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First-principles study of electronic structure and metal–insulator transition of plutonium dihydride and trihydride
Computational Materials Science 51 (2012) 127–134
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First-principles study of electronic structure and metal–insulator transition of plutonium dihydride and trihydride Juanjuan Ai a,⇑, Tao Liu a, Tao Gao a, Bingyun Ao b a b
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China China Academy of Engineering of Physics, P.O. Box 919-71, Mianyang 621900, Sichuan, PR China
a r t i c l e
i n f o
Article history: Received 29 December 2010 Received in revised form 4 June 2011 Accepted 2 July 2011 Available online 28 August 2011 Keywords: Plutonium hydride Electronic structure Metal–insulator transition
a b s t r a c t The electronic structures of cubic PuH2 and hexagonal PuH3 have been calculated by combining the full potential linearized augmented plane wave method (FLAPW) with the local spin density and generalized gradient approximation plus a Hubbard parameter U (LSDA + U and GGA + U) for considering the strong Coulomb correlation between localized Pu 5f electrons. Our study indicates that PuH2 is metallic, while PuH3 is a semiconductor with a small band gap about 0.26 eV. The bonds in PuH2 system have some covalent character. For PuH3, besides the covalent bonds, particularly, the bonding between Pu and octahedral H atoms is of prominent ionicity. In addition, the conductivity and resistivity data is also worked out at 300 K and low temperature of 4 K. The conductivity decreases from a metallic behavior of PuH2 to the semiconducting region of PuH3. The experimentally undetermined metal–insulator transition has been firstly discovered in Pu–H system theoretically. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Plutonium is the most complex element with many anomalous properties [1]. Investigating the physical and chemical properties of its compounds especially has great value in technological and environmental implications. In recent years, plutonium oxides have been widely studied theoretically [2–6], the investigations on its hydrides, however, are quite sparse. In fact, plutonium reacts with hydrogen facilely at low temperatures, which contributes greatly to the power metallurgy and plutonium recovery [7]. It is hard to produce the bulk samples of plutonium hydride, yet the powdered samples have the deficiency of high reactivity and uncertain composition. The cubic hydride is very active and often has spontaneous ignition and burning characteristics on exposure to air [8]. Due to the difficulty in the experiments, it is of great significance to investigate the plutonium hydrides within a theoretical framework. In 1990s, Huiberts et al. [9] discovered the notorious metal– insulator transition on the lanthanum and yttrium hydrides films-switch from a shiny mirror to a transparent window upon hydrogenation. It is well-known that plutonium hydrides are quite similar with that of rare-earth metal in terms of chemistry, crystal structure and phase diagram [10]. Hence, we are motivated to predict a metal–insulator transition in Pu–H system theoretically. A proton NMR study [11] indicated that Pu ions in hydrides possess localized 5f electrons, so both PuH2 and PuH3 are strongly ⇑ Corresponding author. Tel./fax: +86 28 85405234. E-mail addresses: [email protected] (J. Ai), [email protected] (T. Gao). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.07.006
correlated systems. However, the conventional density functional theory [12] (DFT) cannot predict the metal–insulator transition for strongly correlated systems. For example, Dekker et al. [13] and Wang and Chou [14] ever predicted that LaH3 and YH3 were semimetals, yet both of them are insulators [9]. Recently, Sun et al. [5] and Jomard et al. [6] showed respectively that PuO2 and Pu2O3 are metals in standard LDA and GGA rather than insulators observed from experiments [15–17]. The DFT + U [18–21] theory has been proposed to treat the correlation effects carefully. This so-called Hubbard U parameter method [22–26] captures well the localization effect of d or f electrons, and many properties of the transition metal compounds [19] as well as metal plutonium [22,25,26] and its oxides [5,6] can be described successfully. Plutonium is known to absorb hydrogen strongly [27] and the cubic dihydride is of wide hydrogen composition with the range from 1.9 to 2.7 [10,28]. Stoichiometric PuH2 is a face-centred cubic dihydride, which has CaF2-type fluorite structure with the tetrahedral interstices being occupied by H atoms. For x > 2.0, a continuous solid solution PuHx is existed over the range 2.0 < x < 3.0 when extra hydrogen atoms go to the octahedron interstices [8]. As x > 2.75, the fcc dihydride partially undergoes a first-order phase transition followed by the formation of hexagonal close packed structure [10,29]. Some studies [10,28–31] indicated that the hexagonal trihydride with the composition PuH3 was existed, and it is nonstoichiometric validated by the PVT equilibrium measurements [32]. Muromura et al. [29] noted a contraction of lattice upon increasing hydrogen composition also observed in rare-earth metal hydrides [33]. The phase relationships of plutonium hydride are quite similar with those of lanthanide difluoride and
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lanthanide trifluoride systems [8]. The hexagonal PuH3 crystallized in the form of LaF3 was observed in the terminal of plutonium hydride [8]. X-ray diffraction results [34] also showed that hexagonal PuH3 has the disordered LaF3-type structure. The magnetic susceptibility measured by Aldred et al. [35] indicated that cubic plutonium dihydride was antiferromagnetic ordering at 30 K, and hexagonal trihydride was ferromagnetic at 101 K. However, a later experiment performed by Willis et al. [36] showed that the samples of x = 1.93, 2.16, 2.42, 2.52, and 2.65 all order ferromagnetically between 44 and 67 K. In his experiment, Willis et al. also measured the resistivity on the five compositions, it rised from metallic to semiconductive behavior with the increase of x, and the value of hydride was larger than that of pure metal, which is contrary to the trend found in Ln hydrides [37]. In spite of the much information obtained, the electronic structure, however, is almost not touched upon in the previous studies of Pu–H system. In 2007, Balasubramanian et al. studied the plutonium hydrogen reaction based on the atomistic level relativistic quantum modeling. The electronic structure was computed for the low-lying electronic states of plutonium hydrides, PuHn (n = 2–4) [38]. Eriksson et al. [39] calculated self-consistently the electronic structure of paramagnetic PuH2, which showed that Pu 6d and H 1 s states hybridize strongly, reflecting appreciable covalent character in the bonding of PuH2 system. In the present paper, we mainly study the electronic structure, having an insight into the bonds in PuH2 and PuH3 systems and predicting the metal–insulator transition, and then calculate the conductivity and resistivity data compared with the experiment. The remainder of this paper is organized as follows. In Section 2 we describe the methods and details of calculations. Section 3 is devoted to the equilibrium properties and electronic structures analysis, and a metal–insulator transition is predicted in plutonium hydrides. Meanwhile, the character in the bonding is discussed for the PuH2 and PuH3 systems. In Section 4 we calculate the conductivity and resistivity of PuH2 and PuH3, suggesting the metal–insulator transition in terms of electric properties. Besides, the resistivity–temperature curves of PuH2 and PuH3 are also presented in this part. The last Section gives a summary.
2. Method and calculational details 2.1. Method The present study has been performed using the WIEN2 K package [40]. All electron calculation is achieved by employing the FLAPW method [41]. Our previous work [42] on the d-Pu and PuO investigated by Liu et al. also used the same method to calculate the electronic and structural properties. Space unit is divided into non-overlapping muffin-tin spheres and the remaining interstitial regions. Inside the muffin-tin spheres, the charge density and potential function are expanded in spherical harmonics function. In interstitial regions, the charge density, potential function and basis functions are expanded in plane waves. The muffin-tin radii Rmt are chosen allowing that the spheres are not overlapped. The charge convergence is set to 0.0001, and the total energy convergence is set to 0.0001 Ry for all the iterations. The cutoff parameter RmtKmax is set to 3 and 4 for PuH2 and PuH3 respectively in that the system including hydrogen has a short bondlength and thus a very small Rmt. Here Kmax is the plane wave cut-off. The charge density is Fourier expanded up to Gmax = 20 for the two systems. Plutonium is a heavy element, thus we add relativistic effects during the calculation. The scalar relativistic treatment is set for valence states and fully relativistic treatment for core ones. The valence electron configuration is 5f66s2p67s2, and there are 78 electrons occupying the core states.
