Chapter 10 DIELECTRICS. Dielectrics

Transcription

1 86 Dlctcs Chat DILCTRICS Dlctcs : Dlctcs a fct nsulatos. In dlctcs lctons a vy tghtly bound to th atoms so that at odnay tmatus thy do not conduct any lctc cunt. xamls: Solds: glass, ocln; gass: H, N ; lquds: CH 3 Cl, u wat Thy a of two tys. ( Pola dlctcs ( Non-ola dlctcs Pola dlctcs a thos dlctcs whos molculs contans (a chaactzd by th mannt dol momnts. x - H O, NaCl, KCl. Non-ola dlctcs a thos dlctcs whos molculs do not contan th mannt dol momnts. x - Sold A. H H H O: lctongatvty of O s hgh than H so t wll hav mo ngatv chag, so t contan mannt dol momnt. It s th nhnt oty of molculs. If w aly xtnal lctc fld on non-ola dlctcs thn t wll b olazd and ths olazaton s calld nducd olasaton o nducd dol momntum. Thus, n n... ( wh, s ootonalty constant and known as olazablty of atom o molcul and s al lctc fld. Dol momnt : If w hav two qual and oost chags q and q, saatd by a dstanc, thn th dol momnt s dfnd as q. Th dol momnt s dctd fom th ngatv to ostv chag. Polazaton: Th olazaton ( P s dfnd as th dol momnt unt volum.., P V P also n and P Nn N... ( wh s lctc susctblty and N s numb of dols unt volum.

2 Dlctcs 87 N Snc, N Fo non-ola dlctcs: If w hav a lag aalll lat caacto and w fll a non-ola dlctc btwn ts lats. Suos xtnal ald fld s. Du to ths, non-ola dlctcs wll b olazd thn lats occu som bound chag and lctc fld dvlo s whch s lss than. Thus, sultant lctc fld, mac P n Macoscoc lctc fld s avag lctc fld sn btwn th lats. If th s a molcul btwn lats thn t wll bhav as dol and sultant fld on ths molcul s dffnt fom and ths lctc fld s calld al fld. mac 3 wh s xtnally ald lctc fld, s dolazaton fld, ( s lctc fld du to th nduc chags on th sufac of th cavty (olazaton fld. s macoscoc fld, and s lctc fld du to all th chags nsd th cavty. Rsultant of all ths lctc flds s th 3 al fld. Tak a shcal cavty out fom th suoundng of molculs. Ths cavty s calld Lontz cavty. If th dol s at th cnt of th cavty thn chags on th cavty wll b symmtc about cnt. So, 3 (du to symmty Now, mac mac P 3 snc P 3 If sold contans N atoms (o molculs unt volum, ach atoms du to th alcaton of lctc fld wll bcom dol, so th wll b N dols. P N n P N... (3

3 88 Dlctcs Fom quaton ( and quaton (3, w gt N mac N ( mac ( N mac (snc ( N ( 3 wh, s lctc olazablty and s dlctc constant. Ths laton s known as Classus-Mossot laton. Ths s vald only fo non-ola molculs. Physcal sgnfcanc of Classus-Mossot laton: Classus-Mossot laton s a latonshs btwn and. s a mcoscoc quantty and s macoscoc quantty (dlctc constant bcaus cosonds to dol momnt and cosonds to olasaton. Fo ola molculs, ths quaton bcoms Langvn - Dby quaton. Tys of olasablts: Th a th tys of olasablts ( lctonc olasablty ( ( Ionc olasablty ( ( Dola olasablty ( d Thus total olasablty s sum of lctonc, onc and dola olasablts..., d nducd Pmannt ( lctonc olasablty ( : Ths ty of olasablty ass du to dslacmnt of lcton cloud of an atom latv to ts nuclus n th snc of ald lctc fld. 3 Th lctonc olasablty s gvn by 4 R, wh R s adus of th atom. Ths ty of olasablty s ndndnt of tmatu but dnds on th fquncy of ald lctc fld. Th fquncy dndnc of s gvn by m( wh m s mass of th lcton, s lctonc chag, s natual fquncy of oscllaton of atom and s fquncy of ald lctc fld. Unt of : In C.G.S. unts, has unt of volum (cm 3, and n M.K.S. unts, s masud n F m.

