Consider two planes of “Galamsey” gold (Au) atoms from Tarkwa subjected to a homogeneous shear stress. The shear stress is assumed to act in the slip plane along the slip direction. The distance between the atoms in the slip direction is the Burgers vector (

$b$

b) and the spacing between the adjacent lattice planes is the lattice parameter (

$a$

a). The shear stress causes a displacement, 

$x$

x, in the slip direction between the pair of adjacent lattice planes.

i. Derive an expression for the theoretical shear strength of a perfect gold crystal.

ii. Given that the Young’s Modulus of the Galamsey Gold (Au), 

$E=79.0\hspace{0.17em}GPa$

E=79.0GPa, calculate the maximum theoretical shear strength of Gold (Au).

iii. Explain briefly the relationship between the measured shear strength and the theoretical shear strength.

iv. What type of crystal structure will Gold (Au) have and what is the total number of gold atoms that can be found in a unit crystal of gold?

b.

A relatively large plate of glass is subjected to a tensile stress of 40 MPa. If the specific surface energy and modulus of elasticity for this glass are 0.3 J/m² and 69 GPa, respectively, determine the maximum length of a surface flaw that is possible without fracture.

c.

Briefly explain how dislocations multiply via Frank-Read sources. Explain the implications of such interactions for the strengthening of solids via dislocation interactions.