A Previously Unknown Simple Cubic Phase in the SnS Binary System

Feb 24, 2015 - Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel. •S Supporting...
2 downloads 0 Views 6MB Size
Download PDF
Letter pubs.acs.org/NanoLett

New Nanocrystalline Materials: A Previously Unknown Simple Cubic Phase in the SnS Binary System Alexander Rabkin,†,‡,§ Shmuel Samuha,†,‡,§ Ran E. Abutbul,†,‡ Vladimir Ezersky,‡ Louisa Meshi,†,‡ and Yuval Golan*,†,‡ †

Department of Materials Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

‡

S Supporting Information *

ABSTRACT: We report a new phase in the binary SnS system, obtained as highly symmetric nanotetrahedra. Due to the nanoscale size and minute amounts of these particles in the synthesis yield, the structure was exclusively solved using electron diffraction methods. The atomic model of the new phase (a = 11.7 Å, P213) was deduced and found to be associated with the rocksalt-type structure. Kramers−Kronig analysis predicted different optical and electronic properties for the new phase, as compared to α-SnS. KEYWORDS: SnS, nanoparticles, electron diffraction, octadecylamine, binary phase, structure determination

T

phase is highly curious, especially in light of the study published by Burton and Walsh,39 which examined the stability of various structures in this system and concluded that ZB-type SnS is expected to be unstable. Additionally, recent work by Biacchi et al.15 has shown cube and spherical polyhedron shaped SnS particles with a pseudotetragonal structure. These authors noted the possibility of incorrect assignment of the ZB-type structure to nanoscale SnS.15 In this work, we report on the synthesis and full structure solution of highly symmetric tetrahedra-shaped SnS nanoparticles. Due to the nanoscale size and low fraction of these particles in the synthesis yield, structural study using conventional X-ray diffraction methods20−23 was deemed impossible. On the other hand, these properties made these SnS nanoparticles a perfect candidate for structure solution exclusively using electron diffraction (ED). There exist two main ED data collection techniques: (1) collection of zonal data extracted from different precession electron diffraction (PED) zone axis (ZA) patterns; and (2) collection of “off-axis” ED patterns (with or without precession) with small angular steps between them. In the present work, determination of the structure of SnS nanoparticles was carried out using the second approach, namely the precession electron diffraction tomography (PEDT) method.40−43 It was concluded that the studied phase is cubic (a = 11.7 Å, P213), consisting of 64 atoms in the unit cell. The atomic model was deduced and found to be associated with the rocksalt-type rather than the previously reported ZB-type structure.22,23 Structural relations were

in sulfide (SnS) has bulk band gaps of 1.07 eV (indirect) and 1.3 eV (direct), exhibiting a high absorption coefficient and excellent hole mobility.1,2 These properties, coupled with ability to affect bandgap by nanoparticle size,3−5 are attracting increasing scientific and technological attention, with possible applications ranging from devices such as solar cells,6−9 field effect transistors,10 photodetectors,11 and electrochemical capacitors, 12 to Li ion battery anodes13 and photocatalysis.14 Moreover, the low toxicity of tin, compared with related metal sulfide systems such as lead and cadmium, presents an advantage for tin sulfide over other sulfide nanoparticles. Previous studies in the field of SnS nanoparticle synthesis focused mostly on optical and structural characterization of platelet shaped particles exhibiting the orthorhombic tin sulfide structure.15−18 Others have shown synthesis or thin film growth of SnS with cubic structures, mostly of rocksalt (NaCl)19,20 and zincblende (ZB)21−23 types. The growth techniques used included physical vapor deposition,20 chemical vapor deposition,21 and colloidal chemistry.22 Long hydrocarbon chain alkylamine surfactants, particularly octadecylamine (C 1 8 H 3 7 NH 2 ) and hexadecylamine (C16H33NH2), are widely used as capping agents in order to confine nanomaterials to a restricted size and shape.24−33 Moreover, these surfactants crystallize in a lamellar structure34 that can strongly affect nanoparticle synthesis and assembly.35−37 However, for SnS synthesis, the use of oleylamine (C18H35NH2) is much more common.22,23,38 Of particular interest is the report on the synthesis of ZB-type SnS particles by Greyson et al.,23 which exhibited a highly uniform and symmetric tetrahedron shape and the synthesis by Deng et al.,22 resulting in truncated tetrahedron shaped ZB-type particle. The combination of the shape and the structure of the reported © XXXX American Chemical Society

