Reading assignment. Dielectric behavior. Dielectric strength. Topic 9

Transcription

1 Reading assignment Dielectric behavir Tpic 9 Askeland and Phule The Science and Engineering f Materials 4 th Ed. Sec and Shackelfrd Materials Science fr Engineering Sec Chung Cmpsite Materials Ch. 7. Insulatrs and dielectric prperties Materials used t insulate an electric field frm its surrundings are required in a large number f electrical and electrnic applicatins. Electrical insulatrs bviusly must have a very lw cnductivity r high resistivity t prevent the flw f current. Prcelain alumina crdierite mica and sme glasses and plastics are used as insulatrs. Dielectric strength Maximum electric field that an insulatr can withstand befre it lses its insulating behavir Lwer fr ceramics than plymers Dielectric breakdwn - avalanche breakdwn r carrier multiplicatin 1

2 Plarizatin in dielectrics Capacitr An electrnic device cnstructed frm alternating layers f a dielectric and a cnductr that is capable f string a charge. These can be single layer r multi-layer devices. Permittivity - The ability f a material t plarize and stre a charge within it. Linear dielectrics - Materials in which the dielectric plarizatin is linearly related t the electric field; the dielectric cnstant is nt dependent n the electric field. Dielectric strength - The maximum electric field that can be maintained between tw cnductr plates withut causing a breakdwn. Plarizatin mechanisms in materials: (a) electrnic (b) atmic r inic (c) high-frequency diplar r rientatin (present in ferrelectrics) (d) lw-frequency diplar (present in linear dielectrics and glasses) (e) interfacial-space charge at electrdes and (f ) interfacial-space charge at hetergeneities such as grain bundaries. 003 Brks/Cle a divisin f Thmsn Learning Inc. Thmsn Learning is a trademark used herein under license. A charge can be stred at the cnductr plates in a vacuum (a). Hwever when a dielectric is placed between the plates (b) the dielectric plarizes and additinal charge is stred.

3 Q D A V d D Σ 8.85 x 10-1 C/(V.m) Slpe C Q V ΣA Σd A d 3

4 4 A Q D D m κ κ D m κ Σ Σ C d A d A V Q C m κ κ κ κ Σ Σ P D m D κ Σ Σ (κ 1) Σ E

5 5 1 Q Q Q κ κ P 1 Σ κ χ (bund charge)d (κ 1) Qd P A 1)Q ( Ad 1)Qd ( Vlume mment Diple κ κ C m Q V κ κq D m A ΣA x A x A C m κ x x A A V Σ Σ

6 Table 7.6 Values f the relative dielectric cnstant κ f varius dielectric materials at 1 khz (Data frm Ceramic Surce 86 American Ceramic Sciety Clumbus Ohi 1985 and Design Handbk fr DuPnt Engineering Plastics). Al O 3 (99.5%) BeO (99.5%) Crdierite Nyln-66 reinfrced with glass fibers Plyester Material κ D m Dˆ m Σ ˆ iωt Σe Σˆ ( csωt + isinωt) e [ + i sin( ωt δ )] ( ωt δ ) Dˆ cs( ωt δ ) i Dˆ m Dˆ Σˆ m e m ( ωt δ ) i e tanδ -iδ Dˆ Σˆ Σˆ e m iωt ( csδ isinδ ) Imaginary part f Real part f κ κ 6

7 i c dq dv i c C dt dt ν V sin ωt π ω πf dv C dt T ωcv csω t V csωt 1/ ωc π sin ωt + π π sinωt cs + csωt sin csωt i c V π sin ωt + 1/ ωc i R ν V sinωt R R i c V π sin ωt + 1/ ωc i R ν V sinωt R R V/R 1 tanδ VωC ωcr 7

8 τ 0 τ Energy stred νi Cdt V ωcsinωt csωtdt 0 τ V ωc sin ωt dt 0 V ωc τ cs ωt 0 4ω 1 [ ] ( cs 1) CV ωτ 4 Maximum energy stred ½ CV This ccurs when cs ωt -1 Energy lss per cycle due t cnductin thrugh the resistr R Energy lss V R ωr π / ω 0 V π sinωt sinωt dt 1 ( 1 csωt ) d( ωt) 0 π V 1 1 ω sin ω ωr t t V 1 ( 0 0 0) R π + ω V π. ωr 0 8

9 The smaller is R the greater is the energy lss. Energy lst per cycle V π / ωr π maximum energy stred πcv / ω 1 CR tanδ 9

10 Frequency dependence f plarizatin mechanisms. On tp is the change in the dielectric cnstant with increasing frequency and the bttm curve represents the dielectric lss. Quartz plarizatin nly under stress 10

11 003 Brks/Cle a divisin f Thmsn Learning Inc. Thmsn Learning is a trademark used herein under license. (a) The xygen ins are at face centers Ba+ ins are at cube crners and Ti+4 is at cube center in cubic BaTi03. (b) In tetragnal BaTi03 the Ti+4 is ff-center and the unit cell has a net plarizatin. 11

