Equilibrium crystal structure of cementite . White, yellow, and red spheres represent , , and C atoms, respectively. All nearest-neighbor Fe–C bonds are also shown.
Phonon dispersion relations for (a) cementite, (b) diamond, and (c) bcc Fe along various high-symmetry directions in the Brillouin zone. All calculations were performed using 128 atom supercells and a -point mesh. For diamond, experimental data (circles) are taken from Warren et al. (Ref. 31). For bcc Fe, experimental data are taken from Brockhouse et al. (Ref. 32) (circles) and Klotz and Braden (Ref. 33) (triangles). Results from frozen-phonon calculations are shown as filled circles.
First-principles calculated EOS of cementite in comparison with experimental measurements. The error bars for the experimental data from Li et al. (Ref. 37) are not available.
Representational surface showing the directional dependence of Young’s modulus (in GPa) in cementite.
Site and angular momentum projected electronic DOS of cementite. The vertical line denotes the Fermi level.
Plot of (a) total charge density and (b) difference charge density, all in , on the (010) plane of containing the nearest-neighbor Fe–C bonds.
Experimental and theoretical structural properties of cementite. denotes the internal atomic coordinates of atom .
Deformation matrices used to calculate the nine independent single-crystal elastic constants of an orthorhombic crystal.
Single-crystal elastic constants (in GPa) of cementite calculated in the present study. The values shown in parentheses are from unrelaxed calculations, i.e., without allowing for internal atomic relaxations.
The sound velocities in an orthorhombic crystal. denotes the density of the material.
Polycrystalline elastic moduli (in GPa) of cementite obtained from first-principles calculations and experiments. Experimental values of the first pressure derivative of bulk modulus are shown within parentheses.
The shear and compressibility anisotropy factors of cementite obtained from first-principles calculations. The linear bulk moduli (in GPa) along the , , and axes, defined as , are also shown.
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