4 Dlctcs 89 = = n ( Ionc olasablty α : Ths ty of olasablty ass du to ncas o dcas n th bond-lngth of ons. Ths ty of olasablty s ndndnt of tmatu but dnds on th fquncy of ald fld. Th onc olasablty dnds on fquncy n followng mann. Fo an onc sold, th olasablty s gvn by m M Na Cl wh m s mass of on on (say Na, M s mass of anoth on (say Cl, and s natual fquncy of th vbaton of molcul (NaCl. In gnal,. d ( Dola olasabltyα : Ths ty of olasablty ass du to th mannt dol momnt of th molcul. Th dola olasablty s gvn by d 3k T q O q wh, s mannt dol momnt of th molcul, T s tmatu and k s oltzmann constant. Fom abov quaton t s cla that Hnc total olasablty, d d dnds on both tmatu and fquncy of th fld. 3k T Ths laton s known as Langvn - Dby quaton. Ths s vald fo only ola molculs.

5 9 Dlctcs Fquncy dndanc of total olasablty: In vsbl gon, total olasaton s lctonc olasaton (... xstnc of,, dnds uon th laxaton tm (. Lss th, fast th d sons.. f. Mcowav IR Vsbl UV Total Polasablty ( d O Fquncy ( f Fom ths fgu, d At otcal fquncy o vsbl fquncy: W hav n n N n 3 Ths laton s known as Lontz-Lontz laton. Statc dlctc constant fom Langvn-Dby quaton: Total olasablty d Polazaton : P ( N If mac mac 3k T Ths s ossbl f saaton btwn atoms and molculs s so lag that th s no ntacton btwn th dols lk n lqud o gass. So, P ( N mac Thus, w gt 3 N ( ( N k T.., Mo slo Mo ola and Lag ntct Mo lctonc and onc olazablts. If gah s flat mans molcul s non-ola.

6 Dlctcs 9 ( N Slo 3 k T ( O N ( /T O /T 3k ( A O /T O /T Fom abov fgu t s cla that A s mo ola bcaus of mo slo. Thos hav mannt dol momnt a sntd by. Som of molculs that a chaactzd mo and lss ola a gvn blow: ( CH 4 A ( CO A ( H O (v CO (v HCl (v CS A (v SO (vno /T Pzolctcty: Ctan cystals.g. quatz (cystalln SO and ato 3 bcom olazd whn mchancally stssd. Aaanc of sufac chag lads to voltag dffnc btwn th two sufacs of th cystal. Sam cystal also xhbt mchancal stan o dstoton whn thy xnc lctc fld. A L Only ctan cystal that xhbt no cnt of symmty, shows zolctcty. xaml: NaCl ty has cnt of symmty. xaml: Hxagonal fc P = P = P

7 9 Dlctcs Non-cnto symmtc dcton of olazaton dnds on th dcton of ald stss. Gnally, an ald sts n on dcton can gv s to nducd olazaton n oth cystal dcton. Suos, T J s ald mchancal stss along som j dcton, P s nducd olazaton along som dcton. Two a lnaly latd as P = d j T j, wh d j s zolctc coffcnt. Th convs zolctc ffct s that btwn an nducd stan S j along j dcton and an ald lctc fld along dcton. S j = d j Thy a calld tansducs bcaus thy convt lctcal sgnal, lctc fld to mchancal sgnal, stan & vc-vsa usd n mcohons, ultasonc tansducs. lcto-mchancal coulng facto k s dfnd as k o L k lctcal ngy convtd to mchancal ngy Inut of lctcal ngy Mchancal ngy convtd to lctcal ngy Inut of mchancal ngy Folctc cystal: Ctan cystal a th occunc of sontanous olazaton n ctan cystal such as aum Ttanat (ato 3. Folctc cystal hav a mannt olazaton as a sult of sontanous olazaton. Th dcton of can b dfnd by th alcaton of an xtnal fld. Pyolctc cystal: Ths matal s a ola dlctc (such as ato 3 n whch a tmatu chang and T nducs a ootonal chang n th olazaton that s T,wh s yolctc coffcnt of th cystal. a O * T 4 c-axs d dt, wh = yolctc coffcnt s usd n nfad dtctos ath. nomal to th lats changs th stod chag whch s of lvanc.

