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

International Tables for Crystallography (2006). Vol. C, ch. 2.9, pp. 129-130

Section 2.9.7. Applications of neutron reflectometry

G. S. Smitha and C. F. Majkrzakb

aManuel Lujan Jr Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

2.9.7. Applications of neutron reflectometry

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2.9.7.1. Self-diffusion

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One of the simplest, yet powerful, examples of the use of neutron reflectivity is in the study of self-diffusion. Most techniques to measure diffusion coefficients rely on chemical and mechanical methods to measure density profiles after a sample has been annealed. Then a model for the diffusion is assumed, and the coefficients are calculated. Using standard techniques, researchers are unable to detect the movement of an atom through a sample of like atoms. However, using single bilayers of amorphous 10B and 11B, it was shown (Smith, Hamilton, Fitzsimmons, Baker, Hubbard, Nastasi, Hirvonen & Zocco, 1992[link]) through neutron-reflectivity measurements that the diffusion of boron in boron could be measured by studying the density profile (see Figs. 2.9.7.1[link] and 2.9.7.2[link] ) of one isotope in the other as a function of annealing time. Also, because of the sensitivity of the technique to the interfacial density profile, it was found that standard Fickian diffusion models could not explain the measured density profiles.

[Figure 2.9.7.1]

Figure 2.9.7.1 | top | pdf |

Measured neutron reflectivities from boron bilayers [from Smith et al. (1992[link])].

[Figure 2.9.7.2]

Figure 2.9.7.2 | top | pdf |

The fitted real part of the scattering density profiles for the measured reflectivities of Fig. 2.9.7.1[link]. Note the pinning of the concentration of 10B at the interface [after Smith et al. (1992[link])].

2.9.7.2. Magnetic multilayers

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In order to understand interlayer coupling mechanisms, it is necessary to know what the magnetic superstructure is for a given nonmagnetic spacer layer thickness and/or applied field strength. Fig. 2.9.7.3[link] shows the spin-dependent reflectivities for a Co/Cu (111) multilayer along with the nuclear (Nb) and magnetic (Np) scattering-density profiles deduced from the data of Schreyer, Zeidler, Morawe, Metoki, Zabel, Ankner & Majkrzak (1993[link]). In this specific case, the in-plane ferromagnetic Co layers are themselves coupled ferromagnetically across the nonmagnetic Cu, all at a constant angle.

[Figure 2.9.7.3]

Figure 2.9.7.3 | top | pdf |

Co/Cu(111) spin-dependent reflectivities (top). Nuclear (Nb) and magnetic (Np) scattering densities (bottom). Also shown is the (constant) moment direction [after Schreyer et al. (1993[link])].

2.9.7.3. Hydrogenous materials

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There are a substantial number of applications of neutron reflectometry in the study of hydrogenous films and multilayers, including diblock copolymer, surfactant, Langmuir–Blodgett, self-assembled monolayer, and lipid bilayer films. Reviews of the extensive research that has already been done have been written by Russell (1990[link]) and Penfold & Thomas (1990[link]). Only one specific example will be given here.

Fig. 2.9.7.4[link] shows neutron reflectivity data and the corresponding density profile for a Langmuir–Blodgett film composed of alternating bilayers of deuterated and hydrogenated stearic acid [after Wiesler, Feigin, Majkrzak, Ankner, Berzina & Troitsky (1995[link])]. Also shown in Fig. 2.9.7.4[link] is the scattering-density profile for the same sample as seen by X-rays. It is obvious that the X-rays are more sensitive to the high-Z barium in the head group, whereas the neutrons are especially good at distinguishing the degree of mixing between adjacent hydrogenated and deuterated hydrocarbon tails. This is a good example of the complementary nature of neutron and X-ray reflectivities.

[Figure 2.9.7.4]

Figure 2.9.7.4 | top | pdf |

(a) Measured neutron reflectivity for the Langmuir–Blodgett multilayer described in the text along with the fit. (b) Both corresponding neutron and X-ray scattering density profiles. The X-ray reflectivity is more sensitive to the high-Z barium in the head groups whereas the neutron reflectivity can distinguish mixing between adjacent hydrogenated and deuterated hydrocarbon tails [after Wiesler et al. (1995[link])].

References

Penfold, J. & Thomas, R. K. (1990). The application of specular reflection of neutrons to the study of surfaces and interfaces. J. Phys. Condens. Matter, 2, 1369–1412.
Russell, T. P. (1990). X-ray and neutron reflectivity for the investigation of polymers. Mater. Sci. Rep. 5, 171–271.
Schreyer, A., Zeidler, T., Morawe, C., Metoki, N., Zabel, H., Ankner, J. F. & Majkrzak, C. F. (1993). Spin polarized neutron reflectivity study of a Co/Cu superlattice. J. Appl. Phys. 73, 7616–7621.
Smith, G. S., Hamilton, W., Fitzsimmons, M., Baker, S. M., Hubbard, K. M., Nastasi, M., Hirvonen, J.-P. & Zocco, T. G. (1992). Neutron reflectivity study of thermally-induced boron diffusion in amorphous elemental boron. SPIE Proc. Ser. 1738, 246–253.
Wiesler, D. G., Feigin, L. A., Majkrzak, C. F., Ankner, J. F., Berzina, T. S. & Troitsky, V. I. (1995). Neutron and X-ray reflectivity study of Ba salts of alternating bilayers of deuterated and hydrogenated stearic acid. Thin Solid Films, 266, 69–77.








































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