Xray diffraction Xray diffraction Braggs law 2 dhkl

$X-ray diffraction$

X-ray diffraction

$X-ray diffraction Braggs' law = 2 dhkl sin hkl X-rays set of lattice planes$

X-ray diffraction Braggs' law = 2 dhkl sin hkl X-rays set of lattice planes d d sin From this set of planes, only get reflection at one angle -

$X-ray diffraction Braggs' law X-rays another set of lattice planes = 2 dhkl sin$

X-ray diffraction Braggs' law X-rays another set of lattice planes = 2 dhkl sin hkl

$X-ray diffraction Braggs' law = 2 dhkl sin hkl X-rays another set of lattice$

X-ray diffraction Braggs' law = 2 dhkl sin hkl X-rays another set of lattice planes As d —> small, —> large ( is constant) Different sets of planes reflect at different angles

Ewald construction Think of set of planes reflecting in x-ray beam

Ewald construction Think of set of planes reflecting in x-ray beam Center sphere on specimen origin x-ray beam is a sphere diameter

Ewald construction Think of set of planes reflecting in x-ray beam Center sphere on specimen origin x-ray beam is a sphere diameter Construct lines as below

Ewald construction

Ewald construction Most common in single crystal studies is to move (usually rotate) crystal Consider crystal placed at sphere center oriented w/ planes of points in reciprocal lattice as below

Ewald construction Looking down on one plane of points. . the equatorial plane:

Ewald construction Looking down on one plane of points. . the equatorial plane No points on sphere (here, in 2 -D, a circle); must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

Ewald construction Looking down on one plane of points. . the equatorial plane Must rotate reciprocal lattice to observe reflections. rotate around axis here, perpendicular to screen

Ewald construction hk 0 reflected rays all lie in the equatorial plane.

Ewald construction hk 0 reflected rays all lie in the equatorial plane. hk 1 reflected rays lie in a cone.

Ewald construction Sheet of film or image paper wrapped cylindrically around crystal. .

Ewald construction Sheet of film or image paper wrapped cylindrically around crystal. . looks like this after x-ray exposure of oscillating crystal. . . when flattened:

Ewald construction To see reflections: move sphere move crystal change sphere size use polycrystalline sample real space reciprocal space only one set of planes one (hkl)

Ewald construction Ewald sphere reciprocal lattice representation

Ewald construction

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