Thermodynamic Study of Dehydriding Reaction on the PuO2 (110

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Thermodynamic Study of Dehydriding Reaction on the PuO (110) Surface from First Principles 2

Cui Zhang, Yu Yang, and Ping Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01414 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018

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The Journal of Physical Chemistry

Thermodynamic Study of Dehydriding Reaction on the PuO2 (110) Surface from First Principles Cui Zhang,† Yu Yang,∗,† and Ping Zhang∗,† Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China, and Center for Applied Physics and Technology, Peking University, Beijing 100871,China E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China ‡ Center for Applied Physics and Technology, Peking University, Beijing 100871,China † Institute

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Using the first principle atomistic thermodynamic method in combination with the DFT + U theory, we calculate the pressure-temperature phase diagrams of the dehydriding reactions on the hydrogenated PuO2 (110) surface and determine the thermodynamic boundaries that control the feasibility of reaction. Effects of hydrogen coverage on the surface dehydriding processes are investigated. Compared with the dehydriding in form of water molecule accompanied by oxygen vacancy on the surface, desorption of hydrogen molecule is more energetically favorable. However, the relative hydrogen and water vapor pressure could modify the feasibility of two types of dehydriding processes, which may lead to water desorption superior to hydrogen one even at 300 K.

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1 Introduction During the handling and long storage of the plutonium material and device, the plutonium metal confronts various environment-dependent chemical corrosions. In the presence of air, plutonium metal surface is rapidly oxidized to form a protective layer of plutonium dioxide (PuO2 ) and the dioxide can be reduced to sesquioxide (Pu2 O3 ) by plutonium at the oxide-metal interface. 1 When exposed to hydrogen environment, hydriding on the oxide-coated plutonium metal occurs only after the oxide layers are penetrated, therefore, the induction period length of plutonium hydride is largely dependent on the component of the pre-existing plutonium-oxide layers. Early experimental work has showed that, compared with PuO2 layer, Pu2 O3 was found to remarkably shorten the induction period and accelerate the plutonium hydriding reaction under ambient conditions. 1 Recent hydrating experiments conducted by Dinh et al. demonstrated progressively promoted hydriding reactions on scratched and heated PuO2 -coated plutonium surfaces, attributed to the formation of significant additional nucleation sites (Pu2 O3 sites) in the oxide layer. 2 McGillivray et al. have investigated the hydrogen pressure (PH2 ) dependence of hydriding induction period and nucleation rate for dioxide covered plutonium, where the former was determined to vary inversely with PH2 , while the later was proportional to PH2 . 3 The conclusions was consistent with the diffusion barrier model in which hydrogen species need firstly to diffuse through the oxide layer that covers the metal, before reacting with the metal. Following experimental steps, theoretical efforts have been focused on the diffusion and dissociation of H2 on the oxide surfaces, which are the key process to determine the reactivity of plutonium and hydrogen. Previous study of Sun et al. showed that despite the exothermic dissociative adsorption of hydrogen molecule on the PuO2 (111) surfaces, the collision-induced dissociation barriers of H2 are 3.2 eV and 2.0 eV for stoichiometric and reduced surfaces, respectively. In contrast, H2 molecules can easily diffuse into α-Pu2 O3 (111) surface due to the presence of surface oxygen vacancies. More recently, Yu et al. found that the dissociation of hydrogen molecule on the PuO2 (110) surface is energetically favorable, with an energy barrier of 0.48 eV, and it can occur even below room temperature. 4 The dissociating hydrogen atoms are strongly bonded at the surface oxygen atom 3



sites. Further calculations indicated that hydrogen permeation through the stoichiometric PuO2 (110) surface is both thermodynamically and kinetically inhibited with a high energy barrier of 2.15 eV. 5 Attributed to underestimating the strong on-site Coulomb repulsion of 5 f electrons in plutonium, standard exchange-correlation approximations in density functional theory (DFT) fail to provide correct electronic structure and magnetic properties of PuO2 . 6–8 Previous works have shown that the DFT + U approach allow us to achieve a reliable description on the interactions of strongly correlated 5 f electrons. By adding an energy term of the effective Hubbard parameter, the antiferromagnetic Mott insulator feature and electronic as well as structural properties of PuO2 bulk material are well described. 8–17 Jomard and Bottin applied the DFT + U method to investigate the influence of electronic correlations on thermodynamic stability of PuO2 surfaces and obtained a proper description on the electronic features of the insulating PuO2 surfaces, which is a prerequisite to explore chemical reactions on the PuO2 surfaces. 18 Sun et al. systematically studied the effects of thickness and oxygen vacancy concentration on the stability and chemical activity of the PuO2 surfaces and showed that the surface stability is affected by the oxygen environment. 19 Moreover, Rak et al. revealed that hydroxylation of the PuO2 surfaces can reverse the stability trend found for the clean surface. 20 Despite experimental and theoretical advances in the distinct effects of oxide layers on the plutonium hydriding reactions, a detailed understanding of the role of the oxides and the controlling factors in the process has not yet been achieved. The defect and impurity are expected to increase the solubility of hydrogen in the plutonium dioxide, promoting the hydriding process. The condition and feasibility to form such catalytic sites on the PuO2 surface are essential in establishing a predictive model of plutonium hydriding. In this work, we consider a series of hydrogenated PuO2 (110) surfaces, which are the products of hydrogen dissociation on the PuO2 (110) surface, and performed DFT-based electronic structure calculations, together with ab initio thermodynamics, to investigate the reaction feasibility and mechanism of catalytic site generation on the PuO2 (110) surface. We introduce our methodological approach in section 2 and discuss the results in section

