Fill in the blank
For all three of the cubic lattices (unit cells), all of the ______ and _____ are the same size.
(body center, face center, simple cubic)
I think the answers probably are that the edge lengths are the same; i.e., a = b = c and all the angles are the same. The angles are 90 degrees in all cases. The way I read the question, however, it seems to ask what is true for ALL three of the cubic lattices. And the answer above doesn't fit that. If the answers above are correct then the question is poorly worded. If the answer is not correct, then I've missed the point. Post a clarification if there is more to it than that.
For simple cubic lattice, a = b = c and all angles are 90 degrees.
The same is true for face centered cubic and for body centered cubic lattices. However, it is NOT true that a, b, and c in the simple cubic, a,b, and c of the bcc and a,b, and c of the fcc are equal. It still is true that all of the angles are 90 for each and for all. I hope this helps.
the axes and the angles (90 degrees)
For all three of the cubic lattices (unit cells), all of the unit cell edges and angles are the same size.
To understand why this is the case, let's first define what a lattice and a unit cell are in the context of crystal structures. A lattice refers to an infinite three-dimensional arrangement of points in space, while a unit cell is the smallest repeating unit of a lattice that, when repeated in space, generates the entire lattice.
Now, let's discuss the three types of cubic lattices:
1. Simple Cubic: In a simple cubic lattice, each lattice point is located at the corners of the unit cell. The unit cell is a cube with edges of equal length. Therefore, all the unit cell edges and angles are the same size.
2. Body-centered Cubic: In a body-centered cubic lattice, each lattice point is located at the corners and at the center of the unit cell. The unit cell is again a cube, but this time, the lattice point at the center increases the size of the cube compared to the simple cubic lattice. However, the addition of this lattice point does not change the size of the unit cell edges or angles. In other words, they remain the same size.
3. Face-centered Cubic: In a face-centered cubic lattice, each lattice point is located at the corners and at the center of each face of the unit cell. The unit cell is still a cube, but this time, the lattice points at the face centers increase the size of the cube compared to the simple cubic and body-centered cubic lattices. However, like the body-centered cubic lattice, the addition of these lattice points does not change the size of the unit cell edges or angles. They remain the same size.
In summary, regardless of the type of cubic lattice (simple cubic, body-centered cubic, or face-centered cubic), all of the unit cell edges and angles will be the same size.