4. You are using dark-field TEM to examine a metal sample that possess populations of dislocations produced by a small amount of gentle, room-temperature deformation. You wish to study these dislocations by making use of the \"invisibility criteria\" for diffraction contrast imaging. The standard approach for doing this is to test a range of different g-vectors and see which ones satisfy the invisibility criteria (i.e. the dislocations disappear). With this in mind, and making sure to show your work, answer the following questions: (a) /1.5pts] Assume the material under study has an FCC crystal structure and you want to a identify the dislocations with Burgers vector b = 5[1 10]. Which of the following g- vectors will satisfy the invisibility criteria for these particular dislocations? g1=[111], g2=[004], g3=[220], gs=[123], gs=1[220] (b) /0.5pt] As discussed in lecture, the results of the invisibility criteria calculation can actually be used for to estimate the relative magnitudes of the imaging contrast at different g-vectors (i.e. larger values indicate stronger contrast or visibility). With this generalized \"contrast criteria\" in mind, which of these g-vectors will provide the strongest imaging contrast for the dislocations in part (a)? () [1.0pt] While you were performing these measurements you noticed that there was another set of dislocations that disappeared under the g2 and gs conditions. What is the Burgers vector for these dislocations