如何增強BiFeO3磁電交互作用一直以來是個熱門議題。本研究將鉛、鈣摻雜於鉍鐵氧中並利用中子散射技術，研究摻雜前後晶體結構及磁有序的關係。文獻[1]指出Bi0.9Pb0.1FeO3 不只擁有長短程有序的R3C結構，還有長程有序的Pm-3m結構。此外，Pb的離子半徑較Bi大，而Ca則相反，以此思之，Fe及Fe之間的距離也應因摻Pb而變長和因摻Ca而變短，進而使Fe-Fe磁交互作用(及反鐵磁性)呈現相反變化，摻Pb者變弱，而摻Ca者變強。故理論上摻Ca之TN應升高、摻Pb者應下降；但吾人中子繞射實驗卻發現兩者之TN皆升高(摻Ca的TN=708K，摻Pb的TN=680K)，因此詳細分析室溫300oC至高溫7500C 之晶體結構，發現R3c和Pm-3m兩相並存，但晶格常數及Fe-Fe鍵長及Fe-O-Fe鍵角之變化不同於原本之預期, 而是因Pb及Ca的氧化價均為二價, 為維持電中性, 導致氧缺陷之發生。故Bi0.9Ca0.1FeO3 的Fe-Fe鍵長較BFO短而Fe-O-Fe鍵角約等於BFO,而Bi0.9Pb0.1FeO3的Fe-Fe鍵長較BFO稍長而Fe-O-Fe鍵角則較BFO者大且趨向180度; 類似現象也發生於Pm-3m相。根據Goodenough-Kanamori-Anderson (GKA) 守則 [2] 不論摻Pb或Ca之磁耦合均變強,，故導致Bi0.9Pb0.1FeO3 (TN=680K)及Bi0.9Ca0.1FeO3 (TN=708K)兩相呈現高於BFO的643K。

關鍵字:鉍鈣鐵氧、鉍鉛鐵氧、六方晶係、立方晶係、尼爾溫度、Goodenough-Kanamori-Anderson

In this study, we used neutron scattering to understand the evolution of crystal and magnetic phases of Pb or Ca doped bismuth iron oxide. This is an interested topic have great potential for future applications, but with only few research reports. Earlier study[1] has pointed out that Bi0.9Pb0.1FeO3 consisted of long-range order R3c and Pm-3m structures. Because the radius of lead ion is larger and of calcium ion is smaller than that of bismuth ion. The bond length between irons should reflect the same tendency: longer bond length for lead doped samples and shorter for calcium doped samples. However, the neutron diffraction results do not support these assumptions. The TN temperatures go up, 708K for the BCaFO sample and 680K for the BPbFO sample, for both samples. By analyzing neutron diffraction data, we find that R3c phase dominates at room temperature while its percentage decreases at high temperature. Bond valence calculation on both Neutron and X-ray diffraction data, XRD data was taken only at 300K, show that Pb and Ca are in divalent state, therefore, we expect oxygen vacancies must appear to provide charge balance. The existence of oxygen vacancies, theFe-Fe bond lengths and Fe-O-Fe angles are found to become shorter and to close to 180o. The Fe-Fe lengths are found BPbFO>BFO>BCaFO, and the Fe-O-Fe bond angles are BPbFO>BFO~BCaFO. Similar relationships can also be observed in Pm-3m phase. According to Goodenough-Kanamori-Anderson (GKA) rule [2] , their magnetic coupling were enhanced coincides with our results, TN were enhanced in both doping.
Key word: Bismuth calcium Iron oxide、Bismuth lead iron oxide、Hexagonal、Cubic、Neel temperature、Goodenough-Kanamori-Anderson

