Experiments performed by GA personnel at the Brookhaven National Laboratory prior to the construction of the prototype TRIGA reactor showed that zirconium hydride has very unusual moderating properties for thermal neutrons. These experimental results can be explained by assuming that the hydrogen-atom lattice vibrations can be described by an Einstein model with a characteristic energy, hν = 0.140 eV. This description is consistent with the theory that the hydrogen atom occupies a lattice site at the centre of a regular tetrahedron of zirconium atoms.
The results of these experiments showed that:
The results of the experiments show that hydrogen atoms bound in a ZrH lattice (Figure 2) act like harmonic oscillators, or Einstein oscillators. In the so-called Einstein model, each atom is thought of as being bound isotrop to a fixed centre about which it can oscillate harmonically.
Such an oscillator has possible energy states [n + (3/2)]hν, h being Planck's constant (6.62 x 10-34 Js), ν the oscillator frequency, and n an integer. In a scattering event with such an individual oscillator, a neutron can hence gain or lose an integral multiple, hν, of energy.
The following theoretical model was therefore adopted. The hydrogen atoms behave as if isotrop bound in an approximately harmonic potential well and have identical frequencies, ν, such that hν = 0.140 eV, as was observed. The observed frequency spectrum is somewhat broadened by the thermal motions of the zirconium atoms to which the hydrogen atoms are bound. Successive levels may not be spaced quite evenly because of non-harmonic contributions to the potential.
In such a model, a neutron is caused to slow down by losing energy in multiples of hν, as long as its energy is above hν. Below 0.14 eV the neutron can still lose energy by the inefficient process of exciting acoustic Debye-type modes in which the hydrogen atoms move in phase with the zirconium atoms, which in turn move in phase with one another. These modes therefore, correspond to the motion of a group of atoms whose mass is much greater than that of hydrogen, and indeed even greater than the mass of zirconium. Because of the large effective mass, these modes are very inefficient for thermalising neutrons, but for neutron energies below 0.14 eV they provide the only mechanism for neutrons slowing down. (In a TRIGA core, the water provides for neutron thermalisation below 0.14 eV.) In addition, it is possible in the ZrH for a neutron to gain one or more energy units of ~0.14 eV in one or several scatterings, from excited Einstein oscillators. Since the number of excited oscillators present in a ZrH lattice increases with temperature, this process of neutron speeding-up is strongly temperature-dependent and plays an important role in the behaviour of ZrH moderated reactors.
With the assumption of an Einstein model for the slowing down of neutrons in zirconium hydride, the basic physical processes, which occur when the fuel-moderator elements are heated can be described. A rise in temperature of the hydride increases the probability that a thermal neutron (~0.025 eV) in the fuel element will gain energy from an excited state of an oscillating hydrogen atom in the lattice. Since it has a longer mean free path for collision, the speeded-up neutron has an increased chance of escaping from the fuel-moderator element before being captured. However, the water channels between the fuel elements are very effective in re-thermalising any speeded-up neutrons which escape from the fuel; thus, the probability that a neutron will return to the fuel element before being captured elsewhere is not dependent on the temperature of the hydride but is in fact a function of the water.