8 Dlctcs SOLVD PROLMS 93. Th lctonc olazablty of th A atom s.7 4 Fm. What s th statc dlctc constant of sold A (blow 84 K f ts dnsty s.8 g cm 3. N N Ad Soln. wh N = M o N o Usng Clausus-Mosott quaton,.63 N o Consd a u S Cystal that has 9. (a What s th lctonc olazablty du to valnc lcton S atom (f on could oton th obsvd cystal olazaton to ndvdual atoms? (b Suos that a S cystal saml s lctodd on oost facs and has a voltag ald acoss t by how much s th al fld gat than th ald fld? (c What s th Rasonant fquncy of cosondng N/v = 5 8 m o.9 Soln. (a N 5.9 (b Local fld s P 3 o 4 Fm o P (c Snc olazaton s du to valnc lctons and th a fou fo S atom, w can Us W o / / 9 Z o 5.6 Hz.65 ad s m (Fo 3. Consd th CsCl cystal whch has on Cs -Cl a unt cll and a lattc aamt a of.4 nm. Th lctonc olasablty of Cs and Cl ons s Fm and Fm sctvly, and th man onc olasablty on a s 6 4 Fm. What s th dlctc constant at low fquncs and that at otcal fquncs. Soln. Th CsCl stuctu has on caton Cs and on anon (Cl n th unt cll. Gv lattc aamts a =.4 9 m, Numb of ons unt volum n N s /a 3. Numb of ons unt volum also concntaton of Catons and Anons 8 3 m

9 94 now N 3 Cs N Cl N (At low fquncy 7.56 (At hgh fquncy otcal fquncy onc olazaton n two sluggs N 3 Cs N Cl,.7 Dlctcs 4. Consd a Pzolctc saml n th fom of a cylnd. Suos that th zolctc coffcnt d = 5 mv and. Th zolctc cylnd has a lngth of mn and a damt of 3 mm. Th snlc ga s n a and has a bak down voltag of about 3.5 kv. What s th foc qud to sak th ga? Soln. Inducd olazaton T = Stss, P = dt df A Inducd olazaton lads to nducd sufac olazaton changs gvn by Q = AP. If C s th caactanc, thn th nudcd voltag s Q AP LP L df / A dlf V C o A o o A L o F AV 87.6 N dl 5. Dtmn th cntag of onc olasblty n NaCl cystal whch has otcal ndx of facton and th statc dlctc constant as.5 and.6 sctvly. Soln. N 3.6 and n = N N n N n 3 Dvdng quaton ( by quaton (, w gt 7 N N N n n % N (... (

10 Dlctcs 95 PRACTIC ST. In a do of wat of adus 3 m, th molcula dols a ontd n th sam dcton. If th dol 3 momnt of th wat molcul s 6 C-m, ts olazaton wll b (a 8.4 C/ m (b C/ m (c C/ m (d 8.4 C/ m. Th latv mttvty of agon at ºC and on atmosh s.435, th lctonc olazablty of th agon atom wll b 38 (a Fm (b.43 4 Fm (c.43 4 Fm (d.43 Fm 3. A hoton of wavlngth 4Å s absobd by cold mcuy vaou and two oth hotons a mttd. If th wavlngth of on of thm s 85 Å, th wavlngth of th oth hoton wll b (a 5755Å (b 5855Å (c 5955Å (d 655Å 4. Dtmn th % of onc olasablty n NaCl cystal whch has otcal ndx of facton as.5 and dlctc constant as Dlctc olazablty s a ootonalty constant n th laton btwn (a lctc dol momnt and al lctc fld (b Dslacmnt vcto and al lctc fld (c lctc dol momnt and chag dnsty (d Dslacmnt vcto and chag dnsty 6. N s 3 (a Lontz laton (c Clausus-Mosott laton (b nstn laton (d Non of ths 7. Fo fomagntc matals, th mablty µ s (a < (b = (c > (d >> 8. Dol momnt of a cunt loo s gvn by (a na (b nqa (c n A q (d na wh n = numbs of tuns, = cunt and A = aa of coss scton of th loo, q = chag. 9. lctons a mttd wth zo vty fom a ctan mtal sufac whn t s xosd to a adaton of wavlngth 685Å. Th wok functon of th mtal s (a.83 V (b.83 V (c.83 V (d 3.83 V. Whn a sufac of co s adatd by lght of wavlngth 849Å, th stong otntal s found to b.7 volts. Th thshold fquncy of th mtal s (a c/ s (b c/ s (c c/ s (d c/ s ANSWR KY. (a. (c 3. (a 4. (5.4% 5. (a 6. (c 7. (d 8. (a 9. (b. (c