaturedrops.

tgó

t,I\\ I, I" I

101(} IOn 10' 10 V'4 cis_f

Fig. 1. Diagrammatic representation of the frequency spec-trum of the dielectric losses in glass; a gives the spectrum atapproximately room temperature, b shows how the spectrumappears at a very low temperature. The fully-drawn curvegives the total losses. It can be analyzed into four kinds oflossesoccurring at different frequencies, as represented by thebroken-line curves: 1 conduction losses, 2 relaxation losses,3 deformation losses, 4 vibration losses. It is seen how thevibration losses, occurring at high frequencies, are displacedto still higher frequencies as the temperature falls. The con-duction and relaxation losses, on the other hand, are displacedtowards lower frequencies, while the deformation losses in-creaseover the whole line. These diagrams are of only theoreti-cal significance. The frequency range here extends from 1 to1014 cis; this article deals only with the range between 50and 1010 cis (vertical broken lines).

From what is already known about the behaviourof the dielectric losses in other solids an attemptmay be made to analyze the loss spectrum of glass

...

JUNE 1952 DIELECTRIC LOSSES IN GLASS 361

into various components, taking into account thespecific property distinguishing glass from crystal-line materials, namely the relatively great disorderin the orientation of the ions from which glass isbuilt up.

It will be seen that there are differences in the.manner in which the various kinds of losses dependupon the composition of the glass. Thus from theanalysis of the losses some idea can be obtained asto how the composition has to be varied in order toreduce or increase the losses at certain frequencies.The result of the analysis has been graphically

represented in fig. 1 by the broken-line curves.Four kinds of losses are to be distinguished, namedrespectively conduction losses, relaxation losses,deformation losses and vibration losses, which willnow be dealt with in that order.

Conduction losses

Glass is not a perfect insulator. Under the in-fluence of an electric force the network-modifyingions move through the whole of the network 1), andin doing so they give off part of the energyobtained from this force to the network in theform of heat.

The co~duction losses (curve 1 in fig. 1) dependupon the conductivity a according to the formula

atan (j =--, - ,

we eo

where w (, 2:n;f) represents the angular frequencyof the electric alternating field and e' the dielectricconstant of the glass (eo is the dielectric constant ofvacuum). Thus tan (j is inversely proportional to thefrequency (since (j and e' are not frequency depen-dent, or scarcely so), and the energy dissipation pertime unit does not depend upon the frequency. Thisis a well-known property of a conductor. Whentan (j for a lime glass (a = 10-10 .a-Im-l, e' = 6) iscalculated according to the above formula for afrequency of 1000 cis one finds the small value of3 X 10-4, whereas an actual measurement givestan (j = ioo X 10-4, so that at this frequency theremust be other causes of losses much more importantthan conduction. As a general rule, for frequencieshigher than 50 cis the conduction losses are negli-gible compared with the other losses. In this article,therefore, conduction losses will no longer be con-sidered. '

, '

1) The structure of glass, and especially the conceptions ofnetwork-modifying ions and network-forming ions, havebeen dealt with in a previous article recently publishedin this journal (J. M. Stevels, Philips Techn. Rev. 13,293-300, 1952, No. 9), which will further he referred to asarticle I. .

Relaxation lossesIt is not only the transport of network modifiers

through the whole piece of glass considered thatcauses losses, but also the transport over atomicdistances in the glass plays a part. Infig. 2 the varia-tion of the potential energy of the ions in an arbi-trary part of the network is indicated for anarbitrary direction (x) in that network.

-x

Fig. 2. The undulated curve represents the potential tp of thenetwork-modifying ions along an arbitrary direction in theglass. The movement indicated by a can only be carried outby high-energy ions and corresponds to conduction, while the,movement b is carried out by ions with less energy and re-sults in,relaxation losses.

(1)

The successive potential barriers, with varyingheights and distances, form obstacles preventingan ion from travelling further through the glass.The potential barriers arise partly from electricalcauses (mutual repulsion of the ions) and partlyfrom purely geometrical causes: the movement ofthe ion concerned may be obstructed by the otherions. Similar potential barriers are found also incrystals, but there the distances and heights arevery regularly distributed.

When an electric field is applied the ions tendto move in the direction of this field. Usually thefield alone will not be sufficient to carry the ionsover the potential barriers. For that to take placethe ions have to take up extra enargy, and this isobtained from collisions with other ions due to thethermal movement in the glass. It takes sometime, however, before the ions have accumulatedsufficient energy to pass over a potential barrier;this time is called the relaxation time T. If the elec-tric field is an alternating field with angular fre-quency w, and w is not large compared with liT, thenduring each half cycle the ions will have ample timeto jump over one or more potential barriers, therebygaining energy from the field, which is transmittedto the network in the form of heat; one then speaksof losses. ,At very low frequencies (w ~ liT) theselosses are small, because then the ions already jumpwhen the instantaneous value of the field differsbut little from zero: the energy gain of the ions isthen small and the lattice receives little energy.

362 PHILIPS TECHNICAL REVIEW VOL. 13, No. 12

When, however, w becomes of the order of 1/. then,on the average, the ions will not pass over the po-tential bar~ier until the field has practically reachedthe maximum value. The ions then gain much energyàY{dthe losses are large. If the frequency of thealternating field is much higher than 1/. the ionsjump independently of 'the phase of the alternatngfield and the losses are again small.

The relation between these relaxation lossesand the angular frequency w of the field is expressedas w.

tan 0 = 2' • • • • • • (2)1+ w .2

which is entirely in accordance with the foregoingreasoning: the losses occur only at angular frequen-cies round about 1/r.

