Remote crystal alignment at cryogenic temperature for neutron scattering

Abstract

A non-magnetic sample stick for top-loading cryostats providing single crystal alignment for neutron scattering is described. This special stick, called Goniostick, allows to tilt crystals by $\pm 6^{\circ}$ in any direction with $\pm {0.02}^{\circ}$ precision over the 1.5–300 K temperature range. The sample inclination and rotation around the vertical axis are motorised and the sample height is adjustable manually. This Goniostick facilitates neutron scattering experiments and allows the alignment in sample environments which cannot be tilted.

Keywords

Neutron scattering sample environment goniometer

1. Introduction

The alignment of the lattice planes of single crystals relative to the scattering plane of neutron instruments is generally performed by inclining the sample environment with a goniometer placed on the sample table. Such goniometers are commonly available on diffractometers and triple-axis spectrometers and able to host heavy equipment. At the ILL, they are also non-magnetic to avoid the strong magnetic forces generated by the stray fields of large cryomagnets. Users tilt cryostats up to 10– $15^{\circ}$ and cryomagnets to only 2– $3^{\circ}$ to avoid touches between the internal radiations shields which would lead to immediate failure.

With the advent of large position sensitive detectors (PSD), it became possible to investigate single crystals with Time-of-Flight spectrometers. The flight chambers of these instruments being evacuated to avoid spurious diffuse scattering, the environments are fixed to a vacuum-tight flange centred on the sample axis and located at the top of the flight chamber. The construction of large vacuum-tight tilting mechanisms is not worth considering because of its cost and inability to operate with some environments.

The use of tilting mechanisms is also very limited when using vacuum boxes on diffractometers and three-axis spectrometers, cryomagnets and zero-field polarimeters like Cryopad [4] and muPad [2]. Vacuum chambers are as large as possible to reduce diffuse scattering. They often match the internal diameter of an oscillating collimator and sometimes contain optical components that cannot be tilted. In zero-field polarimeters, the sample volume is restricted and limits considerably the possibility to align the crystal. The inclination of a cryomagnet is risky and puts the field out of the vertical axis. In addition, it becomes important for many magnetic samples to have the possibility to correct for minute misalignments between sample crystallographic axes and applied field axis in-situ, i.e. without the pain of removing the sample from the magnet.

For these reasons, we constructed a non-magnetic sample stick providing in-situ remote alignment capabilities inside vacuum boxes, top-loading cryostats and cryomagnets. We present in the next sections the mechanical solution, the equations allowing to control remotely the inclination of the sample, and the performances measured on the time-of-flight spectrometer IN5 at ILL [6].

Fig. 1.

Overview of the goniometer head without the control rods. The combined rotations of the two identical levers provoke the inclination of the sample axis around a spherical surface.

2. Hardware design

The design of the Goniostick is based on the idea of Berneron et al. [1] who built a prototype eucentric goniometer head in the 80s. The sample is glued on a sample holder mounted on an axis crossing a spherical reference surface (cupola). The inclination is performed by two right angled levers acting on this axis. As shown in Fig. 1, when rotating around their orthogonal horizontal axes, the levers displace orthogonal horizontal rods engaged in grooves made in the axis of the sample holder. Berneron’s prototype was made from stainless steel and the levers were driven with rotating rods coming from the top of the cryostat and attached to the levers with nylon cables. The system presented here is an evolution of this prototype:

The body of the goniometer is more compact (Ø36 mm) to fit inside most ILL cryostats and cryomagnets. It is much lighter and machined in a bar of rigid aluminium alloy EN AW-5083 to reduce the cool-down time, ensure rigidity and allow its usage in magnetic fields. It is also designed to host a Cernox CX1050-AA thermometer near the sample whilst protecting the wires.

The translation of the two control rod assemblies was redesigned to reduce heat load, improve precision and tightness. Previously, the translation was performed by screwing Ø4 mm rods in threads located in the cold region. These rods are replaced with rigid tubes translating in guides inside the sample stick between the room-temperature sliding seal and the bottom sliding guide. The translation is performed manually with micrometer screws or remotely with miniature linear translation stages from Newport [5]. At the top, springs maintain each tube in high position against the piston of the linear translation. A sphere is placed between the piston and the tube to prevent friction and the tightness is ensured with O-rings placed around the pistons. At the bottom of the tubes, similar rods with tuneable height extend the tubes down to the levers. With this design, it is possible to exchange the linear translation stages without dismounting the stick from the cryostat.