Received: January 19, 2015 Revised: February 20, 2015

A

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

orthogonal projection, an edge-beam parallel projection, and a face/vertex-centered orthogonal projection (additional description of the geometry can be seen in Figure S1 in Supporting Information). This shape is much closer to that reported by Greyson et al.,23 compared to the truncated particles observed by Deng et al.22 Attempts to index the ED patterns taken from this phase in terms of either orthorhombic or other related structures were unsuccessful. Thus, structure solution was performed. For structure solution, a series of off-axis PED patterns were taken from a single SnS nanoparticle of the π-phase, with a constant angular separation of 1° within a ± 65° tilt range. Then, this series was analyzed and processed using the software package EDT-PROCESS.46 First, combination of the individual off-axis PED frames resulted in the reconstruction of the threedimensional reciprocal space. Next, the lattice parameters were directly derived from the data set as a = 11.801, b = 11.775, c = 11.658 Å, α = 90.6, β = 92.7, and γ = 88.75°, suggesting that the π-phase is cubic with lattice parameters of a ≈ 11.7 Å. In terms of this unit cell, a successful indexing of all recorded zonal-PED patterns was performed, indicating that the dimensions of the unit cell are correct. Figure 2a−c presents the projections of the reconstructed reciprocal space of the π-phase along the highest symmetry orientations: [100], [110], and [111], respectively. As can be seen, the patterns consist of sharp reflection nodes and a unique distribution of strong reflections. In addition, sharp peaks seen in the cylindrical projection of the reconstructed reciprocal space (Figure 2d), point to low azimuthal errors in the determination of the tilt axis projection. Thus, the data can be used for structure solution. Despite successful data collection, it should be noted that due to the geometrical limitation of the goniometer tilt range, the reconstructed reciprocal space is not complete. This is a wellknown problem referred to as the “missing cone”41 and a representation of its magnitude is illustrated in Figure 2e. In order to specify the space group of the π-phase, PED patterns of the highest projected symmetry were analyzed (for example, [100] and [111] orientations, shown in Figure 3a and b, respectively). Careful examination of the systematic absences in the PED patterns revealed a single reflection condition: l = 2n for the 00l. It can be readily seen in Figure 3c, where reflections forbidden by symmetry are marked by arrows. This reflection condition can be associated with either P213 (No. 198) or P4232 (No. 208) space groups.47 Because zero-order Laue zone PED pattern exhibited a 2mm and not 4mm symmetry along the [100] orientation (see Figure 3a), the P213 space group was unambiguously concluded.48 For the P213 space group, the completeness of data in the PEDT data set, up to the 0.82 Å diffraction resolution was found to be 99% with 584 unique reflections. Additionally, correlation of the PED to bright field TEM images (specifically Figure 3a to Figure 1c and Figure 3b to Figure 1e), allows unequivocal assignment of the tetrahedron faces and edges as crystallographic {111} planes and ⟨110⟩ directions, respectively. Considering the unit cell volume of the π-phase (1601.6 Å3), and its composition as measured by EDS in TEM, the content of the unit cell was calculated as 32 Sn and 32 S atoms. Applying the Averaged Alternating Reflections (AAR) algorithm49 in the Jana2006 software,50 a preliminary atomic model was obtained with a reliability factor of RI = 0.25. Because there were no additional “true” atoms in the Fourier difference map, the obtained model was considered as complete. The structural model consisted of eight unique atom positions, four for each

represented through the construction of the Bärnighausen tree.44,45 Examination of as-synthesized material in the transmission electron microscope (TEM) revealed two distinct morphologies, of which the majority were elongated platelets (Figure 1a),

Figure 1. TEM bright field images of the different shapes and sizes of synthesized SnS particles: (a) Orthorhombic platelets. Top right inset shows a small tetrahedron alongside the platelets. Bottom right inset shows SAED taken from the area marked as a dashed circle showing the [010] orientation. (b−e) Tetrahedra for the π-phase: (b) tetrahedra of different sizes, (c) edge-centered orthogonal projection, (d) edge-beam parallel projection, and (e) face/vertex-centered orthogonal projection.