As may he understood from fig. 2, in glass thereis more than one relaxation time r, since the localstructures differ considerably. This makes the re-laxation losses perceptible over a relatively ratherwide range of frequencies. The spectrum of theserelaxation losses (broken-line curve 2 in fig. 1)shows a wide peak, the limits of the range in whichthe losses occur lying, at room temperature, atabout 10-3 and 106 c/s. As already remarked, atfrequencies higher than 50 cJs the relaxation lossesexceed the conduction losses considerably.

The conduction losses could also be regarded as a kind ofrelaxation losses. The ions which collect sufficient energy topass over the highest potential barriers will be able to travelthrough the whole piece of glass. In order to pass over thehighest barriers, a very long relaxation time will obviouslybe required, and in that case formula (2) becomes

1tanlj~- ,WT

. . . (3)

tan Ij being inversely proportional to the frequency, a relationapplying, indeed, for conduction losses.

Deformation losses

Relaxation losses are therefore due to an after-effect phenomenon. There is reason to assume thatanother kind of losses occur in glass which bear thecharacter of after-effect losses. These are denoted bythe name of deformation lossesto distinguishthem from the relaxation losses just dealt with.Deformation losses do not arise from the movementof individual network modifiers, but from the move-ment of whole sections of the network, in particulara sort of kinking movement of the chains of thenetwork (see I). As is rather obvious, such a phe-nomenon has a very short relaxation time: it isto be imagined that the chains make movements

resembling the jumping of a bent leaf spring.Here again there are a large number of differentrelaxation times •. Since on the average. is verysmall, for the range of not too high frequenciesformula (2) may be written approximately (for themise where there would he only one relaxation time)as:

tan 0 ~ w.. . . .'. . . . (4)

From this formula it follows that the deformationlosses increase about proportionately with the fre-quency and in most cases will he very small. Thespectrum of the defor~ation losses is representedin fig. 1 by the broken-line curve 3.

Vibration losses

The fourth kind of dielectric losses to be expectedin glass are due to a resonance phenomenon. Theions in the glass - both the network formers andthe network modifiers, as well as the oxygen ions -may vibrate with a certain frequency round abouttheir state of equilibrium, and this they will in factdo as a consequence of the thermal movement.Regarding the ion as a harmonic oscillator, itsfrequency of vibration may be approximatelyrepresented by the formula

Wres = 0,/ ;;, . . . . . . (5)

where a is the proportionality factor denoting therelation between the restoring force and the dis-placement from the state of equilibrium, and Mis the mass of the ion in question. Consequently ionsof different mass and ions at different places in thecrystal (with different a) will usually vibrate withdifferent frequencies.When an electric force is applied with a frequency

approximately equal to the vibration frequency ofan ion, then resonance may occur. Since the vibra-tions of the ions are always damped, this resonanceis accompanied by losses. If all the ions had thesame resonant frequency, then the spectrum ofthese vibration losses would show a maximumround about that frequency. But, as already ob-served, there are a large number of resonance fre-quencies. This, and the possibility of the vibrationsof the ions being strongly damped, leads to a widemaximum in the spectrum of the vibration losses.This spectrum is represented in fig. 1 by the broken-line curve 4. Unfortunately, with one single ex-ception, the actual maximum has never yet beendetermined, since measurements so far carried outhave not gone beyond 1010 cJs.

JUNE 1952 DIELECTRIC LOSSES IN GLASS 363

Vibration losses in glass are directly comparable to the well-known infra-red absorption in polar crystals, which arisesfrom a similar resonance phenomenon. In the case of a crystallike rock salt this absorption takes place at about 1013 to 1014cis, where the maximum is very narrow. The fact that in thecase of glass "spurs" of the vibration losses are to be observedat much lower frequencies (about 1010 cis) may be ascribed, asalready explained above, on the one hand to the presence ofions with low resonance frequencies and on the other hand tothe possibility of a strong damping of the ion vibrations inglass, which leads to a considerable widening of the loss spec-trum. As may be understood theoretically, strongly dampedresonance vibrations form, as it were, a transition to therelaxation vibrations previously discussed. The question inhowfar the vibration losses in glass are to be regarded purely as aresonance phenomenon or as a sort of after-effect phenomenoncan to a certain extent he answered, as willpresently he shown,when the temperature dependency of the losses is investigated.It is to be added, however, that in order to gain a deeper in-sight into these phenomena it is necessary to study the lossesin glass in the infra-red at the frequencies of 1011to 1013 cisunfortunately it is extremely difficult to carry out ab-sorption measurements in that range.

Having now dissected the total loss spectrum infig. I into four components, the spectrum can bewell understood qualitatively. For a quantitativeinvestigation great difficulties have to be overcome,due to the irregular structure of glass. Some con-firmation of the picture formed is, however, to beobtained when we come to investigate the tempera-ture dependency of the various kinds of losses. Itis then found that their behaviour is roughly asrepresented in figs la and b, the relaxation andconduction losses being displaced towards lowerfrequencies as the temperature drops, while thedeformation losses increase over the whole line. Asto the vibration losses, there are indications thatwith falling temperature these are displaced to-wards higher frequencies, and this would be inagreement with what is to be theoretically expectedfor this kind of loss.

