New Insights into the Crystal Structures of Plutonium Hydrides from

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New Insights into the Crystal Structures of Plutonium Hydrides from First-Principles Calculations Shichang Li, Bingyun Ao, Xiaoqiu Ye, Ruizhi Qiu, and Tao Gao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11464 • Publication Date (Web): 20 Apr 2018 Downloaded from http://pubs.acs.org on April 20, 2018

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The Journal of Physical Chemistry

New insights into the crystal structures of plutonium hydrides from first-principles calculations Shichang Li,† Bingyun Ao,‡ Xiaoqiu Ye,∗, ‡ Ruizhi Qiu,‡ and Tao Gao*,† † 2‡

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China

ABSTRACT: One of the important research contents on hydrogen corrosion of plutonium is the determination of the complex crystal structures of plutonium hydrides and the bonding interactions between plutonium and hydrogen. However, it is very difficult to carry out the structural characterization of plutonium hydrides due to their high activity, high toxicity and radioactivity. In this work, the crystal structures, lattice vibrations and bonding properties of plutonium hydrides under ambient pressure are investigated by means of the density functional theory (DFT) + U approach. Results show that PuH3 exists many competition phase structures. After considering spin polarization, strong correlation (U), and spin-orbit coupling (SOC) effects on the total energy and lattice dynamics stability, it is found that PuH3 at ambient pressure is more likely to be hexagonal P63cm or trigonal P3c1 structure, instead of the usual supposed structures of hexagonal P63/mmc structure (LaF3-type) and face centered cubic (BiF3-type). The calculated electronic structures clearly indicate that P63cm (P3c1) PuH3 is a semiconductor with a small band gap about 0.87 eV (0.85eV). The Pu-H bonds in Pu hydrides are dominated by the ionic interactions.

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INTRODUCTION In recent years there has been renewed interest and focus on plutonium hydrides for consideration of long-term storage of Pu metal1-3 and the application of the hydrogenation reaction for the disposition of excess weapons-grade plutonium.4 Plutonium hydrides, surface-corrosion products of metallic Pu, are extremely reactive and have spontaneous ignition and burning characteristics on exposure to air at room temperature.5 When Pu metal is subjected to extended storage in a sealed vessel, plutonium hydride can form as the Pu metal reacts with outgassed water vapor.2 The sequence of reactions is: Pu(s) + xH2O (l, g) → PuO2+x(s) + xH2(g); Pu(s) + x/2H2(g) → PuHx(s).6-8 For the safe and long-term storage of plutonium, a systematic knowledge of plutonium hydrides is required. In fact, preparation of the bulk samples of plutonium hydride in the experiments was difficult. Powdered samples are highly reactive, toxic, and radioactive; therefore, a number of basic properties associated with their structure are still unknown, 5 including chemical bond and Raman spectroscopy. As an example, take plutonium trihydride (PuH3, the highest hydride of plutonium at ambient pressure); no unifying crystal structure has been determined for PuH3. Mulford et al.9 first reported a LaF3-type hexagonal structure for PuH3 with the space group P63/mmc based on an X-ray diffraction pattern. In another experiment, a face-centered cubic (fcc, fluorite type) phase of Pu trihydride was observed by Muromura et al.10 at room temperature using X-ray diffraction. However, Haschke et al. 5 believed that the PuH3 had an orthorhombic YF3 (Pnma) structure. More recent studies of the related lanthanide hydrides and fluorides suggest that trigonal space group P 3c1 more likely represents the stable phase.11 The structural behavior of the PuH3 is complex and remains to be fully characterized. Since experimental measurements of plutonium hydride formations and properties are scarce because of safety constraints in handling plutonium, density-functional theory (DFT) is one of the most popular modeling methods in condensed matter physics, computational chemistry, and materials science, and has been widely used in studies of the physical and structural properties of Pu-H systems.12-17 Several important corrections including strong on-site Coulomb repulsion (U), collinear spin-polarized, and noncollinear spin-orbit coupling (SOC) effects

