http://www.phy.hk/wiki/englishhtm/Interference.htm MATS 227 / MAE 251 - - PDF document

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http://www.phy.hk/wiki/englishhtm/Interference.htm MATS 227 / MAE 251 - - PDF document

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http://www.phy.hk/wiki/englishhtm/Interference.htm MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 1 Constructive interference Destructive interference MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 2 1 MATS 227 / MAE 251 / CHEM 222 Lecture

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http://www.phy.hk/wiki/englishhtm/Interference.htm

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Destructive interference Constructive interference

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θ θc

θ θ

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(110) (200) (211)

z x y a b c

Diffraction angle 2θ Intensity (relative)

z x y a b c z x y a b c

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A O

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θ 2θ

r = 1/λ

A O P

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a b c α γ β

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Tetragonal (a=b!c, !="=# =90˚) 1 dhkl $ % & ' ( )

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= h2 + k 2 a2 + !2 c 2 Orthor hombic (a!b!c, !="=# =90˚) 1 dhkl $ % & ' ( )

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= h2 a2 + k 2 b2 + !2 c 2 Monoclinic (a!b!c, !=" = 90˚* # ) 1 dhkl $ % & ' ( )

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= 1 sin2 # h2 a2 + k 2 b2 + !2 sin2 # c 2 + 2hk cos# ab $ % & ' ( ) Hexagonal (a=b!c, !=" = 90˚,# = 120˚) 1 dhkl $ % & ' ( )

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= 4 3 h2 + hk + k 2 a2 + k 2 b2 $ % & ' ( ) + !2 c 2 R hombohedral (a=b=c, !=" = # * 90˚) 1 dhkl $ % & ' ( )

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= h2 + k 2 + !2

( )sin2 ! + 2(hk + !k + h!)(cos2 ! + cos!)

a2(1+ 2cos3 ! + 3cos2 !)

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(000)

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Intensity 2θ

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(000)