Martin Magnuson
Linköping University, IFM, Faculty Member
The electronic structure of nanocrystalline nc-TiC/a-C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are compared to... more
The electronic structure of nanocrystalline nc-TiC/a-C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are compared to those of Ti metal and amorphous C. The corresponding intensities of the electronic states for the valence and conduction bands in the nanocomposites are shown to strongly depend on the TiC carbide grain size. An increased charge-transfer between the Ti 3d-eg states and the C 2p states has been identified as the grain size decreases, causing an increased ionicity of the TiC nanocrystallites. It is suggested that the charge-transfer occurs at the interface between the nanocrystalline TiC and the amorphous C matrix and represents an interface bonding which may be essential for the understanding of the properties of nc-TiC/a-C and similar nanocomposites.
Research Interests:
We show the first evidence of dissociation during resonant inelastic soft X-ray scattering. Carbon and oxygen K-shell and sulfur L-shell resonant and non-resonant X-ray emission spectra were measured using monochromatic synchrotron... more
We show the first evidence of dissociation during resonant inelastic soft X-ray scattering. Carbon and oxygen K-shell and sulfur L-shell resonant and non-resonant X-ray emission spectra were measured using monochromatic synchrotron radiation for excitation and ionization. After sulfur, L2,3 -> π*, σ* excitation, atomic lines are observed in the emission spectra as a consequence of competition between de-excitation and dissociation. In contrast the carbon and oxygen spectra show weaker line shape variations and no atomic lines. The spectra are compared to results from ab initio calculations and the discussion of the dissociation paths is based on calculated potential energy surfaces and atomic transition energies.
Research Interests:
"The L2,3 x-ray emission of Cu metal has been measured using monochromatic synchrotron radiation. The self-absorption effect in the spectra is shown to be very small in our experimental geometry. From the quantitative analysis of... more
"The L2,3 x-ray emission of Cu metal has been measured using monochromatic synchrotron radiation. The
self-absorption effect in the spectra is shown to be very small in our experimental geometry. From the
quantitative analysis of spectra recorded at different excitation energies, the L3 /L2 emission intensity ratio and
the partial Auger width are extracted. High-energy satellite features on the L3 emission line are separated by a
subtraction procedure. The satellite intensity is found to be slowly increasing for excitation energies between
the L3 , L2 , and L1 core-level thresholds due to shake-up and shake-off transitions. As the excitation energy
passes the L2 threshold, a step of rapidly increasing satellite intensity of the L3 emission is found due to
additional Coster-Kronig processes."
self-absorption effect in the spectra is shown to be very small in our experimental geometry. From the
quantitative analysis of spectra recorded at different excitation energies, the L3 /L2 emission intensity ratio and
the partial Auger width are extracted. High-energy satellite features on the L3 emission line are separated by a
subtraction procedure. The satellite intensity is found to be slowly increasing for excitation energies between
the L3 , L2 , and L1 core-level thresholds due to shake-up and shake-off transitions. As the excitation energy
passes the L2 threshold, a step of rapidly increasing satellite intensity of the L3 emission is found due to
additional Coster-Kronig processes."
Research Interests:
"The electronic structure of CoO is studied by resonant inelastic soft x-ray scattering spectroscopy using photon energies across the Co 2p absorption edges. The different energy-loss structures in the Raman scattering spectra are... more
"The electronic structure of CoO is studied by resonant inelastic soft x-ray scattering spectroscopy using
photon energies across the Co 2p absorption edges. The different energy-loss structures in the Raman scattering
spectra are identified as due to d-d and charge-transfer excitations. For excitation energies close to the L3
resonance, the spectral features are dominated by quartet-quartet and quartet-doublet transitions of the 3d7
configuration. At excitation energies corresponding to the satellites in the Co 2p x-ray-absorption spectrum of
CoO, the emission features are instead dominated by charge-transfer transitions to the 3d8L21 final state. The
spectra are interpreted and discussed with the support of simulations within the single-impurity Anderson
model with full multiplet effects which are found to yield consistent spectral functions to the experimental data."
photon energies across the Co 2p absorption edges. The different energy-loss structures in the Raman scattering
spectra are identified as due to d-d and charge-transfer excitations. For excitation energies close to the L3
resonance, the spectral features are dominated by quartet-quartet and quartet-doublet transitions of the 3d7
configuration. At excitation energies corresponding to the satellites in the Co 2p x-ray-absorption spectrum of
CoO, the emission features are instead dominated by charge-transfer transitions to the 3d8L21 final state. The
spectra are interpreted and discussed with the support of simulations within the single-impurity Anderson
model with full multiplet effects which are found to yield consistent spectral functions to the experimental data."