18

have been added to the DFT

method, which can greatly improve predictions of the properties of strongly-correlated materials.19-22 However, to our best knowledge, previous theoretical works mainly focused on the Fm3m 12-14, 16, 23-24

and P63/mmc phases

15

for PuH3, no theoretical work systematically investigated the phase

stabilities of the Pu-H system. The present study therefore aims to conduct a theoretical exploration of the Pu-H phase diagram. The possible structures of PuHn (n = 1–3) are investigated using the CALYPSO (Crystal structure ACS Paragon Plus Environment

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AnaLYsis by Particle Swarm Optimization) method25-27 at atmospheric pressure. We examine in detail the evolution of the optimum ground-state static structures and magnetic states of the various hydrides, as well as their phonon spectra and zero-point energies (ZEP). In addition, the Raman-active and the Infrared-active modes are predicted and assigned at the Γ point. The delocalized chemical bonding interactions in plutonium hydride were predicted by the electronic band structures, the charge density (difference), and Bader charge analysis.28 The theoretical framework and details are fully described in the following section.

METHODOLOGY We searched for thermodynamically stable crystalline structures of stoichiometric PuHn (n = 1-3) with simulation cell sizes of 1-4 formula units (f.u.) under ambient pressure using the crystal structure analysis by particle swarm optimization (PSO) methodology29 as implemented in the CALYPSO code.30 The local structural relaxations and electronic band structure calculations were performed in the framework of density functional theory within the generalized gradient approximation and frozen-core all-electron projector-augmented wave (PAW) method,31 as implemented in the VASP program.32 The exchange and correlation interactions are treated in the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional. The strong on-site Coulomb repulsion among the localized Pu 5f electrons is described by using the GGA+U approach formulated by Dudarev et al.33 To verify the dependence upon the effective U parameter (Ueff = U – J,; i.e., the difference between the Coulomb U and exchange J parameters, hereafter referred to as U), we optimized the lattice parameters for Ueff ranging from 0 to 6 eV for PuH3. We found that the lattice parameters for Ueff = 4 eV is in consistency with experimental values available present,9 in good agreement with previous work by Yang16 and our colleagues. In light of this and other studies, we choose an effective Ueff = 4 eV for Pu-H systems, as employed previously in the literature. The Pu 6s27s26p66d25f 4 and the H 1s1orbitals are treated as valence electrons, respectively. A kinetic energy cutoff of 550 eV is used for the set of plane waves. A dense k-point grid 34 with a spacing of 2π × 0.03 Å−1 is used to sample the Brillouin zone, which was shown to yield excellent convergence criteria of 10−6 eV for total energies in all calculations. The atom positions are allowed to relax until the net interatomic forces are below 0.001 eV/Å. Both spin-polarized and spin-orbit coupling (SOC) are included in structural optimizations. Here we consider three possibilities for the magnetic states: nonferromagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM). In the AFM calculations, we use the collinear 1 - k structure where the atomic spin moment is along the [001] direction. Phonons and Raman scattering are carried out using ACS Paragon Plus Environment


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the direct method35 as implemented in the PHONON36 code.

RESULTS AND DISCUSSION The Predicted Structures for Different Stoichiometries. The global energy minimum

ground-state structures of varying stoichiometries PuHn (n =1, 2, 3) are obtained using particle swarm optimization methodology as shown in Figure 1. The structure search readily reproduced the reported structures 9, 11 of fcc PuH2 (CaF2-type, Fm 3m , Figure 1b) and hcp PuH3 (LaF3-type, P63/mmc, Figure 1c), with Pu-H separations of 2.34 Å (the experimental value is 2.32Å

11

) and 2.20 Å (the

experimental value is 2.18 Å9), respectively. The energetically most stable structure of PuH is predicted to be the tetragonal P42/mmc phase (Z = 2, Z is the number of single molecule in the unit cell), see Figure 1a, in which hydrogen atoms are located in tetrahedral interstices of Pu, with Pu-H separations of 2.35 Å at ambient pressure.

