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Phonon lifetimes are a key component of quasiparticle theories of transport, yet first-principles lifetimes are rarely directly compared to inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to be reliable. In this work, we demonstrate that the reciprocal space voxel ($q$-voxel), which is the finite region in reciprocal space required in INS data analysis, must be explicitly accounted for within theory in order to draw a meaningful comparison. We demonstrate accurate predictions of peak widths of the scattering function when accounting for the $q$-voxel in CaF$_2$ and ThO$_2$. Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green's function, serving as critical benchmark of theory, and indicating that other material properties should be accurately predicted; which we demonstrate for thermal conductivity.

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of the elastic constant tensor and the thermal expansion in thoria (ThO$_2$) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data driven applications.

The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry. In the realm of nonlinear dynamics, however, additional nonlinear propagating modes are possible. Nonlinear propagating modes have unique properties that are important in many disciplines including optical communications, conducting polymers, biology, magnetism, and nuclear physics. Yet, despite the crucial importance of crystal lattice vibrations in fundamental and applied science, such additional propagating modes have not been observed in ordinary crystals. Here, we show that propagating modes exist beyond the phonons in fluorite-structured thoria, urania, and natural calcium fluoride using neutron scattering and first-principles calculations. These modes are observed at temperatures ranging from 5 K up to 1200 K, extend to frequencies 30–40% higher than the maximum phonon frequency, and travel at velocities comparable to or higher than the fastest phonon. The nonlinear origin of the modes is explained in part via perturbation theory, which approximately accounts for nonlinearity. Given that these modes are still clearly observed at 5 K, they are likely an inherent feature of the quantum ground state. The existence of these waves in three-dimensional crystals may have ramifications for material properties. Under extreme conditions, nonlinear lattice dynamics in a material can manifest and reveal unexpected properties. Here, using inelastic neutron scattering and first-principles calculations the authors find the presence of nonlinear travelling waves in a fluorite structured system, which exhibit characteristics different from regular phonons.

Alloys of hexagonal $\delta$-phase UZr$_2$ have been synthesized and studied by means of heat capacity, magnetic susceptibility, magnetization, electrical resistivity, magnetoresistance, thermoelectric power, thermal conductivity measurements, for the first time, at temperatures from 1.8 to 300 K and in magnetic fields up to 8 T. The weak temperature dependence of the magnetic susceptibility and the small value of both Seebeck (0.75 $\mu$V/K at room temperature) and of the Sommerfeld coefficient (13.5 mJ mol$^{-1}$ K$^{-2}$) point to 5$f$-electrons in this material having a delocalized nature. The electrical resistivity and magnetoresistance indicate the presence of significant electronic disorder in $\delta$-UZr$_2$, consistent with the disorder in its crystal structure. Density functional theory calculations have been performed and compared to experimental results., Comment: Accepted by Philosophical Magazine Letters

Here we present four independent advances which facilitate the computation of phonons and their interactions from first-principles. First, we implement a group-theoretical approach to construct the order N Taylor series of a d-dimensional crystal purely in terms of space group irreducible derivatives (ID), which guarantees symmetry by construction and allows for a practical means of communicating and storing phonons and their interactions. Second, we prove that the smallest possible supercell which accommodates N given wavevectors in a d-dimensional crystal is determined using the Smith Normal Form of the matrix formed from the corresponding wavevectors; resulting in negligible computational cost to find said supercell, in addition to providing the maximum required multiplicity for uniform supercells at arbitrary N and d. Third, we develop a series of finite displacement methodologies to compute phonons and their interactions which exploit the first two developments: lone and bundled irreducible derivative (LID and BID) approaches. LID computes a single ID, or as few as possible, at a time in the smallest supercell possible, while BID exploits perturbative derivatives for some order less than N (e.g. Hellman-Feynman forces) in order to extract all ID in the smallest possible supercells using the fewest possible computations. Finally, we derive an equation for the order N-2 volume derivatives of the phonons in terms of the order N ID. Given that the former are easily computed, they can be used as a stringent, infinite ranged test of the ID. Our general framework is illustrated on graphene, yielding irreducible phonon interactions to fifth order. Additionally, we provide a cost analysis for the rock-salt structure at N=3, demonstrating a massive speedup compared to popular finite displacement methods in the literature.

Advanced nuclear reactor concepts aim to use fuels that must withstand unprecedented temperature and radiation extremes. In these fuels, thermal energy transport under irradiation is directly related to fuel longevity, reactor safety, and is arguably one of the most important performance metrics. Here we provide a comprehensive, first-principles-informed treatment of phonon mediated thermal transport in a defect-bearing actinide oxide with direct comparison to experimental measurements. Pristine and proton irradiated thorium dioxide was chosen as a model system to treat the complexity of thermal transport in the presence of lattice defects. A thermal transport model is implemented using the linearized Boltzmann transport equation (LBTE) with input from first principles calculations and defect evolution models. Density functional theory is used to calculate phonon dispersion in thorium dioxide and used as an input to calculate both intrinsic and extrinsic, defect-induced relaxation times. In addition, a defect evolution model is benchmarked using microstructure characterization of as-irradiated thorium dioxide using a combination of electron microscopy and optical spectroscopy. The output of the LBTE is compared directly to mesoscopic measurements of thermal conductivity on length scales commensurate with defect accumulation. Parametric measurements of conductivity with irradiation dose and temperature suggest a saturation in the reduction of thermal conductivity with increasing defect generation, which is partially captured in our defect evolution model and LBTE framework. This comprehensive, atomistic- to meso-scale treatment provides the necessary basis to investigate thermal transport under irradiation in more complex systems that exhibit strong electron correlation.