Thermal Expansion of Rutile and Anatase

Rao, K. V. S. Rama; Seetala, Naidu V.; Iyengar, Leela

doi:10.1111/j.1151-2916.1970.tb12051.x

Cited by 171 publications

(60 citation statements)

References 9 publications

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“…We corrected the GW gap values for the lattice expansion effect by using the thermal expansion coefficient reported in Ref. [13]. In particular, the a and c lattice parameters of rutile TiO 2 increase by 0.3 % from 0 to 250 K. The inclusion of both the phonon-induced and the thermal expansion-induced effects leads to a net blueshift of the bandgap of ∼ 120 meV (in the case of the E (3) u mode) and 60 meV (in the case of the A 2u mode).…”

Section: S2 Ab Initio Calculationsmentioning

confidence: 99%

“…Moreover, the lattice expansion term E th (T ) is generalized to the case of an anisotropic (tetragonal) crystal, using the expressions for the linear thermal expansion coefficients of rutile TiO 2 as in Ref. [13]. The value of the bulk modulus is taken from Ref.…”

Section: S4 Softening Of Exciton IVmentioning

confidence: 99%

“…To our knowledge, this is the first example of a band insulator showing an opposite T behaviour of the excitations along the two polarization channels. In rutile TiO 2 , the thermal expansion along both axis has a regular T dependence and thus should contribute to a softening of the optical transition energies as the lattice expands with increasing T [13]. Thus, the evolution of peak I and III with T is anomalous and is likely related to peculiar effects of the EPI at finite T.…”

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confidence: 99%

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Anomalous anisotropic exciton temperature dependence in rutile TiO2

et al. 2017

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Elucidating the details of the electron-phonon coupling in semiconductors and insulators is a topic of pivotal interest, as it governs the transport mechanisms and is responsible for various phenomena such as spectral-weight transfers to phonon sidebands and self-trapping. Here, we investigate the influence of the electron-phonon interaction on the excitonic peaks of rutile TiO2, revealing a strong anisotropic polarization dependence with increasing temperature, namely an anomalous blueshift for light polarized along the a-axis and a conventional redshift for light polarized along the c-axis. By employing many-body perturbation theory, we identify two terms in the electron-phonon interaction Hamiltonian that contribute to the anomalous blueshift of the a-axis exciton. Our approach paves the way to a complete ab initio treatment of the electron-phonon interaction and of its influence on the optical spectra of polar materials.The temperature (T) dependence of elementary excitations is a central subject in condensed matter physics, as it provides insightful information on the microscopic details of many-body interactions and correlations. To this end, over the past five decades, considerable efforts have been devoted to studying the T-effects on the optical spectra of materials, where elementary excitations in the long-wavelength regime possess a clear spectroscopic fingerprint. In this regard, an old topic is represented by the T-dependence of interband transitions and excitons in standard band semiconductors and insulators [1,2]. The energy of these excitations (E exc ) typically undergoes a sizeable softening with increasing T, but in a few exceptional cases, the opposite effect or more complex T dependences have been observed [3][4][5]. Part of this renormalization is accounted for by the thermal expansion of the lattice, but the major contribution arises from the structure of the electron-phonon interaction (EPI).To model the measured dependences of E exc , simple algebraic expressions have been initially used, the most common of which is the empirical Varshni law [6]. More accurate fits were obtained by using Bose-Einstein statistical factors with average acoustic and optical phonon frequencies, an approach that finds theoretical justification in pseudopotential theory [7]. Within this framework, anomalous T-dependences of E exc can be described by assuming that the contributions due to phonons with lowand high frequencies retain opposite signs [8]. A more rigorous generalization of this approach, using a distribution of phonon energies, was proposed [9], in which E exc (T ) can be described as (1) where E 0 is the energy gap at zero T, n BE is the BoseEinstein statistical factor (e ω/kBT -1) −1 , f(ω) is a weighing factor and the last term E th (T ) accounts for the lattice thermal expansion. The weighing factor f(ω) can be decomposed into a product of the phonon density of states (PDOS) and a factor related to the EPI strength. However, this method suffers from intrinsic complexity, requiring detailed knowl...

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Section: S2 Ab Initio Calculationsmentioning

confidence: 99%

Section: S4 Softening Of Exciton IVmentioning

confidence: 99%

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confidence: 99%

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Anomalous anisotropic exciton temperature dependence in rutile TiO2

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“…The analysis was completed by fitting the sample diffraction to an appropriate model where the lattice constants, scale factor, peak profile functions, and atomic potentials were varied to produce a simulated diffraction pattern nearly identical to the experimental XRD data. The models were chosen based upon knowledge of synthesis, reaction conditions, and phases previously identified in similar studies, that is, Rh metal, Fe metal, Fe-Rh alloys (FeRh and Fe0.7Rh0.3), FeO, Fe2O3, Fe3C, Fe2C, Fe5C2, anatase TiO2, and rutile TiO2 [20][21][22][23][24][25][26][27][28][29][30][31][32]. A complete refinement provides information about phase quantification, lattice constants, and particle size.…”