Jnfluence of temperature upon the losses

The foregoing conclusions may be briefly explained as fol-lows.The temperature dependency of conduction losses is

governed entirely by that of the conductivity. As is presumablyknown, for a fixed frequency the conductivity 11 decreaseswith falling temperature, and thus, according to formula (1),also the conduction losses decrease.The relaxation times T oceurring with relaxation losses and

deformation losses will be greater as the temporuture T 'falls,since the mutual collisionsof the ions are then fewer and weakerand it takes longer for the ions to accumulate the energyrequired to overcome a potential barrier. An increase in Tmeansa displacement of the losses to lower frequencies, as is indeed

• observed in the case of relaxation losses when T drops.As to the deformation losses described by formula (4), an

increase in T means that the losses,increase over the whole of

the frequency range with which we are concerned. For it

quantitative calculation of the temperature dependencyof relaxation and deformation losses it is necessary to takeinto account the great variety of relaxation times occurringin glass, but in their generality the conclusions still hold. Toillustrate the relation between the losses at medium frequen-cies and the temperature, in fig. 3 a curve has been plottedrepresenting tan (j of a lime glass as a function of temperatureat the frequency 1.5 X 106 c!s. It appears that, for tempera-tures round about 70 OK, tan (j shows a broad maximum, thenbecoming rather small at about 150 OK and rising againrapidly at temperatures higher than 200 °IC The broadmaximum is due to the deformation losses, while the rise above200 OK is to be ascribed to relaxation losses, as may beunderstood from the following.

tg(J.lO~

t120

lOO

()gO/4

6

fQ1,5·106 I/

1/0

/'

_/'"7

0 ~,.. ... r-......_ =-./' P-

O

DV

80

o 100 150 200 250 300-T

50

Fig. 3. Dielectric losses in a lime glass at the frequency 1.5 X106 cis as a function of temperature. The maximum at lowtemperatures corresponds to the deformation losses, the riseof the curve on the right is due to relaxation losses.

For a fixed frequency it is possible to determine the tempera-ture at which the deformation losses have reached theirmaximum. The relaxation times are always much smaller forthe deformation losses than for the 'relaxation losses, so thatthe frequency mentioned will be situated on the right-handdescending part of the frequency curve for the relaxationlosses. When the temperature rises both the spectrum of thedeformation losses and that of the relaxation losses will bedisplaced towards higher frequencies. The maximum of thedeformation losses will, therefore, move away from the fixedfrequency, whereas the maximum of the relaxation lossesmoves towards this frequency.A note is to be added here. The conduction loss is also a

kind of relaxation loss, with such a great relaxation time as tooccur always on the right-hand descending part of the curverepresenting the relation between losses and frequency. Theconclusion already arrived at in another way, that these con-duction losses diminish with falling temperature, is thereforenot surprising when considered also from this point of view.

Purely vibrational losses will be displaced towards higherfrequencies as the temperature falls. This is because the vi-brating ions have on the average higher resonant frequenciesat lower'temperatures, as may be understood from quantumtheory. It has already been pointed out that the vibrationlosses in glass probably form a transition to relaxation losses.Since the temperature dependency of relaxation losses is justthe reverse of that' for vibration losses, it is not possible topredict the influence of temperature on these losses at thehighest frequencies without carrying out further experiments

364 - VOL. 13, No. 12PHILlPS TECHNICAL REVIEW

"in the far infra-red. The indication, already mentioned, that'with falling temperature these losses are displaced to higherfrequencies makes it highly probable, however, that thecharacter they bear is preponderantly that of resonance.

We now have to consider the influence of thecomposition of the glass upon the different kinds oflosses. First its influence upon the relaxation losseswill he dealt with, and then the influence upon thevibration losses; as mentioned above, the conductionlosses will be disregarded, since, whatever thecomposition of the glass may be, for frequenciesabove 50 cIs they are of no importance; as to thedeformation losses too little is yet known aboutthem,

Influence of the chemical composition of glass uponrelaxation losses

The manner in which relaxation losses are affectedwill be considered under five headings.

Nature of the ions

As a rule only those network modifiers whichreadily migrate through the glass will be capable ofyielding a considerable component towards therelaxation losses. The mobility of the ions in a givenpotential field is determined mainly by their size:it is particularly the relatively small tr+ and Na+ions which play an important part in this respect.Glasses containing a large proportion of these ionsshow high relaxation losses. The K+ ion is so muchlarger that it contrihutes much less towards thelosses. By way of illustration mention may be madeof a series of low-melting glasses of the composition53.3 mol % Si02, 10.2 mol % PbO, 4.5 mol %CaF2 and 32 mol % M20, with M representing analkali metal. For a frequency of 1.5 X 106 cIs andat a temperature of 20 oe, the value of tan fJ forM= Li is 132 X 10-\ for M=Na tan fJ is 106X 10-4and for M= K it is 54 X 10-4.Divalent ions, owing to their larger charge, are

bound more strongly to their surroundings andthus are usually less mobile. An exception is thesmall Mg2+ ion which appears to be capable ofyielding a considerable contribution towards thelosses.

From now on the Li+, Na+ and Mg2+ ions willbe denoted by the name of mobile ions, whilst thedivalent network modifiers, such as Ca2+, Ba2+,Pb2+, will be called immobile ions.

It will be clear that the losses depend alsolargelyon the nature of the network. This influencecan be reduced to three effects.

Influence of R

As explained in article I, the ratio R of the num-ber of oxygen ions to the number of network-formingions is a measure for the coherence of the :ç._etworkfrom which the glass is built up. The larger the ratio,R, the less coherent is the network and the less denseis the structure of the glass. This lends more mobil-ity to the network modifiers, and the relaxationlosses may be expected to increase.

Influence of the àddition of immobile ions

If metal ions showing little mobility - eitherbecause they are large or because they are stronglybound electrically - are added to a glass of a certaincomposition, then there will be less possibility fordisplacement of the mobile ions. Thus, given equalconcentration of mobile ions, the addition of immo-bile ions to a glass reduces its loss angle.

The effects mentioned here can be quantita-tively described by the formula:

tan fJ = A CmR (1 - BCi), . . . (6)

wheretgó'lO'

t 660

Cm represents the concentration of the

69615

2

5

13(\

5 _I,0 05 ]i 106

0} !