12 Different plymrphs f BaTiO 3 and accmpanying changes in lattice cnstants and dielectric cnstants. Table 7.3 Cntributin t diple mment f a BaTiO 3 unit cell by each type f in. In Ba + (+)(1.6 x ) 0 0 Ti 4+ (+4)(1.6 x ) +0.10(10-10 ) 6.4 x O - (side f cell) O - (tp and bttm f cell) Charge (C) (-)(1.6 x ) (-)(1.6 x ) Displacement (m) -0.10(10-10 ) -0.13(10-10 ) Diple mment (C.m) 6.4 x x Ttal 17 x P C.m - C.m m 3 1

13 - E c E 13

14 c) Plycrystalline BaTiO3 shwing the influence f the electric field n plarizatin. The effect f temperature and grain size n the dielectric cnstant f barium titanate. Abve the Curie temperature the spntaneus plarizatin is lst due t a change in crystal structure and barium titanate is in the paraelectric state. The grain size dependence shws that similar t yield-strength dielectric cnstant is a micrstructure sensitive prperty. (b) single crystal. Effect f grain size Ferrelectric dmains in plycrystalline BaTiO3. 14

15 Depling Piezelectric aging rate r u u u 1 1 r lg t t 1 E u : parameter such as capacitance t: number f days after plarizatin Ferrelectric -A material that shws spntaneus and reversible dielectric plarizatin. Piezelectric A material that develps vltage upn the applicatin f a stress and develps strain when an electric field is applied. 15

16 003 Brks/Cle a divisin f Thmsn Learning Inc. Thmsn Learning is a trademark used herein under license. The (a) direct and (b) cnverse piezelectric effect. In the direct piezelectric effect applied stress causes a vltage t appear. In the cnverse effect (b) an applied vltage leads t develpment f strain. Direct piezelectric effect Reverse (cnverse) piezelectric effect 16

17 E E 17

18 Direct piezelectric effect P dσ P d σ κ d Σ σ d: Piezelectric cupling cefficient (piezelectric charge cefficient) Table 7.1 The piezelectric cnstant d (lngitudinal) fr selected materials Piezelectric cnstant d Material (C/N m/v) Quartz.3 x 10-1 BaTiO 3 PbZrTiO x x 10-1 PbNb 80 x 10-1 O 6 P D m D κ Σ Σ (κ 1) Σ V Σ Σ ld σ 1 ( κ ) P ( κ 1) d σ 1 ( κ ) V l Σ ld σ V 1 g ( κ ) d ( κ ) 1 V lg σ g: piezelectric vltage cefficient 18

19 Reverse piezelectric effect S dσ S d Σ Σ σ S P Σ S σ P Reverse piezelectric effect Σ S σ -1 Σ Σ σ ( κ ) ( κ ) S 1 Σ Σ S σ -1 Σ ( κ ) Σ σ Σ σ d κ ( ) S dσ 1 d ( κ ) 1 19

20 Σ σ d ( κ ) g 1 d ( κ ) 1 Σ gσ Σ g σ Hke s law σ ES Σ gσ Σ ges S dσ Σ S ge 1 d ge 1 E gd Electrmechanical cupling factr (electrmechanical cupling cefficient) k k k utput mechanical energy input electrical energy utput electrical energy input mechanical energy 0

21 Substitutin f A and B sites in BaTiO 3 PZT: PbZrO 3 -PbTiO 3 slid slutin r lead zircntitanate Table 7.4 Prperties f cmmercial PZT ceramics PZT-5H Prperty (sft) Permittivity (κ at 1 khz) Dielectric lss (tan δ at 1 khz) Curie temperature (T c C) Piezelectric cefficients (10-1 m/v) d d d Piezelectric cupling factrs PZT4 (hard) k k k

22 Table 7. Measured lngitudinal piezelectric cupling cefficient d measured relative dielectric cnstant κ calculated piezelectric vltage cefficient g and calculated vltage change resulting frm a stress change f 1 kpa fr a specimen thickness f 1 cm in the directin f plarizatin. PZT Material Cement paste (plain) Cement paste with steel fibers and PVA Cement paste with carbn fibers d (10-13 m/v) * ± ± ± κ g (10-4 m /C) Vltage change (mv) Piezplymer Bimrph (bi-strip) Mnie Cymbal Cantilever beam cnfiguratin fr actuatin Cmpsites with piezelectric/ferrelectric material sandwiched by metal faceplates f enhancing the piezelectric cupling cefficient

23 Pyrelectric - The ability f a material t spntaneusly plarize and prduce a vltage due t changes in temperature. p dp dt Σ dκ dt p pyrelectirc cefficient P plarizatin Table 7.5 Pyrelectric cefficient (10-6 C/m.K) 0 BaTiO 3 PZT 380 PVDF 7 Cement paste 0.00 Px V ( κ -1) Vltage sensitivity dv P dx x + dσ ( κ -1) dσ ( κ 1) dp dσ Cmpliance Piezelectric cupling cefficient d 3

24 Piezelectric cmpsite When any material underges plarizatin (due t an applied electric field) its ins and electrnic cluds are displaced causing the develpment f a mechanical strain in the material. plarizatin. This phenmenn is knwn as the electrstrictin. Examples f ceramic capacitrs. (a)single-layer ceramic capacitr (disk capacitrs). (b) Multilayer ceramic capacitr (stacked ceramic layers). 4