Article

# Electronic-structure origin of the anisotropic thermopower of nanolaminated Ti3SiC2 determined by polarized x-ray spectroscopy and Seebeck measurements

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## 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 Ti3SiC2 single-crystal thin films and trace the origin to anisotropies in element-specific electronic states. In bulk polycrystalline form, Ti3SiC2 has a virtually zero Seebeck coefficient over a wide temperature range. In contrast, we find that the in-plane (basal ab) Seebeck coefficient of Ti3SiC2, measured on single-crystal films has a substantial and positive value of 4-6 muV/K. Employing a combination of polarized angle-dependent x-ray spectroscopy and density functional theory we directly show electronic structure anisotropy in inherently nanolaminated Ti3SiC2 single-crystal thin films as a model system. The density of Ti 3d and C 2p states at the Fermi level in the basal ab-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 3d 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 ab-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 Ti3SiC2 in polycrystals is negligible over a wide temperature range.

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... For Cr, we find a x, y-displacement of 0.097 Å and a z-displacement of 0.114 Å from the phonon calculations. For Ge, the x, y-displacement is 0.128 Å and the z-displacement 0.081 Å, while for the C-atoms, the x, y-displacement is 0.085 Å and the z-displacement 0.109 Å. Rapidly moving atoms is known to change the electronic DOS at E F [44]. However, the relatively small magnitude of these displacements alone cannot account for the large difference in DOS between experiment and theory for Cr 2 GeC. ...
... The lowest-frequency vibrations are associated with the Ge atoms in Cr 2 GeC, similarly to the case of Al in Cr 2 AlC [36] and Ti 3 AC 2 (A = Si, Al, and Ge), where the lowest-energy vibrations are from the A element [37, 44, 47]. This finding is consistent with the fact that the Cr–C bonding type is the stiffest. ...
... Here, for Cr 2 GeC, the anisotropy of the C-K edge is present in the XAS and XES data presented infigure 3, although it may also be somewhat influenced by the presence of amorphous C, resulting from contamination of the sample. The anisotropy is consistent with the case of other M AX n n 1 + —phase systems such as V 2 GeC [38] and Ti 3 SiC 2 [44]. Although the local symmetry at each atomic site is important, the distribution of the electronic states also obeys the whole k-space topology of the M AX n n 1 + -phase unit cell, that is not highly symmetric. ...
Article
The anisotropy in the electronic structure of the inherently nanolaminated ternary phase Cr$_{2}$GeC is investigated by bulk-sensitive and element selective soft x-ray absorption/emission spectroscopy. The angle-resolved absorption/emission measurements reveal differences between the in-plane and out-of-plane bonding at the (0001) interfaces of Cr$_{2}$GeC. The Cr $L_{2,3}$, C $K$, and Ge $M_{1}$, $M_{2,3}$ emission spectra are interpreted with first-principles density-functional theory (DFT) including core-to-valence dipole transition matrix elements. For the Ge $4s$ states, the x-ray emission measurements reveal two orders of magnitude higher intensity at the Fermi level than DFT within the General Gradient Approximation (GGA) predicts. We provide direct evidence of anisotropy in the electronic structure and the orbital occupation that should affect the thermal expansion coefficient and transport properties. As shown in this work, hybridization and redistribution of intensity from the shallow $3d$ core levels to the $4s$ valence band explain the large Ge density of states at the Fermi level.
... This was demonstrated by Chaput et al. who showed that the negligible Seebeck coefficient of a polycrystalline Ti 3 SiC 2 sample could be understood from the compensation of electronlike states along the c axis by holelike states within the basal plane orientation at the Fermi level. 5,20,21 An accurate description of both the electronic structure and the transport properties is all the more desirable that MAX phases exhibit complex Fermi surfaces with generally more than two bands [see Fig. 1(b) for Ti 2 AlC], 22 and that the chemical bonding in these materials is based on complex charge transfers involving metallic, ionic, and covalent bonds. 23 The aim of this paper is to understand the anisotropy of Ti 2 AlC transport properties by characterizing both charge carriers and the anisotropy of the resistivity. ...
... The good results obtained for the bulk sample could then be due to cancellation of errors between the different components of the Hall tensor when computing the trace. This is in agreement with recently published results on the Seebeck coefficient of Ti 3 SiC 2 , 21 where it is shown that the in-plane component obtained with similar calculations is 25% lower than the experimental value at room temperature, whereas the trace of the Seebeck coefficient gave very good results compared to experimental data obtained on a polycrystalline sample. 20 The validity of the isotropic relaxation time approximation is however not directly comparable between Hall constants and Seebeck coefficient. ...
... This explanation is coherent with Ti 3 SiC 2 Seebeck coefficient data which were recently published. 21 The resistivity measurements also clearly evidence a strong anisotropy of Ti 2 AlC electronic properties. Comparing the data recorded on the thin film to those obtained on the bulk sample, which are interpreted in terms of an effective medium approach, it is shown that the room temperature resistivity ρ zz is more than one order of magnitude larger than ρ xx . ...
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... In the case of polycrystalline Ti 3 SiC 2 , thermopower was found negligible over a wide temperature range [15], a fact later explained by a compensation of electron and holelike contributions (although those contributions take place out of or in plane, respectively, and are thus not compensated in single crystals, polycrystals average them over all random directions, thus leading to a net zero thermopower). For single crystals, a substantial thermopower anisotropy was predicted [16][17][18], and later confirmed by in-plane measurements performed on single-crystalline thin films [19]. A prominent role is played by highly anisotropic intertwined pockets centered on the H point of the hexagonal Brillouin zone (BZ). ...
... In contrast, all other bands are mainly delocalized in the ab plane. As explained in [18,19], the peculiar thermopower properties of polycrystalline Ti 3 SiC 2 were previously assigned to the prevailing influence of bands 49 and 50 [16]. From the point of view of thermoelectric power, the carriers in band 50 were found to behave as electrons along c [16], and those of band 49 as holes. ...
... The band showing a d z 2 component would show the highest signal in the ARPES spectra at a low angle while bands with other orbital character would be visible at a higher angle, closer to the BZ boundaries. Although Si orbitals participate to a lesser extent in the states at E F , and are not discussed here, they are key for ensuring delocalization along c, and were, for instance, experimentally evidenced and discussed in [19]. ...
Article
An in-depth study of the Fermi surface and electronic structure of the ternary nanolamellar carbide Ti3SiC2 is reported. The outputs of angle-resolved photoemission spectroscopy (ARPES) measured on single crystals and density functional theory calculations are systematically compared. The band structure is found to be dominated by Ti d orbitals near the Fermi level. Band inversions near K points are responsible for the intricate shape of the Ti3SiC2 pockets. Previous theory found that those pockets were giving opposite contributions leading to zero thermoelectric power in polycrystalline samples. Here we directly visualize them by ARPES, describe their precise shape, and examine the way they should behave regarding thermoelectric power. The presence of linear band crossings and the effect of spin-orbit coupling on the near Fermi level electronic structure are discussed, as well as potential consequences for magnetotransport and spin Hall effect.
... This was demonstrated by Chaput et al. who showed that the negligible Seebeck coefficient of a polycrystalline Ti 3 SiC 2 sample could be understood from the compensation of electronlike states along the c axis by holelike states within the basal plane orientation at the Fermi level. 5,20,21 An accurate description of both the electronic structure and the transport properties is all the more desirable that MAX phases exhibit complex Fermi surfaces with generally more than two bands [see Fig. 1(b) for Ti 2 AlC], 22 and that the chemical bonding in these materials is based on complex charge transfers involving metallic, ionic, and covalent bonds. 23 The aim of this paper is to understand the anisotropy of Ti 2 AlC transport properties by characterizing both charge carriers and the anisotropy of the resistivity. ...
... The good results obtained for the bulk sample could then be due to cancellation of errors between the different components of the Hall tensor when computing the trace. This is in agreement with recently published results on the Seebeck coefficient of Ti 3 SiC 2 , 21 where it is shown that the in-plane component obtained with similar calculations is 25% lower than the experimental value at room temperature, whereas the trace of the Seebeck coefficient gave very good results compared to experimental data obtained on a polycrystalline sample. 20 The validity of the isotropic relaxation time approximation is however not directly comparable between Hall constants and Seebeck coefficient. ...
... This explanation is coherent with Ti 3 SiC 2 Seebeck coefficient data which were recently published. 21 The resistivity measurements also clearly evidence a strong anisotropy of Ti 2 AlC electronic properties. Comparing the data recorded on the thin film to those obtained on the bulk sample, which are interpreted in terms of an effective medium approach, it is shown that the room temperature resistivity ρ zz is more than one order of magnitude larger than ρ xx . ...
