Physics Sample Assignment

Studies of surface and interface phenomena by grazing angle neutron reflectometry:

Introduction and theory:

Physics Assignment Help Order Now Grazing-angled neutron reflectometry is a technique for studying the roughness, the interfacial diffusions and the chemical contaminations at the surfaces and the interfaces of the both liquids and solids samples. Many of these classical phenomenons in the optics are demonstrated with the thermal and the cold neutrons like the total reflection, the refraction, the diffraction and the interference. These interactions between de Broglie waves and condensed matters are generally described by the indices of the refraction having same mathematical expressions as that for the X-rays. Thus taking into the account this intrinsic characteristic of neutron wave, information which is obtained using the new technique is unique. some examples are given which illustrates possibilities of these techniques for studying the thin film and the stratified media. Neutron reflectometry is laboratory technique used for measuring structure of the thin film, very similar to often complementary technique like the X-ray reflectivity's and the ellipsometry's. These techniques provide the valuable information in the wide variety including the scientific and the technological applications which includes the chemical aggregation, the polymer and the surfactant adsorption, the structure of the thin films magnetic systems, the biological membranes and many others. These techniques involve the shining of highly collimated beams of neutron impacted on extremely flat surfaces and also measuring intensities of the reflected radiations as function of the angles or neutron wavelengths. The exact and accurate shapes of reflectivity profiles provide the detailed information of the structures of the surfaces that includes the thickness, the density and the roughness of any of the thin film which is layered on substrates.


The Neutron reflectometry can be said to be the specular reflection technology, where angles of incident beam are equal to angles of reflected beam. These reflections are generally described in the terms of the momentum transfer vectors, which are denoted by qz and describe changes in the momentum of the neutrons after getting reflected from various materials. By the convention z axis is taken as film's normal directions and for the specular reflections, the scattering vector is having only the z-components. The typical/normal neutron reflectometry plots display reflected intensity which is relative to incident beam in form of function of scattering vector.

The wavelengths of neutrons that are used for the reflectivity are typically of the orders of 0.2-1 nanometers (2-10 Angstroms). These techniques require the neutron sources, which can be either research reactors or spallation sources that are based on the particle accelerators. Like all neutron's scattering techniques, the neutron reflectometry also is sensitive against the contrast which arises from the different nuclei than as compared with the electron density (measured in the x-ray's scattering). This thus allows this technique in differentiating between the various isotope of the elements. Neutron reflectometry also measures neutron's scattering long density (SLD). Thus it can also be used for accurately calculating the material density provided that the atomic compositions are also known.

The other reflectivity technique like the optical reflectivity, the x-rays reflectometry operates with the same general principle/theory; the neutron measurement is advantageous in few other significant ways. As the technique also probes the nuclear contrast along with the electron density, it's more sensitive in measuring some of the elements, generally the lighter elements like carbon, hydrogen, oxygen and nitrogen. Its sensitivity to the isotopes allows contrasts which are greater and selective in enhancement in some systems of the interests having the isotopic substitutions and the multiple experiment that differs only by the isotopic substitutions that can be used in resolving the phase problems which general to the scattering techniques. Moreover, the neutrons are very highly penetrating, non-perturbing also which thus allows great flexibilities in the sample environment and also use of the delicated sample materials like biological specimen. In contrast to the x-rays exposures, this can cause damage in some materials while laser lights can cause modification in some materials like photoresists. The optical technique may include the ambiguity because of birefringence or the optical anisotropy, which these complementary neutron's measurement can resolve well. Dual polarisations interferometry is the one optical method that provides the analogous result to that of neutron reflectometry in comparable resolutions although underpinning mathematical models are somewhat simpler as it can derive only the thickness/birefringence meant for the uniform layer's density.

The disadvantages of the neutron reflectometry are inclusive of higher cost of required infrastructure, facts that some of the materials may change to radioactive when being exposed to beams and insensitivity toward chemical states of the constituent atoms. Also, relatively lower fluxes and the higher backgrounds of these techniques compared to the x-rays reflectivity limits maximum value qz can attain thus measurement resolution.

Instrumentation: Technically, the neutron reflection experiment is very simple.

There are two ways of performing the experiment:

  1. the reflectivity of a mono- chromatic neutron beam is measured as a function of the incidence angle,
  2. the reflectivity of a fixed incidence angle beam is measured as a function of the neutron wavelength, this method is called the time-of-flight technique. Our neutron reflectivity measurements were performed with the latter technique. Accurately, it consists of a single chopper with a wavelength band from 3 to 30 A. Its angular speed defines the repetition rate. The deflection of the polychromatic incident neutron beam is obtained by using four Ni mirrors located just before the sample. The neutron beam reflected from the sample surface is detected using a 3He gas X-Y multi detector (128' 128 pixels with a pixel size 1.5 x 1.5 ram2). We use a Hc-Ne laser beam along the neutron flight path for the initial alignment of the sample (liquid or solid samples). Ex0crlments were performed at a grazing angle, of the order of 2.2 x 10 ^2 tad. The intensity of the specular reflected beam is recorded versus neutron wavelength or momentum K.
Experimental results:

Bulk material:
The neutron reflectivity curve of a polished borosilicate glass sample is shown which represent a decimal logarithmic plot versus momentum K - 2~- gin 011/A. The grazing angle was 00 = 2.5 10 2 rad. We discern two regions: the total reflection plateau (K < K~ = 2"n- sin Oo/, ~ c) and the vitreous region (K~K). the experimental reflectivity is always lower than the theoretical one which corresponds to the bulk substrate. For simulating the expert-mental neutron reflectivity curve, one has to consider an anti-reflection homogeneous thin layer at the top of the bulk glass. This surface layer is characterized by an index of refraction n~L (or neutron scattering length density Pb~l-1.1 10 -6, ~-z) and a thickness d~l = 50 A. For the bulk substrate the refractive index is n~ (or a neutron scattering length density J~'bsu h = 4.2 10-~ ~-z). This surface layer is due to mechanical polishing. The high difference between Hb,i and .,-]~b,,h indicates that the surface layer is very hydrated.

