X-ray diffraction

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X-ray diffraction
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X-ray diffraction
Braggs' law ? 2dhkl sin ?hkl
From this set of planes, only get reflection at
one angle - ?
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X-ray diffraction
Braggs' law ? 2dhkl sin ?hkl
another set of lattice planes
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X-ray diffraction
Braggs' law ? 2dhkl sin ?hkl
X-rays
another set of lattice planes
Different sets of planes reflect at different ?
angles
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Ewald construction
Think of set of planes reflecting in x-ray beam
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Ewald construction
Think of set of planes reflecting in x-ray
beam Center sphere on specimen origin x-ray
beam is a sphere diameter
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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
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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
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Ewald construction
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Ewald construction
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Ewald construction
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Ewald construction
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Ewald construction
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Ewald construction
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Ewald construction
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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
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Ewald construction
Looking down on one plane of points.... the
equatorial plane
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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
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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
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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
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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
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Ewald construction
hk0 reflected rays all lie in the equatorial
plane.
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Ewald construction
hk0 reflected rays all lie in the equatorial
plane. hk1 reflected rays lie on a cone.
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Ewald construction
hk0 reflected rays all lie in the equatorial
plane. hk1 reflected rays lie on a cone.
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Ewald construction
Sheet of film or image paper wrapped
cylindrically around crystal....
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Ewald construction
Sheet of film or image paper wrapped
cylindrically around crystal.... looks like
this after x-ray exposure of oscillating
crystal .....when flattened
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Ewald construction
To see reflections move sphere move
crystal change sphere size
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Ewald construction
reciprocal lattice representation
Ewald sphere
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Ewald construction