Article
Full-text available
The anisotropy of Ti2AlC transport properties is investigated focusing on the Hall effect and resistivity vs temperature measurements performed on a highly (000l)-oriented thin film and a bulk polycrystalline sample. Experimental data are interpreted on the basis of density functional theory calculations including transport coefficients obtained with the Boltzmann semiclassical transport equation in the isotropic relaxation time approximation. It is shown that the Hall constant is independent of the temperature and that the charge-carrier sign depends on the investigated crystallographic orientation. Charge carriers exhibit a holelike character along the basal plane of the Ti2AlC, whereas the bulk sample Hall constant is negative. The resistivity anisotropy is also evidenced: using an effective medium approach, the room temperature basal plane resistivity is shown to be more than one order of magnitude lower than that along the c axis. This very important anisotropy is shown to result from the anisotropy of the Fermi surface increased by electron-phonon interactions. These interactions are much more important along the c axis than within the basal plane, a situation opposite to that observed in literature for Ti2GeC where resistivity was reported to be isotropic.
... As a consequence, even if DFT calculations predict that many MAX phases would show a quasi-2D electronic band structure (see, e.g., [3,10,17]), direct and reliable measurements of the band structure anisotropy are thus required in order to decorrelate effects due to the electronic structure from effects due to the relaxation time. Concerning electronic structure, anisotropy is most often determined by comparing spectra obtained by various techniques to those predicted by DFT calculations [18][19][20][21][22][23]. The anisotropy of polarization-dependent soft x-ray emission spectra was reported for thin layers of V 2 GeC [18], Ti 3 SiC 2 [19], and Cr 2 GeC [20]. ...
... Concerning electronic structure, anisotropy is most often determined by comparing spectra obtained by various techniques to those predicted by DFT calculations [18][19][20][21][22][23]. The anisotropy of polarization-dependent soft x-ray emission spectra was reported for thin layers of V 2 GeC [18], Ti 3 SiC 2 [19], and Cr 2 GeC [20]. It is directly due to the anisotropy of electronic structure, valence bonds, and hybridization. ...
Article
We report an experimental and theoretical study of the electronic band structure and Fermi surfaces (FSs) of V2AlC single crystals using angle-resolved photoemission spectroscopy and density functional theory (DFT) calculations. We provide evidence of the existence of equivalent, complex hole FSs with a nearly tubular form along the c axis, and of an intricate electron FS exhibiting tubes parallel to c connected to one another by smaller tubes with axes parallel to the ab plane. The electron FS thus exhibits a small delocalization along the c axis. The local orbital character of each observed band is experimentally and theoretically assessed. DFT calculations show an excellent agreement with experiment. We also report the observation of an unstable surface state.
... Electron energy-loss spectroscopy (EELS) [9] was used to investigate their dielectric response at the nanometer scale [10,11]. Other studies were based on polarized x-ray emission or absorption spectroscopies [12,13] in order to investigate the anisotropy of the site-projected densities of states of the different M, A, and X elements. ...
Article
The electronic conductivity anisotropy of Ti3SiC2is directly evidenced from data collected on (i) a thin film epitaxially grown on a (11-20)-oriented SiC single crystal and (ii) a single crystal. Density Functional Theory calculations, including linear response approach, and coupled to a Bloch-Grüneisen model show that the electron-phonon interactions are mainly responsible for the observed anisotropy. Detailed analysis of the electron-phonon coupling constants allows for the rationalization of these scattering processes in terms of the Ti3SiC2nanostructure, giving insights into the possibility to modify the electron-phonon interaction in this system by substitution effects.
... XES and XAS, combined with first-principles calculations, were used to study the electronic structure of Ti 2 AlC [29], Ti 2 AlN [30], Ti 4 SiC 3 [31], [32]. However, studies specifically dedicated to electronic structure anisotropy and polarization-dependent core-level spectroscopies have been limited to V 2 GeC [33], Ti 3 SiC 2 [34], and Ti 3 AlC 2 [35]. The spectroscopic data (EELS, XES, or XAS) are generally compared to the local density of states (LDOS) obtained from band-structure calculations, which do not include the core-hole effect [36] inherently involved in such experiments. ...
Article
Full-text available
The anisotropy of the electronic structure of the MAX phase Cr2AlC has been investigated by electron-energy-loss spectroscopy (EELS) at the C K edge, and x-ray-absorption spectroscopy (XAS) at the Al K, Cr L2,3, and Cr K edges. The experimental spectra were interpreted using either a multiple-scattering approach or a full-potential band-structure method. The anisotropy is found to be small around C atoms because of the rather isotropic nature of the octahedral site, and of the averaging of the empty C p states probed by EELS at the C K edge. In turn, a pronounced anisotropy of the charge distribution around Al atoms is evidenced from polarized XAS measurements performed on textured Cr2AlC sputtered thin films. From the analysis of the XAS data using the multiple-scattering feff code, it is demonstrated that the probed thin film is constituted of 70% (0001) and 30% (101¯3) grains oriented parallel to the film surface. A decomposition of the calculated spectrum in coordination shells allows for the ability to connect XAS fine structures to the Cr2AlC structure. Combining high-resolution data with up-to-date multiple-scattering calculations, it is shown that the crystalline orientations of the grains present in a probe of 100×100 μm2 can be determined from the Cr K edge. Interestingly, it is also revealed that a static disorder is involved in the studied thin films. These findings highlight that, given the overall agreement between experimental and calculated spectra, the Cr2AlC electronic structure is accurately predicted using density functional theory.
... Therefore, the Seebeck coefficient macroscopically sums up to zero in a randomly oriented sample. This was experimentally confirmed by Magnuson et al [231], who demonstrated that the in-plane Seebeck coefficient is positive and substantial and evidenced the anisotropic states in the electronic structures, which is the underlying source of the nearzero Seebeeck coefficient in bulk, polycrystalline Ti 3 SiC 2 . ...
Article
Full-text available
Inherently and artificially layered materials are commonly investigated both for fundamental scientific purposes and for technological application. When a layered material is thinned or delaminated to its physical limits, a two-dimensional (2D) material is formed and exhibits novel properties compared to its bulk parent phase. The complex layered phases known as 'MAX phases' (where M = early transition metal, A = A-group element, e.g. Al or Si, and X = C or N) are an exciting model system for materials design and the understanding of process-structure-property relationships. When the A layers are selectively etched from the MAX phases, a new type of 2D material is formed, named MXene to emphasize the relation to the MAX phases and the parallel with graphene. Since their discovery in 2011, MXenes have rapidly become established as a novel class of 2D materials with remarkable possibilities for composition variations and property tuning. This article gives a brief overview of MAX phases and MXene from a thin-film perspective, reviewing theory, characterization by electron microscopy, properties and how these are affected by the change in dimensionality, and outstanding challenges.
... For the combined defects, the notation (a), (b), (c), and (d) refers to Fig. 6 The charge carriers [electrons (n) and holes (p)] would then compete and cancel out the induced Seebeck voltage. This is in analogy with metals, which have low Seebeck coefficients, and an extreme case is Ti 3 SiC 2 with S = 0 over a wide temperature range [63][64][65]. In the present case, both p-type and n-type behaviors were observed depending on the composition with a transition at room temperature happening at δ = -0.03 in CrN 1+δ . ...
Article
Full-text available
We report the results of a combined experimental and theoretical study on nonstoichiometric CrN 1+δ thin films grown by reactive magnetron sputtering on c-plane sapphire and MgO (100) substrates in an Ar/N 2 gas mixture using different percentages of N 2. There is a transition from n-type to p-type behavior in the layers as a function of nitrogen concentration varying from 48 to 52 at. % in CrN films. The compositional change follows a similar trend for all substrates, with a N/Cr ratio increasing from approximately 0.7 to 1.06-1.11 by increasing the percentage of N 2 in the gas flow ratio. As a result of the change in stoichiometry, the lattice parameter and the Seebeck coefficient increase together with the increase of N in CrN 1+δ ; in particular, the Seebeck value coefficient transitions from-50 μV K-1 for CrN 0.97 to +75 μV K-1 for CrN 1.1. Density functional theory calculations show that Cr vacancies can account for the change in the Seebeck coefficient, since they push the Fermi level down in the valence band, whereas N interstitial defects in the form of N 2 dumbbells are needed to explain the increasing lattice parameter. Calculations including both types of defects, which have a strong tendency to bind together, reveal a slight increase in the lattice parameter and a simultaneous formation of holes in the valence band. To explain the experimental trends, we argue that both Cr vacancies and N 2 dumbbells, possibly in combined configurations, are present in the films. We demonstrate the possibility of controlling the semiconducting behavior of CrN with intrinsic defects from n to p type, opening possibilities to integrate this compound in energy-harvesting thermoelectric devices.
