3D PHASE FIELD SIMULATION OF MECHATRONIC COUPLE FOR PZT FERROELECTRIC CERAMICS

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1 44 Ø 8 Vol.44 No Ý ACTA METALLURGICA SINICA Aug. 8 pp.97 9 PZT Ú Ñ «ß Æ 1) ) 1) 1) 1) Þ ÐÑ Ýµ ¹Ò ÒÖÞ, 18 ) Þ Å, 18 «º Æ Ä ¾ Ñ Ã. ½, ± Ü Ï ß «Á ¹ÀÓ. Ç ±, Ì³ Đ «Å Ù 9, ÔÉ Å. Ò» ÛÇÀ Æ Ò ÛÇ. Ö,, º, ÙÐ TG Ý A Ð (8) D PHASE FIELD SIMULATION OF MECHATRONIC COUPLE FOR PZT FERROELECTRIC CERAMICS LIU Pingli 1), MA Xingqiao ), CHU Wuyang 1), QIAO Lijie 1) 1) Key Laboratory of Environmental Frature (Ministry of Eduation), Corrosion and Protetion Center, University of Siene and Tehnology Beijing, Beijing 18 ) Department of Physis, University of Siene and Tehnology Beijing, Beijing 18 Correspondent: QIAO Lijie, professor, Tel: (1)645, lqiao@ustb.edu.n Supported by National Natural Siene Foundation of China (Nos.5576, 561 and 54811) Manusript reeived 8 14, in revised form ABSTRACT Using D phase field theory, the spontaneous polarization, hysteresis loop and effet of mehatroni oupling of domain swithing of PZT ferroeletri eramis have been simulated. The results show that the domain swithing under applied eletri field is realized through nuleation and growth of new domains. When the applied eletrial field varies gradually, the reversal proess is through 9 domain swithing near the oerive field. A tensile or ompressive strain perpendiular to the eletri field an hinder or promote domain swithing. KEY WORDS ferroeletri material, mehatroni oupling, D phase field simulation, domain swithing È BaTiO Pb(Zr,Ti)O (PZT) Curie ¾ Ð, Ti 4+ É, Õ ½ Ü. º ÜÈ» ½ Ã, À ÅØ Õ Óº. È Ó z Ð¼, Ó Ð¼ a, Ó y Ð¼ b. ²Á Ð, Ti 4+ z È, Õ a, ¼ [1]. ÅØ Õ À ½ÞÅ ÆÔ Ì. Đ À Ô Ã Ô Ì BaTiO Ä À [,]. ÈÐ BaTiO Ä ½ÐÕ Đ ÁÃ ºÓ Â [4,5]. * Ä ß Å 5576, Â ÐË : 8 14, ÐË : Ë²Ã :,, 1978, Û ÐÆ ÓÜÙ ( ß [6] ½ [7] Đ Æ Ù [8] ) Đ / Ì Õ Â ² Ä, Æ Ì ÐÕ ÐÂ Ð, ÕÈ ÙÝ³ ÂË Ì [9]. ÕÔ ¾, Ý ÐÂÆ ºÁ [4,5]. À Đ (Å ) ÅÐÂ Ô, ĐÚ Â Ë Ì [9 1]., Wang [9,1] Ö»À ÐÕ PZT Ì, ± ±, Ý ÞÅ ÐÂÆ ºÁ, Î. ± Æ 9 ÜÆ 18, ± Æ 9, Æ Í Ð 18 ; ÂË Ì Ê Đ Å Ì [9,1]. Ò, Ô ² Ýß Û, Æ Í E Æ P r ÅØ

2 44 t f,n h P. r /H + 5< 5 u H v Y p s ^ g_ X, `/H+ +5< %a+ > az ;6.IYeÆ, 5V a=e, g z + az n6 ^ Y L. 1 z}hf a6 l, H + U, <,N h q. - 6Y M t <,q o Z P. & I a+ 7 + T ; t f 6 l, M t <,q P~ lj J e,; P 9 9 F Q R 1l, s FT z 4 Y 6^. H+ +? Ginzburg Landau l<,nhy 98 [11] Pi (r, t) δf = L t δpi (r, t) (i = 1,, ) (1) u?, Pi(r, t), t l~1:, r = (, y, z) Y<,Nh o C y C z CY ; L,e i9 ; F,9 M 9, M 9.hn+ 9 Y :R: VT Z F = fl + fg + fdip + fela + fele dv () V u?, f, Landau M 9. h, <,q (P, P, P ) Y %Z o N u v; f, <, h 9,? 6 9; f,a <KYaS*T 9; f,o`9; f,&ia+ a <KYS*T 9, V,5<9 Y :., C S(, n(t% 9 <g_5,:, Y(g_ Fourier, R_, JLA [1]. *n PZT >C PbTiO l % M A [1], NMt<,Nh P =. C/m Curie h T = (A [1]? P =.757 C/m, T = 479 ) UMp s 1.?- C ^Y4E, 1 nm 1 nm 1 nm, M vhmt<,q P~, P Æ 64 ^,?C 4E, 64 nm 64 nm 64 nm. $ BG` ` N. z}sk.1 eqob 8tl, $ zp 9 s- L6?Y P~ e b; J Gauss 5d, o? Z (1) [/ Y6 # 1 v, H?R;VY'#y SYzI. I ljym., M 9 F EPYiQR1, <,Nh Y imt<,hæ. (l5&a+, u ()? f =. m 5 1.(, o PY<,Nh lj,? P =.55. (l z P? Z (1) [/ Ya6 # 1b v. # 1b 9, ab d y 6YS` S, H? 6?- ^ M P (P~ P) EP,,6J is. `/6 L# 1, H? as L 1 G dip ela ele [1] [14] ele 4 1 PZT {uls;+l 'X5 Fig.1 Simulated domain strutures of PZT sample before (a) and after (b, ) spontaneous polarization (a) and (b) are the (1) ross setions of the entre of the sample, arrows indiating the polarized diretion () D struture simulated after 5 14 steps, a 6,!aS, b 6, 1aS, 6.? # Yr/6^ YU CPv # 1a H.. a+ d p b nmt<,(y6^ (# 1) o PI5 E = E/E ()