Research Interests:
"Resonant soft x-ray Raman scattering measurements on NiO have been made at photon energies across the Ni 2p absorption edges. The details of the spectral features are identified as Raman scattering due to d–d and chargetransfer... more
"Resonant soft x-ray Raman scattering measurements on NiO have been made
at photon energies across the Ni 2p absorption edges. The details of the
spectral features are identified as Raman scattering due to d–d and chargetransfer
excitations. The spectra are interpreted within the single-impurity
Anderson model, including multiplets, crystal-field and charge-transfer effects.
At threshold excitation, the spectral features consists of triplet–triplet and
triplet–singlet transitions of the 3d8 configuration. For excitation energies
corresponding to the charge-transfer region in the Ni 2p x-ray absorption
spectrum of NiO, the emission spectra are instead dominated by charge-transfer
transitions to the 3d9L−1 final state. Comparisons of the final states with other
spectroscopical techniques are also made."
at photon energies across the Ni 2p absorption edges. The details of the
spectral features are identified as Raman scattering due to d–d and chargetransfer
excitations. The spectra are interpreted within the single-impurity
Anderson model, including multiplets, crystal-field and charge-transfer effects.
At threshold excitation, the spectral features consists of triplet–triplet and
triplet–singlet transitions of the 3d8 configuration. For excitation energies
corresponding to the charge-transfer region in the Ni 2p x-ray absorption
spectrum of NiO, the emission spectra are instead dominated by charge-transfer
transitions to the 3d9L−1 final state. Comparisons of the final states with other
spectroscopical techniques are also made."
Research Interests: Materials Science, Spectroscopy, Strongly-correlated electron systems, Transition-Metal Oxides, NIO, and 9 moreCharge and Electron Transfer, Transition Metal Oxide Nano Particles, Electronic Structure Theory, Condesed Matter Physics, Nickel Oxide nanoparticles, Nickel Oxide, Wide Band Gap, Ligand Field Theory, and Charge Transfer Inslulator
We report resonant inelastic x-ray scattering RIXS excited by circularly polarized x rays on Mn-Zn ferriteat the Mn L 2,3 resonances. We demonstrate that crystal-field excitations, as expected for localized systems,dominate... more
We report resonant inelastic x-ray scattering
RIXS
excited by circularly polarized x rays on Mn-Zn ferriteat the Mn
L
2,3
resonances. We demonstrate that crystal-field excitations, as expected for localized systems,dominate the RIXS spectra and thus their dichroic asymmetry cannot be interpreted in terms of spin-resolvedpartial density of states, which has been the standard approach for RIXS dichroism. We observe large dichroicRIXS at the
L
2
resonance which we attribute to the absence of metallic core hole screening in the insulatingMn ferrite. On the other hand, reduced
L
3
-RIXS dichroism is interpreted as an effect of longer scattering timethat enables spin-lattice core hole relaxation via magnons and phonons occurring on a femtosecond time scale.
RIXS
excited by circularly polarized x rays on Mn-Zn ferriteat the Mn
L
2,3
resonances. We demonstrate that crystal-field excitations, as expected for localized systems,dominate the RIXS spectra and thus their dichroic asymmetry cannot be interpreted in terms of spin-resolvedpartial density of states, which has been the standard approach for RIXS dichroism. We observe large dichroicRIXS at the
L
2
resonance which we attribute to the absence of metallic core hole screening in the insulatingMn ferrite. On the other hand, reduced
L
3
-RIXS dichroism is interpreted as an effect of longer scattering timethat enables spin-lattice core hole relaxation via magnons and phonons occurring on a femtosecond time scale.
Research Interests:
X-ray absorption and resonant X-ray emission measurements at the O 1s edge of the uranium oxides UO2, U3O8 and UO3 are presented. The spectral shapes of the O Kα X-ray emission spectra of UO3 exhibit significant excitation energy... more
X-ray absorption and resonant X-ray emission measurements at the O 1s edge of the uranium oxides UO2, U3O8 and UO3 are presented. The spectral shapes of the O Kα X-ray emission spectra of UO3 exhibit significant excitation energy dependence, from an asymmetric to a symmetric form, which differs from those of UO2 and U3O8. This energy dependence is attributed to a significant difference in the oxygen-uranium hybridization between two different sites in the crystal structure of UO3. The spectral shapes of UO2 and U3O8 are also found to be different but without significant energy dependence. The experimental spectra of the valence and conduction bands of the uranium oxides are compared to the results of electronic structure calculations available in the literature.
