Unconventional Long-Range Cation Ordering in Copper Selenide

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Unconventional Long-Range Cation Ordering in Copper Selenide Nanocrystals Jaeyoung Heo, Daniel Dumett Torres, and Prashant K. Jain Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04053 • Publication Date (Web): 20 Dec 2018 Downloaded from http://pubs.acs.org on December 22, 2018

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Chemistry of Materials

Unconventional Long-Range Cation Ordering in Copper Selenide Nanocrystals Jaeyoung Heo1, Daniel Dumett Torres2, and Prashant K. Jain*2,3,4,5 1Department

of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 3Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 4Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 5Beckman Advanced Institute of Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 2Department

ture of bulk Cu2-xSe has been extensively studied,7,16,17 we find from high-resolution electron microscopy (HRTEM) of Cu2-xSe NCs, a Cu+ super-lattice with an unusually long-range 14-Å periodicity that is not known in the bulk solid. Density functional theory (DFT) indicates that this unconventional cation arrangement is metastable; but may become favored in the presence of a Cu-deficient composition and/or a nanoscale morphology. Our results suggest that previously unknown forms of metastable long-range order may be found in NCs.

ABSTRACT: Long-range order imparts both complexity and

diversity to crystalline solid materials, resulting in novel crystal phases and new physical properties. We report the finding of an unconventional long-range ordering of copper ions (Cu+) in Cu2-xSe, a well-known ion conductor. High-resolution electron microscopy of Cu2-xSe nanocrystals (NCs) reveals atomic super-lattices with an unusually long period of 14 Å. This unconventional arrangement results from copper vacancy layers occurring half as frequently in some NCs as compared to bulk Cu2Se. This longer-range vacancy-order is metastable, as indicated by electronic structure computations, but can be stabilized by Cu deficiency or nanocrystalline morphology. These findings prelude that nanostructures may host as-yet undiscovered forms of atomic order. Crystalline solids are defined by the periodic arrangement of their constituent atoms, which manifest certain symmetries. Breakdown of this symmetry makes a crystal more complex but also allows new thermal, mechanical, and optoelectronic properties to be manifested.1–6 A prime example by which such a loss of symmetry can take place is by the inclusion of a structural motif, such as a defect, that repeats itself less frequently than the underlying lattice planes. A crystal with such long-range order not only represents a distinct crystallographic phase, but also provides insight into the nature of atomic co-ordination in solids and enables discoveries of emergent behavior. Here, we report an atypically long-range ordering of copper ions (Cu+) in some Cu2-xSe nanocrystals (NCs).7,8 Cu deficiencies appear to be responsible for the sustenance of this atypical ordering in these NCs. The longerrange ordering is predicted to result in a narrowing of the band-gap, with possible influences on optoelectronic characteristics and charge transport.

Cu2Se is an earth-abundant ionic conductor9 with potential applications in solid electrolytes and thermoelectric devices.10–12 The ion transport characteristics of this solid are closely linked to the structural arrangement of the Cu+.8,10,13,14 In its high-temperature phase (α-Cu2Se), the Cu+ sub-lattice is mobile, whereas in its low-temperature phase (β-Cu2Se), the Cu+ forms an ordered super-lattice.7,15–17 While the peculiar struc-

Figure 1. HRTEM images capture a new form of Cu+-vacancyordering in Cu2-xSe NCs. (A) HRTEM image of a representative NC exhibiting the conventional arrangement of Cu+ vacancies in a super-lattice with a 7-Å period, found also in bulk β-Cu2Se. (B) HRTEM image for a NC exhibiting an unconventional arrangement of Cu+ vacancies in a super-lattice with a longer 14-Å periodicity. Additional HRTEM images are provided in the SI. (C) Pie chart showing the % of NCs found to exhibit a CVO (red) or UVO (blue) arrangement or a lack of vacancy ordering (green). The full population of NCs analyzed came from multiple batches of synthesis. Inset shows a representative low-magnification image of a wide-field of multiple NCs.

