Lattice Dynamics of the Rhombohedral Polymorphs of CaSi2

Article pubs.acs.org/IC

Lattice Dynamics of the Rhombohedral Polymorphs of CaSi2 Sarah M. Castillo,† Zhongjia Tang,† Alexander P. Litvinchuk,*,‡ and Arnold M. Guloy*,† †

Department of Chemistry and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204-5003, United States ‡ Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204-5002, United States ABSTRACT: The structures of two trigonal-rhombohedral CaSi 2 polymorphs (space group R3̅m) were studied by X-ray diffraction and polarized Raman scattering spectroscopy. Raman-active even-parity vibrational modes of A1g and Eg are unambiguously identified and assigned to the specific lattice eigenmodes. Experimental data are found to be in very good agreement with those predicted by density functional theory lattice dynamics calculations. The transformation of 6R structural modification of CaSi2 into its 3R polymorph, by high-temperature annealing in vacuum is also reported.

■

INTRODUCTION Layered silicon nanomaterials due to compatibility with current silison-based microelectronics and their role in future nanoscale electronic and optical devices have received considerable interest because of many promising properties.1−3 Although CaSi2 has been known for over 150 years,4 interest in AB2 materials expanded since the discovery of superconductivity in magnesium diboride (MgB2) at temperatures as high as Tc = 39 K.5 The title compound has also attracted special attention among Zintl phases for many reasons. Among others, CaSi2 was shown be an effective material for use as an anode for lithiumion batteries.6 High-quality epitaxial films of CaSi2 could be grown on silicon substrates (see, e.g., refs 7 and 8), which makes them compatible with silicon-based electronic devices. Because of its layered silicon substructure, special interest in CaSi2 has focused on its topochemical reactions with acids that have resulted in the synthesis of novel layered “siloxenes” and polysilanes.9−12 More recently, the synthesis of silicon monolayer sheets13 and silicene, the silicon analogue of graphene,14 from redox-assisted exfoliation of CaSi2 has been reported. Free-standing silicene has been shown to exhibit unique properties and touted as a great potential material in the next generation of electronics.15 Recently, the silicon layers in CaSi2 were found to exhibit electronic properties similar to those of graphene in that the silicon-based π/π* bands of CaSi2 also form massless Dirac-cone states.16 Despite the varied physical and chemical interest on CaSi2, its lattice dynamics, which is helpful in understanding the structural features and possible structural changes that it may undergo, is still unreported. Many AB2 compounds, including MgB2, crystallize in the socalled AlB2-type structure (hexagonal space group P6/mmm), which comprises graphite-like boron planes and 12-fold boroncoordinated Al atoms sandwiched between the boron sheets © XXXX American Chemical Society

and located at the center of the boron hexagonal prisms. In contrast, the crystal structure of calcium disilicide (CaSi2) features17−19 a pronounced buckling of the silicon sheets, associated with the formation of lone pairs on the formally three-bonded Si− atoms. Several related polymorphs of CaSi2 are known (see ref 19 for details): those with one-layer (socalled EuGe2 structure, space group P3m1), two-layer (2H, space group P63mc, which exists under pressure only and exhibits superconductivity below 14 K),20 and three- and sixlayer (3R and 6R, respectively; space group R3m ̅ for both compounds) silicon substructures within the unit cell. The structural transformation between trigonal-rhombohedral (3R and 6R) polymorphs of CaSi2 was recently investigated by Nedumkandathil et al.19 They reported that the 3R phase could be obtained through sintering of CaSi2 pressed pellets under a hydrogen atmosphere at a pressure of 30 bar and temperatures between 200 and 700 °C. The observed behavior was found to contradict the results from density functional theory calculations that suggest greater stability of the 6R polymorph at high temperatures. This discrepancy was explained to be due to either the possible incorporation of hydrogen into the lattice or the introduction of extraneous defects, which stabilize the 3R structure over 6R.19 In the present paper, we report an annealing procedure that allows for the transformation (at ambient pressure) of CaSi2 single crystals from 6R into the 3R polymorph. The structures of the two crystallographic modifications are characterized by X-ray diffraction, as well as polarized Raman scattering spectroscopy. Received: June 10, 2016

A

DOI: 10.1021/acs.inorgchem.6b01399 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

■

SAMPLE PREPARATION AND X-RAY DIFFRACTION RESULTS We started with commercially available samples of crystalline CaSi2 from Sigma-Aldrich. Powder X-ray diffraction analysis of these samples shows that they mostly contain a mixture of 3R and 6R polymorphs, as well as minor crystalline phases of Ca14Si19 and α-Si. The estimated contents (by volume) of the crystalline phases are 59% (3R), 24% (6R), 9.3% (Ca14Si19), and 7.7% (α-Si). Well-crystallized and faceted lamella-like chunks of CaSi2 (3−4 mm diameter) were initially selected for X-ray diffraction. The selected crystalline chunks were ground and found to be pure 6R, as shown in Figure 1, bottom panel.