Research Interests:
The electronic structure and chemical bonding of the recently discovered inverse perovskite Sc 3 AlN, incomparison to those of ScN and Sc metal, have been investigated by bulk-sensitive soft-x-ray emissionspectroscopy. The measured... more
The electronic structure and chemical bonding of the recently discovered inverse perovskite Sc
3
AlN, incomparison to those of ScN and Sc metal, have been investigated by bulk-sensitive soft-x-ray emissionspectroscopy. The measured Sc
L
, N
K
, Al
L
1
, and Al
L
2,3
emission spectra are compared with calculatedspectra using first-principles density-functional theory including dipole transition-matrix elements. The mainSc 3
d
–N 2
p
and Sc 3
d
–Al 3
p
chemical bond regions are identified at −4 and −1.4 eV below the Fermi level,respectively.Astrongly modified spectral shape of 3
s
states in the Al
L
2,3
emission from Sc
3
AlN in comparisonto that for pure Al metal is found, which reflects the Sc 3
d
–Al 3
p
hybridization observed in the Al
L
1
emission. The differences between the electronic structures of Sc
3
AlN, ScN, and Sc metal are discussed inrelation to the change in the conductivity and elastic properties
3
AlN, incomparison to those of ScN and Sc metal, have been investigated by bulk-sensitive soft-x-ray emissionspectroscopy. The measured Sc
L
, N
K
, Al
L
1
, and Al
L
2,3
emission spectra are compared with calculatedspectra using first-principles density-functional theory including dipole transition-matrix elements. The mainSc 3
d
–N 2
p
and Sc 3
d
–Al 3
p
chemical bond regions are identified at −4 and −1.4 eV below the Fermi level,respectively.Astrongly modified spectral shape of 3
s
states in the Al
L
2,3
emission from Sc
3
AlN in comparisonto that for pure Al metal is found, which reflects the Sc 3
d
–Al 3
p
hybridization observed in the Al
L
1
emission. The differences between the electronic structures of Sc
3
AlN, ScN, and Sc metal are discussed inrelation to the change in the conductivity and elastic properties
Research Interests:
Angle-resolved valence-band resonant-photoemission of nickel metal has been measured close to the 2 p core-level thresholds with synchrotron radiation. The well-known 6-eV correlation satellite has an intensityenhancement of about two... more
Angle-resolved valence-band resonant-photoemission of nickel metal has been measured close to the 2
p
core-level thresholds with synchrotron radiation. The well-known 6-eV correlation satellite has an intensityenhancement of about two orders of magnitude at resonance. The angular dependence of the photoemissionintensity has been studied as function of photon energy and provides unambiguous evidence for interferenceeffects all the way up to the resonance maximum. The observation of different angular asymmetries,
, for thevalence band and the satellite is discussed in connection to the origin of the resonant-photoemission processand the character of the satellite.
p
core-level thresholds with synchrotron radiation. The well-known 6-eV correlation satellite has an intensityenhancement of about two orders of magnitude at resonance. The angular dependence of the photoemissionintensity has been studied as function of photon energy and provides unambiguous evidence for interferenceeffects all the way up to the resonance maximum. The observation of different angular asymmetries,
, for thevalence band and the satellite is discussed in connection to the origin of the resonant-photoemission processand the character of the satellite.
Research Interests:
" The excitation energy dependence of the three-hole satellites in the L 3 - M 45 M 45 and L 2 - M 45 M 45 Augerspectra of nickel metal has been measured using synchrotron radiation. The satellite behavior in... more
" The excitation energy dependence of the three-hole satellites in the
L
3
-
M
45
M
45
and
L
2
-
M
45
M
45
Augerspectra of nickel metal has been measured using synchrotron radiation. The satellite behavior in the nonradi-ative emission spectra at the
L
3
and
L
2
thresholds is compared and the influence of the Coster-Kronig channelexplored. The three-hole satellite intensity at the
L
3
Auger emission line reveals a peak structure at 5 eV abovethe
L
3
threshold attributed to resonant processes at the 2
p
5
3
d
9
shake-up threshold. This is discussed inconnection with the 6-eV feature in the x-ray-absorption spectrum."
L
3
-
M
45
M
45
and
L
2
-
M
45
M
45
Augerspectra of nickel metal has been measured using synchrotron radiation. The satellite behavior in the nonradi-ative emission spectra at the
L
3
and
L
2
thresholds is compared and the influence of the Coster-Kronig channelexplored. The three-hole satellite intensity at the
L
3
Auger emission line reveals a peak structure at 5 eV abovethe
L
3
threshold attributed to resonant processes at the 2
p
5
3
d
9
shake-up threshold. This is discussed inconnection with the 6-eV feature in the x-ray-absorption spectrum."