... In one such effect the (charge) Seebeck Coefficient changes as a function of a device's magnetization configuration -known as the magneto-Seebeck effect or magnetothermopower -in analogy with the magnetoresistance. Recently observed experimentally [2,3,8,10,11,15,17] and studied theoretically [6,7,9], the magneto-Seebeck effect enables one to tune the thermal properties of an MTJ via magnetic field, potentially enabling thermal spin-logic or assisting in the recycling of wasted heat. We numerically study two devices: CoPt|MgO|Pt (which we call an anisotropic MTJ) and CoPt|MgO|CoPt (a normal MTJ). ...
Article
Full-text available
We theoretically investigate the Tunneling Anisotropic Magneto-Seebeck effect in a realistically-modeled CoPt|MgO|Pt tunnel junction using coherent transport calculations. For comparison we study the tunneling magneto-Seebeck effect in CoPt|MgO|CoPt as well. We find that the magneto-Seebeck ratio of CoPt|MgO|Pt exceeds that of CoPt|MgO|CoPt for small barrier thicknesses, reaching 175% at room temperature. This result provides a sharp contrast to the magnetoresistance, which behaves oppositely for all barrier thicknesses and differs by one order of magnitude between devices. Here the magnetoresistance results from differences in transmission brought upon by changing the tunnel junction's magnetization configuration. The magneto-Seebeck effect results from variations in asymmetry of the energy-dependent transmission instead. We report that this difference in origin allows for CoPt|MgO|Pt to possess strong thermal magnetic-transport anisotropy.
... Electronic anisotropy in band structure is due to a few or no bands crossing when E F is moving only out-of-plane directions with several bands crossing the E F in the in-plane directions. This phenomenon is responsible for non-identical electric conductivity in the c-axis and in the basal planes of bulk MAX phases and thin-films [83][84][85][86]. The width of conduction bands increases, and unoccupied valance bands move to downwards at Γ (shown by black arrow) as C is replaced by N atom at the X-site of Ti 2 ZnX. ...
Article
Full-text available
MAX phase family has been extended by the addition of late transition metals at the A-site with the expectation of diverse functional properties. Here, we present our systematic density functional investigation on the thermodynamic and phonon stabilities, elastic properties, including elastic constants, elastic moduli and elastic anisotropy of newly synthesized Ti2ZnX (X = C, N) phases in comparison with conventional Ti2AlX (X = C, N). Due to the smaller size of N as compared to C, the unit cell dimension is reduced when C atoms are replaced by N atoms at the X-site. The Ti2ZnC and Ti2ZnN are stable at the equilibrium volume of 110.84 Å3 and 105.70 Å3. The thermodynamic, mechanical and dynamical stabilities are validated by estimating the formation energies, elastic constants and phonon dispersions, respectively. The elastic properties of Ti2ZnN are less anisotropic as compared to those of Ti2ZnC. To understand the thin-film characteristics in Ti2ZnX, the surface properties with (001)-terminated slabs are investigated. Both Ti2ZnX bulk and (001)-surfaces exhibit metal-like electronic structures. There is a strong covalent bonding between Ti-X and Ti-Zn atoms confirmed by the charge density map and Mulliken population analysis. Additional states are generated at the Fermi level (EF) due to the unusual d-p states hybridization between Ti and Zn atoms. The anisotropy in chemical bonding is confirmed by the cleavage energy difference between Ti-X and Ti-Zn. Here, Ti(X)-001 and Zn-001 terminations are stable surfaces; however, in terms of chemical potentials, Zn-001 termination is the most favourable in Ti2ZnX.
... So far, most of the produced samples were highly poly- crystalline, so that it was not possible to evidence anisotropic physical properties in a straightforward manner. In recent years, several groups have produced single crystals of MAX phases in the form of bulk crystals [11][12][13] or thin layers [14][15][16][17]. It thus becomes feasible to investigate anisotropic physical properties such as electrical transport [16]. ...
Article
Full-text available
We propose a general, yet simple model for describing the weak field magnetotransport properties of nearly-free electrons in two-dimensional hexagonal metals. We modify this model so as to apply it to the magnetotransport properties of the Mn+1AXn phases, a particular class of nanolamellar carbides and nitrides. We argue that the values of the in-plane Hall coefficient and the in-plane parabolic magnetoresistance are due to the specific shape of the Fermi surface of almost two-dimensional hole and electron bands. If the contribution of the electron pockets to in-plane resistivity is often (but not always) predicted to be a minor one, in contrast, both holes and electrons should substantially contribute to the overall value of the in-plane Hall coefficient. The relevance of our model is supported by elementary considerations and a set of experimental data obtained from single crystals of V2AlC and Cr2AlC. In particular, we obtain a high ratio between the in-plane (ρab) and parallel to the c axis (ρc) resistivities.
... The density of states (DOS) at E F is thus most often quite high [18]. Numerous previous works already describe features related to the electronic structure and some of its anisotropies, both on theoretical and experimental grounds (see, e.g., [28][29][30][31][32][33]). They are more exhaustively listed in a recent review article up to year 2017 [24]. ...
Article
The nanolamellar M2AC or carbon-based “211 MAX” phases, where M is an early transition metal, A belongs to groups 13–15, and C is carbon, can be described by rigid band models. The same band model applies to all possible A elements belonging to a given group of the periodic table. Changing M for a given A is then equivalent to shifting the Fermi energy EF through a band structure common to all phases in the group. This is shown by comparing predictions of density functional theory (DFT) to angle-resolved photoemission spectroscopy (ARPES) measurements. In particular, the Fermi surface of a given Al-based MAX phase can be obtained with an acceptable degree of accuracy by simply selecting the appropriate ARPES isoenergy surface of another Al-based phase. In V2AlC, and in addition to conventional metal energy bands, both DFT and ARPES show the existence of a gapped nodal line located around 0.2 eV below EF or complex crossing points at EF with Dirac-like features in some directions. Application of the rigid band model suggests that these topological features as well as others, also predicted by DFT, can be positioned at or close to EF by an appropriate choice of M and A, or by using an appropriate combination of various M and A elements.
... The density of states (DOS) at E F is thus most often quite high [18]. Numerous previous works already describe features related to the electronic structure and some of its anisotropies, both on theoretical and experimental grounds (see, e.g., [28][29][30][31][32][33]). They are more exhaustively listed in a recent review article up to year 2017 [24]. ...
Conference Paper
We report a study of the electronic structure of 211 MAX phases and how relatively simple rigid band models can equally describe the band structures (BSs) and Fermi surfaces (FSs) of those compounds. Rigid band structures were built up from Density Functional Theory (DFT) calculations, but their applicability and limits have been tested by comparing their outcomes with experimental results from Angle Resolved Photoemission Spectroscopy (ARPES) on Cr2AlC, V2AlC and Ti2SnC. The charge transfer between A, M, and X atoms was also assessed. A remarkable agreement is found between theory and experiment, therefore confirming the applicability of rigid band models to describe MAX phases electronic structure. From those results, we propose a new classification of the 211 MAX phases.
... Nevertheless, such an intrinsic band structure anisotropy is similar to that of typical hexagonal-close-packed materials [37], and therefore cannot be used to quantitatively explain the peculiar transport properties of Cr-containing MAX phases. In this respect, scattering processes and charge carrier-phonon coupling should be taken into account [38]. ...
Article
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The magnetic properties, electronic band structure and Fermi surfaces of the hexagonal Cr(2)GeC system have been studied by means of both generalized gradient approximation (GGA) and the +U corrected method (GGA + U). The effective U value has been computed within the augmented plane wave theoretical scheme by following the constrained density functional theory formalism of Anisimov and Gunnarsson (1991 Phys. Rev. B 45 7570-74). On the basis of our GGA + U calculations, a compensated antiferromagnetic spin ordering of Cr atoms has been found to be the ground-state solution for this material, where a Ge-mediated super-exchange coupling is responsible for an opposite spin distribution between the ABA stacked in-plane Cr-C networks. Structural properties have also been tested and found to be in good agreement with the available experimental data. Topological analysis of Fermi surfaces has been used to qualitatively address the electronic transport properties of Cr(2)GeC, and found an important asymmetrical carrier-type distribution within the hexagonal crystal lattice. We conclude that an appropriate description of the strongly correlated Cr d electrons is an essential issue for interpreting the material properties of this unusual Cr-based MAX phase.
