Theoretical prediction of some layered Pa₂O₅ phases: structure and properties

Abstract

Density functional theory (DFT) was used to predict and study protactinium pentoxide (Pa₂O₅), which presents a fluorite and layered protactinium oxide-type structure. Although the layered structure has been observed with the isostructural transition Nb and Ta metal pentoxides experimentally, the detailed structure and properties of the layered Pa₂O₅ are not clear and understandable. Our theoretical prediction explored some possible stable structures of the Pa₂O₅ stoichiometry according to the existing M₂O₅ structures (where M is an actinide Np or transition Nb, Ta, and V metal) and replacing the M ions with protactinium ions. The structural, mechanical, thermodynamic and electronic properties including lattice parameters, bulk moduli, elastic constants, entropy and band gaps were predicted for all the simulated structures. Pa₂O₅ in the β-V₂O₅ structure was found to be a competitive structure in terms of stability, whereas Pa₂O₅ in the ζ-Nb₂O₅ structure was found to be the most stable overall. This is consistent with Sellers's experimental observations. In particular, Pa₂O₅ in the ζ-Nb₂O₅ structure is predicted to be charge-transfer insulators. Furthermore, we predict that ζ-Nb₂O₅-structured Pa₂O₅ is the most thermodynamically stable under ambient conditions and pressure.

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1. Introduction

The structure and properties of actinide-based oxides have been extensively studied using many theoretical^1–5 and experimental approaches^6–17 due to their technological importance in the nuclear material cycle. However, protactinium pentoxide (Pa₂O₅) is an underexplored area of the protactinium–oxygen phase diagram, and its practical applications have received little attention owing to its instability relative to the fluorite and layered protactinium oxides.^18,19 One of its intriguing features is that it represents the composition of a transition point between the fluorite and layered protactinium oxides, with reports of it forming in both types of structures. Since reports about the structure and properties of Pa₂O₅ are extremely limited in the literature, most likely owing to its scarcity, high radioactivity and toxicity, theoretical prediction provides a way to predict and study the structure and properties of this material.

In the actinide elements, uranium (U) exhibits rich oxide phases, such as UO₂, U₂O₃, U₂O₅, and U₃O₈,^20–27 and its two prominent oxidation states are U⁴⁺ and U⁶⁺. Plutonium (Pu) has stable Pu⁴⁺, Pu⁵⁺, and Pu⁶⁺ oxidation states in aqueous solutions. Neptunium (Np) has two stable oxides, NpO₂ and Np₂O₅, corresponding to stoichiometric Np⁴⁺ and Np⁵⁺, respectively. Protactinium (Pa), like actinide Np and the transition niobium (Nb), tantalum (Ta), and vanadium (V) metals, has the predominant oxidation state of Pa⁵⁺. In particular, protactinium pentoxide is isostructural with the transition metals Nb and Ta, sharing a closed shell pentavalent oxidation state.²⁸ In addition, a study on Pa is considered to be a unique opportunity for studying the potential periodic properties of the actinide elements and their compounds with respect to their physics and chemistry, including structure and bonding. Wilson recently reported about protactinium as a potential intersection between the d-transition metals (Nb and Ta) and the 5f actinide elements U, Np and Pu owing to the participation of 5f and 6d orbitals cross in energy.²⁸ Although U, Np and Pu oxide systems are known, a detailed structural study of the layered protactinium pentoxide (Pa₂O₅) has not been systematically reported to date.

