PROCESS DYNAMIC+CONTROL-EBOOK>I<
4th Edition
ISBN: 2819480255712
Author: Seborg
Publisher: INTER WILE
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The periodic array below denotes a hypothetical lattice in 2D.
1. Is this a Bravais lattice? Why or why not?
2. Draw 3 different versions of unit cells. Of those 3, make one a primitive unit cell.
3. There is a special type of primitive unit cell that is called a ’Wigner-Seitz’ cell (look it up on-
line, or in text books). In words, describe how it is defined, and draw it for the lattice above.
4. Why would it be useful to draw the primitive unit cell of a lattice as a Wigner-Seitz cell, rather
than another random choice? Hint : What geometric property of a lattice was described to be useful in guessing material properties
The schematic figure below shows a face-centered cubic (FCC) lattice with a lattice constant
of a.
Draw the lattice vectors of a primitive unit cell for the FCC lattice. Also write them in equation form and derive an expression for the reciprocal lattice vectors of an FCC lattice
Using these sets of reciprocal lattice vectors, draw (or generate) the reciprocal lattice of FCC in re-
ciprocal space. Show that this reciprocal lattice is equivalent to a body-centered cubic lattice with a lattice
constant of 4pi/a
Derive the 3D density of states for a system of electrons with the dispersion relation (in the picture)
Assume that there is no spin degeneracy
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