X-Ray Diffraction Path Length Phase Difference For a new atom in a unit cell xa yb.
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Transcript of X-Ray Diffraction Path Length Phase Difference For a new atom in a unit cell xa yb.
X-Ray Diffraction
• Path Length
• Phase Difference
• For a new atom in a unit cell
xa
yb
• Diffraction angle:• 2 d sin = • sin = /2d
Bright spot d
(h,k,l)
• Reflection from plane through new atom
• Planes at same angle
• New plane at spacing = (hx + ky + lz) d
• Extra path length: x = sin• On each side
sin
sin
• Extra path length: x = 2 sin • But sin = /2d Bragg spot
x = /d
sin
sin
x
• phase difference:• 2 radians in one • x 2/ = 2 /d
sin
sin
• phase difference: = 2 (hx + ky + lz)
sin
sin
• phase difference: = 2 (hx + ky + lz)
sin
sin
2ix/e
e2ix/+
• phase difference: = 2 (hx + ky + lz)
sin
sin
2ix/e
e2ix/e2i(hx+ky+lz)
Systematic Extinctions
• Body Centered Cubic
• x = ½ y = ½ z = ½ = 2 (hx + ky + lz) = 2 (h/2 + k/2 + l/2)
xa
yb
Systematic Extinctions
• Body Centered Cubic
• (1,1,1): = 2 (1/2 + 1/2 + 1/2)
• (1,1,1): = 3 waves cancel
• h+k+l = even
xa
yb