To develop new nuclear materials and understand their basic physical and chemical properties, a systematic study about the structure and properties of protactinium oxides is critical from a theoretical perspective. Pa₂O₅ is used for the preparation of metal Pa and other oxides (PaO and PaO₂), high temperature dielectrics for ceramic capacitors, in nuclear industry, etc.^19,29 Sellers et al.¹⁹ experimentally showed that protactinium pentoxide has a fluorite structure and an orthorhombic structure. The fluorite Pa₂O₅ was prepared by heating the hydrated oxide in air (500 °C). Also, density data for fluorite Pa₂O₅ is not available, which suggests that it is more likely to be a defective fluorite PaO₂.¹⁹ The orthorhombic Pa₂O₅, which is isostructural with Nb₂O₅ and Ta₂O₅, was obtained in the course of an attempt to prepare a fluoride by action of CuF₅ on the oxide (500 °C). Sellers' diffraction experiment suggested that Pa₂O₅ is a layered phase. Our theoretical work explores some possible structures of Pa₂O₅ by replacing the metal ions with protactinium ions from existing metal pentoxide structures. To study the potential structure and properties of layered Pa₂O₅, we report the structural, elastic, thermodynamic and electronic properties of some possible layered Pa₂O₅ phases using the Perdew–Burke–Ernzerhof generalized gradient approximation+U implemented in density functional theory (DFT). Our aim is to develop reliable structural models to aid the identification of possible phases and give a quantitative description of their relative stability.

2. Methodology

Theoretical calculations were performed using the projector augmented wave (PAW) method, as implemented in the Vienna Ab Initio Simulation Package (VASP).^30,31 The generalized gradient approximation (GGA) functional in the Perdew–Burke–Ernzerhof (PBE)³² parametrization was adopted for structural optimization. The crystal structures of all systems concerned were relaxed using a Γ-centered k-mesh determined by requiring the product of the number of k points and the length of the lattice vectors to be ∼30 Å and a large kinetic energy cutoff of 550 eV for plane waves. The energy convergence criterion was 10⁻⁶ eV, and the force convergence criterion was 10⁻⁴ eV Å⁻¹. After relaxation, the electronic structures were calculated with a kinetic energy cutoff of 500 eV.

The Dudarev approach³³ to the Perdew–Burke–Ernzerhof generalized gradient approximation GGA (PBE)+U implementation^34–38 was employed to enforce localization of the Pa 5f electrons. The effective U_eff (U–J) parameter of 4.0 eV (ref. 39) was used. This value was tested for PaO₂ and all simulated Pa₂O₅ structures, where the actinide (U, Np, and Pu) oxides in the literature^{6,16,17,27,40–43} predicted good calculated structural properties. Spin–orbit coupling was not included in any of the calculations described herein since it has been previously demonstrated on actinide dioxides^10,44 that its effects on the structural properties and relative stabilities are inconsequential. The cutoff energy of 550 eV was reached for the convergence of the energy and the Γ-centered Monkhorst–Pack k-meshes of ζ-Nb₂O₅ 4 × 6 × 6; Nb₂O₅ 4 × 6 × 4; R-Nb₂O₅ 6 × 6 × 4; B-Ta₂O₅ 4 × 6 × 6; Z-Ta₂O₅ 6 × 6 × 6; β-Ta₂O₅ 6 × 6 × 6; β-V₂O₅ 3 × 6 × 4; α-V₂O₅ 2 × 6 × 2; and Np₂O₅ 4 × 6 × 4 were automatically generated. The enthalpies of formation as a function of pressure and thermodynamic properties are presented in Fig. S1–S5.†

