La competencia profesional: definición, enfoque, perspectivas y modelos integrales

This section begins by discussing the motivation behind performing neutron diffrac- tion measurements. Following this, details of the user facility where these measure- ments took place are outlined. This includes specific information about the Spallation Neutrons at High Pressure (SNAP) diffraction beamline which is located at Oak Ridge National Laboratory (ORNL).

Motivation for neutron diffraction

Neutron diffraction is an elastic scattering process, where high energy neutrons in- teract with, and scatter off of atomic nuclei. In contrast with XRD scattering cross sections which scale with the number of electrons present per atom, the cross sections for neutron scattering do not scale with atomic number or isotope, but vary signif- icantly between different elements and isotopes. This means that unlike for XRD, some light elements, such as H2_{, B}11_{, and C, have relatively large scattering cross-}

sections [180]. Because of this, quality diffraction spectra with very high Q-space can be obtained for disordered light element structures, such as GC. These spectra can then be Fourier transformed so that details of interatomic distances can be extracted. This is the motivation for using neutron diffraction in this thesis.

The SNS facility and neutron production

This subsection provides a brief description of the SNS facility, starting with the initial ion source and going right through until the point where the neutrons enter experimental hutches. A labelled schematic drawing of the SNS facility is shown in Fig. 3.18(a).

Figure 3.18: (a) A schematic image of the SNS at ORNL. Image adapted from ref [186]. (b) The SNS instrument hall, showing the location of the liquid mercury target (black circle) and the SNAP beamline. Image adapted from ref [187].

The initial source produces a pulsed beam of H− ions with an energy of 2.5 MeV. These pulses are accelerated using a linac to 1 GeV where they pass through a stripper foil converting them to H+ _{ions before they enter an accumulation ring. While moving}

around the accumulation ring the ions are bunched into shorter, more intense pulses which are ∼1 µs long. 60 pulses per second are released from the accumulator ring

and are directed toward a liquid mercury target inside the SNS instrument hall, as shown in Fig. 3.18(b). The SNS instrument hall contains 18 individual beamlines which are spread radially around the liquid mercury target. Once the ion beam hits the target, neutrons are ejected with a large range of energies in all directions. Between the target and individual experimental beamlines the emitted neutrons must be “cooled” to remove the highest energy neutrons. This is done by passing them through a moderator. This cooling is the final step before the beam can enter into an individual experimental hutch [188].

The SNAP beamline and measurement acquisition

Shown in Fig. 3.19 is a schematic drawing of the experimental setup inside the hutch of beamline number 3 in the SNS experimental hall. This beamline is commonly referred to as SNAP.

Figure 3.19: A schematic drawing of the SNAP neutron diffraction stage adapted from ref. [189].

Pulses of neutrons emitted from the liquid mercury target in the centre of the SNS instrument hall enter the SNAP beamline hutch following the blue arrow shown in Fig. 3.19 toward the sample. A long parabolic guide comprised of KB mirrors is used to focus the neutron beam down to a∼2-3 mm spot on the sample [190]. If necessary, a hexagonal-BN collimator (or pinhole) can be inserted between the guide and the sample to make the spot size even smaller and to reduce air scattering, however this is a direct trade-off with a loss of flux. The sample can be aligned with the beam

using a high precision hexapod-stage, and both detectors can be moved independently radially around the sample to provide optimised Q-space collection [189].

Once the neutrons reach the sample some of them scatter and get collected at one of the two SNAP detectors, as shown in Fig. 3.19. These detectors are scintillator based Auger detectors with sub-mm pixels [191].

The fact that discrete pulses of neutrons are fed from the target towards the sample allows the use of a time-of-flight measurement technique. This is where the specific energy of each neutron can be determined by the time it takes for them to reach the detectors. By knowing both the scattered neutrons energy and which specific pixel detected the scattered neutron (corresponding to the scattering angle), d-spacings within the sample can be determined by a method of which I will now describe.

The wavelength of the scattered neutrons, λ, is inversely proportional to their momentum, P, and can be expressed as

λ= h

P =

h Mnν

(3.3)

where, h is Planck’s constant, Mn is the neutron mass, and v is the neutrons

velocity. This ν is simply a ratio of the distance the scattered neutron traveled to the detector, L, over the time it takes to get there,t. So by recognising this and also expressing the wavelengthλ in terms of Bragg’s law,

nλ= 2dhklsin(θ) (3.4)

it is possible to express the atomic d-spacings as

dhkl =

nh

2Mn

t

Lsin(θ) (3.5) which means that dhkl is proportional to

dhkl ∝ t

Lsin(θ) (3.6) Using this relation (Eq. 3.5), and multiplying the length, L, by the sine of half of the measured scattering angle, t can be used to calculate a d-spacing for each scattered neutron that reaches the detectors [189].

Reducing and analysing the data

The image projected onto the SNAP detectors will appear similar to the image shown in Fig. 3.20(a), where the blue sections at either side are a feature caused by the apparatus. Features such as these, along with any other background interference, can be removed with a mask (or digital filter) that is applied using the MANTID software package [192]. This mask removes the signal from specified pixels, as shown in Fig. 3.20(b).

Figure 3.20: A raw image of scattering data collected on the SNAP detectors (a) before and (b) after a mask has been applied. Image adapted from ref. [189].

All remaining counts are then binned to create an intensity spectrum that is relative to Q-space, which is related to dhkl by the simple formula

Q= 2π

d (3.7)

The resultant spectrum is referred to as the total intensity spectrum, I(Q), similar to the one shown in Fig. 3.20(a).

The I(Q) spectrum is then normalised relative to the number of neutrons produced by the target during the time of the scan. This is done to account for variations of scan length and fluctuating beam intensity between different experiments. If a background scan (or empty scan) has been taken it is subtracted from the I(Q) now. It is important that any normalisation procedures or masking are applied in the exact same method to the background scan before it is subtracted. All normalisation procedures and background removal steps are all undertaken using MANTID [192].

The data must then be normalised forλ-dependent factors. This is done by collect- ing a spectrum of polycrystalline vanadium, V(Q), which is an incoherent neutron scatterer. The sample data (after background subtraction) is then divided by the vanadium scan to generate a structure factor as follows

S(Q)∝ I(Q)−background

V(Q) (3.8)

The structure factor, S(Q), is then Fourier transformed to generate a radial dis- tribution function, G(r). This is a plot of intensity vs distance and can be used to determine co-ordination numbers, density, and interatomic spacings. This process was performed using a program called StoG, which is a function written using the reverse Monte-Carlo profile (RMC-profile) software package [193,194]. StoG accepts the S(Q) data and required Q-space range, and then generates G(r).