Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti${}_{3}$SiC${}_{2}$ determined by polarized x-ray spectroscopy and Seebeck measurements

Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti $_{3}$ SiC $_{2}$ determined by polarized x-ray spectroscopy and Seebeck measurements

Martin Magnuson, Maurizio Mattesini, Ngo Van Nong, Per Eklund, and Lars Hultman

Phys. Rev. B 85, 195134 – Published 22 May 2012

Abstract

Nanolaminated materials exhibit characteristic magnetic, mechanical, and thermoelectric properties, with large contemporary scientific and technological interest. Here we report on the anisotropic Seebeck coefficient in nanolaminated Ti $_{3}$ SiC $_{2}$ single-crystal thin films and trace the origin to anisotropies in element-specific electronic states. In bulk polycrystalline form, Ti $_{3}$ SiC $_{2}$ has a virtually zero Seebeck coefficient over a wide temperature range. In contrast, we find that the in-plane (basal $a b$ ) Seebeck coefficient of Ti $_{3}$ SiC $_{2}$ , measured on single-crystal films, has a substantial and positive value of 4–6 $μ$ V/K. Employing a combination of polarized angle-dependent x-ray spectroscopy and density functional theory we directly show electronic structure anisotropy in inherently nanolaminated Ti $_{3}$ SiC $_{2}$ single-crystal thin films as a model system. The density of Ti $3 d$ and C $2 p$ states at the Fermi level in the basal $a b$ plane is about 40 $%$ higher than along the $c$ axis. The Seebeck coefficient is related to electron and hole-like bands close to the Fermi level, but in contrast to ground state density functional theory modeling, the electronic structure is also influenced by phonons that need to be taken into account. Positive contribution to the Seebeck coefficient of the element-specific electronic occupations in the basal plane is compensated by 73 $%$ enhanced Si $3 d$ electronic states across the laminate plane that give rise to a negative Seebeck coefficient in that direction. Strong phonon vibration modes with three to four times higher frequency along the $c$ axis than along the basal $a b$ plane also influence the electronic population and the measured spectra by the asymmetric average displacements of the Si atoms. These results constitute experimental evidence explaining why the average Seebeck coefficient of Ti $_{3}$ SiC $_{2}$ in polycrystals is negligible over a wide temperature range. This allows the origin of anisotropy in physical properties of nanolaminated materials to be traced to anisotropies in element-specific electronic states.

Received 29 May 2011

DOI:https://doi.org/10.1103/PhysRevB.85.195134

Authors & Affiliations

Martin Magnuson¹, Maurizio Mattesini^2,3, Ngo Van Nong⁴, Per Eklund¹, and Lars Hultman¹

¹Thin Film Physics Division, Department of Physics, Chemistry and Biology, IFM, Linköping University, SE-58183 Linköping, Sweden
²Departamento de Física de la Tierra, Astronomía y Astrofísica I, Universidad Complutense de Madrid, Madrid, E-28040, Spain
³Instituto de Geociencias (CSIC-UCM), Facultad de CC. Físicas, E-28040 Madrid, Spain
⁴Department of Energy Conversion and Storage, Technical University of Denmark, Risö Campus, 4000 Roskilde, Denmark

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Vol. 85, Iss. 19 — 15 May 2012

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Images

Figure 1
Illustration of the hexagonal crystal structure of Ti $_{3}$ SiC $_{2}$ and electronic orbitals of the chemical bonds across ( $d_{3 z^{2} - r^{2}}$ , $p_{z}$ ) and in ( $d_{x y}$ , $d_{x^{2} - y^{2}}$ , $p_{x}$ , $p_{y}$ ) the laminate plane. The Ti atoms have two different sites, denoted Ti $_{I}$ and Ti $_{II}$ and every fourth layer of the TiC slabs is interleaved by a pure Si layer.Reuse & Permissions
Figure 2
Top-right: Experimental Ti $2 p$ SXA-TFY spectra of Ti $_{3}$ SiC $_{2}$ following the $2 p_{3 / 2, 1 / 2}$ $\to$ $3 d$ dipole transitions. Left top-to-bottom: Resonant Ti $L_{2, 3}$ SXE spectra with excitation energies 458.0, 459.7 eV, indicated by the vertical arrows in the SXA spectra, and nonresonant spectra at 490.0 eV. Bottom: Calculated spectra of the two different crystallographic Ti sites, Ti $_{I}$ and Ti $_{II}$ using the experimental spin-orbit peak splittings and $L_{3} / L_{2}$ branching ratios.Reuse & Permissions
Figure 3
Top-right: C $1 s$ SXA-TFY spectra of Ti $_{3}$ SiC $_{2}$ . Left top-to-bottom: Resonant spectra excited at 283.0 and 285.3 eV indicated by the vertical arrows and nonresonant C $K$ SXE spectra at 310.0 eV. All spectra are plotted on a photon energy scale (top) and a relative energy scale (bottom) with respect to the top of the valence band using the C $1 s$ core-level x-ray photoelectron spectroscopy (XPS) binding energy of 282.0 eV measured on the same sample.Reuse & Permissions
Figure 4
Top panel: Si $L_{1}$ SXE spectra of Ti $_{3}$ SiC $_{2}$ excited at 180 eV in comparison to pure amorphous Si (a-Si). The dashed curves are corresponding calculated $3 p_{x y}$ and $3 p_{z}$ spectra with an $L_{2, 3}$ spin-orbit splitting of 0.646 eV and an $L_{3}$ / $L_{2}$ ratio of 2:1. Bottom panel: Si $L_{2, 3}$ SXE spectra excited at 120 eV in comparison to amorphous Si. The dashed curves are corresponding calculated $3 s d_{x y, x^{2} - y^{2}}$ and $3 s d_{3 z^{2} - r^{2}}$ spectra. A common energy scale with respect to the top of the valence band edge (vertical dotted line) is indicated between the top and bottom panels.Reuse & Permissions
Figure 5
Top panel: Calculated phonon frequency spectra (PhDOS) of the Si atoms in Ti $_{3}$ SiC $_{2}$ . Bottom panel: Calculated Si $3 d$ spectra of Ti $_{3}$ SiC $_{2}$ for in-plane ( $x y$ -basal plane) displacement and displacement along the $c$ axis (out-of-plane). The selected core-excited Si atom has been moved either along the $x y$ plane or perpendicular to it. The applied in-plane displacements correspond to 0.615 Å along both $x$ and $y$ crystallographic axes, giving a total displacement vector modulus of 0.870 Å. The out-of-plane displacement vector modulus is 0.884 Å along the $z$ axis.Reuse & Permissions
Figure 6
Calculated and measured Seebeck coefficients of Ti $_{3}$ SiC $_{2}$ . (a) $S_{x x}$ calculation,[16] (b) $S_{x x}$ measurement (present work), (c) polycrystal Ti $_{3}$ SiC $_{2}$ .[11]Reuse & Permissions

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