... This behavior is referred to as electronic anisotropy. The electronic anisotropy has already been reported experimentally for many bulk MAX phases and thin-films, however, the experimental evidences for M 3 AuC 2 phases are yet to come [65][66][67][68]. Fig. 3 shows the total and partial density of states (DOS) for M 3 AuC 2 in which a finite value of total DOS at the E F indicates metallic characteristic. ...
Article
Using first-principles density functional theory (DFT), the ground state physical properties of the newly synthesized noble-metal-containing Ti3AuC2 MAX phase have been investigated. The effect of transition-element Ti replacement (V and Cr) on physical properties, including structural, elastic, electronic, thermal, and optical are presented. The optimized lattice parameters of Ti3AuC2 MAX phase are in good agreement with the experimental values and decrease when we replace Ti with V and then Cr. The magnetic properties of M3AuC2 are predicted by using generalized gradient approximation (GGA) incorporating onsite electron correlation parameter (Hubbard U parameter) within DFT. Out of three studied MAX phases, V3AuC2 and Cr3AuC2 phases exhibit magnetism. The thermodynamical stability of M3AuC2 (M = Ti, V, and Cr) phases is discussed by the formation enthalpy with respect to their most competing phases. The electronic structure reveals that these phases have metallic nature and are electrically anisotropic. The M-element replacement has an effect on the bonding properties of M3AuC2. The bonding between M-C is in the order of Cr3AuC2 > V3AuC2 > Ti3AuC2 according to their peak positions and heights of the density of states in the occupied site, which is also confirmed from the charge density distribution. The elastic properties indicate that M3AuC2 phases are ductile, machinable, less stiff, and better resistant to thermal shock and are elastically anisotropic. To understand the properties of M3AuC2 for the extreme environment, we employed a quasi-harmonic Debye model at the pressure and temperature range of 0-50 GPa and 0-1600 K, respectively. Additionally, we evaluated thermal conductivity and melting temperature to further understand the potential of these MAX phases in coating applications at elevated temperatures. In relation to optical properties, these MAX phases have a reasonable absorption coefficient in the visible as well as in the ultra-violet regions. The reflectivity of M3AuC2 phases is polarization-dependent and of 45 % against the visible region, which reveals its potential as a coating material to minimize solar heating.
... This is analogous to metals, which have low Seebeck coefficients, an extreme case being Ti 3 SiC 2 with S = 0 over a wide temperature range. [35][36][37] As observed for CrN 1.18 , a direct consequence of the presence of the two types of charge carrier in similar quantities in the material is the reduction in the absolute Seebeck coefficient to low negative values (0 to −50 µV·K −1 ) compared with the values of −150 to −300 µV·K −1 reported in the literature. 15,[28][29][30] In contrast, the Cr 0.96 Al 0.04 N 1.17 thin film exhibited positive Seebeck coefficients of around +140 µV·K −1 in the 200-350 Table I. 2θ and d-spacing values of the diffraction peaks of the CrN 1.18 film, the reference of the cubic CrN from ICDD data, and a possible cubic superstructure. ...
Article
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Thermoelectric properties of chromium nitride (CrN)-based films grown on c-plane sapphire by dc reactive magnetron sputtering were investigated. In this work, aluminum doping was introduced in CrN (degenerate n-type semiconductor) by co-deposition. Under the present deposition conditions, over-stoichiometry in nitrogen (CrN1+δ) rock-salt structure is obtained. A p-type conduction is observed with nitrogen-rich CrN combined with aluminum doping. The Cr0.96Al0.04N1.17 film exhibited a high Seebeck coefficient and a sufficient power factor at 300 °C. These results are a starting point for designing p-type/n-type thermoelectric materials based on chromium nitride films, which are cheap and routinely grown on the industrial scale.
Article
Superconductivity of Nb2AlC has been previously reported, but the origin is not clear. In this paper, in situ Raman spectra of Nb2AlC are measured in the temperature range from 80 to 380 K at ambient pressure. The line-width of E2g (ω1) mode increases with temperature which originates from the anharmonic phonon–phonon scattering. On the contrary the line-widths of E2g (ω2) and A1g (ω4) modes decrease continuously at elevated temperature. The phenomenon is explained by the electron–phonon coupling. The origin of superconductivity is therefore interpreted by the coupling of Nb 4d electrons with E2g (ω2) and A1g (ω4) phonon modes. Copyright © 2013 John Wiley & Sons, Ltd.
Article
In this paper, in situ Raman spectra of Ta2AlC are measured in the temperature range of 80–500 K at ambient pressure. The frequencies of the Raman modes decrease with increasing temperature, which have been explained by the anharmonic and thermal expansion effects. The line-width of E2g (ω3) mode increases at elevated temperatures, which is found to be due to the anharmonic phonon–phonon scatterings. On the other hand, the line-widths of E2g (ω1) and A1g (ω4) modes decrease continuously with increasing temperature, which is explained by the electron–phonon couplings of these two phonon modes with the Ta 5d electrons. The electron–phonon coupling strengths are obtained both in experiments and density functional calculations. Finally, Ta2AlC is predicted to be a new superconductive MAX phase. Copyright © 2014 John Wiley & Sons, Ltd.
Article
Single crystalline platelets of the nanolaminated Cr2AlC phase have been produced by high temperature solution growth, with typical areas in the range of a few mm2. We present a set of characterization experiments which confirm the single crystalline character of the samples and focus on some specific aspects, all related to the nano-lamellar structure of this material. We show that the crystals can be cleaved or delaminated parallel to the basal plane, and we present atomic force microscope observations of those cleaved surfaces.
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We report thermal expansion coefficients of the end members and solid-solution compounds in the Cr2(Alx,Ge1−x)C system. All samples studied were essentially phase-pure Cr2AlxGe1−xC except the Cr2GeC sample, which contained a substantial fraction of Cr5Ge3Cx. X-ray diffraction performed in the 25–800 °C temperature range shows that the in-plane thermal expansion remains essentially constant at about 14 ± 1 × 10−6 K−1 irrespective of Al content. The thermal expansion of the c axis decreases monotonically from 17 ± 1 × 10−6 K−1 for Cr2GeC to ∼12 ± 1 × 10−6 K−1 with increasing Al content. At around the Cr2(Al0.75,Ge0.25)C composition, the thermal expansion coefficients along the two directions are equal; a useful property to minimize thermal residual stresses. This study thus demonstrates that a solid-solution approach is a route for tuning a physical property like the thermal expansion. For completeness, we also include a structure description of the Cr5Ge3Cx phase, which has been reported before but is not well documented. Its space group is P63/mcm and its a and c lattice parameters are 7.14 Å and 4.88 Å, respectively. We also measured the thermal expansion coefficients of the Cr5Ge3Cx phase. They are found to be 16.3 × 10−6 K−1 and 28.4 × 10−6 K−1 along the a and c axes, respectively. Thus, the thermal expansion coefficients of Cr5Ge3Cx are highly anisotropic and considerably larger than those of the Cr2(Alx,Ge1−x)C phases.
Article
We present a comprehensive scattering study of nanostructured silicon. Neutron and x-ray scattering experiments elucidate structural and dynamical properties of electrochemically etched, porous silicon membranes with pores roughly 8 nm across. In particular, inelastic cold neutron scattering techniques reveal the phonon dispersion of the nanostructured, single crystalline samples in the linear Debye regime for energy transfers up to 4 meV. A modified dispersion relation characterized by systematically reduced sound velocities manifests itself in altered elastic properties of porous silicon when compared to bulk silicon. Its relevance for nanostructured silicon as thermoelectric material of interest is discussed.
Chapter
Introduction Response of Quasi-Single Crystals to Compressive Loads Response of Polycrystalline Samples to Compressive Stresses Response of Polycrystalline Samples to Shear Stresses Response of Polycrystalline Samples to Flexure Stresses Response of Polycrystalline Samples to Tensile Stresses Hardness Fracture Toughness and R-Curve Behavior Fatigue Resistance Damage Tolerance Micromechanisms Responsible for High K1c, R-Curve Behavior, and Fatigue Response Thermal Sock Resistance Strain Rate Effects Solid Solution Hardening and Softening Machinability Summary and Conclusions References
Article
This is a critical review of MAX-phase carbides and nitrides from an electronic-structure and chemical bonding perspective. This large group of nanolaminated materials is of great scientific and technological interest and exhibits a combination of metallic and ceramic features. These properties are related to the special crystal structure and bonding characteristics with alternating strong MC bonds in high-density MC slabs, and relatively weak MA bonds between the slabs. Here, we review the trend and relationship between the chemical bonding, conductivity, elastic and magnetic properties of the MAX phases in comparison to the parent binary MX compounds with the underlying electronic structure probed by polarized X-ray spectroscopy. Spectroscopic studies constitute important tests of the results of state-of-the-art electronic structure density functional theory that is extensively discussed and are generally consistent. By replacing the elements on the M, A, or X-sites in the crystal structure, the corresponding changes in the conductivity, elasticity, magnetism and other material properties make it possible to tailor the characteristics of this class of materials by controlling the strengths of their chemical bonds.