5 l j\ 1/

0 05 r\ /0 \0 /5

r-, V5

. %Li2°1--

5

Si

4

4

3

3

2

f • ¥ ¥ ~ ¥ ~ ~ • qo ~ V ~ ~ ~ ~ ~ ~ ~

-%No20Fig. 4. Replacement of part of the Li+ ions in a lithium-silicateglass by ~ a+ ions gives a very rigid structure and thus re-duces the relaxation losses. If, however, this replacement iscarried too far the structure becomes less rigid again. The curve,for tan ó therefore shows a minimum at about equal coneen-trations of Na+ and Li+ ions (measured at the frequency of1.5 X 106 els).

JUNE 1952 DIELECTRIC LOSSES IN GLASS

fgel·/OG fgÓ'IOG

tiJD t IJO

120 / 120 /0 \110 IlO

100

\lOO .I/IgO 90

80 80

7D v·II

60 . M=Na

50II,

x"4 40

\ I xJO JO

'1,'A.R. D.R. A.R. " D.R.• 20 20 I, I, I, IID ID

DD DD2468/01214 16 18 20 22 24 26 28 30 2 4 6 8 Kl 12 /4 16 18 20 22 24 26 28 3D

-%1>440l2. -- %1>420

69617 E..

mobile 'ions and ei that of the immobile ones;the coefficient A depends on the frequency andtemperature; B is. a geometrical factor 2).

Difference in packing, with equal R

If in a glass containing only one kind of networkmodifiers, some of these ions are replaced by othernetwork modifiers having a different radius, thena more compact network can be obtained. As theglass cools from the melt: the mutually coherentchains of network-forming ions will then preferen-tially so arrange themselves that the largest :interstices in the network are occupied by largenetwork modifiers and the smallest interstices bysmall network modifiers. The resulting denserstructure leads to a reduction of the losses. This isillustrated infig. 4, relating to the glass of the com-position mentioned in the beginning of this section,with M representing partly lithium and partlysodium. The value of tan Cl (measured for a fre-quency of 1.5 X lOG cis) varies with the variationof the proportions of Na+ and Li'"; the losses are

2) See, e.g., J. M. Stevels, Progress in the theory of thephysical properties of glass, Elsevier Publ. Co., Amsterdam1948, p. 76.

the smallest with about equal molecular concen-trations of Na+ions and Li+ions.

Relaxation losses in borate glasses

In article I it has already been discussed how incertain respects the structure of borate glassesdiffers from that of other glasses. In a glass of thecomposition x Na20-y B20a, if x < 18 mol % (the

Fig. 5. Phase diagram of the ternary system M20-B203-Si02,

the borosilicate glasses. M represents an alkali metal. Tworegions can he distinguished: "the accumulation region A.R.and the destruction region D.R.

Fig. 6. Variation of tan t5 with the Na20 or Li20 content of borocilicate glasses; a) corre-sponds to the compositions a in fig. 5, b) corresponds to the compositions b. The curvefor tan t5 shows a sharp minimum on the A.R.-D.R. separating line. It is also seen that Liions cause a larger loss angle than Na-ions, because the former are more mobile. Measure-ments were taken at the frequency of 1.5 X lOG cis.

365

366 PHILIPS TECHNICAL REVIEW VOL. 13, No. 12

accumulation region), the network-modifyingNa+ ions are incorporated in the network withoutany breaking of oxygen bridges, and thus there areno non-bridging oxygen ions. This is due to thefact that the BH ions may occur both in the centreof an oxygen triangle and in that of an oxygentetrahedron. With larger concentrations of Na20,however, oxygen bridges tend to be broken, andthis range of concentrations is called the destruc-tion region.

With increasing concentration of NazO in theaccumulation region, the network becomes more andmore rigid until the maximum rigidity is reachedjust at the transition concentration of 18 mol %NazO, above which it begins to loose its rigidityagain. Such has been illustrated in article I withreference to the behaviour of the expansion coeffi-cient of the glass as a function of its composition.A similar phenomenon arises in the case of

borosilicate glasses. In fig. 5 a phase diagram isgiven for the system MzO-BzOa-SiOz, where Mstands for a monovalent network modifier. Thisdiagram can be divided into an accumulation regionA.R. and a destruction region D.R. The composi-tions found along the line separating these tworegions are characterized by a maximum rigidityof the structure.

Obviously the dielectric losses (conduction andrelaxation losses) will be influenced by this changein structure. As was to be expected, the losses showa decided minimum just on the dividing line, as isillustrated in fig. 6. Fig. 6a corresponds to thecompositions indicated by the arrow points a infig. 5. Fig. 6b applies for the compositions b in fig. 5.Both Li+ and Na+ have been chosen as monovalentnetwork-modifying ions, thus giving two perfectlyanalogous curves.

J7 Influence of the chemical composition of the glassupon the vibratiou losses

It is possible to shift the frequency range of thevibration losses by changing the composition of theglass. The influence of the chemical compositionwill again be considered from a number of pointsof view.

Nature of the ions

. One of the most important factors affecting thefrequency of the vibration losses is the mass of theion (cf. formula (5)). The heaviest ions will givethe lowest resonant frequency; thus the additionof heavy ions causes the vibration losses to bedisplaced to lower frequencies. The charge of theons plays a less important part' (this occurs in the

restoring force constant a, which expresses theinteraction of the ion with the surroundings).

