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Interaction potential for silicon carbide: A molecular dynamics study of elastic constants and vibrational density of states for crystalline and amorphous silicon carbide
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Image of FIG. 1.
FIG. 1.

(Color) Two-body interaction potential as a function of distance, as described in Eq. (6).

Image of FIG. 2.
FIG. 2.

(Color) Angular dependence of our three-body interaction potential defined in Eq. (3), continuous curve. For comparison the Stillinger-Weber three-body interaction potential is also displayed, dashed curve. In this plot the constant angle and , as given in Table I.

Image of FIG. 3.
FIG. 3.

(Color) Energy per particle as a function of volume per particle. The difference in energy per particle between zinc-blende and wurtzite structures is . Dashed lines are a fit of Murnaghan equation of state, Eq. (7). A common tangent between zinc-blende and rock-salt energy curves determines the pressure of the structural transformation to be around 90 GPa. Energy at the 3C-SiC minima is at the unit cell volume and the corresponding minima for wurtzite is at the unit cell volume .

Image of FIG. 4.
FIG. 4.

(Color) Energy per particle and volume ratio, , as a function of temperature. is the volume of the system at zero temperature. Dotted lines are a guide for the eye and the vertical dashed dotted line represents the calculated melting temperature of 3250 K.

Image of FIG. 5.
FIG. 5.

(Color) Calculated elastic properties for 3C-SiC as a function of density. (a) Elastic constants , , and ; (b) Young modulus, , shear modulus, , and bulk modulus, . The vertical dashed line corresponds to the experimental density of .

Image of FIG. 6.
FIG. 6.

(Color) Elastic properties for amorphous SiC. (a) Calculated elastic constants and shear, , as a function of density; (b) Young modulus, , shear modulus, , and bulk modulus, . The solid arrow marks the observed 3C-SiC density and the vertical dashed line marks the density at which the amorphous SiC has zero internal pressure.

Image of FIG. 7.
FIG. 7.

(Color) Si–C bond distance as a function of applied pressure.

Image of FIG. 8.
FIG. 8.

(Color) (a) Si–C pair distribution function and coordination number as a function of pressure, and the corresponding (b) Si–C–Si bond angle distribution.

Image of FIG. 9.
FIG. 9.

(Color online) Generalized stacking fault energy for 3C-SiC calculated from MD (continuous line) and DFT (dashed line) (private communication).

Image of FIG. 10.
FIG. 10.

(Color) (a) Vibrational density of states from MD and experimental density of states obtained from phonon dispersion relations; (b) partial density of states for Si and C from MD.

Image of FIG. 11.
FIG. 11.

(Color online) (a) Calculated specific heat at constant volume, and experimental as a function of temperature for 3C-SiC. (b) Debye temperature is calculated using the well-known low-temperature expression . Continuous lines are our calculated results and the open circles experimental results calculated using (Ref. 87).

Image of FIG. 12.
FIG. 12.

(Color) MD vibrational density of states and partial densities of states for amorphous SiC at density of .

Image of FIG. 13.
FIG. 13.

(Color) Constant volume specific heat calculated from the MD vibrational density of states for amorphous SiC for several densities. Results for 3C-SiC at are also shown.

Image of FIG. 14.
FIG. 14.

(Color) Comparison of the pair distribution functions between liquid SiC at 4000 K and amorphous SiC at 300 K. Si–C bond length as well as Si–Si and C–C nearest distance remain practically unchanged in the liquid.

Image of FIG. 15.
FIG. 15.

(Color online) (a) Neutron, , charge-charge, , and x-ray, static structure factors calculated for molten SiC at 4000 K; (b) partial structure factors as defined in Eq. (15).


Generic image for table
Table I.

Parameters for two- and three-body parts of the interaction potential used in the MD simulation of structural, dynamical, and mechanical properties of SiC.

Generic image for table
Table II.

Calculated and experimental values for a selected number of physical quantities for 3C-SiC.

Generic image for table
Table III.

Molecular dynamics results, Murnaghan equation of state fit to the MD data, and experimental data for minimum energy per particle, volume of the unit cell, bulk modulus, , and first derivative of the bulk modulus, , for zinc-blende, wurtzite, and rock-salt structures. For rock salt the cohesive energy and bulk modulus are calculated at the minimum of the energy vs volume curve shown in Fig. 3.

Generic image for table
Table IV.

Elastic constants, bulk modulus, , Young modulus, , shear modulus , as well as Poisson ratio , are calculated using our proposed interaction potential, together with the experimentally reported values. Predictions are made for the elastic properties of the amorphous phase, .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interaction potential for silicon carbide: A molecular dynamics study of elastic constants and vibrational density of states for crystalline and amorphous silicon carbide