Research Interests:
The dispersive part of the refractive index, 1 − δ , of vanadium is determined by measuring the angular dependence of the Bragg peakat the V L 2 , 3 edge energy region using a Fe/V superlattice. This X-ray scattering technique... more
The dispersive part of the refractive index, 1
−
δ
, of vanadium is determined by measuring the angular dependence of the Bragg peakat the V L
2
,
3
edge energy region using a Fe/V superlattice. This X-ray scattering technique provides access to the direct determination of the dispersive part of the refractive index across an absorption resonance and to the change of values from below unity to above unity. Wedemonstrate that previously tabulated values tend to underestimate the amplitude of the change in the real part of the refractive index. We alsoexamine the need for applying absorption and polarization corrections.
−
δ
, of vanadium is determined by measuring the angular dependence of the Bragg peakat the V L
2
,
3
edge energy region using a Fe/V superlattice. This X-ray scattering technique provides access to the direct determination of the dispersive part of the refractive index across an absorption resonance and to the change of values from below unity to above unity. Wedemonstrate that previously tabulated values tend to underestimate the amplitude of the change in the real part of the refractive index. We alsoexamine the need for applying absorption and polarization corrections.
Research Interests:
The magnetic properties, electronic band structure and Fermi surfaces of the hexagonal CrGeC system have been studied by means of both generalized gradient approximation (GGA) and the +U corrected method (GGA+U). The effective U value... more
The magnetic properties, electronic band structure and Fermi surfaces of the hexagonal CrGeC 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 et al. [Anisimov1991]. On the basis of our GGA+U calculations, a compensated anti-ferromagnetic 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 have been used to qualitatively address the electronic transport properties of CrGeC 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.
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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... more
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 microV/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. This allows the origin of anisotropy in physical properties of nanolaminated materials to be traced to anisotropies in element-specific electronic states.
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The spin transition in LaCoO3 is investigated by temperature-dependent resonant soft X-ray emission spectroscopy near the Co 2p absorption edges. This element-specific technique is more bulk sensitive with respect to the temperature... more
The spin transition in LaCoO3 is investigated by temperature-dependent resonant soft X-ray emission spectroscopy near the Co 2p absorption edges. This element-specific technique is more bulk sensitive with respect to the temperature induced spin-state of the Co3+ ions in LaCoO3 than other high-energy spectroscopic methods. The spin transition is interpreted and discussed with ab-initio density-functional theory within the fixed-spin moment method, which is found to yield consistent spectral functions to the experimental data. The spectral changes for LaCoO3 as a function of temperature suggest a change in spin-state as the temperature is raised from 85 to 300 K while the system remains in the same spin state as the temperature is further increased to 510 K.
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The electronic structure of the heavy fermion compound CeB6 is probed by resonant inelastic soft X-ray scattering using photon energies across the Ce 3d and 4d absorption edges. The hybridization between the localized 4f orbitals and the... more
The electronic structure of the heavy fermion compound CeB6 is probed by resonant inelastic soft X-ray scattering using photon energies across the Ce 3d and 4d absorption edges. The hybridization between the localized 4f orbitals and the delocalized valence-band states is studied by identifying the different spectral contributions from inelastic Raman scattering and normal fluorescence. Pronounced energy-loss structures are observed below the elastic peak at both the 3d and 4d thresholds. The origin and character of the inelastic scattering structures are discussed in terms of charge-transfer excitations in connection to the dipole allowed transitions with 4f character. Calculations within the single impurity Anderson model with full multiplet effects are found to yield consistent spectral functions to the experimental data.
Research Interests:
threshold. At threshold, the emission feature changes character and after a rather narrow transition region it appears at constant emission energy instead. Clear signatures of interference between the direct photoemission and... more
threshold. At threshold, the emission feature changes character and after a rather narrow transition region it appears at constant emission energy instead. Clear signatures of interference between the direct photoemission and autoionization channels are identified.
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A Reply to the Comment by Stefan Hüfner, Stefan Schmidt, and Frank Müller.