第一章 研究動機與簡介………………...…………………………….....1
1-1鐵電材料特性…………...……………………………….…..4
1-2磁性種類………………...…………………………………...5
1-3 BiFeO3 鉍鐵氧材料特性…………………………………...10
1-4 BiFeO3 鉍鐵氧磁性質……………………………………....11
第二章 基本理論與文獻回顧
2-1 中子基本特性..……………………………………………..12
2-2中子核散射理論..………………………………………..….13
2-3中子磁散射理論..…………………………………………...14
2-4中子核散射實驗技術與裝置…..………………………..….15
2-5 Rietriveld 精算法………………..………………………….17
2-6 Goodenough-Kanamori-Anderson rule………………..…….24
第三章 第三章實驗方法………………………………………………...25
3-1 粉末製作………………………………………………..……..25
3-2中子繞射(Neutron Diffraction) …………………………………25
3-3 Rietveld結構精算…………………………….……………....26
第四章 實驗結果討論…………………………….…………………....30
第五章 結論………………………………………………………….....51
Reference………………………………………………………………....52
附錄……………………………………………………………………..55

[1] J. Chaigneau, PRB, 80, 184107 (2009)
[2-1] Goodenough 1995 J. B. Phys. Rev. 100 564
[2-2] Kanamori, J. 1959 J. Phys. Chem. Solids. 10 87
[2-3] Anderson, P. W. In Solid State Physics; Seitz, F., Turnbull, D. 1963 Eds.; Academic Press: NewYork. 14 99
[3]R.Ramesh, and N.A.Spaldin,Nature Mater.6,21(2007)
[4] J. R. Teague, R. Gerson, and W. J. James, Solid State Commun. 8, 1073 (1970)
[5] P. Fischer, M. Polomska, I. Sosnowska, and M. Szymanski, J. Phys. C 13, 1931 (1980)
[6] 鮑正恩,The ferroelectric property of La and Pb codoped multiferroic(2008)
[7] G. Catalan Phys. Rev. B 79, 212415 2009
[8] J. Chaigneau, PRB, 80, 184107 (2009)
[9]鮑正恩, The ferroelectric property of La and Pb codoped multiferroic BiFeO3
[10] 戴仰含, Study of Bi0.9Pb0.1FeO3 Thin Film Feroelectricity(2011)
[11] J.Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, “Epitaxial BiFeO3 Multiferroic Thin Film Heterostructures”, Science 299 1719 (1970)
[12]Benjamin Ruette, S. Zvyagin, A. P. Pyatakov, A. Bush, J. F. Li, V. I. Belotelov, A. K. Zvezdin, and D. Viehland, “Mangetic-field-induced phase transition in BiFeO3 observed by high-field electron spin resonance: Cycloidal to homogeneous spin order”.Phys. Rev. B 69 064114 (2004)
[13] G. L. Squires, Introduction to The Theory of Thermal Neutron
Scattering (Cambridge, 1987).
[14] S. Y. Wu, W. T. Hsieh, W-H. Li, K.C. Lee, and Y.Y. Chen, Chinese, J.
Phys. 31, 663 (1993).
[15] C. Kittel, Introduction to Solid State Physics, 6th ed, (John Wiley &
Sons, 1991).
[16] 楊仲準,鋰離子電池材料鋰-錳-鈷氧化物之結構與磁性研究
[17] Jose Baruchel, Jean-Louis Hodeau, et al., Neutron and Synchrotron
Radiation for Condensed Matter Studies, Vol. II, 100-102 (1994).
[18]Australia Anston website
[19] ANSTO goverment website
[20] H. M. Rietveld, J. Appl. Cryst. 2, 65 (1969).
[21] R. A. Young edited, The Rietveld Method, (Oxford Univ. Press, New
York, 1993).
[22] R. J. Hill and I. C. Madsen, Powder Diffraction, 2, 146 (1987).
[23] R. J. Hill and C. J. Howard, J. Appl. Cryst. 18, 173 (1985).
[24] Coey Magnetism and Magnetic Material
[25] 劉貴嘉,Study of film growth ferroelectricity on Bi0.9Pb0.1FeO3/SrRuO3/SrTiO3 (2012).