We perform the self-consistent LSDA + U and GGA + U calculations derived from Dudarev et al. [43] for the equilibrium properties and electronic structure of PuH2 and PuH3. The LSDA (GGA) + U method has been validated to describe the electronic and structural properties of d-Pu and PuO correctly in our previous paper [42]. Two approximations are chosen as exchange–correlation potentials: LSDA using the von Barth–Hedin density functional [44] and GGA with the Perdew–Burke–Ernzerhof functional (PBE) [45]. The eigenvalues are calculated using modified tetrahedron grid method of Blöchl et al. [46] in the irreducible wedge of the Brillouin zone. The K points are 5000 in GGA/GGA + U and 15,000 in LSDA/LSDA + U for PuH2, and 200 for PuH3. Our calculations are based on the experimental results that PuH2 and PuH3 were ferromagnetic [35,36]. The spin–orbit (SO) coupling is neglected because it has a little effect on the ferromagnetism system [47]. In order to achieve the orbital-dependent potential, the effect of spin polarization is needed. 2.2. Details of calculation The space group of PuH2 is Fm3m. Its atomic positions are (0, 0, 0) for Pu, (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75) for H. The atomic density is 3 atoms per unit cell. The space group of PuH3 is fixed on P63/mmc of LaF3. Its crystallographic positions [11] are 2Pu ±(1/3, 2/3, 1/4), 2HI ±(0, 0, 1/4), 4HII ±(1/3, 2/3, Z) and ±(2/3, 1/3, 1/2 + Z), here Z = 0.607. The atomic density is 8 atoms per unit cell. The equilibrium volume V0 and bulk modulus B0 are derived from the energy–volume curve by fitting a Birch–Murnaghan equation of state [48]. The optimized results of PuH2 are shown in Table 1. Unlike the cubic PuH2, the lattice parameter is optimized simultaneously when dealing with the volume, the hexagonal structure, however, needs to be done from two dimensions of volume and lattice parameters respectively. The two jobs are intercrossed, and the former result is viewed as a starting point of the later one so that it can approach the energy minimization step by step to obtain the most stable structure. The optimized results of PuH3 are shown in Table 2. It is widely accepted that the value of U is 0.29 Ry (4.00 eV [25]) for Pu given the correlation effect of 5f electrons. By setting up the supercell [49], the calculated value in our work is about 0.28 Ry for PuH2 system, which is very close to that typical value. For comparison, the calculated Hubbard parameter U of PuH2 is somehow smaller than that of the d-Pu and PuO with the values of 0.31 Ry (4.15 eV) and 0.33 Ry (4.49 eV) respectively [42]. It results from the fact that the environment of the ligand in the Pu–H system is different from that of the metal Pu and PuO system. For PuH3, however, GGA + U cannot open a band gap with U = 0.29 Ry. When U tuned from 0.05, 0.11, 0.18 through 0.23 Ry, the band gap will
Table 1 Equilibrium properties of PuH2. Structural parameters of lattice constant a0, equilibrium volume V0 and bulk modulus B0 are reported in the four frameworks: GGA, LSDA, GGA + U, and LSDA + U. Besides, we also show some theoretical values and parts of experimental data from other studies. The Hubbard parameter U is 0.29 Ry.
a b
Method
a0 (Å)
V0 (Å3)
B0 (GPa)
GGA LSDA GGA + U LSDA + U LMTOa RLMTOa spin-polarized LMTOa Exp.b
5.09 4.94 5.46 5.29 4.74 4.89 4.98 5.395 ± 0.002
32.89 30.20 40.73 37.11 – – – 39.26
74.61 93.29 63.70 65.56 – – – –
Ref. [49]. Ref. [10].
J. Ai et al. / Computational Materials Science 51 (2012) 127–134 Table 2 Equilibrium properties of PuH3. Some experimental values are given for comparison. The Hubbard parameter U is 0.29 Ry for LSDA + U and 0.23 Ry for GGA + U, respectively.
a
Method
a0 (Å)
c0 (Å)
V0 (Å3)
B0 (GPa)
GGA LSDA GGA + U LSDA + U Exp.a
3.60 3.52 3.77 3.65 3.78 ± 0.01
6.28 6.11 6.62 6.48 6.76 ± 0.01
70.45 65.44 81.36 74.68 83.65
97.80 122.36 75.77 88.41 –
Ref. [10].
increase from 0.27, 0.53, 0.90 to 1.14 eV accordingly (data read from the density of states). Moreover, the gap will disappear when U is increased further from the value of 0.24 Ry. Hence, the parameter U is determined as 0.23 Ry for a relatively good gap under the GGA + U calculation for PuH3 (Because only the difference of U and J is important [43], the U–J is labeled as a single parameter U for simplicity, while the exchange energy J is nonzero during calculations). To our delight, the same value can yield perfect volume and bulk modulus in the GGA + U calculation on the work of d-Pu [23]. Evidently, the amplitude of U depends on the selection of exchange–correlation potential, which agrees with the viewpoints from other studies [6,50]. 3. Results and analysis
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gested the same trends. Consequently, it is a universal result owing to the one-electron approximation of pure DFT theory. 3.2. Electronic structure of PuH2 The density of states (DOS) is shown in Fig. 1. The total DOS curve crosses over the Fermi level (EF) with a nonzero occupation of Pu 5f electrons on it, exhibiting the metallic ground-state of the material in agreement with the conductivity measurement [36]. Inside the metal and hydrogen M–T spheres, the total DOS is decomposed into its angular momentum components as shown in Fig. 2. The DOS of PuH2 is almost composed by that of Pu atoms, the contribution from H atoms is vanishingly small especially at Fermi level. The DOS of Pu atoms is dominated by the 5f partial DOS. It is remarkable that two fairly sharp peaks appear in the 5f partial DOS; the one at Fermi level implies that 5f electrons are of strong many-particle nature and heavy-fermion behavior, which also appeared in the electronic structure of d-Pu [24]. Besides, Pu d orbits have their main weight above Fermi level, the H 1 s states, however, are centered at about 5 eV below it. When on-site Coulomb interaction is considered, prominent changes happen in the DOS spectrum of LSDA + U calculation (see Fig. 1). The two main peaks of 5f partial DOS are much sharper and further separated than that of LSDA, which reveals that the localization of 5f electrons is highly strengthened in LSDA + U calculation.
3.1. Equilibrium properties From the data in Table 1 of PuH2, both LSDA and GGA strongly underestimate the lattice parameter with respect to the experimental value. The same case happens on PuH3 from Table 2. After turning on Hubbard parameter U, the lattice constants of both PuH2 and PuH3 are much closer to experimental values as shown in the two tables. This is because when U is added, it will enhance the localization of 5f electrons and decrease the cohesion of the crystal and then lead to the increase of the lattice parameter. The result from GGA + U of PuH2 is a0 = 5.46 Å, which overestimates experimental value by 1.2%, such a trend also happened in the PuO2 system [5]. Note that our results are much better than some theoretical values calculated in other methods [51] of LMTO, RLMTO and spin-polarized LMTO for PuH2, suggesting an advantage of the present method for treating the strongly-correlated electron system over others. It is a little surprise that equilibrium volume V0 is severely underestimated by 23.1% in LSDA and 16.2% in GGA for PuH2. However, the results are greatly improved in GGA/LSDA + U frameworks. The data is around experimental equilibrium volume, deviating only by 5.5% in LSDA + U and 3.8% in GGA + U. This tendency is also found in PuH3 (see Table 2). Due to the effective Coulomb interaction, Pu 5f electrons are much more localized and participate less and less in the chemical bonding, so the increase of equilibrium volume is expected naturally. As concerns bulk modulus B0, the result from GGA/GGA + U is much lower than that from LSDA/LSDA + U, respectively for both PuH2 and PuH3, which results from the overbinding characteristic of LSDA approximation. We see the trend was also observed in the PuO2 system [5]. Furthermore, B0 of the standard DFT is higher than that of DFT + U for both the two systems. Hence the bulk modulus tends to decrease when the electron correlation in the 5f shell is taken into account. Apparently, pure DFT underestimates equilibrium volume V0 whereas overestimates bulk modulus B0 in comparison with experimental data and DFT + U results. The similar case was found in a study of d-Pu [23] and the work by Söderlind et al. [52] also sug-
Fig. 1. The density of states (DOS) in LSDA and LSDA + U approaches for cubic PuH2. The Fermi level stands at 0 eV. For LSDA + U, the Hubbard parameter U is 0.29 Ry (4.00 eV).
