Article pubs.acs.org/IC
Prediction of Host−Guest Na−Fe Intermetallics at High Pressures Yuanyuan Zhou,† Hui Wang,*,† Chunye Zhu,† Hanyu Liu,† John S. Tse,*,†,‡ and Yanming Ma*,† †
State Laboratory for Superhard Materials, Jilin University, Changchun 130012, Jilin, China Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2
‡
S Supporting Information *
ABSTRACT: High pressure can fundamentally alter the electronic structure of elemental metals, leading to the unexpected formation of intermetallics with unusual structural features. In the present study, the phase stabilities and structural changes of Na−Fe intermetallics under pressure were studied using unbiased structure searching methods, combined with density functional theory calculations. Two intermetallics with stoichiometries Na3Fe and Na4Fe are found to be thermodynamically stable at pressures above 120 and 155 GPa, respectively. An interesting structural feature is that both have form a host−guest-like structure with Na sublattices constructed from small and large polygons similar to the host framework of the self-hosting incommensurate phases observed in Group I and II elements. Apart from the one-dimensional (1D) Fe chains running through the large channels, more interestingly, electrides are found to localize in the small channels between the layers. Electron topological analysis shows secondary bonding interactions between the Fe atoms and the interstitial electrides help to stabilize these structures.
1. INTRODUCTION One of the most exciting discoveries in the studies of highpressure elemental solids is the determination of many unusual open-structure, incommensurate, modulated, and incommensurate−modulated structures.1 These observations challenge the conventional textbook descriptions of a few dense packed structures and allude to the fact that the electronic structures of the elements are dramatically modified by pressure. Recent experimental and theoretical studies on sodium at high pressure have discovered many unusual phase transitions2−4 and complex structures.5 Perhaps one of the most complex modifications is the incommensurate host−guest tI19* structure.5 This structure shares the same 16-atom tetragonal host framework observed in incommensurate K(III)6 and Rb(IV),7,8 but is slightly different from the incommensurate Ba(IV)9 and Sr(V)10 that shares a 8-atom host framework. Experiments, as well as first-principles calculations, on Group I and II elements have shown that electron can transfer from the s-band to the d-band with compression,8,11−13 and this is believed to be the driving force for destabilizing the complex host−guest structure of elemental solids.7,14 It is interesting to note that the pressure-driven s → d transition makes Group I and II elements more like transition metals, hence increasing their tendency to alloy with other transition metals. Experiments have already shown that pressure can induce the alloying of K with Fe at high temperature.15 Fe is the most abundant transition metal on Earth; it is found in all parts of the planet, comprising ∼5% of the Earth’s crust but making up perhaps as much as 80% of the planet’s core. Besides Fe, the Earth’s core is also thought to contain a small amount of light elements.16 Therefore, it is of © XXXX American Chemical Society
great interest to study the alloys of Fe and light elements (e.g., Si, S, and H)17−21 under compression, which might not only provide mineralogical constraints on the composition of Earth’s core but also enrich the structural complexity of alloys at high pressure. Sodium, which is a lighter element than iron, is the sixth most abundant elements in the Earth’s crust (after oxygen, silicon, aluminum, iron, and calcium), and might be a candidate core light element. In this work, we systematically investigated the phase stabilities of stoichiometric Na−Fe alloys with different Na contents under various pressures ranging from 100 GPa to 360 GPa. We found that only Na-rich Na−Fe alloys can be stable at the studied pressures. The two stable alloys predicted at pressures above 120 and 155 GPa are Na3Fe and Na4Fe, respectively. An unusual structural feature of the two alloys is that Na could form two-dimensional (2D) and three-dimensional (3D) structures constructed by small and large polygons similar to that of the incommensurate phase of Group I and II elements.5 Moreover, except for the 1D Fe chains running through the large channels, 1D electride chains are embedded in the small channels. Electron topological analysis shows secondary bonding interactions between the Fe atoms and the interstitial charges help to stabilize the structure.
2. METHODS We have performed structure searches using the CALYPSO method22−24 for the Na−Fe system with different stoichiometries under pressures of 100−360 GPa with simulation cells consisted of 2− Received: April 12, 2016
A
DOI: 10.1021/acs.inorgchem.6b00881 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry 4 formula units. The CALYPSO method has been benchmarked on various known systems, ranging from elements to binary and ternary compounds.2,25−30 The underlying structural relaxations were performed using density functional theory (DFT) within the Perdew−Burke−Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA),31 as implemented in the Vienna ab initio simulation package (VASP) code.32 The all-electron projectoraugmented wave (PAW) method was adopted with the PAW potentials, where 3s23p63d64s2 and 2s23p63s1 are treated as valence electrons for Fe and Na atoms, respectively. For the lowest enthalpies structure, additional calculations were made with an energy cutoff of 1200 eV, with dense Monkhorst−Pack k-meshes, to ensure that all of the enthalpy calculations were well-converged to better than 1 meV/ atom. The QTREE integration algorithm33 implemented in the CRITIC2 program34,35 is adopted to calculate the electron population of basins associated with electrides. Phonon calculations were calculated with the supercell approach, as implemented in the PHONOPY code.36
3. RESULTS AND DISCUSSIONS The phase stabilities of the Na−Fe systems are investigated by calculating the enthalpy of formation (hf) at 100, 150, and 360 GPa. The hf value of NayFe1−y (0 < y < 1) compounds, with respect to the decomposition to elemental Na and Fe, is given by the following expression: Figure 1. Stability of new Na−Fe compounds: (a) convex hull diagram for the Na−Fe system at selected pressures (at a given pressure, the compounds located on the convex hull are thermodynamically stable), and (b) pressure−composition phase diagram of the Na−Fe system. Thick solid lines represent thermodynamically stable phases, and dashed lines represent metastable phases.
