弛滯體因存在奈米極化區域而導致局部電極化的現象，其性質有別於一般鐵電材料，但形成機制和成因至今依然未有定論。目前較被採信的理論為弛滯體有一隨機場會影響鐵電材料的淨電極化量而導致極化電域破碎而形成奈米極化區域。而隨機場易生成於電荷分佈不平衡或空間分佈不平衡的結構中[1]，而鍶鋇鈮系列材料卻能藉由相同電荷的鍶離子和鋇離子之比例控制而展現出弛滯體的特性，至今仍然沒有確切的模型可以解釋。
本研究先使用第一原理做計算，依照不同鍶含量做結構優化，並跟實驗上的數據做比對，發現八面體中鈮氧鍵長會因為鍶含量的差異和鄰近格隙陽離子而有所改變，進而影響整體結構的自發極化量。本研究也計算格隙間不同陽離子到氧離子之間的距離也都有差異，本研究認為這些差異便是影響材料性質的主要原因。接著在利用分子動力學拓展模型的原子尺度，並觀察不同鍶含量下的SBN之極化電域，並觀察格隙間陽離子之排列方式是否會影響極化電域。

Strontium barium niobate-based series material SrxBa1-xNb2O6 (SBN) has excellent ferroelectric properties, as well as pyroelectric and piezoelectric properties. SBN can transform from ferroelectric material to relaxor by tuning Sr/(Sr+Ba) ratio. When Sr/(Sr+Ba) ratio is 0.25 (x > 0.25), it shows normal ferroelectric behavior. As the Sr/(Sr+Ba) ratio increases from 0.6, it begins to show relaxor behavior until Sr/(Sr+Ba) ratio reaches 0.75. For Sr/(Sr+Ba) ratio above 0.8, it lost spontaneous polarization and shows no ferroelectric properties. In this study first-principles calculation was used to reveal the Sr/(Sr+Ba) ratio dependent ferroelectric properties of SBN. The structure of SBN with x = 0.4, 0.6, 0.8 were determined by special quasirandom structure (SQS) method first and then optimized by the Vienna Ab initio simulation package (VASP). The results show that Sr/(Sr+Ba) ratio will influences the deviation of Niobium ions in octahedral sites and the distance between cation and anion. Those displacements of ions are then proved to have large influence on the magnitude of spontaneous polarization; thus it is considered to be the mechanism that responsible for the Sr/(Sr+Ba) ratio dependent ferroelectric properties of SBN. Besides we also developed born model for SBN to simulate polar nanoregion by molecular dynamic simulation. It is found that pattern of polar nanoregions is closely related to Sr/(Sr+Ba) ratio in SBN.

1. C. Laulhé et al., Random local strain effects in homovalent-substituted relaxor ferroelectrics: a first-principles study of BaTi 0.74 Zr 0.26 O 3. Physical Review B, 2010. 82(13): p. 132102.
2. http://scitechvista.most.gov.tw/zh-tw/articles/c/0/9/10/1/418.htm.
3. http://www.itrc.narl.org.tw/Publication/Newsletter/no68/p10.php.
4. S. Lee et al., Ferroelectric-thermoelectricity and Mott transition of ferroelectric oxides with high electronic conductivity. Journal of the European Ceramic Society, 2012. 32(16): p. 3971-3988.
5. L. Bursill and P.J. Lin, Chaotic states observed in strontium barium niobate. Philosophical Magazine B, 1986. 54(2): p. 157-170.
6. W. Kleemann, The relaxor enigma—charge disorder and random fields in ferroelectrics, in Frontiers of Ferroelectricity. 2006, Springer. p. 129-136.
7. A. Bokov, and Z.-G. Ye, Recent progress in relaxor ferroelectrics with perovskite structure, in Frontiers of Ferroelectricity. 2006, Springer. p. 31-52.
8. L.E. Cross, Relaxor ferroelectrics. Ferroelectrics, 1987. 76(1): p. 241-267.
9. G. Burns, and F. Dacol, Glassy polarization behavior in ferroelectric compounds Pb (Mg13Nb23) O3 and Pb (Zn13Nb23) O3. Solid state communications, 1983. 48(10): p. 853-856.
10. B. Meyer, and D. Vanderbilt, Ab initio study of ferroelectric domain walls in PbTiO 3. Physical Review B, 2002. 65(10): p. 104111.
