Toward the solution of the inverse problem in neutron reflectometry Page: 4 of 20
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
1. Introduction
Neutron reflection experiments are important in understanding the physics of many
surface and interfacial structures, in fields as diverse as polymers and magnetism [1-2].
The measurement of the reflected intensity (hereafter referred to as reflectivity) R(q)
as a function of the perpendicular component of the incoming wave vector q = 2n sin
0 / X, with k the neutron wavelength and 0 the reflection angle, provides information
about the atomic or magnetic density profile of the sample along its depth z. The
reflectivity is the square of the complex reflection coefficient rq). For a given
scattering-length density profile F(z). the reflection coefficient can be calculated
straightforwardly, e.g. by means of the optical matrix method [3]
F(z) = 4n N(z) (b(z) p(z)) -+ r(q) . (1)
Here, N(z) is the atomic number density and b(z) the average coherent scattering
length. If the reflecting sample is magnetized parallel to the interface, also the average
'magnetic scattering length', p(z) = Cp, contributes to 1(z), where g is the average
magnetic moment per atom in units Bohr magneton pB, and C = 2.70 fm/ps. The + and
- signs represent spin-up (neutron spin parallel to magnetization) and spin-down states,
respectively. If r(q) were known in amplitude and phase, the inversion of Eq.(1) can
in principle be.performed, and practical algorithms have been developed [4-9]. If the
phase is not known, as is the case in a standard reflection experiment where only R(q)
is determined, generally least-squares methods are used to determine t(z) [10-11], but
in general the solution is not unique. In the literature, methods to retrieve phase
information from the measured reflectivity are discussed [12-16]. For one reflectivity
profile these methods yield many solutions for the phase. stressing the non-uniqueness
of the solution. To decide which solution is correct, extra information is required. This
information could be knowledge of the structure as deduced from either its preparation
or its analysis by way of complementary depth-profiling techniques [17]. Another way
to get more information about the sample is the use of contrast variation in neutron
reflectivity as obtained for instance by isotopic substitution [18-19].
Phase information can be obtained by depositing the unknown (non-magnetic) film on
a magnetized reference substrate, and carrying out the measurements with polarized
neutrons- Sivia and Pvnn [20] and Majkrzak et al. [21] have shown schemes for
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
De Haan, V. O.; Van Well, A. A.; Sacks, Paul E.; Adenwalla, S. & Felcher, G. P. Toward the solution of the inverse problem in neutron reflectometry, report, August 1, 1995; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc694730/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.