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Fig. 2. The angular momentum components of total DOS for PuH2 in the muffin-tin spheres of metal Pu and H atoms under LSDA + U framework.
Fig. 4. Charge-density contour map (in electrons/Å3) from the LSDA + U calculation of PuH2 in the (1 0 1) plane.
The situation at Fermi level is always attractive. Compared with LSDA, there is a striking reduction of density of states at the Fermi level in LSDA + U (see Fig. 1). It reveals that when Coulomb correlation is considered, 5f electrons no longer pin at the Fermi level, but withdraw from it and move toward the lower energy. This reflects the fact that electron correlation will prevent 5f electrons from participating in the bonding. In order to analyze Pu–H interaction, the projected DOS for Pu d-t2 g and H 1 s orbitals are plotted in Fig. 3. Within the lower part of valence bands, Pu d-t2 g and H 1 s DOS spectrums appear sharp peaks at the equivalent energy, the hybridization, to some extent, exists between the Pu d-t2 g and H 1 s occupied states. The interesting hybridization effect implies certain covalent character in the bonding of PuH2 system. This agrees well with the conclusion in the study of surface PuH2 [39]. The charge-density contour map is presented in Fig. 4. The charge density is increased gradually when approaching Pu atomic nuclei. It reflects that most of the electrons are bound up around atomic nuclei, only a few valence electrons can get rid of the bondage of them. It can be clearly seen that appreciable charge exists in the outer regions of Pu and H atoms, and Pu atoms are also proved to lose much charge to the interstitial regions [39]. In particular, notice that the charge, to some extent, piles up in the bonding regions between different atoms. This feature reflects that the bonding of Pu and H atoms has certain covalent character in PuH2 system, which is in line with the conclusion of hybridization analysis. In addition,
Fig. 5. Total and projected density of states of hexagonal PuH3 in the GGA and GGA + U approaches. The Fermi energy is set to be zero. The value of U is 0.23 Ry.
there is much light charge buildup with the typical characteristic of metallic bonding in the interstices regions away from the bonds, which suggests again that PuH2 is metallic as indicated by the DOS analysis. 3.3. Electronic structure of PuH3
Fig. 3. The projected DOS for Pu d-t2 g and H 1 s orbitals of PuH2.
The density of states in GGA/GGA + U and LSDA/LSDA + U schemes are plotted in Figs. 5 and 6, respectively. There is a nonzero occupation of Pu 5f states at the Fermi level either in pure LSDA or GGA, hence standard DFT predicts an incorrect metallic ground state for PuH3. This is a result of the one-electron
J. Ai et al. / Computational Materials Science 51 (2012) 127–134
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Fig. 7. The partial DOS for the Pu d, tetrahedral H 1 s and octahedral H 1 s of PuH3.
Fig. 6. Total and projected density of states in the LSDA and LSDA + U calculations of PuH3. The Fermi level is set to be zero. The value of U is 0.29 Ry.
assumption of standard DFT theory, the delocalization of Pu 5f electrons is thought to be strong with the idea that there is no interaction among electrons. However, when switching on U (see Figs. 5 and 6), the Pu 5f state begins to split with the occupied state broken away from the unoccupied part, which tends to open a gap D starting from the Fermi level. Obviously, LSDA/GGA + U frameworks with proper values of U can give rise to a semiconducting behavior for PuH3 in qualitative agreement with electric measurements [36]. It is readily observable that the result in LSDA + U is much better than that in GGA + U (see Figs. 5 and 6). The GGA often causes the ‘‘underbinding’’ effect of the crystal, yet the crystal structure is more compact in LSDA. Thus the cohesion in LSDA + U is stronger than that in GGA + U. In this way, it is harder for the interactions of 5f electrons to be validly shielded in LSDA + U, the repulsion is stronger between 5f electrons. This can be testified from the amplitude of Hubbard parameter U. It is 0.29 Ry in LSDA + U with a lower value of 0.23 Ry in GGA + U. Intense repulsion leads to the rapid increase of the energy in the system and it goes into extreme instability instantly. Then the system will automatically develop to the equilibrium following the stronger localization of 5f electrons. Hence there are fewer electrons shared among atoms, exhibiting the more prominent insulating behavior. The partial DOS for Pu d, tetrahedral H 1 s and octahedral H 1 s are plotted in Fig. 7. Hybridizations exist between Pu d and the both H 1 s orbitals. In particular, Pu d and the tetrahedral H 1 s hybridize pronouncedly, which illuminates that the bonding between them has certain covalent character. Because of the large separation of orbitals, the hybridization between Pu d and the octahedral H 1 s is much weaker, there is little covalent character in the bonds. This viewpoint can be strengthened by the charge density analysis subsequently.
The electronic band structures in LSDA and LSDA + U calculations are shown in Figs. 8 and 9, respectively. In the case of LSDA (see Fig. 8), both valence bands and conduction bands cross over the Fermi level and lead to the partial filling of them, thus pure LSDA predicts a metallic behavior for PuH3. When U is added as shown in Fig. 9, the valence electrons (mainly 5f electrons) are much more localized, the decrease of energy will force the valence bands to shift downward. Besides, the position of Fermi level is 0.65943 Ry in LSDA + U, which is lower than 0.86511 Ry in LSDA, hence the Fermi level removes downward as well. The removal of valence bands and Fermi level leads to an open of the energy gap. We see from Fig. 9 that the top of valence bands and the bottom of conduction bands are positioned at the same high-symmetry point, so PuH3 is a semiconductor of direct energy gap. However, the gap is very narrow with the value around 0.26 eV. Some studies about lanthanum [53,54] and yttrium [13,55] hydrides also showed that the gap calculated by density functional theory is universally much smaller than the experimental value. In fact, the DFT
Fig. 8. Electronic band structure of PuH3 in the LSDA calculation along several symmetry directions of the hexagonal Brillouin zone.
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Fig. 11. Charge-density contour map (in electrons/Å3) from the LSDA + U calcula plane. tion of PuH3 in the (1120)
Fig. 9. Electronic band structure of PuH3 in the LSDA + U calculation. A gap D is opened at the Fermi level (energy is zero), and the value is around 0.26 eV.
is established for calculating the ground-state energy, so it is difficult to give a satisfied answer for the description of excited states. In this case, the GW [56,57] approximation with the quasiparticle calculation is needed to obtain a precise gap value. Chang et al. [58] ever calculated the quasiparticle band structure of lanthanum hydride with GW method and found a large band gap in LaH3. To gain an insight into the metal–hydrogen bonding of PuH3 system, we plot the charge-density contour maps in the different planes as shown in Figs. 10 and 11. On the first map (see Fig. 10), the four H atoms lined out in the map occupy the tetrahedral interstices. Appreciable charge is distributed in the outer space of Pu and tetrahedral H atoms. To some extent, there is a buildup of charge in the bonding regions between the different atoms. Therefore, the bonding of them has some covalence, which agrees well with the hybridization analysis. As concerns the second map shown in Fig. 11, the two H atoms marked out occupy octahedral interstices. The charge density is rather low around Pu and octahedral H atoms in the interstices. Notice that almost no charge accumulates in the bonding regions
of Pu and octahedral H atoms, and there is little charge for them to share. Most of the valence electrons of Pu are firmly bound up around their atoms, and the strong localization reflects the main feature of the ionic chemical bonds. Therefore, the bonding of Pu and octahedral H atoms has strong ionic character. Apparently, beside the covalent bonds, there are remarkable ionic bonds in the PuH3 system. Just note the similar case was also found in the studies of lanthanide trifluorides [59,60], which indicated that the chemical bonds of LaF3 were significantly ionic with the presence of partial covalent character. Moreover, the existence of ionic bonds also implies that hexagonal PuH3 has certain insulating properties. According to the electronic structure analysis of PuH2 and PuH3, we are informed that PuH2 is metallic, while PuH3 exhibits some insulating behavior. We highlight that the experimentally undetermined metal–insulator transition has been firstly discovered in the Pu–H system theoretically. 4. Electrical properties and discussion 4.1. Conductivity and resistivity BoltzTraP [61] is a program designed for calculating band-structure dependent quantities. It relies on the Fourier expansion of the band energies and its theoretical background is in principle the Boltzmann theory. In this part, the code is employed to calculate the electrical conductivity and resistivity of PuH2 and PuH3. The results are presented in Table 3. At 4 K, the conductivity and resistivity of PuH2 are 1.3 106 X 1 m 1 and 75 10 8 X m, respectively, and the corresponding values of PuH3 are 8.7 104 X 1 m 1 and 11 10 6 X m. Obviously, there is a large
Table 3 The electrical conductivity and resistivity of PuH2 and PuH3 at the temperature of 300 K and 4 K, respectively. Some experimental data of the PuH1.93 and a-Pu measured at 4 K is listed as well. Compound
Temperature (K)
Conductivity (X
PuH1.93a PuH2
4 4 300 4 300 4
1.4 106 1.3 106 1.0 106 8.7 104 5.6 104 5.0 106
PuH3
Fig. 10. Charge-density contour map (in electrons/Å3) from the LSDA + U calculation of PuH3 in the (0 0 0 4) plane.
a-Pua a
Ref. [36].
