Neutron Scattering - JUWEL - Forschungszentrum Jülich

More documents

Recommendations

Info

HEiDi 11 To make sure the comparisability of all reflections with each other, all intensities and errors are normalized to the same time of measurement (or monitor count rate) and undergo the Lorentz and (in the x-ray case) polarization correction. Finally in advance of the data refinement there can be done an numerical (e.g. with DataP, [8]) or an empirical absoprtion if necessary. The quality of a measurement is checked in advance of the data refinement by comparing symmetry equivalent reflections and systematic extinctions to confirm the Laue group and space group symmetry. The result is written as internal R-value: Rint = (�k=1 m (�j=1 n k (- Ij) 2 ))/ (�k=1�j=1 n k(Ij 2 )k) Rint represents the mean error of a single reflection j of a group k of nk symmetry equivalent reflections, corresponding to its group and the total number m of all symmetrically independent groups. Therefore Rint is also a good mark to check the absorption correction. After these preliminary steps one can start the final data refinement. At the beginning one has to develop a structural model. The problem with that is that we measure only the absolut values |Fhkl| and not the complete structure factor Fhkl = |Fhkl|exp(��) including its phase �. Therefore, generally the direct fouriertransform of the reflection information Fhkl from reciprocal space into the density information � in the direct space (electron density for x-rays, probability density of atomic cores for neutrons) with �(x) ~ �h�k�l Fhkl exp(-2�(hx+ky+lz)) not possible. This can be done only by direct methods like patterson, heavy atom method or anomal dispersion for x-rays. In the so called refinement program a given structural model (space group, lattice constants, atomic form factors, MSD, etc.) are compared with the experimental data and fitted. In a leas squares routine those programs try to optimize (typically over several cycles) the free parameters to reduce the difference between the calculated structure factors Fcalc and intensities |Fcalc| 2 respectively and the experimentally found Fobs and |Fobs| 2 respectively. To quantisize the quality of measurement there are several values in use: 1. unweighted R-value: Ru = �hkl |Fobs 2 -Fcalc 2 |/�hkl Fobs 2 This value gives the alignment of the whole number of reflections without their specific errors. 2. weighted R-value: Rw = (�hkl w (Fobs 2 -Fcalc 2 ) 2 )/�hkl w Fobs 4 This value represents the alignment of the whole number of reflections including their specific errors or weights (w~1/� 2 ). Sometimes weights are adopted in a way to suppress unwanted influence of the refinement algorithm by weak or badly defined reflections. Be aware that such corrections have to be done extremely carefully because otherwise the refinement adopts the data to the selected structural model and not the model to the experimental data! 3. Goodness of Fit S: S 2 =(�hkl w (Fobs 2 -Fcalc 2 )/(nhkl-reflections - nfree parameter) S should have a value near one if the weighting scheme and the structure model fit to the experimental data set.
12 M. Meven 4 Sample Section 4.1 Introduction La2-xSrxCuO4 is one of the cuprate superconductors with K2NiF4- structure for whose discovery the noble prize was granted in 1988 (Bednorz and Müller [9]) . Pure La2CuO4 is an isolator. Doping with earth alcali metals (Ca 2+ , Sr 2+ , Ba 2+ ) on the La 3+ lattice positions generates in dependence of the degree of doping superconductivity. Sr doping of x=0.15 yields a maximum Tc of 38 K. Pure La2CuO4 undergoes at Tt-o=530 K a structural phase transition from the tetragonal high temperature phase (HTT) F4/mmm: a=b=5.384 Å, c=13.204 Å, �=�=�=90° at T=540 K to the orthorhombic low temperature phase (LTO) Abma: a=5.409 Å, b=5.357 Å, c=13.144 Å, �=�=�=90° at room temperature. The phase transition temperature Tt-o drops for La2-xSrxCuO4 with increased doping and disappears above x=0.2. Fig.. 6 left: J. Birgenau, G. Shirane, HTC Superconductors I, World Scientific (1989) Fig.. 6 right: Stuctural parts of La2CuO4 in the LTO phase
