Quantum solids

Quantum solids

A class of solids whose atoms or molecules undergo large zero-point motion even in the quantum ground state (at temperature T = 0 K = -459.67°F) as a result of their small mass and the weak attractive part of their interaction potential. The most striking examples are the isotopes of helium, ³He and ⁴He, which have a root-mean-square displacement from their lattice sites of approximately 25%. Further examples are the molecular hydrogens, H₂, D₂, and HD, as well as some heavier molecular solids. See Intermolecular forces, Quantum mechanics

These materials display quantum effects in their bulk properties when cooled to temperatures near absolute zero so that the chaotic thermal motion is reduced. Both of the helium isotopes remain liquid all the way to absolute zero, unless external pressure (∼3 megapascals ≈ 30 atm) is applied. This is because the atoms are not at rest at 0 K; the zero-point motion acts as an internal pressure which must be overcome in order to bring the atoms close enough together for solidification. All other substances, including the hydrogens, freeze under their own vapor pressure above 10 K.

The two melting curves are quite different in detail because of the different types of quantum statistics which the particles obey. There is a pronounced minimum in the ³He melting pressure which is unique, and can be understood by considering the entropies of the liquid and the solid. The pressure minimum leads to the bizarre situation of the addition of heat causing freezing. The inverse of this process, the adiabatic formation of the solid by compression, is an important process which has been used extensively to cool liquid and solid ³He to temperatures of approximately 1 mK. See Cryogenics, Liquid helium