Elastic constants of nickel: Variations with respect to temperature and pressure

The temperature dependence and pressure derivatives of the adiabatic second- and third-order elastic coefficients of metallic nickel are calculated from molecular dynamics. We employ a Morse potential parametrized from lattice sums for nickel to model the interactions between the atoms. The elastic coefficients are obtained at three different temperatures (T=300, 482, and 671 K) from statistical fluctuation expressions. By use of the zero-pressure second- and third-order elastic coefficients, the pressure derivatives of second-order elastic coefficients of nickel on the aforementioned isotherms are also obtained. The difference between the theoretical and experimental second-order elastic coefficients are found to vary from 4% to 14%. The largest differences are seen for higher temperatures. The theoretical values for C11 and C12 are smaller than the experimental values, whereas the results for C44 are larger than the experimental values. The parametrized Morse potential used in the calculations cannot quantitatively reproduce the third-order elastic coefficients of nickel at 300 K. For example, the differences between the calculated results and the experimental values at T=300 K are larger than 20% for some moduli. The comparably large magnitude of fluctuation terms appearing in the statistical formulas for the elastic coefficients shows the importance of the thermal and anharmonic effects which are not accounted for in lattice sums and harmonic lattice dynamics.