---
title: "How a dilution refrigerator keeps carrying heat away"
description: "Helium-3 absorbs heat as it crosses a liquid boundary. Heat exchange, wire anchors, sample contact and thermometry determine how cold the sample becomes."
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language: "en"
page_type: "story"
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  zh-CN: "https://sandboxphysics.com/zh/stories/instruments/dilution-refrigerator/"
last_modified: "2026-11-12"
---

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Inside the instrument

# How a dilution refrigerator keeps carrying heat away

A bundle of wires brings signals to a very cold sample. It also brings heat. A dilution refrigerator continuously carries heat away with circulating helium-3, and the places where those wires touch intermediate cold plates can change the sample's final temperature.

Sandbox Physics · 2026-11-12

## Helium-3 absorbs heat between two liquids

The mixing chamber contains two liquid layers. The upper layer is rich in helium-3; the lower layer is mostly helium-4 with some dissolved helium-3. Helium-3 carries more energy per mole after crossing into the dilute lower liquid. It takes that extra energy from its surroundings. A metal connection carries heat from the sample into the chamber.

Continuous cooling needs a continuous departure from the lower liquid. A warmer vessel called the still evaporates and removes helium-3. The circulation system sends it back to the upper liquid. Entry, mixing and removal form a loop that carries away heat as new heat arrives.

The 1971 NBS analysis relates low-temperature cooling to the circulation rate and the temperature of the incoming liquid. Warmer incoming helium leaves less cooling available for the sample at the same flow. Twenty millikelvin means just two hundredths of a kelvin above absolute zero.

Sources: [1] [2]

## The returning liquid cools the incoming liquid

The dilute liquid leaving the mixing chamber is still cold. Run it beside the incoming liquid in the opposite direction and heat passes from the incoming stream to the return stream. This counterflow heat exchanger lets one part of the circulation help cool the next.

Higher up, a refrigerator has room-temperature, 50K and 4K stages, followed by the still, cold plate and mixing chamber. Stage names are conventional; operating temperatures vary. Precooling establishes the liquids and circulation before millikelvin operation begins. The low-temperature mixing law describes that final operating interval.

Sources: [1] [3]

## Wires hand heat to intermediate plates

Room-temperature instruments need an electrical path to the sample. That path also conducts heat. Thicker and shorter wires generally carry more heat across the same temperature difference. Coiling and clamping a wire onto an intermediate plate lets heat leave the wire there, where that refrigeration stage can remove it.

The clamp has a finite thermal resistance. A loose junction can stay warmer than its plate and pass more heat onward. Follow the actual route: heat arrives from the warmer end, part enters the cold plate, and the rest continues toward the mixing chamber.

Adding wires can increase both measurement access and heat load. Their material, length, area and contact quality therefore belong in the experimental design.

Sources: [2] [3]

## The sample needs its own route for heat

A sample heater, measurement current or outside interference can deposit heat at the sample. That heat must pass through the mount into the mixing chamber. A finite contact needs a temperature difference to carry heat, so the sample can remain warmer. A thermometer near the sample and enough settling time help reveal the difference.

Sources: [2] [4]

## Heat keeps flowing at a stable temperature

A temperature trace levels off when incoming heat matches the heat removed by circulation. Wires still conduct heat and electrical currents still dissipate power. Continuous refrigeration holds the temperature there.

Attach a small heater of known power to the mixing chamber and increase its electrical power. The temperature rises at first. In this low-temperature relation, a warmer mixing chamber can absorb more heat, and it eventually settles at a higher temperature. Several settled temperatures and heater powers show how the apparatus responds to added heat. Keep circulation and wiring unchanged so those observations describe the same cooling curve.

Sources: [1]

## A thermometer can warm itself

A resistance thermometer passes a small current and measures voltage. Even that current produces heat. A sensor with weak thermal contact may report its own slightly warmer temperature. Reducing the excitation and checking whether the reading agrees is a direct test.

In 2021, Myers, Li and Csáthy compared ruthenium oxide thermometers with different mounting and filtering. Improved shielding and filtering let one sensor retain sensitivity at lower temperatures. They also measured increasingly long equilibration times as it cooled. Calibration, installation and excitation all help determine whether a refrigerator's temperature reading is trustworthy.

Sources: [4] [2]

## [Change the coldest temperature with a wire clamp](https://sandboxphysics.com/labs/dilution-refrigerator/)

Loosen the thermal anchor and compare mixing, sample and reversed-current thermometer traces.

Calculates two-node energy storage, finite wire anchoring and raw thermometry in an already precooled 20–40 millikelvin interval.

## Sources and further reading

1. [Radebaugh and Siegwarth (1971), Dilution refrigerator technology, Cryogenics 11, 368–384](https://trc.nist.gov/cryogenics/Papers/Review/1971-Dilution_Refrigerator_Technology.pdf)

   Reads printed369–373, especially equations6–11 on371 and the dilute-stream heat capacity on373. Uses the historical94/12 and equal-temperature82 coefficients; the107.2T exchanger-stream heat capacity is treated separately. Coefficients retain the paper's solubility choice and low-temperature approximation.

2. [N. H. Balshaw, Practical Cryogenics, Oxford Instruments, 2001 imprint](https://andor.oxinst.com/downloads/uploads/practical-cryogenics.pdf)

   Uses35–37 for liquid phases and circulation,56–61 for staged wiring and four-wire resistance, and67 for the conductivity integral. High-temperature material tables are not extrapolated to20 millikelvin.

3. [Bluefors (2023), Components of the Dilution Refrigerator Measurement System](https://bluefors.com/stories/components-of-the-dilution-refrigerator-measurement-system/)

   Uses the manufacturer's February14,2023 description of stages, precooling, heat switches and closed circulation. Stage names differ from operating temperatures; commercial cooling specifications are not simulation observations.

4. [Myers, Li and Csáthy (2021), A ruthenium oxide thermometer for dilution refrigerators operating down to 5 mK](https://arxiv.org/abs/2110.03788)

   Reads calibration, self-heating and equilibration sections. Adopts independent reference temperatures, changed-excitation checks, and the effects of mounting and filtering. The simulated power law, amplitude, contact and response time are separate synthetic assumptions.

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