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Using density functional theory, we calculated the formation energy of native point defects (vacancies, interstitials and antisites) in MAX phase Ti2GeC and Ti3GeC2 compounds. Ge vacancy with a formation energy of 2.87 eV was the most stable defect in Ti2GeC while C vacancy with a formation energy of 2.47 eV was the most stable defect in Ti3GeC2. Ge vacancies, in particular, were found to be strong phonon scattering centres that reduce the lattice contribution to thermal conductivity in Ti2GeC. In both compounds, the reported high thermal and electrical conductivity is attributed to the electronic contribution that originates from high density of states at the Fermi level.
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The Niobium based Nb4AlC3, Nb4SiC3, Nb4GeC3 and Nb4GaC3 were investigated by means of density functional theory. Together with the known Nb4AlC3, the role of group III, IV elements in Nb4AC3 (A= Al, Si, Ga, Ge) on various properties were systematically investigated, and particularly the bulk moduli, shear moduli, and Young’s moduli helped us to approach the ductility. All studied compounds were found to be mechanically stable, and they also exhibit the metallic nature that results from the Nb-4d states being dominant at the Fermi level. The typical 4d-2p hybridization leads to strong Nb-C covalent bonding and the relatively weaker 4d-3p (4p) hybridization between Nb and A is identified. The latter does perturb the performance of materials. By varying A elements in the compounds, the position and the width of p states as well as hybridizations are altered, which determines the covalency and the iconicity of the chemical bonds. A high density of states at the Fermi level and the nesting effects in the Fermi surface are identified in Nb4SiC3, and link to its unusual anisotropic behavior. Furthermore, Nb4GeC3 is predicted to be a very promising candidate solar heating barrier material. Overall, the present work gives insight to the role of A elements on the electronic structure and physical properties of Nb4AC3 compounds. The tendencies and rules established here will fertilize the design of functional ceramic materials with desirable properties.
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Herein, we critically assess magnetotransport in the MAX phases and their 2D derivatives, MXenes. For some MAX phases, a simple, 2D hexagonal metal model describes weak-field magnetotransport of their nearly free electrons reasonably well. For others, experimental and/or theoretical Fermi surfaces need to be mapped—a crucial task required for true understanding. Even less is known about MXenes. The density of apparent mobile carriers in Ti3C2Tx—assuming a single-band model—is ≈1 × 10¹⁴ cm⁻² (10²⁸ cm⁻³), which justifies it being sometimes described as a 2D metal. Much work is needed before a clearer picture emerges. Impact statement Magnetotransport in the MAX phases and their 2D derivatives MXene are critically reviewed for the first time. For some, a 2D hexagonal metal can explain magnetotransport; in others not.
Chapter
Introduction Electrical Resistivities, Hall Coefficients, and Magnetoresistances Seebeck Coefficients, Θ Optical Properties Magnetic Properties Superconducting Properties Summary and Conclusions References
Thesis
MAX phases are layered early transition metal ternary carbides and nitrides so called because they are composed of M, an early transition metal, A, a group A element and X is C and/or N. MAX phase structure is composed of near close-packed planes of M atoms with the X atoms occupying all the octahedral sites between them. Their physical properties (stiffness, damage and thermal shock resistance, high thermal and electrical conductivity) along with the fact they are readily machinable, make them extremely attractive in terms of the potential technological applications.In 2011, it was discovered that by immersing Al-containing MAX phases in HF acid, it was possible to selectively etch the Al, resulting in two-dimensional (2D) materials, that were labeled MXene to denote the removal of the A-group element and make the connection to another conducting 2D material, graphene. This new member of 2D materials family owns stronger, more chemically versatile, and have higher conductivity than other materials. As such they are highly interesting on new applications, e.g. specialized in vivo drug delivery systems, hydrogen storage, or as replacements of common materials in e.g. batteries, sewage treatment, and sensors.In this thesis, as its self-telling title indicated, we present our work on the synthesis, structural characterization and the electron transport in the MAX phases and their 2D derivatives, MXenes.For MAX phase: motivated by the theoretically expected anisotropic properties of these layered materials, producing bulk single crystals is a natural way to obtain samples where the anisotropy of the physical properties can be experimentally probed. Also, knowledge of low-temperature behavior of single crystal is vital because it can provide insight into MAX intrinsic physical properties. Using high temperature solution growth and slow cooling technique, several MAX phases single crystals have been successfully grown, including Cr2AlC, V2AlC, Ti3SiC2, etc. Structural characterization confirms the single crystalline character of the samples. Experimentally, a set of experimental data was obtained from single crystals of V2AlC and Cr2AlC as a function of temperature and magnetic field. In particular, we obtain a very high ratio between the in-plane and parallel to the c-axis resistivity, which is very substantial, in the range of a few hundreds to thousands. From MR and Hall effect measurement, in-plane transport behaviors of MAX phases have been studied. The extracted mobility is in the range from 50 to 120 cm2/V·s, which is the same order of magnitude of polycrystalline sample. Theoretically, a general, yet simple model was proposed for describing the weak field magneto-transport properties of nearly free electrons in two-dimensional hexagonal metals. It was then modified to be applicable for the transport properties of layered MAX phases.For MXene: Large scale V2CTx MXene flakes was successfully synthesized by conventional HF-etching of V2AlC single crystals. Mechanical delamination of multilayered V2CTx flakes into few layer flakes and transfer on Si/SiO2 substrate was also achieved. Structural characterization demonstrated an enlarged interplane distance, while prior DMSO intercalation seems to have no effect on this type of MXenes. From EDS results, we concluded that -OH terminations on V2CTx is the dominated, and the most energetically favorable, compared to -F and -O functional groups. We then detail the electrical device fabrication process and proceed with electrical measurements results, performed down to low temperature, with the aim to extract useful information on charge carrier behavior. We successfully obtained some first hand transport data on V2CTx MXenes, the average value for the resistivity of V2CTx MXenes is 2 × 10-5 Ω ∙m, which is in consistent with reported other MXene samples. The mobility, 22.7 cm2/V·s , which stays in the same order of magnitude as its parent MAX phase.
Article
Recent research has highlighted the potential of MAX phase properties including its machinability, good mechanical behaviour, high electric and thermal conductivity as well as good oxidation and erosion resistance to a range of applications including electrical contact coatings, high-temperature heating elements, and barrier- and protection coatings in gas-turbine engine. Successful engineering of MAX phases requires an understanding of how the manufacturing conditions and the deposition parameters influence the composition, crystallographic, electronic structure and morphology. It is, in turn, important to know how these determine the anisotropy of physical, mechanical and technological properties of the material. A focus point of this part of the review is the systemic study of the regular trends in the preparation parameter–structure–properties relationships of MAX phase coatings. In particular, the Cr–Al–C (Y) coating synthesised by the HIPIMS technique will be considered and compared with other synthesised MAX phase bulk ceramics and coatings.
Chapter
This chapter gives an overview of the class of layered, machinable, Mn+1AXn or MAX, phases (where M = early transition metal; A = A-group element, e.g., Al or Si; and X = C or N) precursor to MXene. These materials exhibit an unusual combination of metallic and ceramic properties: good electrical and thermal conductivity, machinability, and resistance to thermal shock. Some are also quite oxidation and creep resistant and plastic at high temperatures. These remarkable properties originate from their layered structure and the mixed metallic-covalent nature of the strong M-X bonds together with M-A bonds that are relatively weak. They are also the common precursors for the class of 2D materials known as MXenes, which are typically formed by selectively etching, mostly Al, from the MAX phases. Within a couple of years of the first report, MXenes have established themselves as a fascinating class of 2D materials with remarkable possibilities for composition variations and property tuning.
Article
Ti2AlN MAX phase with a hexagonal crystal structure exhibits great potential as structural material for operation under harsh environments due to its excellent mechanical performance. For a reliable application, a comprehensive understanding of the mechanical behavior, and in particular of the anisotropic properties is needed. Thus, in this study, we combined nanoindentation and electron-backscatter diffraction experiments to correlate elastic modulus and hardness of Ti2AlN to the crystallographic orientation. We used two different modeling approaches to better understand, validate, and in the long run to predict the anisotropic mechanical behavior of MAX phase materials. While we observed consistent trends in both experiments and modeling, elastic modulus and hardness showed different dependencies on the crystal orientation.
