For the closest packed plane in a copper single crystal (FCC): -What are hkl and uvw for the plane and plane normal? -Sketch the crystal unit cell and show where this closest packed plane is located -Draw the atomic arrangement of this closest packed plane in a 2-d sketch of the plane.
Two planes that are not parallel intersect at a line. -For the (11bar0) and (12bar1) planes give the direction of this line of intersection. (use an equation). -Does the plane (3bar12) also belong to these planes of a zone? (use an equation) -Sketch a cubic unit cell showing this zone axis and the (11bar0) plane (make sure to label the crystallographic axes a b c). -For a copper single crystal what crystallographic planes will be part of the [001] zone (make sure you use the right brackets for planes)?
-In a Wulff net what angle separates a plane normal (pole) from the projection of the plane? -How does the projection of a plane appear on the Wulff net? -How is a direction, such as a zone axis, shown on a Wulff net? -Given these three pieces of information, how can planes of a zone be determined on a Wulff net?
All of the normal Bravis Lattices could be drawn as primitive cells (e.g. BCC or FCC). -Why is this not normally done (you will need to say what a primitive cell is).
Salt, NaCl, has a B1 crystal structure. This was the first crystal structure that was determined using XRD by Bragg. Bragg didn’t know the wavelength of x-rays but he knew it must be a very small length. He also knew Bragg’s Law, d = l/(2 sinq), and the density of salt that he could convert to 0.0223 NaCl’s per cubic Angstrom. By inspection of the diffraction pattern from NaCl Bragg could assign (he guessed) the first two reflections he observed in XRD (lowest angles) to the (111) and (200) planes. These reflections occurred at 27.4° and 31.6° in his pinhole diffraction photograph. Assuming a cubic system: -Calculate the unit cell volume and lattice parameters for NaCl. -Calculate the wavelength of the x-rays that Bragg used (show your work). To which anode does this correspond? -Bragg later placed a sample of aluminum in his x-ray camera and found two reflections at 38.5° and at 44.7°. Assuming aluminum is an A1 structure, what are the lattice constants using the previous wavelength?