associated with the stable orthorhombic crystal structure (ICDD PDF file #39-0354). Typically, they were found to be oriented with the [010] axis parallel to the incident TEM beam. The lateral dimensions of the platelets ranged from a few tens to several hundreds of nanometers. Elemental analysis in the TEM using energy dispersive spectroscopy (EDS) (comparing to a commercial orthorhombic SnS standard, Sigma cat. # 741000), confirmed a 1:1 Sn/S ratio. The second morphology was a minority phase of a few percent in the synthesis yield. It consisted of nanotetrahedron shaped SnS particles (as confirmed by EDS in TEM). This phase (designated as π) was observed with varying edge lengths, ranging from below 30 nm (top right inset in Figure 1a) to over 300 nm (Figure 1b). The shape is very close to that of a regular tetrahedron, as demonstrated in Figure 1c−e, showing an edge-centered B

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 2. Three dimensional reconstructed reciprocal space from PEDT data taken from single particle of the π-phase. (a-c) Views along the [100], [110], and [111] orientations, respectively. (d) Cylindrical projection of the reconstructed reciprocal space. (e) Representation of the “missing cone”.

Figure 3. PED patterns taken along the (a) [100], (b) [111], and (c) [210] orientations. A 2mm projection symmetry can be seen in (a). Mirrors are labeled by m. Forbidden reflections are marked by arrows on (c).

Table 1. Atomic Parameters and Isotropic Thermal Motion Parameters, Biso, for the π Structure atom positions atom

Wyckoff site

x

y

z

Biso [Å2]

Sn1 Sn2 Sn3 Sn4 S1 S2 S3 S4

4a 12b 4a 12b 4a 12b 4a 12b

0.2697(5) 0.0264(5) 0.2793(5) 0.0214(5) 0.9566(83) 0.0516(14) 0.039(2) 0.2413(15)

0.7303(5) 0.9797(5) 0.7793(5) 0.7416(5) 0.9566(83) 0.7612(13) 0.961(2) 0.8013(15)

0.2303(5) 0.2292(5) 0.7207(5) 0.9701(5) 0.9566(83) 0.1962(14) 0.461(2) 0.9401(84)

0.031(2) 0.329(17) 0.029(2) 0.0306(16) 0.056(8) 0.038(4) 0.068(9) 0.044(4)

type of atom, distributed over two unique nonequivalent crystallographic Wyckoff sites. Prior to the validation of the proposed atomic model, a kinematical least-squares refinement on F2 was carried out using the Jana2006 software.50 The stability of the structural model was checked after each refinement cycle. Overall, 55 parameters were refined, including the atomic positions and displacement parameters. The final solution was regarded as stable since at the last refinement cycle, all atoms had reasonable atomic displacement parameters and no significant shifts in the atomic positions were observed.

The structural model (see Table 1) converged with reliability factors of R1 = 0.237, wR2 = 0.515. The proposed atomic model can be confirmed also by chemical reasonability (i.e., composition) and acceptable interatomic distances (shortest distance of 2.6 Å was found among the Sn2 and S2 atoms). It should be noted that although much lower reliability factors are usually obtained for structures solved from X-ray diffraction (XRD) data, the reliability factors in this work are acceptable for the structure solution performed using ED data (see Samuha et al.51 and references therein). The correctness of the model can be supported by comparison of C

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

(coordination number, CN = 6) formed around either S or Sntype atoms, see Figure 5a. Their linkage is through the vertices and edges. Under the same composition, temperature, and pressure range, a stable SnS phase cannot possess two crystallographic structures. Because it is known that orthorhombic α-SnS is the equilibrium structure, the appearance of the π-phase should be explained. In previous studies, SnS was reported to possess the ZB-type21−23 and the NaCl-type19,20 structures under different metastable conditions. It is clear that neither of these formed here. However, the structure of the new π-phase was found to be structurally related to one of them. The successful construction of the Bärnighausen tree44,45 (Figure S2 in Supporting Information), where NaCl structure is an arystotype, suggests a group−subgroup relationship among the NaCl and the π-phase. The same was tried with the ZB-type structure (as an arystotype), but the resulting structure was found to be distinctively different from that of the π-phase. As an example, Figure 5b and c shows polyhedral representation of such calculated structures based on ZB and NaCl, respectively. The tetrahedra in the ZB-type have nothing in common with the octrahedra in the π and NaCl-type structures. Moreover, a check of structure similarity between the π structure and the calculated structure (based on the NaCl-type), performed using the COMPSTRU tool53 in the Bilbao server, yielded a measure of similarity of Δ = 0.082, meaning a close similarity. It is important to note that the close similarity between the stable orthorhombic SnS and NaCl-type structures has been previously discussed.20 It was stated that under suitable physical conditions which may effectively “undistort” or dilate the lattice, the NaCl-type structure can form.20 It is plausible to suggest that in the current research, such physical conditions were attained due to the surfactant coating and subsequent nanoscale size of the studied particles. These conditions imposed crystallization of the SnS phase as a defect ordered variant of the NaCl-type structure, allowing formation of the πstructure. Furthermore, classification of this phase as a defect-ordered variant of NaCl-type structure is also supported by Burton and Walsh,39 who examined the stability of various structures in the Sn−S system. Using a first-principles electronic structure method based on density functional theory, enthalpies of formation of different phases were calculated. Their results predicted the ZB-type SnS phase to be thermodynamically unstable. We therefore suspect that the previous assignment as ZB-type phase for regular tetrahedra (identical morphology to that obtained in this work)23 and for truncated tetrahedra