3. Results and discussion

3.1 Structural properties

The different structures of the layered Pa₂O₅ composition were simulated. Nb₂O₅,^45–47 Ta₂O₅,^48,49 V₂O₅,^50,51 Np₂O₅ (ref. 52) structured M₂O₅ (where M is an actinide or transition metal) structures were investigated by replacing the metal ion with protactinium. All the relaxed simulated structures retained the coordination environments of the original M₂O₅ structures. We report the experimental structures of ζ-Nb₂O₅ and Np₂O₅ in comparison to our calculated structure of Pa₂O₅ in the ζ-Nb₂O₅ and Np₂O₅ structures. For Pa₂O₅ in the Np₂O₅ structure, the calculated lattice parameters (Table 1) are in good agreement with the experimental results of Np₂O₅, most likely because of the similarity between the protactinium and neptunium atomic radii (0.78 and 0.75 Å, respectively). Although the large protactinium cation (0.78 Å) substitutes the transition metal ions V (0.54 Å), Nb (0.69 Å) and Ta (0.69 Å), PBE+U demonstrates that the cell volume for Pa₂O₅ in the ζ-Nb₂O₅ structure is excellent compared to the experimental value of the original ζ-Nb₂O₅. An important reason for this is the change from transition metal ions to protactinium ions in the coordinate environment of the substitute position. The original ζ-Nb₂O₅ structure has an alternating MO₆-rich perovskite structure, and the replaced Pa₂O₅ in ζ-Nb₂O₅ phase was transformed into alternating MO₉ distorted hexahedron and quadrangular pyramid layers. The structural and mechanical properties of all the simulated systems are shown in Tables 1 and 2 and their relaxed structures are presented in Fig. 1–5.

Table 1 Predicted properties of some layered Pa₂O₅ phases^a

Phase	Method	Lattice parameters (Å)			Lattice parameters (deg)			Vol. (Å^3)	Space group	E gap (eV)	B (GPa)	E form (eV)
		a	b	c	α	β	γ
a The enthalpy of formation (Eform = E(Pa2O5) − 2E(Pa) − 5E(O)) was calculated with respect to the energy of the Pa metal (8.72 eV per Pa) and the O2 molecule (−4.90 eV per O). The energy of an O atom was predicted to be −4.90 eV, as calculated from an O2 molecule in a 25 Å box using the Γ point.
Pa2O5	Expt^19	13.84	4.02	4.18	90.0	90.0	90.0
ζ-Nb2O5	Expt^47	12.740	4.883	5.561	90.0	105.02	90.0	334.12	C2/c (15)
	PBE+U	12.620	5.387	5.387	90.0	114.68	90.0	332.72	C2/c (15)	2.67	198.33	−27.92
Nb2O5	PBE+U	14.446	4.282	15.035	90.0	163.64	90.0	262.02	P1 (1)	3.05	170.67	−26.41
R-Nb2O5	PBE+U	4.235	4.283	14.445	90.0	90.29	90.0	262.00	C2/m (12)	3.49	170.61	−26.40
Z-Ta2O5	PBE+U	6.302	4.077	6.517	90.0	107.37	90.0	159.82	C2/m (12)	2.21	282.70	−26.16
β-Ta2O5	PBE+U	6.991	4.048	8.474	90.0	90.0	90.0	239.84	Pccm (49)	1.93	178.87	−24.13
β-V2O5	PBE+U	6.645	3.937	7.412	90.0	78.57	90.0	190.05	P21/m (11)	3.28	198.91	−27.89
α-V2O5	PBE+U	11.576	4.220	10.664	90.0	90.0	90.0	520.93	Cmcm (63)	3.05	120.63	−25.01
Np2O5	Expt^52	8.17	6.58	9.31	90.0	116.01	90.0	449.81	P2/c (13)
	PBE+U	8.150	6.887	9.404	90.0	115.69	90.0	470.35	P2/c (13)	3.29	166.76	−26.95

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Table 2 Coordination and charges of protactinium in the simulated Pa₂O₅ structures

Pa environment	No. of Pa environments per simulated unit cell
	ζ-Nb2O5	Nb2O5	R-Nb2O5	Z-Ta2O5	β-Ta2O5	β-V2O5	α-V2O5	Np2O5
Pa^5+ distorted octahedron		4	4				8
Pa^5+ octahedron					2			4
Pa^5+ pentagonal bipyramid					2			4
Pa^5+ distorted hexahedron and quadrangular pyramid	8			4
Pa^5+ 7-fold						2
Pa^4+ 7-fold						2