Influence of R

The larger the ratio J!., the less dense is the net-work. The ions become more loosely bound to theirsurroundings and the resonant frequencies are

tgflO460

50

J,() f"I \

..... /12 0__

,./'~t- p..-lO

01 10 10' 10J 10' 10' 10" 10 Id' 109 1010 10" cis

_t69614

Fig. 7. Example of a glass (phosphate glass) in which theresonant frequencies lie very low, within the frequency rangeaccessible for measurements.

shifted to lower frequencies. Phosphate glasses areof a kind in which many non-bridging oxygen ionsoccur and thus the ratio R is high. Fig. 7 shows thatin a certain phosphate glass the resonant frequen-cies are shifted so far that the maximum of the1',

o

150

100

50

%L~O~302826242220 181614 I

Ob 2 l ;, )1 10 ;2 14 16 18108642020 22 24 26 28 30

---%MgO (Jg(J!g

Fig 8. The more compact structure of a silicate glass due tothe presence of different kinds of network modifiers leads toa reduction of the vibration losses, measured at a frequencyof 2.4 X 1010 c/s. This diagram is fully comparable with fig. 4.It is to be noted that the value of R in this diagram, going tothe right, drops somewhat, the reason for this being thatMg2+ ions, if present in large concentrations, have the ten-dency to act as network formers. This diagram relates to aglass of the composition 70% Si02 and 30% (Li20+ MgD).

JUNE 1952 DiELECTRIC LOSSES IN GLASS 367'

tgÓ.104 tgc'Jo104ro r30

\120 120

110 110

100 100 . /-

'/I90

80

70 V ,~"..60

I '50 I

I

40

30 30

20 2

10 10

00 0024681012 14 16 18 20 22 24 26 2B 30 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

--%NoJO12.

-%No;zO()06i!() E.

Fig. 9. The vibration losses in borate glass, just as the relaxation losses, are affected bychanges in composition going from the A.R. to D.R. region. Fig. 9a relates to the composi-tions a in fig. 5, fig. 9b to the compositions b, with Na+ as network modifier. The vibrationlosses have been measured at 2.4 X 1010 cjs; for comparison also the relaxation lossesmeasured at 1.5 X lOGcjs are reproduced from ·fig. 6.

vibration losses is situated below 1010 cIs (this is sofar the only case where it has been possible tomeasure such a maximum).

The addition of so~e metal oxides, such as A1203

and ZnO, which reduce R, will lower the losses athigher frequencies, as follows from the foregoing.

Difference in packing, with equal R

As already seen when discussing the relaxationlosses, the structure of the network becomes morecompact the more the network-modifying ionsoccurring in the glass differ from each other in theirdimensions, even when R remains constant. Themore compact the .network, the higher are theresonant frequencies of the vibration losses andthus the less are these losses noticed in the range ofthe relatively low frequencies where the measure-ments are taken. An illustration of this is given injig. 8, which is directly comparable with fig. 4.

Vibration losses in borate glasses

The effect of the transition from A.R. to D.R.upon the vibration losses is exactly comparable tothe effect upon the relaxation losses; In the neigh-

bourhood of the transition' the network is veryrigid, and thus the resonant frequencies are veryhigh. The "spur" of the vibration zone that can bemeasured is then ~mall. This is illustrated infig. 9~

Some examples of the spectrum of dielectric lossesin glass

Fig. 10 gives the tan 0 as a function of frequencyfor a number of glasses. The region of the relaxation(and conduction) losses on the left and that of the"spurs" of the vibration losses on the right areclearly distinguished. The glass A contains a largeproportion of mobile ions and thus shows verylarge losses. The fact that the curve D, for leadglass, rises relatively more steeply at high frequen-cies than the other curves can be explained, accor-ding to the foregoing, by the presence of .a largenumber of heavy ions, as a consequence of whichthe resonant frequencies lie lowe: than those in theother glasses.

Fig. 11 shows the losses of a lead-containingglass at a number of frequencies as a function oftemperature. This is to be compared with fig. 3.The influence of the deformation loss. at lowtemperatures is clearly seen. This influence is of

6981t

PHILlPS TECHNICAL REVIEW VOL. 13, No. 12368

0 \\ .\\\l\

0 \ -, IA/I'--.. .......V

r--':::: B=--r-.:::::: =:::::::--

~ s-:..- 00

1,00

350

250

200

15

100

5

10 IcY K1 10" 105 106 107 108 /09 cf S__ t

Fig. ID. Loss spectra of a number of glasses. A soda-lime glass;the losses, especially the relaxation losses on the left, are veryhigh, owing to the large proportion of mobile Na+ ions con-tained in the glass. B alkali-free silicate glass, and C borosili-cate glass: these glasses have Iow losses.D lead glass: the lossesfor this glass show a relatively steep rise at higher frequencies,because the resonant frequencies in this glass are Iow.

particular importance for higher frequencies, asfollows also from the theory. The increase in thelosses at higher temperatures is again due torelaxation losses.

tg(NO~

t50

69853

/I

'-3,75./08 V~-'-

..........b6 /'r-; fD1,5./rfi-L ......

1"-- --;:W

20

10

200 :;so 300 BJ 4orJO/f.-T

Fig. 11. Loss angle of the glass with the composition 45%Si02' 32% PbO, 5% CaF2, 4% Na20 and 14% K20, as afunction of temperature, at different frequencies, The defor-mation losses (on the left of the diagram) are relatively con-siderable (cf. fig. 3), particularly at high frequencies.

50 100 /SO

Practical applications

Glasses with low dielectric losses

Although in practice glasses with high dielectriclosses are sometimes desired for special purposes,these will not be discussed here. It has already beenmade sufficiently clear how such glasses can beproduced.

Of most importance are the glasses which showsmall dielectric losses at normal working tempera-tures; these are used for the construction of allsorts of electronic tubes and valves. From theforegoing comments it follows that a distinction hasto be made between (1) glasses intended for useat intermediate frequencies (radio valves), wherethe dielectric losses are mainly relaxation losses,and (2) glasses intended for constructions wherevery high frequencies .are applied and mainly vi-bration losses occur. These are two entirely differentfields; a glass that is satisfactory in one field neednot at all be so in the other. It is certainly not difficult.to find a glass with low dielectric losses at allfrequencies - such as fused silica --' but the dif-ficulty lies in the fact that for these applicationsthere are nearly always important secondaryrequirements to be met, e.g, that the glass shouldbe easily workable, that its viscosity should not beinfluenced much by temperature, and so on. In

tgd'/O~

r 698540T=3OffK

/ v......0.......~---~.....

