1 Copper oxide (a) YBCO is a common high-temperature superconductor material that contains CuO2 layers, shown in the figure bellow. The black balls represent the Cu atoms and the white balls the oxygen. Draw a set of primitive lattice vectors. If the nearest neighbour distance between two Cu atoms is a, give an expression for the primitive lattice vectors and the basis vectors. Sketch the Wigner-Seitz cell superimposed on the crystal structure. (b) What are the reciprocal lattice vectors for this structure? Hint: you can define an appropriate third lattice vector in order to be able to use the formulas derived in class for calculating the reciprocal lattice vectors. (c) In some materials, the CuO2 layers develop a slight corrugation. In the figure below, alternative diagonal rows of oxygen atoms are displaced by a small amount c, denote with +,. Give an expression the primitive lattice vectors, basis vectors and sketch the Wigner-Seitz cell superimposed on the distorted layer crystal structure