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Pa₂O₅ in Nb₂O₅ structure. The ζ-,⁴⁵ R-⁴⁶ and Nb₂O₅ (ref. 47) polymorphs were simulated. The ζ-Nb₂O₅ and Pa₂O₅ in the ζ-Nb₂O₅ structure are shown in Fig. 1a and b, respectively. Although the ζ-Nb₂O₅ structure is a skutterudite-like structure, the optimized Pa₂O₅ in the ζ-Nb₂O₅ phase can be considered a diamond-like (for 4 protactinium ions) structure, which has alternating MO₉ distorted hexahedron and quadrangular pyramid layers. As shown in Fig. 2a and b, the Nb₂O₅ and R-Nb₂O₅ phases are anatase-like structures and have layers of edge-sharing MO₆ octahedra, respectively. For the R-Nb₂O₅ structure, the layers are continuous in the c direction, while they are separated by 2 layers of a skutterudite-like structure for the Nb₂O₅ structure. All the protactinium ions for the R- and Nb₂O₅ phases are Pa⁵⁺ in the distorted octahedral coordination (Table 2).

Fig. 1 (a) Original ζ-Nb₂O₅ structure and (b) Pa₂O₅ in the ζ-Nb₂O₅ structures.

Fig. 2 Pa₂O₅ in (a) Nb₂O₅ and (b) R-Nb₂O₅ structures.

Pa₂O₅ in Ta₂O₅ structure. We simulated the Z-⁴⁸ and β-Ta₂O₅ (ref. 49) polymorphs (Fig. 3a and b, respectively). Although many polymorphs exist for this oxide, they are generally very similar to Nb₂O₅. In particular, the structure of B-Ta₂O₅ is very similar to ζ-Nb₂O₅. β-Ta₂O₅ is a typical two-layer orthogonal structure. Z-Ta₂O₅ does not resemble the anatase structure and is more comparable to a distorted brookite structure (Fig. 2b). For the β-Ta₂O₅ and ζ-Nb₂O₅ structures, all the protactinium ions are Pa⁵⁺ in the distorted octahedral coordination (Table 2). In contrast, all the protactinium ions for the β-Ta₂O₅ structure are in the octahedral coordination.

Fig. 3 Pa₂O₅ in (a) Z-Ta₂O₅ and (b) β-Ta₂O₅ structures.

Pa₂O₅ in V₂O₅ structure. Two polymorphs, α-⁵⁰ and β-V₂O₅,⁵¹ are presented in Fig. 4. The β-V₂O₅ structure is built of infinite chains made of quadruple units of edge-sharing PaO₆ octahedra along the b axis. The chains are linked by sharing corners of two octahedra along the c axis. The α-V₂O₅ structure has a layered structure with orthorhombic symmetry consisting of PaO₅ square pyramids sharing edges and corners.

Fig. 4 Pa₂O₅ in (a) α-V₂O₅ and (b) β-V₂O₅ structures.

Pa₂O₅ in Np₂O₅ structure. The simulated Np₂O₅ structure consists of 8 protactinium environments,⁵² 4 with pentagonal bipyramidal coordination and 4 with octahedral coordination (Fig. 5 and Table 2). All the protactinium ions are predicted to be Pa⁵⁺.

Fig. 5 Pa₂O₅ in the Np₂O₅ structure.

3.2 Stability

To confirm the thermodynamic stabilities of the predicted structures, the enthalpy of formation (E_form) for the simulated Pa₂O₅ structures are listed in Table 1. The relative enthalpy of formation E_form was calculated for each stoichiometry with respect to all the simulated Pa₂O₅ structures and gas O₂, as follows:

E_form = E(Pa₂O₅) − 2E(Pa) − 5E(O) (1)

For clarity, the energies against the volume per Pa₂O₅ unit are plotted in Fig. 6. There is a clear dependence of the formation energy on the volume, with a decrease in stability for volumes smaller or larger than the most stable phases (ζ-Nb₂O₅).

