Journal of Nuclear Materials 452 (2014) 6–9

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Journal of Nuclear Materials

journal homepage: www.elsevier .com/locate / jnucmat

First results on oxygen self-diffusion in a-Pu2O3 investigatedby molecular dynamics

http://dx.doi.org/10.1016/j.jnucmat.2014.04.0440022-3115/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: National Key Laboratory for Surface Physics andChemistry, P.O. Box 718-35, Mianyang 621907, China. Tel.: +86 816 3626740.

E-mail address: yuhuilong2002@126.com (H. Yu).

Huilong Yu a,b,⇑, Daqiao Meng a, He Huang a, Gan Li a

a National Key Laboratory for Surface Physics and Chemistry, P.O. Box 718-35, Mianyang 621907, Chinab Department of Engineering Physics, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

Article history:Received 13 December 2013Accepted 26 April 2014Available online 10 May 2014

a b s t r a c t

The oxygen self-diffusion of a-Pu2O3 has been investigated by molecular dynamics method. The empir-ical potential of a-Pu2O3 has been fitted. Based on this new potential, the calculation results, such as cellparameters, bulk modulus and dielectric constants, are well consistent with experimental data and pre-vious reports. In this study, we systematically calculated the oxygen self-diffusion coefficients of a-Pu2O3

in the temperature range of 750–2100 K and the activation energy of a-Pu2O3 was obtained from thesecalculations.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Plutonium oxides have been extensively investigated because oftheir great importance in nuclear fuel cycle and in long-term stor-age of Pu-based radioactive waste, as well as their unique physicaland chemical properties. When metallic plutonium is exposed todry air ambient, a sandwiched structure is formed which consistsof a plutonium dioxide (PuO2) outer layer and a thin plutoniumsesquioxide (Pu2O3) inner layer on the metal substrate [1,2]. ThePuO2 layer can be further reduced to Pu2O3 via an oxygen diffusionprocess through the Pu2O3 layer to react with Pu metal, when it ispresent in reductive ambient, such as Ultra High Vacuum (UHV), ata temperature above �20 �C [3]. The reduction of PuO2 is acceler-ated in vacuum as the temperature goes up to 150 �C [2].

The actinide sesquioxide can be crystallized into three differentcrystal structures, the hexagonal La2O3 structure, the monoclinicSm2O3 structure, and the cubic Mn2O3 structure, respectively [4].However, only Mn2O3 (a-Pu2O3) and La2O3 structures (b-Pu2O3)have been successfully synthesized in experiments[4]. a-Pu2O3 isa very important material for long-term Pu-based radioactivewaste storage and it can be obtained by reducing PuO2 at low tem-perature in reductive ambient[3]. On the other hand, b-Pu2O3 canonly be obtained at relatively higher temperature (above1500 �C) by reducing PuO2 with plutonium metal [5], dry hydrogen[6], or carbon [7]. a-Pu2O3 can be transformed into b-Pu2O3 and thetransformation temperature is about 450 �C. Consequently,a-Pu2O3 is the only metastable phase at low temperatures [8].

For long-term radioactive waste storage at room temperature,a-Pu2O3 is mostly in its a phase. Therefore, in our study, allcalculations are based on a-Pu2O3.

Usually, a-Pu2O3 is considered as the ideal stoichiometric cubicplutonium sesquioxide containing 32 Pu atoms and 48 O atoms perunit cell, while crystalline PuO2 with a CaF2 crystal structurecontains 4 Pu atoms and 8 O atoms per unit cell and these Puand O atoms further form both face-centered and simple cubicsublattices (Fig. 1). Actually, the two types of oxides are correlated,because an a-Pu2O3 unit cell can be obtained by removing 25% of Oatoms from a PuO2 2 � 2 � 2 supercell to create 25% O vacancies inthe 16c (0.25, 0.25, 0.25) sites [9,10] (Fig. 1).