Figure 1. Predicted ground-state structures of PuHn (n=1, 2, 3) at atmospheric pressure. (a) PuH_P42/mmc (b) PuH2_

Fm 3m (c) PuH3_P63/mmc. The lines indicate Pu−H separations shorter than 2.50 Å. Green balls are Pu, red hydrogen.

It is worth mentioning that the Fm 3m PuH3, the most usually reported in the literature,12, 14, 16 is not the energy minimum structure. In the experiment, Muromura et al.10 also found that the Fm3m PuH3 partially undergoes a first-order phase transition followed by the formation of LaF3-type structure that coexisted with the cubic phase in solid solution. The calculated lattice parameters and zero-point vibrational energies (ZPEs) and total energies of PuHn (n = 1, 2, 3) are summarized in Table 1. We can see that the errors existing in the optimized results and the experimental structural parameters are no more than 5.0%. The calculated Pu−H separations of 2.354 Å, 2.345 Å, 2.340 Å and 2.203 Å for P42/mmc PuH, Fm3m PuH2, Fm3m PuH3 and P63/mmc PuH3, respectively. The results show that the lattice contraction occurs with increasing H composition due to the small H atomic radius and the large atomic distance between Pu and Ho atoms thus favoring the chemical bonding. ACS Paragon Plus Environment

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The results of the lattice contraction behavior, from Fm3m PuH2 to Fm3m PuH3, are also in agreement with the experimental observations.37 Table 1 Calculated Zero-Point Energies(ZPE) and total energies (E), per formula unit, for PuHn (n = 1–3). Also given are the spin (µs) and orbital (µl) contribution to the magnetic moments, all in µB. U= 4 eV System

Space Group

Mag.

Method

Lattice parameters

µs(µB)

PuH

P42/mmc

FM

GGA+U

a = 3.810; c =5.169

5.22

GGA+U+SOC

a =3.802; c =5.159

4.87

GGA+U

a = 3.785; c =5.205

5.20

GGA+U+SOC

a =3.781; c =5.200

4.86

GGA+U

a = 5.524

5.62

GGA+U+SOC

a =5.375

4.60

GGA+U

a =5.502

5.52

GGA+U+SOC

a =5.415

4.29

Exp.

5.395±0.0029

GGA+U

a = 5.339

5.27

GGA+U+SOC

a =5.341

4.33

GGA+U

a =5.350

5.30

GGA+U+SOC

a =5.340

3.37

Exp.

5.340±0.019

GGA+U

a = 3.821; c = 6.853

5.04

GGA+U+SOC

a = 3.816; c = 6.835

4.67

GGA+U

a = 3.819; c = 6.844

5.07

GGA+U+SOC

a = 3.812; c = 6.832

4.71

Exp.

a = 3.781; c = 6.7619

(Z = 4) AFM

PuH2

Fm3m

FM

(Z = 4) AFM

PuH3

Fm3m

FM

(Z = 4) AFM

P63/mmc

FM

(Z = 2) AFM

µl(µB)

-3.43

-3.35

-3.04

-2.83

-2.86

-2.23

-2.29

-2.31

ZPE (meV)

E(eV)

202.814

-16.664

200.347

-20.268

202.925

-16.653

199.799

-20.260

311.715

-20.906

360.803

-24.503

303.667

-20.854

326.733

-24.519

520.959

-23.938

474.224

-28.172

521.320

-24.002

433.905

-28.194

505.348

-25.007

504.418

-28.899

506.870

-25.025

512.331

-28.874

Generally, the most minimum energy of metal hydrides tends to decompose into other phases with the similar chemical compositions. To confirm the thermodynamic stabilities of the predicted ground-state structures, we plot the convex hull diagram of the relative enthalpy of formation ∆H for different Pu−H phases in the states of FM and AFM magnetism, as shown in Figure 2. The relative enthalpy of formation ∆H is calculated for each stoichiometry with respect to fcc δ-Pu38 (Z = 4,

Fm3m ) and gas H2, as



H ( PuH n ) − H ( Pu ) − ∆H =

n +1 2

n 1 x= 2 n +1 2

n H (H 2 ) 2

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(1)

