Volume 25 Number 9 The Chinese Journal of Nonferrous Metals Sep. 2015

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1 Volue 25 Nuber 9 The Chinese Journal of Nonferrous Metals Sep (2015) SrBi 4 Ti 4 O 15 (( ) ) SrBi 4 Ti 4 O 15 (SBTi)(EET) SrBi 4 Ti 4 O 15 (SBTi) SBTi (Aaa) (I4/) SBTi a μc/c 2 O641.1 A Ferroelectric phase transition and ferroelectricity of SrBi 4 Ti 4 O 15 XIAO Xiao-hong, LI Shi-chun (College of Mechanic and Electronic Engineering, China University of Petroleu (East China), Qingdao , China) Abstract: The cheical bonds structures were analyzed by the atoic environent calculation ethod, and the valence electron structure of orthorhobic phase SrBi 4 Ti 4 O 15 was calculated according to the EET theory, the nubers of the effective valence electrons of each ato in SrBi 4 Ti 4 O 15 were obtained. Furtherore, according to the theory of crystal space group, the structures of orthogonal paraelectric phase (Aaa) and the tetragonal paraelectric phase (I4/) in the ferroelectric paraelectric phase transition were constructed, and the atoic displaceents in the phase transition were calculated by the atoic coordinate analysis. The spontaneous polarization in SrBi 4 Ti 4 O 15 was studied based on the atoic displaceents and atoic effective valence electrons nubers. The calculated spontaneous polarization strength in ferroelectric SrBi 4 Ti 4 O 15 along the a axis is μc/c 2, which is in good agreeent with the experiental and other theoretical results. Key words: valence electron structure; epirical electron theory; ferroelectric phase transition; atoic displaceent; spontaneous polarization (BLSF) AURIVILLIUS [1] 1949 Aurivillius (A n 1 B n O 3n+1 ) 2 (Bi 2 O 2 ) 2+ c (Bi 2 O 2 ) 2+ (A n 1 B n O 3n+1 ) 2 [2] [3] [4 5] SrBi 4 Ti 4 O 15 (SBTi) 2 (Bi 2 O 2 ) 2+ 4 ( ) ( )(YCX ) E-ail lishchlishch@163.co

2 B Ti O TiO 6 A Sr/Bi SBTi SBTi SBTi REANEY [6] SBTi HERVOCHES [7] SBTi A2 1 a Aaa I4/ A2 1 a Aaa a KING-SMITH [8] Berry RESTA [9] KNbO 3 Berry [10 11] [12 13] BROWN [14] Pauling s d d 0 s=exp[(d 0 d)/0.37] Brown Pauling [15] (EET) (BLD) [15 16] [17 19] EET [20 23] SBTi SBTi EET SBTi SBTi SBTi 1 [7] SBTi A2 1 a(no.36) a= n b= n c= n Z=4 A Bi Sr (SOF) x 1 y 1 z SrBi 4 Ti 4 O 15 [7] Table 1 [7] Crystal structure paraeters of SrBi 4 Ti 4 O 15 Ato Site x 1 y 1 z 1 SOF Bi1 4a Sr1 4a Bi2 8b Sr2 8b Bi3 8b Ti1 8b Ti2 8b O1 4a O2 8b O3 8b O4 8b O5 8b O6 8b O7 8b O8 8b [24] (AEC) I (1) [15] I = ISIMIK (1) I S I M I K 1

3 25 9 SrBi 4 Ti 4 O AEC SBTi I S I M d I 2 2 SBTi 2.1 (BLD) [15 16] EET EET D u v n = R ( 1) + R (1) β lg n u u v Dn v (2) R u (1) R v (1) u v n β N A B C DN D u v s t n D R R R R A n = u ( 1) + v (1) s (1) t (1) + β lg n A (3) u v s t n A n r = = j n cj n cj I r n A j n (4) (3) (4) N n N D n ) ( BLD n 2.2 BLD SBTi [16] Sr 7 Bi 4 Ti 18 O 4 σ h C h t C t n c n l R(1) EET EET n Brown [14] n SrBi 4 Ti 4 O 15 Table 2 Hybridization state paraeters of atos in SrBi 4 Ti 4 O 15 Ato σ C t n l n c R(1)/n Bi Sr Ti O EET q (5) q 1 = 2 I n (5) 1 SBTi SBTi SBTi (A2 1 a) (Aaa) (I4/) ABRAHAMS [25 26] van AKEN [27] YMnO 3 SBTi ( 1) 1(a) SBTi () (ab ) ( 1(b)) SBTi Bi/Sr x 1 y 1 z 1 x 1 =x

