Perovskites結構的材料是最普遍的鐵電材料，近年來廣泛的應用在電子原件的製造上，因此我們也希望能從理論上了解其塊材及電極化的特性。
在本論文中，我們利用第一原理的方法做了很多Perovskites材料的塊材與鐵電性質在0K的計算。我們的重點主要是放在兩種典型的鐵電材料鈦酸鋇(BaTiO3)與鈦酸鉛(PbTiO3)上。經過計算結果我們得到兩者的電極化值與實驗上的數值是吻合的。在我們研究的過程中也發現電偶極矩的定義造成一些ambiguities可能在未來尚有值得探討改進的地方。
除了以上兩種材料以外，其他15種可能有鐵電性質的材料我們也加以計算，由density of states分析中我們也發現一些材料不是絕緣體、而是金屬，因此無法計算電極化，也就是沒有鐵電材料的特性。我們也嘗試將其晶格形變的情形與電極化的強度作關聯。

Perovskites are the most commonly seen ferroelectrics, which have been widely used in the industry of devices in the last few decades. Therefore we wish to probe into them theoretically.
In this thesis, we studied bulk and ferroelectric properties of several Perovskites at 0K by doing calculations in ab-initio ways. We put our attentions mostly on Barium Titanate (BaTiO3) and Lead Titanate (PbTiO3). Our results match the experimental ones. We also found that the ambiguities in definition of dipole moments can be studied furthermore in the future.
Besides BaTiO3 and PbTiO3, we also calculated fifteen compounds which possibly possess ferroelectric properties, and from their density of states (DOS), we identified some of them not to be insulators, which are metals, and therefore we cannot calculate their polarization, i.e. they have no ferroelectric properties. Furthermore, we tried to relate their ferroelectric properties with the deformation of the lattices.

Richard M. Martin, Phys. Rev. B 9, 1998 (1974).
B. I. Bennett and A. A. Maradudin, Phys. Rev. B 5, 4146 (1972).
R. Resta, Ferroelectrics 136, 51 (1992).
R. D. King-Smith and David Vanderbilt, Phys. Rev. B 47, 1651 (1992).
M. V. Berry, Proc. Roy. Soc. Lond. A 392, 45 (1984); R. Resta, J. Phys.: Condens
Matter 12, R107 (2000);
G. Kresse and J. Furthmller, Phys. Rev. B 54, 11169 (1996).
M. P. Teter, M. C. Payne, and D. C. Allan, Phys. Rev. B 40, 12255 (1989); D. M.
Bylander, L. Kleinman, and S. Lee, Phys. Rev. B 42, 1394 (1990).
E. R. Davidson, Methods in Computational Molecular Physics edited by G. H. F.
Diercksen and S. Wilson Vol. 113 NATO Advanced Study Institute, Series C (Plenum,
New York, 1983), p.95; B. Liu, in Report on Workshop ``Numerical Algorithms in
Chemistry: Algebraic Methods’’ edited by C. Moler and I. Shavitt (Lawrence Berkley
Lab. Univ. of California, 1978), p.49.
D. M. Wood and A. Zunger, J. Phys. A, 1343 (1985); P. Pulay, Chem. Phys. Lett. 73,
393 (1980).
S. Blugl, Ph.D Thesis, RWTH Aachen (1988); D. D. Johnson, Phys. Rev. B 38,
12087 (1988) ; P. Pulay, Chem. Phys. Lett. 73.
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
N. David Mermin, Phys. Rev. 137, A1441 (1965).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
F. Herman, J. P. Van Dyke, and I. P. Ortenburger, Phys. Rev.Lett. 22, 807 (1969)
R. P. Feynman, Phys. Rev. 56, 340 (1939).
R. Resta, Europhys. Lett. 22, 133 (1993).
Hendrik J. Monkhorst and James D. Pack, Phys. Rev. B 13(12), 5188 (1976).
Gerald Burns and B. A. Scott, PRL 25, 167 (1970).
W. L. Zhong, B. Jiang, P. L. Zhang, J. M. Ma, H. M. Cheng, Z. H. Yang, and L. X. Li, J. Phys.: Condens. Matter 5, 2619 (1993).
A. Asthagiri, Z. Wu, N. Choudhury, and R. E. Cohen, Ferroelectrics 333, 69
(2006).