(2)

A particular Pu−H compound is defined to be “stable” only if its enthalpy of formation is the lowest, while a defined“metastable” system is one which is found on the convex hull.25 Notably, the stable or metastable systems, as defined above, might be experimentally synthesizable and its ∆H is lower than the sum of enthalpy values of the two decomposition products (Pu and H2). Due to the small mass of the hydrogen atom, the ZPEs may well be large enough to affect the relative stabilities of the computed phases.39 We estimated the ZPEs for each PuHn, δ-Pu, and H2 within the harmonic approximation, and all energies have been corrected for ZPEs at the GGA+U/GGA+U+SOC level. In order to achieve a systematic knowledge of the hydrogenation process of metal Pu, nonstoichiometric plutonium hydride (PuH2.25、PuH2.5、PuH2.75) of enthalpy of formation are also depicted in Figure 2 for both FM and AFM configurations. We observe a relative energy difference of 954.5 meV/atom between fcc PuH2 and hcp PuH3, and the relative enthalpies of formation difference of 48.6 meV/atom (1.121 kcal/mol).

Figure 2. Relative enthalpies of formation per atom for FM and AFM PuHn (n=1, 2, 2.25, 2.5, 2.75, 3) phases with ACS Paragon Plus Environment

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The Journal of Physical Chemistry respect to Pu and H2 from GGA + U and GGA + U +SOC (Ueff = 4 eV) calculations. The hydrogen molar content (x = 0 corresponds to pure plutonium, x = 1 to pure hydrogen) at atmospheric pressure for the ground state. The stoichiometric index n (in PuHn) is indicated at the bottom. The convex hulls are shown by solid lines. The symbols on the solid line indicate that the hydride is stable, while those on the dashed line are metastable phases.

Figure 3. The theoretical enthalpies of formation for PuHn (n =1, 2, 3) obtained by the application of the GGA + U/

GGA + U + SOC functional at T = 0 K. The experimental values are for T = 298 K.

In order to compare with the experimental value, we also calculate enthalpy of formation (heat of formation) using GGA + U and GGA + U +SOC methods for PuHn (n =1, 2, 3). The calculated enthalpy of formation and the available experimental values40 are plotted in Figure 3. From Figure 2 and Figure 3, we can see that all PuHn (n =1, 2, 3) for both the FM and AFM phases are thermodynamically favorable and can occur spontaneously, and the FM plutonium hydride are more favorable than the AFM. Guo et al.12 and Zheng et al.14 suggested that the SOC play a critical role in correctly describing ground-state properties of plutonium hydride. To further correctly characterize the ground-state properties of these compounds, the effect of spin–orbit coupling is taken into account based on the approach of GGA+U (U = 4 eV). When the SOC is included in calculations, we can find that: (i) The relative enthalpies of formation and enthalpies of formation are more favorable than the without SOC approach for both the FM and AFM phases. The enthalpies of formation for PuH2 and PuH3 are found to be in consistency with experimental values available present. 40 (ii) The relative enthalpy of formation of the AFM phase is lower than that of the FM phase for PuH2, while the FM phase is more stable for fcc PuH3, which is also agree well with previous theoretical results.14 (iii) The nonstoichiometric plutonium hydride (PuH2.25、PuH2.5、PuH2.75) and fcc ACS Paragon Plus Environment


PuH3 are metastable with respect to decomposition or disproportionation into other hydrides or hydrogen. (iv) For PuH3, the hcp phase is energetically lower than that of the fcc phase for both FM and AFM configurations, and the AFM phases are favored over the FM one. As mentioned above, we find that only by including SOC in the calculations one can reach the correct ground-states. In the following studies, the calculations are performed by the GGA+U+SOC framework for the AFM PuHn (n =1, 2, 3). For PuH2, though a body-centered tetragonal (bct) PuH2 (I4/mmm phase) is thermodynamically favorable, the phonons spectrum of bct PuH2 has large negative frequency (see Supporting Information). In the experiment, Mulford et al. 9 reported that Pu hydrides in the range PuH2 to about PuH2.75 belong to fcc types (fluorite structure), and between compositions PuH2.75 and PuH3, a hexagonal hydride phase appeared that coexisted with the cubic phase in solid solution. The properties of fcc PuH2 and fcc PuH3 have been widely studied in the literature.12,

14, 16

Thus, in the following, only the hcp PuH3 are

investigated in detail.

