Thermal Transport in Defective Uranium Nitride: Effects of Point Defects, Anharmonicity, and Electronic Contributions

Abstract: The impact of point defects on thermal transport in uranium nitride (UN) is investigated using a MLIP combined with Green-Kubo (GK) and normal mode analysis (NMA) methods over 300-1500 K. In pristine UN, temperature-dependent calculations of lattice thermal conductivity reveal that four-phonon scattering is essential yet sufficient to accurately capture high temperature anharmonic phonon transport, as evidenced by close agreement between GK and ShengBTE calculations including three- and four-phonon processes. In defective systems, all types of point defects significantly reduce thermal conductivity at low temperature. Mode-resolved analysis further shows that interstitial defects introduce new phonon states due to a stronger local strain effect. Notably, the uranium interstitial leads to strong defect-phonon scattering over broad phonon spectrum, while the other point defects produce more selective scattering, with even reduced phonon scattering for some acoustic modes. The optical contribution to thermal conductivity remains nearly constant in the presence of IU, but decreases with increasing temperature for pristine and the other defect types. The total thermal conductivity, incorporating electron-phonon coupling and an estimated electronic contribution, yields excellent agreement with experiment in the pristine system, with electronic contributions dominating thermal transport above 600 K. Moreover, with defect-electron contribution introduced through a semiclassical electron-defect scattering model, it is found that (i) the total conductivity degradation follows IU, VU, IN, and VN in descending order, and (ii) electron-phonon coupling becomes negligible in defective systems. These results provide a unified understanding of defect-dependent thermal transport in UN.

• The paper combines machine-learning molecular dynamics, Green–Kubo analysis, normal-mode methods, EPW electron–phonon rates, and resistivity modeling to quantify lattice and electronic thermal transport in UN with 0.46% point defects.
• Four-phonon scattering is essential for reproducing pristine UN conductivity at high temperatures, while uranium interstitials cause the strongest lattice-transport degradation below about 900 K and mobile nitrogen interstitials can create misleading Green–Kubo heat-flux signals.
• Electronic conduction dominates total thermal transport above roughly 600 K, shifting the defect-impact ranking to uranium interstitials, uranium vacancies, nitrogen interstitials, and nitrogen vacancies, although hard-sphere electron–defect assumptions limit predictive accuracy.

Overview

Uranium nitride (UN) is a candidate accident-tolerant nuclear fuel whose thermal conductivity arises from both lattice and electronic channels. This work by Chen et al. presents a systematic computational study of how the four elementary point defects—uranium interstitials ($\mathrm{I}_\mathrm{U}$), nitrogen interstitials ($\mathrm{I}_\mathrm{N}$), uranium vacancies ($\mathrm{V}_\mathrm{U}$), and nitrogen vacancies ($\mathrm{V}_\mathrm{N}$)—at a fixed concentration of 0.46% affect thermal transport in rock-salt UN over 300–1500 K. The methodology combines a previously validated machine learning interatomic potential (MLIP) (2605.17726) with Green–Kubo (GK) equilibrium molecular dynamics, normal mode analysis (NMA) within the relaxation time approximation (RTA), DFT-derived electron–phonon scattering rates from EPW, and a semi-classical electrical resistivity model that explicitly includes electron–defect scattering. The study extends prior defect studies in UN (2605.17726) by covering all four defect types for the lattice channel and by incorporating electron–phonon coupling into the total conductivity.

Lattice thermal conductivity of pristine UN

For pristine UN, GK calculations agree closely with ShengBTE Boltzmann transport results that include both three- and four-phonon processes using the same MLIP. Fitting to a Klemens–Callaway form $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$ yields nearly identical parameters between GK and ShengBTE(3ph+4ph), with $B \approx 2.0\times10^{-4}$ W$^{-1}\cdot$m and $C \approx 1.8\times10^{-7}$ W$^{-1}\cdot$m$\cdot$K$\mathrm{I}_\mathrm{N}$0. Because the GK formalism implicitly captures all anharmonic processes present in the potential while ShengBTE treats them explicitly, this agreement supports the claim that four-phonon scattering is essential yet sufficient to describe high-temperature anharmonic transport in pristine UN; three-phonon-only BTE calculations systematically overestimate $\mathrm{I}_\mathrm{N}$1 at elevated temperature. The classical treatment is justified because the lowest simulated temperature (300 K) lies near the upper bound of reported Debye temperatures (181–364 K), so quantum corrections are negligible.

NMA results track GK closely at high temperature but redistribute the fitted temperature dependence toward stronger higher-order scattering (smaller $\mathrm{I}_\mathrm{N}$2, larger $\mathrm{I}_\mathrm{N}$3). NEMD data based on the angular-dependent potential of Kuksin et al. show anomalously high $\mathrm{I}_\mathrm{N}$4 between 700–1000 K, which the authors attribute to the ADP's truncated higher-order interaction terms producing an overly quasi-harmonic description; these points were excluded from fitting.

