Strain Stabilization of Superionicity in Copper and Lithium Selenides

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Strain Stabilization of Superionicity in Copper and Lithium Selenides Daniel Dumett Torres, and Prashant K. Jain J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00236 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 20, 2018

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The Journal of Physical Chemistry Letters

Strain Stabilization of Superionicity in Copper and Lithium Selenides Daniel Dumett Torres1 and Prashant K. Jain1,2,* 1

Department of Chemistry, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States

2

Materials Research Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States *Corresponding Author: E-mail: [email protected].

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Abstract

Superionic (SI) phases have utility as solid electrolytes for next generation battery technology, but these phases are typically not stable at room temperature. Our density functional theory calculations demonstrate that compressive lattice strain can stabilize SI phases of Cu2Se and Li2Se, two potential solid electrolytes. Electronic and bonding insights into this effect are obtained. In the ordered, non-SI phase, cations are localized primarily in tetrahedral (T) interstices with little access to the higher-energy octahedral (O) sites. But 1-2 % compressive strain promotes attractive stabilization of the O cations with six-fold coordination to Se anions, at the expense of the stability of four-fold-coordinated T cations. In such compressed lattices, cations can access both T and O sites, resulting in a cationdisordered, SI phase. Thus, lattice strain is demonstrated as a handle for controlling ionic structure and transport and accomplishing ambient temperature superionicity.

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Keywords: solid electrolyte • ionics • nanocrystal • transport • electronic structure theory

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We present an electronic structure study of superionic (SI) materials, a class of ionic solids with peculiar characteristics.1,2 SI materials possess a rigid anionic sub-lattice, which imparts them with the mechanical properties of common solids. On the other hand, the cations form a mobile, “liquid-like” sub-lattice.3–5 In fact, the cations have the ability to diffuse through the crystal at speeds typical of transport through a liquid. The resultant fast-ion transport of SI solids makes them prime candidates for solid-state electrolytes in next generation Li+ or Na+ battery technologies.6,7 Batteries comprised of a solid-state electrolyte offer increased safety, enhanced lifetime, higher potential capacity, and greater ease of battery miniaturization over current designs, which involve flammable, corrosive, leak-prone liquid electrolytes.8 Cu2Se, which is a classic example of a SI conductor, and also one that is earth abundant, is the model system we study. Our findings are also extended to a Li-homolog. In these SI solids, the Se anions are fixed in a nearly face-centered cubic (fcc) crystalline arrangement,9 whereas the smaller cations form the conductive network. One obstacle limiting the implementation of SI conductors is that they are often stable only as hightemperature phases. For example, the SI form (α-phase) of bulk Cu2Se is stable above a Tc of ~400 K.10 At room temperature, Cu2Se has a fully-ordered phase, called the low-temperature β-phase, wherein the Cu cations are constrained to their most stable sites and the cation mobility is rather low.11–13 Recent findings in our group14 showed that ~2 nm diameter Cu2Se nanocrystals are SI at room temperature, quite unlike bulk Cu2Se. This led us to hypothesize that compressive strain present within such nanocrystals stabilizes the SI phase over the ordered phase. Here, we use density functional theory (DFT) to examine such a strain-mediated effect and understand its electronic origin. The larger goal is to develop fundamental understanding of the structure and bonding within a SI solid. Our calculations show that, in both Cu2Se and Li2Se, compressive strain promotes cation-filling of otherwise high-energy octahedrally-co-ordinated sites. Such strain-induced distribution of cations over tetrahedral (T) and 3 ACS Paragon Plus Environment


octahedral (O) sites is responsible for lower temperature-stabilization of a SI phase. Our work informs how strain and/or crystal structure may be used as handles for tuning SI phases and properties to those desirable for technological use of these promising materials.

Figure 1. Structural models for AF and SI Cu2Se. a) AF Cu2Se unit cell and projected lattice shown along b) the [111] and c) [001] directions. Cu cations are restricted to T sites and do not occupy other interstitial sites. d) SI Cu2Se unit cell with projections shown along the e) [111] and f) [001] directions, where both T and O sites are occupied by Cu cations, shown in orange and blue respectively. Se anions are shown in yellow. Structures were visualized using the VESTA15 and XCrysden16 programs.

