## Neutron scattering |

### From inside the book

Results 1-3 of 71

Page 22

One Scattering Center If we take one nucleus centered at the origin, the

scattering cross section is obtained by taking the integral in Eq. (13) over the

volume of the nucleus. As for all relevant values of r and for thermal neutron

scattering, |Q • r| « 1, we obtain a constant value inn z Jnuci where h is called the

scattering length and has been defined to be the negative value of the amplitude

of the scattered wave. As most scattering amplitudes are negative (see, e.g.,

Turchin, 1965) ...

One Scattering Center If we take one nucleus centered at the origin, the

**nuclear**scattering cross section is obtained by taking the integral in Eq. (13) over the

volume of the nucleus. As for all relevant values of r and for thermal neutron

scattering, |Q • r| « 1, we obtain a constant value inn z Jnuci where h is called the

scattering length and has been defined to be the negative value of the amplitude

of the scattered wave. As most scattering amplitudes are negative (see, e.g.,

Turchin, 1965) ...

Page 23

plied with N, to the double sum and subtracting it from the sum of 6R2, one

obtains (averaging is denoted by a bar) ={\h\>-\B\>}+m> Zexp(iQ-R) (16) Clearly,

only the second term contains any information on collective properties of the

scattering system whereas the first term in brackets, representing incoherent

scattering, arises from the deviations of the scattering length from a mean value,

caused by

scattering cross ...

plied with N, to the double sum and subtracting it from the sum of 6R2, one

obtains (averaging is denoted by a bar) ={\h\>-\B\>}+m> Zexp(iQ-R) (16) Clearly,

only the second term contains any information on collective properties of the

scattering system whereas the first term in brackets, representing incoherent

scattering, arises from the deviations of the scattering length from a mean value,

caused by

**nuclear**-spin interaction or isotope (**nuclear**) disorder. The incoherentscattering cross ...

Page 496

G. Kostorz. where <r0 is the spin-independent part corresponding to zero

electron or

polarization cross section. One advantage of polarizing filters over polarizing

monochromators (Section III.E) is that the angular divergence of the beam may

be larger. In addition, filters may cover an extended energy range and are thus

potentially useful for magnetic diffuse scattering studies where a poor wavelength

resolution (A/.

G. Kostorz. where <r0 is the spin-independent part corresponding to zero

electron or

**nuclear**polarization, and ap = \(a+ — <r~) is the spin-dependent orpolarization cross section. One advantage of polarizing filters over polarizing

monochromators (Section III.E) is that the angular divergence of the beam may

be larger. In addition, filters may cover an extended energy range and are thus

potentially useful for magnetic diffuse scattering studies where a poor wavelength

resolution (A/.

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### Contents

Neutron Production and Detection | 12 |

Basic Scattering Theory | 21 |

Diffraction from Crystals | 30 |

Copyright | |

16 other sections not shown

### Other editions - View all

Neutron Scattering: Treatise on Materials Science and Technology, Volume 15 G. Kostorz Limited preview - 2013 |

### Common terms and phrases

alloys amplitude antiferromagnetic atoms average Bragg peaks Bragg scattering calculated chain chapter by Kostorz Chem coherent collimation concentration cross section Crystallogr defect density dependence detector direction dispersion curves displacements distribution domain elastic electron energy experimental ferroelectric ferromagnetic fluctuations flux line Fourier transform frequency hydrides hydrogen impurity incoherent scattering inelastic scattering Institut Laue-Langevin intensity interaction isotope Kostorz and Lovesey Lett magnetic scattering materials matrix measurements metal mode molecules monochromator neutron beam neutron diffraction neutron SAS neutron scattering nuclear obtained orientation parameters particles peak phase Phase Transitions phonon Phys plane polarized neutron polymer Proc quasi-elastic reactor reciprocal lattice reflection resolution sample scattering cross section scattering function scattering length scattering vector Schelten Schmatz shown in Fig single crystal solid solution spin structure factor studies symmetry technique temperature theory thermal neutron tion transition unit cell values wave vector wavelength width x-ray

### References to this book

Einführung in die Kristallographie Will Kleber,Hans-Joachim Bautsch,Joachim Bohm No preview available - 1998 |