
系統識別號 
U00022408201711062700 
中文論文名稱

雙鈣鈦礦YBa(Cu1xFex)2O5的中子繞射研究 
英文論文名稱

Neutron Powder Diffraction Study of the Double Perovskite Oxides YBa(Cu1xFex)2O5 
校院名稱 
淡江大學 
系所名稱(中) 
物理學系碩士班 
系所名稱(英) 
Department of Physics 
學年度 
105 
學期 
2 
出版年 
106 
研究生中文姓名 
賴君豪 
研究生英文姓名 
ChunHao Lai 
學號 
604210038 
學位類別 
碩士 
語文別 
英文 
口試日期 
20170622 
論文頁數 
73頁 
口試委員 
指導教授杜昭宏 委員林大欽 委員楊仲準

中文關鍵字 
YBa(Cu1xFex)2O5
中子繞射與磁性結構

英文關鍵字 
YBa(Cu1xFex)2O5
Neutron diffraction and Magnetic structure

學科別分類 
學科別＞自然科學＞物理

中文摘要 
我們透過固態反應法合成一系列的YBa(Cu1xFex)2O5，藉此研究銅、鐵的比例對樣品的結構與磁性所產生的影響。根據磁化率的量測結果，我們得知在銅鐵比例相同的條件下此樣品具有兩個反鐵磁相變溫度(TN1 和 TN2)；同時，中子繞射的結果顯示在這兩個相變點附近會發生磁結構的相變(正配相→非正配相)，在溫度較低的情況下正配相非常微弱。然而，隨著鐵的化學劑量越高第二相變溫度TN2也跟著升高，此相變只發生在0.490 ≤ x ≤ 0.515的範圍之內，無論是磁化率量測以及中子繞射都得到相同的結果。唯一不同的是當0.510 ≥ x時，鐵的參雜會誕生出新的磁結構相變取代了原有的正配非正配相變，並與原有的正配相共存。 
英文摘要 
Structural and magnetic properties of variety Cu/Fe ratio of the double perovskite YBa(Cu1xFex)2O5 were investigated by using neutron powder diffraction (NPD) and magnetization measurements. The crystal structures of all the samples are formed in a space group of P4/mmm with in the x range between 0.45 and 0.55. Susceptibility measurements of YBaCuFeO5 exhibited two antiferromagnetic transitions at TN1 ~ 450 K and TN2 ~ 175 K, accompanied with two anomalous spin ordering. The refinement results show an antiferromagnetic commensurate (CM) phase with propagation vector Qc1=(1/2,1/2,1/2), between TN1 and TN2, which as a collinear magnetic structure.
Below TN2, two satellite incommensurate (ICM) magnetic reflections were observed at around each commensurate ones with Qi=(1/2,1/2,1/2+q), indicating the appearance of spiral magnetic structure. Furthermore, these observations revealed that TN2 is very sensitive to the concentration of Fe, and explained the paradox of transition temperatures in the past reports. For x ≥ 0.510, extra magnetic reflections emerge with a propagation wavevector Qc2=(1/2,1/2,0), suggesting the coexistence of two commensurate magnetic phases with propagation wavevectors of (1/2,1/2,1/2) and (1/2,1/2,0), respectively. 
論文目次 
Table of Contents
Table of Contents vi
List of Figures viii
List of Tables xiii
Chapter 1 General properties of YBaCuFeO5 1
Chapter 2 Neutron Powder Diffraction and Magnetic Structure 9
21 Neutron powder diffraction 9
21.1 Introduction to NPD 9
21.2 High intensity powder diffractometer WOMBAT 22
21.3 High resolution powder diffractometer ECHIDNA 23
22 Introduction to Magnetic structure 24
23 Rietveld refinement 31
23.1 Introduction 31
23.2 Refinable parameters 32
23.3 Criteria of fit 38
23.4 Refinement strategy 40
Chapter 3 Sample Characterizations 42
31 Sample synthesis 42
32 Xray diffraction 43
32.1 Introduction to XRD 43
32.2 Xray diffraction results 47
33 Susceptibility against temperature 50
Chapter 4 Neutron powder diffraction results 52
41 Refinement results of NPD 52
42 The magnetic phase identification 61
43 New magnetic structure of YBa(Cu1xFex)2O5 68
Chapter 5 Summary and Conclusion 71
References 72
List of Figures
▲ Figure 11 The crystal model of YBaCuFeO5 with S.G = P4/mmm is a centrosymmetric structure about the mirror Y3+ plane with Cu/Fe sites split. The occupancy of Fe sites is same as the occupancy of Cu sites, which is equal to 0.5. 2
▲ Figure 12 Temperature dependence of the spin susceptibility of YBaCuFeO5 single crystal, measured with the field of 1 T applied either parallel or perpendicular to the caxis from 2 K to 1000 K [5]. 3
▲ Figure 13 The low angle part of NPD patterns at 1.5 and 300 K are shown separately above 2D contour plot, which suggests the temperature dependence of the NPD patterns for YBaCuFeO5 with transition temperatures [2]. 4
▲ Figure 14 Rietveld refinement result of YBaCuFeO5. The numbers of criteria of fit are RB = 4.529 and χ2 = 9.10. 5
▲ Figure 15 (a) The collinear magnetic order of CM phase shows the magnetic moments align with either aaxis or baxis orientation. The magnitude of Fe3+ ion moment (blue) is about 0.80 μ_B, and the one of Cu2+ ion (red) is approximate to 0.16 μ_B. The ratio between 2 moments, 5, is based on the ratio between their spin quantum number, that is to say, S_Fe^(3+)=5/2 and S_Cu^(2+)=1/2 . (b) The model of circular spiral magnetic order of ICM phase displays the spiral ordering (+,,,+) transmit along Ldirection, where the magnitudes of magnetic moments are same as the ones of CM phase. The rotating angle φ is suggested by q value as 165° at 1.5 K, while the phase difference θ is revealed as 146° by the refinement result. 6
▲ Figure 16 The temperature dependence of the wavevector of the magnetic reflection ( 1/2,1/2,3/2±q) [5]. 7
▲ Figure 17 The linear scans through ( 1/2,1/2,1/2 ) along Ldirection at different temperatures, (a) the commensurate phase at 250 K, (b) the mixed phase at 160 K, and (c) the incommensurate phase at 10 K [5]. 8
