The fracture strength of glass may be increased by etching away a thin surface layer. It is believed that the etching may alter the surface crack geometry (i. e. reduce crack length and increase tip radius). Calculate the ratio of the etched and original crack tip radii if the fracture strength is increased by a factor of 4 when 16% 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?