The Dynamic Stability and Competitive Structures for PuH3. Phonon dispersion curves can provide one criterion to judge the structure stability.41 The calculated results indicate that both P42/mmc PuH and Fm3m PuH2 are dynamically stable, while the phonon dispersion curves show a pronounced soft mode for the P63/mmc PuH3 (3×3×2 supercell) as shown in Figure 4c. The imaginary vibration modes around K points indicate that P63/mmc PuH3 is dynamically unstable. Strongly unstable mode at K (6.75i THz) point correspond to the A "2 vibrational modes, with the instability region in the phonon partial density of states (PPDOS) plot almost exclusively associated with H motions. The directions of the A "2 displacement modes are indicated by yellow arrows in Figure 4a. LaF3-type structure is usually considered as the more stable phase42 for hpc PuH3, however, the existence of negative phonon frequency indicate that there are more stable ground-state structures than P63/mmc PuH3. To determine the more stable phase, the interstitial hydrogen is displaced by about 0.1 Å along the negative phonon frequency direction of the P63/mmc supercell. After re-optimization, we find two minimum energy structures: hexagonal P63cm phase (185, Z=6, see Figure 5e) and tripartite P3c1 phase (158, Z=6, see Figure 5d). Interestingly, in 2006, Clark et al.11 pointed out that, between composition PuH2.95 to PuH3, there exist a structure similar to that of disordered tysonite LaF3 ( P 3c1 , 165, Figure 5c), or orthorhombic YF3(Pnma, 62, Figure 5b) structure. Cheetham et al.43 also suggested that the disordered tysonite LaF3 structure is more likely space group rather than P63/mmc phase. Our results further confirm that the P63/mmc phase is not the more stable ground-state structure for PuH3. ACS Paragon Plus Environment

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Figure 4. (a) The unit cell of hexagonal PuH3 (space group P63/mmc). (b) The Brillouin zone of a the hexagonal close-packed lattice showing the high-symmetry Г-A-H-K-Г-M-L-H path used in phonon calculations. b1, b2, and b3 are the primitive reciprocal lattice vectors. (c) Phonon dispersion curves along the high-symmetry k path and the PPDOS normalized to the primitive cell in FM configurations. In the PPDOS plot, green, red, and blue curves represent contributions of Pu, H1, and H2 atoms, respectively.

All the possible crystal structures of PuH3 are shown in Figure 5, and the lattice parameters are listed in Table 2. For P63/mmc PuH3 (LaF3，Z = 2), two-thirds of hydrogen atoms occupy the tetrahedral interstices (4f) by Pu with Pu−H separations of 2.20 Å, and one-third the central triangle plane (2b) with Pu-H separations of 2.35 Å; The Pnma structure has an orthorhombic YF3-type structure (No. 62) composed of four formula units (f.u.). The structures of P3c1 and P63cm are very similar to each other, the hydrogen atoms are located in the disordered tetrahedral interstices and slightly away from the central triangle plane, respectively. As for P3c1 structure, the differences are only the central triangle plane hydrogen atoms displaced from the center to form a conic with Pu atoms. The last three different structures, to some extent, can be viewed as the variant type of the LaF3 structure.



Figure 5. The competitive structures of PuH3. (a) P63/mmc (b) Pnma (c) P 3c1 (d) P3c1 (e) P63cm. The lines indicate Pu−H separations shorter than 2.5 Å. Green balls are Pu, red hydrogen.

