Debye–Waller Factor in Neutron Scattering by Ferromagnetic Metals

Paradezhenko, G. V.; Melnikov, Nikolai B.; Reser, Boris I.

doi:10.1134/s0040577918040098

Cited by 10 publications

(7 citation statements)

References 29 publications

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“…The coefficient that corresponds to the elastic phonon scattering is called the Debye-Waller factor (DWF). Numerical results and discussion of the DWF in metals are given in our paper [3]. In particular, we showed that an estimate of the DWF in the harmonic approximation can be sufficient for calculating the correction to local magnetic characteristics.…”

Section: Introductionmentioning

confidence: 85%

“…Usually the DWF is obtained by a lengthy calculation of the mean-square displacement (see, e.g., [4]), which is valid both in the harmonic and anharmonic approximations. In the paper [3], we give a simple derivation of the same expression for the DWF in the harmonic approximation. Our derivation is based on the formula for canonical average of exponentials of operators linear in the atomic displacements, which was obtained by Mermin [5].…”

Section: Introductionmentioning

confidence: 99%

“…Our derivation is based on the formula for canonical average of exponentials of operators linear in the atomic displacements, which was obtained by Mermin [5]. Here we present some theoretical details on the lattice vibrations in the harmonic approximation that are used in our paper [3].…”

Section: Introductionmentioning

confidence: 99%

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Lattice vibrations in the harmonic approximation

Paradezhenko,

Melnikov,

Reser

2017

Preprint

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We present some theoretical results on the lattice vibrations that are necessary for a concise derivation of the Debye-Waller factor in the harmonic approximation. First we obtain an expression for displacement of an atom in a crystal lattice from its equilibrium position. Then we show that an atomic displacement has the Gaussian distribution. Finally, we obtain the computational formula for the Debye-Waller factor in the Debye model.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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Lattice vibrations in the harmonic approximation

Paradezhenko,

Melnikov,

Reser

2017

Preprint

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“…0.66 a.u., which correlates well with the transmission for the martensitic phase in Figure 2. A possible explanation of the observed drop in the transmitted neutron intensity is the so-called Debye-Waller factor [15,16]. The Debye-Waller factor describes the scattering of neutrons at an oscillating lattice.…”

Section: In Situ Monochromatic Imagingmentioning

confidence: 99%

“…A sheathed type K thermocouple, inserted in a bore hole close to the welded surface, allowed the measurement of the temperature. A possible explanation of the observed drop in the transmitted neutron intensity is the so-called Debye-Waller factor [15,16]. The Debye-Waller factor describes the scattering of neutrons at an oscillating lattice.…”

Section: Polychromatic Imagingmentioning

confidence: 99%

Time-Resolved Neutron Bragg-Edge Imaging: A Case Study by Observing Martensitic Phase Formation in Low Temperature Transformation (LTT) Steel during GTAW

et al. 2021

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Polychromatic and wavelength-selective neutron transmission radiography were applied during bead-on-plate welding on 5 mm thick sheets on the face side of martensitic low transformation temperature (LTT) steel plates using gas tungsten arc welding (GTAW). The in situ visualization of austenitization upon welding and subsequent α’-martensite formation during cooling could be achieved with a temporal resolution of 2 s for monochromatic imaging using a single neutron wavelength and of 0.5 s for polychromatic imaging using the full spectrum of the beam (white beam). The spatial resolution achieved in the experiments was approximately 200 µm. The transmitted monochromatic neutron beam intensity at a wavelength of λ = 0.395 nm was significantly reduced during cooling below the martensitic start temperature Ms since the emerging martensitic phase has a ~10% higher attenuation coefficient than the austenitic phase. Neutron imaging was significantly influenced by coherent neutron scattering caused by the thermal motion of the crystal lattice (Debye–Waller factor), resulting in a reduction in the neutron transmission by approx. 15% for monochromatic and by approx. 4% for polychromatic imaging.

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Neutron Scattering in Metals

Melnikov

Reser

2018

Dynamic Spin-Fluctuation Theory of Metallic Magnetism

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Debye–Waller Factor in Neutron Scattering by Ferromagnetic Metals

Cited by 10 publications

References 29 publications

Lattice vibrations in the harmonic approximation

Lattice vibrations in the harmonic approximation

Time-Resolved Neutron Bragg-Edge Imaging: A Case Study by Observing Martensitic Phase Formation in Low Temperature Transformation (LTT) Steel during GTAW

Neutron Scattering in Metals

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