Chatterjee, S K

Rajeshwari

English

IACS Institutional Repository

28 DIELECTRIC CONSTANTS OF SOME SOLID INSULATING MA TERIALS A T ULTRA SHORT WAVES Bv R. K. l'IL\T'fHRJlm A'\1l l\IISS RAJESWARI ABSTRACT PklC'cllil'«'n,UlJlhof "Hlnl ilhl1Jlltillg'matetiah ill tlle {otl1l of lhlll .,Iabs Itay{: l,e{:11 nH?lhnree] JlI the Lecher \\ In' melhncJ 0\ cr fi \\fi\'('lellgth range' of It" cm, to 5i i ('Ill- 1>llJc,llICloll,tallt':1I thl tll't' of ltlatf>liIlJ, ulldel il1\,t',tiglllloll ha\,!" been flll1U!l to \illy \11th \\(lI,I\-II,(!th,. III th! (11'1.' of <.olid pnrnfiin, lIiell'elr;!' ('onijtanlshnve heen ['lUud to illl'1la,c' II itlt \\ an>lcngth~ be,'o11ling ,,))orter 111 other C'a't'., dielectric ('()n~tanh ,hoI\' Jl cle('rca~ilJg tel1!ienry \lith llfiVtlcllgth ,lecrcal>ill,l: IN '1' R () 1) t' (' T r () N The behaVIOur 01 il1f>ulutiug lIIakriab lludu cle.:cl! il ~tll'~:-' i"l a lIIattc'l' of lundamcnl:ll importancc to cOlllmuuication eng;uers, 'l'hc l111ccrtailltic:-. of dielectric hdwviour of solids mi:.e hom tht: fact that 11ll<1t:1 high frecluency cxcitation vnriou:-. factors become opu'ativl within the hody of the material depending on lis physical and chemical cOllsti i utiOll, Hartshorn (IY20) s tresscd 011 I h~' 11('(:(1 of a thorough III vl':-.I igat i(11l (If varion!> catl:-.e:-. 1 cs\,ullsiulc.: for the uncertain dielectric hdJa\'iolll , The usc uf an~r lIIalL'1 ial a!'> a dielectric ill the region of Clll. \\'avt:~ Jlresuppose.:~ a kllO\\ ledge uf the (\it:lcctril COllstant and loss factor of the matel ia! in the particnlar 1 'nlHI 01 fr('ljnencie~. Variou:-. methods have been evolved for the study of lIre didl'l'll if' hdw"iolll of difier"nt materiab. 1'h" frequency variation of an of>cJlIator, due to the insertion of the matll'ial in the.: tau k condcllSel, has been uti1.~ed hy :\" h <':11 (Hill 1, Ily:-.lop and Carman (1l1':W), KlIr I Iq;::6) and in amoc1ifi"d f0l111 hy WYl1lan (1930 etc. to dekrlllillL th" c1ielectric consinllt" of val'iou!. 1J1aterial!.. Capacitance variation I1ldhod has been employed by Hal bIrom alld Wald 11936) to determine tire dielectric COllstallt of various ceramic materials. 'fhe difference in the \\'avdenl..'.lh of standing wa\'es ploduced hy J esonance on paraIJeJ wires with lhe wires heing fir:-.t \ ... holly illll1lersed ill air and thcn ill lIre dielectric hasbecJ111tilised first hy Cohen rISC)1) and laicr on more cxtcnsively by Drude l!{q;'i', Rudop (19131 dc. Insteau of paraIlel \\irt:s, concentric tulles have h"en used hy Drake, Pierct.' and Dow (1930', 'l'h{,' standing wave mcthod has been suitably modified by King (1l.)3i) to measure dic.:ll'ctril: COll:-.tallt~ of a thin slab of materials, Theoretical a 11<1 t'xperilllental development of resonator systems suitable for the determination of dielectric constant has been achieved by Horner and olhers (1946). The measurement of '0' of a reso1lator ha~ heeJl utillised hy Dakin and Boggs (1944) and El1gland (1944). Wave-guide propertie!