1
m
1
)
Resistivity (X m) 70 10 75 10 96 10 11 10 18 10 20 10
8 8 8 6 6 8
J. Ai et al. / Computational Materials Science 51 (2012) 127–134
Fig. 12. The resistivity–temperature curves of PuH2 and PuH3.
decrease of the conductivity from PuH2 to PuH3, while the resistivity changes with the inverse trend. The similar case is also found at 300 K (see Table 3). It can be easily checked that the conductivity of PuH2 and PuH3 is within the metallic and semiconducting region, respectively. From this viewpoint, the metal–insulator transition, indeed, takes place from PuH2 to PuH3, which is consistent well with the previous conclusion of the electronic structure analysis. 4.2. Discussion Willis et al. [36] ever measured the conductivity and resistivity of plutonium dihydrides in the range 1.93 6 x 6 2.65 over the temperature of 1–300 K. At 4 K, the observed conductivity was 1.4 106 X 1 m 1 for x = 1.93, and the estimated resistivity was 70 10 8 X m. Compared with the present calculation, the results of PuH2 are close to the measured values of PuH1.93, which makes our study more reliable and convinced. Besides, Willis et al. indicated that the conductivity of five compositions in the range 1.93 6 x 6 2.65 decreases with the increase of hydrogen content from the metal of PuH1.93 to a semiconducting behavior of PuH2.65. Our work also gives the similar tendency from PuH2 to PuH3 especially the conductivity of PuH2 is slightly smaller than that of PuH1.93. It is intrigued to compare the conductivity at x = 1.93 with that of a-Pu in their experiment (see Table 3). Apparently, the conductivity of PuH1.93 is smaller than the value of a-Pu. In our study, the calculated conductivity of PuH2 is also smaller than the experimental data of a-Pu. It is due to the fact that the interactinide distances in the hydrides are larger than that in the Pu metal, which causes the reduction of 5f overlap and the 5f electrons are much more localized [39]. And then there are fewer electrons contributing to the conductivity which is decreased in plutonium hydride naturally. In the present study, the resistivity–temperature (q vs. T) curves are also given for PuH2 and PuH3 as shown in Fig. 12. The features of the q–T relationships are reproduced qualitatively in our work. The curve of PuH2 has positive dq/dT behavior near 300 K whereas the one of PuH3 exhibits a negative ratio under the same condition. Besides, in the case of PuH2, a turning point is appeared around 70 K. These features also resemble the behaviors of plutonium dihydrides in the above experiment. 5. Conclusion In this paper, the LSDA + U and GGA + U frameworks are employed to calculate the equilibrium properties and electronic
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structure of cubic PuH2 and hexagonal PuH3. PuH2 is metallic whereas PuH3 is of semiconducting behavior. For PuH3, we see intuitively from the band structure that the valence bands and conduction bands are well separated and a gap is opened at the Fermi level with a rather small value of about 0.26 eV. The hybridization and charge density analysis imply that there are certain covalent bonds in PuH2 system, yet for PuH3, particularly, the bonding between Pu and octahedral H atoms has prominently ionic character, showing certain insulativity. Therefore, it is predicted that the metal–insulator transition may take place from plutonium dihydride to trihydride as observed in rare-earth hydrides. On the other hand, the conductivity and resistivity of PuH2 and PuH3 are calculated using the BoltzTraP program. The results of PuH2 are very close to the values of PuH1.93 measured in an electrical experiment. We find that the conductivity decreases from a metal of PuH2 to the semiconducting region of PuH3, which confirms that the metal–insulator transition indeed exists in the plutonium hydrides. Furthermore, the resistivity–temperature relationships of PuH2 and PuH3 are also obtained in our work; the features of the curves are very similar with that of plutonium dihydrides measured by Willis et al. in the electrical experiment. Acknowledgements This work was supported by the National Nature Science Foundation of China (No. 20971114). We are grateful to Shi Peng and Cai Tuo for helpful comments and discussion. References [1] K.T. Moore, G. van der Laan, Rev. Mod. Phys. 81 (2009) 235–298. [2] I.D. Prodan, G.E. Scuseria, J.A. Sordo, K.N. Kudin, R.L. Martin, J. Chem. Phys. 123 (2005) 014703. [3] I.D. Prodan, G.E. Scuseria, R.L. Martin, Phys. Rev. B 73 (2006) 045104. [4] I.D. Prodan, G.E. Scuseria, R.L. Martin, Phys. Rev. B 76 (2007) 033101. [5] B. Sun, P. Zhang, X.-G. Zhao, J. Chem. Phys. 128 (2008) 084705. [6] G. Jomard, B. Amadon, F. Bottin, M. Torrent, Phys. Rev. B 78 (2008) 075125. [7] G.L. Stifter, M.H. Curtis, The preparation of plutonium powder by a hydriding process: initial studies, US Atomic Energy Commission, March 1960, Rep., HW64289. [8] For an overview of plutonium hydride J.M. Haschke, R.G. Haire, in: D.C. Hoffman (Ed.), Handbook on the Advances in Plutonium Chemistry 1967– 2000, American Nuclear Society, La Grange Park, Illinois USA, 2002, pp. 215– 220 (Chapter 9). [9] J.N. Huiberts, R. Griessen, J.H. Rector, R.J. Wijngaarden, J.P. Dekker, D.G. de Groot, N.J. Koeman, Nature (London) 380 (1996) 231. [10] R.N.R. Mulford, G.E. Sturdy, J. Am. Chem. Soc. 77 (1955) 3449; R.N.R. Mulford, G.E. Sturdy, J. Am. Chem. Soc. 78 (1956) 3897. [11] G. Cinader, D. Zamir, Z. Hadari, Phys. Rev. B 14 (1976) 912–919. [12] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864; W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [13] J.P. Dekker, J. van Ek, A. Lodder, J.N. Huiberts, J. Phys.: Condens. Matter 5 (1993) 4805. [14] Y. Wang, M.Y. Chou, Phys. Rev. Lett. 71 (1993) 1226. [15] M. Butterfield, T. Durakiewicz, E. Guziewicz, J. Joyce, A. Arko, K. Graham, D. Moore, L. Morales, Surf. Sci. 571 (2004) 74. [16] M.T. Butterfield, T. Durakiewicz, I.D. Prodan, G.E. Scuseria, E. Guziewicz, J.A. Sordo, K.N. Kudin, R.L. Martin, J.J. Joyce, A.J. Arko, K.S. Graham, D.P. Moore, L.A. Morales, Surf. Sci. 600 (2006) 1637. [17] T. Gouder, A. Seibert, L. Havela, J. Rebizant, Surf. Sci. 601 (2007) L77. [18] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [19] V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, J. Phys.: Condens. Matter 9 (1997) 767; For a review V.I. Anisimov (Ed.), Strong Coulomb Correlations in Electronic Structure Calculations: Beyond the Local Density Approximation, Gordon and Breach Science Publishers, Amsterdam, 2000. [20] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. _ [21] M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 49 (1994) 14211. [22] S.Y. Savrasov, G. Kotliar, Phys. Rev. Lett. 84 (2000) 3670. [23] J. Bouchet, B. Siberchicot, F. Jollet, A. Pasturel, J. Phys.: Condens. Matter 12 (2000) 1723. [24] A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin, V.I. Anisimov, Phys. Rev. B 72 (2005) 024458. [25] A. Shick, V. Drchal, L. Havela, Europhys. Lett. 69 (2005) 588. [26] A. Shick, L. Havela, J. Kolorenc, V. Drchal, T. Gouder, P.M. Oppeneer, Phys. Rev. B 73 (2006) 104415.
