X-Ray Fluorescence Analytical Techniques - CNSTN : Centre ...

fluoresced X-ray intensity from a multi-element specimen subjected to a monochromatic nondivergent
incident radiation of energy E that only accounted for primary absorption:
S Ω Cg i i Ei Ii i E
Ii
=
4πsinψ1µ i
+
sin ψ1 sin ψ2
κ ( , ) µ ( )
, (VI.5)
( E)
µ ( E )
where:
Ii: Intensity of observed characteristic line of element i.
E: Energy of incident radiation.
Ei: Energy of the characteristic line of element i being measured.
S: Irradiated surface area of specimen.
Ci: Concentration of element i in the specimen.
gi: Proportionality constant for characteristic line of element i.
ψ1: Angle between the specimen surface and the incident x-rays.
ψ2: Angle between the specimen surface and the detector.
Ω: Solid angle subtended by the detector.
κ(Ei,Ii): Response of instrument at energy Ei of characteristic line energy of element i.
µi(E): Mass absorption coefficient of element i at incident energy E.
µ(E): Total absorption coefficient of specimen at incident energy E.
µ(Ei): Total absorption coefficient of specimen at characteristic line energy of element i.
Also note that:
( E) ∑C
( E)
µ = j µ j . (VI.6)
j
Sherman later developed his theory to express the emitted X-ray intensity from a multielement
specimen subjected to a polychromatic radiation source. Sherman’s theory was then
further refined by Shiraiwa and Fujino:
⎧
⎪
J 1 E
i − S Ω ⎪ max
τi
( E)
Ji−1
Ii = κ ( Ei, Ii) Cipiω( )
4 sin i ⎨ ∫ Io E dE + Cjpjωj∑ Jiπ ψ1 ⎪ Eiedge µ ( E)
µ ( Ei
)
j 2Ji
+
⎩
⎪ sin ψ1 sin ψ2
Emax τi( Ej) τ j ( E) ⎡ ⎛
sin 1 ( E)
⎞ ⎛
sin 2
( Ei
) ⎞⎤
⎫
ψ µ
ψ µ
⎪
∫
• ⎢ ln ⎜1+ ⎟+ ln ⎜1+ ⎟⎥
dE⎬
Eiedge µ ( E) µ ( Ei
) ⎢µ ( E) ⎜ µ ( Ej) sin ψ ⎟ µ
1 ( Ei)
⎜ µ ( Ej)
sin ψ ⎟⎥
+ ⎢ 2
⎣ ⎝ ⎠ ⎝ ⎠⎥⎦
⎪
⎭
sin ψ1 sin ψ2
, (VI.7)
where;
Ji: Jump ratio of the photoelectric mass absorption coefficient at the absorption edge for the
line of element i being measured.
ωi: Fluorescent yield for the line of element i being measured.
Io(E): Intensity of incident radiation at energy E.
τi(E): Mass photoabsorption coefficient of element i at incident energy E.
τi(Ei): Mass photoabsorption coefficient of element i at energy Ei of characteristic line
energy of element i.
pi: Transition probability of observed line of element i.
Ei edge: Energy of the absorption edge of the characteristic line of element i.
Emax: Maximum energy of the incident radiation.