Vibrational properties of 2D silica and kagome lattice materials.

November 9, 2016 - Little is known about vibrational properties of two-dimensional silica (2D-SiO₂) and its Raman spectrum. A study by European scientists with contribution of the SALVE project, now identified several previously uncharacterized vibrational states of 2D-SiO₂. At finite temperatures, the stability of the lattice is strongly influenced by phonon-phonon interaction, the study finds. It provides insights into 2D-silicas lattice type in general and also suggests a quick nondestructive method to detect 2D silica.

The researchers first became involved in the study of 2D SiO₂, which is one of the thinnest insulating materials and can be used in catalysis and for isolating graphene from metal substrates [1-6], after such a monolayer was accidentally grown at the Max-Planck-Institute in Stuttgart. After their groundbreaking results published in the journals Science, Nano Letters, and Scientific Reports [7-9], they now turn to investigate the vibrational properties of crystalline 2D silica.

“By studying the vibrational properties using a combination of Raman spectroscopy and High-Resolution Transmission Electron Microscopy (HRTEM), we identified signatures of crystalline and amorphous structures, and ascertained their origin by Density Functional Theory.” said Ute Kaiser, director of the SALVE project.

Using a combination of Raman spectroscopy and first-principle calculations, they performed an in-depth investigation of the lattice dynamics and showed that the crystalline 2D-SiO₂ structure actually represents a kagome lattice (Fig. 1). [10] The kagome lattice has long been a model system for theoretical studies of various physical properties, primarily magnetism, in systems with particular topology, but also mechanical properties. [11] It was theoretically shown that if the kagome lattice consists of rigid triangles that interact only with their nearest neighbor it is on the border of mechanical instability. Compression of the lattice would lead to rotations of the triangles, as shown in Fig. 1, at no cost in energy.

For their investigation, they assigned the Raman spectra to regions of 2D silica by correlated HR-TEM measurements using freestanding graphene over a TEM grid as sample support (Fig. 2). The atomic structure visible in the HR-TEM image confirms that the deposited layer on graphene indeed contains 2D-SiO₂ (Fig. 2i).

The Raman spectrum consists of an intensive narrow mode at 1045 cm–1 and much weaker peaks at 409, 454, 500, and 715 cm–1 (Figure 3a). According to several previous studies [13-15] of bulk systems that contained Si–O–Si bonds it was assigned to a Si–O–Si stretching mode when oxygen bridges silicon atoms with an angle of 180°. However it is not clear how this can be related to the significantly different 2D structure of 2D-SiO₂.

In the paper published in the journal ACS Nano Björkman et al. investigated the vibrational properties by DFT calculations (Figure 3). They found good agreement of experiment and theory for the peak at 1045 cm−1. This corresponds to the calculated Raman active E1g mode at 1053 cm−1, which an asymmetric Si–O–Si bond stretching mode illustrated in Figure 3a. With the exception of this mode, the calculations appear to consistently underestimate the vibrational frequencies by approximately 8−10%. [1] With this systematic error, the overall agreement is reasonably good, and the observed modes could be identified and symmetry labels could be assigned.

“These results enable us to use Raman spectroscopy as a quick and nondestructive method to identify the 2D-SiO₂ bilayer,” said Prof. Viera Skakalova from Vienna University. “Our studies are just the beginning of that search. The possibility of using these peaks as a measure of disorder in the sample, in a manner similar to the D peak in graphene, could be further investigated with access to samples with larger well-defined areas of 2D-SiO₂.”

The scientists also searched specifically for what might be responsible for the stability of 2D-SiO₂. As the ground state of 2D-SiO₂ is a kagome lattice at zero temperature, it should be instable under compressive strain. In the paper they identify the phonon modes typical of a kagome lattice, which are in the low-energy phonon spectrum (Fig. 4). The energy dependence on the normal mode coordinate for a series of strains revealed that the energy minimum is shifted away from zero, which leads to phonon–phonon interaction which at finite temperatures may serve to stabilize the crystal lattice. [16].

To confirm their assumption, they used molecular dynamics (MD) calculations in addition to DFT simulations. The stability of the kagome lattice was studied at 0 temperature and at 300 K for a series of biaxial strains. The new research indicates that for ε = < −1%, the kagome lattice collapses at 0 K, where unphysical negative frequencies arise (Figure 5e). The two kagome modes that consist of rigid rotations of tetrahedra, shown in green and red, will merge into a single unstable mode at the Γ point. By contrast, Figure 5h clearly shows the kagome modes remaining clearly identifiable at 300 K, stabilized by phonon−phonon interactions at finite temperature. At ε = −2% Figure 5I shows that the lattice does become unstable also at 300 K, but the distortion is not the simple rotation of the kagome lattice given by the B2u mode at the Γ point, but through the lowest, flat kagome mode, shown in red in Figure 4a, and at the M point.

The molecular dynamics calculations were used to show particle trajectories for two compressive strains for 300 K (Fig. 5a-c). It is clear that the atoms spread out significantly around their average positions as the lattice is compressed, but that the average positions are those of the undistorted structure, with no apparent rotation of the tetrahedra. The MD trajectories cannot show the small distortion at the M-point for ε = −2% on the time scale of the simulation. Only at a compressive strain of about ε = −4%, the kagome lattice folds up into a locked configuration, and the atoms become much more localized near their equilibrium positions (Figure S3). Thus, the kagome lattice is stabilized at finite temperature by the inclusion of phonon−phonon interactions from the anharmonic potential induced by the compression.

SALVE associate Arkady Krashenninikov from the Universities of Dresden and Aalto said the study also highlights the fundamental insights obtained into the structural stability and properties of kagome lattices in general.

“This work is an example of another 2D material, which was for the first time synthesized and studied in recent years.” Ute Kaiser added. “As already the important conclusion that could be drawn from our study of the amorphous phase of 2D silica for amorphous materials in general, this study not only improves our understanding of crystalline 2D silica but also of common properties of kagome lattice structure materials.”

Resource: Björkman, T., Skakalova, V., Kurasch, S., Kaiser, U., Meyer, J. C., Smet, J. H., & Krasheninnikov, A. V. (2016). Vibrational properties of a two-dimensional silica kagome lattice. ACS nano, 10: 10929, doi: 10.1021/acsnano.6b05577, [PDF], see also the supporting information.