Glancing Angle X-ray Diffraction (GAXRD) Technique

Scattering contd..
Collecting the relevant formulas for our purpose we get
1 2
ε '
k'= ⎡ ⎤
⎢⎣ε⎥⎦ k
ε cosα = ε'cosα' Equation (1) is required by the Maxwell’s equations and (2) is
Snell’s law (since the indices of refraction equal the square roots
of the respective permittivity
Amplitude of the refracted wave is linearly related to the amplitude
of the incident , and is written as
ur ur
E ' =Φ.
E
where φ is a 2 nd rank tensor whose components can be expressed as
Scattering contd..
2 ( εε −ε
1
2 2 α )
+ ( − )
2 ' cos
Φ = xx
ε'sinα εε'ε cos α
1
2 2 2
Eqs. (3) & (4), when expressed in more elementary terms
for the separate cases of parallel and perpendicular
polarization, are sometimes known as Fresnel’s equations
(1)
(2)
(3)
Φ yy =
2 εsinα 1
2 2
εsinα + ( ε'−εcosα) 2εsinα Φ = zz
1
2 2 2
ε'sinα + ( εε'−ε cos α)
Φ =Φ =Φ =Φ =Φ =Φ = 0
xy yx xz zx yz zy
(4)
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