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The bulk plasmon excitation anisotropy of Cr 2 AlC, a nanolaminated ternary carbide, is investigated by electron energy-loss spectroscopy (EELS) and ab initio calculations. Depending on the crystallographic orientation, the valence EELS signal is dominated either by a single plasmon or split into a superposition of two independent plasmons with mutually orthogonal momentum transfers. This splitting arises from the electron-hole interaction anisotropy, important along the hexagonal structure c axis and negligible within the basal plane. It is shown that within the basal plane, the plasmon behavior can be reproduced from an effective medium theory considering Cr 2 AlC as an atomic scale superlattice built from pure aluminum and CrC planes.
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The vibrations of ions in solids at finite temperature depend on interatomic force–constants that result from electrostatic interactions between ions, and the response of the electron density to atomic displacements. At high temperatures, vibration amplitudes are substantial, and electronic states are affected, thus modifying the screening properties of the electron density. By combining inelastic neutron scattering measurements of Fe1-xCoxSi as a function of temperature, and finite-temperature first-principles calculations including thermal disorder effects, we show that the coupling between phonons and electronic structure results in an anomalous temperature dependence of phonons. The strong concomitant renormalization of the electronic structure induces the semiconductor-to-metal transition that occurs with increasing temperature in FeSi. Our results show that for systems with rapidly changing electronic densities of states at the Fermi level, there are likely to be significant phonon–electron interactions, resulting in anomalous temperature-dependent properties.
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Herein, we report on the crystal structures of the isostructural Ti3SiC2 and Ti3GeC2 phases determined by Rietveld analysis of neutron diffraction data in the 100° to 1100 °C temperature range. The results show that the Si and Ge atoms vibrate anisotropically with the highest amplitudes and within the basal planes. The equivalent isotropic thermal motion behavior does not differ significantly between the two phases; the anisotropic thermal motion, interatomic distances, and bond angles, however, show strikingly different behavior. Furthermore, while the Ti-Si bonds increase linearly with increasing temperature, the Ti-Ge bonds apparently do not. The anisotropic motion of the Ge atoms in the basal plane with the correlated motion between the Ti and the Ge atoms is invoked as a possible explanation. The volume expansions are 9.0(±0.1)×10−6 K−1 and 8.7(±0.1)×10−6 K−1 for Ti3SiC2 and Ti3GeC2, respectively; the expansions along the a and c axes are αa=8.9(±0.1)×10−6 K−1 and αc=9.4(±0.1)×10−6 K−1 for Ti3SiC2 and αa=8.5(±0.1)×10−6 K−1 and αc=9.2(±0.1)×10−6 K−1 for Ti3GeC2. A dramatic increase in error bars and a discontinuity in thermal motion parameters of the TiII atoms in Ti3GeC2 were also observed between 300 and 500 °C during both heating and cooling. This discontinuity may in turn explain why the internal friction rises dramatically in that temperature range.
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Layered ternary carbides contain alternative stacking of structural slabs in the unit cells. Many mechanical and structural features are inherited with respect to their binary carbide counterparts, and some novel properties also appear because of new chemical bonds and atomic coordination at the boundaries of different slabs. In this review, we highlight important recent achievements that focus on theoretical prediction, microstructure characterization preparation, and macroscopic properties of newly developed layered ternary transition-metal carbides. These results provide insights into understanding the relationship between the structure (including crystal structure, chemical bonding, and microstructure) and the properties of these layered ternary carbides and further highlight their technological applications as high-temperature and ultrahigh-temperature structural materials.
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The electronic structures of epitaxially grown films of Ti(3)AlC(2), Ti(3)SiC(2), and Ti(3)GeC(2) have been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured high-resolution Ti L, C K, Al L, Si L, and Ge M emission spectra are compared with ab initio density-functional theory including core-to-valence dipole matrix elements. A qualitative agreement between experiment and theory is obtained. A weak covalent Ti-Al bond is manifested by a pronounced shoulder in the Ti L emission of Ti(3)AlC(2). As Al is replaced with Si or Ge, the shoulder disappears. For the buried Al and Si layers, strongly hybridized spectral shapes are detected in Ti(3)AlC(2) and Ti(3)SiC(2), respectively. As a result of relaxation of the crystal structure and the increased charge-transfer from Ti to C, the Ti-C bonding is strengthened. The differences between the electronic structures are discussed in relation to the bonding in the nanolaminates and the corresponding change of materials properties.
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Epitaxial Ti3SiC2(0001) thin films have been deposited by dc magnetron sputtering from three elemental targets of Ti, C, and Si onto MgO(111) and Al2O3(0001) substrates at temperatures of 800-900 degreesC. This process allows composition control to synthesize M(n+1)AX(n) (MAX) phases (M: early transition metal; A: A-group element; X: C and/or N; n=1-3) including Ti4SiC3. Depositions on MgO(100) substrates yielding the Ti-Si-C MAX phases with (10 (1) over bar5), as the preferred orientation. Samples grown at different substrate temperatures, studied by means of transmission electron microscopy and x-ray diffraction investigations, revealed the constraints of Ti3SiC2 nucleation due to kinetic limitations at substrate temperatures below 700 degreesC. Instead, there is a competitive TiCx growth with Si segregation to form twin boundaries or Si substitutional incorporation in TiCx. Physical properties of the as-deposited single-crystal Ti3SiC2 films were determined. A low resistivity of 25 muOmega cm was measured. The Young's modulus, ascertained by nanoindentation, yielded a value of 343-370 GPa. For the mechanical deformation response of the material, probing with cube corner and Berkovich indenters showed an initial high hardness of almost 30 GPa. With increased maximum indentation loads, the hardness was observed to decrease toward bulk values as the characteristic kink formation sets in with dislocation ordering and delamination at basal planes.
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Cr 2 GeC thin films were grown by magnetron sputtering from elemental targets. Phase-pure Cr 2 GeC was grown directly onto Al 2 O 3 (0001) at temperatures of 700–800 • C. These films have an epitaxial component with the well-known epitaxial relationship Cr 2 GeC(0001)//Al 2 O 3 (0001) and Cr 2 GeC(11 ¯ 20)//Al 2 O 3 (1 ¯ 100) or Cr 2 GeC(11 ¯ 20)//Al 2 O 3 (¯ 12 ¯ 10). There is also a large secondary grain population with (10 ¯ 13) orientation. Deposition onto Al 2 O 3 (0001) with a TiN(111) seed layer and onto MgO(111) yielded growth of globally epitaxial Cr 2 GeC(0001) with a virtually negligible (10 ¯ 13) contribution. In contrast to the films deposited at 700–800 • C, the ones grown at 500–600 • C are polycrystalline Cr 2 GeC with (10 ¯ 10)-dominated orientation; they also exhibit surface segregations of Ge as a consequence of fast Ge diffusion rates along the basal planes. The room-temperature resistivity of our samples is 53–66 μμcm. Temperature-dependent resistivity measurements from 15–295 K show that electron-phonon coupling is important and likely anisotropic, which emphasizes that the electrical transport properties cannot be understood in terms of ground state electronic structure calculations only.
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The optical properties of Ti <sub>2</sub> AlN and Ti <sub>2</sub> AlC were determined in the 2–80 eV energy range by electron energy loss spectroscopy and in the visible-ultraviolet range, from 1.6 to 5.5 eV, by spectroscopic ellipsometry. Both experimental techniques are angular resolved and in very good agreement over their overlapping energy range. We observe a dependence of the dielectric function as a function of the crystallographic orientation of the crystals. In particular, we notice a shift of the energy position of the plasmon absorption of Ti <sub>2</sub> AlC with respect to Ti <sub>2</sub> AlN . Moreover, a drastic change is also observed in the shape of the dielectric function as a function of the composition (or valence electron concentration). The dielectric functions are fitted to an empirical semiclassic Drude–Lorentz model to obtain physical parameters such as the relaxation times. These microscopic parameters are then used in a macroscopic model to yield the transport properties such as the static conductivity as function of the crystal orientation. Ti <sub>2</sub> AlN is found to be a better conductor than Ti <sub>2</sub> AlC in all orientations, which is consistent with experimental measurements. A comparison of the electrical and optical properties of these two compounds is made in terms of different electronic properties and interband-intraband transitions deduced from our model.
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This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.
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The efficiency of thermoelectric energy converters is limited by the material thermoelectric figure of merit (zT). The recent advances in zT based on nanostructures limiting the phonon heat conduction is nearing a fundamental limit: The thermal conductivity cannot be reduced below the amorphous limit. We explored enhancing the Seebeck coefficient through a distortion of the electronic density of states and report a successful implementation through the use of the thallium impurity levels in lead telluride (PbTe). Such band structure engineering results in a doubling of zT in p-type PbTe to above 1.5 at 773 kelvin. Use of this new physical principle in conjunction with nanostructuring to lower the thermal conductivity could further enhance zT and enable more widespread use of thermoelectric systems.
