DIELECTRIC AND MAGNETIC PROPERTIES OF MATERIALS

Transcription

1 DILCTRIC AD MAGTIC PROPRTIS OF MATRIALS

2 Dilctric Proprtis: Dilctric matrial Dilctric constant Polarization of dilctric matrials, Typs of Polarization (Polarizability). quation of intrnal filds in liquid and solid (On Dimnsional) Claussius Mussoti-quation, Frquncy dpndnc of dilctric constant, Dilctric Losss,

3 Magntic Proprtis: Magntization, Dia, para and frro magntism, Langvin s thory for diamagntic matrial, Phnomna of hystrsis and its applications.

4 Dilctrics ar th matrials having lctric dipol momnt prmantly. Dipol: A dipol is an ntity in which qual positiv and ngativ chargs ar sparatd by a small distanc.. DIPOL momnt (µ l ):Th product of magnitud of ithr of th chargs and sparation distanc b/w thm is calld Dipol momnt. µ = q. x coul m q -q All dilctrics ar lctrical insulators and thy ar mainly usd to stor lctrical nrgy. x: Mica, glass, plastic, watr & polar molculs X

5 Th chargs inducd on th surfac of th dilctric (insulator) rduc th lctric fild.

6 Polarization of a dilctric in an lctric fild givs ris to thin layrs of bound chargs on th dilctric s surfacs, crating surfac charg dnsitis +s i and s i.

7 o xtrnal -Fild Random orintation of molculs xtrnal -Fild Partial Alignmnt of Molculs

8 ot: is not th fild producd by th dipol Th forc acting on ach charg is F = q Th nt forc on th dipol is zro Th forcs produc a nt torqu on th dipol 2a = 2Fa sin = p sin p=2aq = p x

9 Th lctric dipol momnt (p) is a vctor dirctd along th lin joining th chargs from q to +q, p=2aq A dipol has two qual but opposit sign chargs Assum th distanc btwn th chargs is 2a

10 Dilctric Constant Dilctric Constant is th ratio btwn th prmittivity of th mdium to th prmittivity of fr spac. r Th charactristics of a dilctric matrial ar dtrmind by th dilctric constant and it has no units.

11 Th procss of producing lctric dipols by an lctric fild is calld polarization in dilctrics. Polarizability: Th inducd dipol momnt pr unit lctric fild is calld Polarizability. Th inducd dipol momnt is proportional to th intnsity of th lctric fild. polarizability Is a Polarizability constant constant

12 lctric suscptibility: Th polarization vctor P is proportional to th total lctric flux dnsity and dirction of lctric fild. Thrfor th polarization vctor can b writtn 1 1) ( r r P P

13 Whn th spcimn is placd insid a d.c. lctric fild, polarization is du to four typs of procsss. 1.lctronic polarization 2.Ionic polarization 3.Orintation polarization 4.Spac charg polarization

14 Whn an F is applid to an atom, +vly chargd nuclus displacs in th dirction of fild and ẽ could in opposit dirction. This kind of displacmnt will produc an lctric dipol with in th atom. i., dipol momnt is proportional to th magnitud of fild strngth and is givn by or whr α is calld lctronic Polarizability constant

15 Th ionic polarization occurs, whn atoms form molculs and it is mainly du to a rlativ displacmnt of th atomic componnts of th molcul in th prsnc of an lctric fild. Whn a F is applid to th molcul, th positiv ions displacd by X 1 to th ngativ sid lctric fild and ngativ ions displacd by X 2 to th positiv sid of fild. Th rsultant dipol momnt µ = q ( X 1 + X 2 )..

16 cat ion lctric fild x x 1 2 anion

17 It is also calld dipolar or molcular polarization. Th molculs such as H 2, 2,O 2,Cl 2, CH 4,CCl 4 tc., dos not carry any dipol bcaus cntr of positiv charg and cntr of ngativ charg coincids. On th othr hand molculs lik CH 3 Cl, H 2 O,HCl, thyl actat ( polar molculs) carris dipols vn in th absnc of lctric fild. How vr th nt dipol momnt is ngligibly small sinc all th molcular dipols ar orintd randomly whn thr is no F. In th prsnc of th lctric fild ths all dipols orint thm slvs in th dirction of fild as a rsult th nt dipol momnt bcoms normous.

