Molecular dynamic calculation of elastic constants of silicon

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Abstract
Stillinger and Weber have introduced a model potential to study the solid and liquid forms of silicon. This potential has been used in a number of computer simulation studies of silicon. We have calculated the elastic constants of silicon using the Stillinger–Weber potential at three different temperatures T=888, 1164, and 1477 K. The adiabatic elastic constants are calculated using fluctuation formula appropriate for the microcanonical ensemble. We find that the calculated shear modulus C44 is smaller than the experimental values by ∼30% at T=888 K, ∼40% at the two higher temperatures, and the modulus C12 is larger than the experimental value by 25%–30%. Simulations with N=216 and 1728 particles were carried out to check on the number dependence of the results. These two particle numbers give equivalent results for the elastic constants. The calculated elastic constants show the same softening with rising temperature as shown by the experimental values.