the experimental and calculated [110] PED patterns (Figure 4a and b, respectively), which clearly exhibit a similar intensity

Figure 4. (a) Experimental zonal PED pattern taken from a particle of the π-phase and (b) the corresponding simulated pattern, calculated based on the proposed model using JEMS software.52

distribution of the strong reflections. Crystallographic information on the π-phase and refinement data can be found in Supporting Information (Table S1). The final structure of the π-phase can be described through a buildup of four different types of linked coordination octahedra

Figure 5. Polyhedral representative description viewed along the [111] orientation of the (a) π-phase model of the structure obtained in this work, (b) calculated model based on the ZB-type structure, and (c) calculated model based on the NaCl-type structure. Light gray and yellow circles represent Sn and S type atoms, respectively. Octahedra formed around different S atom positions are distinguished by color. For clarity, the inset in (a) presents an isolated coordination polyhedron formed around S atom, viewed along the [111] orientation. D

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

synthesized π-phase nanotetrahedra using ED methods, which are more appropriate for structure solution of nanosized crystals. Geometry of the unit cell and full atomic model were deduced from PEDT data, whereas the space group was evaluated through analysis of symmetry of zonal PED patterns. It was concluded that the studied phase is cubic (a = 11.7 Å, P213), consisting of 64 atoms in the unit cell. The final atomic model was found to be associated with the NaCl-type and not to the ZB-type structure, which is in agreement with reported stability assessment.39 Kramers−Kronig analysis of the STEM EELS low loss region shows notable variation of the dielectric function, suggesting that significant differences should be expected in the optical and electrical properties of the orthorhombic and the π-phase. Efforts are being made for synthesizing nanopowders with larger fractions of the π-phase, which will allow structural and optical investigations using complementary techniques.

(slightly different morphology)22 should be revisited. Moreover, we note that the synthesized π-phase has maintained structure following the storage period of above six months, which would likely not to have been observed for a highly metastable phase. Finally, single particle scanning TEM (STEM) electron energy-loss spectroscopy (EELS) low loss measurements have been used in order to monitor possible dielectric function differences between elongated platelet and tetrahedron shaped SnS particles. This was done by use of Kramers−Kronig analysis54 in the Digital Micrograph (Gatan) software, which provides an indication for both the real (ε1) and imaginary (ε2) parts of the dielectric function. The results can be seen in Figure 6. A notable difference between the two phases was

■

ASSOCIATED CONTENT

* Supporting Information S

Detailed experimental procedures and characterization techniques; geometrical description of regular tetrahedron orthogonal projections; summary of structure solution results and refinement parameters of the π-phase; Bärnighausen tree presenting the crystallographic group-subgroup relations among the original NaCl type structure to the π structure via series of hypothetical intermediates. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Author Contributions §

These authors contributed equally.

Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by the Israel Science Foundation under Grant #340/2010. ABBREVIATIONS SnS, tin sulfide; NaCl, rocksalt; ZB, zincblende; ED, electron diffraction; PED, precession electron diffraction; ZA, zone axis; PEDT, precession electron diffraction tomography; TEM, transmission electron microscope; ICDD PDF, International Centre for Diffraction Data powder diffraction file; EDS, energy dispersive spectroscopy; AAR, Averaged Alternating Reflections (in Jana2006); XRD, X-ray diffraction; CN, coordination number; STEM, scanning transmission electron microscope; EELS, electron energy-loss spectroscopy

Figure 6. Single particle analysis of STEM EELS low loss spectra for each morphology shows variation of the dielectric constant: (a) ε1 as a function of energy and (b) ε2 as a function of energy.

