45 2 Û Vol.45 No Ó ACTA METALLURGICA SINICA Feb pp
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1 4 2 Û Vol.4 No Ó ACTA METALLURGICA SINICA Feb Pb. Sr. TiO 3 É Æ ÓÐÖÎ Đ Þ 1,2,3) ĐÝÛ 1,2,3) Đ 4) ÐßÜ 4) 1) ½ ¾ ¾ÆÈÊ, ) ½ ¾, 139 3) Å¾Ù Đ¾, 716 4) ž Đ ¾ ¾, Ò Ù ÇÇÙ, ±ÍÈ ÉÙ Â ± µ«ë (VCA), Pb. Sr. TiO 3 (PST) Ð Þ ±. ÅÞ PST ± Ë Ë Á, ÅÕ A Ѿ ÙÏÐÆ. ¾ Ï: Ù PST ± Ë, Í Ti ÆÞ ËË [1] Đ Ð.12 nm Ó Ñ, PST Ï. O 2 Ti 3d» ÖÁÁ Å O Pb O Sr» ÖÁ ÝÜ TiO 6 ËË Ì, Ë, Á PST ÏÐ. Ä Pb. Sr. TiO 3 (PST),, Ïб, ±, µ«ë (VCA) Ù Ì O641 ½ A ؼ (29) FIRST PRINCIPLE ANALYSYS ON FINE STRUCTURE OF Pb. Sr. TiO 3 ZHANG Weihu 1,2,3), ZHANG Fuchun 1,2,3), ZHANG Zhiyong 4), YAN Junfeng 4) 1) Xi an Intitute of Otic and Preciion Mechanic, Chinee Academy of Science, Xi an ) Graduate Univerity of Chinee Academy of Science, Beijing 139 3) College of Phyic & Electronic Information, Yan an Univerity, Yan an 716 4) Information Science and Technology Intitution, Northwet Univerity, Xi an Correondent: ZHANG Weihu, rofeor, Tel: , ydzwh@163.com Suorted by Secial Foundation of Education Deartment of Shaanxi Province (No.8JK487) Manucrit received , in revied form ABSTRACT The electronic tructure and roertie of Pb. Sr. TiO 3 (PST) were calculated by the lane wave ultra oft eudo otential and virtual crytal aroximate (VCA) technologie baed uon the denity function theory (DFT) within the general gradient aroximation. The changed trend of the total energy of PST olid olution wa analyzed, and the equilibrium configuration of A ite cation (Pb and Sr) in the ferroelectric hae wa determined. The calculated reult revealed that the energy of PST aeared minimum when the off center dilacement of Ti atom wa u to.12 nm along (1) direction. The trong hybridization between O 2 and Ti 3d and art hybridization between O Pb and O Sr howed an increae in the ditortion of TiO 6 octahedron and a reduce in the ytem total energy, which led to the formation of ferroelectric domain. KEY WORDS Pb. Sr. TiO 3 (PST), fine tructure, ferroelectric, firt rincile, virtual crytal aroximation (VCA) ºµ Ѳ Ì Ú Ñ Ñ Ñ Ñ ² Ë Ì Ò ², ÉÐ, Ú Ñ Ñ ¹ ËÎĐ [1 3] ź» Ì (Pb. Sr. - TiO 3, PST) Ä NTC (negative temerature * Ð Ú È 8JK487 ¹ Ü : , ¹ ³ Ü : :,, 1961, Ú» coefficient) PTC (oitive temerature coefficient) ÎƲ [4] º, ½Ä ÑË ÎƲ Ø ². À Æ NTC PTC ÎƲ, Ç PTC NTC Ë ±, Æ ÚÓÚ² Æ À Ì Ë NTC PTC Ô Æ Ò² ¹¹ ËÎĐ, ÉÐÒºÒ ¼ Æ. ÌÆ Ñ ² ÑƲØ, É Ã º Ð Ë,
![218 ¾ ½ Å 4 ÆÆ ÎƲ Ñ PST É Ã«. ƺ «Þ, ß Ñ Ì Ø, ² À µ BaTiO 3 [], PbTiO 3 [6] SrTiO 3 [7] ABO 3 ºµ Ñ Ñ Đ ÑƲ. Ì ËÎ Ñ Æ ² Ì ÂÛ, ß Ò, Ì Æ Î¾. ÑÆÖ [8] ¹ [9] Î ² KTa.44 Nb.6 O 3, PbFe. Nb. O 3 B Ò Ñ Đ.](/docs-images/74/71399544/images/2-0.jpg "ÔÎÕ ÚÊÚ ÃÉ ¾ µøì Ì (virtual crytal aroximate, VCA) Pb. - Sr. TiO 3 (Ð PST) ² Ì Đ, ÃÅ A Ò Ò Ê Ñ Đ Ñ ² Â. 1 Í Ô 1.")