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The synthesized NCs exhibited a localized surface plasmon resonance (LSPR) absorption band in the near-infrared region (Fig. S1), which results from holes arising from ionized Cu deficiencies.10,18,19 From the peak of the LSPR band, the NCs

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ngement in the lattice fringe pattern is shown in Fig. 2 (left).

were estimated to have an average composition of Cu1.83Se, i.e., x = 0.17. High-resolution micrographs of a substantial population of Cu2-xSe NCs were obtained and analyzed (Figs. 1, S2 and S3). These NCs have a spherical or parallelepiped shape (Fig. S2). Based on the lattice fringe pattern exhibited, three sub-sets of NCs were identified (Fig. 1c). One sub-set (36 %) of NCs showed lattice fringes every 3.5 Å, which corresponds to the Se2--Se2- interplanar spacing along [111]c, where the subscript refers to a cubic basis. This lattice fringe pattern signifies the lack of Cu+-vacancy-ordering,10,11 which is characteristic11 of the superionic α-Cu2Se phase with a mobile Cu+ sub-lattice.8 It is possible that electron beaminduced heating led to a phase transition of these NCs into the high-temperature α-phase. Alternatively, these NCs may be oriented along a zone-axis at which the ordered super-lattice does not appear. NCs that did not show a super-lattice were not studied further; we focused our attention on NCs that exhibited an ordered Cu+ sub-lattice.

The third sub-set of NCs (Fig. 1b and Fig. S3b) exhibited a unique lattice fringe pattern, which is distinct from that of βCu2Se. This atypical contrast pattern (Fig. 1b), which is quite striking, consists of dark fringes interspersed with wider regions of bright contrast. The dark fringes are spaced by 14 Å along [111]c, a period twice as long as that seen in β-Cu2Se. Thus, it appears that in this NC subset, a Cu+-vacancycontaining layer is located every eighth Cu+ layer, which is half as frequently as in β-Cu2Se, resulting in a super-lattice of an unusually long period of 14 Å, which we term as unconventional vacancy-ordering (UVO) in contrast to the conventional vacancy-ordering (CVO) with the shorter 7-Å periodicity.

Can a 14 Å–periodicity fringe pattern simply appear at a different orientation of the conventional β-Cu2Se lattice? This is not possible, as evidenced by the full diffraction pattern for the conventional β-Cu2Se crystal structure (Fig. 3b). There is no reflection around 14 Å, so the conventional lattice would not exhibit a 14-Å periodicity at any orientation. We find in HRTEM examples where two NCs have the same zone-axis, i.e., the same crystallographic orientation with respect to the incident electron beam; yet one shows the 7-Å periodicity pattern, whereas the other shows a 14-Å periodicity pattern (Fig. S4). Clearly, the NCs differ in their lattice structure, with the former exhibiting a CVO arrangement and the latter a UVO one. Moreover, the presence of the 14-Å periodicity reflection, diagnostic of the UVO arrangement, does not appear to be dependent on image defocus (Fig. S5). Thus, we are able to validate the uniqueness of the 14-Å periodicity super-lattice found in 7% of all the NCs studied. No NCs exhibited both types of order in co-existence.

Another sub-set (56 %) of the NCs exhibited a lattice fringe pattern typical of bulk β-Cu2Se (Fig. 1a and Fig. S3a). Bright contrast regions and dark fringes alternate along [111]c with dark fringes appearing at a period of 7 Å. This fringe pattern is an outcome of the well-known ordered arrangement of Cu+ and vacancies within the pseudo-fcc Se2- sub-lattice.8,10,20,21 βCu2Se has a structure based on anti-fluorite structure, but with a fraction of the interstitial tetrahedral sites missing Cu+,8,10,22 which are instead located in other interstitial sites. These tetrahedral vacancies arrange in a manner such that they are located in every fourth Cu+ layer along [111]c.8,10,20 Since the Cu+-Cu+ interlayer distance along [111]c is half that of the Se2-Se2- interlayer distance of 3.5 Å, the Cu+-vacancy layers are located every 4/2 x 3.5 Å = 7 Å along [111]c, which is manifested in the observed periodicity of the fringes. The βCu2Se cell geometry which exhibits this vacancy-ordered arra-