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3. Our main conclusions are presented in section 4.

2 Methods The calculations were performed using Vienna ab initio simulation package (VASP), 21 using projector augmented wave (PAW) 22,23 potential within DFT framework. The gradient corrected functional Perdew-Burke-Ernzerhof (PBE), 24,25 with a on-site Coulomb potential (Hubbard U) correction was used to describe the exchange correlation interactions of the 5 f electrons of plutonium. The Coulomb energy U and exchange energy J were selected with the following values: U = 4.75 eV and J = 0.75 eV. The lattice parameter of bulk PuO2 crystal calculated with the above values is 5.35 Å, in good agreement with the experimental value of 5.398 Å. 26 The optPBE exchange functional was adopted for the van der Waals correlation to describe the dispersion forces within the system. 27–30 optPBE is an optimized PBE-style functional, which yields a low mean absolute deviation from the CCSD(T) results on the S22 set (a set of 22 weakly interacting dimers) and precise descriptions for the water hexamers. 29,30 Spin-polarization was included in all calculations. The PuO2 (110) surface models investigated in this study are periodic (2×1) slabs, consisting of six atomic monolayers, with a vacuum spacing of 15 Å along surface normal direction (z). The surfaces are adsorbed with two, four, six and eight hydrogen atoms on the surface oxygens, corresponding to 0.25, 0.50, 0.75, and 1.0 ML coverage, respectively, as shown in Figure 1(a)-(d). In all structural optimizations, the atomic positions were allowed to relax until the total energy change was less than 10−4 eV per unit cell and all components of forces were smaller than 0.01 eV/Å. A plane wave cutoff of 680 eV was used. The Brillouin zone of the slabs were sampled by 5×7×1 Monkhorst-Pack k-point meshes. We consider two possible dehydriding processes on the hydrogenated PuO2 (110) surface: PuO2 − H * ) PuO2 + H2 ,

(1)

PuO2 − H * ) PuO2 − Ovac + H2 O.

(2)

5



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One is to release hydrogen molecule (Eq. 1) and the other is to produce water molecule accompanied by an oxygen vacancy formed on the surface (Eq. 2). The diagrams are shown in Figure 1(e) and (f), respectively. To investigate the thermodynamic effects of the reaction on the PuO2 (110) surface when exposed to gas environments, it is necessary to take into account the temperature and the partial pressure. 31–34 The change of the Gibbs free energy or desorption Gibbs free energy, ∆G(T, P), of the reactions is

∆G(T, P) = GPuO2 −H (T, P) − Ggas (T, P) − GPuO2 (T, P),

(3)

where GPuO2 −H (T, P), Ggas (T, P) and GPuO2 (T, P) are the Gibbs free energy of the hydrogenated PuO2 (110) surface, the desorbed gas molecule and the remaining surface after desorption, respectively. ∆G(T, P) can be written as ∆G(T, P) = ∆E DFT +U − µgas (T, P),

(4)

where µgas (T, P) is the chemical potential of the desorbed gas molecule and ∆E DFT +U is the desorption energy of the reaction, which can be calculated by

DFT +U DFT +U DFT +U ∆E DFT +U = EPuO − EPuO − Egas . 2 −H 2

(5)

Assuming that the environmental atmosphere forms an ideal-gas-like reservoir, chemical potential µgas (T, P) can be expressed as

µgas (T, P) = µgas (T, P0 ) + kB T ln(Pgas /P0 ),

(6)

where kB is Boltzmann constant, Pgas is the vapor partial pressure and µgas (T, P0 ) is given by

µgas (T, P0 ) = ∆Hgas (T, P0 ) − T ∆Sgas (T, P0 ),

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(7)

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where ∆Hgas and ∆Sgas are the enthalpy and entropy difference of the gas between temperature T and 0 K at the reference pressure P0 , respectively.