All structural data listed above are in good agreement with those reported earlier.19,25−27 One has to note a strong preferred orientation exhibited by the 3R polymorph, which manifests itself in the strong intensity of the (006) diffraction peak at 2θ ∼ 34°. We also note that the two trigonalrhombohedral polymorphs are very similar in that they both consist of corrugated layers of silicon, separated by trigonal layers of calcium (Figure 2). They differ, however, in the stacking sequence.19

Figure 2. Crystallographic structure of the three-layer (3R, left panel) and six-layer (6R, right panel) CaSi2 polymorphs. Si atoms are shown in gray and Ca atoms in green.

■

Figure 1. Powder X-ray diffraction patterns of the six-layer (6R, bottom panel) and three-layer (3R, top panel) polymorphs of CaSi2.

RAMAN SCATTERING AND LATTICE DYNAMICS: THEORY AND EXPERIMENT Raman scattering spectra of CaSi2 were measured using a JobinYvon T64000 spectrometer in single-stage mode, equipped with a Notch filter, polarizers of incident and scattered light, an optical microscope, and a liquid-nitrogen-cooled chargecoupled-device detector. An 100× objective was used to both focus the incident laser beam into a spot of 1−2 μm diameter and collect scattered light in the backward scattering geometry. A 514.5 nm Ar+ laser line was used for excitation. The laser power did not exceed 0.5 mW in order to avoid heating and damage of the sample surface. The spectral resolution did not exceed 1.5 cm−1. All measurements were performed at room temperature. The first-principles density functional theory (DFT) calculations of the electronic ground state of CaSi2 were performed within the local density approximation with a Perdew−Wang local functional,28 using the Dmol3 code.29,30 Integration over the Brillouin zone was performed over the 4 × 4 × 4 Monkhorst−Pack grid in reciprocal space.31 The selfconsistent-field tolerance was set to 10−6. Electrons in the lowest-lying atomic orbitals were treated in the same manner as the valence electrons. The lattice was optimized so that equilibrium forces on atoms did not exceed 10−3 eV Å−1. The

Subsequently, similarly shaped crystalline pieces, confirmed to be of the 6R polymorph, were selected and placed in sealed evacuated fused-silica ampules. These were then annealed at 800 °C for 2 days and cooled to room temperature. X-ray diffraction of the resulting annealed polycrystalline samples clearly indicated the presence of the 3R phase, as shown in Figure 1, top panel. In contrast, X-ray diffraction of the CaSi2 (6R) samplesenclosed in welded niobium tubes under an argon atmosphere, protected from air by silica jackets, and further annealed at 800 °C for 2 daysdid not indicate the presence of the 3R polymorph. The possible role of hydrogen in stabilization of the 3R polymorph, as indicated by Nedumkandathil et al.,19 cannot be discounted in these experiments because of the degassing properties of fused silica at these temperatures.21−23 Refinement of the unit cells and powder profiles by means of the Le Bail algorithm within the JANA software package24 yields the following results: for the 3R polymorph, a = 3.8228(2) Å, c = 15.8768(9) Å, and V = 200.931(2) Å3, while for the 6R polymorph, a = 3.8545(2) Å, c = 30.661(1) Å, and V = 394.61(3) Å3. B


Article

Inorganic Chemistry ⎛ c 0 0⎞ ⎛a 0 0⎞ ⎜ ⎟ ⎜ ⎟ A1g = ⎜ 0 a 0 ⎟ , Eg(1) = ⎜ 0 −c d ⎟ , ⎜ ⎟ ⎜ ⎟ ⎝0 0 b ⎠ ⎝0 d 0⎠ ⎛ 0 −c −d ⎞ ⎜ ⎟ Eg(2) = ⎜ −c 0 0 ⎟ ⎜ ⎟ ⎝− d 0 0 ⎠

finite displacement method was further used to access the lattice dynamics properties. The unit cell of the 3R CaSi2 has the R3̅m (D53d) space group and contains27 three Ca atoms in the Wyckoff position 3a (site symmetry D3d) and six Si atoms in the Wyckoff position 6c (site symmetry C3v). Due to symmetry, Ca atoms do not contribute any even-parity Raman-active modes as they occupy centrosymmetric positions in the lattice.32 On the contrary, Si atoms produce one fully symmetric A1g mode (displacements along the c axis) and one degenerate Eg mode (displacements within the x−y plane; see Table 1).