Thin films: penetration depth:
The absence of any charge or accompanying electric field enables the neutron to penetrate most materials with relative ease. For illustrating the high penetration depth of neutron waves relative to the X-ray waves, a thin titanium film deposited by thermal evaporation on Borkron glass is studied. The aimed thickness was dTi = 500 A. The GANR experiment is carried out at On = 1.50 10 2 rad. The theoretical value of the nuclear scattering length density J//bTi is - 1.95 10-0 ~-z. At K < K:, the de Broglie neutron waves are totally reflected. This total reflection phenomenon is imposed by the Borkron substrate whose neutron scattering length density is positive (the thallium possesses a negative neutron scattering length density and thus it cannot satisfy the total reflection relation). For K K e, fringes are observed. A comparison of the experimental data with the theoretical fringes shows that a particular minimum at K, = 0.74 x10-:~-~ near the total reflection plateau does not figure in the theoretical profile. This is attributed to a layer situated between the titanium layer and the bulk glass substrate. The simulation is done by taking a stack of nine layers deposited on the Borkron glass substrata. The top of the titanium layer (zone 1) is gradually contaminated and constrains both titanium and other elements whose scattering length density is positive. Its thickness is around 105 A. Zone 2 is composed of quasipure titanium whose thickness d, is of the order of 351), ~. Zone 3 is a sub layer less dense than the bulk substrate whose extension is d~=631, ~. One can note that the experimental thickness of the contaminated titanium layer found by simulation agrees with the theoretical value, being, respectively, d~! ~, = 455 A against d~th~ = 500 A. The total probed thickness is then dk, ~ = 1086 A. Neglecting the dispersion effect inside the layers, the penetration depth L~ is considerably greater than the thickness of the stack d~, which is given by L~, = 2 dJO. This gives 7.4 #m.

Thin films: oxidation effects:
The change in the sign of the neutron scattering length density makes the GANR very sensitive to oxidation and hydrogenation effects. The sample studied consists of a thin film titanium layer deposited on to Borosilicate glass. The expected layer thickness is approximately d~' ~- ltl00 A. The simulation shows that we are dealing with a stack on six layers laid down on the massive substrate. As it is indicated, the simulation, ~b(z) profile is always positive, this indicated that the titanium is oxidized. Moreover, Jb(z) decreases gradually from the thin-film-substrate interface to the air-thin-film interface. This suggests that the oxidation phenomenon decreases when the titanium film grows. The small increase of Jt"b(z) at the air-titanium-film interlace is due to an atmospheric alteration. The simulation gives a total thickness of 460 Angstrom which is less than the expected value, indicating a calibration error during the deposition process.

Multilayer: Magnetic effects:
To illustrate multilayer magnetic effect, a 10(Ni-Ti)/layer horusilieate glass multilayer was studied. The expected thickness of nickel and titanium layers measured b v a crystal quartz oscillator are 400 Angstrom. To investigate the overall characteristics of this periodic stack, the monochromator is first scanned on the non-polarized neutron reflecometer DESlR at 2.4 x l0 rad. Bragg order was detected. Assuming uniform densities and sharp boundaries, the nickel and titanium layers can be considered to be nominally about d~ = d~ n = 330. The simulated value of the mullibilayer period is then A^sin = 660 against A^the = 800 A which is the theoretical value. Taking into ac- count the great difference between the simulated and the theoretical values, this suggests that dif- fusion has taken place during the sputtering as in the previous example. The simulated neutron scattering length densities are +9.4 10^6 and -0.5 10^6 respectively. This confirms the diffusion of nickel into titanium. Second, stimulated neutron measurements were carried out. It should be noted that the [+] Bragg peaks are shifted relative to the [-] ones. Moreover, the [+ ] spin reflectivity becomes larger than that of the [-] spin at the filth-order Bragg position at KB(= 5) = 0.51 10^-2. This is most easily explained by assuming that some inter-diffusion occurs between the nickel and titanium layers which is in agreement with the previous unpolarized GANR results. As is indicated above, the critical parameter are different and their average values are 0.31 10^2 and 0.27 10^2 respectively. This indicates that Nickel is also magnetic in the thin film structure.


From a formal point of view, the de Broglie cold neutron waves behave as electromagnetic waves in the S polarization state. It is then permitted to apply all the classical optics computation for S electromagnetic waves in neutron optics and particularly for stratified media. Due to some key properties of neutrons, the GANR technique is sensitive to different features at solid surfaces and interfaces. The simple relation between the refractive index and the chemical composition means that neutron reflectivity profiles probe surface and interfacial structures more directly than light reflectivity. The irregular variation, of the neutron scattering amplitude with the atomic number allows the identification of light elements in some heavy compounds with much greater certainty. The variation of the neutron scattering amplitude with the mass number allows the identification of isotopes of a given element; especially in the case of hydrogen and deuterium. Then, the neutron reflectometer is an excellent probe tool in biology and polymer surface studies. The variation of the sign of the neutron scattering amplitude allows to determine easily the way of the interfacial diffusion and the degree of contamination in thin films and stratified media. The neutron magnetic interaction is also a key property. The polarized neutron reflectometry is a good tool for magnetic surface studies in magnetic multilayer and superconductors. It is therefore fortunate that the absorption coefficient of the neutron beam is small and the neutrons are indeed able to penetrate larger samples. Finally, a few previous examples show clearly the capabilities of this new technique for the investigation of surface and interface phenomena.

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