observed. This signifies that appreciable differences in refractive index and electrical properties between the two nanoparticle types are expected. In summary, although previous studies have demonstrated synthesis of similar, tetrahedron-shaped SnS particles by use of colloidal chemistry (surfactant assisted) methods, the structure of these particles has been classified as ZB-type by use of XRD.22,23 This work reports full structure solution of the

■

REFERENCES

(1) Parenteau, M.; Carlone, C. Phys. Rev. B 1990, 41, 5227−5234. (2) Ramasamy, K.; Kuznetsov, V. L.; Gopal, K.; Malik, M. A.; Raftery, J.; Edwards, P. P.; O’Brien, P. Chem. Mater. 2013, 25, 266−276. (3) Nozik, A. J. Chem. Phys. Lett. 2008, 457, 3−11.

E

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters (4) Xu, Y.; Al-Salim, N.; Bumby, C. W.; Tilley, R. D. J. Am. Chem. Soc. 2009, 131, 15990−+. (5) Yue, G. H.; Wang, L. S.; Wang, X.; Chen, Y. Z.; Peng, D. L. Nanoscale Res. Lett. 2009, 4, 359−363. (6) Sharon, M.; Basavaswaran, K. Sol. Cells 1988, 25, 97−107. (7) Sinsermsuksakul, P.; Sun, L. Z.; Lee, S. W.; Park, H. H.; Kim, S. B.; Yang, C. X.; Gordon, R. G. Adv. Energy Mater. 2014, 4, 1400496 1− 7. (8) Burton, L. A.; Walsh, A. Appl. Phys. Lett. 2013, 102, 132111 1−3. (9) Park, H. H.; Heasley, R.; Sun, L.; Steinmann, V.; Jaramillo, R.; Hartman, K.; Chakraborty, R.; Sinsermsuksakul, P.; Chua, D.; Buonassisi, T.; Gordon, R. G. Prog. Photovoltaics: Res. Appl. 2014, DOI: 10.1002/pip.2504. (10) Deng, Z. T.; Cao, D.; He, J.; Lin, S.; Lindsay, S. M.; Liu, Y. ACS Nano 2012, 6, 6197−6207. (11) Chao, J. F.; Wang, Z. R.; Xu, X.; Xiang, Q. Y.; Song, W. F.; Chen, G.; Hu, J. B.; Chen, D. RSC Adv. 2013, 3, 2746−2753. (12) Jayalakshmi, M.; Rao, M. M.; Choudary, B. M. Electrochem. Commun. 2004, 6, 1119−1122. (13) Vaughn, D. D.; Hentz, O. D.; Chen, S. R.; Wang, D. H.; Schaak, R. E. Chem. Commun. 2012, 48, 5608−5610. (14) Chao, J. F.; Xie, Z.; Duan, X. B.; Dong, Y.; Wang, Z. R.; Xu, J.; Liang, B.; Shan, B.; Ye, J. H.; Chen, D.; Shen, G. Z. CrystEngComm 2012, 14, 3163−3168. (15) Biacchi, A. J.; Vaughn, D. D.; Schaak, R. E. J. Am. Chem. Soc. 2013, 135, 11634−11644. (16) Liu, X.; Li, Y.; Zhou, B.; Wang, X. L.; Cartwright, A. N.; Swihart, M. T. Chem. Mater. 2014, 26, 3515−3521. (17) Patra, B. K.; Sarkar, S.; Guria, A. K.; Pradhan, N. J. Phys. Chem. Lett. 2013, 4, 3929−3934. (18) Zhang, Y. J.; Lu, J.; Shen, S. L.; Xu, H. R.; Wang, Q. B. Chem. Commun. 2011, 47, 5226−5228. (19) Bilenkii, B. F.; Mikolaic, Ag; Freik, D. M. Phys. Status Solidi 1968, 28, 115−117. (20) Mariano, A. N.; Chopra, K. L. Appl. Phys. Lett. 1967, 10, 282− 284. (21) Avellaneda, D.; Nair, M. T. S.; Nair, P. K. J. Electrochem. Soc. 2008, 155, D517−D525. (22) Deng, Z. T.; Han, D. R.; Liu, Y. Nanoscale 2011, 3, 4346−4351. (23) Greyson, E. C.; Barton, J. E.; Odom, T. W. Small 2006, 2, 368− 371. (24) Efrima, S.; Pradhan, N. J. Am. Chem. Soc. 2003, 125, 2050− 2051. (25) Pradhan, N.; Katz, B.; Efrima, S. J. Phys. Chem. B 2003, 107, 13843−1385. (26) Albeniz, S.; Vicente, M. A.; Trujillano, R.; Korili, S. A.; Gil, A. Appl. Clay Sci. 2014, 99, 72−82. (27) Jiang, Z.; Tian, Y. H.; Ding, S. Mater. Lett. 2014, 136, 310−313. (28) Onwudiwe, D. C.; Mohammed, A. D.; Strydom, C. A.; Young, D. A.; Jordaan, A. Superlattices Microstruct. 2014, 70, 98−108. (29) Purkayastha, D. D.; Sarma, B.; Bhattacharjee, C. R. Mater. Lett. 2013, 107, 71−74. (30) Purkayastha, D. D.; Sarma, B.; Bhattacharjee, C. R. J. Lumin. 2014, 154, 36−40. (31) Sun, J. L. Mater. Lett. 2013, 108, 193−195. (32) Taylor, R.; Monson, T.; Gullapalli, R. Nanoscale Res. Lett. 2014, 9, 1−12. (33) Yang, H. J.; He, S. Y.; Chen, H. L.; Tuan, H. Y. Chem. Mater. 2014, 26, 1785−1793. (34) Belman, N.; Israelachvili, J. N.; Li, Y.; Safinya, C. R.; Bernstein, J.; Golan, Y. J. Am. Chem. Soc. 2009, 131, 9107−9113. (35) Belman, N.; Israelachvili, J. N.; Li, Y.; Safinya, C. R.; Ezersky, V.; Rabkin, A.; Sima, O.; Golan, Y. Phys. Chem. Chem. Phys. 2011, 13, 4974−4979. (36) Belman, N.; Israelachvili, J. N.; Li, Y.; Safinya, C. R.; Bernstein, J.; Golan, Y. Nano Lett. 2009, 9, 2088−2093. (37) Rabkin, A.; Belman, N.; Israelachvili, J.; Golan, Y. Langmuir 2012, 28, 15119−15123.

