我們透過固態反應法合成一系列的YBa(Cu1-xFex)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。

Structural and magnetic properties of variety Cu/Fe ratio of the double perovskite YBa(Cu1-xFex)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.

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
2-1	Neutron powder diffraction	9
2-1.1	Introduction to NPD	9
2-1.2	High intensity powder diffractometer WOMBAT	22
2-1.3	High resolution powder diffractometer ECHIDNA	23
2-2	Introduction to Magnetic structure	24
2-3	Rietveld refinement	31
2-3.1	Introduction	31
2-3.2	Refinable parameters	32
2-3.3	Criteria of fit	38
2-3.4	Refinement strategy	40
Chapter 3  Sample Characterizations	42
3-1	Sample synthesis	42
3-2	X-ray diffraction	43
3-2.1	Introduction to XRD	43
3-2.2	X-ray diffraction results	47
3-3	Susceptibility against temperature	50
Chapter 4  Neutron powder diffraction results	52
4-1	Refinement results of NPD	52
4-2	The magnetic phase identification	61
4-3	New magnetic structure of YBa(Cu1-xFex)2O5	68
Chapter 5  Summary and Conclusion	71
References	72


 
List of Figures
▲	Figure 1-1 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 1-2 Temperature dependence of the spin susceptibility of YBaCuFeO5 single crystal, measured with the field of 1 T applied either parallel or perpendicular to the c-axis from 2 K to 1000 K [5].	3
▲	Figure 1-3 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 1-4 Rietveld refinement result of YBaCuFeO5. The numbers of criteria of fit are RB = 4.529 and χ2 = 9.10.	5
▲	Figure 1-5 (a) The collinear magnetic order of CM phase shows the magnetic moments align with either a-axis or b-axis 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 L-direction, 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 1-6 The temperature dependence of the wavevector of the magnetic reflection ( 1/2,1/2,3/2±q) [5].	7
▲	Figure 1-7 The linear scans through ( 1/2,1/2,1/2 ) along L-direction 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 2-1 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(Cu1-xFex)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 x-axis 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 y-axis (OP lies in the x-y plane) [7].	45
▲	Figure 3-3 X-ray scattered by an atom. The path difference of scattered beams in 2θ direction is CB-AD.	46
▲	Figure 3-4 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 X-ray 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 3-6 Lattice parameters versus Cu/Fe ratio x.	49
▲	Figure 3-7 Magnetic susceptibility against temperature of YBa(Cu1-xFex)2O5 is measured at 1 KOe by ZFC.	51
▲	Figure 4-1 The crystal model of YBa(Cu1-xFex)2O5	52
▲	Figure 4-2a NPD pattern of x = 0.485 measured by ECHIDNA at 1.5 K.	54
▲	Figure 4-2b NPD pattern of x = 0.490 measured by ECHIDNA at 1.5 K.	55
▲	Figure 4-2c NPD pattern of x = 0.495 measured by ECHIDNA at 1.5 K.	56
▲	Figure 4-2d NPD pattern of x = 0.500 measured by ECHIDNA at 1.5 K.	57
▲	Figure 4-2e NPD pattern of x = 0.505 measured by ECHIDNA at 1.5 K.	58
▲	Figure 4-2f NPD pattern of x = 0.510 measured by ECHIDNA at 1.5 K.	59
▲	Figure 4-2g NPD pattern of x = 0.515 measured by ECHIDNA at 1.5 K.	60
▲	Figure 4-3 Specifically magnetic Bragg reflections of YBa(Cu1-xFex)2O5 NPD patterns, where 0.485 ≤ x ≤ 0.515.	61
▲	Figure 4-4a 2D contour plot of x = 0.475	63
▲	Figure 4-4b 2D contour plot of x = 0.485	63
▲	Figure 4-4c 2D contour plot of x = 0.490	64
▲	Figure 4-4d 2D contour plot of x = 0.495	64
▲	Figure 4-4e 2D contour plot of x = 0.500	65
▲	Figure 4-4f 2D contour plot of x = 0.505	65
▲	Figure 4-4g 2D contour plot of x = 0.510	66
▲	Figure 4-4h 2D contour plot of x = 0.515	66
▲	Figure 4-4i 2D contour plot of x = 0.525	67
▲	Figure 4-5 Rietveld refinement result of YBa(Cu1-xFex)2O5. The numbers of criteria of fit are RB = 4.537 and χ2 = 9.09.	68
▲	Figure 4-6 The models of collinear magnetic order of CM2. Here, magnetic moments of the spin ordering (+,-,-,+) array on only a, or b, or c-axis. 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 10-12 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 turn-on sequence [15~16].	41
	Table 3-1 Transition temperatures TN2 of variant Cu/Fe ratio.	50
	Table 4-1a Refinement result of x = 0.485	54
	Table 4-1b Refinement result of x = 0.490	55
	Table 4-1c Refinement result of x = 0.495	56
	Table 4-1d Refinement result of x = 0.500	57
	Table 4-1e Refinement result of x = 0.505	58
	Table 4-1f Refinement result of x = 0.510	59
	Table 4-1g Refinement result of x = 0.515	60

[1] L. Er-Rakho et al., J. Solid State Chem., 73, 531-535 (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] Yen-Chung 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. Als-Nielsen, D. McMorrow (2011), Elements of modern X-ray 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] Klaus-Dieter Liss et al., Physica B, 385–386, 1010–1012, (2006).
[14] Andrew Wills, J. Phys.IV France, 11, Pr9-133 - Pr9-158, (2001).
[15] R. A. Young et al. (1993), The Rietveld Method. New Yerk: Oxford University Press.
[16] Juan Rodriguez-Carvajal et al., User manual of FullProf. (Laboratoire Leon Brillouin, Gif sur Yvette, 2001).
[17] L. W. Finger et al., J. Appl. Cryst., 27, 892-900, (1994).
[18] R. D. Shannon et al., Acta Cryst., A32, 751, (1976).