in a standard orthogonal basis. Because the Raman scattering intensity for a given scattering configuration is determined by 2

I∼

Table 1. Position, Symmetry, and Irreducible Representation of the Atoms in the Unit Cell of the 3R (Upper Part) and 6R (Lower Part) Polymorphs of CaSi2 atom

Wyckoff notation

site symmetry

lattice position z/c

irreducible representation

Ca Si

3a 6c

D3d C3v

0 0.197

A2u ⊕ Eu A1g⊕A2u⊕Eg⊕Eu

Ca Si1 Si2

6c 6c 6c

C3v C3v C3v

0.083 0.183 0.350

A1g⊕A1u⊕Eg⊕Eu A1g⊕A1u⊕Eg⊕Eu A1g⊕A1u⊕Eg⊕Eu

∑

e i 9ρσes

ρ,σ=x ,y ,z

[here ei (es) is the polarization of the incident (scattered) light and 9ρσ are the elements of the Raman tensor], it could easily be shown that, for parallel polarizations of incident and scattered light, the Eg mode has a nonzero intensity in all experimentally available configurations, except zz. On the other hand, the A1g mode is allowed in all parallel polarizations and forbidden in all crossed polarizations. The polarized Raman scattering spectra of 3R CaSi2 are shown in Figure 3, left panel. The two-letter notations next to

The unit cell of the six-layer 6R polymorph of CaSi2 has the same space group,27 but all atoms within the cell occupy 6c Wyckoff sites. Of principal importance here is the fact that, due to the Ca site symmetry reduction upon going from the 3R to 6R polymorph, Ca contributes Raman-active modes in the latter. In summary, the number and symmetry of Raman modes of the two rhombohedral CaSi2 modifications are as follows: 3R: 6R:

ΓR = A1g(Si) ⊕ Eg(Si)

ΓR = A1g (Ca) ⊕ 2A1g(Si) ⊕ Eg(Ca) ⊕ 2Eg(Si)

Thus, a considerable increase of the number of phonon modes is expected for the six-layer compound compared to its three-layer counterpart. One has to mention, however, that the Si−Si and Ca−Ca bond distances are very similar in both polymorphs, being only 1.5% and 0.8% longer, respectively, in 6R. For this reason, one would expect that in-plane Eg siliconrelated vibrations will have rather close frequencies in 3R and 6R modifications, albeit slightly lower in the latter. Similarly, there is no reason to expect a considerable difference between modes originating from crystallographically inequivalent Si1 and Si2 atoms in the 6R polymorph because their respective sublattices, in terms of bond distances, are identical to within 0.3%. Therefore, activation of the calcium-related modes in 6R structural modification should be a key difference in distinguishing CaSi2 rhombohedral polymorphs. Before the experimental and theoretical lattice dynamics results are discussed, it is instructive to analyze the Raman scattering tensors for the D3d point group in order to find experimental scattering configurations, where the long-wavelength zone-center A1g and Eg vibrations are allowed. According to ref 32, the scattering tensors are

Figure 3. Room temperature polarized Raman scattering spectra of 3R (left panel) and 6R (right panel) CaSi2 polymorphs in different scattering configurations. The spectra are shifted vertically for clarity.

each curve denote polarization of the incident and scattered light, respectively (the x′ and y′ axes are rotated by 45° with respect to x and y). The two lines with maxima at 393 and 427 cm−1 dominate the spectra of the three-layer modification of CaSi2. It is obvious that the lower-frequency mode corresponds to the A1g(Si) phonon because it disappears in the crosspolarized xy spectrum. The higher-frequency line is due to the Eg(Si) vibration because its intensity vanished only in the zz spectrum. The observed mode frequencies are in good agreement with those obtained from the DFT lattice dynamics calculations, as shown in Table 2. It is not surprising that the inplane silicon vibration frequency is higher with respect to the caxis A1g vibration because of a closely packed silicon double layer. A detailed theoretical study of other intermetallic AB2 C