3 8E #B Z : PZT _ = _X W^-F): 99 u?, E,5,( Y & + N h; E,& a+ N h; frsg y 6, 6, o PY<,Nh P A E = P T T /(ε C ), H?, P, M t <,N h,.55(e =) g 7.5(E =.5). g a+ 7 T, h, T, Curie h, ε, ) b a,, C E =1., (l[y X 6.I (6 e) q s, Curie,, n PZT v, P =. C/m, o a+ P Y6 S l I, # b.? H, <,N T =, 1/(ε C )=.8 1 m N/(C ), h P g 7.419(E =1.). EPg a+ E 7 1.5,.,.1,.,..4, m 4 1 ( T =5, Aq V E =.1 1 V/m. P & I a+ E =.5 l, 6Y P Æ lj l. # 1b? ab 6 5 V 4 Y6 ^, N? l[ FTL6 H Æ. # y P y P e7 ef, q d 6 o~ y P e7 gh, E =.4 ly D 6^, as, a 6,!a, b 6. # a v. # a / > v, # 1b Y ijkl S? o P E =.5 l, m 4 1 ( 5V4 YLz a 6^ PYa6 Ia+ E =.5 (, EP,oa+, # d v. P YX6. (sy, Ia+(, oa+py n-z E 9HY P, Aq5V<,T 6 ( abd S ) 6 eq.i; "z/oa+ E, #?Y ABCDF. A E =. Y D ^wt, E PYX6AA 7<a+PYra6?.I PR\a+, <,Nh l;r, 7 E =. $<, ( ijkl S ). ( s% a+ ; Y6 l TE #? F GHI v. IvPa+, TEA H R, g_, m 4 1 lj.(ft4æ, # a? mnop I, (l?z[/y6^ # 4a v. PvPa+ E 5 [1] 7 %H`*#H, n`*wo`5x\ =5 dr5 kf^/64uk5 Fig. Domain swithing proess through initiating domain wall motion along the field diretion () with inreasing the eletri field, simulated for 4 1 steps (a) E =.5, domain wall ab in Fig.1b migrated to ef, d to gh; a new domain ijkl formed from a zone ijkl in Fig.1b (b) E =1., the zone efgh and ijkl enlarged, but zone mnop dereased () E =.4, the zone mnop vanished, but the zone efgh and zone ijkl ontinuously enlarged (d) E =.5, single domain

$E FevP$I7., TEFT K ^ (# ). EPR\~a+, "TEo KJL 7 L ^, ( l E =.5,?Z[/Y6^ # 4 v. a+ E g 7.6 l, 6vtf 9 6 ( # 4d). # 4?Y abd efgh 6o y P,,o P,? tf 9 6 ; q# 4?Y def 6"A~ P,~ y P, tf 9 6. f 9.6.4 H P *.$

4 44 t A I :Y.5 $7 J :Y.6 l, a6vtf 9 6 (# 4b). # 4a? abd 6 > efgh 6 o ~ P, # 4b?f 1o~ y P,?tf 9 6 ; q# 4a Y def 6"A y P, P (# 4b), tf 9 6.? l, <,Nh P tf ", A.1416(E =.5),.971(E =.6), n #?Y J ^. E FevP$I7., TEFT K ^ (# ). EPR\~a+, "TEo KJL 7 L ^, ( l E =.5,?Z[/Y6^ # 4 v. a+ E g 7.6 l, 6vtf 9 6 ( # 4d). # 4?Y abd efgh 6o y P,,o P,? tf 9 6 ; q# 4?Y def 6"A~ P,~ y P, tf 9 6. f H P *. G B D F C A I. L J -.4 K D -.5. E* G*4;4UX`<D Fig.4 4 Fig. D hysteresis loop obtained by D phase field simulation 9 T'* h `5 use 9 5G, Q8`<Db;+MgX! domain swithing of all kind of domains near the oerive field, resulting in a jump of the polarization in Fig. (a) point I in Fig. (E =.5), zone abd and efgh are domains, zone def is +y domain (b) point J in Fig. (E =.6), zone abd and efgh are y domains, zone def is + domain, 9 domain swithing ours () point L in Fig. (E =.5), zone abd and efgh are +y domains, zone def is domain (d) point G in Fig. (E =.6), zone abd and efgh are + domains, zone def is y domain, 9 domain swithing ours

8 : PZT Ï ¹ µ 91, Ë Í, È P = Ð, Í E = E /E =.5, À Í E =1.67 1 7 V/m. Ò PZT-5H, Ô ²Î E =1.1 1 6 V/m, À ÛÊ 1 Å. ½ É ÝÔ Á Ï Đ ½ ßÚ ½, Õ Û Ê ÚÈ Ï ºÁ, Ê ² ÀÚÈ.

