1. Laue equations and reciprocal lattice  

2. Laue camera Unfiltered X-radiation through collimator back reflexion photo (spots on hyperbolas) forward reflexion photo (spots on ellipses) crystal held on goniometer head SiGe continuous band of wavelength provided suitable for determination of crystal orientation & symmetry each spot corresponds to planes of atoms of spacing d satisfying 2dsin  = diffraction pattern exhibits the symmetry of the crystal in the direction of k 0 spots corresponding to reciprocal vectors [h,k,l] and [h,k,l] are symmetric with respect to the centre of the diffraction pattern

3. Rotating crystal axis of rotation=crystal axis monochromatic X-ray beam trap film held against inside wall of cylinder unwrapped film r  Let axis of rotation be the C-axis so that Laue eqn C(cos  -cos  0 )=l Since    /2, C cos  =l. For l=0 “cone” is a plane  C. For l=1,2 d l =rcos  l. Therefore

4. Powder method monochromatic X-ray 22 wrapped film cone of x-rays satisfying the Laue eqn powder sample: many crystallites in random orientations r unwrapped film Lack of orientation make crystal structure determination difficult

5. Powder method gradient=( /2a) 2 Slide paper until matched

6. Powder method 0 1 2 5 4 3 6 7 11 10 8 9 1213 1415 16 simple cubic BCC FCC diamond 110 200 211220 310 222 321 111 200 111 220 311 222 400 h+k+l=even all even or all odd all odd+ even when h+k+l=4n 7,15,23,28,31…. m 2 (8n-1) can not be expressed as h 2 +k 2 +l 2 : useful gaps in sequence

7. Electron and Neutron diffraction Electron diffraction Suitable for study only thin films and crystals, surfaces because of strong interaction of the electrons with atoms and electrons in solids LEED –Low Energy Elastic Diffraction: probes structure of 2D surface of solids. Surface should be free of absorbed atoms Wavelength of the electron  Å)= =12/  e (eV), =1Å for  e =150eV (  h/p,  e =p 2 /2m) Neutron diffraction Weak interaction with charged particles, but strong interaction with magnetic nuclei and electronic magnetisation Wavelength of the neutron  Å)= =0.28/  e (eV), =1Å for  e =0.08eV (  h/p,  e =p 2 /2M) 30 o 50 o 70 o Fe