The contribution of nitrogen Frenkel-pair formation to the high-temperature heat capacity of uranium mononitride

Abstract: The high-temperature heat capacity of uranium mononitride (UN) remains uncertain due to conflicting measurements and models above ~1700 K. To assess whether intrinsic defect formation contributes to the observed superlinear behavior of $C_P(T)$, we perform large-scale molecular dynamics simulations using two interatomic potentials to quantify nitrogen diffusion and Frenkel-pair populations from 1800--2600 K. Both models show increasing anion mobility, but the Tseplyaev potential yields substantially larger Frenkel concentrations, producing a defect heat-capacity contribution of up to ~10 J/(mol-K). This defect-driven term is consistent with the curvature seen in historical correlations and recent ab initio results, suggesting that nitrogen sublattice disorder provides a plausible intrinsic mechanism for the high-temperature heat capacity of UN.

• The paper identifies nitrogen Frenkel-pair formation as a plausible intrinsic source of uranium mononitride’s superlinear high-temperature heat capacity, linking anion disordering with rising nitrogen mobility above roughly 1800–2000 K.
• The simulations find strong potential dependence: the Tseplyaev model predicts nitrogen diffusivity up to 3.4 × 10⁻¹¹ m²/s and a defect heat-capacity contribution near 10 J/(mol·K) at 2600 K, while the Kocevski model predicts roughly 1 J/(mol·K).
• The results suggest that defect formation may explain part of the historical heat-capacity curvature independently of UO₂ contamination, but high-purity calorimetry and diffusion measurements are needed to determine the intrinsic behavior of UN.

Background: conflicting high-temperature heat capacity data for UN

Uranium mononitride (UN) is a candidate accident-tolerant fuel, yet its specific heat $C_P(T)$ above roughly 1700 K remains contested. The widely used Hayes et al. correlation exhibits a strongly superlinear rise—approaching a nearly $T^5$ dependence at the highest temperatures—derived from the enthalpy measurements of Conway and Flagella, which extend to about 2600 K and remain the only data reaching that range. The sole competing high-temperature dataset, from Affortit (up to ~2300 K), shows an almost linear temperature dependence and higher values in the 1200–1900 K window; Hayes et al. disregarded it. A central complication is that the Conway–Flagella samples contained approximately 20 wt.% UO$_2$. Because UO$_2$ undergoes a premelting superionic transition driven by oxygen Frenkel defects, producing large excess enthalpy and a broad $C_P$ anomaly near 2700 K, the reconstructed UN correlation may have inherited defect-driven curvature belonging to its UO$_2$ impurity rather than to intrinsic UN behavior.

Theoretical predictions diverge along similar lines: AIMD simulations report nearly linear $C_P(T)$; classical MD with the Tseplyaev angular-dependent potential (ADP) reproduces the steep Hayes-like rise; the Kocevski EAM potential predicts near-linear behavior; and recent AIMD combined with the disordered local moment (DLM) method—a first-principles treatment of lattice dynamics and magnetic disorder on equal footing—predicts a moderate, $T^2$-like increase. This last result is significant because it provides independent evidence that some nonlinear increase in $C_P(T)$ is intrinsic to UN, even if less dramatic than the historical correlation implies.

Simulation methodology

The authors performed classical molecular dynamics with LAMMPS using two interatomic potentials—the Tseplyaev ADP and the Kocevski EAM—in $50 \times 50 \times 50$ supercells of $T^5$0 atoms with periodic boundary conditions and a 1 fs time step, covering 1800–2600 K. Diffusivities were extracted from the long-time limit of the mean-squared displacement over 5 ns NPT-equilibrated trajectories, using the slope over the final 3 ns. No defects were inserted; all mobile species arose from spontaneously generated Frenkel pairs. Uranium remained effectively immobile throughout, while nitrogen mobility increased sharply with temperature.

Point-defect populations were quantified via Wigner–Seitz (WS) defect analysis in OVITO over 200 ps trajectories sampled every 10 ps, with time-averaged means and standard deviations reported as error bars. The defect contribution to the heat capacity was evaluated as

$T^5$1

using centered finite differences on the simulated populations and assuming a formation enthalpy $T^5$2 eV, consistent with DFT estimates and the $T^5$3 K formation energies of both potentials.