Figure 2. For a representative NC with (left) CVO and (right) UVO arrangement, the diagnostic vacancy super-lattice fringe pattern imaged in HRTEM (scale bars of 2 nm; [111]c along the horizontal) is shown in the bottom row along with the proposed geometry (Se2- in yellow; Cu+ in red; unit cells outlined by boxes) for each arrangement in the top row. The NC with CVO structure corresponds to the one shown in Fig. 1 a.

Starting from the known Se2- sub-lattice arrangement of βCu2Se, we developed a structural model (Fig. 2, top row) of the proposed UVO arrangement, where every eighth Cu+ layer is a Cu+-vacancy layer. For comparison, a structural model of the CVO arrangement where every fourth layer is a Cu+-vacancy (VCu) layer was also developed. These structural models were geometry-optimized using density functional theory (DFT) by allowing Cu+ to relax freely (Fig 3a). Diffraction patterns simulated for the Cu+-relaxed CVO and UVO geometries show good agreement with experimental patterns (Fig. 3b) obtained by averaging line profiles along [111]c of the FFT of HRTEM images of five representative NCs. Thus, the proposed geometries reflect the lattice structures captured by HRTEM. By comparison with simulated patterns (Fig. 3b), the observed diffraction peaks for the CVO lattice are accounted for: the 7-Å reflection originates from the Cu+ sub-lattice, specifically the super-lattice (VCu-VCu) spacing along [111]c. The 3.5-Å reflection corresponds to the Se2--Se2- interlayer spacing along [111]c, which the UVO structure also exhibits. The UVO structure shows a strong 14-Å diffraction peak, which the CVO structure lacks (Fig. 3b). This peak is confirmed to correspond to the Cu+ sub-lattice and is assigned to the doubled superlattice (VCu-VCu) spacing along [111]c. Second and third-order harmonics of this super-lattice reflection appear as 7-Å and 4.5-Å peaks, respectively, in both experimental and simulated diffraction patterns. A portion of the 7-Å peak intensity is also contributed by the interplanar spacing between filled Cu+ planes along [111]c.

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DFT computations (Fig. 3) show that the UVO arrangement was preserved when the Cu+ were allowed to relax but the Se2were constrained in their ideal β-Cu2Se positions. But when all


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Chemistry of Materials constraints were lifted and both Cu+ and Se2- were allowed to relax freely, the UVO arrangement (14-Å periodicity) was lost and the structure adopted the CVO arrangement (7-Å periodicity). On the other hand, the CVO arrangement is maintained, with small rearrangements, upon relaxation of the Cu+ and also in the fully-unconstrained relaxation. Thus, the CVO arrangement represents the most stable structure of β-Cu2Se. The UVO structure, calculated to have an energy higher compared to the CVO structure by 0.02 eV per Cu2Se formula unit, represents a metastable phase.

Figure 3. DFT computations suggest that UVO is metastable. (a) Two-step structural relaxation of cells with (left) CVO and (right) UVO structures. Se2- are shown in yellow, Cu+ in orange, and Cu+-vacancy layers normal to [111]c are labeled by red boxes. In the first step, the Se2- were fixed and the Cu+ were allowed to relax freely (red arrow). The resulting geometries, indicated by boxes, were used as inputs for the diffraction simulations shown in panel b. In the second relaxation step, all atoms were allowed to relax freely (green arrow). The average Se2-Se2- interplanar distance along [111]c, d(Se2-Se2-), is reported (± its range) for each cell and the total energy per Cu2Se formula unit is reported for the geometry-optimized cells. (b) Simulated diffraction patterns (black curves) and the separate contributions of the Se2- (red sticks) and Cu+ (blue stick) sub-lattices for the (left) CVO and (right) UVO structures are shown. Normalized experimental patterns (pink curves) for the two structures are shown for comparison, with vertical sticks marking key reflections from the Cu+ (blue) and Se2- (red) sub-lattices. Key peaks in each sub-lattice pattern are assigned to specific lattice planes. Second (2nd) and third (3rd)-order harmonics of the VCu-VCu reflection are also shown.