(38) Koktysh, D. S.; McBride, J. R.; Geil, R. D.; Schmidt, B. W.; Rogers, B. R.; Rosenthal, S. J. Mater. Sci. Eng., B 2010, 170, 117−122. (39) Burton, L. A.; Walsh, A. J. Phys. Chem. C 2012, 116, 24262− 24267. (40) Kolb, U.; Gorelik, T.; Kubel, C.; Otten, M. T.; Hubert, D. Ultramicroscopy 2007, 107, 507−513. (41) Kolb, U.; Gorelik, T.; Otten, M. T. Ultramicroscopy 2008, 108, 763−772. (42) Kolb, U.; Mugnaioli, E.; Gorelik, T. E. Cryst. Res. Technol. 2011, 46, 542−554. (43) Mugnaioli, E.; Gorelik, T.; Kolb, U. Ultramicroscopy 2009, 109, 758−765. (44) Baernighausen, H. MATCH 1980, 9, 139−75. (45) Müller, U. Symmetry Relations between Crystal Structures; Oxford University Press: New York, 2013. (46) Oleynikov, P. EDT-COLLECT and EDT-PROCESS software packages; Analitex: Täby, Sweden, 2011. (47) Hahn, T. International Tables for Crystallography, 5th ed.; Springer: New York, 2005. (48) Morniroli, J. P. Atlas of Electron Diffraction Patterns. 2013, No. http://www.electron-diffraction.fr/. (49) Palatinus, L. Acta Crystallogr., Sect. B: Struct. Sci. 2013, 69, 1−16. (50) Petricek, V.; Dusek, M.; Palatinus, L. Z. Kristallogr. 2014, 229, 345−352. (51) Samuha, S.; Mugnaioli, E.; Grushko, B.; Kolb, U.; Meshi, L. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2014, 70, 999−1005. (52) Stadelmann, P. A. Ultramicroscopy 1987, 21, 131−145. (53) Tasci, E. S.; de la Flor, G.; Orobengoa, D.; Capillas, C.; PerezMato, J. M.; Aroyo, M. I. Contribution of Symmetries in Condensed Matter 2012, 22, 00009 DOI: 10.1051/epjconf/20122200009. (54) Egerton, R. F. Electron Energy-Loss Spectroscopy in the Electron Microscope, 3rd ed.; Springer: New York, 2011.

F

DOI: 10.1021/acs.nanolett.5b00209 Nano Lett. XXXX, XXX, XXX−XXX