hf (Na yFe1 − y) = h(Na yFe1 − y) − yh(Na) − (1 − y)h(Fe) (1)
where h(NayFe1−y) is the enthalpy of the compound, h(Na) the enthalpy of elemental Na, and h(Fe) is the enthalpy of elemental Fe. The cI16 at 90−152 GPa, tI19 at 152−260 GPa and hP4 above 260 GPa structures of Na are used at the corresponding stable pressure ranges.2,4 For Fe, the hexagonal close packing (hcp) structure is adopted throughout the explored pressures. The phase stabilities of a variety of NayFe1−y (y = 0.20, 0.25, 0.33, 0.40, 0.50, 0.60, 0.67, 0.75, and 0.80) compounds are evaluated using their enthalpies of formation, relative to the products of dissociation into constituent elements at 100, 150, and 360 GPa. The enthalpy− stoichiometry (convex hull) plots in Figure 1a indicate the following: The stable structures of Na3Fe and Na4Fe start to emerge at ∼150 and 360 GPa, respectively. Note that, at every pressure point studied, Na3Fe is the most stable stoichiometry. Figure 1b shows that, in principle, Na3Fe may be synthesized above 120 GPa. Na4Fe is stable, with respect to Na3Fe and Na, at pressures of >155 GPa. The thermodynamically stable Na3Fe at 150 GPa has a crystal structure with P4/mbm symmetry (Figure 2a). The planar arrangement consists of Na forming edge-shared squares and heptagonal rings stacking in a ···AAA··· pattern along the cdirection. The Fe atoms are sandwiched between Na layers parallel to the ab-plane and form one-dimensional linear chains along the c-axis through the center of the seven-membered rings. Crystals that have a planar heptagonal structure are rare and have not been predicted or observed in any high-pressure compounds. The complex structure arises from the Na3 unit composed of two inequivalent Na atoms, Na1 and Na2 (Figure 2b). The Na1−Na1 distance is 2.08 Å, slightly longer than the Na1−Na2 bond length of 1.98 Å and ∠Na1−Na1−Na2 = 128° (Figure 2b). The fused four- and seven- membered ring structure is constructed as follows. Two Na1−Na1 bonds are linked to form a square. The Na2 atoms of the two building units are then bonded respectively to Na1 of different Na3 units. This process is then repeated to form a 2D net of the ab-
plane. This structure type, although uncommon, is not without precedent. Equivalent structures have been reported in rareearth borocarbide compounds (MB2C, where M = Y, Dy, and Th).37−39 The 2D net of these compounds is made of four- and seven-membered fused rings constructed from B and C atoms. The rare-earth atoms are arranged in a plane between the layers and are aligned in a line along the channels formed by the seven-membered rings. Our results predict this YB2C-type structure for the first time in a high-pressure intermetallic compound. The open P4/mbm structure also shares similarities to the high-pressure self-clathrate crystal structures of Group II Rb-III and Ba-IV. The difference is that the Group II element has a host structure formed from the stacking of 2D planes composed of fused squares and octagons with guest Rb or Ba atoms forming 1D chains running through the centers of the octagons but incommensurate with the host lattice. The 3D ELF contour surface for Na3Fe is shown in Figure 3b. Electrons are found to localize in the channels of the square polygons and between adjacent Na 2D layers. As shown in the contour map of the Laplacian of the electron density in Figure 4a, the solid contour line corresponding to the negative Laplacian value (∇2ρ) is clearly visible in the square formed by four Fe atoms. A negative Laplacian reveals that the potential energy is in local excess, indicative of a non-nuclear maximum (NNM) (attractor).40 The gradient of the electron density plotted in the [002] (included the Fe and localized electrons), [001] (consisted of Na atoms in the plane), and [100] planes cutting through a quasi-1D Fe chain are shown in Figures 4b, 4c, and 4d, respectively. The Na in the plane forms bond paths that are connected to the nearest neighbors. Furthermore, Figure 4b illustrates an important role of the electrides as bond paths were found radiating from the interstitial electrons and B
DOI: 10.1021/acs.inorgchem.6b00881 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 2. Schematic depiction of (a) the P4/mbm structure of Na3Fe at 150 GPa, (b) the Na layer (Na1 and Na2 are yellow and blue atoms, respectively), and (c) the Na3 unit.