(a)

(b)

(c)

(e)

(d)

(f)

Figure 1: Upper panel: Top views of the hydrogenated PuO2 (110) surfaces with different hydrogen coverage: (a) 0.25 ML; (b) 0.5 ML; (c) 0.75 ML and (d) 1.0 ML. Grey, red and blue balls represent Pu, O and H atoms. Lower panel: Diagrams of two possible desorption processes on the hydrogenated PuO2 (110) surfaces for a coverage of 0.25 ML. The black box denotes an oxygen vacancy.

3 Results and Discussions Optimized structures of the hydrogenated PuO2 (110) surfaces are shown in the upper panel of Figure 1. For the desorption process taking place on the surface of a 0.25 ML coverage, the possible products are one H2 molecule, or one H2 O molecule with an oxygen vacancy formed on the surface. Similarly for the case of 1.0 ML, the reactions may occur to produce one to four H2 molecules, or one to four H2 O molecules accompanied by the same number of oxygen vacancies on the surface. As discussed, Eq. 7 allows us to obtain the aspired temperature dependence of µgas simply from the differences in the enthalpy and entropy of a gas molecule with respect to the

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T = 0 K limit. For reference pressure P0 = 1 bar, theses values are tabulated in thermochemical tables 35 that leads to µgas (T, P0 ) of H2 and H2 O molecules, as reported in Table 1. Our results for H2 molecule are consistent with previous calculations. 34 The desorption energy, calculated by Eq. 5, of releasing one H2 molecule from the hydrogenated PuO2 (110) surface are -2.03, -1.41, -0.80 and -0.21 eV, corresponding to a coverage of 0.25, 0.50, 0.75 and 1.0 ML, respectively,. It indicates that the reaction of hydrogen desorption on the hydrogenated PuO2 (110) surface is more energetically favorable for high coverage and the hydrogenated surface is more stable with low coverage.

Table 1: Chemical potential of hydrogen (µH2 ) and water (µH2 O ) in gas phase as a function of temperature in the range of 300−1500 K. The entropy and enthalpy changes used to obtain µ via Eq. 7 are taken from thermochemical tables at P0 = 1 bar. 35 T (K)

µH2 (eV)

µH2 O (eV)

298.15

-0.317

-0.482

300

-0.320

400

T (K)

µH2 (eV)

µH2 O (eV)

900

-1.254

-1.807

-0.486

1000

-1.426

-2.047

-0.460

-0.688

1100

-1.600

-2.291

500

-0.608

-0.899

1200

-1.777

-2.540

600

-0.763

-1.117

1300

-1.957

-2.792

700

-0.923

-1.342

1400

-2.140

-3.047

800

-1.086

-1.572

1500

-2.324

-3.306

Having determined the chemical potential and desorption energy values of H2 and H2 O molecules, we now examine the thermodynamic effect on the feasibility of the desorption on the hydrogenated PuO2 (110) surface. Note that the change of the Gibbs free energy ∆G(T, P) defined by Eq. 3 is required to be positive for a stable desorption reaction, and hence, the stability of the reaction is limited by the temperature T of the system and the pressure of the gas with respect to the reference state (Pgas /P0 ). These two variables define the phase diagram boundaries that determined by Eq. 4. For the desorption reactions of H2 molecule on the PuO2 (110) surface, the calculated pressuretemperature phase diagram is shown in Figure 2. The temperature and partial pressure region 8


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beneath phase diagram boundary is where the hydrogen desorption reaction is feasible. The region below the black boundary indicates the states that no hydrogen atom is adsorbed on the PuO2 (110) surface, independent of the initial surface hydrogen coverages. As labelled in Figure 2, the areas between two boundary curves are corresponding to the cases that the PuO2 (110) surface remains adsorbed with hydrogen for a coverage ranging from 0.25 to 1.0 ML. At atmospheric pressure, hydrogen desorption on the hydrogenated PuO2 (110) surface for 1.0 ML coverage is predicted to always occur, and for lower surface hydrogen coverage, the desorption initiation temperatures rise to around 600, 1000 and 1350 K, respectively, corresponding to 0.75, 0.50 and 0.25 ML. At certain temperature, low hydrogen partial pressure encourages hydrogen desorption process on the surface of low hydrogen coverage.