We studied how compressive strain influences the structure and energetics of Cu2Se lattices comprised of Cu cations arranged within an fcc cage of Se anions (which closely approximates the structure of Cu2Se).9 A range of cation arrangements were examined. On one end of this range is the antifluorite (AF) form of Cu2Se.17,18 In the AF structure, all Cu cations are localized in T sites, which form highly stable holes within the fcc anionic cage (Fig. 1a-c), forming a ordered cation sub-lattice 4 ACS Paragon Plus Environment

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(Fig. 1b,c). Although Cu vacancy ordering and resulting crystallographic distortion, characteristic of βCu2Se11–13 are difficult to include, our model AF cell captures the essential crystallography of the lowtemperature phase.14 On the other end of the range lies the SI form of Cu2Se, which we model by an arrangement of Cu cations distributed equally over T and O sites (Fig. 1d). Our structural model is based on crystallographic studies of SI Cu2Se nanocrystals, where significant occupation of the O sites was found alongside the partial filling of the canonical T sites.14 Early studies of bulk α-Cu2Se also report O site occupancy in the SI phase, placing up to half of all Cu cations in the O sites, amounting to saturation of the four O sites available per unit cell.19,20 Furthermore, cation occupation of the O interstitials is a steady-state signature of the kinetic disorder and ion mobility of the SI phase: O sites are halfway points in tetrahedral-octahedral-tetrahedral (TOT) cation migration pathways.8 The access of Cu cations to both T and O interstitial sites forms a more diffuse network of cations spread across the Cu2Se lattice (as seen in Fig. 1e, f), which can be contrasted with the ordered arrangement of alternating cation and anion layers of the AF cell (Fig. 1b, c).

Figure 2. Compressively strained lattices of Cu2Se: a) Total energy as a function of compressive strain for unit cells of varying extents of O site occupation. As O site occupation increases from 0 (8T) to saturation (4T4O), the energetic minimum shifts in favour of compressively strained lattices. b) Plot of the effective lattice constant (for the lowest-energy structure from a variable-cell relaxation) versus the O/T ratio. The resulting strain in the fully relaxed cell relative to the experimental lattice constant of bulk Cu2Se is shown on the right-hand axis.



In addition to the AF and SI structures, we also investigated cation arrangements spanning these two extremes. In other words, the ratio of occupied O sites to occupied T sites was varied from 0 to 1. O/T = 0 corresponds to the AF cell and O/T = 1 corresponds to the SI cell in which all O sites are saturated. The total energy of all these cells is plotted in Fig. 2a as a function of applied strain (see ‘Model structures and relaxations’ section in Calculation Methods). The AF cell (8T) increases in energy upon application of compressive strain. In direct contrast, the SI cell (4T4O) undergoes energy stabilization under compression and is most stable at an applied strain of -1.62 %. Such contrasting behavior of AF and SI structures is reiterated in Fig. 3a. Application of -1.6% strain stabilizes the SI structure by ~0.015 eV per Cu2Se formula unit, whereas the AF structure is destabilized by ~0.042 eV per Cu2Se formula unit. Intermediate cation arrangements show that the response to applied strain (Fig. 2a) varies systematically with increasing O occupation. Compressive strain is destabilizing for arrangements with small or no O occupation. On the other hand, 5T3O and 4T4O cells, in which O sites approach or reach saturation, become stable under the application of a small degree of compression. In general, our electronic structure calculations indicate that cationic occupation of O sites in Cu2Se is closely correlated with a compressively strained lattice. In fact, this effect is directly demonstrated in the lattice constants determined from the most-stable (fully relaxed) cell structure at each cation occupation ranging from O/T = 0 to 1 (Fig. 2b). As O site occupancy increases, the lattice constant decreases. The SI structure is found to prefer a lattice compressed by ca. 2 % relative to bulk AF Cu2Se. It is worth noting that this strain is similar in magnitude to that in ca. 2 nm diameter Cu2Se nanocrystals, which exhibit a stable SI phase at ambient temperature.14


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Figure 3. Electronic effect of strain: With increasing compressive strain: a) Total energy of the SI cell decreases, whereas that of the AF cell increases. b) Se site energies decrease in both structures c) T Cu sites are stabilized in the AF structure whereas they are destabilized in the SI structure, and d) O Cu site energies decrease in the SI structure. The AF structure has no O Cu, so there is no plot for the AF structure in d). Total energies are presented on a per-Cu8Se4-super cell basis, whereas site energies are presented on a per-atom basis. e) The application of compressive strain induces the Cu to transition from T-coordinated sites to O-coordinated sites. 7 ACS Paragon Plus Environment


