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   

Extra path length:  x = 2  sin  But sin  = /2d Bragg spot  x =  /d    sin  xx

phase difference: 2  radians in one  x 2  / = 2   /d    sin  

phase difference:  = 2  (hx + ky + lz)    sin  

phase difference:  = 2  (hx + ky + lz)    sin  2  ix / e e 2  ix/ + 

phase difference:  = 2  (hx + ky + lz)    sin  2  ix / e e e 2  i(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