Section: In Situ Structure Determinationsmentioning

confidence: 99%

The effect of Fe–Rh alloying on CO hydrogenation to C2+ oxygenates

Palomino

Magee

Llorca³

et al. 2015

Journal of Catalysis

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a b s t r a c t A combination of reactivity and structural studies using X-ray diffraction (XRD), pair distribution function (PDF), and transmission electron microscopy (TEM) was used to identify the active phases of Fe-modified Rh/TiO2 catalysts for the synthesis of ethanol and other C2+ oxygenates from CO hydrogenation. XRD and TEM confirm the existence of Fe-Rh alloys for catalyst with 1-7 wt% Fe and '""2 wt% Rh. Rietveld refinements show that FeRh alloy content increases with Fe loading up to '""4 wt%, beyond which segregation to metallic Fe becomes favored over alloy formation. Catalysts that contain Fe metal after reduction exhibit some carburization as evidenced by the formation of small amounts of Fe3C during CO hydrogenation. Analysis of the total Fe content of the catalysts also suggests the presence of FeOx also increased under reaction conditions. Reactivity studies show that enhancement of ethanol selectivity with Fe loading is accompanied by a significant drop in CO conversion. Comparison of the XRD phase analyses with selectivity suggests that higher ethanol selectivity is correlated with the presence of Fe-Rh alloy phases. Overall, the interface between Fe and Rh serves to enhance the selectivity of ethanol, but suppresses the activity of the catalyst which is attributed to the blocking or modifying of Rh active sites.

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“…Las fases de rutilo y anatasa han sido ampliamente estudiadas en los últimos años por sus aplicaciones en fotocatálisis y fotoelectroquími-cos. Mientras que la fase brookita ha sido menos estudiada, debido a que no se utiliza comercialmente y su estructura es relativamente complicada, todo esto ha despertado interés en el estudio de sus propiedades [1,2]. La fase rutilo posee una estructura tetragonal con grupo espacial P4 2 /mnm y paráme-tros de red a = 4.587 Å, c = 2.954 Å, y u = 0.305 Å [3], los cuales fueron determinados y verificados usando las técnicas de rayos X [4,5] y difracción de neutrones [3,6]. Experimentalmente se ha medido una brecha de energía prohibida directa alrededor de 3.0 eV [3 -6].…”

Section: Introductionunclassified

Efectos de intercambio y correlación en las propiedades estructurales y electrónicas del TiO2 en la fase rutilo / Exchange and correlation effects on the structural and electronic properties of TiO2 on the rutile phase

et al. 2017

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ResumenEn este trabajo, se estudiaron las propiedades estructurales y electrónicas del TiO 2 en la fase rutilo a partir de cálculos de primeros principios. Los efectos de intercambio y correlación electrónica fueron estudiados utilizando funcionales en la aproximación de densidad local (LDA), la aproximación de gradiente generalizado (GGA) de Perdew-Burke-Ernzerhof (PBE), Perdew-Burke-Ernzerhof revised for solids (PBEsol), Perdew-Wang 91 (PW91) y revised Perdew-Burke-Ernzerhof (rPBE), y la aproximación de gradiente meta-generalizado (meta-GGA) de Tao-Perdew-Staroverov-Scuseria (TPSS) y revised-TPSS (RTPSS), en el marco de la Teoría del Funcional de la Densidad (DFT). Encontramos que el funcional PBEsol proporciona mejores resultados para el cálculo de los parámetros de red (a y c) y las longitudes ecuatorial y axial (d eq y d ax ); mientras que para la energía de cohesión (E coh ), el módulo volumétrico (B 0 ) y los ángulos (2θ y α) los funcionales PBE, rPBE y TPSS, respectivamente, se acercan más a los valores experimentales. Se confirma que el TiO 2 presenta propiedades de semiconductor directo en Γ − Γ.Palabras clave: Cálculo de primeros principios, DFT, GGA, meta-GGA, rutilo. AbstractIn this work, we study the structural and electronic properties of TiO 2 in the rutile phase based on first principles calculations. The electronic exchange and correlation effects were studied using functionals in the local density approximation (LDA), the generalized gradient approximation (GGA) by Perdew-BurkeErnzerhof (PBE), Perdew-Burke-Ernzerhof revised for solids (PBEsol), Perdew-Wang 91 (PW91) and revised Perdew-Burke-Ernzerhof (rPBE), and the meta-generalized gradient approximation (meta-GGA) by Tao-Perdew-Staroverov-Scuseria (TPSS) and revised-TPSS (RTPSS) in the frame of the Density Functional Theory (DFT). We found that the PBEsol functional provides better results for the lattice parameter values (a y c) and the equatorial and axial lengths (deq and dax); while for the cohesion energy (Ecoh), volumetric module (B 0 ) and angles (2θ y α) the PBE, rPBE and TPSS functionals respectively, are closer to the experimental values. It is confirmed that the TiO 2 presents properties of direct semiconductor in Γ − Γ.Keywords: First principles calculations, DFT, GGA, meta-GGA, rutile. Efectos de intercambio y correlación en las propiedades estructurales y electrónicas del TiO 2 en la fase rutilo

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Thermal Expansion of Rutile and Anatase

Cited by 171 publications

References 9 publications

Anomalous anisotropic exciton temperature dependence in rutile TiO2

Anomalous anisotropic exciton temperature dependence in rutile TiO2

The effect of Fe–Rh alloying on CO hydrogenation to C2+ oxygenates

Efectos de intercambio y correlación en las propiedades estructurales y electrónicas del TiO2 en la fase rutilo / Exchange and correlation effects on the structural and electronic properties of TiO2 on the rutile phase

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