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

25 9 2015 9 Volue 25 Nuber 9 The Chinese Journal of Nonferrous Metals Sep. 2015 1004-0609(2015)-09-2501-09 SrBi 4 Ti 4 O 15 (( ) 266580) SrBi 4 Ti 4 O 15 (SBTi)(EET) SrBi 4 Ti 4 O 15 (SBTi) SBTi (Aaa) (I4/) SBTi a 25.81 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 266580, 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 25.81 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 (50371059) ( )(YCX2014052) 2015-01-292015-04-01 0532-86983503-8320 E-ail lishchlishch@163.co

2502 2015 9 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=0.54507 n b=0.54376 n c= 4.09841 n Z=4 A Bi Sr (SOF) 0.667 0.333 x 1 y 1 z 1 1 1 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 0.250 0.258 0.000 0.667 Sr1 4a 0.250 0.258 0.000 0.333 Bi2 8b 0.255 0.248 0.10409 0.667 Sr2 8b 0.255 0.248 0.10409 0.333 Bi3 8b 0.245 0.263 0.21881 1 Ti1 8b 0.277 0.250 0.45032 1 Ti2 8b 0.268 0.242 0.34697 1 O1 4a 0.306 0.203 0.500 1 O2 8b 0.080 0.462 0.0515 1 O3 8b 0.301 0.298 0.40348 1 O4 8b 0.023 0.505 0.14058 1 O5 8b 0.286 0.212 0.30456 1 O6 8b 0.010 0.502 0.2502 1 O7 8b 0.017 0.481 0.457 1 O8 8b 0.047 0.516 0.352 1 [24] (AEC) I (1) [15] I = ISIMIK (1) I S I M I K 1

25 9 SrBi 4 Ti 4 O 15 2503 2 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 0.005 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 2 3 2 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 1 0 0 5 0.1399 Sr 7 0 0 2 0.1202 Ti 18 1 0 4 0.1053 O 4 1 0 2 0.07895 EET q (5) q 1 = 2 I n (5) 1 SBTi 4 3 3.1 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 1 0.25

