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Phonon related properties of transition metals, their carbides, and nitrides: A first-principles study
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10.1063/1.2747230
/content/aip/journal/jap/101/12/10.1063/1.2747230
http://aip.metastore.ingenta.com/content/aip/journal/jap/101/12/10.1063/1.2747230

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Trends in bulk moduli of group metal monocarbides and mononitrides within structure. The filled circles refer to the carbides, and the squares stand for the nitrides.

Image of FIG. 2.
FIG. 2.

(Color online) The phonon spectra of and bcc metals along high symmetry directions in the Brillouin zone. In (a) the spectrum for V is depicted for which there is no available inelastic neutron scattering experiment results. The squares and circles are results of early TDS experiments (Ref. 112) and refer to the LA and TA modes, respectively. Experimental points for Nb (b), Ta (c), Mo (d), and W (e) are taken from (Refs. 108–111), respectively. , , and refer to [100] [111], and [110] directions, respectively. mode corresponds to the lowest mode along the direction near the point, LA is the highest mode, and mode lies between these two modes at the same point. These modes are specified for Ta.

Image of FIG. 3.
FIG. 3.

(Color online) The phonon spectra of group metal carbides and nitrides along high symmetry directions in the Brillouin zone: (a) ScC, (b) ScN, (c) YC, and (d) YN. No experimental data available for stoichiometric group metal carbides and nitrides. , , and correspond to the [100] [110], and [111] high symmetry directions, respectively..

Image of FIG. 4.
FIG. 4.

(Color online) Phonon dispersion curves for group metal carbides and nitrides along high symmetry directions in the Brillouin zone. Experimental points for TiC (a), TiN (b), ZrC (c), ZrN (d), HfC (e), and HfN (f) are taken from Refs. 39, 52, 41, 53, 36, and 54, respectively. The circles and squares refer to the transversal and longitudinal modes for both acoustic and optical brances. Note the reverse order for LO and TO modes for HfN and ZrN.

Image of FIG. 5.
FIG. 5.

(Color online) Phonon dispersion relations for group metal carbides [(a)–(c)] and nitrides [(d)–(f)] along high symmetry directions in the Brillouin zone. For B1 VC (a) there are no experimental data. For NbC (b) and TaC (c) experimental points are from Refs. 36 and 34, correspondingly. The nitrides with ten valence electrons exhibit dynamical instability near the point.

Image of FIG. 6.
FIG. 6.

(Color online) The phonon spectra for NbN within hexagonal NiAs- (a) and WC- (b) type structures along high symmetry directions in the Brillouin zone. The phonon spectra for hexagonal WC (c), WN (d), and WN (e) within cubic NaCl-type structure along high symmetry directions in the Brillouin zone are also presented.

Image of FIG. 7.
FIG. 7.

(Color online) The phonon spectrum for MoC (a), MoN (b), and MoC within hexagonal WC- type (c) structure, and TiO (d) along high symmetry directions in the Brillouin zone.

Image of FIG. 8.
FIG. 8.

(Color online) Fermi surface sheets for NbC (a), TiN (b), VC (c), ScC (d), YC (e), and TiC (f). FSs for ScC and YC look quite similar.

Image of FIG. 9.
FIG. 9.

(Color online) Illustration of the nesting behavior of the Fermi surface sheets for NbC (a) and VC (b).

Tables

Generic image for table
Table I.

Ground state parameters for bcc (V, Nb, Ta, Cr, Mo, and W), DHCP (La), and HCP (Y, Sc, Ti, Zr, and Hf) metals using ultrasoft pseudopotentials generated in this work. For each metal first we show results of our calculations, and on the next line available experimental (Ref. 87 if nothing specified) and theoretical data are presented.

Generic image for table
Table II.

Equilbrium lattice parameters and bulk moduli for TMC. For each TMC first we show calculated lattice constants and bulk moduli, and then available experimental and theoretical data are given on the next line.

Generic image for table
Table III.

Ground state parameters for transition metal nitrides within structure. Results of other calculations and experimental date are shown on the next line after results of our calculations.

Generic image for table
Table IV.

Comparison of calculated phonon frequencies for bcc metals in high symmetry and points (in THz).

Generic image for table
Table V.

Comparison of calculated phonon frequencies of TiC in high symmetry points , , and (in THz).

Generic image for table
Table VI.

Comparison of calculated phonon frequencies for NbC in high symmetry , , and points (in THz).

Generic image for table
Table VII.

(Color online) Tables illustrating dynamic stability boundary for TMC (a) and TMN (b) within structure in dependence on , the total number of valence electrons in the unit cell. The red columns stand for dynamically unstable TMC and TMN, and the green and blue columns refer to stable TMC and TMN. The green columns are for superconducting TMC and TMN.

Generic image for table
Table VIII.

Electron-phonon coupling constants and superconducting transition temperature for bcc metals, ScC and YC with seven valence electrons, and isoelectronic group metal nitrides and group carbides with nine valence electrons in the unit cell. For each metal and compound in the first line we present results of our calculations, except , the Coloumb pseudopotential. Available experimental and theoretical data are shown in the next line.

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/content/aip/journal/jap/101/12/10.1063/1.2747230
2007-06-25
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phonon related properties of transition metals, their carbides, and nitrides: A first-principles study
http://aip.metastore.ingenta.com/content/aip/journal/jap/101/12/10.1063/1.2747230
10.1063/1.2747230
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