Page 1 and 2:
Member of the Helmholtz Association
Page 4 and 5:
Forschungszentrum Jülich GmbH Jül
Page 6: �� 1 PUMA
Page 9 and 10: 2 O. Sobolev, A. Teichert, N. Jünk
Page 17 and 18: 10 O. Sobolev, A. Teichert, N. Jün
Page 23 and 24: 2 POWDER DIFFRACTOMETER SPODI Conte
Page 25 and 26: 4 POWDER DIFFRACTOMETER SPODI 2. Ba
Page 27 and 28: 6 POWDER DIFFRACTOMETER SPODI Ewald
Page 29 and 30: 8 POWDER DIFFRACTOMETER SPODI Powde
Page 31 and 32: 10 POWDER DIFFRACTOMETER SPODI Rela
Page 33 and 34: 12 POWDER DIFFRACTOMETER SPODI Prof
Page 35 and 36: 14 POWDER DIFFRACTOMETER SPODI neut
Page 37 and 38: 16 POWDER DIFFRACTOMETER SPODI The
Page 39 and 40: 18 POWDER DIFFRACTOMETER SPODI 4 U
Page 41 and 42: 20 POWDER DIFFRACTOMETER SPODI 7. E
Page 43 and 44: 22 POWDER DIFFRACTOMETER SPODI Figu
Page 45 and 46: 24 POWDER DIFFRACTOMETER SPODI Cont
Page 47 and 48: 2 M. Meven Contents 1 Introduction
Page 49 and 50: 4 M. Meven a (hkl) Plane. Each plan
Page 51 and 52: 6 M. Meven wavelengths � in the s
Page 53 and 54: 8 M. Meven intensities (I~Z 2 ) tha
Page 55: 10 M. Meven This has to be taken in
Page 59 and 60: 14 M. Meven Fig. 8 (a) orthorhombic
Page 61 and 62: 16 M. Meven 4.3 Oxygen Position The
Page 63 and 64: 18 M. Meven To direct the secondary
Page 65 and 66: 20 M. Meven For a given spectrum
Page 67 and 68: 22 M. Meven References [1] Th. Hahn
Page 69 and 70: 24 M. Meven
Page 78 and 79: SPHERES Backscattering spectrometer
Page 80 and 81: SPHERES 3 1 Introduction Neutron ba
Page 82 and 83: SPHERES 5 Fig. 2: The monochromator
Page 84 and 85: SPHERES 7 While the primary spectro
Page 86 and 87: SPHERES 9 neutron is scattered, it
Page 88 and 89: SPHERES 11 The stationary equilibri
Page 90 and 91: SPHERES 13 4. Summarize the tempera
Page 92 and 93: ________________________ DNS Neutro
Page 94 and 95: DNS 3 1 Introduction Polarized neut
Page 96 and 97: DNS 5 Monochromator horizontal- and
Page 98 and 99: DNS 7 3 Preparatory Exercises The p
Page 100 and 101: DNS 9 important and always necessar
Page 102: DNS 11 Contact �� Phone:
Page 105 and 106: 2 O. Holderer, M. Zamponi and M. Mo
Page 107 and 108:
4 O. Holderer, M. Zamponi and M. Mo
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
10 O. Holderer, M. Zamponi and M. M
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
2 H. Frielinghaus, M.-S. Appavou Co
Page 121 and 122:
4 H. Frielinghaus, M.-S. Appavou Th
Page 123 and 124:
6 H. Frielinghaus, M.-S. Appavou Fi
Page 125 and 126:
8 H. Frielinghaus, M.-S. Appavou mo
Page 128 and 129:
________________________ KWS-3 Very
Page 130 and 131:
KWS-3 3 1 Introduction Ultra small
Page 132 and 133:
KWS-3 5 2. The standard Q-range of
Page 134 and 135:
KWS-3 7 Table 2. Samples for practi
Page 136 and 137:
KWS-3 9 References [1] Eskilden, M.
Page 138 and 139:
________________________ RESEDA Res
Page 140 and 141:
RESEDA 3 1 Introduction Neutrons ar
Page 142 and 143:
RESEDA 5 various length values l ac
Page 144 and 145:
RESEDA 7 In this expression, a norm
Page 146 and 147:
RESEDA 9 spin flip from up to down
Page 148 and 149:
RESEDA 11 The neutrons are counted
Page 150:
RESEDA 13 Contact ��
Page 153 and 154:
2 S. Mattauch and U. Rücker Conten
Page 155 and 156:
4 S. Mattauch and U. Rücker Fig. 2
Page 157 and 158:
6 S. Mattauch and U. Rücker 4 Expe
Page 159 and 160:
8 S. Mattauch and U. Rücker Contac
Page 161 and 162:
2 H. Morhenn, S. Busch, G. Simeoni
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 178 and 179:
Schriften des Forschungszentrums J
Page 180 and 181:
Page 182 and 183:
show all

Neutron Scattering - JUWEL - Forschungszentrum Jülich

Create successful ePaper yourself

Delete template?

Save as template?