Abstract:Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC1−x), maintain structural stability even if they accommodate abundant anion vacancies. This unique character endows them with variable-composition, diverse-configuration and controllable-performance through composition and structure design. Herein, the evolution of carbon vacancy (VC) configuration in sub-stoichiometric ZrC1−x is investigated by combining the cluster expansion method and first-principles calculations. We r… Show more
“…In another study, a superlattice was identified using a combination of electrical resistivity, differential thermal analysis, and x‐ray diffraction (XRD) measurements on a specimen of ZrC 0.7 that was prepared by arc‐melting and annealing . Crystal structures of nonstoichiometric ZrC x have also been studied by computational methods, which predicted the stability of the Fd crystal structure at carbon stoichiometries as low as x = 0.5 using mixing enthalpy calculations . Phase stability of highly carbon‐deficient compositions (eg, x ≤ 0.5) has been studied using formation enthalpy calculations, which showed that the Fd structure, with ordered vacancies, was the most stable .…”
Ordered carbon vacancies were detected in zirconium carbide (ZrCx) powders that were synthesized by direct reaction. Zirconium hydride (ZrH2) and carbon black were used as starting powders with the molar ratio of ZrH2:C = 1:0.6. Powders were reacted at 1300°C or 2000°C. The major phase detected by x‐ray diffraction (XRD) was ZrCx. No excess carbon was observed by transmission electron microscopy (TEM) in powders synthesized at either temperature. Ordering of the carbon vacancies was identified by neutron powder diffraction (NPD) and further supported by selected area electron diffraction (SAED). The vacancies in carbon‐deficient ZrCx exhibited diamond cubic symmetry with a supercell that consisted of eight (2 × 2 × 2) ZrCx unit cells with the rock‐salt structure. Rietveld refinement of the neutron diffraction patterns revealed that the synthesis temperature did not have a significant effect on the degree of vacancy ordering in ZrCx powders. Direct synthesis of ZrC0.6 resulted in the partial ordering of carbon vacancies without the need for extended isothermal annealing as reported in previous experimental studies.
“…In another study, a superlattice was identified using a combination of electrical resistivity, differential thermal analysis, and x‐ray diffraction (XRD) measurements on a specimen of ZrC 0.7 that was prepared by arc‐melting and annealing . Crystal structures of nonstoichiometric ZrC x have also been studied by computational methods, which predicted the stability of the Fd crystal structure at carbon stoichiometries as low as x = 0.5 using mixing enthalpy calculations . Phase stability of highly carbon‐deficient compositions (eg, x ≤ 0.5) has been studied using formation enthalpy calculations, which showed that the Fd structure, with ordered vacancies, was the most stable .…”
Ordered carbon vacancies were detected in zirconium carbide (ZrCx) powders that were synthesized by direct reaction. Zirconium hydride (ZrH2) and carbon black were used as starting powders with the molar ratio of ZrH2:C = 1:0.6. Powders were reacted at 1300°C or 2000°C. The major phase detected by x‐ray diffraction (XRD) was ZrCx. No excess carbon was observed by transmission electron microscopy (TEM) in powders synthesized at either temperature. Ordering of the carbon vacancies was identified by neutron powder diffraction (NPD) and further supported by selected area electron diffraction (SAED). The vacancies in carbon‐deficient ZrCx exhibited diamond cubic symmetry with a supercell that consisted of eight (2 × 2 × 2) ZrCx unit cells with the rock‐salt structure. Rietveld refinement of the neutron diffraction patterns revealed that the synthesis temperature did not have a significant effect on the degree of vacancy ordering in ZrCx powders. Direct synthesis of ZrC0.6 resulted in the partial ordering of carbon vacancies without the need for extended isothermal annealing as reported in previous experimental studies.
“…We suppose that C atoms are fully occupying the 24e sites. Partial occupancy of the carbon sublattice can be important in some carbides 28,29 , but in this carbide we do not expect it to play a role of significance because the carbon vacancy formation enthalpy is very large (~1.05 eV/C vacancy) 30 .Figure 1( a ) The γ-Cr 23 C 6 supercell consists of one conventional unit cells with four inequivalent metal sites, namely, the 4a, 8c, 32f, and 48h sites, according to Wyckoff notation. The C atoms are located at the 24e sites.…”
The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr23−xFexC6 (x = 0–3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M23C6 structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M(4a) M12(48h)) and negatively charged cubo-octahedron (M8(32f) C6(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M23C6 carbides may facilitate further development of high-chromium heat-resistant steels.
“…20 was successfully applied to metals and non-polar semiconductors [1,6,12,14,23,28,33,34], the same strategy breaks down in the case of polar materials. In fact the singularity in Eq.…”
We develop a method for calculating the electron-phonon vertex in polar semiconductors and insulators from first principles. The present formalism generalizes the Fröhlich vertex to the case of anisotropic materials and multiple phonon branches, and can be used either as a post-processing correction to standard electron-phonon calculations, or in conjunction with ab initio interpolation based on maximally localized Wannier functions. We demonstrate this formalism by investigating the electron-phonon interactions in anatase TiO2, and show that the polar vertex significantly reduces the electron lifetimes and enhances the anisotropy of the coupling. The present work enables ab initio calculations of carrier mobilities, lifetimes, mass enhancement, and pairing in polar materials.PACS numbers: 71.38.-k, 63.20.dk The electron-phonon interaction (EPI) is a cornerstone of condensed matter physics, and plays important roles in a diverse array of phenomena. Recent years have witnessed a surge of interest in ab initio calculations of EPIs, leading to new techniques and many innovative applications in the case of metals and non-polar semiconductors [1][2][3][4][5][6][7][8][9][10][11][12]. In contrast to this fast-paced progress, in the case of polar semiconductors and insulators the study of EPIs from first principles has not gone very far, owing to the prohibitive computational costs of EPI calculations for polar materials. For example, a fully ab initio calculation of the carrier mobility of a polar semiconductor has not been performed yet, while such calculations have recently been reported for non-polar semiconductors such as silicon [13] and graphene [14]. Given the fast-growing technological importance of polar semiconductors, from light-emitting devices to transparent electronics, solar cells and photocatalysts [15][16][17], developing accurate and efficient computational methods for studying EPIs in these systems is of primary importance.At variance with metals and non-polar semiconductors, in polar materials two or more atoms in the unit cell carry nonzero Born effective charge tensors [18]. As a consequence, the fluctuations of the ionic positions corresponding to longitudinal optical (LO) phonons at long wavelength generate macroscopic electric fields which can couple strongly to electrons and holes, leading to the so-called Fröhlich interaction [19]. Up to now this interaction has not been taken into account in ab initio calculations of EPIs; the two key obstacles towards a description of Fröhlich coupling from first principles are (i) the Fröhlich coupling was designed to describe simple isotropic systems with one LO phonon, and (ii) the electron-phonon vertex diverges for q → 0, where q is the phonon wavevector. The first obstacle relates to the fundamental question on how to define the Fröhlich coupling in the most general way. The second obstacle renders first-principles calculations extremely demanding, since a correct description of the singularity requires a very fine sampling of the Brillouin zone.In...
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