First-principles investigation of electrons’ thermal excitations in UN, UAl2 and ThN

https://doi.org/10.1016/j.ssc.2020.114131Get rights and content

Highlights

  • The calculated (γ) electronic coefficient of UN’s heat capacity agrees with the evaluated experimentally for 300 K-1700 K.

  • The calculated γ of ThN is low (0.00289 J mol-1 K-2), but still higher than the evaluated experimentally for 300 K-1700 K.

  • The evaluated experimentally γ for UN, at low temperatures, is much higher than the calculated.

  • Electronic energy correction for ThN, UAl2, UN (magnetic) are one order of magnitude smaller than the Grüneisen parameters.

  • Electronic anharmonicity effect can be neglected in thermal expansion calculations for ThN, UAl2, UN (magnetic).

Abstract

We investigated the electronic heat capacity and energetics of thermal excitations of electrons around Fermi energy of selected metallic compounds (UN, UAl2 and ThN) using first-principles methods. The effect of magnetism was evaluated for UN and UAl2. The generalized gradient approximation (GGA) of the Perdew, Burke, and Ernzerhof functional, developed for solids (/PBEsol) as implemented in Quantum ESPRESSO (QE) was used for UN and UAl2 while the earlier PBE was used for ThN. We found that electrons' thermal excitations would only slightly affect the equilibrium lattice constants in considered compounds except for non-magnetic UN, where it needs to be taken into account. The electron density of states at Fermi energy is larger and therefore an increased effect was found. The calculated electronic heat capacity i predicted to be the largest for non-magnetic UN and very small for non-magnetic ThN. The electronic heat capacity is lower for ferromagnetic UN and UAl2 and larger for all compounds in a non-magnetic state when the lattice constant decreases. Electronic heat capacity increases with temperature and becomes more significant at higher temperatures. The predicted γ coefficients are smaller than the evaluated experimentally at low temperatures, but is in a better agreement with the lower values evaluated at 300 K–1700 K temperature range. Our evaluations of the respective electronic energy correction parameters due to electrons’ thermal excitations show that except for non-magnetic UN, they are at least one order of magnitude smaller than the Grüneisen parameter for ferromagnetic UN, both non-magnetic and ferromagnetic UAl2 and ThN.

Introduction

Traditional urania fuel is not suitable for some designs of new generation reactors (e.g., SuperCritical Water Reactor) due to its low thermal conductivity [1]. In the context of finding a sustainable development solution to non-renewable energy sources, innovative research towards enhanced accident-tolerant nuclear fuel (EATF) that can withstand the loss of coolant for a long time is gaining momentum. EATF materials must have higher thermal conductivities (κ) to prevent meltdown [2].

High-density metallic fuels, U3Si2 and uranium nitride (UN) have been proposed as alternative EATF fuels [2]. U-density (34.2 atoms/nm3) in UN is higher than in UO2 (24.47 atoms/nm3); therefore, it is more suitable for implementation as a lower enrichment (LEU) fuel.

The thermal conductivities of UN and UO2 have been compared in Ref. [3]. It was shown that, in contrast to a typical ceramic-like UO2, the thermal conductivity of UN increases with temperature due to a large electronic transport. In our recent papers [4,5], we calculated for the first time the electronic thermal conductivities of UN and UAl2 using first-principles codes: EPW [6], Boltztrap [7] and Quantum Espresso (QE) [8]. The calculations confirm that UN and UAl2 have higher thermal conductivity than urania at higher temperatures due to the increase with temperature of the electronic contributions, as also observed experimentally. ThN is another metallic fuel of recent interest, although it has been investigated experimentally for some time [9].

First-principles calculations are expensive; therefore, classical molecular dynamics codes like LAMMPS [10] are often used to investigate thermomechanical properties. However, as these codes cannot evaluate the electronic contributions, we attempt, in this work, to evaluate it using first-principles methods based on density functional theory (DFT).

Section snippets

Calculation methodology

To evaluate the geometrical and electronic structures for both non-magnetic and ferromagnetic UN, UAl2 and non-magnetic ThN, we used QE code [8] since there is already an interface provided between QE and Boltzmann Transport Properties (BoltzTraP) [7], EPW [6] codes and a software package: ShengBTE [11]. In this work, we used ShengBTE to evaluate the Grüneisen parameter (ς), which is defined for individual frequency modes (ωi) as:ςi=ln(ωi)ln(V)

It defines a nonlinear response to a frequency

Results

We used previously determined equilibrium structures [4,5] for UN and UAl2 with norm-conserving pseudopotentials: U.pbesol-n-nc.UPF, N.pbesol-nc.UPF and Al.pbesol-n-nc.UPF from QE code. The equilibrium lattice constants for both the UN and UAl2 were larger for the ferromagnetic state (0.497 nm and 0.77894 nm) than for the non-magnetic state (0.489 nm, 0.76429 nm). ThN has been studied recently [13], and we adopted here the same parameters and norm-conserving pseudopotentials: Th2·UPF and

Summary

We have found that first-principles calculations using Quantum ESPRESSO (QE) with the generalized gradient approximation (GGA) predict the electronic parameter (γ) smaller than evaluated experimentally from polynomial fit for low temperatures (below 100 K) [14] for UN but in good agreement for 300 K–1700 K temperature range [15]. Our result agrees with the previous similar discrepancy for U3Si2 [16] at low temperature. Therefore we conclude that further investigations are required to clarify

Author contribution

Barbara Szpunar: Conceptualization, Methodology, Software, Writing, Jayangani. Ranasinghe: Investigation, Software, Linu Malakkal: Investigation, Software, Jerzy A. Szpunar: Conceptualization, Reviewing and Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge access to high-performance supercomputers at Compute Canada (CalculQuebec and WestGrid) and Plato at the University of Saskatchewan.

Free access to Quantum Espresso and ShengBTE codes with technical support is acknowledged. The first author acknowledges beneficial private communication with Dr. K. Gofryk.

This work was supported by the Discovery grant of Dr. B. Szpunar from the Natural Sciences and Engineering Research Council of Canada.

References (17)

  • J.A. Webb et al.

    J. Nucl. Mater.

    (2012)
  • B. Szpunar et al.

    J. Phys. Chem. Solid.

    (2020)
  • S. Poncé et al.

    Comput. Phys. Commun.

    (2016)
  • G.K.H. Madsen et al.

    Comput. Phys. Commun.

    (2006)
  • S.J. Plimpton

    Fast parallel algorithms for short-range molecular dynamics

    J. Comput. Phys.

    (1995)
  • W. Li et al.

    Comput. Phys. Commun.

    (2014)
  • D. Pérez Daroca et al.

    J. Nucl. Mater.

    (2016)
  • S.S. Parker et al.

    J. Nucl. Mater.

    (2019)
There are more references available in the full text version of this article.

Cited by (1)

View full text