2504 2015 9 3 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-O5 0.1748 1 1 2 2 4 1.4403 O6-O6 0.2725 2 2 2 2 4 0.0258 Ti1-O2 0.1900 1 1 2 2 4 0.8795 O4-O4 0.2726 2 2 2 2 4 0.0257 Ti1-O7 0.1912 1 1 2 2 4 0.8470 O3-O4 0.2729 1 1 2 2 4 0.0255 Ti2-O4 0.1924 1 1 2 2 4 0.8136 O8-O8 0.2731 2 2 2 2 4 0.0253 Ti2-O8 0.1927 1 1 2 2 4 0.8055 O7-O7 0.2733 2 2 2 2 4 0.0251 Ti1-O3 0.1940 1 1 2 2 4 0.7727 O2-O1 0.2737 1 2 2 1 4 0.0248 Ti1-O7 0.1980 1 1 2 2 4 0.6794 O3-O7 0.2754 1 1 2 2 4 0.0235 Ti2-O4 0.1999 1 1 2 2 4 0.6394 O2-O2 0.2757 2 2 2 2 4 0.0233 Ti1-O2 0.2015 1 1 2 2 4 0.6053 O2-O1 0.2773 1 2 2 1 4 0.0221 Ti2-O8 0.2022 1 1 2 2 4 0.5927 O2-O3 0.2777 1 1 2 2 4 0.0218 Ti1-O1 0.2059 1 2 2 1 4 0.5255 O3-O8 0.2786 1 1 2 2 4 0.0212 Bi3-O6 0.2233 1 1 2 2 4 0.9183 Bi/Sr2-O8 0.2796 1 1 2 2 4 0.1480/0.0781 Bi3-O6 0.2296 1 1 2 2 4 0.7495 O4-O8 0.2798 1 1 2 2 4 0.0204 Bi3-O6 0.2319 1 1 2 2 4 0.6957 O5-O6 0.2809 1 1 2 2 4 0.0197 Ti2-O3 0.2343 1 1 2 2 4 0.2095 O7-O1 0.2814 1 2 2 1 4 0.0194 Bi3-O6 0.2404 1 1 2 2 4 0.5281 O8-O5 0.2829 1 1 2 2 4 0.0184 Bi/Sr2-O4 0.2406 1 1 2 2 4 0.5235/0.2763 O3-O4 0.2846 1 1 2 2 4 0.0174 Bi/Sr1-O1 0.2434 2 2 1 1 4 0.4780/0.2523 O5-O4 0.2847 1 1 2 2 4 0.0174 Bi/Sr2-O8 0.2470 1 1 2 2 4 0.4260/0.2249 O7-O3 0.2853 1 1 2 2 4 0.0170 Bi/Sr2-O4 0.2485 1 1 2 2 4 0.4053/0.2139 O2-O3 0.2862 1 2 2 4 0.0165 Bi/Sr2-O3 0.2493 2 2 2 2 8 0.3949/0.2085 O2-O7 0.2863 1 1 2 2 4 0.0165 Bi/Sr1-O2 0.2558 2 1 1 2 4 0.3198/0.1688 O8-O5 0.2867 1 1 2 2 4 0.0163 Bi/Sr2-O2 0.2629 1 1 2 2 4 0.2542/0.1342 O5-O4 0.2892 1 1 2 2 4 0.0150 Bi3-O5 0.2633 1 1 2 2 4 0.2512 O5-O6 0.2935 1 1 2 2 4 0.0131 Bi/Sr1-O7 0.2645 4 2 1 2 8 0.2416/0.1275 O5-O6 0.2980 1 1 2 2 4 0.0113 O2-O7 0.2659 1 1 2 2 4 0.0319 Bi/Sr2-O3 0.3010 2 2 2 2 8 0.0738/0.0390 O8-O4 0.2679 1 1 2 2 4 0.0299 Bi/Sr1-O1 0.3036 2 2 1 1 4 0.0680/0.0359 Bi3-O5 0.2683 1 1 2 2 4 0.2135 O5-O6 0.3118 1 1 2 2 4 0.0072 O8-O3 0.2694 1 1 2 2 4 0.0285 Bi/Sr2-O7 0.3146 2 2 2 2 8 0.0475/0.0251 O6-O6 0.2719 2 2 2 2 4 0.0263 Bi/Sr1-O2 0.3164 2 1 1 2 4 0.0449/0.0237 O7-O1 0.2725 1 2 2 1 4 0.0258 Bi/Sr2-O2 0.3205 1 1 2 2 4 0.0392/0.0207 β=0.71 ΔD(n ) =0.0018 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 O8 2.788 1.471 5.657 2.987 6.713 8.619 9.002 2.156 4.439 3.887 4.825 4.047 6.094 4.396 4.135 y 1 =y 1 0.258 z 1 =z 1 2 A Bi/Sr (c=0) ( 1 nn oo pp O2 O4 O6 O7 O8 ) x 1 =x 1

25 9 SrBi 4 Ti 4 O 15 2505 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 0.000 0.000 0.000 4a 0.000 0.000 0.000 0.000 0.000 0.000 Sr1 4a 0.000 0.000 0.000 4a 0.000 0.000 0.000 0.000 0.000 0.000 Bi2 8b 0.005 0.010 0.10409 8f 0.000-0.010 0.10409 0.005 0.000 0.000 Sr2 8b 0.005 0.010 0.10409 8f 0.000 0.010 0.10409 0.005 0.000 0.000 Bi3 8b 0.005 0.005 0.21881 8f 0.000 0.005 0.21881 0.005 0.000 0.000 Ti1 8b 0.027 0.008 0.45032 8f 0.000 0.008 0.45032 0.027 0.000 0.000 Ti2 8b 0.018 0.016 0.34697 8f 0.000 0.016 0.34697 0.018 0.000 0.000 O1 4a 0.056 0.055 0.500 4a 0.000 0.000 0.500 0.056 0.055 0.000 O2 8b 0.080 0.462 0.0515 8f 0.000 0.462 0.0515 0.080 0.000 0.000 O3 8b 0.051 0.040 0.40348 8f 0.000 0.040 0.40348 0.051 0.000 0.000 O4 8b 0.023 0.505 0.14058 8f 0.000 0.505 0.14058 0.023 0.000 0.000 O5 8b 0.036 0.046 0.30456 8f 0.000 0.046 0.30456 0.036 0.000 0.000 O6 8b 0.010 0.502 0.2502 8f 0.000 0.502 0.2502 0.010 0.000 0.000 O7 8b 0.017 0.481 0.457 8f 0.000 0.481 0.457 0.017 0.000 0.000 O8 8b 0.047 0.516 0.352 8f 0.000 0.516 0.352 0.047 0.000 0.000 1 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