Thus, cell energy and lattice constant calculations indicate that compressive strain has a favourable effect on O site occupancy in Cu2Se and possibly a destabilizing effect on T site occupancy. To elucidate the origin of this strain effect, we separately determined energies of occupied Se, Cu T, and Cu O sites (Fig. 3) and analysed their response to applied strain. For both AF and SI structures, the average Se site energy decreases with increasing compressive strain (Fig. 3b). This trend is understood as follows: lattice compression brings Se anions and Cu cations closer in distance, which increases SeCu attractive interaction and stabilizes Se anions. The Se stabilization is greater for the SI cell as compared to the AF cell, which is explained by the difference in the Se-Cu coordination. In the AF structure where all Cu cations are in T sites, there is four-fold co-ordination between all Se-Cu pairs. On the other hand, for the SI structure, Se has four-fold coordination with T Cu cations and six-fold coordination with O Cu. The higher effective co-ordination in the SI structure accounts for the marginally larger attractive stabilization of Se upon lattice compression. The T Cu cations of the AF structure become energetically more stable, on average, with increasing compressive strain (Fig. 3c). This effect is the result of the increased Cu-Se attraction as the lattice is compressed. In contrast, the T Cu of the SI cell undergo destabilization past an applied strain of -0.6% strain. The source of this destabilization is Cu(O)-Cu(T) repulsion, which is strongest between O-T pairs, which are close in distance. The increase in this repulsive interaction appears to more than offset the increase in the Cu-Se attraction resulting from lattice compression. The AF cell, where O sites are unfilled does not experience such a strengthening of Cu(O)-Cu(T) repulsive interactions and therefore, does not exhibit destabilization of T Cu upon compression. However, Cu(T)-Cu(T) repulsion, which is prevalent in the AF structure, is weaker between T-T pairs and is readily offset by the increased Se-Cu attraction in compressed lattices. Fig. 3d shows the average O Cu site energy of the SI cell, which undergoes dramatic stabilization, with increasing compressive strain. The O Cu of the SI cell exhibits the greatest extent of compressive


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strain stabilization of any species in both AF and SI cells. The six-fold coordination between O Cu and Se is responsible for the large attractive stabilization of O Cu observed upon lattice compression.

Figure 4. Plot of the effective lattice constant (for the lowest-energy structure from a variable-cell relaxation) versus the O/T ratio. The resulting strain in the fully relaxed cell relative to the experimental lattice constant of bulk Li2Se is shown on the right-hand axis. Inset shows the model for AF Li2Se.

This structural insight obtained from Cu2Se also applies to Li2Se, a closely related solid with utility for solid-state Li+ conduction. Just as for Cu2Se, Li2Se is known to exhibit an fcc arrangement of Se anions and an AF structure.21,22 We investigated the effect of compressive strain on various Li+ arrangements in Li2Se, ranging from an AF structure (O/T = 0) to an SI idealization (O/T = 1). Similar to Cu2Se, we find that higher O site occupancy is directly correlated with a compressed lattice (Fig. 4), which may suggest that the co-ordination principles discussed above may be of general significance. Our current study is limited to Cu2Se and Li2Se because they both possess an anti-fluorite crystal structure comprised of a small monovalent cation co-ordinated with a larger divalent anion. Future studies may determine whether the effect of strain holds more generally in ionic solids with compositions and/or crystal structures different from the ones studied here. In summary, under small degrees of compressive strain, O sites, which otherwise form high-energy bottlenecks in cation networks of Cu2Se and Li2Se, become more energy-equivalent to T sites.23 The resulting access of the cations to a larger set of interstitial sites results in a diffuse cationic sub-lattice, 9 ACS Paragon Plus Environment


the hallmark of SI behavior. Our results confirm that compressive strain, rather than other nanoscale size effects, such as quantum confinement-induced changes in the electronic structure or energetic influence of surface ligands and/or surface faceting, is at the origin of the observed room-temperature stabilization of the SI phase in nanocrystals.14 The insights provided here motivate the use of compressive strain for accessing SI phases at lower temperatures. Aside from nano-sizing,24–26 roomtemperature SI behavior may be accomplished in the bulk forms of Cu2Se or other similar solids by application of lattice strain through epitaxial methods,27 heterostructuring,28 applied potential,29 or photoexcitation.30 The prediction of strain-induced SI behavior of Li2Se merits experimental testing, so does the generality of our findings to other chalcogenides such as Cu2S.31–33 In addition to the equilibrium stability of the SI phase, it would be valuable to investigate the influence of strain on the activation energy barrier for cation hopping, which is likely to dictate the magnitude of ion conductance in the SI phase. Computational approaches such as the nudged elastic band method and molecular dynamics would allow the estimation of hopping barriers and ion conductance. Strain-mediated tuning of ionic structure, energetics, and transport in solid-state electrolytes can be a rich area of exploration.