> have heen llsed hy Lamolll (1l)4o) for snch measure-ments. A new technique has heen developed hy MacLean (1946 1 for dielt:ctric Dielectric Constants of some Solid Insulating Materials etc. 181 loss measure1llents. '1'1)(: object of the prc~cut iuvestigation b to llleaSUle dielcctnc constants of thin slahs of insulating materials over a wide band of ultra ohort waves by employing a week source of oscillation and following the methotl outlined by King. T IT E () R E '1' TeA I. 'I'he velocity l' of a sinusoidal cun ent ill the steady state on two parallel wires, immersed wholly in air, is l' = OJ/ (3 where, (3 i~ the I etardation angle per unit length of the line and VI is the al1gulU1 velocIty of thl! implessed e. n1. f. in radians per second. If the parallel "'ires an; iml1lcr!>ed in mediullI of dielectric constant f, the velOCIty 1", i~ given hy ," = "/ V., the fl equency fJl/2iT of the wave being constant, Or, we call write Jo... =,\v" This amounts to, as if, the length of the wite has been shortened from ,\ to ,\ ... due to the insertion of the dielectric. If instead of ill1mersin~ the parallel wire wholly in the dielectt ic, a thin slab of the dielectric' is interposed, then calculating the input admitt.ll1ce (Killg, 1937) of the \\ hole !:>ystem from the telegraphist's line equation at ulha high frequencies, it can be shown that tan ~ (3 1.\ 1 - \2) = II tan ~ lI(3s1 or, tall ~ (:1 (max. shift + ~l) = 11 tan ~ n{JSl (I) whel e, .1 1 - '\2 = maximum shift due to the introduction of the slab, .\, = thickness of the slab, 11 = refractiVl: index of the material. The retardation an.t.:lc /1 is t.:lvcn hy (Drake and PielC(', J()3(1) where, 1 {J = H'. V(. (r -1/\) ~ .fUll ( 1 'I =...! and \ = J!... aIHi {", C(,' I (/1 I = I + II • t- r I ( 2) ~ 1 J I' I .2 where, a!> !:>hO\\1l hy PieJll' (1(}.22), wbere', r, ( and l=reslslance, capacity, Hn(l in(lnctalH'l' rl'spL'ctiveiy per loop unit length of a smooth lill\.', e 1 =vclocity of dedroll1agnctic waws in vaCUUlIl, g= leakage comluctance pel unit loop Icngth of the line. (J c l = VE. (I-I}S)~ J(II) Then the velocity 1" = '" c1 or = 1'/_, 1'. 182 S. K. Chatterjee and Miss Rajeswari Hut the ratio of wavelengtlI ill vacuum to that 1D the dielechic is the inde,. of refraction n. Therefore n == ..; -;; .(1 -7]s)i .j(h) For a short and well insulated line, g may be considered to be negligibly small. Moreover, at em. waves w is very high. So, lew 2 » 19 and rew> glw Therefore, nnd The expression for the index of I efraction, therefore, nt ultra short ,,,aves for a short well insulated line, reduccf> to So by finding out the maximum hridge shift for a certain material, the refractive index and hence the dielectric constant of the material call he ca}(.'ulated with the help of the cf)uations (I) and (2'. EXPERIMENTAl. The experimental technique mainly consi~ts of the following: J. The wavelength of the oscillator atong the I~echer wire, when the tatter is wholly immersed in air is determined by finding bl idge positions for three consecutive maxima of the indicator reading. The bridge then being placed in its first position of maxima, the oscillator is moved in its truck parallel to the Lecher wire till the indicator :-hows its maximum. The oscil1ator is kept fixed in this position throughout the experiment. 