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Don’t Ever Give Up!. X-ray Diffraction. Typical interatomic distances in solid are of the order of an angstrom. Thus the typical wavelength of an electromagnetic probe of such distances Must be of the order of an angstrom. .

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x ray diffraction
X-ray Diffraction

Typical interatomic distances in solid are of the order of an angstrom.

Thus the typical wavelength of an electromagnetic probe of such distances

Must be of the order of an angstrom.

Upon substituting this value for the wavelength into the energy equation,

We find that E is of the order of 12 thousand eV, which is a typical X-ray

Energy. Thus X-ray diffraction of crystals is a standard probe.

bragg s law
Bragg’s Law

The integer n is known as the order of the corresponding

Reflection. The composition of the basis determines the relative

Intensity of the various orders of diffraction.

reciprocal lattice vectors
Reciprocal Lattice Vectors
  • The reciprocal lattice is defined as the set of all wave vectors K that yield plane waves with the periodicity of a given Bravais lattice.
  • Let R denotes the Bravais lattice points;consider a plane wave exp(ik.r). This will have the periodicity of the lattice if the wave vector k=K, such that

exp(iK.(r+R)=exp(iK.r)

for any r and all R Bravais lattice.

reciprocal lattice vectors37
Reciprocal Lattice Vectors
  • Thus the reciprocal lattice vectors K must satisfy
  • exp(iK.R)=1