20

1.0 ML 0.75 ML

0

0.50 ML 0.25 ML

-20

0.25 ML - 1H2 0.50 ML- 1H2

2

ln ( PH / P0 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.75 ML - 1H2

-40

No hydrogen adsorption

1.0 ML - 1H2

-60

-80 300

600

900 T (K)

1200

1500

Figure 2: Phase diagram of hydrogen adsorption on the PuO2 (110) surface. We have determined reaction boundaries for the hydrogen desorption on the hydrogenated PuO2 (110) surface within a range of temperature and hydrogen partial pressure. On the hydrogenated PuO2 (110) surface, the other possible dehydriding reaction is the water desorption accompanied by the formation of oxygen vacancy on the surface. The desorption energy of a water molecule on the hydrogenated PuO2 (110) surface is -7.45 eV for a coverage of 0.25 ML. As ex9



pected, the desorption reaction of water molecule on the surface is less energetically favorable than that of hydrogen molecule, due to the creation of oxygen vacancy defect. The calculated phase diagram boundary of water desorption on the PuO2 (110) surface for 0.25 ML is shown in Figure 3, compared with that of hydrogen desorption. Water desorption on the 0.25 ML surface only take place at extremely low water partial pressure, although the partial pressure boundary is elevated as temperature increases. Under equal vapor partial pressure, hydrogen desorption reaction dominates the dehydriding process, especially in the low temperature region.

0

0

-50

H2 desorption

-100

-100

H2

2

2

H2O

ln (PH O / P0)

-50

ln ( PH / P0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-150

-150

H2O desorption -200

-200

-250

-250

-300

-300 300

600

900 T (K)

1200

1500

Figure 3: Phase diagram of hydrogen and water desorption on the hydrogenated PuO2 (110) surface for a coverage of 0.25 ML. Black and red lines indicate the phase diagram boundaries of H2 and H2 O vapor, respectively. We notice that the dehydriding process would also be affected by the hydrogen and water pressure ratio (PH2 /PH2 O ). Considering the same Gibbs free energy change for hydrogen and water desorption on the hydrogenated PuO2 (110) surface, ∆GH2 (T, P) = ∆GH2 O (T, P), the phase diagram boundary determined by the hydrogen and water pressure ratio is shown in Figure 4. The region below the phase diagram boundary corresponds to the hydrogen production and the area above the boundary is the cases of forming water and vacancy defect. At 300 K, in the extreme

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condition that the pressure of hydrogen is much higher than that of water, hydrogen formation is suppressed and water production accompanied by surface oxygen vacancy can be expected. At certain ratio of hydrogen and water pressure, the feasibility of water desorption reaction on the PuO2 (110) surface is boosted as temperature rises. We also assess the effect of hydrogen coverage on the phase diagram boundary of dehydriding reactions on the PuO2 (110) surface and we observe that, despite of similar qualitative behavior, lower hydrogen coverage on the surface favors water and vacancy formation at lower vapor pressure ratio.

250 0.25 ML 0.50 ML 0.75 ML 1.0 ML

200

150

2

2

ln ( PH / PH O)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100

50

0 300

600

900 T (K)

1200

1500

Figure 4: Phase diagram of dehydriding reactions on the hydrogenated PuO2 (110) surface.

4 Conclusions Using the ab initio atomistic thermodynamic method combined the DFT + U theory, we have established phase diagrams for dehydriding reactions on the PuO2 (110) surface, within a range of temperature and vapor partial pressure, and assessed the influence of surface hydrogen coverage on the feasibility of the reactions. Thermodynamic calculations reveal that at certain temperature,

11



low vapor partial pressure promotes the initiation of dehydriding process on the PuO2 (110) surface of low hydrogen coverage. For certain vapor partial pressure, the boundary temperature of dehydriding reaction rises as the surface hydrogen coverage decreases. At 300 K, the hydrogen desorption on the PuO2 (110) surface for a coverage of 1.0 ML can take place even when the hydrogen partial pressure is higher than the atmospheric pressure. Although the dehydriding process in form of water and surface vacancy is less energetically favorable than in form of hydrogen, the relative hydrogen and water vapor pressure could modify the feasibility of two types of dehydriding reactions. When vapor pressure of water is extremely low with respect to that of hydrogen, the dehydriding reaction of producing water and surface oxygen vacancy, the latter of which is the catalytic site for plutonium hydriding, is feasible on the PuO2 surface even at 300 K.

5 Acknowledgements This work was supported by the Science Challenge Project under Grant No. TZ2016004, the Natural Science Foundation of China under Grants No. 21503019 and No.11625415, the President Fund of China Academy of Engineering Physics under Grant No. 201402034, and NSFC-NSAF under Grants No. U1530258 and No.U1630248.

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TOC Graphic

0

0

-50

-100

-100

H2

2

2

H2O

ln (PH O / P0)

-50

ln ( PH / P0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-150

-150

-200

-200

-250

-250

-300

-300 300

600

900 T (K)

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Thermodynamic Study of Dehydriding Reaction on the PuO2 (110

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