2. The optimum position of the slab is determined so that the bridge shift (Sl- S2) may be a maximum. This procedure minimises the error in the determination of e. The slab is provided with two holes at the centre, the diameters of the two holes being almost of the same size as that of the wires, so that the contact between slab and wires is properly ensured, while at the same time the blab can be moved smoothly and snugly along the wires. Tbe slab is placed between the indicator and the bridge. The bridge is moved till the indicator reads maximum. Then moving the slab towards the bridge. Dielectric Constants 0/ some Solid Insulating Materl'als etc. 183 step by step, the bridge shift at each step is measured. 1<'ig. I shows the relation between bridge shift and the slab position for one of the materials. Po~ition of Didt:ctric Slab. FIG. 1 3. The wavelength of excitation being varied f10m 140 CIlIS to 57.7 cms maximuIll bridge shift 1.1 I - ~21 at each step corresponding to the optimum position of the slah is noted. 'l'he wavelength of excitation is checked before and after each observation. 4. The thickness of the material is measured. s' _ .. Io·t j ----~--------~f~, I .. ohdl .. I I I 'l'he above procedure is repeated for ten ditfercllt materials, in the form of thin slabs. The experimental arrau~emcut is shown in figure 2. 1'he oscillator used is of the resonant type with two \:155 tuLe~ ill parallel. Two oscillators have heeD used. Oue of them co\crs a rall1ge of 142 cms to 96 cms. Tbe other covers a range of 98 to 56 cms. TIle resonant 184 S. K. Chatterjee and Miss Rajeswari lines of the first oscillator are 9 ClIIS ill length and 0.3 cms in diameter and !>paclllg bctween lines i~ 0.43 cm~. The filal11ent chokes for the oscillator l'ollbists of nil' cored wi!!> of 50 turn::. and diameter 0.4 CIllS made from I(JOA 't' r----t==========:r-~>NIII--.H.T . O-.30ppF ....... --*---u---..... ----. H.T. t '*' L.T.-Fw. 3 20 S.W.C. enamelled coppel wire. For the second oscillator, the resonant lincs are of It;!ngtb 3.6 e1115 •• diameter 0.3 Clll. and spacing 0.5 C111. The filamcnt chokes of diameter 0.3 cm. cou~isb of 40 tum" made frolll the ballle gauge of wIre as above. The frequency of the oscillator~ i!> varied by changing the ~IHcillg between re&Onallt lines and also by adju:.tiog the tl iml11er shunting tl:e end of the resonant line!). The o!>cillator circuit diaglalll is shown ill Fig. 3. The indicator used COl1!>l!>tS of a crystal ddector'lIIicro-anllncter combina-lion fixed at one end tlf tIlC Lecher wire line 1. The diameter ot the Lecher wires 0·326 cm. and till' spacing S ems. fro111 centre to centre have been chosen to satisfy the requirements of the parallel \\ ire theory with regard to the ratio of the wirc diameter to the ",ire separa-tion'Viz. (d/a)2«I. 'fhe expcrimental f('sults for till: difIercnt materials are tabulated as follows. It, ordcl to calculate the refractive index from the e1luation I Newtonian approximation Sanden and Jahnkes tablc!> ha\oe heen used. 'rAm.II I :'Iaterial I A ((,111~ )1 ~1:t)..:hjl~ ~11J~.): : I I qn(1 ~ 7 5 1 12(1 fl :; 7 :;.:; I Ill,] S ~.., 5 ~ CeiCfOI\ I 100 Ll :;.n 1 7 Bakelite (Thickl1e~, 88.2 ,·3 4':; ('fhirkncb., Sl = 1.33 em) I 78·9 .:; 1 1 'i 1"1-=0 on ('In) 71.