![1 Ï (Pb,Sr)TiO 3 Đ ²Î Kang [1], Jain [11] Kim [12] X «ß Đ, [ 2 2 Z q q r R q + ρ( r) r r d r + ] V xc ( r) ψ i ( r) = ε i ψ i ( r) (2) ρ( r) = i n i ψ i ( r)ψ i ( r) (3) ², 2 Lalace Æ; Z q Ñ ; ψ i (](/docs-images/74/71399544/images/2-1.jpg "r) ψ i ( r) «³ËÑ ¹ ; n i ³ Â Ñ ß ; ρ( r) ³ Ñ ÊÚ; r, r  R q Ñ Ì Ñ Ò ; ε i i Ñ Å; V xc ÙÅ ³.")
2 218 ¾ ½ Å 4 ÆÆ ÎƲ Ñ PST É Ã«. ƺ «Þ, ß Ñ Ì Ø, ² À µ BaTiO 3 [], PbTiO 3 [6] SrTiO 3 [7] ABO 3 ºµ Ñ Ñ Đ ÑƲ. Ì ËÎ Ñ Æ ² Ì ÂÛ, ß Ò, Ì Æ Î¾. ÑÆÖ [8] ¹ [9] Î ² KTa.44 Nb.6 O 3, PbFe. Nb. O 3 B Ò Ñ Đ. ÔÎÕ ÚÊÚ ÃÉ ¾ µøì Ì (virtual crytal aroximate, VCA) Pb. - Sr. TiO 3 (Ð PST) ² Ì Đ, ÃÅ A Ò Ò Ê Ñ Đ Ñ ² Â. 1 Í Ô 1.1 Ï (Pb,Sr)TiO 3 Đ ²Î Kang [1], Jain [11] Kim [12] X «ß Đ, [ 2 2 Z q q r R q + ρ( r) r r d r + ] V xc ( r) ψ i ( r) = ε i ψ i ( r) (2) ρ( r) = i n i ψ i ( r)ψ i ( r) (3) ², 2 Lalace Æ; Z q Ñ ; ψ i ( r) ψ i ( r) «³ËÑ ¹ ; n i ³ Â Ñ ß ; ρ( r) ³ Ñ ÊÚ; r, r  R q Ñ Ì Ñ Ò ; ε i i Ñ Å; V xc ÙÅ ³. ² (2) ² 1 É Ì Ñ ; 2 É ßÑ Coulomb, ß Ì ² ²Îº µ (norm conerving eudo otential) Ä; 3 ß ABO 3 ºµĐ, Sr(Pb) ß A Ò 8 Ô, O ß TiO 6 ÌÌ 6 Ì Ò, Ti ß. ß Ì, Î Material Viualizer [13] É Æ Ç ßÒ ºÕ, Đ 1 ³. ß PST ¾, ¹ [9] ÑÆÖ [8], Ö SrTiO 3 (Ð ST) PbTiO 3 [1] Ó Õ¾ (Pb,Sr)TiO 3, Đ 2 ³. PST 1 Pb. Sr. TiO 3 µ«ë Fig.1 Virtual crytal aroximate model of Pb. Sr. TiO 3 E tot(pbx Sr 1 x TiO 3 ) = xe tot(pbtio3 )+ (1 x)e tot(srtio3 ) (1) ², x Ú SrTiO 3 Pb Pb/Sr, E tot(pbx Sr 1 x TiO 3 ), E tot(pbtio3 ) E tot(srtio3 ) «Ë Ì. 1.2 Ã Ø Material Studio 4.1 CASTEP (Cambridge erial total energy ackage) Ô [13]. À É ÊÚ»: Î ØÌ µ, Ö µî µíé, Ñ ØÌ É²Þ, Ñ Ñ À Î ÙÅ ³µ ÊÚ (local denity aroximation, LDA) ǹÈÈÚ (general gradient aroximation, GGA), À Đ Î º¹ Ñ Đ [13,14]. ÚÊÚ Ã, ËÑ Õ Schordinger  ³ ( ËÒ) 2 Pb. Sr. TiO 3 ½«Fig.2 Pb. Sr. TiO 3 uercell