For a long term, thermal properties of PuO2 and a-Pu2O3 arefound to play an important role in handling and storage ofplutonium. The knowledge of plutonium oxide about thermalproperties, such as specific heat, thermal expansion, and thermalconductivity, is essential to evaluate the plutonium’s performancewhich is in related to the defects, recrystallization and creep deter-mined by the diffusion of intrinsic ions. However, the experimentalstudies of Pu and its compounds have been limited because mainlyof radio-toxicity of Pu atoms. Moreover, single-phase a-Pu2O3 isstable only when the temperature is above 300 �C [11] and it istoo active to be readily detected in the atmosphere. However,molecular dynamics method (MD) is free from these limitationsfor this kind of materials. As an atomic scale method it has beenextensively used to study self-diffusion processes in metals[12,13] and ceramics [14] with empirical interatomic potentials.Therefore, it is also a facile and effective tool to investigate thethermal properties of nuclear materials. MD has been widelyapplied to evaluate the thermal properties of nuclear materialsand oxide fuels such as PuN [15], UO2 [16–19], PuO2 [16,19],

Fig. 1. (a) PuO2 unit cell and (b) a-Pu2O3 unit cell. Blue and red spheres denote Pu and O atoms, respectively. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

H. Yu et al. / Journal of Nuclear Materials 452 (2014) 6–9 7

(U,Pu)O2 [19–21], a-Pu2O3 [22]. However, very few MD studiesabout oxygen self-diffusion in a-Pu2O3 have been reported.

In this study, the self-diffusion behaviors of oxygen in a-Pu2O3

has been studied by theoretical calculations with empirical poten-tials. Compared to previously reported data, our results showedadvantages in such process analyses.

Table 1Potential parameters for a-Pu2O3.

Type ofinteraction

A (eV) q (Å) C (eV Å6) K2O–O (eV Å�2) Cutoff (Å) Source

Oshell–Oshell 22764 0.1490 31.984 – 12 [24]Oshell–Pucore 1304.8 0.3653 – – 10 This paperOcore–Oshell – – – 37.05 0.6 This paper

Charges: Ocore = 0.86; Oshell = �2.86; Pucore = 3.

2. Details of calculation

The method used in our work is based on implementing inter-atomic potentials and conducted by using the General Utility Lat-tice Program (GULP) [23]. The Born–Mayer–Huggins (BMH)potential and shell model potential were used for the Pu–O system.The BMH potential function is defined as:

UijðrÞ ¼ZiZje2

rijþ A exp � rij

q

� �� C

r6ij

ð1Þ

where A, q and C are adjustable parameters, rij is the distancebetween ion species i and j, Zi and Zj are the charge of ions i and j.

In Eq. (1), the term A exp � rij

q

� �describes the short-range repulsion

between ions i and j; ZiZje2

rijis the long-range Coulomb energy, and

� Cr6

ijis the attractive van der Waals interaction. The potential param-

eters A, q and C for O–O pairs are obtained from Ref. [24] and theones for Pu–O pairs are determined by the try-and-error methodhere in order to reproduce the experimental cell parameters, den-sity, space group and high frequency dielectric constants at roomtemperature. The polarization of ions was then taken into accountby the shell model for oxygen ion proposed by Dick and Overhauser[25]. The charges of O core and O shell are 0.86 and �2.86 respec-tively [24]. The interaction between the core and massless shell isconsidered to be that of a harmonic oscillator:

Eiðcore� shellÞ ¼ 1=2K2iR2

i ð2Þ

where K2 is the spring constant and Ri is the distance between thecore and shell. The obtained potential parameters are shown inTable 1.

The diffusion coefficients of anions and cations at a given tem-perature can be calculated by the Einstein formula for the depen-dence of mean square displacement (MSD) on time t. The MSD

function at t corresponds to the average square distance travelledby an atom between t0 and t. It is calculated using the followingequation:

MSDðtÞ ¼ 1N

XN

i¼1

~riðtÞ �~riðt0Þ½ �2 ð3Þ

where N is the total number of ions (plutonium or oxygen),~riðt0Þ isthe initial position of atom i, and~riðtÞ is the position at t. The self-diffusion coefficient, D, is deduced from the MSD function usingthe Einstein’s relations [26]:

D ¼ limt!1

16t

MSDðtÞ ð4Þ

Since the infinite time (t ?1) is not accessible via MD simulations,the self-diffusion coefficients are extrapolated from the asymptoticslope of MSD functions. By repeating the MSD calculation at differ-ent temperatures (T), an Arrhenius plot for the diffusion coefficientD(T) can be obtained. By this plot, the pre-exponential factor, D0,and the activation energy Ea can be directly calculated by fittingthe results of modeling obtained from the following formula:

D ¼ D0 exp � Ea

RT

� �ð5Þ

In the present study, the MD simulation were performed in3 � 3 � 3 unit cells for a-Pu2O3 under the same desired pressureand temperature (NPT), according to potential parameters inTable 1. The molecular statics(MS) optimization criterion for energytolerance of each atom in the final optimization step is less than1.0 � 10�5 eV and the final gradient norm tolerance in the simu-lated system is less than 1.0 � 10�3 eV. Usually, at each tempera-ture and pressure, an equilibrium state of the system was usuallyreached during the first 20,000 MD steps (the step time was 1 fs).