Calculated enthalpy curves for these competitive structures of PuH3 under ambient pressure are depicted in Figure 6 for NM, FM, and AFM states through GGA+U and GGA+U+SOC (U = 4 eV) approaches. In all cases, it is clear that the enthalpy differences between calculation with and without SOC are obvious. Our results and other works14, 16 have consistently shown that the SOC plays a critical role in correctly describing the ground-state properties of plutonium hydride. For Fm3m structure, the FM configurations is the most energetically stable state in GGA+U+SOC schemes, with an energy difference of about 70 meV and 1080 meV with respect to the AFM and NM state, respectively, which are wholly consistent with a recent LDA+U+SOC 14 work. However, the enthalpy of Fm3m structure is significantly higher than the other type of PuH3 structure in both the FM and AFM configurations using the GGA+U/GGA+U+SOC approach. Without including SOC interactions, the enthalpy of Fm3m structure is much higher than the other structures, at around 0.70 eV/f.u. For Pnma (YF3-type) structure, it is also clear that the enthalpy is significantly higher than other structures for both the FM and AFM configurations in GGA+U+SOC approach in Figure 6, and the total energy of the AFM phase is lower than that of the FM phase. Therefore, from the enthalpy, we initially exclude the possibility that the Pnma and Fm3m structure is the ground-state structures of PuH3. While, for P 3c1 , P3c1 and P63cm structures, the energy difference between them is relatively small for both the FM and AFM states, thus it is difficult to determine which configuration is more stable.


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Table 2. Predicted lattice parameters and atomic coordinates for competitive structures of PuH3. Phase

Lattice

Wyckoff

Atomic coordinates (fractional)

Atom parameter (Å, deg)

position

x

y

z

P 3c1

a = b= 6.604

Pu

6f

0.6653

0.0000

0.2500

(No:165, Z = 6)

c = 6.844

H1

12g

0.3254

0.9834

0.4062

α = β = 90

H2

4d

0.6667

0.3333

0.3023

γ=120

H3

2a

0.0000

0.0000

0.2500

P3c1

a = b = 6.596

Pu

6d

0.6657

0.9988

0.2483

(No:158, Z = 6)

c = 6.837

H1

2a

0.3333

0.6667

0.1925

α =β = 90

H2

2b

0. 6667

0. 3333

0.2847

γ = 120

H3

2c

0.0000

0.0000

0.2895

H4

6d

0.6809

0.6674

0.0918

H5

6d

0.6503

0.9844

0.9042

P63cm

a = b= 6.596

Pu

6c

0.3323

0.3323

0.2482

(No:185, Z = 6)

c = 6.835

H1

2a

0.0000

0.0000

0.1917

α = β = 90

H2

4b

0.6667

0.3333

0.2880

γ = 120

H3

6c

0.3175

0.3175

0.9040

H4

6c

0.3472

0.0000

0.0918

Pnma

a = b= 6.615

Pu

4c

0.3332

0.2500

0.0003

(No:62, Z = 4)

c = 3.826

H1

8d

0.1665

0.0945

0.5005

α =β = 90, γ = 120

H2

4a

0.4996

0.2500

0.5003

Figure 6. Calculated enthalpy curves per formula unit for competitive structures of PuH3 under ordinary pressure for NM, FM, and AFM states through GGA+U/GGA+U+SOC (U = 4 eV) approach. ACS Paragon Plus Environment


To future determine the ground-state structure of PuH3, we perform the phonon dispersion curves calculate for P 3c1 , P3c1 and P63cm structure along high-symmetry lines Г-K-H-A-Г-M-L in the Brillouin zone, as shown in Figure 7. The imaginary vibration modes around Г, M, A, and K points indicate that P 3c1 PuH3 is dynamically unstable by phonon calculations. Strongly unstable modes at Г (13.25i THz) points. Therefore, the most stable structure of PuH3 at ambient pressure is more likely to be trigonal P3c1 or hexagonal P63cm structure, instead of the usual proposed structures of hexagonal P63/mmc structure (LaF3-type) or face centered cubic (BiF3-type).

Figure 7. Calculated phonon dispersion curves along the high-symmetry k path for competitive structures of PuH3 in FM configurations (a) P 3c1 (b) P3c1 (c) P63cm through GGA + U + SOC (U = 4 eV) approach.

