Answer the following for a face centered unit cell.
how do i find:
-# atoms / 1 unit cell
-coordination #
r u a teacher??
There are four (4) atoms/unit cell for fcc. That's done this way.
There are 8 corners of the cube shared by 8 other cells; therefore, 8 x 1/8 = 1 atom/unit cell.
Then each face has 1 atom in the center and there are 6 faces. Each face is shared by another cell; therefore, 6/2 = 3 atom/unit cell.
The total is 3 + 1 = 4.
To find the number of atoms in a face-centered unit cell, you need to consider the arrangement of atoms within the unit cell.
For a face-centered unit cell, there are atoms at each of the eight corners of the unit cell, and there is an additional atom at the center of each face of the unit cell. So, to find the number of atoms in the unit cell, you need to count the number of atoms at the corners and the number of atoms on the faces, and then add them together.
1) Number of atoms at the corners:
Each corner atom is shared by eight adjacent unit cells. Since there are eight corners in a unit cell, the contribution of each corner atom to a single unit cell is 1/8. Therefore, the total contribution of corner atoms to one unit cell is 8 x (1/8) = 1.
2) Number of atoms on the faces:
Each face-centered atom is shared by two adjacent unit cells. Since there are six faces in a unit cell, the contribution of each face-centered atom to a single unit cell is 1/2. Therefore, the total contribution of face-centered atoms to one unit cell is 6 x (1/2) = 3.
Now, you can add the contributions from the corner atoms (1) and the face-centered atoms (3) to find the total number of atoms in a face-centered unit cell:
Total number of atoms = number of corner atoms + number of face-centered atoms = 1 + 3 = 4.
So, a face-centered unit cell contains 4 atoms.
Next, let's move on to finding the coordination number.
Coordination number refers to the number of nearest neighboring atoms or ions surrounding an atom/ion in a crystalline lattice.
For a face-centered unit cell, the coordination number can be determined by considering the arrangement of atoms around a central atom.
Each corner atom is shared with eight adjacent unit cells, so each corner atom contributes 1/8 to the coordination number of the central atom. Since there are eight corner atoms, their contribution is 8 x (1/8) = 1 to the coordination number.
Additionally, there are six face-centered atoms in each unit cell. Each face-centered atom is shared by two adjacent unit cells and contributes 1/2 to the coordination number of the central atom. Therefore, the contribution of face-centered atoms is 6 x (1/2) = 3 to the coordination number.
Adding the contributions from the corner atoms (1) and the face-centered atoms (3), we get the coordination number of a central atom in a face-centered unit cell:
Coordination number = number of corner atom contributions + number of face-centered atom contributions = 1 + 3 = 4.
So, for a face-centered unit cell, the coordination number is 4.