The levers are not fully cut out to form a $90^{\circ}$ inner angle and machined in a block of 316L stainless steel to gain in robustness and precision. The actuation of the sample holder is performed with Ø1 mm tungsten carbide rods placed across a groove. The levers axes are made from CuBe and the translation of each control rod assembly is now converted to the rotation of a lever using tungsten carbide pins trapped in grooves instead of nylon wires.

The spherical cupola is now machined in a block of hard aluminium EN AW-5083 and anodised to reduce friction. Its design is modified to extend the angular range of the goniometer. A 1 mm thick disc made from neutron absorbing material (Cd or B₄C) is screwed below the cupola to reduce the quantity of neutrons that may be scattered toward the detector and to prevent the activation of the Goniostick.

With the addition of a wave spring washer, it is now possible to mount the tilted sample axis across the cupola with a tuneable pressure. The friction between the cup and the cupola is also minimised by using a rounded shape in contact with the cupola (0.5 mm radius). A screw/nut assembly was also added to allow the adjustment of the sample position so that it coincides with the centre of the sphere.

The new design of the stick also allows the adjustment of its height and the rotation of the whole stick inside the cryostat with a rotating stage installed at the top of the variable temperature insert of the cryostat.

Fig. 2.

Description of the movement of one lever x or y where the control rod assembly is represented as a vertical thick arrow: (left) in centred position, (right) after pushing down. The sample centred on (s) is tilted by the angle $φ_{x, y}$ when the rod moves down by $n_{x, y} . p$ .

3. Expressions of displacements

The sample tilt is realised with the combined rotations of two levers around perpendicular directions $\vec{x}$ or $\vec{y}$ . Figure 2 presents two positions of one lever indexed x or y. On the left, the lever is in central position and the axis of the sample holder (s) is vertical. The inclination is commanded by translating a control rod assembly protruding from the top flange of the stick. The movement is symbolised with the thick vertical down-arrows drawn on the sketches. The amplitude of the translation is noted $n_{x, y} . p$ where $n_{x, y}$ and p are respectively the number of turns and the pitch of the micrometer screw.

At the bottom of each control rod assembly, there is a tungsten carbide pin translating along a groove machined in the lever and represented by the oblong hole shown on Fig. 2: the vertical translation of the pin is transformed into a rotation of the lever. The pin acts as a push rod on the lever which rotates by an angle $β_{x, y}$ around the horizontal axis. The horizontal distance from the rotation axis of the lever to the rod is called e. It is identical for both rod and lever assemblies and equals to 11.2 mm (see Table 1).

Table 1
Mechanical parameters of the Goniostick

Parameter Rod x (bottom lever) Rod y (top lever)

e 12.1 ± 0.05 mm 12.1 ± 0.05 mm

$d_{x, y}$ 18.0 ± 0.05 mm 16.3 ± 0.05 mm

$h_{x, y}$ 63.2 ± 0.1 mm 57.2 ± 0.1 mm

p (resolution) 0.5 mm (10 μm) 0.5 mm (10 μm)

Parameter	Rod x (bottom lever)	Rod y (top lever)
e	12.1 ± 0.05 mm	12.1 ± 0.05 mm
$d_{x, y}$	18.0 ± 0.05 mm	16.3 ± 0.05 mm
$h_{x, y}$	63.2 ± 0.1 mm	57.2 ± 0.1 mm
p (resolution)	0.5 mm (10 μm)	0.5 mm (10 μm)

The tungsten carbide rod fixed to the lever at a distance $d_{x, y}$ from the rotation axis is displaced. As it crosses a groove made in the sample holder and represented by a “U” shape in Fig. 2, it pushes the sample axis, provoking its rotation onto on a sphere centred on (s) (not shown in Fig. 2 for clarity). The sample is rotated by an angle $φ_{x, y}$ in the plane of the figure.

