Abstract
By means of pulsed neutron diffraction without energy analysis, it is possible not only to study Bragg scattering but also to study processes involving inelastic neutron scattering. Thus the same diffractometer can be employed for examining elementary excitations as for crystal structure analysis. We discuss the nature of the thermal diffuse scattering (TDS) from acoustic phonons, and show that the sound velocity in the crystal can be determined from the TDS ‘edges’ on either side of the Bragg reflection. One edge arises from phonon emission (Stokes process) and the other from phonon absorption (anti-Stokes), and each is best observed in back scattering with 2θ close to 180°. On the other hand, if 20 is 90°, TDS may be forbidden in the neighbourhood of the reflection and the measured Bragg intensity is then free from the ‘TDS error’.
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Abbreviations
- B :
-
reciprocal-lattice vector
- cs :
-
phase velocity of sound
- ℏ:
-
Planck’s constant/2π
- j:
-
polarization index of normal mode
- ko,k:
-
initial and final wave vectors of neutron
- kB :
-
2π/λB
- Δko :
-
ko−kB
- Δk:
-
k−kB
- mn :
-
neutron mass
- q :
-
wave vector of normal mode
- Q :
-
scattering vector (=k-k o )
- \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} \frac{{e1}}{\Theta } \) :
-
Vector defining locus of elastic scattering through angle 2Θ
- t:
-
time-of-flight
- tB :
-
time-of-flight for Bragg scattering
- Δt:
-
t−tB
- vn :
-
neutron velocity
- β:
-
cs/vn
- ε:
-
index for phono sbsorption (−1)or phonon emission (+1)
- ε’:
-
εΔΘΔΘ
- Θ:
-
half the scattering angle
- ΘB :
-
bragg wavelength
- ΔΘ:
-
Θ−ΘB
- λB :
-
bragg wavelength
- ζ:
-
angle between B and q
- ωj(q):
-
frequency of ormal mode (jq)
References
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© 1988 D. Reidel Publishing Company
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Willis, B.T.M. (1988). Some Aspects of Diffraction Physics with Pulsed Neutrons. In: Carrondo, M.A., Jeffrey, G.A. (eds) Chemical Crystallography with Pulsed Neutrons and Synchroton X-rays. NATO ASI Series, vol 221. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4027-7_4
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DOI: https://doi.org/10.1007/978-94-009-4027-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8287-7
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