^{1,a)}, Rajiv K. Kalia

^{1}, Aiichiro Nakano

^{1}and José Pedro Rino

^{2}

### Abstract

An effective interatomic interaction potential for SiC is proposed. The potential consists of two-body and three-body covalent interactions. The two-body potential includes steric repulsions due to atomic sizes, Coulomb interactions resulting from charge transfer between atoms, charge-induced dipole-interactions due to the electronic polarizability of ions, and induced dipole-dipole (van der Waals) interactions. The covalent characters of the Si–C–Si and C–Si–C bonds are described by the three-body potential. The proposed three-body interaction potential is a modification of the Stillinger-Weber form proposed to describe Si. Using the molecular dynamics method, the interaction potential is used to study structural,elastic, and dynamical properties of crystalline (3C), amorphous, and liquid states of SiC for several densities and temperatures. The structural energy for cubic (3C) structure has the lowest energy, followed by the wurtzite (2H) and rock-salt (RS) structures. The pressure for the structural transformation from 3C-to-RS from the common tangent is found to be 90 GPa. For 3C-SiC, our computed elastic constants (, , and ), melting temperature, vibrational density-of-states, and specific heat agree well with the experiments. Predictions are made for the elastic constant as a function of density for the crystalline and amorphous phase. Structural correlations, such as pair distribution function and neutron and x-ray static structure factors are calculated for the amorphous and liquid state.

This work was partially supported by NSF, DOE, DARPA, and ARO. J.P.R. gratefully acknowledges financial support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo, SP-Brazil) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico–Brazil).

I. INTRODUCTION

II. INTERACTION POTENTIAL FOR SiC

III. STRUCTURAL ENERGIES AND MELTING

A. Structural energies for zinc-blende, wurtzite, and rock-salt structures

B. Melting of 3C-SiC

IV. ELASTIC PROPERTIES OF CRYSTALLINE AND AMORPHOUSSiC

A. Elastic properties of 3C-SiC

B. Elastic properties of amorphousSiC

V. ZINC-BLENDE TO ROCK-SALT STRUCTURAL TRANSFORMATION UNDER PRESSURE, SURFACE ENERGY, AND STACKING FAULT ENERGY FOR SiC

A. Structural transformation under pressure

B. Surface energy

C. Stacking fault energy

VI. VIBRATIONAL DENSITY OF STATES FOR CRYSTALLINE AND AMORPHOUSSiC

A. Vibrational density of states for 3C-SiC

B. Specific heat for 3C-SiC

C. Vibrational density of states for amorphousSiC

D. Specific heat for amorphousSiC

VII. MOLTEN SiC

A. Pair distribution function

B. X-ray and neutron static structure factors for molten SiC

VIII. CONCLUSIONS

### Key Topics

- Elasticity
- 30.0
- Crystal structure
- 28.0
- Amorphous state
- 18.0
- Elastic moduli
- 14.0
- Electron densities of states
- 14.0

## Figures

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

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

(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.

(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.

(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 .

(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 .

(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.

(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.

(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 .

(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 .

(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.

(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.

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

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

(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.

(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.

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

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

(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.

(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.

(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).

(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).

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

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

(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.

(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.

(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.

(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.

(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).

(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).

## Tables

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

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

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

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

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.

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.

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, .

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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