X-Ray Diffraction

1
X-Ray Diffraction

• Path Length
• Phase Difference
• For a new atom in a unit cell

yb
xa
2

• Diffraction angle
• 2 d sin? ?
• sin? ?/2d

?
Bright spot ?
d
(h,k,l)
3

• Reflection from plane through new atom
• Planes at same angle

?
??
4

• New plane at spacing
• ? (hx ky lz) d

?
?
??
5

• Extra path length
• ?x ? sin?
• On each side

?
?
? sin?
?
??
? sin?
6

• Extra path length
• ?x 2 ? sin?
• But sin? ?/2d Bragg spot
• ?x ??/d

?
? sin?
?
?x
? sin?
7

• phase difference
• 2? radians in one ?
• ?x 2?/? 2? ?/d

?
? sin?
?
??
? sin?
8

• phase difference
• ?? 2? (hx ky lz)

?
? sin?
?
??
? sin?
9

• phase difference
• ?? 2? (hx ky lz)

2?ix/?
?
e
? sin?
?
2?ix/???
e
? sin?
10

• phase difference
• ?? 2? (hx ky lz)

2?ix/?
?
e
? sin?
2?ix/?
e
e
2?i(hxkylz)
?
? sin?
11
Systematic Extinctions
yb

• Body Centered Cubic
• x ½ y ½ z ½
• ?? 2? (hx ky lz) n? with n odd
• ?? 2? (h/2 k/2 l/2) n?

xa
12
Systematic Extinctions
yb
xa

• Body Centered Cubic
• (1,1,1) ?? 2? (1/2 1/2 1/2)
• (1,1,1) ?? 3? waves cancel
• h k l even for reflection to appear