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Nanolaminates such as the M(n + 1)AX(n) (MAX) phases are a material class with ab initio derived elasticity tensors published for over 250 compounds. We have for the first time experimentally determined the full elasticity tensor of the archetype MAX phase, Ti(3)SiC(2), using polycrystalline samples and in situ neutron diffraction. The experimental elastic constants show extreme shear stiffness, with c(44) more than five times greater than expected for an isotropic material. Such shear stiffness is quite rare in hexagonal materials and strongly contradicts the predictions of all published MAX phase elastic constants derived from ab initio calculations. It is concluded that second order properties such as elastic moduli derived from ab initio calculations require careful experimental verification. The diffraction technique used currently provides the only method of verification for the elasticity tensor for the majority of new materials where single crystals are not available.
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Porous solids are of great technological importance due to their ability to interact with gases and liquids not only at the surface, but throughout their bulk. Although large pores can be produced and well controlled in a variety of materials, nanopores in the range of 2 nm and below (micropores, according to IUPAC classification) are usually achieved only in carbons or zeolites. To date, major efforts in the field of porous materials have been directed towards control of the size, shape and uniformity of the pores. Here we demonstrate that porosity of carbide-derived carbons (CDCs) can be tuned with subångström accuracy in a wide range by controlling the chlorination temperature. CDC produced from Ti3SiC2 has a narrower pore-size distribution than single-wall carbon nanotubes or activated carbons; its pore-size distribution is comparable to that of zeolites. CDCs are produced at temperatures from 200-1,200 degrees C as a powder, a coating, a membrane or parts with near-final shapes, with or without mesopores. They can find applications in molecular sieves, gas storage, catalysts, adsorbents, battery electrodes, supercapacitors, water/air filters and medical devices.
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Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, could play an important role in a global sustainable energy solution. Such a development is contingent on identifying materials with higher thermoelectric efficiency than available at present, which is a challenge owing to the conflicting combination of material traits that are required. Nevertheless, because of modern synthesis and characterization techniques, particularly for nanoscale materials, a new era of complex thermoelectric materials is approaching. We review recent advances in the field, highlighting the strategies used to improve the thermopower and reduce the thermal conductivity.
Article
A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.
Article
A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.
Article
We investigated the effect of Sb-dimer-induced Si(001) relaxation on the Si 2p core level by high-resolution photoemission spectroscopy. Two surface components, S* and C*, were identified in the Si 2p core level measured on the Sb/Si$$001$$-$$2×1$$ surface at 1 monolayer Sb coverage. By using the Sb-Ge site exchange process, a Ge layer was inserted between the Sb dimers and the Si substrate to separate the Si 2p contribution arising from different atomic layers. We demonstrated that S* includes the contribution of the first, second, and third layers, whereas only the third layer contributes to C*.
Article
Present physical laws do not deny the existence of high-quality thermoelectric (TE) materials (with ZT>3–4ZT>3–4 or even more). But despite a fifty-year study, most of the known matters show ultra low heat-electricity conversion abilities (with ZTZT lower than 1). In this work, we take a canceling out of a Seebeck coefficient (thermopower, SS) of inner grains in some polycrystalline materials with highly anisotropic band structures, as one of the clues to the above contradiction. We show that an SS could be drastically decreased about several hundred times (or even more) in some polycrystalline materials, compared to their single crystalline counterparts. These polycrystals can thus show low-estimatedZTZT (proportional to S2S2), and should be re-examined in their single crystalline forms. Moreover, we also point out that the absence of a conductivity effective mass database at present means that there are blind spots in understanding and predicting some semiconductors’ orientation-dependent transport properties.
Article
Atomic step edges can exhibit a morphological instability under step-flow conditions (the so-called Bales-Zangwill instability). Such instabilities are ascribed to the fact that adatoms approaching a step from opposite directions do not see the same energy barrier to step incorporation (Ehrlich-Schwoebel or ES effect). Due to the very low solubility of carbon in the melt, Ti3SiC2 grown from a Ti-Si liquid phase is an experimental example of two-dimensional (2D) growth. In addition, the ratio between the incorporation rates at a step from the lower terrace and from the upper terrace is probably very high. The latter particularity makes the steps lying below a terrace including an unstable step independent from the forming instability, so that an instability front may appear just on one terrace, whereas the neighboring steps remain stable. Besides, foreign-particle-assisted growth can result in the production of extremely elongated islands or peninsulas on a given terrace, which then form very long grooves between the island edge and the upper terrace step. This provides the ability to test the respective stability of lines and grooves on a single terrace, and to verify that shrinking grooves are more stable than simple steps, as recently demonstrated by another author.
Article
A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.
Article
We have investigated the control of crystal orientation in misfit-type layered cobaltite Ca3Co4O9 thin films by rf-planar magnetron sputtering and succeeded in growing epitaxial films with c-axis, a-axis and b-axis orientations normal to the substrate. Anisotropic transport properties (parallel to the CoO2 layers and perpendicular to the CoO2 layers) were measured using the b-axis-oriented epitaxial films with a layered structure perpendicular to the substrate surface. The resistivity parallel to the CoO2 layers (rhoa) is about 8 mOmega cm at room temperature while that perpendicular to the CoO2 layers (rhoc) is about 300 mOmega cm; the anisotropy is estimated to be about 40. Thermoelectric anisotropy is not considerably pronounced; the parallel Seebeck coefficient Sa is measured to be 110 muV/K and the perpendicular Sc is 40 muV/K at room temperature.
Article
Thermal properties of ternary carbides with composition Ti3SiC2, Ti3AlC2, and Ti3GeC2 were studied using the first-principles phonon calculations. The thermal expansions, the heat capacities at constant pressure, and the isothermal bulk moduli at finite temperatures were obtained under the quasiharmonic approximation. Comparisons were made with the available experimental data and excellent agreements were obtained. Phonon band structures and partial density of states were investigated. These compounds present unusual localized phonon states at low frequencies, which are due to atomiclike vibrations parallel to the basal plane of the Si, Al, or Ge elements.
Article
The constant relaxation time approximation is investigated through the calculation of the thermopower, anisotropy of the conductivity, and Hall tensor of elemental zinc. It is shown that this approximation is reliable at high enough temperature (≳150 K). Moreover, when a magnetic field is applied to the system, the relaxation time is shown to fulfill a sum rule due to Onsager reciprocity relations. This reduces the range of possible approximations for the relaxation time in Hall tensor calculations. The way in which the basic equations of transport theory have to be used to get better numerical efficiency is also discussed.
Article
The dynamical theory of x-ray spectra due to Nozières and De Dominicis (ND) is evaluated here numerically for numerous model systems including cases where the corehole potential possesses a bound state. It is shown that the resulting emission spectra obey the final-state rule rather accurately. An approximate but analytical derivation of this rule is given which provides insight into the mechanisms leading to the final-state rule. The evaluations are performed with the use of two methods, one based on an integral equation together with a separable core-hole potential and the other based on determinantal wave functions for a finite number (N) of electrons in a box. The equivalence of the two methods is demonstrated both formally and numerically. By comparing them we prove the finite- N approach to be accurate already for rather small N. We also show that a separable potential does not give rise to any spurious results but can actually be chosen to yield the same ND spectrum as a local potential. The ND theory of x-ray photoemission spectra is discussed and form calculations of the exponent function α(ω) for several model systems closely corresponding to simple metals we conclude the equivalence of this theory and its asymptotic approximation as far as the extraction of asymmetry indices is concerned. Recent criticism of the major conclusions reached here and in previous work is refuted.
Article
The Seebeck coefficient of the Ti3SiC2 compound has recently been measured and found to be constant and negligible over a wide range of temperature. Materials with essentially zero thermopower allow us to measure the absolute thermopower of another material and could therefore be considered as reference material in thermoelectric measurements. In this paper we analyze the origin of this unusual behavior. The thermopower is calculated from ab initio electronic structure in the framework of Boltzmann transport theory. Under the Mott approximation for the relaxation time, we found the thermopower negative along the z axis and positive in the basal plane. The very small value which is experimentally observed can be ascribed to a compensation between the nonequivalent crystallographic axes.
Article
In this work we calculate the x-ray absorption spectra at the L2,3 edges of the early 3d elements by solving the Bethe-Salpeter equation. We focus our discussion on the origin of the observed deviation of the branching ratio between L2 and L3 edges from its statistical value. Using the absorption edge of Ca in CaF2 we show that the deviation is related to the mixing between the excitations from 2p1/2 and 2p3/2 core levels. Furthermore we find that the mixing is triggered by the exchange term of the electron-hole Hamiltonian. This term does not depend on the dielectric function, therefore such coupling is also present in metals explaining the high values of the branching ratios observed in the metals Ca and Ti. The calculated Ti L2,3 spectra of SrTiO3 and the anatase and rutile phases of TiO2 reproduce even all fine details of the experimental spectra.
