Abstract
The accuracy of neutron scattering cross sections is the gauge for the realistic outcome of a neutron transport simulation. To improve the traditional harmonic physics model used in such simulations, we revisit the slow neutron transport theory in crystalline materials and aim to develop a unified model that has good performance for neutron transport problems in crystals in a wide range of temperatures and pressures. The quasi-harmonic approximation (QHA) correlates phonon evolution explicitly with unit cell volume. Therefore, it is capable of evaluating a variety of material properties at finite temperatures. In this work, we show numerically that it is a very effective tool for our application as well. Within the framework of QHA, we calculate the temperature dependent characteristics of phonons in three elemental crystals, namely Be, Mg and Al. Based on the obtained results, our calculated neutron total cross sections agree closely with experimental transmission cross sections in a large temperature range below the melting point. We show that as the harmonic cross section model ignores the effects of phonon softening in these crystals, it underestimates the total inelastic cross sections at high temperatures. In the case of Al, we observe that such underestimation is up to 7% at room temperature. In addition, we study the phonon–phonon scatterings in Al. We observe that the cross section is insensitive to the finite phonon lifetimes even at 800 K.
Highlights
The objectives of this work are twofold
We show the limitations of the traditional harmonic neutron cross section model and the closer agreement with data when employing the quasi-harmonic approximation (QHA)
We investigate the feasibility of studying the deviation of vibrational density of states (VDOSs) using the transmission cross sections measured at different conditions
Summary
The objectives of this work are twofold. We show the limitations of the traditional harmonic neutron cross section model and the closer agreement with data when employing the quasi-harmonic approximation (QHA). After the pioneer works [1,2,3] on the neutron scattering in crystals in the 1950s, researchers from General Atomic established a practical methodology [4, 5] to produce neutron scattering cross sections in crystalline materials. In this methodology, force constants are obtained by fitting simple interatomic force models with measured neutron scattering data to calculate the lattice VDOSs The VDOS produced by modern density functional theory (DFT) calculations [12] have been used to estimate neutron cross sections (e.g. in [13,14,15]) to either revisit neutron transport problems or account for missing materials in the standard neutron data libraries
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