Nitrogen diffusivity and Frenkel-pair populations

Both potentials show rapidly increasing nitrogen self-diffusion above 1800–1900 K, but with systematically different magnitudes. For the Tseplyaev potential, $T^5$4 rises from $T^5$5 m$T^5$6/s at 1900 K to $T^5$7 m$T^5$8/s at 2600 K—nearly four orders of magnitude—while the Kocevski potential yields values typically one order of magnitude lower, reaching $T^5$9 m$_2$0/s at 2600 K. The onset of rapid nitrogen transport coincides with the temperature range where the Conway–Flagella enthalpy data deviate from linearity, suggesting a common microscopic origin in anion-sublattice disordering.

Frenkel-pair concentrations follow Arrhenius behavior, $_2$1, with effective activation energies of $_2$2 eV for the Tseplyaev potential and $_2$3 eV for the Kocevski potential. Notably, the Kocevski potential has the lower activation energy yet produces lower defect populations at all temperatures, indicating that the prefactor—not the activation energy alone—controls the population difference between models. The Tseplyaev potential yields concentrations growing from $_2$4 at 1800 K to $_2$5 at 2600 K, large enough to materially affect thermodynamics; the Kocevski populations are far smaller.

Defect contribution to heat capacity

The computed $_2$6 inherits this order-of-magnitude disparity: the Tseplyaev potential produces up to ~10 J/(mol·K) at 2600 K, whereas the Kocevski potential remains around 1 J/(mol·K). This directly explains why the Tseplyaev potential reproduces the strong curvature of the Hayes correlation while the Kocevski potential yields a nearly linear $_2$7—the latter underestimates the Frenkel-pair contribution and therefore misses the superlinear component. A key observation is that the temperature interval of most rapid growth in both nitrogen diffusivity and Frenkel concentration (roughly 1800–2000 K) coincides with the onset of deviations from purely phononic heat capacity in experiment and in AIMD+DLM, supporting the interpretation that UN undergoes an anion-sublattice disordering crossover qualitatively analogous to the oxygen superionic transition in UO$_2$8.

The implication is twofold: first, nitrogen Frenkel-pair formation constitutes a plausible intrinsic mechanism for superlinear $_2$9 in UN, decoupling the anomaly from the UO$_2$0 contamination argument; second, because the true intrinsic behavior likely lies between the two potential-dependent limits, the magnitude of the effect cannot be settled by classical MD alone.

Limitations and open questions

The authors state plainly that the calculated $_2$1 should be regarded as qualitative. Defect populations are highly sensitive to the choice of interatomic potential—an order-of-magnitude uncertainty propagates directly into the heat-capacity estimate—and the finite-difference evaluation of Eq. (3) is a simplified treatment that neglects, among other things, configurational entropy contributions beyond the simple formation-enthalpy scaling. The assumed $_2$2 eV is itself model- and method-dependent. Whether the AIMD+DLM $_2$3-like rise reflects the same Frenkel mechanism, or instead magnetic-disorder-coupled phonon softening, remains unresolved. The decisive test is experimental: high-purity UN samples with carefully controlled oxygen content, combined with high-temperature calorimetry and tracer-diffusion measurements, are required to confirm whether an anion-mobility crossover and correlated superlinear $_2$4 enhancement occur near the predicted temperatures.

Conclusion

This work identifies nitrogen Frenkel-pair formation as a physically plausible intrinsic contributor to the high-temperature heat capacity of uranium mononitride, with defect contributions ranging from ~1 to ~10 J/(mol·K) at 2600 K depending on the interatomic potential. The coincidence of anion mobility onset with the temperature range of observed $_2$5 curvature links the empirical anomaly to sublattice disordering analogous to superionic behavior in UO$_2$6, while leaving the precise magnitude—and hence the correct high-temperature correlation for UN—contingent on improved potentials and definitive high-purity experiments.