Question

Consider a 2D side-centered rectangular lattice with one side 3 times the length of the other side. Take the short side lattice constant as a and consider the long side to run in the x-direction. Atom A is at a corner; atom B is halfway along the long side of the rectangle.

a) Sketch lattice and give lattice vectors and basis in vector notation.

b) Find the packing fraction of the lattice assuming the A and B atoms are the same size.

c) Use vector algebra to find reciprocal lattice vectors

Answer 1

ore un vectes A 12 AB then, Ladtice vectors ore. given b) And B have The same Let r be Ahe of B Then Ln One n oe ectongulovr cell here are 4uh A atons ond suoh B atoms

S,Pfertive no ademsper Tdar cell Area eccupied ky afowns 9 a Packing Prati 〈 > o Rind reciproc al verder, toe need prenatte latice vecfer 2 A- A-すす A vectors are 02 Le+ reciprocal lattice vecens are宗Žandb mcal lattice,

and 8,,o r ij え, , 2. GI 23 Ca VeC