One possibility worth consideration is whether the nonequilibrium conditions of HRTEM imaging (i.e., low pressure in the column and 300 keV electron beam illumination) induce or stabilize the UVO arrangement? If the electron-beam illumination were to be responsible, then some NCs with an initially CVO arrangement would have been found to undergo a transition to the UVO arrangement under the influence of the beam. After all, the two arrangements can appear at the same zone-axis (Fig. S4). But we did not encounter any such CVO-toUVO transition. Likewise, if the low-pressure conditions in the column were responsible for stabilizing the UVO structure, then the UVO structure would have become increasingly prevalent over the course of our typical three-hour microscopy session. We did not observe such a phenomenon.

Structures that are otherwise metastable can be favored in NCs due to the perturbative effect of surface atoms present as a sizable fraction of the lattice. To investigate whether this is the case, we examined the effect of NC size and shape on the prevalence of the UVO structure (Fig. S2). Although no discernible size-dependence was found in the limited size range investigated here; the UVO structure was found to be more common in NCs with a spherical morphology than those with a parallelepiped morphology (Fig. S2), however it must be acknowledged that the population of parallelepiped morphology NCs available for study was smaller. NCs of these shapes differ in terms of their fraction of surface atoms and their specific surface energies. Surface energies have been estimated for various facets of Cu2Se yielding an average of 0.5 J/m2.23 The average surface area of the spherical NCs is ~1017 nm2 resulting in a total surface energy of ~3175 eV per NC. The average volume of the NCs is ~3052 nm3 and the volume per Cu2Se formula unit from DFT is 0.0506 nm3, resulting in an estimate of ~60318 Cu2Se formula units per NC and a total surface energy of ~0.05 eV per Cu2Se formula unit. As a comparison, the energy difference between the two types of vacancy-ordering is calculated to be only ~0.02 eV per Cu2Se formula unit (Fig. 3a). Thus, the NC surface energy is estimated to be a large-enough perturbation of the relative stabilities of CVO and UVO phases in the NCs. Energetic contributions from ligands attached to the NC surface may also contribute to stabilization of the otherwise metastable UVO structure.

Figure 4. DFT computations of sub-stoichiometric Cu15Se8 cells with CVO (left) and UVO (right) arrangements. Cell geometries shown were obtained from a structural relaxation wherein Cu+ were allowed to relax freely while Se2- where held fixed. Se2- are shown in yellow, Cu+ in orange, and Cu+vacancy layers normal to [111]c are labeled by red boxes. The calculated total energy per Cu1.875Se formula unit for each cell is indicated. The site from which the Cu was removed to achieve the sub-stoichiometry is labeled by a purple circle.

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However, the Cu-deficient stoichiometry of our NCs emerges as a prime factor in the stabilization of the UVO structure. In copper chalcogenides, including Cu2-xS and Cu2-xSe, substoichiometry is known to result in a rich diversity of crystallographic phases.18,24–27 Therefore, we investigated if the pres-



ruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: [email protected]).

