ECE 350 Homework Set #5
Due Wed. Sept. 9(Work in Class)
These questions relate to the close packed sphere model of the face-centered cubic lattice. This model is constructed of two sets of (111) planes each consisting of 6 spheres arranged in an equilateral triangle. On the first set the atoms are labeled with letters B through G and on the second set they are labeled H through M. There are two single spheres labeled A and N. The two sets of 6 spheres are stacked on top of each other so that the spheres of one set are nestled into the hollows between the spheres of the other set. The sphere A is placed on top of the first set of 6 atoms and the sphere N is placed behind the second set to form a face-centered cubic structure.Fix a coordinate system such that the center of sphere H is the origin and a line through the centers of spheres H and E is the x axis, a line through H and N is the y axis and the z axis lies through H and F.
1. What are the direction indices of the vector BG (consider BG as short hand notation for the vector from the center of sphere B to sphere G)?
2. What are the direction indices of vector BC?
3. Determine the miller indices of the plane containing BG and BC.
4. Determine the direction indices of the normal to the plane containing BG and BC.
5. Locate a tetrahedral interstitial position by giving the letters of the labels of 4 spheres located at the corners of the tetrahedron and also the coordinates of the center of the tetrahedron with respect to the fixed coordinate system.
6.Locate an octahedral interstitial position by giving the letters of the labels of 6 spheres located at the corners of the octahedron and also the coordinates of the center of the octahedron with respect to the fixed coordinate system.
7. Give the position coordinates of all the tetrahedral interstitial positions in the unit cell.
8. Determine the miller indices of the plane passing through the centers of the spheres I, B, and D.
The following questions pertain to the hard sphere model of the hexagonal close-packed structure.Take the unit cell axes to be the vectors AB, AC, and AK.
9. What are the coordinates of the center of the sphere H with respect to the unit cell axes defined above?
10. Determine the direction indices of the following vectors:
AB, AD, AL, AN.
11. Determine the miller indices of the planes BLND, BLMC,BKC (Where plane is defined by passing through points located at centers of the labeled spheres).
12. Locate a tetrahedral interstitial position by giving the letters of the labels of 4 spheres located at the corners of the tetrahedron and also the coordinates of the center of the tetrahedron with respect to the fixed coordinate system.
13.Locate an octahedral interstitial position by giving the letters of the labels of 6 spheres located at the corners of the octahedron and also the coordinates of the center of the octahedron with respect to the fixed coordinate system.