5 8 : PZT Ï ¹ µ 91, Ë Í, È P = Ð, Í E = E /E =.5, À Í E = V/m. Ò PZT-5H, Ô ²Î E = V/m, À ÛÊ 1 Å. ½ É ÝÔ Á Ï Đ ½ ßÚ ½, Õ Û Ê ÚÈ Ï ºÁ, Ê ² ÀÚÈ.. Û Ò Đ Ó y ÜÈÁ± ε y =5 1, ÜÈ Á ±, Ñ 4 1 Ì, ÎÌ Æ P, Ð, Õ ÎÌ¹Þ. y ÜÈ Æ²Á, È E =.5 Ð½ Þ ÅÓ ÜÈ Ä, d. ÆÞÅ εy =5 1, È E =.5 Ð, ¼µÎ. E. Ð, ¼µÎ ( 5a). E Þ¼ Ì.5 Ð, ½ Ä («d). ¹, ¼ ÜÈ Ç Ó ÜÈ. Ó y ÜÈÁ± ε y = 5 1, È E =. Ð, ¼µ½; È E =.4 Ð, Ðµ½ ( 5b), À D «d. ¹, ¼ ÜÈ Ó ÜÈ. È À Ð, ¼ ÜÈ Ò Æ Ä Á; Æ ¼ Æ µæ Ê ( 5). Ý Ì FGHIJ ÈÊ ÚÈ, Ð Ì 18. ÈÉ Ì ¾, µî F Ø, ¼ ÁÞÅÚÈ, Ð 18., È E =.1 Ð, 9, (Ó y ÜÈ ³ z ÜÈ), È E =. Ð, ÞË Ó ÜÈ 18. È E =.8 Ð, Ñ º, Æ ÚÓ ÜÈ, Ø 18. ¼ ÁÚÈ E =. ÈÊ E =. Î ÈÆ Ë, Æ Â Þ ÐÕ. Polarization P * X () y y y E * 5» ÛÇ À ÑÒ ÛÇ Å Ã Fig.5 Domain swithing in the sample under tensile strain (a) and ompressive strain (b) and polarized urves under stress () (a) εy =5 1, E =. tensile strain, not single domain struture (b) εy = 5 1, E =.4 ompressive strain, single domain struture () effets of tensile and ompressive strains on polarization

6 9 Đ «44 Ø Ü (1)»À Đ Á ÅØ ², Õ Î, ÐÕ Ò Ä. ()»À ¾, ² Ý ºÁĐ ÜÈ.. () Í, «9 Ê Æ (4) ¼ ÜÈ Ç Ó ÜÈ. Î The Pennsylvania State University»²ÉÏ Ï Á ß À ÛÑ Đ. Ø [1] Yang W. Mehatroni Reliability. Heidelberg, Germany: Springer, : 1 [] Wang R M, Zhao X W, Chu W Y, Su Y J, Qiao L J. Mater Lett, 7; 61: 116 [] Wang F, Su Y J, He J Y, Qiao L J, Chu W Y. Sr Mater, 6; 54: 6 [4] Wang R M, Chu W Y, Su Y J, Li J X, Qiao L J. Mater Si Eng, 6: B15: 141 [5] Zhao X W, Chu W Y, Su Y J, Li J X, Gao K W, Qiao L J. Ata Metall Sin, 6; 4: 1 (±, Ï Ø, ÕÐ,, ÐÎ, Ç., 6; 4: 1) [6] Huber J E, Flek N A, Landis C M, MMeeking R M. J Meh Phys Solids, 1999; 47: 166 [7] Hwang S C, Lynh C S, MMeeking R M. Ata Metall Mater, 1995; 4: 7 [8] Hwang S C, MMeeking R M. Int J Solids Strut, 1999; 6: 1541 [9] Wang J, Shi S Q, Chen L Q, Li Y L, Zhang T Y. Ata Mater, 4; 5: 749 [1] Wang J, Li Y L, Chen L Q, Zhang T Y. Ata Mater, 5; 5: 495 [11] Hu H L, Chen L Q. J Am Ceram So, 1998; 81: 49 [1] Li Y L, Choudhury S, Liu Z K, Chen L Q. Appl Phys Lett, ; 8: 168 [1] Loge R E, Suo Z. Ata Mater, 1996; 44: 49 [14] Huang H Y, Chu W Y, Su Y J, Li J X, Qiao L J. Appl Phys Lett, 6; 89: 1494

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