Speaker
Description
For solid moderators, the incoherent approximation has been widely used to calculate thermal neutron scattering laws at different temperatures. The only input needed in the incoherent approximation is the phonon density of states. Traditionally, the phonon densities of states are calculated by fitting the interatomic force constants to experimental data, such as low-temperature inelastic neutron scattering measurements of phonon dispersion relations. Nowadays, phonon frequencies are routinely calculated by using first-principles calculations. First-principles ground state energy calculations are performed at zero Kelvin, assuming fixed-ion approximation. It is worth mentioning that the interatomic force constants are assumed harmonic, i.e., the forces that follow Hook’s law, and the obtained phonon density of states are temperature independent. That is, there are inherent uncertainties in the calculated scattering laws at different temperatures, due to the use of such phonon densities of states. These uncertainties become more significant if the scattering law of a given solid is calculated at high temperatures.
In this work, we will present the calculated results for the inelastic and coherent elastic scattering cross-sections of aluminum at high temperatures, starting from first-principles Temperature-dependent phonon density of states. These phonon densities of states will be compared with measured ones using inelastic neutron scattering at different temperatures. Aluminum has a relatively low melting point of 933 K, and anharmonicity effects at elevated temperatures are of technological and scientific importance. In addition to its low density, cost, and high radiation resistance, aluminum is considered a transparent element to thermal neutrons; this is by virtue of its relatively low neutron absorption and scattering cross-sections. Aluminum alloy Al6061 is considered a convenient material for different structural elements of neutron sources and is used as a sample holder in neutron scattering experiments. It is worth noting that the current ENDF/B-VIII evaluation of aluminum uses measured phonon density of states at 80 K [1] to calculate thermal neutron scattering laws up to 800K. Granada used a Debye phonon density of states to study neutron slowing down in Al6061 at low temperatures [2]. The evaluation of neutron thermalization in aluminum at high temperatures becomes a necessity.
References
[1] Stedman, R., Almqvist, L. & Nilsson, G. Phonon-Frequency Distributions and Heat Capacities of Aluminum and Lead. Phys. Rev.162, 549 (1967).
[2] Granada, J. R. Slow neutron total cross-section of Al6061 at low temperatures. J. Nucl. Mater.277, 346–350 (2000).