Materials and construction

The drive shaft has the same limitations with regard to heat load as the wiring described in section3.2.1. Thin-walled stainless steel tube was used to make the drive shaft, broken by short lengths of G10 (a type of glass-fibre reinforced resin) at low temperature to keep heat flow low. Short lengths of silver wire join the drive shaft to the refrigerator plates to intercept as much of the heat load as possible. The end result was that fitting the drive shaft made no detectable difference to the base temperature of the refrigerator.

For the feed-through at the top-plate of the fridge, a very low leak rate even whilst rotating is necessary as the fridge usually stays cold for a several months with the rotator being run regularly. This was achieved with a magnetic coupled feedthrough consisting of a steel “top hat” shape, the brim of which forms a KF40 vacuum seal. Within the top hat is a brass drive shaft, with magnets around its circumference, and outside the top hat is a brass carrier with more magnets which is driven by the motor.

One key aspect of the design that is essential for precise running is adjustability. No part will ever be made exactly as drawn, rather it will be within some tolerance of what was intended. Most of the rotator is not really a precision device, the frame and standoff need only be accurate to a millimetre or so, but the gears are rather more important. The problem varies slightly between spur and bevel gears, but in essence if the gears are too close they will run rough and jump, if they are too far apart there will be backlash. For the spur gears, one axis of adjustment is enough – the distance between rotation centres. Bevel gears are more complicated, and four axes of adjustment are allowed for: both gears can move along their axes of rotation; and the wheel∗

can be rotated about either axis perpendicular to the rotation axis using shims. Correct setting of all these adjustments is necessary to gain a backlash of less than 0.2◦_{. Whilst less essential} the standoff can also be adjusted, to get the exact length to the field centre correct and to keep it from touching the radiation shield, from which it has only 0.75 mm clearance. In practice, preventing contact by adjusting it is awkward and not all that reliable, so a spacer which will hold the rotator away from the wall was also built. This uses a web of kevlar thread to support a tufset triangle, providing mechanical stiffness with a very low heat flow.

Having chosen a design with minimal friction in the drive mechanism, it makes sense to also minimise the friction in the bearings, and for this two types of jewel bearings were used. For the platform itself, which rotates about a horizontal axis with minimal thrust load V-jewels and non-magnetic steel pivots were used. For the vertical sections of the drive shaft olive ring jewels

∗_{With bevel gears, the large gear is known as the wheel and the small one as the pinion. In most cases the} pinion drives the wheel.

to constrain the bearing radially and flat end-stones to take any thrust load were used.

The rotator platform and frame are made from Phosphor Bronze, as a compromise of strength, stiffness, low electrical conductivity (to avoid eddy current heating), no superconductivity (which would damage thermal conductivity) and good machineability. In theory the lack of magnetic solutes also avoids magnetocaloric effects, but in practice the material used may contain more solutes than desired. The standoff between the mixing chamber and the rotator frame initially used 316LN steel, which should be free of magnetism[51], but this was found to have a large increase in specific heat at low temperatures, so was replaced with OFHC copper.

A major challenge was thermalising the platform to keep it cold even in the presence of heat from measurements and eddy currents as the magnetic field changes. At 200 mK this is easy enough, using a few strands of silver or copper wire, but as the thermal conductivity of a metal scales with T by the Weidman Franz law∗ _{it becomes increasingly difficult at low temperatures.}

As well as needing very conductive wires to carry the heat, it was necessary to make sure the ends of these wires made good thermal contact with the rotator platform and mixing chamber. The heat flow through a junction depends on the force with which it is clamped, not the area[57]. This requires bolting the wires down firmly, and using bolts with thermal expansion coefficients that would tighten, not loosen, as the system cooled.

The best choice for thermalising things is silver wire. It has a high thermal conductivity and is readily available quite pure with good RRR. It is better than copper in that it has a small, saturating magnetoresistance, so retains its high thermal conductivity in a strong field. Wire is better than rod of the same cross section as it will heat less by eddy currents, and of course is flexible. A good starting material is 99.99 % purity silver wire from Advent Research Metals, which was measured to have an RRR of 79. The residual resistance is dominated by electron scattering from impurities, and Advent indicate 100 ppm copper, and 10 ppm each of iron and a number of other metals. The iron is of particular interest as it can form magnetic scattering centres with much higher cross section than the others. A similar thing happens in copper, and the solution is to anneal in an oxygen atmosphere[52] which clusters the iron into non-magnetic Fe3O4 centres. Though much less common, this also works with silver[58], so some wires were

treated in a similar way. Some lengths of 0.37 mm wire were annealed at 750◦C for 20 hours with a pressure of about 5×10−4 _{mbar of flowing oxygen, then cooled to room temperature}

under vacuum over two hours. This resulted in visible grains of over 1 mm in size, and an RRR, provided the wires are handled carefully, of over 1500. Mechanical stresses reduce the RRR very quickly, winding the wire into a 4 mm diameter bobbin and unwinding it stiffens it and reduces the RRR to 250. One can assume therefore the low temperature scattering is dominated by crystalline defects after work hardening. The wires installed on the rotator will maintain an high RRR over most of their length, but will have a moderate RRR where they bend to come onto

∗_{Assuming the resistivity is saturated at the residual value, which is true for most metals at dilution refrigerator} temperatures

the rotator platform, but even with this reduction they are at least 5 times as conductive as the untreated wire.

With the very low friction jewel bearings, the main resistance to rotating the platform comes from the wires. It makes sense therefore to try to minimise the the force, which was achieved by winding the wires around the axle of the sample platform inside the bevel wheel. Thin 25µm wire for the twisted pairs was used to reduce their stiffness. The winding also increases the distance the rotator can turn before the wires pull tight: with just the silver thermalising wires and the 18 twisted pairs on the primary solder-board, the platform can rotate through slightly more than 360◦. On some cooldowns more than 18 pairs were required, and/or some coaxes for my colleague’s measurements. The coaxes, though flexible at room temperature, are not very flexible when cold. The coaxes used∗ consist of a stranded copper core, a thin Teflon dielectric, woven copper braid and fluorinated ethylene propylene (FEP) outer insulator. The inner three layers are fairly flexible, but the FEP insulation freezes and cracks off when the cable is bent at low temperature. This problem was solved by cutting the insulation into rings with a scalpel, with cuts separated by about one cable diameter, then removing about one ring in ten. With the remaining rings of FEP spread out, they have a gap about equal to the half their thickness between each ring, which allows the cable to bend with a radius of about 2 cm whilst maintaining the insulation of the braid from the frame of the rotator. This radius is still too wide to wind the coaxes in with the other wires, so they go directly to the platform, limiting the angle through which the platform can rotate to a little over 180◦. Also added were an extra 12 pairs on a secondary solder-board which can be used when more than 18 are needed, with similar constraints on rotation angle.