Fig. 6 Stability plot of the formation energy per Pa₂O₅ in electronvolt vs. volume per Pa₂O₅ unit. Phases are named with the original M₂O₅ structures for clarity.

The distribution of protactinium charges and protactinium coordination influence the stability. The ζ-Nb₂O₅-structured Pa₂O₅ is the most stable overall, although this structure contains all the Pa in a distorted hexahedron and quadrangular pyramid coordination. β-V₂O₅ was found to be just slightly less stable than ζ-Nb₂O₅ (0.03 eV) in terms of formation energy. The stability of the other phases follows the order of Np₂O₅ > Nb₂O₅ > R-Nb₂O₅ > Z-Ta₂O₅ > α-V₂O₅ > β-Ta₂O₅. Since Pa⁵⁺ prefers higher coordination numbers compared to the 6-fold distorted octahedral coordination, all the structures featuring protactinium ions entirely in the 6-fold coordination are consequently less stable. The V₂O₅-structured oxides are the least stable with the β-polymorph less stable than the α-V₂O₅ structure due to the presence of Pa in mixed oxidation states (Pa⁴⁺ and Pa⁵⁺) compared to α-V₂O₅, which is comprised of only Pa⁵⁺ ions.

The DFT work from Molinari et al.²⁵ predicted that the Np₂O₅-structured U₂O₅ is the most stable among those considered under ambient conditions. However, the observed δ-U₂O₅ structure is found to be the second most stable. In particular, Pa₂O₅ in the β-V₂O₅ structure, given that it contains only octahedrally coordinated Pa, is closely followed by β-V₂O₅. The higher coordination numbers are also very similar to U₂O₅ since U is closely followed by R-Nb₂O₅.

These energetics show that Pa₂O₅ can crystallize in the ζ-Nb₂O₅ structure, but due to the relative instability of the Pa₂O₅ stoichiometry compared to the other protactinium oxides, it has not been synthesized or reported experimentally. The difficulty in synthesizing layered Pa₂O₅ is likely to stem from the fact that Pa⁵⁺ is more stable in the pentagonal bipyramidal coordination. One can also consider the formation of the studied Pa₂O₅ phases as a function of pressure, representing a range of conditions from low pressure to high pressure. The formation enthalpies as a function of pressure are presented in Fig. S1† and are normalized with respect to the most stable Pa₂O₅ (i.e., the ζ-Nb₂O₅ structure) such that

δH_f = ΔH(x) − ΔH(ζ-Nb₂O₅) (2)

where x is the phase in question and ΔH(x) corresponds to E_form in Table 1. Interestingly, we predicted that at high pressure (above 100 kbar), Pa₂O₅ will be more thermodynamically stable in the ζ-Nb₂O₅ structure.

Using the density functional perturbation theory (DFPT)^53,54 calculated for each unit cell, the Helmholtz free energy, F_vib (Fig. S2†), vibrational entropy, S_vib (Fig. S3†), vibrational energy, E_vib (Fig. S4†), Helmholtz free energy, F_tot = E_form + F_vib (Fig. S5†), and the heat capacity, C_v (Table 3), were evaluated. The Helmholtz free energy, F, entropy, S, internal energy, E, and constant volume specific heat capacity, C_v, can be directly calculated as a function of temperature using the following equations:

where the indices ω is the phonon frequency, g(ω) is the normalized phonon density of states , r is the number of degrees of freedom in the primitive unit cell, and N is the number of primitive unit cells. ħ is Planck's constant, k_B is the Boltzmann constant, and T is the temperature in kelvin [K]. All these properties are expressed per Pa₂O₅ unit, and a sample of their values at 300 K is presented in Table 3. A full calculation of the phase stability for the Pa₂O₅ phases is beyond the scope of this work; however, our calculations show that the energy-minimized ζ-Nb₂O₅ phase has a lower enthalpy of formation (E_form) and vibrational entropy (S_vib) than the other phases. Hence, using our calculated values, ζ-Nb₂O₅ is predicted to be the preferred structure at around 300 K and 0 bar (Fig. S5†).

