lattices which may be obtained from the stacking of two-dimensional lattices. 14.Write an essay which describes and explains the effects due to grain boundaries during precipitation from solid solution. 15.Consider a straight edge dislocation in a crystal.Discuss the types of forces that can operate on the dislocation.For one type of force,give an explicit answer in terms of the Peach-Koehler formula. 16.Discuss in detail the classification of types of kinks on dislocations,the physical basis for their presence on dislocations,and macroscopic properties that indicate the presence of kinks.Give an expression for the velocity of a dislocation moving under a rate-controlling process of kink formation. 17. Consider cleavage fracture of a single crystal of LiF.The crack plane Is the (001)and the crack front-lies parallel to the [100]direction.The surface energy of LiF Is .35 j/m and the slip systems are a/2 <110>{110).Assume cross slip does not occur. (a)Assuming Jc >2y,predict the characteristics(size,shape,dislocation makeup) of the plastic zone as the applied J Increases from zero to above 2Y.Also, describe any distinguishing differences between the surface zone and the midthickness zone. (b)If the material is altered in some way such that J>2Y,what happens to the plastic zone? (c)Assuming that J=2y (exactly),sketch and describe the loading/unloading load-displacement curve for a cracked single crystal DCB specimen with an Initial slot of length a(and"a"can't be less than a )In constructing your sketch assume that crack extension occurs. 18. Discuss the microstructural basis for the Orowan-Friedel relation.Consider the validity of the relation in view of the approximations involved In its derivation.For what types of microstructural features should the relation apply? 15.(a)Symmetry axes are sometimes described in terms of rotation axes and rotation-reflection axes.rather than rotation axes and inversion axes.The operation of a rotation-reflection axis Sn consists of a rotation through 27/n followed by reflection in a plane normal to the rotation-reflection axis.Sketch stereograms showing the operation of 1,2,3,4,and 6-fold reflection axes on a single pole in a general position.Deduce the inversion axis to which each is equivalent. (b)Pure Au and pure Cu are both cubic with atoms at 0,0,0;0,1/2,1/2;1/2,0,1/2; 1/2,1/2,0.The compound Cu-Au is cubic with an Au atom at 0,0,0 and Cu atoms at 0,1/2,1/2;1/2,0,1/2;1/2,1/2,0.Determine the lattice type of Au,Cu,and Cu3Au,and in each case state the number of atoms associated with each latticelattices which may be obtained from the stacking of two-dimensional lattices. 14. Write an essay which describes and explains the effects due to grain boundaries during precipitation from solid solution. 15. Consider a straight edge dislocation in a crystal. Discuss the types of forces that can operate on the dislocation. For one type of force, give an explicit answer in terms of the Peach-Koehler formula. 16. Discuss in detail the classification of types of kinks on dislocations, the physical basis for their presence on dislocations, and macroscopic properties that indicate the presence of kinks. Give an expression for the velocity of a dislocation moving under a rate-controlling process of kink formation. 17. Consider cleavage fracture of a single crystal of LiF. The crack plane Is the (001) and the crack front-lies parallel to the [100] direction. The surface energy of LiF Is .35 j/m and the slip systems are a/2 <110> {110}. Assume cross slip does not occur. (a) Assuming Jc > 2y , predict the characteristics (size, shape, dislocation makeup) of the plastic zone as the applied J Increases from zero to above 2Y. Also, describe any distinguishing differences between the surface zone and the midthickness zone. (b)If the material is altered in some way such that J→2Y, what happens to the plastic zone? (c) Assuming that J = 2y (exactly) , sketch and describe the loading/unloading load-displacement curve for a cracked single crystal DCB specimen with an Initial slot of length a (and “a” can't be less than a ). In constructing your sketch assume that crack extension occurs. 18. Discuss the microstructural basis for the Orowan-Friedel relation. Consider the validity of the relation in view of the approximations involved 1n its derivation. For what types of microstructural features should the relation apply? 15. (a) Symmetry axes are sometimes described in terms of rotation axes and rotation-reflection axes, rather than rotation axes and inversion axes. The operation of a rotation-reflection axis Sn consists of a rotation through 2π /n followed by reflection in a plane normal to the rotation-reflection axis. Sketch stereograms showing the operation of 1, 2, 3, 4, and 6-fold reflection axes on a single pole in a general position. Deduce the inversion axis to which each is equivalent. (b) Pure Au and pure Cu are both cubic with atoms at 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. The compound Cu-Au is cubic with an Au atom at 0,0,0 and Cu atoms at 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. Determine the lattice type of Au, Cu, and Cu3Au, and in each case state the number of atoms associated with each lattice