\ 1 .' I 3·9 h5·~ 4" 1 (, 600 11 (I I 3. 11 577 4" ,l·/l llliP 120 {J 11 1.1 lOO C) 88.~ 71l <) jl I (" 2 iJe),fl .<77 1-5 14 } 3 4·3 3 .~ :; :I ' ~ • I 2 () .14 20 I f I I 5·7 5.6 5·5 ':;,5 '1·5 .1-.'i ,.8 .18 ,15 3·! Dielectric Constanta 01 some Solid Insulating Materials etc. 185 l\I~ cult'1I-IThickm.·" R. =0.97 ('1111 Matedal 14u . C' 12\10 111.1 10".0 ~1l.~ I ,8 <) 71.1 6$.2 I hi) () 5i·, I 1 I -, Y ..J.() 4·U 43 J.4 45 ·\·5 .\.0 4·3 'l'AHI.E I-(collld.l :\Jatt'l lni_J_" ~ 111'\ 1_~"~~"IIII~<:I:_)_ 5 2 1·9 C; I l\l il .. .\ S (BI()wlJ) ,·5 S.1l (TIJid,ne" .'> 7 5 • ..; U <>3 C1l1 'i., 5. 2 5·~ Ltu.O 12().u III I 1/ )('.0 81'-2 78 t) 71.1 Il'i 2 6o.(J 5;·7 I 5·lI 4 .. \ l <) 4·<) ~.8 \·7 4·8 'I·Y 1 5 4·S " ('111') I :\la~ ShIft (CIII" '--1- I --':--14u.O 3·7 4·\) J20.() I 3 7 $ (l l\[,Jicriul I" 1'1\1') I :'Iloll.. I-ihift (el11') I -- --1 -I -- --1-140.() :J.6 I 3.8 I 12()OI\ \.5 ,3.8 :.\IILUlllltC Thick llt" o.()~ ( 111 rlbre Thickll( " 064 ('III Paraffin Wn" '['h ickness 2.I.l (,JlIf> III I 37 50 IOU 0 3., ' " 8il2 35 41{ ,8.1) .\ 2 \.5 iL\ 3 41 b~.2 ;\ 4 4·7 flo.! I J ~ 4 5 S7·7 3 2 4 S 14o. lI 120.0 III I 100 () 88.2 71l.l) 71 4 652 60.c. 577 1400 120.0 II!.1 1000 882 78.9 71 j 65. 2 60.(1 57·7 2 I 20 2() I il 2.0 1 Il 2.0 ] R 2 J 2 I 2 ~ 20 2.1 2.1 1·3 2./1 , S 2 S .1 2 I 4.u 4.0 . \ 8 4 ~ 4 I .;·7 4 I 3 h 4 ." 20 2 I 2 I 2.2 2 l 111.1 \.5 I 18 H[,unile 11)0 0 .\ I> .\.4 '['Jllck ne__ 88 2 2 <) 3 3 I 25 ,'111 78 .l) ~ 0 I 3.4 B('~, \\',l'I . 'J'hicJ..llC" 2 02 (1JI~ 7Ll 3 0 3.4 os 2 3" I 34 b" () 3.0 34 577 l.ll 34 qo.o 120.n II I I IOD.O 8&.~ 7f>.C) 71 .4 11$ .? (lOI) 'i7 ~ ~ b 2·S 2.1 2 , 2., 2 :, 26 2.1 18 loS 2 I) 2.~ 2.1 2 I 23 ~·3 .,-,,1) I.l) J.<) "alllioll I A (I IlIb) ;\[.1". Sh.ft 1\'I1I!» I I ---I ~~-Jo-()--:----~ .\-5- ---.\~o I t200 1.20 2.8 1'lextglsl>S (:\Ieth) I-mel 1.'11' Crvlute) Thil-kt\('&" / 06,1 ('11\ I I 111.1 1.,0 Z.9 1(1(10 ~8 2 I 78 Y 71 <1 (is 2 60 U $77 ] lu ~.9 1.10 2.7 130 29 100 2.9 1.00 2.~ 100 :1.5 l.ou 2 5 186 S. K. Chatterjee and Miss Rajeswari IJISCI'SSION The nature of variation of bridge shift with differeut lJositioll of dielectric slab, as shown in Fig. I, can be shown to agree with that obtained theoretically from the equation (Lamont, I940! whele, 11 cot /31s,(cot {3s1-cot (3s~)+cot (lsI cot (3S2+n2=O S2=S'-(SI+0), 0::0' shift This ~ho\\ s that the shift is a function of the absolute position of the slab. From the stand point of optical analogy, this result seems to be unl;:xpected. 111 optical problems, such results are encountered due to the interference of two separate ttavelling wave~. In the pre~<:nt case, interf<:rence occurs at the boundaries of the dielectric between the incident wave and a portion of it reflected. It has been pointed out by Lamont, that under resonant conditions reflections take place at the diel<:ctric boundaries and at the bridge in ::illch a manuel' that the resulatallt stationary waves show little change of intensity at the bouudaries but exhibit a definite phase change, depending 011 the position of the diel<:ctric slab. This variation of phase chang<: is con· sidered to be n,:spollsible for different amounts of