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

1.2

750K

1200K

1650K

2100K

MSD

/(10-2

0 m2 )

Time/ps

Fig. 3. Oxygen mean square displacements at 750–2100 K with a step size of 450 K.The diffusion coefficients obtained from the slopes are plotted as an Arrhénius plot.

Table 3The oxygen self-diffusion coefficients at different temperature.

Temperature (K) 750 1200 1650 2100D (m2 s�1) 4.63 � 10�12 1.36 � 10�11 2.78 � 10�11 3.92 � 10�11

8 H. Yu et al. / Journal of Nuclear Materials 452 (2014) 6–9

The MD simulation was performed over 5.0 � 104 MD steps toobtain reliable results.

3. Results and discussion

3.1. Static calculations

In our study, the interatomic potentials were employed to cal-culate the properties (cell parameters, bulk modulus and dielectricconstants) of a-Pu2O3 at 298 K and 1 atm pressure. The resultsshown in Table 2 are compared with experimental data and firstprinciples calculations.

The calculated equilibrium lattice constant a and lattice volumeare in good agreement with experimentally determined latticeparameter a (11.04 Å) at 298 K [27]. In our calculation, the spacegroup of a-Pu2O3 calculated is Ia3, and it is the same as the exper-imental data [27]. The entropy (S0) and high-frequency dielectricconstant (e1) are also well consistent with the experimental data[22,27]. Unfortunately, no experimental data of bulk modulus fora-Pu2O3 are available at present. Therefore, the accuracy of thebulk modulus B in our calculations still needs to be verified inthe future by experimental data. In summary, our calculationresults are in good agreement with experimental data and firstprinciples calculations which indicates that the potential we usedin our work are reliable and the optimized values and selectedparameters are appropriate.

3.2. Dynamic calculations

Self-diffusion coefficients as a function of temperature in thesupercell of 3 � 3 � 3 unit cells were calculated in order to studythe oxygen self-diffusion in a-Pu2O3. The calculation was carriedout in a temperature range from 750 K to 2100 K with 450 K incre-ments. The self-diffusion coefficient can be calculated from thelong time slope of MSD function. As shown in Fig. 2, the diffusionrate of cations is very low at 1200 K. Due to presence of 25% oxygen

Table 2Comparisons between calculated and experimental data for a-Pu2O3.

Physical parametersof a-Pu2O3

Calculated Experimental First-principles [28]

a = b = c (Å) 11.04 11.04 [27] 11.17V (Å3) (full cell) 1345.6 1345.6 [27] 1393.7q (g cm�3) 10.39 10.4 [27] 10.04Bulk modulus (GPa) 143 – 122S0 (J K�1 mol�1) 120.1 115.4 [22] –e1 2.59 2.6 [22] –

0 10 20 30 40 50

0.1

0.2

0.3

0.4

0.5

MSD

/(10-2

0 m2 )

Time/ps

Pu3+

O2-

Fig. 2. Mean square displacements of anions and cations at 1200 K.

vacancies in the lattice, the anions arrayed in a simple cubic sublat-tice migrate at a speed of several orders of magnitude higher thanthat of the cations that are arranged in a face centered cubicsublattice.

In Fig. 3, the MSD of oxygen is plotted at all temperatures. Thediffusion coefficients shown in table 3 are obtained from theseslopes. They increase as the temperature goes up. The oxygenself-diffusion coefficient calculated in a-Pu2O3 at 1200 K is almosttwo orders of magnitude higher than that in PuO2 [29]. In partiallyreduced CeO2, the oxygen self-diffusion coefficient is on the orderof 10�10 m2 s�1 at 1200 K [30] which is slightly higher than thatin a-Pu2O3 we obtain in the present study. By investigating thekinetics of this auto-reduction reaction from PuO2 to Pu2O3 at303 K, a value of 1.4 � 10�20 m2 s�1 is obtained for the diffusioncoefficient of oxygen in a-Pu2O3 [31]. The oxygen self-diffusioncoefficient we obtained in the present study is several orders ofmagnitude higher than that of experiments. This may be mainlybecause that the temperature in our study are different with exper-iments. Moreover, defects might exist in the experimental sampleswhich can also affect the oxygen diffusion.