/06

Fig. 12. Frequency spectrum at room temperature of the glassdescribed under fig. 11. The great variety of network modifiers,including, i.a., also immobile Ca2+ and Pb2+ ions, causes thelosses to be small and practically constant over a wide fre-quency range.

electrical engineering the glass is required to havea certain expansion coefficient to allow of it beingfused onto metals such as steel, chromium iron,fernico and tungsten.

Most of the properties just mentioned can beobtained by using a high percentage of Na+ ionsin the glass, but then usually the losses are high.However, by making judicious use of the knowledgenow acquired the losses can be appreciably reduced,while still retaining the other properties.

A good example is a' glass of tbe composition45% Si02, 32% PbO, 5% CaF2, 4% Na20, 14%K20 (weight percentages). Owing to its high c~m-tents of Na.O, K20, CaF2 and PbO, this glass softensat very low temperatures and has such a largeexpansion coefficient (120 X 10-7) that it can befused to iron, while at the same time it showsexceptionally small losses for the intermediatefrequencies( see jig. 12; fig. 11 applies also for thisglass). This is due to the addition of immobile ions

369JUNE 1952 DIELECTRIC LOSSES. IN GLASS

69/J25IgÓ.104

(Pb2+, Ca2+, K+), while the presence of four kinds. t 6

of network modifiers of different sizes promotesa good packing of the network. It is true that thisglass has a relatively large R (viz. 2.64) - whichgives it the low softening temperature - but thisfactor, which is unfavourable for the dielectriclosses, is apparently sufficiently compensated by theother favourable factors mentioned above.

Investigation into the structure of glass with the aidof dielectric losses

Since small changes in the structure of glass oftenresult in great changes in the dielectric losses, byapplying the reverse process of reasoning it is oftenpossible to draw interesting conclusions as to thestructure of a glass from its dielectric losses.

A striking example of this is found in the dielec-tric properties of the borate glasses already discus-sed. The position of the separating line between the

fgó·104r6 69624

5

s132\

0

1\0 \

\

\I'" /f,

'0........0- ,/ 'r'\..0

'\1\

0 \

%Li2O I--

55

45

40

35

3

25

2

15

10

5

~ ¥ ~ ¥ ~ ¥ ~ ~ ~ ?%~'--~~5~~Z~I-~I~Op~5~-I~42~~I~~8-~2~!3~5-~~~9~~2~~~45~~32

--%MgO

Fig. 13. Variation of tan r5 at the frequency l.S. X' 106 cis andat room temperature for a series of glasses of the composition53.3% Si02, 10.2% PbO, 4.5% CaF2 and 32% (Li20+MgO),as a function of the MgO percentage. As described under fig.4,when some of the Li+ions are replaced by Mg2+ions, tan r5at first decreases, because the structure of the network is thenmore rigid. A further increase of the Mg2+contentreduces therigidity of the structure and tan r5 increases. This does notcontinue along the same line, in contrast to fig. 4, since thehigher the Mg2+concentration, the more Mg2+ions begin toact as network formers. Then they no longer contribute to therelax~tion losses, so that ultimately tan r5 drops.

5

0

\

01\\\

01\

\1\\ / --1\ /

0

"V

)6LÏJ° ~

55

45

4

35

30

25

20

15

10

5

32 2~45 24,9 o2p5 17,8 142 10,65 7,1 ~5

10,65 14,2 17,8---%NiO

Fig. 14. This diagram relates to a glass analogous to that offig. 13, but with the Li+ ions replaced by NiH instead ofMg2+ions. The curve has the same trend as that in fig. 13.

~55 7,1 2p5 24,9 28,45 32

accumulation region and the destruction region(figs 5, 6 and 9), predicted on theoretical grounds,can be experimentally determined, i.a.from measure-ments of the dielectric losses.

There is one other example that may be goneinto more deeply. In article 1 it was stated that thereare a number of cations which may occur both in anetwork-modifying and in a network-forming posi-tion. In a number of cases it is possible to see alreadyfrom the colour of the glass how the ions behave.However, there are some ions (Mg2+, Zn2+) whichdo not colour the glass, and then the dielectriclosses may serve as an indication how these ions aresituated in the network. Particularly in the caseof the Mg2+ ion. most valuable information canthereby be obtained, for, as we have seen, this ionyields a rather considerable contribution towardsthe relaxation losses when occupying a network-modifying position, whereas it obviously contributeshardly anything at all to this kind of losses whenit is in a network-forming position. Now it appearsthat, when the Mg2+ ion is presenu-in a large con-centration, it shows a tendency to occupy more andmore the network-forming positions; such a net-work is poor in oxygen ions, so that the Mg2+ ion,can compete successfully against the S~4+ions. Thiseffect is clearly demonstrated in fig. 13 (measure-

·....~~---~~---~-----------------------:------

-<'I:'"'

370 PHILIPS TECHNICAL REVIEW VOL. 13, No. 12

ments : taken at 1.5 •X 106 cis), which is mostinstructive when compared with fig. 4. Whereasin the latter diagram the dielectric losses show, thepreviously discussed deep minimum at the .inter-~ediate concentrations of Nri+ a~d Li+ 'ions.vthecurve in fig. 13 (where two Li+ ions have been re-placed by one Mg2+ion)' shöws that with:small Mg2+concentrations in the glass the curve' fói: theIossesfollows an analogous trend, put with higher' Mg2+concentrations makes a turn arid ends ái à very-lowlevel, such due to the fact that part of the Mg2+ionsno longer contribute towards the losses. As a resultof the Mg2+ions changing, over from network-mo-difying to network-forming positions, the value ofR,g~ing to the right, drops (in fig. 4 R is constant},and this in itself already leads to a further reductionof the losses. .This picture of the situation is illustrated by

fig. 14, for the' case where two Ü+ ion~ ar~ replacedby one Ni2+ion. This curve rese~bles very ~uch thatof fig. 13, and in this case it is indeed possible toconch~de from the change in colour of th~ glassesexamined that, going to the right, more and moreNi2+ions occupy the network-forming positions.