3 2 Û Ð : Pb. Sr. TiO 3 Æ Ð Ý 219 Ñ Coulomb ; 4 ÙÅ ³, ß Ì ² ÊÚ ¹ÈÈÚ ³. ß PST, ¼Û ² Æ µ, A Ò Ä V VCA (x) = xvsr + (1 x)vpb (4) ², V Sr V Pb «Sr Pb µ. Ú, ²Î ݲ ÎÔ, ËÑ ¼ ı Bloch Ö, ²ÎØÌ É²Þ ψ k i ( r) = ex(i k r) g c k i (g)ex(i k r) () ², g Ï g, k Brillouin k, c k i (g) ËÑ ¼ Fourier. µ ²Î Perdew [1] É GGA º Ùų «, Ñ ØÌ É ² Þ. Å Ñ ØÌ É, ԲΠ¾ µºí Ñ À ε, ¼ Ñ ²Â«: Pb d , Sr , Ti 3d 2 4 2, O ÚÏñ, ØÌ ßÝ E c = 38 ev, ÒÉ Ðº Ú ev, À Î º.1 ev/nm, ³ÆÒ º nm, Ë Æ.1 GPa, Brillouin Ϋ² ƽ K ß Brillouin, ³ Fourier Å (fat fourier tranform, FFT) , ÚÏñ. ØÚ SGI 3. 2 Å Ô 2.1 PST Á ÚÇ Ñ Ú Đ Â ĐÉ, PST Ú Pb/Sr Đ, 1 ³. À Â, Î VCA ¾ É, VCA ÅÁ ¾ Æ, Ì Å ÛØÚÜ, ß² Ì Ø. ST Ì Pb Ú x Å Ý, a ÄÅÑ, c/a Pb Ú x ÝÆÐÝÆ. Î Ú x=. c/a Å 1.1,, PST ÌÎ ±ÝÆ. Ú Ú x., ÌÎ c/a ÅØÅ Ý Æ, Í Ú, ±, Å, VCA Ã Đ À Đ [1 12,16,17] Õ. 3 à Pb ß Pb x Sr 1 x TiO 3 Ì Â. É Sr 2+ (.112 nm) Pb 2+ (.118 nm), ST Ì Pb Ú x Å Ý, Ì ²Ñ, Ú Ú x=., 1 ÌÎ c/a Å Â. Đ Pb 2+ ÉÍ Sr 2+, ÖÖ PST ² ÌĐ. Ti Ô Ò ß Pb x Sr 1 x TiO 3 ² Ì Ñ² Ì,  Pb. Sr. TiO 3, β (1) Ti [1] Ô Ò ³, 4 ³. Pb Ý, Ì Ä Å Ø, ÚÆÑ.12 nm Å Å, Ò Æ, ÝÆ. Đ, Î Ti c ß O ßÒ, Ti Ö Ô O ÌÌ, TiO 6 ÌÌÍ Ý, Ñ Ô. É, Û Ti Ô Ò Ø Ì, ÀÐ Ì Ñ. E, ev x, % 3 Pb x Sr 1 x TiO 3 x Á Fig.3 Caculated energy (E) change of Pb x Sr 1 x TiO 3 with molar fraction of Pb (x) ¾ 1 ÂÏÁ Pb x Sr 1 x TiO 3 «³ Table 1 The otimized lattice contant of Pb x Sr 1 x TiO 3 Pb x Sr 1 x TiO 3 a, nm c/a Volume, nm 3 VCA Suercell Exerimental [11,12] x= x= x= x= x= x= x=
4 22 ¾ ½ Å 4 Energy change +3872, ev Ti hift, nm 4 Ti [1] Ó Ñ Pb. Sr. TiO 3 Fig.4 Curve for energy of Pb. Sr. TiO 3 v dilacement of Ti atom along the [1] direction 2.2 Pb. Sr. TiO 3 ÚÇ ³ ξ Pb. Sr. TiO 3 ÈĐ. À Â, PST Ì È Þ È, Æ 2.13 ev, ßË Brillouin ß È G ÈÔ F, ȳÆÒ Brillouin F. Pb. Sr. TiO 3 ÈÉ Â«, ev. «, Pb. Sr. TiO 3 Fermi È O 2  «, Ti 3d ÂÑ ; Ò ev È O 2, Sr 4 Pb d ÂÑ «; ß O 2  «Ú 31. ev È «, ßÀ È À ÎÛ, ÔÖ µåã. ß È «, ß º Ti 3d  «Pb O  «, È «Å 3d  Æ. ÞÈ Å 2.43 ev, ßË Brillouin ß F F, ŵ²Î GGA, Ì ÞÈ Å (E g =2.43 ev) Æ«Ô, LDA GGA ØÃÚ E g ÅÔ Ù ² Ê [18], Ì Ì ß Pb. Sr. TiO 3 Ñ Đ Ã«ß. 6 Pb. Sr. TiO 3 Ì ÌÂÊ Ú (DOS) Ú. À Â, Ú Fermi, «Ti 3d O 2 Æ, Ì Ti 3d O 2 ¼ Â. Đ ³² Ì Pb. Sr. TiO 3 È Å Ti O Ó Ö.  