Specialist #47

The imaginary part of the dielectric constant has a minimum at 20 K

In the microwave range, the loss factor of ice shows a minimum at very low temperatures.

Scientific Explanation

The complex dielectric constant has a real part (energy storage) and an imaginary part (energy loss). The imaginary part, also known as dielectric loss, describes how much electromagnetic energy the material absorbs. For ice, this loss factor shows an unusual minimum at a temperature of approximately 20 kelvin (minus 253 degrees Celsius).

This minimum results from two competing loss mechanisms that dominate at different temperatures. At higher temperatures (above 100 K), the dielectric loss is mainly determined by Debye relaxation — the reorientation of water molecules within the ice lattice. As temperature drops, this relaxation slows exponentially, and the associated loss decreases.

At very low temperatures (below 20 K), a different mechanism comes into play: quantum mechanical tunneling of protons between neighboring equilibrium positions in the ice lattice. This tunneling process is essentially temperature-independent and produces a residual loss that can even increase slightly at very low temperatures.

The minimum at 20 K marks the point where the declining Debye relaxation and the emerging tunneling loss are in balance. The exact position and depth of this minimum depend on frequency and remain actively studied. Some researchers see in this minimum evidence for proton ordering in ice at low temperatures — a topic connected to the question of ice’s ground state and the determination of its residual entropy.

Imaginary Part of Dielectric Constant of Ice vs Temperature Line chart showing that the imaginary part of the dielectric constant of ice (dielectric loss) exhibits a minimum at about 20 Kelvin. Below and above this temperature, the loss factor increases. Dielectric loss (log scale) high low 0 20 50 100 200 Temperature (K) Minimum ~20 K Imaginary Dielectric Constant of Ice
Dielectric loss of ice as a function of temperature, showing a minimum at about 20 K.

Everyday Relevance

Although temperatures around 20 kelvin do not occur in daily life, this effect is important for astrophysics and planetary science. Ice exists on numerous bodies in the solar system — from Saturn’s rings to comets — at temperatures in precisely this range. The dielectric properties determine how radar signals and microwave radiation interact with these ice deposits. Space missions such as Cassini or JUICE use radar measurements to determine the thickness and composition of ice layers on moons like Europa and Enceladus, making an accurate understanding of dielectric loss at low temperatures indispensable.