Question

Consider the diamond structure. Assign Cartesian coordinates to the locations of the centers of all atoms. The corner atoms are at locations 000, 100, 010, 001, 011, 101, 110, 111. These numbers represent the x, y and z coordinates, where a 1 means one lattice constant away from the origin. Locate the face centered atoms (there are 6). For starters, one of the is located at ½ ½ 0. Locate the atoms occupying tetrahedral holes (there are 4). There are two different sets of possible coordinates for these. Find both sets.

Answer 1

Coordinates for only those atoms that are positioned at the centers of both side faces, and centers of both front and back faces need to be specified. For the front and back-center face atoms, the coordinates are 1 11 22 and 0 the respective coordinates are 1 1 , respectively. While for the left and right side center-face atoms, 22 1 1 2 0 2 and 1 1 1 . 2 2 3.26 (a) Here we are asked list point coordinates for both sodium and chlorine ions for a unit cell of the sodium chloride crystal structure, which is shown in Figure 12.2. In Figure 12.2, the chlorine ions are situated at all corners and face-centered positions. Therefore, point coordinates for these ions are the same as for FCC, as presented in the previous problem—that is, 000, 100, 110, 010, 001, 101, 111, 011, 11 2 2 0, 11 2 2 1, 1 11 22 , 0 1 1 22 , 1 2 0 1 2 , and 1 1 1 . 2 2 Furthermore, the sodium ions are situated at the centers of all unit cell edges, and, in addition, at the unit cell center. For the bottom face of the unit cell, the point coordinates are as follows: 1 2 1 1 2 2 00 , 1 0 , 1 10 , 0 0 . While, for the horizontal plane that passes through the center of 2 1 1 111 2 2 2 22 the unit cell (which includes the ion at the unit cell center), the coordinates are 0 0 , 1 0 , 1 1 1 2 2 2 11 , and 01 . And for the four ions on the top face 1 1 2 2 01 , 1 1 , , 1 11 , and 0 1 . 2 (b) This portion of the problem calls for us to list the point coordinates of both the zinc and sulfur atoms for a unit cell of the zinc blende structure,