Ti Ú Pb. Sr. TiO 3 Ñ º Î, Î Ti c ß O ßÒ, Ti ÖÔ O ÌÌ, Ñ Ô, É c Ö¹ Ñ µ = q i r i (ß, q i i Ñ, r i i Ô Ò ), Pb. Sr. TiO 3 Ö c Å Â c = µ/v (ß, c ÂÅ, V ÌÎ), ŠѲ Æ G F Q Z Pb. Sr. TiO 3 Ê Ç Fig. Calculated band tructure of Pb. Sr. TiO 3 by cell DOS, ev model ( i the Fermi level, G, F, Q, Z are high ymmetry Brillouin oint) (a) Energy,eV (b) Pb. Sr. TiO 3 ËÁÉÙ Fig.6 Calculated total DOS (a) and artial DOS (b) of Pb. Sr. TiO 3 7 Sr, Pb, O Ti ¼ «ÂÊÚ. È ev O 2 Ti 3d  «, Å ÂÆ, Â Ø Û Ë,  Ñ, Ti O  ËÚ Ñ ÎÀ ÅÙ ÃÚ PbTiO 3 [] BaTiO 3 [19]. Ú È d G
5 2 Û Ð : Pb. Sr. TiO 3 Æ Ð Ý (a) 8 (b) d (c) (d) d Pb. Sr. TiO 3 Ê Sr, Pb, O Ti» ÁÉÙ Fig.7 Calculated artial DOS of Sr (a), Pb (b), O (c) and Ti (d) in the cell of Pb. Sr. TiO 3 1 ev, Å O 2  Pb 6 Sr 4  ٠ÓÅ, «Ñ À O Pb Sr, Þ Ý ÀÆ Â, Î Ñ. É Ñ, ¼ Coulomb Û Coulomb Ø Đ []. ß È «, Ú È, Ti 3d O 2 «, Ú È Üà «Sr Pb 4 6  «. Ú È O 2  Ti 3d  ¼ Â, O Pb O Sr Ö¼ Â. 2.3 Pb. Sr. TiO 3 È À Õ Ê ÓƲ Ñ, ß Pb. Sr. TiO 3 ¾ «Ñ ÊÚ Ñ. 8 Pb. Sr. TiO 3 1 Ì «Ñ ÊÚ, 2 Pb x Sr 1 x TiO 3 «ß. Ú¾, Sr, Pb Ti Ñ «1.81, ; [1], O Ú TiO ØÌ Ñ.98, Ú PbO ØÌ Ñ.76, Ú SrO ØÌ Ñ.8., À Â, O z Ti Ó¼ z Û.9 nm, Ti 4+ [1] Ö Ô Ò. Pb 2+ 8 Pb. Sr. TiO 3 Ù 1 Ë ÅÐ ÉÙ Fig.8 Plot of electron denity difference (unit: ev) on the 1 lane of Pb. Sr. TiO 3 (.118 nm) Sr 2+ (.112 nm) Æ, Î Pb ÍÉ Sr, TiO 6 ÌÌÍ Ti Ô Ò ; Ì, Pb Ñ Sr Æ, Pb 2+ TiO 6 ÌÌÉ À Ê Æ, TiO 6 ÌÌÉ Pb Ê, ÌÒ ÌÌÉ Ti 4+ ÎÐÔ Pb., Ú Pb. Sr. TiO 3 ² Ì, z Ti O Ñ Ô Ó Ý, Ó¼ Û, ÚÝÆ, Ð x, y z Ti O
