Glossary of symbols

Willis, B. T. M.

doi:10.1107/97809553602060000600

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 6.1, p. 593

Section 6.1.3.1. Glossary of symbols

B. T. M. Willis^d

6.1.3.1. Glossary of symbols

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b	Bound nuclear scattering length
b _free	Free nuclear scattering length
	Potential scattering length
b ′, b′′	Real and imaginary parts of resonant scattering length
b _coh	Coherent scattering length
F (h)	Structure factor for nuclear Bragg scattering
2πh	Reciprocal-lattice vector
H	Scattering vector $[(={\bf k}-{\bf k}_0)]$
I	Nuclear spin
k	Wavevector of scattered neutron
$[{\bf k}_0]$	Wavevector of incident neutron
M	Nuclear mass
	Neutron mass
N	Number of unit cells in crystal
V	Volume of unit cell
	Exponent of temperature factor $[\exp(-W_j) ]$ of jth atom
$[w_{+}]$	Weight of spin state $[I+{1\over2}]$
$[w_{-}]$	Weight of spin state $[I-{1\over2}]$
$[\sigma _{\rm coh}]$	Coherent scattering cross section
$[\sigma _{\rm inc}]$	Incoherent scattering cross section
$[\sigma _{\rm tot}]$	Total scattering cross section $[(=\sigma _{\rm coh}+\sigma _{\rm inc})]$
$[\displaystyle \bigg({{\rm d}\sigma \over{\rm d}\Omega}\bigg) _{\rm coh,el}]$	Differential coherent elastic scattering cross section
$[\displaystyle \bigg ({{\rm d}\sigma\over{\rm d}\Omega}\bigg) _{\rm inc,el}]$	Differential incoherent elastic scattering cross section

The nucleus is the fundamental unit involved in the scattering of neutrons by atoms. For magnetic materials, electronic scattering takes place as well (see Section 6.1.2). Apart from these two main interactions, there are a number of subsidiary ones (Shull, 1967) that are extremely weak and can be ignored in nearly all diffraction studies.

In this section, we discuss the neutron–nucleus interaction only, starting from scattering by a single nucleus, then scattering by an atom, and finally scattering by a single crystal. For a more detailed account, see Bacon (1975).

References

Bacon, G. E. (1975). Neutron diffraction, 3rd ed. Oxford: Clarendon Press.Google Scholar

Shull, C. G. (1967). Neutron interactions with atoms. Trans Am. Crystallogr. Assoc. 3, 1–16.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 6.1, p. 593