▲ Figure 21 Illustration of Bragg reflection from a set of parallel planes [7]. 11
▲ Figure 2 2 The total difference in phase angle between the 2 paths (dash line and full line) is equal to the difference in phase angle between incident beams k∙r plus the one between scattered beams k’∙r. 16
▲ Figure 2 3 The profile of scattering intensity for M = 15 [10]. 19
▲ Figure 2 4 The common geometry of Bragg law. The parallel lattice planes separated by distance d, and the reflection angle equal to incident angle. 20
▲ Figure 2 5 Layout of WOMBAT, the high intensity powder diffractometer at ANSTO [6][11]. 22
▲ Figure 2 6 Layout of ECHIDNA, the high resolution powder diffractometer at ANSTO [6][12]. 23
▲ Figure 2 7 Some different types of magnetic structures [14]. 25
▲ Figure 2 8 Illustration of translational properties with the propagation vector k. In this example, the basis vector for the moment in the zeroth cell is Ψ = (0 1 0), k = (0 0 0.5) and each plane corresponds to a lattice translation of T = (0 0 1) [14]. 26
▲ Figure 2 9 Graphs in reciprocal space for a variety of magnetic structure classes [14]. 28
▲ Figure 2 10 Refinement results of YBa(Cu1xFex)2O5 x = 0.515 (NPD, T = 1.5 K) with (a) S_L = D_L = 0, and (b) S_L = D_L = 0.08877. 36
▲ Figure 3 1 Sintering temperature Ts versus substitution ratio x. 43
▲ Figure 3 2 Linear polarized beam scattered by an electron. The incident beam is along the xaxis and meets the electron at O. The electron scatters a ray in the direction of P, making an angle φ with the electric field along the yaxis (OP lies in the xy plane) [7]. 45
▲ Figure 33 Xray scattered by an atom. The path difference of scattered beams in 2θ direction is CBAD. 46
▲ Figure 34 Atomic form factors are rapidly reduced as 2θ increases. Unless 2θ = 0 or atom is still, the atom form factor is not equivalent to Z. 47
▲ Figure 3 5 Xray powder diffraction patterns of different x at room temperature. The small divergence at specific 2θ range may caused by Cu/Fe ratio x, different lattice parameters, oxygen defect, or even preferred orientation. 48
▲ Figure 36 Lattice parameters versus Cu/Fe ratio x. 49
▲ Figure 37 Magnetic susceptibility against temperature of YBa(Cu1xFex)2O5 is measured at 1 KOe by ZFC. 51
▲ Figure 41 The crystal model of YBa(Cu1xFex)2O5 52
▲ Figure 42a NPD pattern of x = 0.485 measured by ECHIDNA at 1.5 K. 54
▲ Figure 42b NPD pattern of x = 0.490 measured by ECHIDNA at 1.5 K. 55
▲ Figure 42c NPD pattern of x = 0.495 measured by ECHIDNA at 1.5 K. 56
▲ Figure 42d NPD pattern of x = 0.500 measured by ECHIDNA at 1.5 K. 57
▲ Figure 42e NPD pattern of x = 0.505 measured by ECHIDNA at 1.5 K. 58
▲ Figure 42f NPD pattern of x = 0.510 measured by ECHIDNA at 1.5 K. 59
▲ Figure 42g NPD pattern of x = 0.515 measured by ECHIDNA at 1.5 K. 60
▲ Figure 43 Specifically magnetic Bragg reflections of YBa(Cu1xFex)2O5 NPD patterns, where 0.485 ≤ x ≤ 0.515. 61
▲ Figure 44a 2D contour plot of x = 0.475 63
▲ Figure 44b 2D contour plot of x = 0.485 63
▲ Figure 44c 2D contour plot of x = 0.490 64
▲ Figure 44d 2D contour plot of x = 0.495 64
▲ Figure 44e 2D contour plot of x = 0.500 65
▲ Figure 44f 2D contour plot of x = 0.505 65
▲ Figure 44g 2D contour plot of x = 0.510 66
▲ Figure 44h 2D contour plot of x = 0.515 66
▲ Figure 44i 2D contour plot of x = 0.525 67
▲ Figure 45 Rietveld refinement result of YBa(Cu1xFex)2O5. The numbers of criteria of fit are RB = 4.537 and χ2 = 9.09. 68
▲ Figure 46 The models of collinear magnetic order of CM2. Here, magnetic moments of the spin ordering (+,,,+) array on only a, or b, or caxis. However, the direction of magnetic moments must be parallel or perpendicular to the one of CM1 to conserve the original symmetry of tetragonal lattice system. The magnitudes of magnetic moments of Fe3+ ion and Cu2+ ion are consistent to different magnetic phases. The refinement results revealed the magnitude of Fe3+ ion moment is about 1.55 μ_B, and the one of Cu2+ ion moment is approximate to 0.31 μ_B. Since the powder sample is isotropic, there is no way to identify which one of these models as the right one. 69
List of Tables
Table 2 1 Coherent scattering amplitudes, b, in units of 1012 cm [9].. 12
Table 2 2 Symmetry analytical profile functions [15]. 34
Table 2 3 Numerical criteria of fit [15~16]. 39
Table 2 4 Parameter turnon sequence [15~16]. 41
Table 31 Transition temperatures TN2 of variant Cu/Fe ratio. 50
Table 41a Refinement result of x = 0.485 54
Table 41b Refinement result of x = 0.490 55
Table 41c Refinement result of x = 0.495 56
Table 41d Refinement result of x = 0.500 57
Table 41e Refinement result of x = 0.505 58
Table 41f Refinement result of x = 0.510 59
Table 41g Refinement result of x = 0.515 60

