Interaction between x-ray and Matter

Solid State Spectroscopy – XRD 1

Order of magnitudes

𝐸𝐸 = ℏ𝜔𝜔 = ℎ𝑐𝑐𝜆𝜆

= ℏ𝑐𝑐𝑐𝑐

Photon carries energy AND momentum

ℏ = 1.05 x 10-34 m2kg s-1

c = 299 792 458 m s-1

𝐸𝐸[𝑒𝑒𝑒𝑒]~ 2 × 103 𝑐𝑐 [Å−1] 1 eV = 1.602 x 10-19 J

Solid in the real space

𝑎𝑎~ 3Å

a

b

𝑎𝑎∗ =2𝜋𝜋𝑎𝑎

~1 Å−1

a*

b*

Solid in the reciprocal space

Visible light only probes the center

of the reciprocal space !

Equivalently λ >> a No information at the atomic scale

All unit cells are in phase

Solid State Spectroscopy – XRD 2

Solid State Spectroscopy – XRD 3

0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.080.0

0.2

0.4

0.6

0.8

1.0 N = 10000 N = 100 N = 30 N = 10

q

Solid State Spectroscopy – XRD 4

Miller Index

Solid State Spectroscopy – XRD 5

Solid State Spectroscopy – XRD 6

Sample in the real space

𝑎𝑎~ 3Å

a

b

𝑎𝑎∗ =2𝜋𝜋𝑎𝑎

~1 Å−1

a*

b*

Solid in the reciprocal space

Solid State Spectroscopy – XRD 7

sample 𝑐𝑐𝐼𝐼

𝑐𝑐𝐹𝐹 detector

2π/λ

𝑄𝑄

Ewald Sphere

Solid State Spectroscopy – XRD 8

𝑐𝑐𝐼𝐼

𝑐𝑐𝐹𝐹 𝑄𝑄

Diffraction condition: 𝑄𝑄 is a vector reciprocal lattice vector

Solid State Spectroscopy – XRD 9

𝑐𝑐𝐼𝐼

𝑐𝑐𝐹𝐹 𝑄𝑄

Diffraction !!

Measurement strategy 1: rotate the crystal

Solid State Spectroscopy – XRD 10

𝑐𝑐𝐼𝐼

𝑐𝑐𝐹𝐹 𝑄𝑄

Diffraction condition satisfied

but for a different Q!!

Measurement strategy 1: rotate the crystal

Solid State Spectroscopy – XRD 11

𝑐𝑐𝐼𝐼

𝑐𝑐𝐹𝐹 𝑄𝑄

Diffraction condition satisfied

but for a different Q!!

Move the detector

Measurement strategy 1: rotate the crystal

Solid State Spectroscopy – XRD 12

Measurement strategy 2: work with a polychromatic beam λmin< λ < λmax

𝑐𝑐𝐼𝐼𝑚𝑚𝑎𝑎𝑚𝑚

2π/λmin

𝑐𝑐𝐼𝐼 𝑚𝑚𝑎𝑎𝑚𝑚 𝑐𝑐𝐼𝐼 𝑚𝑚𝑚𝑚𝑚𝑚

2π/λmax

Solid State Spectroscopy – XRD 13

Measurement strategy 2: work with a polychromatic beam λmin< λ < λmax

𝑐𝑐𝐼𝐼 𝑚𝑚𝑎𝑎𝑚𝑚 𝑐𝑐𝐼𝐼 𝑚𝑚𝑚𝑚𝑚𝑚

Solid State Spectroscopy – XRD 14

http://minerva.union.edu/jonesc/scientific_photos%202010.htm

Examples of Laue Pattern (cubic unit cell)

4 fold 3 fold 2 fold

Solid State Spectroscopy – XRD 15

Measurement strategy 3: Powder diffraction (see exercises)

Solid State Spectroscopy – XRD 16

Solid State Spectroscopy – XRD 17

http://spie.org/x92215.xml

Solid State Spectroscopy – XRD 18

Solid State Spectroscopy – XRD 19

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