Defect-induced degradation of lattice transport

At 0.46% concentration, all four defects reduce $\mathrm{I}_\mathrm{N}$5 below ~900 K, with degradation ordered as $\mathrm{I}_\mathrm{N}$6 in the GK results. Above ~1100 K, $\mathrm{I}_\mathrm{N}$7 for pristine UN and for the $\mathrm{I}_\mathrm{N}$8, $\mathrm{I}_\mathrm{N}$9, and $\mathrm{V}_\mathrm{U}$0 systems converges, indicating that phonon–phonon scattering dominates in that regime. The severity of $\mathrm{V}_\mathrm{U}$1 follows conventional theory: its large mass variance combined with a strong local strain field scatters phonons across a broad frequency range.

Two notable anomalies appear. First, UN containing $\mathrm{V}_\mathrm{U}$2 exhibits an apparent increase in $\mathrm{V}_\mathrm{U}$3 above 1100 K that scales with defect concentration. The authors attribute this not to physical heat conduction but to the convective term in the microscopic heat current: mobile nitrogen interstitials contribute increasingly to the GK heat flux at high temperature, so the GK method captures defect-dynamics-mediated energy transport that a phonon-quasiparticle framework does not. This constitutes a methodological caution—the distinction between GK and NMA becomes critical in systems with mobile defects. Second, GK systematically yields higher $\mathrm{V}_\mathrm{U}$4 than NMA-RTA in defective systems (the reverse of the pristine case). The authors identify two causes: single-mode RTA neglects coherent off-diagonal contributions from mode–mode coupling induced by disorder (in the sense of Allen–Feldman and Simoncelli et al.), and exponential fitting of rapidly decaying modal autocorrelation functions introduces numerical uncertainty in extracted lifetimes.

Mode-resolved phonon scattering

NMA-extracted relaxation times reveal several defect-specific behaviors. Interstitials introduce new high-frequency vibrational states due to their stronger local strain fields; the lighter $\mathrm{V}_\mathrm{U}$5 produces localized gap modes within the phonon bandgap. The heavy $\mathrm{V}_\mathrm{U}$6 increases scattering rates across the entire spectrum, whereas $\mathrm{V}_\mathrm{U}$7, $\mathrm{V}_\mathrm{U}$8, and $\mathrm{V}_\mathrm{U}$9 produce more selective scattering—and, notably, certain low-frequency acoustic modes exhibit reduced scattering rates relative to pristine UN, implying defect-induced phase-space restriction allows some acoustic modes to propagate with less resistance than in the perfect crystal.

The optical contribution ($\mathrm{V}_\mathrm{N}$0 THz) decreases monotonically with temperature in pristine UN but remains nearly constant at approximately 24% in the $\mathrm{V}_\mathrm{N}$1 system across the full temperature range. This indicates that $\mathrm{V}_\mathrm{N}$2 pushes transport toward a disorder-dominated regime where defect-induced structural scattering, rather than temperature-dependent anharmonicity, constrains branch contributions. For other defects, the relative optical contribution follows $\mathrm{V}_\mathrm{N}$3 pristine, reflecting that defect scattering suppresses acoustic carriers more strongly than optical ones.

Electronic contributions and total thermal conductivity

Combining NMA phonon lifetimes with Matthiessen-composed electron–phonon scattering rates (from EPW) yields $\mathrm{V}_\mathrm{N}$4, and adding $\mathrm{V}_\mathrm{N}$5 estimated via the Wiedemann–Franz law gives $\mathrm{V}_\mathrm{N}$6. Electrical resistivity is modeled semi-classically following Zhou et al., including electron–phonon ($\mathrm{V}_\mathrm{N}$7), electron–electron ($\mathrm{V}_\mathrm{N}$8), residual, saturation, and electron–defect terms, with parameters fitted to Moore et al.'s resistivity data and defect volumes computed with the MLIP. The authors justify this choice over direct DFT-BoltzTraP estimates because the latter omit electron–defect scattering, which dominates the defect contribution to resistivity at these concentrations.

For pristine UN, the predicted $\mathrm{V}_\mathrm{N}$9 agrees well with Takahashi et al.'s measurements at 300 K, whereas prior MD studies neglecting electron–phonon coupling overestimate room-temperature conductivity. Electron–phonon coupling substantially reduces $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$0 at low temperature but becomes negligible above ~600 K, where intrinsic phonon–phonon scattering dominates lattice resistance; electronic conduction dominates total transport above ~600 K.

In defective systems, two findings stand out. First, electron–phonon coupling has a negligible effect on $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$1 for uranium-related defects at all temperatures, remaining noticeable only for nitrogen-related defects near 300 K. Second, the total-conductivity degradation ordering shifts to $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$2—different from the lattice-only GK ordering—because defect-specific suppression of $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$3 via electron–defect scattering governs the high-temperature differences once $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$4 values converge.

Limitations and open questions

The paper is explicit about the principal weakness of its treatment of electronic transport in defective UN. The electron–defect scattering cross section is approximated geometrically as $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$5 from atomic radii, treating defects as hard-sphere scatterers; consequently, the model cannot distinguish defects of the same species with qualitatively different local potentials, and the predicted ordering $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$6 for $\kappa_{\mathrm{L-ph}} = 1/(A + BT + CT^2)$7 degradation reflects primarily the contrast between U and N atomic radii rather than defect-specific electronic structure. The Fermi energy is taken from pristine UN and held fixed, and the electron relaxation time calibrated on pristine resistivity is applied uniformly to defective cases even