11. V. Westphal, W. Kleemann, and M. Glinchuk, Diffuse phase transitions and random-field-induced domain states of the ‘‘relaxor’’ferroelectric PbMg 1/3 Nb 2/3 O 3. Physical review letters, 1992. 68(6): p. 847.
12. B.D. Viehland, Z. Xu, and W.-H. Huang, Structure-property relationships in strontium barium niobate I. Needle-like nanopolar domains and the metastably-locked incommensurate structure. Philosophical Magazine A, 1995. 71(2): p. 205-217.
13. X.-G. Tang, and H.L.-W. Chan, Effect of grain size on the electrical properties of (Ba, Ca)(Zr, Ti) O3 relaxor ferroelectric ceramics. Journal of applied physics, 2005. 97(3): p. 034109.
14. S. Lushnikov, et al., Anomalous dispersion of the elastic constants at the phase transformation of the Pb Mg 1∕ 3 Nb 2∕ 3 O 3 relaxor ferroelectric. Physical Review B, 2008. 77(10): p. 104122.
15. U. Voelker, et al., Domain size effects in a uniaxial ferroelectric relaxor system: The case of SrxBa1− xNb2O6. Journal of Applied Physics, 2007. 102(11): p. 114112.
16. D. Sholl, and J.A. Steckel, Density functional theory: a practical introduction. 2011: John Wiley & Sons.
17. V. Antonov, I.G., N. Trendafilova, D. Kovacheva, K. Krezhov, First principles study of structure and properties of La- and Mn-modified BiFeO3. Solid State Sciences 2012. 14: p. 782-788.
18. R.G. Parr, Density functional theory, in Electron Distributions and the Chemical Bond. 1982, Springer. p. 95-100.
19. W. Myers, and W. Swiatecki, Nuclear properties according to the Thomas-Fermi model. Nuclear Physics A, 1996. 601(2): p. 141-167.
20. E.S. Kryachko, Hohenberg‐Kohn theorem. International Journal of Quantum Chemistry, 1980. 18(4): p. 1029-1035.
21. Sholl, D.a.J.A.S., Density Functional Theory: A Practical Introduction. 2011: John Wiley & Sons.
22. W. Kohn, and L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 1965. 140(4A): p. A1133-A1138.
23. W. Kohn, and L.J. Sham, Self-consistent equations including exchange and correlation effects. Physical review, 1965. 140(4A): p. A1133.
24. J. Irving, and J.G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. The Journal of chemical physics, 1950. 18(6): p. 817-829.
25. Q. Spreiter, and M. Walter, Classical molecular dynamics simulation with the velocity Verlet algorithm at strong external magnetic fields. Journal of Computational Physics, 1999. 152(1): p. 102-119.
26. L. Verlet, Computer" experiments" on classical fluids. ii. equilibrium correlation functions. Physical Review, 1968. 165(1): p. 201.
27. K. Hass, L. Davis, and A. Zunger, Electronic structure of random Al 0.5 Ga 0.5 As alloys: Test of the ‘‘special-quasirandom-structures’’description. Physical Review B, 1990. 42(6): p. 3757.
28. Y. Kong, and B. Liu, First-Principles Calculation of the Structural, Magnetic, and Electronic Properties of the Co x Cu1-x Solid Solutions Using Special Quasirandom Structures. Journal of the Physical Society of Japan, 2007. 76(2): p. 024605.
29. P. Willmott, et al., Experimental and theoretical study of the strong dependence of the microstructural properties of Sr x Ba 1− x Nb 2 O 6 thin films as a function of their composition. Physical Review B, 2005. 71(14): p. 144114.
30. S. Woodley, et al., The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation. Physical Chemistry Chemical Physics, 1999. 1(10): p. 2535-2542.
31. H. Graetsch, Changes of the crystal structure at the relaxor ferroelectric phase transition of strontium barium niobate (SBN53). Crystal Research and Technology, 2014. 49(1): p. 63-69.
32. M. Trubelja, E. Ryba, and D. Smith, A study of positional disorder in strontium barium niobate. Journal of materials science, 1996. 31(6): p. 1435-1443.
33. W. Kleemann, J. Dec, and S. Miga, The cluster glass route of relaxor ferroelectrics. Phase Transitions, 2015. 88(3): p. 234-244.