The fracture strength of glass may be increased by etching away a thin surface layer. It is believed that the etching may alter surface crack geometry (i. e., reduce the crack length and increase the tip radius). Compute the ratio of the etched and original crack-tip radii for a fourfold increase in fracture strength if half of the crack length is removed.

In a unit cell of fcc structure, indicate the position of one of the tetrahedral interstitial sites by plotting the corresponding tetrahedron. do the same for one of the octahedral interstitial sites (in a separate fcc unit cell). mark the positions of all the tetrahedral and octahedral interstitial sites in the unit cells. how many equivalent tetrahedral sites and how many equivalent octahedral sites are contained in a fcc unit cell, respectively. what is the coordination number for a tetrahedral site and what is the coordination number for an octahedral site?