Neutron reflectometry

The neutron is an analytical method for the study of interfaces and thin layers . To do this, neutrons are blasted onto an interface and scattered there . The scattered neutrons are detected and evaluated. The basic principle is therefore comparable to other reflectometric methods such as X-ray reflectometry or ellipsometry , which, however, are based on the reflection of electromagnetic radiation .

The method is suitable for the acquisition of surface and interface information of a solid layer or layer system up to a depth of 150 nm. Materials with magnetic properties can be examined particularly well. The depth dependence of the mean neutron scattering length density results in a high resolution of about one nanometer, so that interdiffusion between adjacent layers of different isotopes can be detected. This “isotope sensitivity” is based on the fact that neutrons prefer to interact with atomic nuclei and not with the atomic shell like electromagnetic radiation.

functionality

For the measurement, a collimated neutron beam with a kinetic energy of a few hundredths of an electron volt is radiated onto a (very smooth) interface and the intensity of the reflected neutrons is measured using the angle of reflection ( directed reflection , angle of reflection corresponds to the angle of incidence). A corresponding neutron source , for example a spallation source , and a neutron guide are necessary for this. The shape of the intensity profile provides various information about the measured surface, such as the layer thickness, density or interface roughness.

According to Louis de Broglie's theory , microscopic particles such as neutrons can be described as waves of matter and assigned a characteristic wavelength . This wavelength depends on the momentum of the neutrons: ${\displaystyle p}$

${\displaystyle \lambda _{\text{Neutron}}={\frac {h}{p}}}$

where is Planck's quantum of action . For neutrons with a kinetic energy of a few hundredths of an electron volt, the De Broglie wavelength and thus the theoretical resolution is a few tenths of a nanometer . ${\displaystyle h}$

From a mathematical point of view, among other things, these relationships can be used to describe the reflection of neutrons similar to the reflection of electromagnetic radiation. This means that a complex refractive index is defined for the material and the principles known from optics are used (cf. law of refraction , Fresnel equations , Abelès matrix formalism and Parratt recusion formula ). The form of the representation is appropriate because, as in the X-ray range, the real part of the refractive index is very close to 1. In the literature, one often only finds the so-called dispersion given. It is usually on the order of 10 ⁻⁶ . The absorption coefficient can be neglected in many cases, since it is except for strongly absorbing isotopes such as. B. boron or lithium is in the order of 10 ⁻¹² . ${\displaystyle n=1-\delta +i\beta }$ ${\displaystyle \delta }$

Similar to X-rays, due to the minimally lower real part of the refractive index than with air / vacuum , external total reflection also occurs with neutrons when the neutrons strike the smooth sample very flat, i.e. at angles of incidence close to 90 ° (from the perpendicular), so-called grazing Incidence. This measurement setup is recommended, since otherwise the intensity of the reflected neutrons would be too low or the losses would be too high for an evaluation.

variants

In addition to the directed reflection, there are two other sampling techniques with grazing incidence:

1. Scattering in the plane of incidence ( off-specular scattering ) and
2. Scattering perpendicular to the plane of incidence.

The methods differ not only in the way in which the neutron spectrum is recorded and which scattering mechanisms work, but also in the depth of information. As mentioned above, the information depth in the case of directional reflection is in the range from 3 nm to 100 nm (sometimes also 150 nm). In the case of scattering perpendicular to the plane of incidence, neutron reflectrometry provides similar depth information (3 nm to 100 nm). The off-specular scattering technique, which provides information from a depth of 600 nm to 60 µm, is different.

presentation

In contrast to "optical" reflectometry, the measurement results are usually not presented in the form of the degree of reflection, absorption or transmission depending on the angle or wavelength, but rather the degree of reflection (reflectivity) as a function of the momentum transfer (in the z-direction, perpendicular to the interface). The momentum transfer vector describes the change in the neutron momentum when it is reflected on the material and can be determined mathematically as follows. ${\displaystyle q_{z}}$

${\displaystyle q_{z}={\frac {4\pi }{\lambda }}\sin(\theta )}$

Here is the De Broglie wavelength and the angle of incidence of the neutrons. ${\displaystyle \lambda }$ ${\displaystyle \theta }$

See also

• Neutron diffractometry

literature

• C. Fernion, F. Ott, A. Menelle: Neutron Reflectometry . In: Jean Daillant, Alain Gibaud (Eds.): X-ray and Neutron Reflectivity: Principles and Applications . Springer, 2008, ISBN 978-3-540-88587-0 ( limited preview in Google book search).
• Neutron Reflectometry . In: Masahiko Utsuro, Vladimir K. Ignatovich (eds.): Handbook of Neutron Optics . John Wiley & Sons, 2010, ISBN 978-3-527-62879-7 , pp. 39 ff . ( limited preview in Google Book search).

Web links

• Adrian Rühm, János Major, Helmut Dosch: Neutron research on low-dimensional materials. Retrieved October 26, 2018 . 

Individual evidence

1. ↑ Investigation of thin layers. Helmholtz-Zentrum Berlin (HZB), accessed on May 2, 2016 . 
2. ↑ Methods - reflectometry. Neutron Research Committee, accessed November 26, 2012 . 
3. ↑ ^{a b c} Jörg Fick: Characterization of biocompatible surfaces by means of vibration sum frequency spectroscopy and neutron reflectometry . 2005 ( online dissertation, Heidelberg University, Faculty of Chemistry and Geosciences).
4. ↑ Florin Abelès: La théorie générale des couches minces . In: Journal de Physique et le Radium . tape 11 , no. 7 , 1950, pp. 307-309 , doi : 10.1051 / jphysrad: 01950001107030700 .
5. ^ LG Parratt: Surface Studies of Solids by Total Reflection of X-Rays . In: Physical Review . tape 95 , no. 2 , 1954, p. 359-369 , doi : 10.1103 / PhysRev.95.359 .
6. ↑ C. Fernion, F. Ott, A. Menelle: Neutron Reflectometry . In: Jean Daillant, Alain Gibaud (Eds.): X-ray and Neutron Reflectivity: Principles and Applications . Springer, 2008, ISBN 978-3-540-88587-0 ( limited preview in Google book search).