Finally, it is to be mentioned that, measured at

f '1010 cis; the replacement of '{,vo .Lt+ ions byone Mg2+ii:m' yields a 'curve not showing anydeflection bût :retailling the normal shape with adeep minimum. At 'these frequencies, where theVibration-losses play a part: it is of no consequencewhetherthe Mg2+ion occupies a network-forming ora network-modifying position. By way of illus-tration refereIlce is made to fig. 8.

Summary. The dielectric losses in glass arise from threecauses: .conduction, after-effect and resonance. The' variousforms of losses are described, it being shown that the conduc-tion losses are of importance only at very low frequencies andhigh temperatures. The after-effect losses can be divided into"relaxation losses", occurring at room temperature in thefrequency range of 10-3 to 106 cis and shifting towards higher,frequencies as the temperature rises.nnd "deformationlosses", .which are approximately proportional to the frequency andare particularly of importance at Iow temperatures. The res-onance' or vibration losses occur mainly at high frequencies(1.010 to 1013 els) and as the temperature rises probably shiftto,vards lower frequencies. The influence of the chemicalcornpositiorï and the structure of the glass upon the variouslosses is .investigated, special attention being paid to the borateglasses, in which an accumulation region and a destructionregion are to be distinguished according to the composition.It is indicated how the losses can he reduced in certain fre-quency ranges, some examples being given. Finally, itis shownhow the dielectric losses can he taken as indications' of thechanges taking place in the structure of a glass when its com-position is modified.

ABSTRACTS OF RECENT SCIENTIFIC PUBLICATIONS OF THEN.v. PHILIPS~GLOEILAMPENFABRIEKEN

Reprints of these papers not marked with an asterisk can he obtained free of chargeupon application to the Administration of the Research Laboratory, Kastanjelaan,Eindhoven, Netherland.

1981: P. C.~ander Willigen: Grepen uit de ontwik-keling van het booglassen (Electro-techniek29, 143-147,1951, No. 8). (Some remarks onthe development of arc welding; in Dutch.)

Two important questions in the field of electricare-welding by hand 'are discussed in this article.The first part deals with the choice between directcurrent and alternating current. Their advantagesand disadvantages are described, including, thequestion of the open circuit voltage of the weldingtransformer. In the second part the differentmethods for welding of steel are examined from thepoint of view of shielding of the deposited metalagainst nitrogen and oxygen from the air. In thisconnection the use of hydrogen and its influenceon the weld are also briefly discussed.

1982: N. Warmoltz: On the application of aPhilips ionization gauge type of ion sourcein a mass spectrometer leak detector(Appl. sci. Res. B2, 61-65, 1951, No. I).

A system of electrodes as in the Philips ionizationgauge can function as ion source giving a divergingion heam.in which the ions have different velocities.When placing this source behind a slit, it is possibleto focus all the ions of the same mass in a secondslit by combining a magnetic field parallel to theslits with an electric field perpendicular to the slitsand to the line joining the slits. Between the slitsthe ions describe a kind of epicycloidal trajectories.In this' way it is possible to construct a simpleleak detector.

JUNE 1952 - ABSTRACTS OP RECENT .SCIENTIFIC PUBLICATIONS 371

1983: C. J. Bouwkamp and H. Br emm er:A not~' on Kline's Bessel-function ex-pariaion (Proc. Kon. Ned. Akad. Wetensch.Amsterdam 'A 5.4, 130-134, 1951, No. 2).

A·certain combination of Bes sel functions, 'viz:Jv ('V sec -&) Y, (z + .j, sec -&) - Yj, ('V sec -&)Jv(z + 'V sec -&), in which y, -&, z are complex numbers,is expanded in a power series in the. variable I/v,This series converges if I 'VI > Iz cos -&1. The firstthree coefficients are given explicitly.

1984:., J. H. van Santen and G. H. J onke'r:t 1 Il ...

Combinaisons ferromagnétiques du man-ganèse à ~ructure pérovskite (J. ,P!n;:s.,Radium 12, 202-204, 1951, No. 3). (Ferro-magnetic combinations of manganese 'withperovskite structure ~ in French.). "

From investigations on the magnetic hehaviourof ferromagnetic mixed crystals with peroy.s~!e

. III 'IVstructure ofthe type (I-x) LaMn Oa·xMeMn Oa(Me = Ca, Sr or Ba). it ~eems pro~able t~atthe (indirect) exchange interaction between Mn!Yand Mnlv is' negative and that between MnIII

and MnIII.is positive. This is the first known ex-ample of a positive indirect exchange interactionin oxidic compounds.

1985: J. J. Wen t: Linear magnetostriction ofhomogeneous nickel alloys (Physica 17,98-116, 1951, No. 2). '

The magnetostriction of homogeneous Ni-alloysis investigated. The magnetostriction is measuredas a function of the composition of the alloy, ofthe induction caused by' an external' magneticfield and of the temperature. A· comprehensivetable of data is given. Several general relationshipsfor binary alloys have been found. The saturationmagnetostriction Às at 0 ,oK can be predicted ifthe saturation induction Is is known; Às at a highertemperature follows directly from the Às' value at'o OK and the relation Is vs T (except for Ni-Mn-alloys). A single relationship hasbeenfoundbetweenÀ and I for alloys except those containing Co orMn. From all these data the magnetostriction for .ternary alloys may be calculated.