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First-principles study of electronic structure and metal–insulator transition of plutonium dihydride and trihydride Juanjuan Ai a,⇑, Tao Liu a, Tao Gao a, Bingyun Ao b a b
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China China Academy of Engineering of Physics, P.O. Box 919-71, Mianyang 621900, Sichuan, PR China
a r t i c l e
i n f o
Article history: Received 29 December 2010 Received in revised form 4 June 2011 Accepted 2 July 2011 Available online 28 August 2011 Keywords: Plutonium hydride Electronic structure Metal–insulator transition
a b s t r a c t The electronic structures of cubic PuH2 and hexagonal PuH3 have been calculated by combining the full potential linearized augmented plane wave method (FLAPW) with the local spin density and generalized gradient approximation plus a Hubbard parameter U (LSDA + U and GGA + U) for considering the strong Coulomb correlation between localized Pu 5f electrons. Our study indicates that PuH2 is metallic, while PuH3 is a semiconductor with a small band gap about 0.26 eV. The bonds in PuH2 system have some covalent character. For PuH3, besides the covalent bonds, particularly, the bonding between Pu and octahedral H atoms is of prominent ionicity. In addition, the conductivity and resistivity data is also worked out at 300 K and low temperature of 4 K. The conductivity decreases from a metallic behavior of PuH2 to the semiconducting region of PuH3. The experimentally undetermined metal–insulator transition has been firstly discovered in Pu–H system theoretically. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Plutonium is the most complex element with many anomalous properties [1]. Investigating the physical and chemical properties of its compounds especially has great value in technological and environmental implications. In recent years, plutonium oxides have been widely studied theoretically [2–6], the investigations on its hydrides, however, are quite sparse. In fact, plutonium reacts with hydrogen facilely at low temperatures, which contributes greatly to the power metallurgy and plutonium recovery [7]. It is hard to produce the bulk samples of plutonium hydride, yet the powdered samples have the deficiency of high reactivity and uncertain composition. The cubic hydride is very active and often has spontaneous ignition and burning characteristics on exposure to air [8]. Due to the difficulty in the experiments, it is of great significance to investigate the plutonium hydrides within a theoretical framework. In 1990s, Huiberts et al. [9] discovered the notorious metal– insulator transition on the lanthanum and yttrium hydrides films-switch from a shiny mirror to a transparent window upon hydrogenation. It is well-known that plutonium hydrides are quite similar with that of rare-earth metal in terms of chemistry, crystal structure and phase diagram [10]. Hence, we are motivated to predict a metal–insulator transition in Pu–H system theoretically. A proton NMR study [11] indicated that Pu ions in hydrides possess localized 5f electrons, so both PuH2 and PuH3 are strongly ⇑ Corresponding author. Tel./fax: +86 28 85405234. E-mail addresses: [email protected] (J. Ai), [email protected] (T. Gao). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.07.006
correlated systems. However, the conventional density functional theory [12] (DFT) cannot predict the metal–insulator transition for strongly correlated systems. For example, Dekker et al. [13] and Wang and Chou [14] ever predicted that LaH3 and YH3 were semimetals, yet both of them are insulators [9]. Recently, Sun et al. [5] and Jomard et al. [6] showed respectively that PuO2 and Pu2O3 are metals in standard LDA and GGA rather than insulators observed from experiments [15–17]. The DFT + U [18–21] theory has been proposed to treat the correlation effects carefully. This so-called Hubbard U parameter method [22–26] captures well the localization effect of d or f electrons, and many properties of the transition metal compounds [19] as well as metal plutonium [22,25,26] and its oxides [5,6] can be described successfully. Plutonium is known to absorb hydrogen strongly [27] and the cubic dihydride is of wide hydrogen composition with the range from 1.9 to 2.7 [10,28]. Stoichiometric PuH2 is a face-centred cubic dihydride, which has CaF2-type fluorite structure with the tetrahedral interstices being occupied by H atoms. For x > 2.0, a continuous solid solution PuHx is existed over the range 2.0 < x < 3.0 when extra hydrogen atoms go to the octahedron interstices [8]. As x > 2.75, the fcc dihydride partially undergoes a first-order phase transition followed by the formation of hexagonal close packed structure [10,29]. Some studies [10,28–31] indicated that the hexagonal trihydride with the composition PuH3 was existed, and it is nonstoichiometric validated by the PVT equilibrium measurements [32]. Muromura et al. [29] noted a contraction of lattice upon increasing hydrogen composition also observed in rare-earth metal hydrides [33]. The phase relationships of plutonium hydride are quite similar with those of lanthanide difluoride and
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lanthanide trifluoride systems [8]. The hexagonal PuH3 crystallized in the form of LaF3 was observed in the terminal of plutonium hydride [8]. X-ray diffraction results [34] also showed that hexagonal PuH3 has the disordered LaF3-type structure. The magnetic susceptibility measured by Aldred et al. [35] indicated that cubic plutonium dihydride was antiferromagnetic ordering at 30 K, and hexagonal trihydride was ferromagnetic at 101 K. However, a later experiment performed by Willis et al. [36] showed that the samples of x = 1.93, 2.16, 2.42, 2.52, and 2.65 all order ferromagnetically between 44 and 67 K. In his experiment, Willis et al. also measured the resistivity on the five compositions, it rised from metallic to semiconductive behavior with the increase of x, and the value of hydride was larger than that of pure metal, which is contrary to the trend found in Ln hydrides [37]. In spite of the much information obtained, the electronic structure, however, is almost not touched upon in the previous studies of Pu–H system. In 2007, Balasubramanian et al. studied the plutonium hydrogen reaction based on the atomistic level relativistic quantum modeling. The electronic structure was computed for the low-lying electronic states of plutonium hydrides, PuHn (n = 2–4) [38]. Eriksson et al. [39] calculated self-consistently the electronic structure of paramagnetic PuH2, which showed that Pu 6d and H 1 s states hybridize strongly, reflecting appreciable covalent character in the bonding of PuH2 system. In the present paper, we mainly study the electronic structure, having an insight into the bonds in PuH2 and PuH3 systems and predicting the metal–insulator transition, and then calculate the conductivity and resistivity data compared with the experiment. The remainder of this paper is organized as follows. In Section 2 we describe the methods and details of calculations. Section 3 is devoted to the equilibrium properties and electronic structures analysis, and a metal–insulator transition is predicted in plutonium hydrides. Meanwhile, the character in the bonding is discussed for the PuH2 and PuH3 systems. In Section 4 we calculate the conductivity and resistivity of PuH2 and PuH3, suggesting the metal–insulator transition in terms of electric properties. Besides, the resistivity–temperature curves of PuH2 and PuH3 are also presented in this part. The last Section gives a summary.
2. Method and calculational details 2.1. Method The present study has been performed using the WIEN2 K package [40]. All electron calculation is achieved by employing the FLAPW method [41]. Our previous work [42] on the d-Pu and PuO investigated by Liu et al. also used the same method to calculate the electronic and structural properties. Space unit is divided into non-overlapping muffin-tin spheres and the remaining interstitial regions. Inside the muffin-tin spheres, the charge density and potential function are expanded in spherical harmonics function. In interstitial regions, the charge density, potential function and basis functions are expanded in plane waves. The muffin-tin radii Rmt are chosen allowing that the spheres are not overlapped. The charge convergence is set to 0.0001, and the total energy convergence is set to 0.0001 Ry for all the iterations. The cutoff parameter RmtKmax is set to 3 and 4 for PuH2 and PuH3 respectively in that the system including hydrogen has a short bondlength and thus a very small Rmt. Here Kmax is the plane wave cut-off. The charge density is Fourier expanded up to Gmax = 20 for the two systems. Plutonium is a heavy element, thus we add relativistic effects during the calculation. The scalar relativistic treatment is set for valence states and fully relativistic treatment for core ones. The valence electron configuration is 5f66s2p67s2, and there are 78 electrons occupying the core states.
