Solid state physics

Reciprocal grid and real space E) The following vectors are given a1 = (1,1) a2 = (1 ,-1), Draw the two-dimensional grid that spans the two vectors. b) Draw the first and second Brillouin zones in this grid. 0) What is the size ratio of the fifth Brillouin zone to the first Brillouin zone? d) An electron beam with a de-Broglie wavelength of approx. 0.1 nm is fired at the above-mentioned grating. The diffraction pattern can be seen on a phosphor screen. Draw the reciprocal grating (schematically, without observing the large scale). How does the diffraction pattern change if the voltage is increased (e.g. by a factor of 2)? e) This electron beam is now shot at a powder. This is simply arranged cubically according to the vectors a1 = (1,1,0) 51,: (1 ,-1,0) and a, =(0,0,1/2). Once again, a projection screen is set up at a distance of 10cm. What is the distance between the first two maxima