1986: G. W. Rathenau and G. Baas: Graingrowth in a texture, studied by means ofelectron-emission microscopy (Physica 17,117-128, 1951, No. 2).

Grain growth and secon?ary recrystallizationin rolled face-entered Ni-Fe-alloys has been studiedby electron-op~cal means, an image of the acti-vated hot metal surface being formed. Grain growthin an imperfect cubic texture proved to be a discon-

tinuous .process. Almost all neighbouring g-,:ainsinvade quickly' one grain or group of grains. Grain!boundary movement at Iow-energy boundariesoccurs 0!l a small scale. The high-energy parts ofthe boundary between a cubic crystal and its (near]twin proved to move in à direction parallel to theco:rpmon (111) plane. 1'he surface tension of theboundary between a secondary crystal and a cubiccrystal which is to be absorbed is about twice thevalue corresponding to the surface between twocubic cnystals. ",

R 160: H. Bremmer: The discharge of a series. ~f equal condensers having arbitraryresistances connected in parallel (PhilipsRes: Rep. 6, 81-85, 1951; No.2).

This paper concerns the discharge of a seriesof condensers through a ballistic galvanometer if~.vari~ble resistor is co~ect~d in parallel to eachcondenser, in 'connection with the model describedin it 159. The flo,~ of current; through the galvano-meter 'is calculated with the aid of the operationalèalculus. .

. "

R 161: B. D. H. Tellegen and E. Klauss:Resonant circuits coupled by a passivefour-pole that may violate the reciprocityrelation (Philips Res. Rep. 6, 86-95,"1951, No. 2).

The system of two resonant circuits, coupled bya passive four-pole that may violate the reciprocityrelation is investigated. To obtain the maximumtransfer for a given form of the resonance curve, thecircuits must be equally damped and equally tuned.To' obtain the maximum transfer with two circuits'coupled by a passive four-pole satisfying the reci-procity relation, the circuits must generally beunequally damped and' unequally t'uned. Whenthe coupled circuits are used as an interstage net-work 'in an amplifier, to minimize the influence ofchanges in valve capacitances on the shape of theresonance curve, the circuits should be equallydamped and' equally tuned. For symmetrical,flat-topped 'resonance curves the maximum trans-fer with non-reciprocal coupling four-poles, theratios of the maximum transfer with reciprocalcoupling four-poles to the transfer with reciprocaltransfer with reciprocal coupling four-poles and toequally damped and equally tuned circuits are(1 + 1"2) : 2 : 1.

R 162: H. G. Beljers and W. J. van de Lindt:Dielectric measurements with two magictees on shorted wave guides (Philips Res.Rep. 6, 96-104, 1951, No. 2).

, j

372 . _ PHILlPS TECHNICAL REVIEW VOL. 13, No. 12

A description is given of the method and calcu-lations ,underlying dielectric measurements atmicrowaves with the aid of wave guides. It isshown that a "magic Tee" (a certain arrangementof four branches of rectangular wave guides at one

. junction) can be used both as a bridge and as meansof establishing any complex waveguide impe-dance. By using these Tees dielectric measurementscan be carried out with greater accuracy than inthe conventional method with a standing-wavedetector. Some details of the construction of theapparatus and the measurement are given. In:conclusion a dielectric measurement of polystyreneis dealt with.

R 163: H. C. Hamaker and Th. Hehenkamp:Minimum-cost transformers and chokes, II(Philips Res. Rep. 6, 105-134, 1951, No. 2).

In the foregoing paper R 150 the equations spec-ifying a transformer design with minimum price,P, when the apparent power, VA, and the losses,W, are prescribed, were solved, and the chief char-acteristics ~f the resultant designs were discussed.This we ,shall call the P-W-class of designs. In thepresent p'aper two alternative classes of designsare considered, namely, (1) the P-M-class ofdesigns giving minimum price for prescribed v~lues .of the power, VA, and the product, M = BS, ofthe peak magnetic flux density and effective elec-tric-current density; and (2) the W-M-class ofdesigns giving minimum losses, W, when VA andM are prescribed. The solutions obtained are castedin such a form that they are directly comparableinter se and with the P-W-solution of the foregoing

paper. When power and losses are prescribed thePoW-class of designs is always cheapest, but ifinstead of the losses we prescribe a value of B orof the specific dissipation of heat, v, per cm2 ofexternal surface, the other classes of designs mayhe preferable. It is shown that the choice of a de-sign depends mainly on the transformer charac-~eristics which are considered as the limiting factors;a choice between the three classes of designs isof secondary importance. These problems arediscussed in detail. In the appendix, a set of tablesis provided by mèans of which the P-M-designsor the W..M-designs can be . rapidly obtained. Aconcluding section deals with the problem of adesign such that the sum of the cost of the trans-formers and the cost of the electric power dissipatedas heat' during its life, is at a minimum. This prob-lem can also be solved by the methods developed.

R 164: P. Schagen: On the mechanism of high-velocity target stabilization and the modeof operation of television-camera tubesof the image-iconoscope type (PhilipsRes. Rep. 6, 135-153, 1951, No. 2).

lp. this article the mechanism of the high-velocitytarget stabilization in the iconoscope and the imageiconoscope is described. Some hypotheses are for-mulated for the mechanism ofthe image iconoscope,and equations are derived therefrom for the po-tentialof target elements as a function of time andfor the signal output of these tubes. This theoreticalapproach indicates that an increase in the secon-dary-emission coefficient of the target and in thetarget capacitance will result in better picturequality. Experiments confirm these predictions.

"

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