Uniaxial Strain: The Research Need
An interesting experiment, but a challenging task
In the field of fundamental superconductivity and magnetism research one of the key objectives is to link the emergent electrical properties of a condensed matter system to its crystal structure. Previously, the only way to continuously tune the structural properties, such as interatomic spacing, was to either apply hydrostatic pressure in a pressure cell, which exerts an influence on all the crystal axes, or by attaching samples directly to piezoelectric materials, but these materials have several features which make this difficult. Firstly, they lose a lot of their stroke at low temperatures, limiting the strain which can be applied unless a mechanism is used to lever them up. Secondly, they expand on cooling. Combined with the contraction of the sample, this typically means that the strain can only be varied over a small range which usually does not include zero. If only constant (rather than continuously tunable) strains are required, the sample can be strained manually between clamps before cool-down, though again, differential thermal expansions would mean that the final strain experienced would be difficult to calculate. One final way of changing the interatomic spacing is by changing the chemical composition of the crystal, which can introduce unknown chemical effects of the crystal, as well as influencing all the crystal axes in a difficult to predict way.
Figure 1. Experimental data showing the startling influence of uniaxial strain on the superconductivity transition temperature of strontium ruthenate. This data was generated using the forerunner of our technology and published in the journal Science. Hicks et al. Science Vol. 344 no. 6181 pp. 283-285
Razorbill Instruments technologies
Razorbill Instruments uniaxial stress and strain cells incorporate a number of unique key technologies that enable them to have such high performance and repeatability. The following sections describe the design improvements in more details.
The Razorbill Instruments cells use a thermal compensation technique pioneered by one of our founders at St Andrews University in the UK and the Max Planck Institute for Chemical Physics of Solids in Germany, and described in the seminal 2014 RSI paper. Several piezoelectric stacks (usually three) are used in a push-pull configuration, such that the thermal expansion of the tension and compression stacks cancels out. This allows the tunable stress or strain range to remain centred near zero. By using piezoelectric stack which are much longer than the sample, we can also tune to much higher percentage strains than the strain the piezoelectric stack experiences itself. This is particularly useful for samples with a large length change on cooling, for example due to a structural transition.
You can read more about the thermal compensation in Razorbill Instruments cells in our application note.
Figure 3. All Razorbill Instruments devices are supplied with a capacitance curve to enable the user to convert from the capacitance of the internal, well-shielded sensor to an applied displacement or force. Without a sensor providing accurate feedback users would be in the dark as to ho much stress or strain they had applied.
As piezoelectric actuators are intrinsically hysteretic, cells built by Razorbill Instruments include a miniature parallel-plate capacitor of our own design. In our strain cells, this measures the displacement of the two sample mounts, and in the stress cells it measures the force applied to the sample. Similar capacitors have long been used in torque magnetometry and in dilatometry. But in those measurements the capacitor is the primary measurement being made, whereas in a stress or strain cell the capacitor must coexist with the actual measurement of the sample. A simple capacitor made by gluing plates directly to the body of the cell would have a significant parasitic capacitance to the cell. Our capacitors are fully shielded - there is a metal guard between the plate and the cell body, and the grounded cell body completely encloses the capacitor and guard assembly. In practice some users have reported that this gives them an order of magnitude better resolution on the capacitance measurement when the sample resistance is also being measured. And interference could go the other way too, but with these guards in place, users have been able to do measurements like NMR without interference from the cell.
Read more about our capacitors and how to measure them in our application note on this subject.
Compliant mechanisms for guidance
While the end of a theoretical piezoelectric stack simply moves outwards when a voltage is applied, real ones are prone to translate in other directions, rotate and/or bulge at the same time. To get precise, uniaxial stress or strain on the sample the ends of the sample need to be guided. But even the highest quality linear guides and roller bearing sets have about a micron of slop. Traditional mechanical parts are also subject to loosening or binding as the temperature changes, or even cold-welding if the wrong materials are used. The movement in Razorbill Instruments stress and strain cells is guided by compliant mechanisms. Thin metal flexures act like leaf springs, soft in one direction but orders of magnitude stiffer in other directions. The compliant mechanisms used in our cells are the result of detailed analytical and finite element calculations, and provide excellent guidance to the sample mounts. The key flexures and hinges are formed from a single piece of metal by wire-EDM, yielding a excellent uniformity and reliability. Some of our cells even have complex three-dimensional mechanisms which allow the piezoelectric stacks to be located under the sample, saving space, or even allowing the sample to sit horizontal in a small magnet bore with long stacks sitting vertical beneath.
Materials for extreme conditions
The main materials used in Razorbill Instruments cells are titanium grades 2 and 4. It would perhaps be easier to use steel, or perhaps titanium grade 5. But these grades were chosen for their very low magnetic susceptibility, significantly lower than "non-magnetic" stainless steel grades. The superconducting critical temperature and fields are also significantly lower than that of grade 5, so the cells maintain a reasonable thermal conductivity down to lower temperatures. Similarly, all of the other components which go into our cells are chosen to be compatible with sub-kelvin temperatures and high magnetic fields. All components are also chosen to minimise outgassing, and outgassing can be further reduced for some of our cells on request. In addition, other more exotic materials, such as Copper Beryllium, can be used for custom units if required for very particular experiments.
Customisation and Integration
Razorbill Instruments can provide fitting kits for PPMS cyrostats, and adaptors for mounting some of our cells on attocube positioners to provide a strain tuning solution that allows a research group to get going with their strain tuning experiment as soon as possible after delivery. We are also happy to work with customers to help them get up and running, and aim to provide small customisations to cells, or mounting brackets or other parts necessary to integrate our cells into existing cryostats as cheaply as possible. Please contact us to talk about your application
Figure 4. A huge amount of finite element analysis is required to ensure the flexures deliver the range of motion required while remaining extremely stiff against unwanted displacements. With any flexure design, the maximum strain in the joint is kept as low as possible to reduce the risk of fatigue over time.