the 3d orbitals, forming linear nanowires, and became slightly ferromagnetic (0.34 μB/Fe) in a spin-polarized calculation. The weak ferromagnetism is the result of partial electron transfer to the host lattice and small effective exchange energy for switching from antiparallel to parallel spin compare to the axial crystal field of the 1D chain, favoring a low spin arrangement. This observation seems not conform to the Lieb− Mattis theorem,41 which states that spontaneous spin polarization is forbidden in one dimension. However, it has also been shown42 that, in the case of sufficiently strong interactions between electrons, deviations can occur and give rise to a ferromagnetic ground state. To confirm the stability of the ferromagnetic state, additional calculations were performed using a structure model built from two unit cells replicated in the c-axis with the initial spins on the first four Fe atoms arranged in parallel (ferromagnetic) and the other four Fe atoms arranged in antiparallel (antiferromagnetic) directions. The antiferromagnetic initial spin state was found to collapse to the metallic solution but the ferromagnetic state remained stable.
Figure 3. (a) Schematic depiction of the calculated spin density (isosurface = 0.045) and (b) ELF (isosurface = 0.7) for Na3Fe.
connected to the four surrounding Fe atoms. Therefore, instead of simply being a concentration of negative charges and ionic interactions with the positive framework, the interstitial charges act as intermediaries and help to promote “bonding” between distant Fe atoms. The Fe in the linear chains in the [010] plane are found to bond with the neighbors along the heptagonal channels but not to the nearest Na atoms. Thus, the Fe atoms bonded through
Figure 4. (a) Laplacian of the electron density in a layer parallel to the Na planes through the Fe atoms and containing the electride (solid contours denote negative values for ∇2ρ). The gradient of the electron density is depicted in panel (b), showing a layer parallel to the Na planes but through the Fe atoms and containing the electride; panel (c) shows the [001] plane containing the Na atoms in a 2D layer, and panel (d) shows a layer through the Fe atoms along the c-axis. C
DOI: 10.1021/acs.inorgchem.6b00881 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 5. Na3Fe at 360 GPa. (a), Fddd structure of Na3Fe at 360 GPa view along the bc-plane. (b) Fddd structure of Na3Fe at 360 GPa view along the bc-plane. (c) Fddd structure of Na3Fe at 360 GPa view along the b-axis. (d) A chemical bonding pattern of Na slab (the top-layer Na atoms are gray, the middle-layer Na atoms are orange, and the bottom-layer Na atoms are green). In panel (e), the orange spheres indicate Na atoms in the middle layer, and the dotted lines connect the longer Na···Na contact of the top layer (see text). For the sake of clarity, this long contact is not shown for the bottom-layer Na atoms, which is anti-parallel to the top layer, shown in panel (f), where the Na atoms of the top and bottom layers are bonded to the Na dimers (middle layer), from a−b perspectives.
Figure 6. Na4Fe at 360 GPa: (a) C2/c structure of Na4Fe along the c-axis; (b) C2/c structure of Na4Fe along the b-axis; (c) C2/c structure of Na4Fe along the a-axis; (d) the guest-component unit cell; (e) the packing pattern of Na atoms in the bc-plane; and (f) the packing pattern of Na atoms in the ac-plane.
The channels observed in the P4/mbm structure are fully developed in the orthorhombic Fddd structure at 360 GPa. The Na atoms form an open framework with two types of channels, in different orientation, in which puckered chains of Fe atoms are occupied. A perspective view down the 1/2(b + c)-axis is
depicted in Figure 3a, showing that the two Fe chains are orthogonal to each other but the local environment of the iron chains are identical (see Figures 5a and 5b). The Fe−Fe distances are all equal to 1.93 Å and is shorter than that at 150 GPa, while ∠Fe−Fe−Fe = 157.3°. The structure of the Na D
DOI: 10.1021/acs.inorgchem.6b00881 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 7. (a) Electronic band structure of Na4Fe at 360 GPa. The sizes of the circles represent the relative contributions from different atomic orbitals. (b) Projected densities of states (DOSs) of Na4Fe. The vertical dashed line indicates the Fermi energy.
host framework with c/a = 0.562. In comparison, the a- and baxes of the monoclinic structure of Na4Fe are similar and the ratio of c/[(a + b)/2] is 0.597. In addition, the Fe atoms form a sublattice with lattice parameters aguest = bguest = 4.687 Å, cguest = 3.864 Å, αguest = 88.8°, βguest = γguest = 91.6° (see Figure 6d). Unlike Ba-IV and tI19 Na, the guest Fe sublattice of Na4Fe is commensurate with the overall unit cell. Another difference between the structures lies in the stacking. The Ba-IV structure is constructed from the stacking of identical 2D layers of Ba atoms packed in the 32.4.3.4 Archimedean tiling pattern along the c-axis; a packing pattern is not observed in Na4Fe. The side view of Na4Fe (Figure 6b) reveals that its 3D structure is constructed from corrugated slabs of Na atoms in the abdirection that are linked along the b-axis, forming the open channels. An isolated Na slab in the bc-plane is shown in Figure 6e. The Na−Na distances range from 1.81 Å to 2.08 Å. Connecting the Na atoms within a nearest neighbor distance of