2506 2015 9 a =0.38542 n b =0.3845 n c c=4.09841 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 3.2 5 6 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 0.000 0.000 0.000 2a 0.000 0.000 0.000 0.000 0.000 0.000 Sr1 4a 0.000 0.000 0.000 2a 0.000 0.000 0.000 0.000 0.000 0.000 Bi2 8f 0.000 0.010 0.10409 4e 0.000 0.000 0.10409 0.000 0.010 0.000 Sr2 8f 0.000 0.010 0.10409 4e 0.000 0.000 0.10409 0.000 0.010 0.000 Bi3 8f 0.000 0.005 0.21881 4e 0.000 0.000 0.21881 0.000 0.005 0.000 Ti1 8f 0.000 0.008 0.45032 4e 0.000 0.000 0.45032 0.000 0.008 0.000 Ti2 8f 0.000 0.016 0.34697 4e 0.000 0.000 0.34697 0.000 0.016 0.000 O1 4a 0.000 0.000 0.500 2b 0.000 0.000 0.500 0.000 0.000 0.000 O2 8f 0.000 0.462 0.4485 8g 0.000 0.500 0.45275 0.000 0.038 0.004 O3 8f 0.000 0.040 0.40348 4e 0.000 0.000 0.40348 0.000 0.040 0.000 O4 8f 0.000 0.505 0.3594 8g 0.000 0.500 0.3557 0.000 0.005 0.004 O5 8f 0.000 0.046 0.30456 4e 0.000 0.000 0.30456 0.000 0.046 0.000 O6 8f 0.000 0.502 0.2502 4d 0.000 0.500 0.250 0.000 0.002 0.000 O7 8f 0.000 0.481 0.457 0.000 0.500 0.45275 0.000 0.019 0.004 O8 8f 0.000 0.516 0.352 0.000 0.500 0.3557 0.000 0.016 0.004

25 9 SrBi 4 Ti 4 O 15 2507 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 25.81 μc/c 2 [7] 23.2 μc/c 2 5 7 Table 7 Atoic displaceents during phase transitions Ato Δu a /Å Δu b /Å Δu c /Å Δu i /Å Bi1 0.0 0.0 0.0 0.0 Sr1 0.0 0.0 0.0 0.0 Bi2 0.027 0.038 0.0 0.029 Sr2 0.027 0.038 0.0 0.029 Bi3 0.027 0.019 0.0 0.028 Ti1 0.147 0.031 0.0 0.148 Ti2 0.098 0.062 0.0 0.101 O1 0.305 0.299 0.0 0.295 O2 0.436 0.146 0.164 0.442 O3 0.278 0.154 0.000 0.271 O4 0.125 0.019 0.164 0.124 O5 0.196 0.177 0.0 0.204 O6 0.055 0.008 0.0 0.054 O7 0.093 0.073 0.164 0.096 O8 0.256 0.062 0.164 0.253 4 SBTi IRIE [28] 1) EET SBTi Sr Bi Ti O 7 1 18 4 SBTi Bi TiO 6 Ti TiO 6 2) SBTi SBTi (Aa) (I4/) 3) SBTi a a (A2 1 a)(aa) a 4) SBTi a 25.81 μc/c 2

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