Article

Inorganic Chemistry Notes

Table 2. Calculated and Experimental Phonon-Mode Frequencies in 3R (Upper Part) and 6R (Lower Part) Polymorphs of CaSi2 mode symmetry and participating atom(s)

theory

experiment

Eu(Si) A2u(Si) A1g(Si) Eg(Si)

168 258 371 429

IR IR 393 427

Eu(Si1+Si2) Eu(Ca) Eg(Ca−Si1−Si2) A2u(Si1−Si2) A2u (Ca) A1g(Ca) A1g(Si2) A1g(Si1) Eg(Si2) Eg(Si1)

102 113 150 151 152 205 343 368 413 425

IR IR

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported in part by the Robert A. Welch Foundation (E-1297), the State of Texas through the Texas Center for Superconductivity at the University of Houston, and a John and Rebecca Moores Endowment.

■

IR IR 213 349 387 416 426

a Odd-parity A2u and Eu are IR-active modes. All data are in cm−1. Signs “+” and “−” in the first column refer to the in-phase and out-ofphase motion of atoms, respectively.

compounds shows33 that this is also true for many other materials, with the exception of MgB2. The appearance of an additional low-frequency A1g symmetry peak (213 cm−1) for the six-layer polymorph is obvious from Figure 3 (right panel). According to the DFT calculations, this line is due to the c-axis calcium vibration. The corresponding Eg calcium-related mode is expected at even lower frequency (150 cm−1) but was not observed experimentally, probably because of its low intensity. At higher frequencies, one clearly observes several silicon-related modes: A1g at 349 and 387 cm−1, as well as Eg at 416 and 426 cm−1, in good agreement with the results of lattice dynamics calculations.

■

CONCLUSIONS In summary, we report a simple annealing procedure that allows for the complete transformation of the trigonalrhombohedral 6R polymorph of CaSi2 crystals into its 3R phase. The crystal structure of both polymorphs and phase purity are confirmed by powder X-ray diffraction. In addition, we present complementary results from polarized Raman scattering measurements of the two CaSi2 polymorphs. In this respect, an important difference between the 3R and 6R polymorphs is the change of the Ca site symmetry, which is accompanied by activation of the corresponding calcium-related Raman active modes in the 6R phase, a fact that is observed experimentally. All Raman-active lines are assigned specific lattice eigenmodes. Experimental mode frequencies are found to be in good agreement with those obtained by first-principles lattice dynamics calculations. Thus, Raman spectroscopy is shown to be an effective tool in distinguishing crystallographically very similar polymorphs of CaSi2.