ence of Cu deficiencies influences the relative energetic stabilities of the CVO and UVO arrangements. DFT computations of Cu15Se8 (sub-stoichiometric composition of Cu1.875Se) cells in CVO and UVO arrangements were performed (Fig. 4 and Fig. S6). The cells were subject to a Se2--constrained structural relaxation, which retained the respective CVO or UVO arrangements. From calculated energies of the relaxed cells, the UVO structure was found to be marginally more stable (at 0K, since no entropic contribution is included in our calculations) as compared to the CVO structure. Thus, in going from a fully stochiometric composition to a Cu-deficient one, the relative stability (ignoring changes in entropic contributions) of the UVO arrangement is predicted to be enhanced. While the average composition of our NCs is determined to be Cu1.83Se (Fig. S1), it is possible that the Cu deficiency level varies from NC to NC and that the UVO arrangement is found in the subset of NCs with substantially Cu-deficient compositions. In a nanocrystalline morphology, there may be interplay between the effect of Cu deficiency and surface energy contributions, which may determine whether the otherwise metastable UVO structure is sustained. Further, we investigated whether longer-range vacancy ordering results in a modification of the optical and electronic properties of the crystal relative to the conventional β-Cu2Se phase. Using DFT and the non-hybrid Perdew-BurkeErnzerhof (PBE) functional,28 the band structures of the UVO and CVO structures were calculated (Fig. S7). The CVO crystal is predicted to have a band-gap (Egap) of 80 meV at the Γ-point, where the valence band maximum and conduction band minimum appear. The UVO crystal has a markedly different band structure: the valence band maximum and conduction band minimum appear in the vicinity of the monoclinic X-point. Moreover, the band-gap is vanishingly small. Although the absolute values of semiconductor band gaps calculated using the non-hybrid PBE functional are known to be underestimated;29,30 a relative comparison can be made, based on which longer-range vacancy-ordering is predicted to cause narrowing of the band-gap.

AUTHOR INFORMATION Corresponding Author * email: [email protected]

Notes

The authors declare no competing financial interests.

Author Contributions

J. H. performed all experimental studies, TEM and diffraction simulations, and data-analysis and co-wrote the manuscript. D.D.T. performed DFT studies and corresponding analysis and co-wrote the manuscript. P.K.J. designed experimental and simulation studies, provided analytical methods and interpretation of results, and co-wrote the manuscript.

ACKNOWLEDGMENT

Funding to support this work was provided by the Energy & Biosciences Institute through the EBI-Shell program. This work was carried out in part at the Frederick Seitz Materials Research Lab. Calculations used the Extreme Science and Engineering Discovery Environment (XSEDE) research allocation.31 Sudhakar Pamidighantam is acknowledged for his help, and SEAGrid is acknowledged for computational resources and services.32,33 We are thankful to reviewers for suggesting that Cu deficiencies may play a central role.

REFERENCES (1) (2) (3)

In conclusion, we observed that a fraction of Cu2-xSe NCs exhibit an unusually long-range ordering of vacancies, which has not been observed for the bulk solid. HRTEM image analysis shows that in this unconventional structure, Cu+-vacancy layers are arranged in a super-lattice at twice the periodicity as that in bulk β-Cu2Se. DFT computations indicate that the unconventional ordering is metastable; however, a Cu-deficient lattice appears to favor this arrangement. Cu2Se with such longer-range vacancy-order is predicted to exhibit a markedly different band structure from that of the conventional β-Cu2Se phase. The present finding represents one example; it is possible that similar forms of long-range order await discovery on the nanoscale.

(4) (5) (6) (7) (8) (9)

ASSOCIATED CONTENT Supporting Information

Experimental and calculation methods; UV-Vis-NIR absorbance spectrum of the NC colloid; correlation of vacancy arrangement with NC size and shape; additional examples of lattice fringe images; additional DFT simulations and calculated band gap energies. The Supporting Information is available free of charge on the ACS Publications website. The UVO crystal structure has been deposited as CSD 1860645 to the inorganic structures database of Fachinformationszentrum Karls-

(10)

(11) (12)

(13)