The obtained results are presented in Fig. 4 in an Arrhénius rep-resentation (i.e. ln(D) as a function of 1/RT). For comparison, theevolution of oxygen self-diffusion coefficients calculated in the bulkof PuO2 and PuO2-x are plotted in the same graph. It can be clearlyseen that the self-diffusion coefficient of oxygen in a-Pu2O3 ishigher than that of PuO2 and PuO2�x, especially at 1000 K. Fromthe calculated diffusion coefficients shown in Fig. 4, the activationenergy of oxygen was deduced using the standard Arrhénius rela-tion. The curves of PuO2 in Fig. 4 were obtained by an isotopeexchange method using stoichiometric PuO2 [32,33]. The activationenergy for oxygen diffusion in these materials was 186.7 and176.4 kJ/mole, respectively. Bayoglu reported an activation energyfor oxygen vacancy diffusion of 46.1 kJ/mole by gravimetric oxida-tion of PuO2�x (x = 0.08, 0.05, 0.03) [34]. In our work, the activationenergy of oxygen self-diffusion is smaller in a-Pu2O3 (20.8 kJ/mole)than in PuO2 and PuO2�x, indicating the oxygen self-diffusioncoefficients in a-Pu2O3 are about the same order at low and hightemperature. In addition, different activation energies in plutoniumoxides could also mean different atomic diffusion pathways. It isalso worth pointing out that the activation energy is consistent withdiffusion coefficients.

0.4 0.6 0.8 1.0 1.2 1.4

-45

-40

-35

-30

-25

ln[D

/(m2 s-1

)]

103 T -1/K-1

α-Pu2O3

PuO2-x

PuO2[32] PuO2[33]

2500 2000 1500 1000T/K

750

Fig. 4. Temperature dependence of oxygen self-diffusion coefficients in PuO2,PuO2�x and a-Pu2O3.

H. Yu et al. / Journal of Nuclear Materials 452 (2014) 6–9 9

In Pu-based materials, the formation of defects are in variousprocesses. For example, the main defects (Pu vacancies) are pro-duced by alpha auto-irradiation during the storage, and the Fren-kel-type defects are created during in-pile operations. PuO2 isassumed to contain Frenkel-type defects which consist of bothoxygen vacancies and interstitials [35]. The point defects of substo-ichiometric PuO2�x are oxygen vacancies, and a-Pu2O3 is also anoxygen deficient material with an abundance of oxygen vacancies.Oxygen diffusion in the plutonium oxides occurs through themigration of either oxygen vacancies or interstitials. The migrationenergy of oxygen interstitial diffusion is relatively higher than oxy-gen vacancy diffusion in PuO2 [36]. It can be concluded that themigration barriers of oxygen diffusion decrease in the order ofPuO2, PuO2-x and a-Pu2O3, which is consistent with our simulationresults. As a result, the dependence of oxygen diffusion on the oxy-gen/plutonium ratio plays an important role in diffusion coeffi-cients and activation energies.

Although the oxygen self-diffusion coefficients in a-Pu2O3 havenot been measured experimentally at high temperature, measure-ments of oxygen self-diffusion have been made in cerium dioxide,a compound with quite similar chemical nature to plutonium diox-ide. The activation energy of oxygen vacancies in CeO1.8 areapproximately 19 kJ/mole [37], which may be the migrationenergy of anion vacancies. This value is very close to the activationenergy of oxygen self-diffusion of our calculations in a-Pu2O3.

4. Conclusion

In this study, we fitted and developed empirical potentials tomodel a-Pu2O3 and simulate the oxygen self-diffusion in bulk a-Pu2O3. A group of critical properties of crystal a-Pu2O3 were calcu-lated in a reasonable way and the results are in good agreementwith experimental data. According to molecular dynamics simula-tions, the oxygen self-diffusion is found to be much faster than theplutonium self-diffusion in a-Pu2O3. In addition, comparing with

PuO2 and PuO2�x, a-Pu2O3 has fairly larger oxygen self-diffusioncoefficients at the same temperature and smaller activation energyfor oxygen atoms.

Acknowledgments

The authors would like to thank J.D. Gale for using the GULPprogram.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jnucmat.2014.04.044.

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