Figure 8. Neutron diffraction for competitive structures of PuH3 under ordinary pressure.


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Figure 9. Raman scattering spectra for competitive structures of PuHn under ordinary pressure. (a) PuH_P42/mmc, PuH2_ Fm3m , PuH3_ Fm 3m , PuH3_P63/mmc. (b) PuH3_ Pnma, PuH3_ P3c1 , PuH3_ P3c1, PuH3_ P63cm.

Neutrons diffraction techniques are widely used to reveal the 3-dimensional arrangement of atoms and magnetic moments, especially for low atomic number materials (e.g. hydrogen). In our work, the neutron diffraction of PuH3 for all available competitive structures are presented in Figure 8. We can find that there exits the similar neutron diffraction for P63/mmc, P 3c1 , P3c1 and P63cm, while the neutron diffraction of Pnma type is clearly different from the other structure. The assignment of the Raman active modes is also essential for crystallographic analysis. The Raman scattering active frequencies of competitive structures of PuHn are clearly assigned and shown in Figure 9. Our results show that the Raman spectra of all competitive structures are not same. Unfortunately, no experimental data of the Raman spectra of PuH3 have been reported. Our calculated results will be very helpful to experimentally determine the ground-state structures of plutonium hydrides in the future. Electronic properties and chemical bonding. The density of states (DOS) and partial density of states (PDOS) projected on the H-s, Pu-6d, and Pu-5f orbitals in PuHn (n = 1, 2, 3) are displayed in Figure 10. The bonding characteristics can be deduced from the PDOS: (i) The electron energy states near the top of the valence bands are mainly composed of Pu 5f and H 1s orbitals, and the hybridization between Pu 5f and H 1s orbitals is more apparent than that between Pu 6d and H 1s orbitals in plutonium hydride. (ii) With the transition sequence of PuH, PuH2 and PuH3, the valence-electron states of H atom move closer to EF, indicated that more H 1s electrons participate in chemical bonding. And as expected, the Pu ion valence state is increasing during this transition. (iii) The Pu-6d states make a greater contribution to the conduction band. (iv) A spectacular ACS Paragon Plus Environment


metal-insulator transition44 occurs on the phase transformation from PuH2 to PuH3, which is in reasonable agreement with the previous results24 using LSDA+U calculations by combining the full potential linearized augmented plane wave method.

Figure 10. The DOS and PDOS of states of PuHn. The total DOS are normalized to one formula unit. The DOS projected onto Pu-5f, Pu-6d, and H-s orbitals. Energy is shifted so that the Fermi level EF equals zero.

Figure 11. Fat-band dispersions of (a) P63cm (b) P3c1 phases of PuH3 through GGA + U + SOC (U = 4 eV) approach, with the Fermi level located at 0 eV. The size of each symbol indicates the weight fraction of each projection from 0 to 100%.


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The electronic fat-band dispersions of P3c1 and P63cm PuH3 are shown in Figure 11. We can see from Figure 11 that the top of valence bands (H 1s orbitals) and the bottom of conduction bands (Pu 6d orbitals) are positioned at the same high-symmetry point, so P63cm (P3c1) structure of PuH3 is a semiconductor with a direct gap of 0.87 eV (0.85 eV). Therefore, it is further confirmed that the metal-insulator transition may take place from PuH2 to PuH3 as observed in rare-earth metal hydrides. To reveal the dependence upon the effective U parameter, the gap of PuH3 with different U values are also investigated (see Table S2). we find the effect of U value on the band gap is obvious.

Figure 12. The charge density (a) and charge density difference (b) for P42/mmc structure of PuH alone the (1 0 0) plane, Fm3m structure of PuH2 alone the (1 1 0) plane and P63cm structure of PuH3 alone the (1 -1 0) plane, respectively, in the units of e/Å3.

