Neutron Scattering - JUWEL - Forschungszentrum Jülich

More documents

Recommendations

Info

HEiDi 9 The linear absorption coefficient is an isotropic property of matter and depends on the wavelength and kind of radiation. For x-rays penetration depths are only a few millimetre or below (e.g. for silicon with μMoK�=1.546 mm -1 , μCuK�=14.84 mm -1 with penetration depths of 3 mm and 0.3 mm respectively). This limits transmission experiments to sample diameter of typically below 0.3 mm. To correct bias of intensities due to different scattering paths through the sample one has to measure accurately the sample size in all directions. Even for sphere liek samples the mean path lenghts depend on 2�� In addition the sample environment must have an extraordinary small absorption Thermal neutrons have for most elements a penetration depth of several centimeters. Thus, sample diameters of several millimeters and large and complex sample environments (furnaces, magnets, etc.) can be used. On the other hand side one needs sufficiently large samples for neutron diffraction which is often a delicate problem. Extinction reduces also radiation intensities. But the character is completely different form that of absorption. In principle extinction can be explained quite easily by taking into account that each diffracted beam can be seen as a new primary beam for the neighbouring lattice planes. Therefore, the diffracted beam becomes partially backscattered towards the direction of the very first primary beam (Switch from kinetic to dynamic scattering theory!). Especially for very strong reflections this effect can reduce intensities dramatically (up to 50% and more). Condition for this effect is a merely perfect crystal. Theoretical models which include a quantitative description of the extinction effect were developed from Zachariasen (1962) and Becker and Coppens [2, 3, 4, 5, 6]. These models base on an ideal spherical mosaic crystal with a very perfect single crystal (primary Extinction) or different mosaic blocks with almost perfect alignment (secundary Extinction) to describe the strength of the extinction effect. In addition, it is possible to take into account anisotropic extinction effect if the crystal quality is also anisotropic. Nowadays extinction correction is included in most refinement programs [7]. In general extinction is a problem of sample quality and size and therefore more commonly a problem for neutron diffraction and not so often for x-ray diffraction with much smaller samples and larger absorption. Polarisation: X-ray radiation is electromagnetic radiation. Therefore, the primary beam of an x-ray tube is not polarized. The radiation hits the sample under an diffraction angle of � where it can be separated into two waves of same intensity, firstly with an electrical field vector parallel E|| and secondly perpendicular E� towards the �-axis. Whilst the radiation with E|| will not be attenuated the radiation with E� will be attenuated with E� � cos(2�) E�. The polarization factor P for the attenuation has then the following formula (I ~ E 2 ): P = (1+cos(2�) 2 )/2 Additional optical components like monochromator crystals also have an impact on the polarization and have to be taken into account accordingly. Lorentz factor: The Lorentz factor L is a purely geometrical factor. It describes that during an �- and �-scan respectively of Bragg reflections towards higher 2� values for the same angular speed ��/�t an effectively elongated stay of the sample in the reflection position results.: L = 1/sin(2�)
10 M. Meven This has to be taken into account for any kind of radiation in an diffraction experiment. 3.4 Summary of Theory of Method The different interactions of x-ray and neutron radiation with the atoms in a crystal make neutrons in general the better choice for a diffraction experiment. But on the other hand one has to take into account the available flux of x-rays and neutrons respectively. The flux of modern neutron sources like the Heinz Maier-Leibnitz neutron source (FRM II) is spread around a broad spectrum of neutron energies. In a sharp band of energies/wavelengths, e.g. ��/�
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: 8 M. Meven intensities (I~Z 2 ) tha
Page 57 and 58: 12 M. Meven 4 Sample Section 4.1 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:
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?