Calculation Methods Electronic structure method: DFT calculations were performed with a plane-wave basis and periodic boundary conditions, as implemented in the Quantum Espresso software suite.34 The Perdew-BurkeErnzerhof (PBE) functional was used for all calculations. A kinetic energy cut-off of 200 Ry. was used in conjunction with a 6 x 6 x 6 automatically generated Monkhorst-Pack k-point grid, determined to be appropriate parameters as per our convergence testing (Table S1). A smearing of 0.019 Ry. (0.026 eV) was used for the electronic occupations. This choice was rationalized by the finding that Cu2Se is calculated to have no band gap, when using the PBE functional.17 In our experience, the lack of


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smearing for the electronic occupations can produce non-convergence of the charge density in the intermediate steps of a structural relaxation.

Model structures and relaxations: Bulk Cu2Se and Li2Se were modeled by a periodically repeating lattice of Cu8Se4 and Li8Se4 unit cells. Se anions occupied ideal sites of a face-centred cubic (fcc) lattice. The 8 cations were placed in a combination of 8 T and 4 O sites. Each combination is defined by the ratio of occupied O sites to occupied T sites (O/T), which ranges from 0 to 1. These ideal cells were subject to a compressive strain (i.e., applied strain) by reducing the lattice constant relative to the known experimental lattice constant of the bulk solid. The experimental lattice constant is reported to be 5.84 Å17–19 for Cu2Se and 6.017 Å21,35 for Li2Se. Compressive strain is indicated by a -ve sign. In each case, the initial cell geometry was subject to energy relaxation using the parameters described in the previous section. Full relaxation of each cell was accomplished in two steps: i) the Cu cation positions were allowed to relax but the Se positions were fixed. For some geometries, this constraint was necessary for preventing the cell reverting to the AF structure. ii) The resulting Cu positions were constrained and Se anion positions were allowed to relax. In this manner, relaxed cell geometries were obtained at different applied strain values. Relaxed geometries are plotted using XCrysden16 in Fig. S1 and total cell energies are listed in Table S2. For each O/T ratio, a variable-cell relaxation was performed to obtain the fully relaxed lattice constant (Figs. 2b and 4). For this relaxation, the input geometry and lattice constant corresponded to those of the strained cell with the lowest energy. For some of the Cu2Se and Li2Se cells (6T2O, in particular, and 5T3O, to some extent), the variable-cell relaxation produced a cell with tetragonal distortion. Therefore, we report in Figs. 2b, 4, and S1 an effective lattice constant, which is the cube root of the volume of the fully relaxed cell. The resulting strain in the fully relaxed cell was determined from the % difference between its effective lattice constant and the bulk experimental lattice constant.

Calculation of site energies: The site energy for the ith occupied site is given by a sum of two terms: 11 ACS Paragon Plus Environment


, = + This is a consequence of the pseudopotential method employed in our calculations. Only valence electrons are treated with DFT. Core electrons and their electronic interactions are calculated via the Ewald method, resulting in the Ewald energy term. The Ewald site energy for species Xi is calculated as the difference in Ewald energy between the complete Cu8Se4 unit cell and the same cell (without relaxation) missing species Xi.

= − − The valence term is calculated from the calculated projected density of states (PDOS) for species Xi as: !"

= ∗ #$

which is an integral over orbital energies from -∞ to the Fermi energy, EF. Output orbital energies are referenced to the average sum of the pseudopotential plus Hartree potential (Vbare + VHartree) in the cell. This VH reference potential is cell-specific. So, to be able to compare site energies across cells we use the Quantum Espresso codes pp.x and average.x to obtain the average value of the Vbare + VHartree potential in the cell. This average VH potential added to all the orbital energies to undo the arbitrary referencing. Although site energies calculated in this way do not correspond to an experimentally measurable physical quantity, they allow comparison across different cation arrangements. Furthermore, the sum of site energies does not yield the total cell energy. Summing all the Ewald terms would result in double-counting of all electrostatic interactions treated with the Ewald method in the cell. Furthermore, DFT Kohn-Sham orbital energies cannot be summed in this manner.36 For each type of site (Se, T Cu, and O Cu), the calculated site energy was averaged over all occupied sites of that type. These average site energies are tabulated in Tables S3-S5 and plotted in Fig. 3b-d.


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Supporting information.

Visuals of relaxed cell geometries that contribute to the main text figures;

convergence tests; and Se, T Cu, and O Cu site energies that expand on the data presented in Fig. 3b-3d.

Notes The authors declare no competing financial interest.

Acknowledgments This project was supported by the Energy Biosciences Institute with funds from Shell. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) research allocation.37 We thank Sudhakar Pamidighantam for his help and Seagrid for computational resources and services.38,39 D. D. performed computational studies and analysis and wrote manuscript. P. K. J. conceived project, performed analyses, and wrote manuscript.

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