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The electronic structure of some poly(phenylenevinylene)s have been investigated by resonant and nonresonant x-ray inelastic scattering spectroscopies. The nonresonant as well as all resonant spectra for each polymer demonstrate... more
The electronic structure of some poly(phenylenevinylene)s have been investigated by resonant and nonresonant x-ray inelastic scattering spectroscopies. The nonresonant as well as all resonant spectra for each polymer demonstrate benzene-like features, indicating a local character of the x-ray emission in which the phenyl ring acts as a building block. Theoretical simulations of x-ray energies and intensities taking the repeat unit as a model molecule of the polymer agree with the experimental spectra fairly well. The edges of the occupied bands have been identified in the nonresonant spectra of each polymer. By subtracting the emission energy of the highest occupied molecular orbital in the nonresonant spectrum from the core excitation energy in the resonant spectrum an alternative way to determine the optical band gap is obtained. As for free benzene the outer π band in the polymer spectra show a depletion of the emission going from the nonresonant to the resonant x-ray emission spectra. It is demonstrated that this transition, which is strictly symmetry forbidden for free benzene, becomes effectively forbidden in the polymer case as a result of strong interference effects, and it is argued that this is the general case for resonant x-ray emission of conjugated polymers as far as the frozen orbital approximation holds.
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The electronic structure of nanocrystalline (nc-) TiC/amorphous C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are... more
The electronic structure of nanocrystalline (nc-) TiC/amorphous C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are compared to those of Ti metal and amorphous C. The corresponding intensities of the electronic states for the valence and conduction bands in the nanocomposites are shown to strongly depend on the TiC carbide grain size. An increased charge-transfer between the Ti 3d-eg states and the C 2p states has been identified as the grain size decreases, causing an increased ionicity of the TiC nanocrystallites. It is suggested that the charge-transfer occurs at the interface between the nanocrystalline TiC and the amorphous C matrix and represents an interface bonding which may be essential for the understanding of the properties of nc-TiC/amorphous C and similar nanocomposites.
Research Interests: Physics, Chemistry, Spectroscopy, Nanocomposites, Nanotechnology, and 8 moreX-Ray Fluorescence (XRF) Spectroscopy, Material Science, Nanocomposites, Nanomaterials Characterization, and Nanomaterials, graphene, carbon nanotubes, nanoparticles, nanorod, quantum dots, Composites and nanocomposites, Nanoscience, Hard Materials, Ceramic Nanocomposites, and Nc-TiC/a-C
A core-excited sulfur state with a lifetime almost one order of magnitude longer than in molecular 2p core-hole states is selectively produced by ultrafast dissociation of S 2p → σ* excited OCS. Clear evidence for this is provided by... more
A core-excited sulfur state with a lifetime almost one order of magnitude longer than in molecular 2p core-hole states is selectively produced by ultrafast dissociation of S 2p → σ* excited OCS. Clear evidence for this is provided by strong atomic peaks (20% of the total intensity) in x-ray fluorescence but very weak ones (2%) in the corresponding resonant Auger spectrum. Corroborating the assignment of the spectra, ab initio calculations explain the enhanced lifetime: the Auger decay of the produced 3D3 (2p53p5) sulfur state is strongly decreased as it contradicts a newly derived propensity rule of the L2,3MM Auger decay.
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The averaged complex dielectric function ɛ=(2V⊥+V∥)/3 of polycrystalline Ti2AlN, Ti2AlC, Nb2AlC, (Ti0.5,Nb0.5)2AlC, and Ti3GeC2 was determined by spectroscopic ellipsometry covering the mid infrared to the ultraviolet spectral range. The... more
The averaged complex dielectric function ɛ=(2V⊥+V∥)/3 of polycrystalline Ti2AlN, Ti2AlC, Nb2AlC, (Ti0.5,Nb0.5)2AlC, and Ti3GeC2 was determined by spectroscopic ellipsometry covering the mid infrared to the ultraviolet spectral range. The dielectric functions V⊥ and V∥ correspond to the perpendicular and parallel dielectric tensor components relative to the crystallographic c-axis of these hexagonal compounds. The optical response is represented by a dispersion model with Drude-Lorentz and critical point contributions. In the low energy range the electrical resistivity is obtained from the Drude term and ranges from 0.48 μΩ m for Ti3GeC2 to 1.59 μΩ m for (Ti0.5,Nb0.5)2AlC. Furthermore, several compositional dependent interband electronic transitions can be identified. For the most important ones, Im(V) shows maxima at: 0.78, 1.23, 2.04, 2.48, and 3.78 eV for Ti2AlN; 0.38, 1.8, 2.6, and 3.64 eV for Ti2AlC; 0.3, 0.92, and 2.8 eV in Nb2AlC; 0.45, 0.98, and 2.58 eV in (Ti0.5,Nb0.5)2AlC; and 0.8, 1.85, 2.25, and 3.02 eV in Ti3GeC2.