Article
The electronic structure and the thermoelectric tensor are calculated for the 312 MAX phases Ti3SiC2, Ti3GeC2, and Ti3AlC2. The thermoelectric tensor is shown to be anisotropic in all cases. However, for Ti3SiC2 and Ti3GeC2 we find the components of the thermoelectric tensor to be negative along the z direction, Sz<0, and positive in the basal plane, Sx>0, whereas Sz>0 and Sx>0 over a large temperature range for Ti3AlC2. This accounts for the different behavior experimentally observed. Moreover, the calculated thermopower as a function of temperature is in good agreement with experiments on polycrystals.
Article
The lack of single crystalline Ti3SiC2 samples is currently limiting the accurate measurement of its basic properties as its layered crystalline structure presents a very strong anisotropy. In this letter, we report the growth of pure Ti3SiC2 single crystals after a careful study of the Ti3SiC2 liquidus surface extent through thermodynamical calculations. From a Raman scattering study on those single crystals, an unambiguous assignment of most of the phonon modes has been established, giving an answer to the discrepancies existing in the literature.
Article
Apart from superconducting materials below their critical transition temperature, all other materials subjected to a temperature gradient will develop an electromotive force or (absolute) thermopower which is itself a function of temperature. We have discovered that the thermopower of Ti3SiC2 is essentially zero over an extended temperature range (from 300 to 850 K). This material should allow the thermopower of other substances to be determined directly at high temperatures, a measurement that has so far been impossible.
Article
This study aims at understanding the anisotropy of the electronic properties of Ti 2 AlN at the nanometer scale. The dielectric response of Ti 2 AlN single grains was recorded in a transmission electron microscope for the 100 and 001 orientations using high-resolution electron energy-loss spectroscopy. The experimental results are interpreted using ab initio calculations based on the density functional theory. The two components of Ti 2 AlN dielectric tensor, corresponding to the response within the basal planes of the hexagonal structure and along its c axis were computed within the random phase approximation. The results, in good agreement with experiments, show strong anisotropy. Local field effects LFE, induced by the electronic density inho-mogeneities, strongly modify the loss function along the 001 direction, which is dominated by a plasmon, a behavior very similar to the one obtained for pure metals. The dielectric response within the basal plane of the hexagonal structure, more complex, exhibits a plasmonlike behavior together with an interband transition. This interband transition is identified as being characteristic of the N-Ti bonds within the Ti 6 N octahedra. This study emphasizes the importance of LFE in the response of Ti 2 AlN to an electromagnetic perturbation.
Article
We have investigated the anisotropy in electronic transport of the layered ternary Ti2GeC by comparing the results of measurements on c-axis oriented epitaxial thin-film and polycrystalline bulk samples. The electrical conductivities, Hall coefficients, and magnetoresistances were analyzed within a multi-band framework. An adequate description of the magnetotransport data on the film with the highest mobility required the use of the explicit field-dependent conductivity tensor with three conduction bands. The analysis indicated that n≈p, although with . The ratio of the a- to c-axis conductivities is small and contrary to theoretical predictions.
Article
We employ monochromatized electron energy loss spectroscopy to study Ti3SiC2 and Ti3AlC2. By probing individual grains aligned along different axes in bulk polycrystalline Ti3SiC2 and Ti3AlC2, this approach enables determination of the anisotropy of the dielectric functions and an estimate of the free-electron lifetime in different orientations. The dielectric functions are characterized by strong interband transitions in the low energy region. The energies plasmon resonance were determined to be and exhibit a strong orientation-dependence. Our measurements show that the free-electron lifetimes are also highly orientation-dependent. These results suggest that scattering of carriers in MAX phases is very sensitive to composition and orientation.
Article
Upon reviewing the correlation between the electronic structure and the elastic properties of nanolaminates based on the previously published ab-initio data, the authors suggest that nanolaminates can be described as interleaved layers of high and low electron density. Mn+1AXn phases (space group P63/mmc) can be characterized by stacking of layers of high (MX) and low (A) electron density. Furthermore, the Mn+1AXn phases possess the bulk-modulus-to-C44 ratio of 1.2–1.7, which in turn gives rise to a combination of ceramic and metallic properties. This design criterion is not only limited to the Mn+1AXn phases, but it can be found in many other phases crystallizing in the same space group (ternary phosphides, Al3BC3, Zr2Al3C5, and W2B5 based phases) and the related space group P6/mmm (Yn+1Co3n+5B2n) as well as in the phases of the cubic $Pm\overline 3 m$ Pm\overline 3 m symmetry (perovskite borides and nitrides).
Article
This article is a critical review of the Mn + 1AXn phases (“MAX phases”, where n = 1, 2, or 3) from a materials science perspective. MAX phases are a class of hexagonal-structure ternary carbides and nitrides (“X”) of a transition metal (“M”) and an A-group element. The most well known are Ti2AlC, Ti3SiC2, and Ti4AlN3. There are ~ 60 MAX phases with at least 9 discovered in the last five years alone. What makes the MAX phases fascinating and potentially useful is their remarkable combination of chemical, physical, electrical, and mechanical properties, which in many ways combine the characteristics of metals and ceramics. For example, MAX phases are typically resistant to oxidation and corrosion, elastically stiff, but at the same time they exhibit high thermal and electrical conductivities and are machinable. These properties stem from an inherently nanolaminated crystal structure, with Mn + 1Xn slabs intercalated with pure A-element layers. The research on MAX phases has been accelerated by the introduction of thin-film processing methods. Magnetron sputtering and arc deposition have been employed to synthesize single-crystal material by epitaxial growth, which enables studies of fundamental material properties. However, the surface-initiated decomposition of Mn + 1AXn thin films into MX compounds at temperatures of 1000–1100 °C is much lower than the decomposition temperatures typically reported for the corresponding bulk material. We also review the prospects for low-temperature synthesis, which is essential for deposition of MAX phases onto technologically important substrates. While deposition of MAX phases from the archetypical Ti–Si–C and Ti–Al–N systems typically requires synthesis temperatures of ~ 800 °C, recent results have demonstrated that V2GeC and Cr2AlC can be deposited at ~ 450 °C. Also, thermal spray of Ti2AlC powder has been used to produce thick coatings. We further treat progress in the use of first-principle calculations for predicting hypothetical MAX phases and their properties. Together with advances in processing and materials analysis, this progress has led to recent discoveries of numerous new MAX phases such as Ti4SiC3, Ta4AlC3, and Ti3SnC2. Finally, important future research directions are discussed. These include charting the unknown regions in phase diagrams to discover new equilibrium and metastable phases, as well as research challenges in understanding their physical properties, such as the effects of anisotropy, impurities, and vacancies on the electrical properties, and unexplored properties such as superconductivity, magnetism, and optics.
Article
From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.
Article
The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.
Article
Extraordinary electron systems can be generated at well-defined interfaces between complex oxides. In recent years, progress has been achieved in exploring and making use of the fundamental properties of such interfaces, and it has become clear that these electron systems offer the potential for possible future devices. We trace the state of the art of this emerging field of electronics and discuss some of the challenges and pitfalls that may lie ahead.
Article
The electronic structure of nanocrystalline (nc-) TiC/amorphous C nanocomposites has been investigated bysoft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of thenanocomposites are compared to those of Ti metal and amorphous C. The corresponding intensities of theelectronic states for the valence and conduction bands in the nanocomposites are shown to strongly depend onthe TiC carbide grain size. An increased charge transfer between the Ti 3d-eg states and the C 2p states hasbeen identified as the grain size decreases, causing an increased ionicity of the TiC nanocrystallites. It issuggested that the charge transfer occurs at the interface between the nanocrystalline-TiC and the amorphous-Cmatrix and represents an interface bonding which may be essential for the understanding of the properties ofnc-TiC/amorphous C and similar nanocomposites.
Article
It is demonstrated that it is possible to investigate details of the electronic structure of an internal atomic monolayer using soft-x-ray-emission spectroscopy. The local and partial density of states of one monolayer and three monolayers of Si, embedded deep below a GaAs(001) surface, was extracted. Clear differences to the density of states for bulk Si were observed.
Article
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
Thermopower of the 312 MAX phases Ti3 Si C2, Ti3 Ge C2, and Ti3 Al C2
• Chaput L.
• Hug G.
• Pecheur P.
• Scherrer H.