Cell cluster calculations of the entropy of cracked crystals

摘要

The harmonic contribution to the entropy of a linear crackrlattice spacings in length in a crystal on the triangular lattice can be written as Dgr;Sr/k= sgr;r+tgr;(r), where sgr; is the surface entropy and tgr;(r) contains the entropy effects due to the crack tips.Pth order cell cluster approximations sgr;(thinsp;p)and tgr;(thinsp;p)(r) can be constructed, where tgr;(thinsp;p)(r) = tgr;(thinsp;p)(infin;) ifrgsim;pndash;1. Calculations of sgr;(thinsp;p)and tgr;(thinsp;p)(infin;) forpquest;6 were obtained. Values of sgr;(thinsp;p)r+tgr;(thinsp;p)(r) can be extrapolated versuspminus;1to yield values for Dgr;Sr/kwhich compare favorably with results obtained from calculations on small crystals.