Simulation project reflectometer: A neutron reflectometer

In this project you should build a model of a Time-Of-Flight (TOF) neutron reflectometer, simulate and analyse the data for a sample at solid/liquid interface. The sample that will be simulated is a lipid bilayer deposited on a silicon crystal in contact with D2O. In a TOF reflectometer the sample is illuminated with a polychromatic neutron beam, this allows for covering the q-range of interest with a limited number (typically 2 or 3) of sample angles.

Question 1 - Determining the scattering angle

Before starting building the reflectometer you should calculate which angles are required to cover the q-range (\(0.005 - 0.25 Å^{-1}\)) with the wavelength range of \(2-30Å\). Two angles should be sufficient to cover the q-range of interest for the sample and at the same time have a good overlap region between the data.

Question 2 - The source-guide system

In a TOF reflectometer, the sample is illuminated with a polychromatic neutron beam produced by a continuous neutron source (neutron reactor) or a spallation source. In this project you should simulate a continuous source (source_simple) producing neutrons in the wavelength range \(2-30Å\). This wavelength range will allow you to cover the appropriate q-range for the sample characterization with only two different sample angles. The source could have \(0.1\) m height and \(0.035\) m width. The neutrons produced by the source will enter in the guide with aperture \(0.080\) m height and \(0.015\) width on both ends. The guide should be straight, \(26\) m long, and with guide material \(m = 2\).

Question 3 - Disk chopper

The neutrons produced by the source must be divided in pulses in order to calculate the TOF at detector. For this purpose, a chopper-system is used to create the neutron pulses. In this project, you should introduce after the guide a \(0.4\) m radius disk chopper with one slit and the following settings:

• \(theta = 45\)
• \(yheight = 0.1\)
• \(nu=16.7\)
• \(isfirst=1\)

Question 4 - Slit-system

The beam needs to be collimated in the horizontal direction, while the divergency of the beam can be wider in the vertical direction. This will allow to illuminate a large area of the sample (to maximize the reflected intensity) and at the same time minimize the uncertainty on the neutron beam incident angle at the surface. Typically, a pair of slits is used to control the beam collimation. You should set one slit after the disk chopper

• \(xwidth=0.044\)
• \(yheight=0.56\)

and a second slit

• \(xwidth=0.005\)
• \(yheight=0.045\)

at \(2\) m after the first slit. These slit settings are suitable for a horizontal reflection plane (vertical sample). You can verify the collimation of the beam after the second slit by using a divergence monitor.

Question 5 - Sample

The sample is normally placed \(\sim 0.010\) m after the second slit. In a solid-liquid experiment the sample is deposited on a flat silicon crystal (e.g. \(50x50\) mm surface area), which is sealed in a cell including a plastic plate facing the reflective surface of the crystal. The plastic plate has an internal serpentine that allows liquids to be injected in the cell. 1 mm of liquid is normally present on top of the reflective surface due to a teflon O-ring placed between the crystal and the plastic plates. The sample is placed vertically with respect to the beam. In this project you should simulate the reflectivity cell including the silicon crystal and the sample deposited on its surface (the lipid bilayer) by using the mirror component and by loading in such component a sample file. You should set the size of the mirror to \(50\) mm both for its width and height and \(m=1\).

Note that by default the mirror is placed with the reflective surface perpendicular to the beam. In this simulation you should rotate the mirror in order to initially place it parallel to the neutron beam. In this condition you can only measure the transmitted beam. By further rotating the mirror you should be able to collect both the reflected and transmitted beam (see Question 6 - Detector).

In a reflectometry experiment, the sample is rotated in order change the incidence angle of the incoming beam. Hence you should first perform the simulation twice, each time for one of the sample angles calculated above. You can change the sample angle either by rotating the mirror with respect to the incoming beam or by placing an arm immediately before the mirror to deflect the incoming beam. Both these options should give the same final result.

Question 6 - Detector

In a TOF reflectometer the neutrons reflected by the sample will be detected by a PSD-TOF detector, on which it is possible both to observe the shape of the reflected beam and to measure the neutron TOF. The neutrons hitting the sample will be both reflected and transmitted by the sample, so two different signals should be expected on the PSD detector. The reflection signal can be easily distinguished from the transmission signal as the first one will change position on the detector by rotating the sample. On the other hand, the transmission signal will appear always at the same position. The simultaneous measurement of the both the reflection and transmission signal is typically used during sample alignment. However, during the actual reflectivity measurement the transmission signal is normally blocked.

In this project you should place a PSD-TOF monitor at 2 m from the sample. The detector area should be large enough to collect both the reflection and transmission signals at both the two sample angles of interest. Hence, the detector should have the following parameters

• \(nq=200\)
• \(xwidth=0.8\)
• \(yheight=0.8\)
• \(T\_zero=0.0\)
• \(restore\_neutron=1\)

After you verified the presence of both the transmitted and the reflected beam in the detector image, you should place a beamstop

• \(xmin=-0.02\)
• \(xmax=0.02\)
• \(ymin=-0.1\)
• \(ymax=0.1\)

in front of the detector in order to block the transmitted beam.

An alternative experiment can be run without the beamstop in front of the detector, but by having a smaller detector and by moving it according to the sample angle in order to collect exclusively the reflected beam. In this project you can reproduce this situation by placing an arm with twice the sample angle with respect to the incoming beam direction and setting the PSD-TOF monitor along this arm. You need to do only one of the two settings. You can obtain information on the neutrons reflected by the sample in terms of their wavelength instead of their TOF by using a lambda monitor with the same size and position of the PSD-TOF.

Question 7 - Data reduction

The intensity measured by the detector as function of the TOF is the intensity of the reflected neutrons. In order to obtain the \(R\) vs \(q\) curve. the reflected intensity must be normalized by the incoming beam intensity.

In a real experiment the sample is placed in such a way that the neutrons will initially go through the silicon crystals, then hit the interfaces between the support surface and the sample and subsequently enter into the liquid (water or buffer) on top of it. At each of those interfaces the neutron beam will get reflected and hence it will pass again through silicon and then be detected by the detector. This configuration has a lower background than having the neutrons reaching the sample/support interface passing through water. Hence the incoming beam at the first interface is the neutron beam transmitted through silicon. In order to normalize the data, the transmission through silicon is measured at the beginning of the experiment, and the reflected intensity is then divided by it to obtain the reflectivity.

An alternative way to normalize the data is calculating the mean intensity below the critical edge and then use that value to normalize the reflected intensity. This second method is based on the assumption that below the critical edge the neutrons are totally reflected and hence the intensity measured below the critical edge actually corresponds to the incoming intensity.

In this project you should use this latter method to normalize the simulated data. This will give you the normalized reflectivity. Subsequently, you should convert the wavelengths measured by the wavelength monitor (which is placed after the TOF monitor) in \(q\) to obtain the \(R\) vs \(q\) curve.