We perform the self-consistent LSDA + U and GGA + U calculations derived from Dudarev et al. [43] for the equilibrium properties and electronic structure of PuH2 and PuH3. The LSDA (GGA) + U method has been validated to describe the electronic and structural properties of d-Pu and PuO correctly in our previous paper [42]. Two approximations are chosen as exchange–correlation potentials: LSDA using the von Barth–Hedin density functional [44] and GGA with the Perdew–Burke–Ernzerhof functional (PBE) [45]. The eigenvalues are calculated using modified tetrahedron grid method of Blöchl et al. [46] in the irreducible wedge of the Brillouin zone. The K points are 5000 in GGA/GGA + U and 15,000 in LSDA/LSDA + U for PuH2, and 200 for PuH3. Our calculations are based on the experimental results that PuH2 and PuH3 were ferromagnetic [35,36]. The spin–orbit (SO) coupling is neglected because it has a little effect on the ferromagnetism system [47]. In order to achieve the orbital-dependent potential, the effect of spin polarization is needed. 2.2. Details of calculation The space group of PuH2 is Fm3m. Its atomic positions are (0, 0, 0) for Pu, (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75) for H. The atomic density is 3 atoms per unit cell. The space group of PuH3 is fixed on P63/mmc of LaF3. Its crystallographic positions [11] are 2Pu ±(1/3, 2/3, 1/4), 2HI ±(0, 0, 1/4), 4HII ±(1/3, 2/3, Z) and ±(2/3, 1/3, 1/2 + Z), here Z = 0.607. The atomic density is 8 atoms per unit cell. The equilibrium volume V0 and bulk modulus B0 are derived from the energy–volume curve by fitting a Birch–Murnaghan equation of state [48]. The optimized results of PuH2 are shown in Table 1. Unlike the cubic PuH2, the lattice parameter is optimized simultaneously when dealing with the volume, the hexagonal structure, however, needs to be done from two dimensions of volume and lattice parameters respectively. The two jobs are intercrossed, and the former result is viewed as a starting point of the later one so that it can approach the energy minimization step by step to obtain the most stable structure. The optimized results of PuH3 are shown in Table 2. It is widely accepted that the value of U is 0.29 Ry (4.00 eV [25]) for Pu given the correlation effect of 5f electrons. By setting up the supercell [49], the calculated value in our work is about 0.28 Ry for PuH2 system, which is very close to that typical value. For comparison, the calculated Hubbard parameter U of PuH2 is somehow smaller than that of the d-Pu and PuO with the values of 0.31 Ry (4.15 eV) and 0.33 Ry (4.49 eV) respectively [42]. It results from the fact that the environment of the ligand in the Pu–H system is different from that of the metal Pu and PuO system. For PuH3, however, GGA + U cannot open a band gap with U = 0.29 Ry. When U tuned from 0.05, 0.11, 0.18 through 0.23 Ry, the band gap will
Table 1 Equilibrium properties of PuH2. Structural parameters of lattice constant a0, equilibrium volume V0 and bulk modulus B0 are reported in the four frameworks: GGA, LSDA, GGA + U, and LSDA + U. Besides, we also show some theoretical values and parts of experimental data from other studies. The Hubbard parameter U is 0.29 Ry.
a b
Method
a0 (Å)
V0 (Å3)
B0 (GPa)
GGA LSDA GGA + U LSDA + U LMTOa RLMTOa spin-polarized LMTOa Exp.b
5.09 4.94 5.46 5.29 4.74 4.89 4.98 5.395 ± 0.002
32.89 30.20 40.73 37.11 – – – 39.26
74.61 93.29 63.70 65.56 – – – –
Ref. [49]. Ref. [10].
J. Ai et al. / Computational Materials Science 51 (2012) 127–134 Table 2 Equilibrium properties of PuH3. Some experimental values are given for comparison. The Hubbard parameter U is 0.29 Ry for LSDA + U and 0.23 Ry for GGA + U, respectively.
a
Method
a0 (Å)
c0 (Å)
V0 (Å3)
B0 (GPa)
GGA LSDA GGA + U LSDA + U Exp.a
3.60 3.52 3.77 3.65 3.78 ± 0.01
6.28 6.11 6.62 6.48 6.76 ± 0.01
70.45 65.44 81.36 74.68 83.65
97.80 122.36 75.77 88.41 –
Ref. [10].
increase from 0.27, 0.53, 0.90 to 1.14 eV accordingly (data read from the density of states). Moreover, the gap will disappear when U is increased further from the value of 0.24 Ry. Hence, the parameter U is determined as 0.23 Ry for a relatively good gap under the GGA + U calculation for PuH3 (Because only the difference of U and J is important [43], the U–J is labeled as a single parameter U for simplicity, while the exchange energy J is nonzero during calculations). To our delight, the same value can yield perfect volume and bulk modulus in the GGA + U calculation on the work of d-Pu [23]. Evidently, the amplitude of U depends on the selection of exchange–correlation potential, which agrees with the viewpoints from other studies [6,50]. 3. Results and analysis
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gested the same trends. Consequently, it is a universal result owing to the one-electron approximation of pure DFT theory. 3.2. Electronic structure of PuH2 The density of states (DOS) is shown in Fig. 1. The total DOS curve crosses over the Fermi level (EF) with a nonzero occupation of Pu 5f electrons on it, exhibiting the metallic ground-state of the material in agreement with the conductivity measurement [36]. Inside the metal and hydrogen M–T spheres, the total DOS is decomposed into its angular momentum components as shown in Fig. 2. The DOS of PuH2 is almost composed by that of Pu atoms, the contribution from H atoms is vanishingly small especially at Fermi level. The DOS of Pu atoms is dominated by the 5f partial DOS. It is remarkable that two fairly sharp peaks appear in the 5f partial DOS; the one at Fermi level implies that 5f electrons are of strong many-particle nature and heavy-fermion behavior, which also appeared in the electronic structure of d-Pu [24]. Besides, Pu d orbits have their main weight above Fermi level, the H 1 s states, however, are centered at about 5 eV below it. When on-site Coulomb interaction is considered, prominent changes happen in the DOS spectrum of LSDA + U calculation (see Fig. 1). The two main peaks of 5f partial DOS are much sharper and further separated than that of LSDA, which reveals that the localization of 5f electrons is highly strengthened in LSDA + U calculation.
3.1. Equilibrium properties From the data in Table 1 of PuH2, both LSDA and GGA strongly underestimate the lattice parameter with respect to the experimental value. The same case happens on PuH3 from Table 2. After turning on Hubbard parameter U, the lattice constants of both PuH2 and PuH3 are much closer to experimental values as shown in the two tables. This is because when U is added, it will enhance the localization of 5f electrons and decrease the cohesion of the crystal and then lead to the increase of the lattice parameter. The result from GGA + U of PuH2 is a0 = 5.46 Å, which overestimates experimental value by 1.2%, such a trend also happened in the PuO2 system [5]. Note that our results are much better than some theoretical values calculated in other methods [51] of LMTO, RLMTO and spin-polarized LMTO for PuH2, suggesting an advantage of the present method for treating the strongly-correlated electron system over others. It is a little surprise that equilibrium volume V0 is severely underestimated by 23.1% in LSDA and 16.2% in GGA for PuH2. However, the results are greatly improved in GGA/LSDA + U frameworks. The data is around experimental equilibrium volume, deviating only by 5.5% in LSDA + U and 3.8% in GGA + U. This tendency is also found in PuH3 (see Table 2). Due to the effective Coulomb interaction, Pu 5f electrons are much more localized and participate less and less in the chemical bonding, so the increase of equilibrium volume is expected naturally. As concerns bulk modulus B0, the result from GGA/GGA + U is much lower than that from LSDA/LSDA + U, respectively for both PuH2 and PuH3, which results from the overbinding characteristic of LSDA approximation. We see the trend was also observed in the PuO2 system [5]. Furthermore, B0 of the standard DFT is higher than that of DFT + U for both the two systems. Hence the bulk modulus tends to decrease when the electron correlation in the 5f shell is taken into account. Apparently, pure DFT underestimates equilibrium volume V0 whereas overestimates bulk modulus B0 in comparison with experimental data and DFT + U results. The similar case was found in a study of d-Pu [23] and the work by Söderlind et al. [52] also sug-
Fig. 1. The density of states (DOS) in LSDA and LSDA + U approaches for cubic PuH2. The Fermi level stands at 0 eV. For LSDA + U, the Hubbard parameter U is 0.29 Ry (4.00 eV).
