Editing X-ray fluorescence (section)

====Crystal materials====
An intuitive understanding of X-ray diffraction can be obtained from the [[Bragg diffraction|Bragg model of diffraction]]. In this model, a given reflection is associated with a set of evenly spaced sheets running through the crystal, usually passing through the centers of the atoms of the crystal lattice. 
The orientation of a particular set of sheets is identified by its [[Miller index|three Miller indices]] (''h'', ''k'', ''l''), and let their spacing be noted by ''d''. 
William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly (mirror-like) from each plane; from that assumption, X-rays scattered from adjacent planes will combine constructively ([[constructive interference]]) when the angle {{mvar|θ}} between the plane and the X-ray results in a path-length difference that is an integer multiple ''n'' of the X-ray wavelength λ.(Fig.7)
: <math>2 d\sin\theta = n\lambda.</math>
<!--copied content from [[:X-ray crystallography]]; see that page's history for attribution-->

The desirable characteristics of a diffraction crystal are:{{citation needed|date=July 2020}}
*High diffraction intensity
*High dispersion
*Narrow diffracted peak width
*High peak-to-background
*Absence of interfering elements
*Low thermal coefficient of expansion
*Stability in air and on exposure to X-rays
*Ready availability
*Low cost

Crystals with simple structures tend to give the best diffraction performance. Crystals containing heavy atoms can diffract well, but also fluoresce more in the higher energy region, causing interference. Crystals that are water-soluble, volatile or organic tend to give poor stability.

Commonly used crystal materials include LiF ([[lithium fluoride]]), ADP ([[ammonium dihydrogen phosphate]]), Ge ([[germanium]]), Si ([[silicon]]), [[graphite]], InSb ([[indium antimonide]]), PE (''tetrakis''-(hydroxymethyl)-methane, also known as [[pentaerythritol]]), KAP ([[potassium hydrogen phthalate]]), RbAP (rubidium hydrogen phthalate) and TlAP (thallium(I) hydrogen phthalate). In addition, there is an increasing use of "layered synthetic microstructures" (LSMs), which are "sandwich" structured materials comprising successive thick layers of low atomic number matrix, and monatomic layers of a heavy element. These can in principle be custom-manufactured to diffract any desired long wavelength, and are used extensively for elements in the range Li to Mg.

In scientific methods that use X-ray/neutron or electron diffraction the before mentioned planes of a diffraction can be doubled to display higher order reflections. The given planes, resulting from Miller indices, can be calculated for a single crystal. The resulting values for ''h, k and l'' are then called [[Laue equations|Laue indices]].
So a single crystal can be variable in the way, that many reflection configurations of that crystal can be used to reflect different energy ranges.
The Germanium (Ge111) crystal, for example, can also be used as a Ge333, Ge444 and more.

For that reason the corresponding indices used for a particular experimental setup always get noted behind the crystal material(e.g. Ge111, Ge444)

Notice, that the Ge222 configuration is forbidden due to diffraction rules stating, that all allowed reflections must be with all odd or all even Miller indices that, combined, result in <math>4n</math>,
where <math>n</math> is the order of reflection.

{| class="wikitable"
|+ Properties of commonly used crystals
|-
!width="100"|material
!width="80"|[[Miller index|plane]]
!width="80"|d (nm)
!width="80"|min λ (nm)
!width="80"|max λ (nm)
!width="80"|intensity
!width="80"|thermal expansion
!width="80"|durability
|-
|[[LiF]]||200||0.2014||0.053||0.379||+++++||+++||+++
|-
|LiF||220||0.1424||0.037||0.268||+++||++||+++
|-
|LiF||420||0.0901||0.024||0.169||++||++||+++
|-
|[[Ammonium dihydrogen phosphate|ADP]]||101||0.5320||0.139||1.000||+||++||++
|-
|[[Germanium|Ge]]||111||0.3266||0.085||0.614||+++||+||+++
|-
|Ge||222||0,1633||forbidden||forbidden||+++||+||+++
|-
|Ge||333||0,1088||0,17839||0,21752||+++||+||+++
|-
|Ge||444||0,0816||0,13625||0,16314||+++||+||+++
|-
|Ge||310||0,1789||forbidden||forbidden||+++||+||+++
|-
|Ge||620||0,0894||0,14673||0,17839||+++||+||+++
|-
|[[Graphite]]||001||0.3354||0.088||0.630||++++||+||+++
|-
|[[InSb]]||111||0.3740||0.098||0.703||++++||+||+++
|-
|[[Pentaerythritol|PE]]||002||0.4371||0.114||0.821||+++||+++++||+
|-
|[[Potassium hydrogen phthalate|KAP]]||1010||1.325||0.346||2.490||++||++||++
|-
|[[RbAP]]||1010||1.305||0.341||2.453||++||++||++
|-
|[[Silicon|Si]]||111||0.3135||0.082||0.589||++||+||+++
|-
|[[TlAP]]||1010||1.295||0.338||2.434||+++||++||++
|-
|[[Yttrium borides#YB66|YB<sub>66</sub>]]||400||0.586||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; || &nbsp;
|-
|6&nbsp;nm LSM||-||6.00||1.566||11.276||+++||+||++
|}