hridgc shifts \\ ith different dielectric ~lab 1.0sitions \\ ith respect to the original standing \1 ave system. Frolll the cxpcrimcntal results, dielectric constants for all the above cases of tuaterials. except solid paraffin wax, have been found to decrease with t he wavelength. As rerorted by Honnell (19021, the dielectric constant of paraffin of different densities varied from 2.13 to 2.22 and frol11 2.16 to 2.25 at wavdengths of 81.68 C111S. and 61·32 ems. respectively. In the present investigation dielectric constants of paraffin (solid) at 78'9 ems. and 60 cms. have been found to be 2.0 and 2.19 respectively. The frequency dependence of dielectric constants may be exvlained by molecular prOLess or by a mechanism of interstitial conduction which requires the presence of adsorbed ions on the surface of structural units as suggested by Murphy and Lowry (1930)' When an ('.m.£. is applied to the dielectric, a polarised distribution of these ions takes place, due to a surface mobility, hut after the source of excitation is lemoved thl: ions return to their normal distribution. The electrical effect of the adsorbed ions is, therefore, similar to that of a dipok and they produce a kind of dielectric polarisation. The structural unit with its adsorbed ions can be represented by an equivalent electrical circuit, where each layer of adsorbed ions is represented by a capacity ill series \dth a resistance. Both the capacities and the resistances become smaller, the greater the distance from the interface of the layers of ions to which they refer. In figure the equivalent electrical circuit c". represents the capacity due to the dielectric polarisation of molecules; CIt C2 " .... ("-11 c" represcnt the capacities due to redistrihution of adsorbed ions on the surface of the micelles i R l , R2 , ...... R .. - 1 , R" repH:~nt the series resistances Dielectric Constants of some Solid Insulating Materials etc. '187 equival~llt to frictional resistalll'cs whtl'11 hinder the process of {ormation of a PQlarised distribution of adsorbed ions and Rd is the D.C. resistance. By an ~----~I~---~~-----IC' lit ~------~t·----~~-------Cit R. ""-'1 ll! SEVWW' 1-. -----I en-. ~_R_"_-_' __ _ len. An -------RJ analysis of the circuit, It can be shown that the equivalent parallel capacity decreases with decreasing wavelength. At very high frequency, the capacity term due to the adsorbed ions, or similar process involving long relaxation time, becomes zero, the only capacity that remains is that due to the polarisa-tion of the charges within the molecules. Iu ~is connection, it is intere~tjllg to note that Debye (I()I2) suggested that if the system is compared ,,,ith a pure capacity C and a resistance R 111 s(.'ries, thc following relatiolls hold good. ,./1 = .!. ( _!{(o)c_) {II I+H~(J)2c when:, "', •. 