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Sands, T. D.; Washburn, J.; Gronsky, R. High Resolution Observations of Copper Vacancy Ordering in Chalcocite (Cu2S) and the Transformation to Djurleite (Cu1.97 to 1.94S). Phys. Status Solidi (a) 1982, 72, 551–559. Wang, Y.; Xiao, R.; Hu, Y.-S.; Avdeev, M.; Chen, L. P2-Na0.6[Cr0.6Ti0.4]O2 Cation-Disordered Electrode for High-Rate Symmetric Rechargeable Sodium-Ion Batteries. Nat. Commun. 2015, 6, 6954. Toumar, A. J.; Ong, S. P.; Richards, W. D.; Dacek, S.; Ceder, G. Vacancy Ordering in O3-Type Layered Metal Oxide Sodium-Ion Battery Cathodes. Phys. Rev. Applied 2015, 4, 064002. Meng, Y. S.; Hinuma, Y.; Ceder, G. An Investigation of the Sodium Patterning in NaxCoO2 (0.5⩽x⩽1) by Density Functional Theory Methods. J. Chem. Phys. 2008, 128, 104708. Arroyo y de Dompablo, M. E.; Van der Ven, A.; Ceder, G. FirstPrinciples Calculations of Lithium Ordering and Phase Stability on LixNiO2. Phys. Rev. B 2002, 66, 064112. Miller, T. A.; Wittenberg, J. S.; Wen, H.; Connor, S.; Cui, Y.; Lindenberg, A. M. The Mechanism of Ultrafast Structural Switching in Superionic Copper (I) Sulphide Nanocrystals. Nat. Commun. 2013, 4, 1369. Milat, O.; Vučić, Z.; Ruščić, B. Superstructural Ordering in LowTemperature Phase of Superionic Cu2Se. Solid State Ion. 1987, 23, 37– 47. Kashida, S.; Akai, J. X-Ray Diffraction and Electron Microscopy Studies of the Room-Temperature Structure of Cu2Se. J. Phys. C: Solid State Phys. 1988, 21, 5329-5336. Takahashi, T.; Yamamoto, O.; Matsuyama, F.; Noda, Y. Ionic Conductivity and Coulometric Titration of Copper Selenide, J. Solid State Chem. 1976, 16, 35–39. White, S. L.; Banerjee, P.; Jain, P. K. Liquid-like Cationic Sub-Lattice in Copper Selenide Clusters. Nat. Commun. 2017, 8, 14514. Liu, H.; Shi, X.; Xu, F.; Zhang, L.; Zhang, W.; Chen, L.; Li, Q.; Uher, C.; Day, T.; Snyder, G. J. Copper Ion Liquid-like Thermoelectrics. Nat. Mater. 2012, 11, 422–425. Lu, P.; Liu, H.; Yuan, X.; Xu, F.; Shi, X.; Zhao, K.; Qiu, W.; Zhang, W.; Chen, L. Multiformity and Fluctuation of Cu Ordering in Cu2Se Thermoelectric Materials. 2015, 3, 6901–6908. Yamamoto, K.; Kashida, S. X-Ray Study of the Average Structures of Cu2Se and Cu1.8S in the Room Temperature and the High Temperature Phases. J. Solid State Chem. 1991, 93, 202–211.


Page 4 of 6

Page 5 of 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials (14) (15) (16)

(17)

(18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28)

(29)

(30) (31) (32)

(33)