■

REFERENCES

(1) Takeda, K.; Shiraishi, K. Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 14916−14922. (2) Cahangirov, S.; Topsakal, M.; Aktürk, E.; Sahin, H.; Ciraci, S. Two- and one-dimensional honeycomb structures of silicon and germanium. Phys. Rev. Lett. 2009, 102, 236804. (3) Liu, C.-C.; Feng, W.; Yao, Y. Quantum spin Hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 2011, 107, 076802. (4) Wöhler, F. Ü ber Verbindungen des Siliciums mit Sauerstoff und Wasserstoff. Liebigs Ann. Chem. 1863, 127, 257−274. (5) Nagamatsu, J.; Nakagawa, N.; Muranaka, T.; Zenitani, Y.; Akimitsu, J. Superconductivity at 39 K in magnesium diboride. Nature (London, U. K.) 2001, 410, 63−64. (6) Wolfenstine, J. CaSi2 as an anode for lithium-ion batteries. J. Power Sources 2003, 124, 241−245. (7) Morar, J.; Wittmer, M. Metallic CaSi2 epitaxial films on Si(111). Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 2618−2621. (8) Würz, R.; Schmidt, R.; Schöpke, A.; Fuhs, W. Solid-phase epitaxy of CaSi2 on Si(111) and the Schottky-barrier height of CaSi2/Si(111). Appl. Surf. Sci. 2002, 190, 437−440. (9) Kautsky, H.; Herzberg, G. Siloxene and its derivatives. Z. Anorg. Chem. 1924, 139, 135−160. (10) Hengge, E.; Olbrich, G. Preparation of layered compounds (SiH)n and (SiF)n. Monatsh. Chem. 1970, 101, 1068−1073. (11) Dahn, J.; Way, B. M.; Fuller, E.; Tse, J. Structure of Siloxene and layered polysilane (Si6H6). Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 17872−17877. (12) Dettlaff-Weglikowska, U.; Hönle, W.; Molassioti-Dohms, A.; Finkbeiner, S.; Weber, J. Structure and optical properties of the planar silicon compounds polysilane and Wöhler Siloxene. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, 13132−13140. (13) Nakano, H.; Mitsuoka, T.; Harada, M.; Horibuchi, K.; Nozaki, H.; Takahashi, N.; Nonaka, T.; Seno, Y.; Nakamura, H. Soft synthesis of single-crystal silicon monolayer sheets. Angew. Chem., Int. Ed. 2006, 45, 6303−6306. (14) Tchalala, M.; et al. Silicon sheets by redox assisted chemical exfoliation. J. Phys.: Condens. Matter 2013, 25, 442001. (15) Tao, L.; Cinquanta, E.; Chiappe, D.; Grazianetti, C.; Fanciulli, M.; Dubey, M.; Molle, A.; Akinwande, D. Silicene field-effect transistors operating at room temperature. Nat. Nanotechnol. 2015, 10, 227−231. (16) Noguchi, E.; Sugawara, K.; Yaokawa, R.; Hitosugi, T.; Nakano, H.; Takahashi, T. Direct Observation of Dirac Cone in Multilayer Silicene Intercalation Compound CaSi2. Adv. Mater. 2015, 27, 856− 860. (17) Loison, C.; Rosner, H. CaSi2, the antibonding-sister of MgB2? Solid State Commun. 2010, 150, 2076−2079. (18) Flores-Livas, J. A.; Debord, R.; Botti, S.; San Miguel, A.; Marques, M.; Pailhés, S. Enhancing the superconducting transition temperature of BaSi2 by structural tuning. Phys. Rev. Lett. 2011, 106, 087002. (19) Nedumkandathil, R.; Benson, D. E.; Grins, J.; Spektor, K.; Häussermann, U. The 3R polymorph of CaSi2. J. Solid State Chem. 2015, 222, 18−24. (20) Bordet, P.; Affronte, M.; Sanfilippo, S.; Núnez-Regueiro, M.; Laborde, O.; Olcese, G. L.; Palenzona, A.; LeFloch, S.; Levy, D.; Hanfland, M. Structural phase transitions in CaSi2 under high pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, 11392−11397.

AUTHOR INFORMATION

Corresponding Authors

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

The manuscript was written through contributions of all authors. D


Article

Inorganic Chemistry (21) Palosz, W.; Wiedemeier, H. Residual gas pressures in sealed fused silica glass ampoules. J. Cryst. Growth 1993, 131, 193−198. (22) Palosz, W. Diffusive gas losses from silica glass ampoules at elevated temperatures. J. Cryst. Growth 1998, 191, 897−903. (23) Palosz, W. Residual gas in closed system I: development of gas in fused silica ampoules. J. Cryst. Growth 2004, 267, 475−483. (24) Petricek, V.; Dusek, M.; Palatinus, L. Crystallographic computing system JANA2006: general features. Z. Kristallogr. - Cryst. Mater. 2014, 229, 345−352. (25) Janzon, K.; Schafer, H.; Weiss, A. Structure of phase CaSi2. Z. Naturforsch., B: J. Chem. Sci. 1968, 23, 1544. (26) Evers, J. Transformation of 3-connected silicon nets in CaSi2. J. Solid State Chem. 1979, 28, 369−377. (27) Fahy, S.; Hamann, D. R. Electronic and structural properties of CaSi2. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41, 7587−7592. (28) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (29) Delley, B. J. Fast calculation of electrostatics in crystals and large molecules. J. Phys. Chem. 1996, 100, 6107−6110. (30) Delley, B. J. From molecules to solids with the DMol(3) approach. J. Chem. Phys. 2000, 113, 7756−7764. (31) Monkhorst, H.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188−5192. (32) Rousseau, D. L.; Bauman, R. P.; Porto, S. P. S. Normal mode determination in crystals. J. Raman Spectrosc. 1981, 10, 253−290. (33) Satta, G.; Profeta, G.; Bernardini, E.; Continenza, A.; Massidda, S. Electronic and structural properties of superconducting MgB2, CaSi2, and related compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 104507.

E


Lattice Dynamics of the Rhombohedral Polymorphs of CaSi2

Recommend Documents