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Fig. 2. The angular momentum components of total DOS for PuH2 in the muffin-tin spheres of metal Pu and H atoms under LSDA + U framework.
Fig. 4. Charge-density contour map (in electrons/Å3) from the LSDA + U calculation of PuH2 in the (1 0 1) plane.
The situation at Fermi level is always attractive. Compared with LSDA, there is a striking reduction of density of states at the Fermi level in LSDA + U (see Fig. 1). It reveals that when Coulomb correlation is considered, 5f electrons no longer pin at the Fermi level, but withdraw from it and move toward the lower energy. This reflects the fact that electron correlation will prevent 5f electrons from participating in the bonding. In order to analyze Pu–H interaction, the projected DOS for Pu d-t2 g and H 1 s orbitals are plotted in Fig. 3. Within the lower part of valence bands, Pu d-t2 g and H 1 s DOS spectrums appear sharp peaks at the equivalent energy, the hybridization, to some extent, exists between the Pu d-t2 g and H 1 s occupied states. The interesting hybridization effect implies certain covalent character in the bonding of PuH2 system. This agrees well with the conclusion in the study of surface PuH2 [39]. The charge-density contour map is presented in Fig. 4. The charge density is increased gradually when approaching Pu atomic nuclei. It reflects that most of the electrons are bound up around atomic nuclei, only a few valence electrons can get rid of the bondage of them. It can be clearly seen that appreciable charge exists in the outer regions of Pu and H atoms, and Pu atoms are also proved to lose much charge to the interstitial regions [39]. In particular, notice that the charge, to some extent, piles up in the bonding regions between different atoms. This feature reflects that the bonding of Pu and H atoms has certain covalent character in PuH2 system, which is in line with the conclusion of hybridization analysis. In addition,
Fig. 5. Total and projected density of states of hexagonal PuH3 in the GGA and GGA + U approaches. The Fermi energy is set to be zero. The value of U is 0.23 Ry.
there is much light charge buildup with the typical characteristic of metallic bonding in the interstices regions away from the bonds, which suggests again that PuH2 is metallic as indicated by the DOS analysis. 3.3. Electronic structure of PuH3
Fig. 3. The projected DOS for Pu d-t2 g and H 1 s orbitals of PuH2.
The density of states in GGA/GGA + U and LSDA/LSDA + U schemes are plotted in Figs. 5 and 6, respectively. There is a nonzero occupation of Pu 5f states at the Fermi level either in pure LSDA or GGA, hence standard DFT predicts an incorrect metallic ground state for PuH3. This is a result of the one-electron
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Fig. 7. The partial DOS for the Pu d, tetrahedral H 1 s and octahedral H 1 s of PuH3.
Fig. 6. Total and projected density of states in the LSDA and LSDA + U calculations of PuH3. The Fermi level is set to be zero. The value of U is 0.29 Ry.
assumption of standard DFT theory, the delocalization of Pu 5f electrons is thought to be strong with the idea that there is no interaction among electrons. However, when switching on U (see Figs. 5 and 6), the Pu 5f state begins to split with the occupied state broken away from the unoccupied part, which tends to open a gap D starting from the Fermi level. Obviously, LSDA/GGA + U frameworks with proper values of U can give rise to a semiconducting behavior for PuH3 in qualitative agreement with electric measurements [36]. It is readily observable that the result in LSDA + U is much better than that in GGA + U (see Figs. 5 and 6). The GGA often causes the ‘‘underbinding’’ effect of the crystal, yet the crystal structure is more compact in LSDA. Thus the cohesion in LSDA + U is stronger than that in GGA + U. In this way, it is harder for the interactions of 5f electrons to be validly shielded in LSDA + U, the repulsion is stronger between 5f electrons. This can be testified from the amplitude of Hubbard parameter U. It is 0.29 Ry in LSDA + U with a lower value of 0.23 Ry in GGA + U. Intense repulsion leads to the rapid increase of the energy in the system and it goes into extreme instability instantly. Then the system will automatically develop to the equilibrium following the stronger localization of 5f electrons. Hence there are fewer electrons shared among atoms, exhibiting the more prominent insulating behavior. The partial DOS for Pu d, tetrahedral H 1 s and octahedral H 1 s are plotted in Fig. 7. Hybridizations exist between Pu d and the both H 1 s orbitals. In particular, Pu d and the tetrahedral H 1 s hybridize pronouncedly, which illuminates that the bonding between them has certain covalent character. Because of the large separation of orbitals, the hybridization between Pu d and the octahedral H 1 s is much weaker, there is little covalent character in the bonds. This viewpoint can be strengthened by the charge density analysis subsequently.
The electronic band structures in LSDA and LSDA + U calculations are shown in Figs. 8 and 9, respectively. In the case of LSDA (see Fig. 8), both valence bands and conduction bands cross over the Fermi level and lead to the partial filling of them, thus pure LSDA predicts a metallic behavior for PuH3. When U is added as shown in Fig. 9, the valence electrons (mainly 5f electrons) are much more localized, the decrease of energy will force the valence bands to shift downward. Besides, the position of Fermi level is 0.65943 Ry in LSDA + U, which is lower than 0.86511 Ry in LSDA, hence the Fermi level removes downward as well. The removal of valence bands and Fermi level leads to an open of the energy gap. We see from Fig. 9 that the top of valence bands and the bottom of conduction bands are positioned at the same high-symmetry point, so PuH3 is a semiconductor of direct energy gap. However, the gap is very narrow with the value around 0.26 eV. Some studies about lanthanum [53,54] and yttrium [13,55] hydrides also showed that the gap calculated by density functional theory is universally much smaller than the experimental value. In fact, the DFT
Fig. 8. Electronic band structure of PuH3 in the LSDA calculation along several symmetry directions of the hexagonal Brillouin zone.
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Fig. 11. Charge-density contour map (in electrons/Å3) from the LSDA + U calcula plane. tion of PuH3 in the (1120)
Fig. 9. Electronic band structure of PuH3 in the LSDA + U calculation. A gap D is opened at the Fermi level (energy is zero), and the value is around 0.26 eV.
is established for calculating the ground-state energy, so it is difficult to give a satisfied answer for the description of excited states. In this case, the GW [56,57] approximation with the quasiparticle calculation is needed to obtain a precise gap value. Chang et al. [58] ever calculated the quasiparticle band structure of lanthanum hydride with GW method and found a large band gap in LaH3. To gain an insight into the metal–hydrogen bonding of PuH3 system, we plot the charge-density contour maps in the different planes as shown in Figs. 10 and 11. On the first map (see Fig. 10), the four H atoms lined out in the map occupy the tetrahedral interstices. Appreciable charge is distributed in the outer space of Pu and tetrahedral H atoms. To some extent, there is a buildup of charge in the bonding regions between the different atoms. Therefore, the bonding of them has some covalence, which agrees well with the hybridization analysis. As concerns the second map shown in Fig. 11, the two H atoms marked out occupy octahedral interstices. The charge density is rather low around Pu and octahedral H atoms in the interstices. Notice that almost no charge accumulates in the bonding regions
of Pu and octahedral H atoms, and there is little charge for them to share. Most of the valence electrons of Pu are firmly bound up around their atoms, and the strong localization reflects the main feature of the ionic chemical bonds. Therefore, the bonding of Pu and octahedral H atoms has strong ionic character. Apparently, beside the covalent bonds, there are remarkable ionic bonds in the PuH3 system. Just note the similar case was also found in the studies of lanthanide trifluorides [59,60], which indicated that the chemical bonds of LaF3 were significantly ionic with the presence of partial covalent character. Moreover, the existence of ionic bonds also implies that hexagonal PuH3 has certain insulating properties. According to the electronic structure analysis of PuH2 and PuH3, we are informed that PuH2 is metallic, while PuH3 exhibits some insulating behavior. We highlight that the experimentally undetermined metal–insulator transition has been firstly discovered in the Pu–H system theoretically. 4. Electrical properties and discussion 4.1. Conductivity and resistivity BoltzTraP [61] is a program designed for calculating band-structure dependent quantities. It relies on the Fourier expansion of the band energies and its theoretical background is in principle the Boltzmann theory. In this part, the code is employed to calculate the electrical conductivity and resistivity of PuH2 and PuH3. The results are presented in Table 3. At 4 K, the conductivity and resistivity of PuH2 are 1.3 106 X 1 m 1 and 75 10 8 X m, respectively, and the corresponding values of PuH3 are 8.7 104 X 1 m 1 and 11 10 6 X m. Obviously, there is a large
Table 3 The electrical conductivity and resistivity of PuH2 and PuH3 at the temperature of 300 K and 4 K, respectively. Some experimental data of the PuH1.93 and a-Pu measured at 4 K is listed as well. Compound
Temperature (K)
Conductivity (X
PuH1.93a PuH2
4 4 300 4 300 4
1.4 106 1.3 106 1.0 106 8.7 104 5.6 104 5.0 106
PuH3
Fig. 10. Charge-density contour map (in electrons/Å3) from the LSDA + U calculation of PuH3 in the (0 0 0 4) plane.
a-Pua a
Ref. [36].
