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

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 slides 4 3 θ θ θ θ c MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 4 2

z z z c c c y y y (110) a a a b b b Intensity (relative) x x x (211) (200) Diffraction angle 2 θ MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 5 O A MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 6 3

P 2 θ θ O A r = 1/ λ MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 7 c a β α γ b MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 8 4

Tetragonal (a=b ! c, ! = " = # =90˚) = h 2 + k 2 2 $ ' 1 + ! 2 & ) a 2 c 2 % d hkl ( Orthor hom bic (a ! b ! c, ! = " = # =90˚) 2 $ ' = h 2 a 2 + k 2 b 2 + ! 2 1 & ) % d hkl ( c 2 Monoclinic (a ! b ! c, ! = " = 90˚ * # ) b 2 + ! 2 sin 2 # 2 $ ' $ ' h 2 a 2 + k 2 + 2 hk cos # 1 1 = & ) & ) sin 2 # % d hkl ( % c 2 ab ( Hexagonal (a=b ! c, ! = " = 90˚, # = 120˚) h 2 + hk + k 2 2 $ ' $ ' 1 = 4 + k 2 ) + ! 2 & ) & % d hkl ( 3 % a 2 b 2 ( c 2 R hom bohedral (a=b=c, ! = " = # * 90˚) ( ) sin 2 ! + 2( hk + ! k + h ! )(cos 2 ! + cos ! ) h 2 + k 2 + ! 2 2 $ ' 1 = & ) a 2 (1 + 2cos 3 ! + 3cos 2 ! ) % d hkl ( MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 9 • • MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 10 5

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(000) MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 13 MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 14 7

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MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 17 MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 18 9

MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 19 Intensity 2 θ MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 20 10

(000) MATS 227 / MAE 251 / CHEM 222 Lecture slides 4 21 11