What would be the area of the primitive unit cell if all empty and filled circles were identical?
What would be the area of the primitive unit cell if all empty and filled circles were identical?
3. Write down a set of primitive lattice vectors and the corresponding basis for this crystal.
3. Write down a set of primitive lattice vectors and the corresponding basis for this crystal.
Would these primitive lattice vectors still be primitive if all empty and filled circles were identical? If not, identify a new primitive unit cell and the associated basis.
Would these primitive lattice vectors still be primitive if all empty and filled circles were identical? If not, identify a new primitive unit cell and the associated basis.
4. Imagine expanding the lattice into the perpendicular direction $z$ (out of the page). We can define a new three-dimensional crystal by considering a periodic structure in the $z$ direction, where the filled circles have been displaced by $\frac{a}{2}$ in both the $x$ and $y$ direction from the empty circles.
4. Imagine expanding the lattice into the perpendicular direction $z$ (out of the page). We define a new three-dimensional crystal by considering a periodic structure in the $z$ direction with a period $a$, where the filled circles are additionally displaced by $a/2$ in the $z$-direction.
The figure below shows the new arrangement of the atoms.
The figure below shows the new arrangement of the atoms.
What lattice do we obtain?
What lattice do we obtain?
Write down the basis of this three-dimensional crystal.
Write down the basis of this three-dimensional crystal.