Table 3 Predicted thermodynamic properties of some layered Pa₂O₅ phases at 300 K

Phase	F vib (meV)	S vib (meV K^−1)	C V (meV)	E vib (meV)	F tot (eV)
ζ-Nb2O5	214.2	1.43	135.5	612.0	−27.71
Nb2O5	18.9	2.03	145.3	628.7	−26.40
R-Nb2O5	45.3	1.95	145.4	629.3	−26.35
Z-Ta2O5	218.3	1.49	123.5	606.7	−25.94
β-Ta2O5	56.6	1.46	105.3	494.2	−24.07
β-V2O5	212.5	1.46	137.2	650.9	−27.68
α-V2O5	47.0	1.46	85.1	395.2	−24.96
Np2O5	107.6	1.72	140.7	622.8	−26.84

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3.3 Elastic properties

To evaluate the mechanical stability of all the simulated structures at ambient pressure, the calculated elastic constants are shown in Table S1,† which were calculated using the strain–stress relationship. The key criterion for the mechanical stability of a crystal is that the strain energy must be positive, which implies that the elastic constants should satisfy the generalized elastic stability criteria. In all the simulated structures, the Pccm phase (β-Ta₂O₅) is the only orthorhombic structure, and the others are monoclinic structures. For the orthorhombic structure, the nine independent elastic constants are C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃ and C₂₃, and the corresponding mechanical stability criteria are given as⁵⁵

C₁₁ > 0, C₁₁C₁₂ > C₁₂₂, C₄₄ > 0, C₅₅ > 0, C₆₆ > 0, C₁₁C₂₂C₃₃ + 2C₁₂C₁₃C₂₃ − C₁₁C₂₃² − C₂₂C₁₃² − C₃₃C₁₂² > 0.

Meanwhile, the monoclinic structure has thirteen independent elastic constants (C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃, C₂₃, C₁₅, C₂₅, C₃₅, C₄₆) and the corresponding mechanical stability criteria are given as⁵⁵

C₁₁ > 0, C₂₂ > 0, C₃₃ > 0, C₄₄ > 0, C₅₅ > 0, C₆₆ > 0, [C₁₁ + C₂₂ + C₃₃ + 2(C₁₂ + C₁₃ + C₂₃)] > 0, (C₃₃C₅₅ − C₃₅²) > 0, (C₄₄C₆₆ − C₄₆²) > 0, (C₂₂ + C₃₃ − 2C₂₃) > 0, [C₂₂(C₃₃C₅₅ − C₃₅²) + 2C₂₃C₂₅C₃₅ − C₂₃²C₃₅ − C₂₅²C₃₃] > 0, {2[C₁₅C₂₅(C₃₃C₁₂ − C₁₃C₂₃) + C₁₅C₃₅(C₂₂C₁₃ − C₂₂C₂₃) + C₂₅C₃₅(C₁₁C₂₃ − C₁₂C₁₃)] − [C₁₅²(C₂₂C₃₃ − C₂₃²) + C₂₅²(C₁₁C₃₃ − C₁₃²) + C₃₅²(C₁₁C₂₂ − C₁₂²)] + C₅₅(C₁₁C₂₂C₃₃ − C₁₁C₂₃² − C₂₂C₁₃² − C₃₃C₁₂² + 2C₁₂C₁₃C₂₃)} > 0.