18 i a 3 1.2µi

19 Considr a dilctric matrial having cubic structur, and assum ionic Polarizability & Orintational polarizability ar zro.. polarization.. P P i whr., i i... whr., P 3 i

20 ...(1) ) 3 (1, ) 3 (1, 3, 3 ) 3 ( i P or P or P P or P P P P P

21 M osottirlation Classius ) 1 3 (1 1 3 ) 1 3 ( ) ( 3 1 1) ( 3 1 1) ( 3 1 1) ( ) 3 (1 (1) & (2) from q 1)...(2) ( th polarization vctor W known that n r r r r r r r r r s P

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23 For a lossy (imprfct) dilctric th dilctric constant can b rprsntd by a complx rlativ dilctric constant: Th imaginary part of this complx dilctric constant, ε at a frquncy, ω is quivalnt to a frquncy-dpndnt conductivity, σ(ω), givn by:

24 DILCTRIC LOSS ε" is also known as th loss factor. Th small diffrnc in phas from idal bhaviour is dfind by an angl δ, dfind through th quation tan δ is known as th loss tangnt or dissipation factor. A quality factor, Q, for th dilctric is givn by th rciprocal of tan δ.

25 Dilctric Loss quivalnt circuit diagrams: (a) capacitiv cll, (b) charging and loss currnt, (c) loss tangnt for a typical dilctric

26 DILCTRIC LOSS From Q = o AV/d = CV If V bing sinusoidal, total charg Q may b writtn as Currnt flow on discharg of th capacitiv cll in tim, t: For a ral dilctric th currnt I has vctor componnts I C and I R : I = I C + I R I Q CV o dq dt it icv

27 DILCTRIC LOSS From magnitud of ths currnts, also w can dfin a dissipation factor, tan, as Quality factor Q is: tan I I R C Q 1 tan avragnrgy stord nrgy dissipatd pr cycl

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30 Magntic prmability - Th ratio btwn inductanc or magntization and magntic fild. It is a masur of th as with which magntic flux lins can flow through a matrial. Magntization - Th total magntic momnt pr unit volum. Magntic suscptibility - Th ratio btwn magntization and th applid fild.

31 Frromagntism - Alignmnt of th magntic momnts of atoms in th sam dirction so that a nt magntization rmains aftr th magntic fild is rmovd. Frrimagntism - Magntic bhavior obtaind whn ions in a matrial hav thir magntic momnts alignd in an antiparalll arrangmnt such that th momnts do not compltly cancl out and a nt magntization rmains. Diamagntism - Th ffct causd by th magntic momnt du to th orbiting lctrons, which producs a slight opposition to th imposd magntic fild.

32 Antifrromagntism - Arrangmnt of magntic momnts such that th magntic momnts of atoms or ions cancl out causing zro nt magntization. Hard magnt - Frromagntic or frrimagntic matrial that has a corcivity > 1 4 A. m -1.

33 Figur 19.3 Th ffct of th cor matrial on th flux dnsity. Th magntic momnt opposs th fild in diamagntic matrials. Progrssivly strongr momnts ar prsnt in paramagntic, frrimagntic, and frromagntic matrials for th sam applid fild.

34 23 Brooks/Col, a division of Thomson Larning, Inc. Thomson Larning is a tradmark usd hrin undr licns. Figur 19.4 Th crystal structur of Mn consists of altrnating layrs of {111} typ plans of oxygn and mangans ions. Th magntic momnts of th mangans ions in vry othr (111) plan ar oppositly alignd. Consquntly, Mn is antifrromagntic.

35 Domains - Small rgions within a singl or polycrystallin matrial in which all of th magntization dirctions ar alignd. Bloch walls - Th boundaris btwn magntic domains. Saturation magntization - Whn all of th dipols hav bn alignd by th fild, producing th maximum magntization. Rmananc - Th polarization or magntization that rmains in a matrial aftr it has bn rmovd from th fild. Hystrsis loop - Th loop tracd out by magntization in a frromagntic or frrimagntic matrial as th magntic fild is cycld.

36 23 Brooks/Col, a division of Thomson Larning, Inc. Thomson Larning is a tradmark usd hrin undr licns. Figur 19.6 Whn a magntic fild is first applid to a magntic matrial, magntization initially incrass slowly, thn mor rapidly as th domains bgin to grow. Latr, magntization slows, as domains must vntually rotat to rach saturation. otic th prmability valus dpnd upon th magnitud of H.

37 Figur 19.7 (a) Th frromagntic hystrsis M-H loop showing th ffct of th magntic fild on inductanc or magntization. Th dipol alignmnt lads to saturation magntization (point 3), a rmananc (point 4), and a corciv fild (point 5). (b) Th corrsponding B-H loop. otic th nd of th B-H loop, th B valu dos not saturat sinc B = μ H + μ M. (Sourc: Adaptd from Prmannt Magntism, by R. Skomski and J.M.D. Coy, p. 3, Fig ditd by J.M.D. Coy and D.R. Tilly. Copyright 1999 Institut of Physics Publishing. Adaptd by prmission.)

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