參考文獻 
[1] L. ErRakho et al., J. Solid State Chem., 73, 531535 (1988).
[2] M. Morin et al., Phys. Rev. B, 91, 064408 (2015).
[3] B. Kundys et al., Appl. Phys. Lett., 94, 072506 (2009).
[4] Yuji Kawamura et al., J. Phys. Soc. Jpn., 79, 073705 (2010).
[5] YenChung Lai et al., Crystal growth and magnetic property studies of YBaCuFeO5 (Tamkang university, Taiwan, 2015)
[6] 李文献、吳浚銘，物理雙月刊(三十卷一期) 2008 年二月。
[7] Clearfield, A., Reibenspies, J. and Bhuvanesh, N. (2008). Principles and applications of powder diffraction. Ames, Iowa: Blackwell.
[8] Kittel, C. (2005). Introduction to solid state physics. Hoboken NJ: John Wiley & Sons.
[9] G.E.Bacon et al., Acta Cryst., A 28, 357, (1972).
[10] J. AlsNielsen, D. McMorrow (2011), Elements of modern Xray physics. West Sussex: John Wiley & Sons.
[11] Andrew Studer et al., Fact sheet of WOMBAT. (ANSTO, NSW).
[12] Max Avdeev et al., Fact sheet of ECHIDNA. (ANSTO, NSW).
[13] KlausDieter Liss et al., Physica B, 385–386, 1010–1012, (2006).
[14] Andrew Wills, J. Phys.IV France, 11, Pr9133  Pr9158, (2001).
[15] R. A. Young et al. (1993), The Rietveld Method. New Yerk: Oxford University Press.
[16] Juan RodriguezCarvajal et al., User manual of FullProf. (Laboratoire Leon Brillouin, Gif sur Yvette, 2001).
[17] L. W. Finger et al., J. Appl. Cryst., 27, 892900, (1994).
[18] R. D. Shannon et al., Acta Cryst., A32, 751, (1976).

論文使用權限 
同意紙本無償授權給館內讀者為學術之目的重製使用，於20170831公開。同意授權瀏覽/列印電子全文服務，於20170831起公開。 