The amplitude of the translation $n_{x, y} . p$ necessary to tilt the sample by an angle $φ_{x, y}$ is determined from the following equations: $\begin{array}{l} ℓ_{x, y} sin φ_{x, y} = d_{x, y} sin β_{x, y} \\ h_{x, y} = ℓ_{x, y} cos φ_{x, y} + d cos β_{x, y} \end{array}$ from which we deduce: $\begin{matrix} (1) & tan φ_{x, y} = \frac{d_{x, y} sin β_{x, y}}{h_{x, y} - d_{x, y} cos β_{x, y}} where tan β_{x, y} = \frac{n_{x, y} . p}{e} \end{matrix}$

When the two rods are actuated by the numbers of turns $n_{x}$ and $n_{y}$ , the change in angular displacement of the sample is characterised by the azimuthal angle θ and the polar angle φ in the frame of the Goniostick. When the tilt is produced with $n_{x}$ only, $θ = 0$ or $180^{\circ}$ and $φ = φ_{x}$ . Similarly, with $n_{y}$ only, $θ = \pm 90^{\circ}$ and $φ = φ_{y}$ . And for a combination of movements, the values of θ and φ are given by: $\begin{array}{l} (2) & tan θ = tan φ_{y} / tan φ_{x} \\ (3) & {tan}^{2} φ = {tan}^{2} φ_{x} + {tan}^{2} φ_{y} \end{array}$

On the instruments, it is often required to apply a known tilt $(θ, φ)$ . In that case, the values of $n_{x}$ and $n_{y}$ are deduced from the equations: $\begin{array}{l} (4) & tan φ_{x} = tan φ cos θ \\ (5) & tan φ_{y} = tan φ sin θ \end{array}$ Taking $t_{x} = tan \frac{β_{x}}{2}$ and $t_{y} = \frac{β_{y}}{2}$ in equations (1), one gets: $\begin{array}{l} (6) & n_{x, y} = \frac{e}{p} \frac{2 t_{x, y}}{1 - t_{x, y}^{2}} \\ (7) & where t_{x, y} = \frac{d_{x, y} - sign (φ_{x, y}) tan φ_{x, y} \sqrt{\frac{d_{x, y}^{2}}{{sin}^{2} φ_{x, y}} - h_{x, y}^{2}}}{tan φ_{x, y} (d_{x, y} + h_{x, y})} \end{array}$

4. Performance

A prototype of Goniostick whose parameters are presented in Table 1 was built at the ILL (see Fig. 3). The mechanical tolerances were calculated to obtain a resolution that is better than $δ β_{x, y} \approx {0.05}^{\circ}$ . After a careful assembly followed by a series of tests at room temperature and later in liquid nitrogen aiming at checking the reliability of the mechanics, we mounted a Ø2 mm ruby single crystal and performed a series of tests on the time-of-flight spectrometer IN5 [6].

Fig. 3.

Photo of the goniometer mounted at the bottom of the sample stick. The sample and the goniometer are in exchange gas inside the cryostat and the temperature is measured with the thermometer installed above the sample (wiring visible on the left).

During these tests, we followed the position of the reflection [1 1 9] in the position sensitive detector while cooling the crystal down to 20 K in the Orange cryostat of the instrument. We first tilted back and forth several times the crystal using one of the micrometer screws. These tests allowed to measure a systematic backlash leading to a displacement of the Bragg peak in the detector corresponding to a misalignment of $δ θ_{B} \approx {0.75}^{\circ}$ where $θ_{B}$ is the Bragg angle. That was easily observable as a shift of 1 cm in the detector corresponds to $δ θ_{B} = {0.14}^{\circ}$ . We repeated the same tests with the second rod and observed the same backlash. Indeed, the friction exerted on the sphere combined with the mechanical plays that are unavoidable at the interfaces {rod-lever} and {lever-sample holder} are responsible for this backlash.

We cancelled this backlash by always finishing a movement toward the same direction and performed a series of $\pm 3^{\circ}$ displacements of the sample using only one or the two rods at 100 and 20 K. The Bragg peak always came back to the same position of the detector and the refinement of the position of the peak revealed a maximum misalignment of $δ θ_{B} < {0.02}^{\circ}$ .

5. Conclusion

We have redesigned the concept of Berneron et al. [1] and produced a Ø36 mm sample stick for cryostats and cryomagnets featuring a robust non-magnetic goniometer providing $\pm 6^{\circ}$ sample tilting with ${0.02}^{\circ}$ resolution. This system called Goniostick accepts samples up to 9 mm height and is now available to users of the ILL and commercially distributed by IRELEC [3].

Footnotes

Acknowledgements

The authors thank the inventors of the design [] and in particular A. Filhol (ILL) who helped the team restarting this development. We are also grateful to G. Marot and G. Hebert from IRELEC who helped us commercialise the Goniostick.

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