11. etc. have t heir usual sign ificancc. Most of the solid dielectrics, for instance, ebonite, fibre, mycalex etc., investigated above, may be classed as either amorphous or of a crystalline type containing many lattice irregularities and impurities. Part of the dielectric constant of these materials may he regarded as due to the presence of dipoles and (or) ions in the dielectric. The electrical dipoles are either due to the polar groups existing in the molecules building up the amorphous substance or to the occluded or impurity molecules, which are more or less subjected to restricted rotation. The ions lllay be considered to originate froDl or belonging to the substance itself or formed by electrolytic impurities, which can both travel over cel'tIliu distances through the structure of the amorphous solid, along crystal flaws or irregularities. The positions of a dipole, whkh is originally bound to certain position by the molecular field of the surroltlldiugs, can only be altered if a certain amount of energy is supplied. Similarly the displacement of the ions also needs a certain amount of energy. 'the amount 188 S: K. Chatterjee and Miss Rajeswari of adivatloll C1ler,!..:), llccded for n:orielltatioll or rotation will be difTere11t for diffcn:nt dipolcs or ions according as the solid is of amorphous or crystalline type. (hI the as,,;umption of a statistical scatterillg of tilt: activation energies determining the progressive 01 rotational diffusion of ions or dipoles, Gevers and Pre' (llJ46) haw Ilorked out a theory which explains the dielectric properties of amOrl'hOllo. dielectrics, It has been COllcluc1cd fro111 this theory that, as a first approximatioll, contribntJOn to the dielectric constant is madc only by those ions and dipoles whoo.e telaxation times (.) exceed the value .= I /~), where ,,) is the al1gular frequency of the alternating field or the part of the dielectric constant which i~ dependent on the ircquency is a function of the activatioll energy corresponding to WT = J, A (' K N ( ) W I. E J) G 1\1 E N 'r The authors express their grateful thanks to Professor S. P. Chakravarty, Head of the Dept., for his keen interest and giving facilities to carry out the above investIgation, IlI!I'ARl'MI\N1' Oi' I'),El"J'1l1("~I. 'l'El"Il'\"OI,O';Y, I)';IllA)'; INSl'lTUTE OI' SCIENCE, 11.\ '\"(;.\Lf IIl1;. REFF.RIINCES Cohen, n. HeerwagclI, 1891, IT'icd. A 1111.,13, .'l43 Dehye, J9J2, Phys. 7.rii., 13, 'i7. Tlmkc F. II., Piercc G. W., etc., 1930, P/IY.,. Rn'., 35, 613. Drl1de, 1895, Wicd. /1/111., 55, 637. llakin, Hogg~, 1944,,1. T. E. E. Tcell. papa, 44,161. England, C. R., lyH, l!cll. Sys. Tccll. Jour., 23, 114, (;('\'er~, 1\1., Pre" F. J.::., 191", Trall.l. Far. SOt'" 42A, 17, Ilart-horn, I,., 192(\, .r. T. E. E., 64, 1152. HflrbhorJ1, I,. and Ward, \\', II , 1936, I,T.E.E., 79, .~47. Hornn,. \<", Tailor, '1' /\., J9.16, J. 1. E. t,;, 93, S3. lIol"mell, W. G., u)o2,l'hil. Jlla/; 3,52, Ih~l()p and Cnrlllfl1J, 1920, Phy. Rei'., 15, 2.1.\. King, R" J937, linl -";ri. 111,,1,,8,2('1. Kl'rJ", 1926, ./olfr. (·/II'1I1. SO(., 128, 27(l). Lmn()nl, JI.R,l. , 1940, Phi!. Mag., 3a, I. I.HII10111. 1940, I'lIiI. Max, 29, 521. M:H'l.eHn, W.R., 1946, 10u/". ,1/,/,. 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Dielectric Constants of Some Solid Insulating Materials at Ultra Short Waves

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Dielectric Constants of Some Solid Insulating Materials at Ultra Short Waves

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