6 222 ¾ ½ Å 4 Bond ¾ 2 Pb. Sr. TiO 3 Ð Ò» Table 2 Calculated Mulliken oulation and bond length of Pb. Sr. TiO 3 SrTiO 3 Pb. Sr. TiO 3 PbTiO 3 Bond length, nm Poulation Bond length, nm Poulation Bond length, nm Poulation O x Ti O y Ti O z Ti O x O y O x O z O y O z O x Sr O y Sr O z Sr O x Pb O y Pb O z Pb Note: O x, O y and O z denote O atom along x, y and z axe Ñ Ó Ñ, ² Ñ ; O Sr Pb O Ñ Ô Ó, Ó, Ú Ñ. Pb. Sr. TiO 3 Ú 1 Ì «Ñ ÊÚ ( 8) ³, Sr O Ñ ÔÊÚ ÓÛ, Ð Ti O Û Ñ ÔÊÚ Ó, Đ Ì Đ «ß ÂÊÚĐ, Ú Pb. Sr. TiO 3 Ì Sr O ÓÐ Ti O Ó Ó «Û., ³Ñ Ô z ÂÆ, ß PST Ѳ º ÄÈ. 3 Å ²Î ² ØÌ µ, Î Ì ¾ PST ² ÌÑ Đ. Đ ³, É, Ð VCA Ð. κ» ² Ì Pb ÝÆ, ÌÎÒĐ, c/a ÅÝÆ, Î x., ² ÌÅ Æ, Đ Æ. ß PST ÌÑ Ô Ó Ñ ÂÊÚ ÈĐ, ܳ PST Ti Ô TiO 6 ÌÌ Ð¹  É, PST ² Ì Ñ² É, PST ² Ì O 2 ¼ Ti 3d ¼  Î. Ë [1] Kang D H, Kim J H, Park J H, Yoon K H. Mater Re Bull, 21; 36: 26 [2] Chung H J, Woo S I. J Vac Sci Technol, 21; 19B: 27 [3] Kim G H, Kim K T, Kim D P, Kim C I. Thin Solid Film, 24; : 688 [4] Hamata Y. J Electron Ceram Jn, 1988; 19: 3 [] Cohen R E. Nature, 1992; 38: 136 [6] Bungaro C, Rabe K M. Phy Rev, 2; 71B: 342 [7] Iniguez J, Vanderbilt D, Bellaiche L, Vanderbilt D, Bellaiche L. Phy Rev, 23; 67B: [8] Peng Y P, Wang Y X, Zhang L, Zhang P L, Zhong W L. Acta Phy Sin, 2; 49: 114 (ÐÅÕ, º, ¼,,. Ú «, 2; 49: 114) [9] Wang Y X, Zhong W L, Wang C L, Zhang P L. Acta Phy Sin, 22; 1: 171 (,,»,. Ú «, 22; 1: 171) [1] Kang H D, Kim J H, Park J H, Yoon K H. Mater Re Bull, 21; 36: 26 [11] Jain A, Majumder S B, Guo R, Bhalla A S, Katiyar R S. Mater Lett, 22; 6: 692 [12] Kim K T, Kim C I. Thin Solid Film, 22; : 44 [13] Segall M D, Lindan P J D, Probert M J. J Phy Conden Matter, 22; 14: 2717 [14] Marlo M. Phy Rev, 2; 62B: 2899 [1] Perdew J P, Chevary J A, Voko S H, Jackon K A, Pederon M R, Singh D J. Phy Rev, 1992; 46B: [16] Somiya Y, Bhalla A S, Eric L. Cro Int J Inorg Mater, 21; 3: 79 [17] Xing X, Chen J, Deng J X, Liu G. J Alloy Comd, 23; 36: 286 [18] Burtein E. Phy Rev, 194; 93: 632 [19] Cohen R E, Krakauer H. Phy Rev, 199; 42B: 6416
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