Observations of the Formation of Lamellar Ferroelectric Domain Structures Having Fractal Aspects

具有分形方面的层状铁电畴结构形成的观察

基本信息

批准号：
06640447
负责人：
OZAKI Toru
金额：
$ 1.34万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

Lamellar ferroelectric domain structures formed in KH_2PO_4 (KDP) have fractal aspects as well as the periodicity along the normal to the 180ﾟdomain walls. Each half-period of the domain structures is characterized by an n-th pre-fractal of the pentad Cantor set having the fractal dimension D=0.756・・・. We call these structures "the pre-fractal domain structures (PFDS) ". On the basis of the internal energy consisting of both the electrostatic energy U_E relevant to a depolarization field E_d and the domain wall energy U_w relevant to a surface energy density sigma on each wall, I got to have the following expectations. (1) The equilibrium period 2L of PFDS should be proportional to the square root of the thickness d of a plate. (2) Five PFDS having the generations n=0-3 and 3' (a derivative of the 3rd PFDS) should be thermodynamically stabler than any other domain structures characterized by an m-adic Cantor set (m*5). To clarify these expectations I carried out the optical observation and the scanning electron microscopic observation of PFDS on KDP (T_c=123K) , RbH_2PO_4 (RDP,T_c=148K) , KD_2PO_4 (DKDP,T_c=220K) , CsH_2PO_4 (CDP,T_c=156K) and triglycine sulfate (TGS,T_c=322K). The results obtained in the present research are summarized as follows. (1) Five generations of PFDS having n=0-3 and 3'were observed in KDP.(2) PFDS formed in KDP demostrated the relation 2L*d^<1/2>. (3) PFDS were also formed in RDP and DKDP.(4) PFDS were also formed in CDP and TGS.The results (1) and (2) prove that both U_E and U_W play important roles in the formation of PFDS.(3) clarifies that PFDS are formed in the presence of E_d irrespective of the amount of sigma. This is because sigma is proportional to the square root of T_c. (4) clarifies that PFDS are formed in the presence of E_d when sigma has anisotropy, no matter how low the anisotropy is.

在KH_2PO_4（KDP）中形成的层状铁电域结构具有分形方面以及沿正常的周期性到180ﾟ域壁。域结构的每个半周期的特征在于五角形插座套件的第n-th-fractal the Pre tractal，其分形尺寸为d = 0.756 ・・・・。我们称这些结构为“骨架前结构域（PFD）”。基于由静电能U_E组成的内部能量，与沉积场E_D和域壁能量u_w相关，u_w与每个壁上的表面能密度sigma相关，我必须有以下预期。（1）等效周期2L PFD应与板厚度D的平方根成正比。（2）具有n = 0-3和3'（第三个PFD的衍生物）的五个PFD，比以M-ADIC Cantor Set（M*5）为特征的任何其他域结构都应在热力学上具有稳定器。为了澄清这些期望，我进行了光学观察和扫描电子显微镜观察PFD（T_C = 123K），RBH_2PO_4（RDP，T_C = 148K），KD_2PO_4（DKDP，T_C = 220K），CSH_2PO_4（csh_2ppo = 156）硫酸盐（TGS，T_C = 322K）。本研究中获得的结果总结如下。（1）在KDP中观察到具有n = 0-3和3'的五代PFD。（2）KDP中形成的PFD脱离了关系2l*d^<1/2>。（3）在RDP和DKDP中也形成了PFD。（4）在CDP和TG中也形成了PFD。结果（1）和（2）证明U_E和U_W在PFD的形成中均起着重要作用。（3）在E_D的存在下形成了PFD在e_d的存在下形成的sigma sigma n sigma n e_d n e_d n Mears n.d sigma sigma sigmam a sigma a sigma a sigma a sigma a sigma a sigmam a。这是因为Sigma与T_C的平方根成正比。（4）阐明当Sigma具有各向异性的情况下，无论各向异性多么低时，PFD都是在E_D存在下形成的。