1
m
1
)
Resistivity (X m) 70 10 75 10 96 10 11 10 18 10 20 10
8 8 8 6 6 8
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Fig. 12. The resistivity–temperature curves of PuH2 and PuH3.
decrease of the conductivity from PuH2 to PuH3, while the resistivity changes with the inverse trend. The similar case is also found at 300 K (see Table 3). It can be easily checked that the conductivity of PuH2 and PuH3 is within the metallic and semiconducting region, respectively. From this viewpoint, the metal–insulator transition, indeed, takes place from PuH2 to PuH3, which is consistent well with the previous conclusion of the electronic structure analysis. 4.2. Discussion Willis et al. [36] ever measured the conductivity and resistivity of plutonium dihydrides in the range 1.93 6 x 6 2.65 over the temperature of 1–300 K. At 4 K, the observed conductivity was 1.4 106 X 1 m 1 for x = 1.93, and the estimated resistivity was 70 10 8 X m. Compared with the present calculation, the results of PuH2 are close to the measured values of PuH1.93, which makes our study more reliable and convinced. Besides, Willis et al. indicated that the conductivity of five compositions in the range 1.93 6 x 6 2.65 decreases with the increase of hydrogen content from the metal of PuH1.93 to a semiconducting behavior of PuH2.65. Our work also gives the similar tendency from PuH2 to PuH3 especially the conductivity of PuH2 is slightly smaller than that of PuH1.93. It is intrigued to compare the conductivity at x = 1.93 with that of a-Pu in their experiment (see Table 3). Apparently, the conductivity of PuH1.93 is smaller than the value of a-Pu. In our study, the calculated conductivity of PuH2 is also smaller than the experimental data of a-Pu. It is due to the fact that the interactinide distances in the hydrides are larger than that in the Pu metal, which causes the reduction of 5f overlap and the 5f electrons are much more localized [39]. And then there are fewer electrons contributing to the conductivity which is decreased in plutonium hydride naturally. In the present study, the resistivity–temperature (q vs. T) curves are also given for PuH2 and PuH3 as shown in Fig. 12. The features of the q–T relationships are reproduced qualitatively in our work. The curve of PuH2 has positive dq/dT behavior near 300 K whereas the one of PuH3 exhibits a negative ratio under the same condition. Besides, in the case of PuH2, a turning point is appeared around 70 K. These features also resemble the behaviors of plutonium dihydrides in the above experiment. 5. Conclusion In this paper, the LSDA + U and GGA + U frameworks are employed to calculate the equilibrium properties and electronic
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structure of cubic PuH2 and hexagonal PuH3. PuH2 is metallic whereas PuH3 is of semiconducting behavior. For PuH3, we see intuitively from the band structure that the valence bands and conduction bands are well separated and a gap is opened at the Fermi level with a rather small value of about 0.26 eV. The hybridization and charge density analysis imply that there are certain covalent bonds in PuH2 system, yet for PuH3, particularly, the bonding between Pu and octahedral H atoms has prominently ionic character, showing certain insulativity. Therefore, it is predicted that the metal–insulator transition may take place from plutonium dihydride to trihydride as observed in rare-earth hydrides. On the other hand, the conductivity and resistivity of PuH2 and PuH3 are calculated using the BoltzTraP program. The results of PuH2 are very close to the values of PuH1.93 measured in an electrical experiment. We find that the conductivity decreases from a metal of PuH2 to the semiconducting region of PuH3, which confirms that the metal–insulator transition indeed exists in the plutonium hydrides. Furthermore, the resistivity–temperature relationships of PuH2 and PuH3 are also obtained in our work; the features of the curves are very similar with that of plutonium dihydrides measured by Willis et al. in the electrical experiment. Acknowledgements This work was supported by the National Nature Science Foundation of China (No. 20971114). We are grateful to Shi Peng and Cai Tuo for helpful comments and discussion. References [1] K.T. Moore, G. van der Laan, Rev. Mod. Phys. 81 (2009) 235–298. [2] I.D. Prodan, G.E. Scuseria, J.A. Sordo, K.N. Kudin, R.L. Martin, J. Chem. Phys. 123 (2005) 014703. [3] I.D. Prodan, G.E. Scuseria, R.L. Martin, Phys. Rev. B 73 (2006) 045104. [4] I.D. Prodan, G.E. Scuseria, R.L. Martin, Phys. Rev. B 76 (2007) 033101. [5] B. Sun, P. Zhang, X.-G. Zhao, J. Chem. Phys. 128 (2008) 084705. [6] G. Jomard, B. Amadon, F. Bottin, M. Torrent, Phys. Rev. B 78 (2008) 075125. [7] G.L. Stifter, M.H. Curtis, The preparation of plutonium powder by a hydriding process: initial studies, US Atomic Energy Commission, March 1960, Rep., HW64289. [8] For an overview of plutonium hydride J.M. Haschke, R.G. Haire, in: D.C. Hoffman (Ed.), Handbook on the Advances in Plutonium Chemistry 1967– 2000, American Nuclear Society, La Grange Park, Illinois USA, 2002, pp. 215– 220 (Chapter 9). [9] J.N. Huiberts, R. Griessen, J.H. Rector, R.J. Wijngaarden, J.P. Dekker, D.G. de Groot, N.J. Koeman, Nature (London) 380 (1996) 231. [10] R.N.R. Mulford, G.E. Sturdy, J. Am. Chem. Soc. 77 (1955) 3449; R.N.R. Mulford, G.E. Sturdy, J. Am. Chem. Soc. 78 (1956) 3897. [11] G. Cinader, D. Zamir, Z. Hadari, Phys. Rev. B 14 (1976) 912–919. [12] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864; W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [13] J.P. Dekker, J. van Ek, A. Lodder, J.N. Huiberts, J. Phys.: Condens. Matter 5 (1993) 4805. [14] Y. Wang, M.Y. Chou, Phys. Rev. Lett. 71 (1993) 1226. [15] M. Butterfield, T. Durakiewicz, E. Guziewicz, J. Joyce, A. Arko, K. Graham, D. Moore, L. Morales, Surf. Sci. 571 (2004) 74. [16] M.T. Butterfield, T. Durakiewicz, I.D. Prodan, G.E. Scuseria, E. Guziewicz, J.A. Sordo, K.N. Kudin, R.L. Martin, J.J. Joyce, A.J. Arko, K.S. Graham, D.P. Moore, L.A. Morales, Surf. Sci. 600 (2006) 1637. [17] T. Gouder, A. Seibert, L. Havela, J. Rebizant, Surf. Sci. 601 (2007) L77. [18] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [19] V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, J. Phys.: Condens. Matter 9 (1997) 767; For a review V.I. Anisimov (Ed.), Strong Coulomb Correlations in Electronic Structure Calculations: Beyond the Local Density Approximation, Gordon and Breach Science Publishers, Amsterdam, 2000. [20] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. _ [21] M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 49 (1994) 14211. [22] S.Y. Savrasov, G. Kotliar, Phys. Rev. Lett. 84 (2000) 3670. [23] J. Bouchet, B. Siberchicot, F. Jollet, A. Pasturel, J. Phys.: Condens. Matter 12 (2000) 1723. [24] A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin, V.I. Anisimov, Phys. Rev. B 72 (2005) 024458. [25] A. Shick, V. Drchal, L. Havela, Europhys. Lett. 69 (2005) 588. [26] A. Shick, L. Havela, J. Kolorenc, V. Drchal, T. Gouder, P.M. Oppeneer, Phys. Rev. B 73 (2006) 104415.
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