Influence of vacancies on the shear moduli

The significant influence of self - interstitials on the shear elastic moduli raise the question of whether vacancies could have a similar effect. It is known that if the lattice is distorted in the neighborhood of a vacancy some new vibrational modes of atoms are created. The effect could lead to softening of the solid. Yet, according to our simulations the shear elastic coefficients are less affected by the vacancies in comparison with self - interstitials, as it is shown in Figs. 4.29-4.30. It is interesting to notice that at high vacancy concentration of $20/2000=1\%$ we observe the noticeable reduction of the shear elastic moduli of vanadium, in contrast to the results obtained for copper by A. Kanigel [67] (See Fig. 4.26). However, at these concentrations interactions between the vacancies are not negligible, and that complicates the physics of the phenomenon.

Figure: Dependence of $C'$ on the concentration of point defects at T = 2300 K and T = 2400 K , showing the difference between influence of vacancies and interstitials. The dashed lines to guide the eye.

Figure: Dependence of $C_{44}$ on the concentration of point defects at T = 2300 K and T = 2400 K , showing the difference between influence of vacancies and interstitials. The dashed lines to guide the eye.