Yamamoto, K.; Kashida, S. X-Ray Study of the Cation Distribution in Cu2Se, Cu1.8Se and Cu1.8S; Analysis by the Maximum Entropy Method. Solid State Ion. 1991, 48, 241–248. Vučić, Z.; Milat, O.; Horvatić, V.; Ogorelec, Z. Composition-Induced Phase-Transition Splitting in Cuprous Selenide. Phys. Rev. B 1981, 24, 5398–5401. Frangis, N.; Manolikas, C.; Amelinckx, S. Vacancy-Ordered Superstructures in Cu2Se. Phys. Status Solidi (a) 1991, 126, 9–22. Heyding, R. D.; Murray, R. M. The Crystal Structures of Cu1.8Se, Cu3Se2, α- and ΓCuSe, CuSe2, and CuSe2II. Can. J. Chem. 1976, 54, 841–848. Dorfs, D.; Härtling, T.; Miszta, K.; Bigall, N. C.; Kim, M. R.; Genovese, A.; Falqui, A.; Povia, M.; Manna, L. Reversible Tunability of the NearInfrared Valence Band Plasmon Resonance in Cu2–XSe Nanocrystals. J. Am. Chem. Soc. 2011, 133, 11175–11180. Luther, J. M.; Jain, P. K.; Ewers, T.; Alivisatos, A. P. Localized Surface Plasmon Resonances Arising from Free Carriers in Doped Quantum Dots. Nat. Mater., 2010, 10, 361–366. Danilkin, S. A.; Skomorokhov, A. N.; Hoser, A.; Fuess, H.; Rajevac, V.; Bickulova, N. N. Crystal Structure and Lattice Dynamics of Superionic Copper Selenide Cu2 - δSe. J. Alloys Compd. 2003, 1–2, 57–61. Namsani, S.; Gahtori, B.; Auluck, S.; Singh, J. K. An Interaction Potential to Study the Thermal Structure Evolution of a Thermoelectric Material: β-Cu2Se. J. Comput. Chem. 2017, 38, 2161–2170. Dumett Torres, D.; Jain, P. K. Strain Stabilization of Superionicity in Copper and Lithium Selenides. J. Phys. Chem. Lett. 2018, 9, 1200– 1205. Liu, B.; Ning, L.; Zhao, H.; Zhang, C.; Yang, H.; Liu, S. (Frank). VisibleLight Photocatalysis in Cu2Se Nanowires with Exposed {111} Facets and Charge Separation between (111) and (111) Polar Surfaces. Phys. Chem. Chem. Phys. 2015, 17, 13280–13289. Mumme, W. G.; Sparrow, G. J.; Walker, G. S. Roxbyite, a New Copper Sulphide Mineral from the Olympic Dam Deposit, Roxby Downs, South Australia. Mineral. Mag. 1988, 52, 323–330. Mumme, W. G.; Gable, R. W.; Petricek, V. The Crystal Structure of Roxbyite, Cu58S32. Can. Mineral. 2012, 50, 423–430. Li, W.; Shavel, A.; Guzman, R.; Rubio-Garcia, J.; Flox, C.; Fan, J.; Cadavid, D.; Ibáñez, M.; Arbiol, J.; Morante, J. R.; et al. Morphology Evolution of Cu2−xS Nanoparticles: From Spheres to Dodecahedrons. Chem. Commun. 2011, 47, 10332–10334. Riha, S. C.; Johnson, D. C.; Prieto, A. L. Cu2Se Nanoparticles with Tunable Electronic Properties Due to a Controlled Solid-State Phase Transition Driven by Copper Oxidation and Cationic Conduction. J. Am. Chem. Soc. 2011, 133, 1383–1390. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. Sham, L. J.; Schlüter, M. Density-Functional Theory of the Energy Gap. Phys. Rev. Lett. 1983, 51, 1888–1891. Chan, M. K. Y.; Ceder, G. Efficient Band Gap Prediction for Solids. Phys. Rev. Lett. 2010, 105, 196403. Towns, J.; Cockerill, T.; Dahan, M.; Foster, I.; Gaither, K.; Grimshaw, A.; Hazlewood, V.; Lathrop, S.; Lifka, D.; Peterson, G. D.; et al. XSEDE: Accelerating Scientific Discovery. Comput. Sci. Eng. 2014, 16, 62–74. Milfeld, K.; Guiang, C.; Pamidighantam, S.; Giuliani, J. Cluster Computing through an Application-Oriented Computational Chemistry Grid. In Proceedings of the 2005 Linux Clusters: The HPC Revolution. 2005. Shen, N.; Fan, Y.; Pamidighantam, S. E-Science Infrastructures for Molecular Modeling and Parametrization. J. Comput. Sci. 2014, 5, 576–589.

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Unconventional Long-Range Cation Ordering in Copper Selenide

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