All About the Microcalorimeter

Perhaps the most intriguing advance in X-ray astronomy instrumentation in the 1990s has been the development of the microcalorimeter, spearheaded by work at NASA’s Goddard Space Flight Center. The microcalorimeter instrument designed at Goddard was called XRS, short for the X-ray Spectrometer.

What is a Microcalorimeter?

Illustration of a microcalorimeter
The components of the calorimeter

A microcalorimeter is basically a thermal device made of an absorber, a thermistor, and a heat sink.

The absorber must do 3 things: absorb X-rays from space efficiently, quickly, completely convert the absorbed energy into heat (thermalize the energy), and have a low heat capacity. There is no material known which excels at all 3 of these properties, so choosing the absorber material involves deciding on the best combination of them.

A thermistor is a device that changes its electrical resistance dramatically with a small change in temperature. Since a thermometer is any device that measures temperature, a thermistor is a kind of thermometer.

The combination of the absorber and the thermistor is what we call the “X-ray detector”. Below, starting from the left, is a diagram of a detector, a photo of a detector array (they are the gray-green rectangles in the middle), and a closeup of the array. The array consists of 32 individual calorimeter detectors. You can (barely) see two black legs from each detector at the top of the image, and one leg from each detector squeezing between a pair of detectors at the bottom. These legs of the detector are what is called the “weak link” to the heat sink.

Diagram of a microcalorimeter detector
Schematic of the Calorimeter
Photo of the microcalorimeter detector arrayArray of Calorimeter Detectors
Close-up photo of microcalorimeter detector arrayClose-up of Calorimeter Array

Diagram of an ADR

The heat sink is what absorbs heat from the detector, keeping it cool. In the case of a recently designed XRS, the heat sink used to keep the detector cool enough to work was a refridgeration unit called the Adiabatic Demagnetization Refrigerator (ADR). An ADR uses the magnetic properties of molecules in the “salt pill” to cool the detector to 60 milliKelvin (or 0.06 degrees above absolute zero).

How Does a Microcalorimeter Work?

An X-ray photon hits the absorber and knocks an electron loose from an atom of the absorber material. This photoelectron (so-called because a photon of light knocked it loose) rattles around in the absorber, ultimately raising the temperature of the absorber by a few milliKelvin (that is, a few thousandths of one degree Kelvin). The temperature-sensitive thermistor is partially isolated from the absorber, to give the absorber time to come into equilibrium before the thermistor begins to see the temperature rise. After a few milliseconds, the thermistor comes to the same temperature as the absorber, a few milliKelvin warmer than the heat sink, which is at 65 milliKelvin. We know it’s a little strange to be talking about ‘heat’ when something is near absolute zero! Next, the thermistor begins to cool as the heat flows out the weak link (the “legs” of the detector) to the heat sink. After a few tens of milliseconds, the thermistor has returned to its normal operating temperature.

Animation of how the calorimeter works

The temperature rise (delta T) measured by the thermistor is approximately proportional to the energy of the X-ray photon:

delta T ~ E/C

where delta T is the change in temperature, E is the energy of the X-ray and C is the heat capacity of the absorber. So by measuring how much the temperature changes, we can determine the energy of the X-ray.

The Science

When an X-ray stops in a detector, it gives all of its energy to one electron. That electron can rattle around in the detector and give energy to other electrons. All these excited electrons would rather go back to their original energy. They want to return to what is called the ground state. Through scattering with other electrons or with vibrations in the solid itself, they can lose that extra energy. But that energy has to go somewhere. What it does is heat the solid and increase its temperature. If you measure the change in temperature, you can measure how much energy the X-ray originally had.

How are heat and energy and temperature all related? Heat is a manifestation of energy. Heat and energy are measured in the same units (Joules). If we are thinking of a large group of objects which can exchange energy with each other, we usually think of this energy as heat. An example would be the energy of a gas: we think of its energy as heat and measure it as a temperature. When an X-ray photon heats a solid, it gives its energy to the whole solid. On average, each atom is vibrating a little bit more than before the X-ray hit. Temperature is also the way we relate the total energy of a system to its state of disorder (entropy). A physical property called “heat capacity” tells us how much the temperature rises in a material if we put in a certain amount of energy.

Suppose we wanted to measure the temperature increase due to an X-ray photon being absorbed. We would want a very sensitive thermometer, something that had some physical property that changed a lot for a small change in temperature. We would also want the detector to have a small heat capacity, so its temperature would change a lot for a small change in energy. Finally, we would want to do the whole thing at very low temperatures, because at room temperature there would already be too much thermal energy in your detector to see the very small change in energy from the X-ray. That is what an X-ray calorimeter does. It uses a silicon thermistor which has an electrical resistance which changes dramatically with small changes in temperature. This termister has a low heat capacity, and operates at less than 0.1 K. That’s Kelvin. Zero on the Kelvin scale is an absolute zero and represents the cessation of all thermal vibrations. Water freezes at 273 K. Nitrogen liquefies at 77 K. Helium liquefies at 4 K. and we operate calorimeters at less than 0.1 K! Calorimeters are able to get the best spectral resolution of any non-dispersive spectrometer.

Why Is the Microcalorimeter a Better Way to Detect X-ray Photons?

In proportional counters and CCDs, the energy of the X-ray photon is shared among many electrons. Each of these electrons end up carrying a typical amount of energy, 3.65 eV in the case of the silicon-based CCDs. These electrons are then collected and counted by the electronics, and it’s the number of the detected electrons that indicates the energy of the X-ray photon in a CCD detector system. An 3.65 keV X-ray photon, for example, will produce 1,000 electrons – give or take. There is an uncertainty in the number, because the details of the X-ray – matter interaction is different each time, giving a slightly different amount of energy to each electron. The uncertainty can be estimated by taking the square root of the number of electrons – 30 or so in this case, so the X-ray energy can be determined to an accuracy of 30/1000 ~ 3%. This is a fundamental limit of X-ray detectors that use conversion to electric charges. If you want a higher spectral resolution – and astrophysicists always do – you have to choose a detector that relies on a completely different principle, such as a microcalorimeter. As a result of its different approach, the microcalorimeter provides 10x better spectral resolution for detecting emission lines of iron.

For the Student

Using the text, and any external printed references, define the following terms: Kelvin, thermistor, heat capacity.

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