February 15, 2023

The Coolest Pressure Sensor

Phase Sensors is collaborating with the University of Alberta (the Davis Group) at the world’s coldest temperatures for measurement and calibration of pressure cells at sub-kelvin temperatures. Down the street from Phase Sensors’ facility in Edmonton, Canada is one of the coldest places in the world. Dr. John P. Davis operates a dilution refrigerator using a demagnetization stage to probe fundamental physics at the lowest obtainable temperatures. Dilution refrigerators are used to provide sub-kelvin temperatures (less than -272.15°C) for fundamental physics and materials experiments. A dilution refrigerator uses a multi-phase mixture of 3He and 4He, where dilution of 3He from a pure phase to a dilute phase acts as the refrigerant.

The measurement of temperature inside of a dilution refrigerator is of primary importance for fundamental studies. Traditional temperature sensors that use resistive elements to measure temperature are not ideal in this range, as running current through a resistive element to measure it generates heat and limits cooling performance. A method with very little power dissipation is ideal, and a method with self calibration is even better. This need resulted in the development of the PLTS-2000 method of temperature measurement for sub-kelvin applications. The PLTS-2000 is based upon the phase diagram of 3He (shown in Figure 1), which has a very distinctive shape in the region below 1 kelvin. When one takes a chamber of liquid 3He, pressurizes it to between 2.93MPa and 3.4MPa and then starts cooling from 1000 mK to 10 mK this fluid will transition from liquid to solid and then back to liquid. This phase behaviour is a fundamental property of 3He and can be used as a primary standard for temperature. Translating this certainty in phase behaviour into a temperature measurement is a beautiful challenge in itself!

Figure 1: (right) The 3He melting pressure pm (full line) and the absolute value of the derivative dpm/dT (dashed line, right-hand scale) vs temperature, from [Durieux and Reesink 1999]i.ii (left) Dr. John Davis’ dilution refrigerator with a demagnetization stage: The coldest place in Canada and home of the worlds coolest pressure sensor

If a mixture of solid and liquid phases of 3He exist at below 300mK, the pressure in the chamber can be used with the PLTS-2000 method to precisely calculate the temperature. A diagram of such a chamber and associated pressure sensor, known as a melting-pressure cell, is shown in Figure 2. Usually, a standard practice would be to put a precision pressure sensor outside of the fridge and connect it via a capillary to the chamber. However, the inversion in the phase diagram, at temperatures below 300mK, creates a solid plug of 3He and isolates it from the pressure sensor.

Figure 2: (left) A diagram of the 3He melting-pressure cell of Greywall and Busch [1982]iii, (right) Photo of 3He melting-pressure cell in Dr.John Davis' laboratory.

This pressure sensor is based upon a capacitively sensed diaphragm. In this design, as the diaphragm flexes due to pressure changes, the capacitance changes. The accuracy of this pressure sensor directly impacts the accuracy of the temperature measurement and therefore this sensor is calibrated before every use. The capacitance is monitored by a capacitance bridge while the pressure in the chamber is externally adjusted and measured to generate a calibration curve between capacitance and pressure. This training includes 10 pressure cycles from 2.9MPa to 4 MPa and is done prior to every sub-kelvin experiment. The most accurate calibration would be to use a primary standard deadweight for this calibration, but this has a significant cost drawback in that a deadweight has a fixed leak rate past the measurement piston (every gram of 3He is currently $1400 USD). Instead, physicists turn to another precise calibration standard: quartz resonant pressure sensors. In the ideal case: a quartz pressure gauge is calibrated against a pressure deadweight and then immediately transferred to calibrate the melting-pressure cell transducer. The XtalX sensor from Phase is that Ideal Case. It is hermetically sealed via a feedthrough and metal to metal seals. Custom calibrations are available for every application, including up to 40 bar absolute pressure at 0.02% full scale accuracy (required for the PLTS-2000 measurement method). For applications with helium, the sensor element is constructed and calibrated without ever touching oils, allowing for the device to be vacuum compatible. The device’s accuracy and 100 micro-bar resolution allow for an accurate calibration of 3He melting pressure cells.


i Durieux M and Reesink AL 1999 7th International Symposium on Temperature and Thermal Measurements in Industry andScience, edited by J. Dubbeldam and M. de Groot pp. 19-26.

ii Supplementary Information for the Realization of the PLTS-2000, Consultative Committee for the Thermometry under theauspices of the International Committee for Weights and Measures. (2014).

iii Greywall DS and Busch PA, 1982 3He-melting-curve thermometry J. Low Temp. Phys. 46 451-465.