Neutron Specular Reflectivity

The theory and analysis of NEUTRON SPECULAR REFLECTIVITY is a major research interest in the NIST Center for Neutron Research.
  • Experimental Demonstration of Phase Determination in Neutron Reflectometry by Variation of the Surrounding Media
    C.F. Majkrzak, N.F. Berk, C.W. Meuse, and V. Silin Proc. of Sixth Surface X Ray and Neutron Scattering Conference (6sxns), Nordwijkerhout, Sep., 1999. To appear in Physcia B.

    The method of phase determination using surround variation was applied to several thin films and the resulting real parts of the reflection coefficients, Re r(Q), were inverted to retrieve the veridical scattering length density (SLD) profiles within the spatial resolution of the measurements (about 20 A). In one experiment two backings, air and heavy water, were used. In another, Si and sapphire served as two frontings. The SLD profiles thus obtained were in excellent agreement with expectations. A new method of diagnosing the quality of measured films using the imaginary part of a measured reflection coefficient is also given. It is proved here that Im r(Q) for a perfect but arbitrary film necessarily has a regular sequence of zeros and that this zero set is sensitive to imperfections, such as large-scale lateral inhomogenieties. A simulated example is given.

    This work was a cooperative effort among scientists in the NCNR (Majkrzak and Berk) and the Biotechnology Division (Meuse and Silin) at NIST.

  • Using Polarized Neutrons to Determine the Phase of Thin Film Structures
    A. Schreyer,C.F. Majkrzak, N.F. Berk, H. Gruell, and C.C. Han. Proc. of Frontiers in Neutron Scattering, Tokyo, Nov., 1998. To appear in Journ. of the Phys. and Chem. of Solids, (1999).

    The method of phase determination using polarized neutrons was applied to a 400 A thick polymer blend film (dPB/PI) on a reference consisting of sputtered Si on ferromagnetic Fe. A new phase fitting procedure using parametric B splines was developed to unambiguously determine the imaginary part of the reflection amplitude from noisy data and to extract the scattering length density profile of the polymer film from two polarized neutron reflectivity spectra. The results confirm a preferential adsorption of the hydrogenous component of the dPB/PI blend at both film edges at room temperature.

    This continuing study is a collaboration of the NCNR (Schreyer, Majkrzak, and Berk) and the NIST Polymers Division (Gruell and Han).

  • Inverting Neutron Reflectometry from Layered Film Structures Using Polarized Neutron Beams
    C.F. Majkrzak and N.F. Berk. Physica B, (1999) in press.

    Experimental applications of the reference layer phase determination method and reflectivity inversion are shown, using a 2-measurement variation of the original 3-measurment procedure. Systems studied include a Au layer over a buried ferromagnetic Fe reference layer, and an organic film on Au over a buried ferromagnetic Fe layer. The single buried ferromagnetic layer effects two references when polarized neutron beams are used.

  • Exact Determination of the Phase in Neutron Reflectometry by Variation of the Surrounding Media
    C.F. Majkrzak and N.F. Berk. Phys. Rev. B 58, 15416 (1998).

    We give an extension of the phase determination method which utilizes controlled variations of the scattering length density of the incident and/or substrate medium instead of reference layers of finite thickness. The procedure algebraically yields the real part of the reflection amplitude uniquely from two reflectivity measurements, which is sufficient for inversion. This technique is of practical importance for thin-film systems involving either gas-liquid or solid-liquid interfaces in which the scattering length density of the liquid can be varied in a known way, as in deuterated aqueous media.

    Experiments are underway at the NCNR to test the surround variation method.

  • Phase Determination and Inversion in Specular Neutron Reflectometry
    C.F. Majkrzak, N.F. Berk, J.A. Dura, S.K. Satija, A. Karim, J. Pedulla, and R.D. Deslattes. Physica B 248, 338 (1998).

    Experiments have been performed to test recent phase determination methods developed at NIST for scattering length density profiles of general shape and for the special case of symmetric fims. Using layers of Cu, Ni, and Mo as references, the real and imaginary parts of the complex reflection amplitude were measured from neutron reflectivities for an asymmetric composite film consisting of deuterated polystyrene and Si. The reflection amplitude was also measured from neutron reflectivity without references for a symmetric deuterated polystyrene film. These amplitudes were inverted using the Gel'fand-Levitan-Marchenko equation to produce scattering length density profiles for the films studied. The inverted profiles compared reasonably well to the expected potentials, and we conclude that such methods are practical with current instrumentation.

    This work was a cooperative effort among scientists in the NCNR, the Polymer Division, and the Physics Division at NIST.

    These experiments are also discussed in the Proceedings of the International Conference on Neutron Scattering, Toronto (August, 1997), Physica B in press.

  • Inverting Specular Neutron Reflectivity from Symmetric, Compactly Supported Potentials
    N. F. Berk and C. F. Majkrzak, Proc. Int. Symposium on Neutron Optics and Related Research Facilities, Kumatori, 1996. J. Phys. Soc. Jpn., 65, Suppl. A, 107 (1996).

    A method is described for inverting specular neutron reflectivities from real symmetric, compactly supported potentials of known thickness. For such potentials, the phase of the complex reflection coefficient is equal to the phase of the transmission coefficient plus a known phase shift and thus can be retrieved from a single measurement of reflectivity using a logarithmic dispersion relation for the transmission. The resulting reflection coeffieicent can be inverted to find the potential by solving the Gel'fand-Levitan-Marchenko integral equation. The method is general, to the extent that symmetric potentials can be formed by abutting two identical specimens of a film of interest.

    Experiments are in progress to test this method and the one described below. Preliminary reports of these were given at the 1997 March Meeting of the APS and at the Fifth Surface X-Ray and Neutron Scattering Conference in Oxford (July, 1997), and at the International Conference on Neutron Scattering in Toronto (August, 1997).

  • Exact Determination of the Phase in Neutron Reflectometry
    C. F. Majkrzak and N. F. Berk, Phys. Rev. B 52, 10827 (1995).

    By using a known reference layer having three tunable values of scattering density, an exact determination of the complex amplitude R=Re R+iIm R for neutron specular reflection can be made for any unknown real potential (i.e., no absorption). This straightforward yet remarkable general result is valid even in the dynamical regime (where the Born approximation fails) and makes it feasible to consider direct inversion methods for obtaining the scattering length density profile normal to the reflecting surface.

    An equivalent method was found independently and published in tandem by V.O. deHaan, A.A. van Well, S. Adenwalla, and G.P. Felcher, Ibid, p. 10830.

    The inverse scattering problem using the Gel'fand-Levitan-Marchenko equation is discussed in the paper on symmetric potentials.

  • Using Parametric B Splines to Fit Specular Reflectvities
    N. F. Berk and C. F. Majkrzak, Phys. Rev. B51, 11296 (1995).

    Parametric B-spline curves offer a flexible mathematical description of scattering length density profiles in specular reflectivity analysis. Profiles mixing smooth and sharp features can be defined in low dimensional representations using spline control points in the density-depth plane which provide graded local influence on profile shape. These profiles exist in vector spaces defined by B-spline order and parameter knot set, which can be systematically densified during analysis using the Oslo spline refinement algorithm. An interactive fitting strategy using the Nelder-Mead simplex method is described.

    The lack of uniqueness inherent in profile determination is discussed.

    References to related methods are given.

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Last modified: October 5, 1999