To further reveal the bonding characteristics between Pu and H in PuHn, we plot the charge density and the charge density difference contour maps for P42/mmc structure of PuH alone the (1 0 0) plane, Fm3m structure of PuH2 alone the (1 1 0) plane and P63cm structure of PuH3 alone the (1 -1 0) plane,

respectively, as shown in Figure 12. The charge density is one of the important features of solid materials, which provides information on the chemical bonding trend. As can be clearly seen from Figure 12a, the electrons tend to pile up near nucleus positions, while the interstitial charge densities ACS Paragon Plus Environment


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are relatively low; no significant directional bonds are evident. To obtain a qualitative perspective on the extent of charge transfer of plutonium hydride, charge density difference ∆ρ is depicted as follows: ∆ρ = ρ(PuHn) - ρ (Pu atom) – ρ (H atom)

(3)

where ρ (PuHn) denotes the charge density of PuHn; ρ (Pu atom) and ρ (H atom) is noninteracting Pu and H charge densities, respectively. The ionic nature of the Pu-H bond for PuHn is clearly revealed in Figure 12b, since a substantial amount of charge density of Pu atoms is transferred to H atoms during the formation of plutonium hydrides.

Figure 13. Calculated average charge transfer for PuHn (n = 1, 2, 3) by GGA + U + SOC calculations in e/atom, respectively.

To further quantify the charge transfer between the Pu atom and the H atom, the Bader charge analysis28 is carried out to evaluate the number of valence charge, as shown in Figure 13 and Table S3. Each divided volume is called Bader cell and contains one atom. The charge amount within each Bader cell is assigned to each atom of the cell. From Figure 13, we can find that: (1) With the transition of PuH → PuH2 → PuH3, the value of Pu atoms’ average charge transfer

QB

(Pu) is

increasing. It is suggested that the introduced H atoms into a Pu lattice enhance the electron losing ability of Pu atoms, and the total ionicity degree of PuHn increases with the increase of n. Thus, it reveals that the Pu-H bonds become stronger with the increase of H composition. (2) The P3c1 and P63cm structure of PuH3 have the same value of the average charge transfer since the two structures are very similar. each Pu atom loses 1.70|e| and a charge of 0.57 |e| is transferred to H atom. (3) The values of

QB

(H) for all PuH3 are greater than 0.5|e|. It suggests that the bonding interactions between ACS Paragon Plus Environment

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H and Pu atom are ionic (4) The

QB

of Fm 3m structure is smaller than P63cm and P3c1 structure for

PuH3. It suggests that the ionic character of Pu-H of P63cm and P3c1 is stronger than Fm 3m phase.

CONCLUSIONS We have explored the stable structures of solid Pu-H systems at ambient pressure by first-principles crystal structure prediction based on the particle swarm optimization algorithm. The comparison with GGA + U and GGA + U + SOC calculations shows that GGA + U + SOC calculations result in a better agreement of the PuH2 structure with experimental findings. The ground-state structure of PuH3 at ambient pressure is predicted to be hexagonal P63cm or trigonal P3c1 phase with the smallest total energies as well as positive phonon spectra by GGA + U + SOC for U = 4 eV, rather than the usually proposed hexagonal P63/mmc or fcc Fm3m structure. The P63cm (P3c1) phase of PuH3 is a semiconductor with a direct gap of 0.87 eV (0.85 eV). We further confirm that the metal-insulator transition indeed exists from plutonium dihydride to trihydride as observed in rare-earth hydrides. The chemical bonding between Pu and H atoms in Pu hydrides has an ionic bonding character. And the Pu-H bonds become stronger with the increase of H composition which partially accounts for the abnormal lattice contraction of plutonium hydrides upon increasing hydrogen composition. We have shown the Raman scattering active frequencies of various Pu hydrides which will be helpful to experimentally determine the ground-state structures of Pu hydrides in the future.

AUTHOR INFORMATION Corresponding Authors *Email address: [email protected]. *Email address: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to Xianggang Kong for their discussions and to a reviewer for useful comments. Calculations were performed using the Center of High Performance Computing at the physics discipline of Sichuan University. The research was supported by the National Natural Science ACS Paragon Plus Environment


Foundation of China (Grants No. 21401173, 21771167, and 21371160) and the Science Challenge Project of China (Grant No. TZ2016004).

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