From the elastic constants listed in Table S1,† we find that the monoclinic phase of Pa₂O₅ in the ζ-Nb₂O₅ structures satisfies their respective mechanical stability criteria at ambient pressure, thus confirming their mechanical stability. However, the Pccm phase of Pa₂O₅ in the β-Ta₂O₅ structure is not the ground-state structure because this orthorhombic phase does not satisfy its mechanical stability criteria. Combining the thermodynamic and mechanical stability results, we conclude that the monoclinic phase is the ground-state structure for ζ-Nb₂O₅-structured Pa₂O₅ at ambient pressure. In addition, there is no evident correlation between the bulk moduli B and the volume (Vol.) or formation energy (E_form) of the layered Pa₂O₅ phases. Our work gives a high bulk modulus, B, for the ζ-Nb₂O₅-structured Pa₂O₅, but the bulk modulus of the Z-Ta₂O₅ structure is the largest.

3.4 Electronic properties

The experimental band gaps of the layered Pa₂O₅ phase are not currently available. In accordance with the higher layered oxide M₂O₅, all the structures are predicted to be ligand-to-metal charge-transfer (LMCT) insulators (O-2p to Pa-5f), with a conductance band composed of Pa 5f states and valence band comprised of O 2p states, with higher energy Pa 5f states at the core. To clearly describe the electronic properties of the most stable structure, the densities of states (DOS), projected density of states (PDOS) and band structure of Pa₂O₅ in the ζ-Nb₂O₅ and β-V₂O₅ structures are provided in Fig. 7 and S6.† These characteristics of Pa are attributed to its partially occupied 5f orbitals, which favors itinerancy for the early actinides. The appearance of significant Pa-5f/O-2p mixing arises from the increasing stabilization of the Pa 5f band due to incomplete shielding of the nuclear charge as one proceeds across the actinide series. There is a great variation in the predicted band gaps, with Pa₂O₅ in the ζ-Nb₂O₅ structure predicted to be 2.67 eV, which is more than the PaO₂ band gap of 1.40 eV.⁵⁶ As a comparison, the DOS and PDOS of Pa₂O₅ in the β-V₂O₅ structure are shown in Fig. 7b. Our PBE+U calculation predicts Pa₂O₅ in the β-V₂O₅ structure as a charge-transfer insulator with a band gap of 3.28 eV, which is bigger than the Pa₂O₅ in the ζ-Nb₂O₅ structure with a predicted gap of 0.61 eV. The presence of Pa 5f states in the valence band suggests a degree of covalent mixing with O 2p (fully ionic bonding would feature no overlapping states).

Fig. 7 Total and projected density of states of Pa₂O₅ in the ζ-Nb₂O₅ (a) and β-V₂O₅ (b) structures computed for the ground states in PBE+U. The Fermi energy stands at 0 eV.

4. Conclusions

In this work, we presented some possible structures of the Pa₂O₅ stoichiometry starting from existing actinide and transition metal pentoxides based on density functional theory. Our calculations showed that the Pa₂O₅ structures prefer the Pa ions in homogeneous Pa⁵⁺ oxidation states and that all are in distorted hexahedron and quadrangular pyramid coordination. Our simulations predict that the ζ-Nb₂O₅-structured Pa₂O₅ is the most stable under zero temperature and ambient conditions. The observed β-V₂O₅ structure was found to be the second most stable structure. Thus, it is expected that protactinium can crystallize with the ζ-Nb₂O₅ structure; however, this has not been observed experimentally. ζ-Nb₂O₅-structured Pa₂O₅ is a charge-transfer insulator and its calculated band gap is 2.67 eV. Thus, this stoichiometry is clearly worthy of synthetic investigation since the ζ-Nb₂O₅ structure is found to be a stable phase. To better understand the fluorite to layered transformation, we will focus on using a more pragmatic approach to model fluorite-based Pa₂O₅ phases in future simulation work.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Project supported by the National Natural Science Foundation of China (No. 21771167).

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Footnote

† Electronic supplementary information (ESI) available: Density functional theory optimized some layered Pa₂O₅ in the fractional format, enthalpies of formation, independent elastic constants, and thermodynamic properties (PDF). See DOI: 10.1039/c9ra06735c

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