(xray) diffraction eth z.pdf

(X-ray)(X-ray) DiffractionDiffraction
Some practical aspects of one of
the most important tools in solid
state sciences
Bragg’sBragg’s LawLaw ofof DiffractionDiffraction
constructive interference only, when:
D = n×l (D= AB+BC)
with:
sinq = (D/2)/d
n×l=2d×sinq
DiffractionDiffraction fromfrom LatticeLattice PlanesPlanes
•Each set of planes
corresponds to
one structure factor
Shkl
DiffractionDiffraction fromfrom SingleSingle CrystalsCrystals
DiffractionDiffraction fromfrom PowderPowder CrystalsCrystals
QuadraticQuadratic
BraggBragg
formulasformulas
WorkingWorking PrinciplePrinciple ofof thethe X-rayX-ray
tubetube
• Tungsten wire at 1200-1800oC
(about 35mA heating current)
• High Voltage 20-60 kV
• max. Power -3 kW
•Typical operating values for
Cu: 40 kV, 35 mA
Mo: 45 kV, 35 mA
SpectrumSpectrum ofof thethe X-rayX-ray tubetube
Characteristic radiation
Bremstrahlung (white radiation)
Emax.= E0 = e×V0 and with E = (h×c)/l:
lmin/Å = (h×c)/e×V0 = /( V0/kV)
•n=1,2,3 (principal quantum number), corresponds to K, L, M... shells
•l=0, 1, ..., n-1 (orbital quantum number)
•j=|l±s|; s=1/2 (spin-orbit coupling)
•mj=j, j-1, j-2, ..., -j
•Rules: Transition only, when Dl¹0
Kb1 Ka2 Ka1
•Allowed
Transitions