4 SrBi 4 Ti 4 O 15 Table 3 Valence electron structure of SrBi 4 Ti 4 O 15 Bond A B d/n I S I M Bond I n d/n A B A B A B A B A B I S I M I n Ti2-O O6-O Ti1-O O4-O Ti1-O O3-O Ti2-O O8-O Ti2-O O7-O Ti1-O O2-O Ti1-O O3-O Ti2-O O2-O Ti1-O O2-O Ti2-O O2-O Ti1-O O3-O Bi3-O Bi/Sr2-O / Bi3-O O4-O Bi3-O O5-O Ti2-O O7-O Bi3-O O8-O Bi/Sr2-O / O3-O Bi/Sr1-O / O5-O Bi/Sr2-O / O7-O Bi/Sr2-O / O2-O Bi/Sr2-O / O2-O Bi/Sr1-O / O8-O Bi/Sr2-O / O5-O Bi3-O O5-O Bi/Sr1-O / O5-O O2-O Bi/Sr2-O / O8-O Bi/Sr1-O / Bi3-O O5-O O8-O Bi/Sr2-O / O6-O Bi/Sr1-O / O7-O Bi/Sr2-O / β=0.71 ΔD(n ) = n 4 SrBi 4 Ti 4 O 15 Table 4 Effective valence electrons nuber of SrBi 4 Ti 4 O 15 Bi1 Sr1 Bi2 Sr2 Bi3 Ti1 Ti2 O1 O2 O3 O4 O5 O6 O7 O y 1 =y z 1 =z 1 2 A Bi/Sr (c=0) ( 1 nn oo pp O2 O4 O6 O7 O8 ) x 1 =x 1

5 25 9 SrBi 4 Ti 4 O y 1 =y 1 z 1 =z 1 a b Bi/Sr 3 SBTi a b a b (Aaa) x 2 y 2 z 2 Wyckoff 5 5 Aa(No.63) Wyckoff 4a (0,0,0) (0 0 1/2) 8f (0 y z) (0 y z+1/2) (0 y z+1/2) (0 y z) Z=4 Δx 1 2 =x 1 x 2 Δy 1 2 =y 1 y 2 Δz 1 2 =z 1 z 2 5 (A2 1 a) (Aa) b c a 3 5 Table 5 Atoic coordinates of reselection cell and orthogonal paraelectric phase Ato A2 1 a Aa Site x 1 ' y 1 ' z 1 ' Site x 2 y 2 z 2 Δx 1 2 Δy 1 2 Δz 1 2 Bi1 4a a Sr1 4a a Bi2 8b f Sr2 8b f Bi3 8b f Ti1 8b f Ti2 8b f O1 4a a O2 8b f O3 8b f O4 8b f O5 8b f O6 8b f O7 8b f O8 8b f Fig. 1 Structure of original orthogonal cell and reselection cell: (a) Structure relationship between original orthogonal cell and reselection cell; (b) Top view of cell structure

6 a = n b = n c c= n SBTi(I4/ No.139) x 3 y 3 z 3 (Aa) (I4/) ( 6) 6 (I4/ No.139) Wyckoff 2a (0 0 0) 2b(0 0 1/2) 4e(0 0 z) (0 0 z) 4d(0 1/2 1/4) (1/2 0 1/4) 8g(0 1/2 z) (1/2 0 z) (0 1/2 z) (1/2 0 z) Z=2 Δx 2 3 =x 2 x 3 Δy 2 3 =y 2 y 3 Δz 2 3 =z 2 z 3 (I4/)SBTi O2 (Aa) O2 O7 z O2 O7 O4 O4 O8 z O4 O8 [7] 1% 2 Fig. 2 Botto surface scheatic diagra of shifted reselection cell Δu a Δu b Δu [25] c 7 Δ u a = Δx a (6) Δ = Δy b (7) u b 3 Fig. 3 Relationship of lattice constant between original orthogonal cell and reselection cell 6 SrBi 4 Ti 4 O 15 Table 6 Atoic coordinates of tetragonal paraelectric phase SrBi 4 Ti 4 O 15 Ato Aa I4/ Site x 2 y 2 z 2 Site x 3 y 3 z 3 Δx 2 3 Δy 2 3 Δz 2 3 Bi1 4a a Sr1 4a a Bi2 8f e Sr2 8f e Bi3 8f e Ti1 8f e Ti2 8f e O1 4a b O2 8f g O3 8f e O4 8f g O5 8f e O6 8f d O7 8f O8 8f

7 25 9 SrBi 4 Ti 4 O Δ = Δz c (8) u c 7 SBTi (A2 1 a) (Aa) (I4/) ab c c 4 ab Δui i a i Δu i ( 7) 4 ab Fig. 4 Atoic displaceent vector scheatic diagra in ab plane a(b)sbti (P r ) 29 μc/c 2 HERVOCHES [7] SBTi (P s ) 23.2 μc/c 2 SBTi (A2 1 a) a b a [10 11, 22] EET (P s ) 2e Ps = V Δ u i q Δu i (9) i q V 4 7 (9) SBTi a μc/c 2 [7] 23.2 μc/c Table 7 Atoic displaceents during phase transitions Ato Δu a /Å Δu b /Å Δu c /Å Δu i /Å Bi Sr Bi Sr Bi Ti Ti O O O O O O O O SBTi IRIE [28] 1) EET SBTi Sr Bi Ti O SBTi Bi TiO 6 Ti TiO 6 2) SBTi SBTi (Aa) (I4/) 3) SBTi a a (A2 1 a)(aa) a 4) SBTi a μc/c 2

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