1012 106 103 10 1 10-1 10-3

Long Wave IR Visible UV X-rays Gamma rays

wavelength (nm)

X-raysX-rays

absorptionabsorption

I/Io = e -µ* x = 1/ e µ* x = 1/ e µ x

µ* = linear attenuation coefficient

µ = mass attenuation coefficient

= density of absorber

I/Io = e -µ* x = 1/ e µ* x = 1/ e µ x

µ* = linear attenuation coefficient

µ = mass attenuation coefficient

= density of absorber

IoIo IIX-raysX-rays

xx

Absorption Absorption

µ - values for elements listed in various texts & International Tables for Crystallography

µ - values for elements listed in various texts & International Tables for Crystallography

Note that µ changes with X-ray wavelength

Higher atomic no. ––>larger µ, in general

Note that µ changes with X-ray wavelength

Higher atomic no. ––>larger µ, in general

Absorption Absorption

What element used for X-ray tube windows?

What element used for X-ray tube windows?

Absorption Absorption

What element used for protection from X-rays?

What element used for protection from X-rays?

I/Io = e -µ* x = 1/ e µ* x = 1/ e µ x

For compounds & mixtures,

calculate µ from

I/Io = e -µ* x = 1/ e µ* x = 1/ e µ x

For compounds & mixtures,

calculate µ from

µcompd or mixture = (wt. fraction)element x µelementµcompd or mixture = (wt. fraction)element x µelement

IoIo IIX-raysX-rays

xx

Absorption Absorption

I/Io = e -µ* x = 1/ e µ* x = 1/ e µ xI/Io = e -µ* x = 1/ e µ* x = 1/ e µ x

µNaCl = (wt. fraction)Na x µNa + (wt. fraction)Cl x µCl

µNaCl = 0.393 x 30.1 + 106 x .607 = 76.2

µNaCl = (wt. fraction)Na x µNa + (wt. fraction)Cl x µCl

µNaCl = 0.393 x 30.1 + 106 x .607 = 76.2

IoIo IIX-raysX-rays

xx

Example for NaCl (CuK:

(wt. fraction)Na = 23/58.5 = 0.393, (wt. fraction)Cl = 0.607

µNa = 30.1 µCl = 106

Example for NaCl (CuK:

(wt. fraction)Na = 23/58.5 = 0.393, (wt. fraction)Cl = 0.607

µNa = 30.1 µCl = 106

Absorption Absorption

Mass attenuation coefficient for an element changes with

X-ray wavelength (energy) like this:

Mass attenuation coefficient for an element changes with

X-ray wavelength (energy) like this:

mass

att

enuati

on c

oeffi

cient

<–– energy wavelength ––>

Kedge

Good news/bad newsGood news/bad news

Absorption Absorption

Bad news

Absorbed energy re-emitted as fluorescent X-rays

Bad news

Absorbed energy re-emitted as fluorescent X-rays

Absorption Absorption

mass

att

enuati

on c

oeffi

cient

<–– energy wavelength ––>

Kedge

Suppose:Suppose:

absorption for element in specimen

X-ray wavelength usedfor diffraction

Then:

Absorption high

Lots of fluorescence

Then:

Absorption high

Lots of fluorescence

Bad newsBad news

Absorption Absorption

X-raysX-rays

detectordetector

specimenspecimen

X-ray fluorescence radiation emitted at all angles X-ray fluorescence radiation emitted at all angles

22

2

I

instead of this:instead of this:

2

I

get this:get this:

Good news - -filtersGood news - -filters

Absorption Absorption

-filter materials have atomic nos. 1 or 2 less than anode

50-60% beam attenuation

-filter materials have atomic nos. 1 or 2 less than anode

50-60% beam attenuation

Good news - -filtersGood news - -filters

Absorption Absorption

X-raysX-rays

detectordetectorfilterfilter

specimenspecimen

placing after specimen/before detector filters most of specimen fluorescenceplacing after specimen/before detector filters most of specimen fluorescence