The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position
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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position
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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position
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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position
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The four-circle single crystal diffractometer
Detect reflections one at a time (conventional
counter) Thus, need to know where reflections
are
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The four-circle single crystal diffractometer
Detect reflections one at a time (conventional
counter) Thus, need to know where reflections
are To get reflection from a particular set of
planes locate reciprocal lattice pt
wrt instrument coords rotate crystal so
that reciprocal lattice vector
coincident w/ diffraction vector
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position Here, counter in position to
receive reflection but crystal not in position
to reflect Crystal is rotated around the axes to
bring it to correct position for reflection
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The four-circle single crystal diffractometer
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position
?? 0 when ?-axis along z
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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position

• ?? 0 when ?-axis along z
• ?? 0 when ?-circle normal to x

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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position

• ?? 0 when ?-axis along z
• ??? 0 when ??????l??
• ????????? x
• 2? 0 when counter at beam position

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The four-circle single crystal diffractometer (se
e Arndt Willis, Single Crystal Diffractometry)
Counter restricted to plane Counter rotated to
appropriate Bragg angle Crystal rotated into
reflecting position

• ?? 0 when ?-axis along z
• ??? 0 when ??????l??
• ????????? x
• 2? 0 when counter at beam position
• ? arbitrary

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The four-circle single crystal diffractometer
Instrument alignment 1. Adjust tube to
instrument - pinhole collimator sees tube
focal spot
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The four-circle single crystal diffractometer
Instrument alignment 1. Adjust tube to
instrument - pinhole collimator sees tube
focal spot 2. Align goniometer using alignment
crystal small sphere (lt 0.3
mm) stable strong reflections low
mosaicity minimum fluorescence ACA ruby
crystals
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The four-circle single crystal diffractometer
Instrument alignment 1. Adjust tube to
instrument - pinhole collimator sees tube
focal spot 2. Align goniometer using alignment
crystal small sphere (lt 0.3
mm) stable strong reflections low
mosaicity minimum fluorescence ACA ruby
crystals
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The four-circle single crystal diffractometer
Instrument alignment 2. Align goniometer using
alignment crystal Centre crystal in
goniometer using telescope Approx. 2? zero
align Locate strong reflection from
crystal Centre diffracted beam from
crystal Shift all 4 axes until reflection
centred
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The four-circle single crystal diffractometer
Instrument alignment 2. Align goniometer using
alignment crystal Centre crystal in
goniometer using telescope Approx. 2? zero
align Locate strong reflection from
crystal Centre diffracted beam from
crystal Shift all 4 axes until reflection
centred Repeat at 2? to find 2? 0 ?
and ? zeroes set during this process
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The four-circle single crystal diffractometer
Crystal alignment Use nearly same procedure -
adjust goniometer head arcs
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The four-circle single crystal diffractometer
Crystal alignment Use nearly same procedure -
adjust goniometer head arcs Films other flat
specimens Can use laser for initial
alignment Adjust specimen height Rotate ?,
adjusting goniometer head arcs until laser
spot stationary
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The four-circle single crystal diffractometer
Crystal alignment Use nearly same procedure -
adjust goniometer head arcs Films other flat
specimens Can use laser for initial
alignment Adjust specimen height Rotate ?,
adjusting goniometer head arcs until laser
spot stationary repeat w/ x-ray reflection
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis What is texture (preferred
orientation)?
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis What is texture (preferred
orientation)? 1st the stereographic
projection
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis What is texture (preferred
orientation)? Now consider 100 pole
distribution in polycrystalline sheet materials
(cubic) use stereographic projection
representation crystals randomly crystals all
aligned oriented
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis What is texture (preferred
orientation)? Now consider 100 pole
distribution in polycrystalline sheet materials
(cubic) use stereographic projection
representation crystals randomly crystals all
aligned oriented For real textured matl,
pole figure is somewhere betwn these
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis 100 pole distribution in
polycrystalline sheet materials (cubic) use
stereographic projection representation Use
four-circle system to get pole density
distribution
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The four-circle single crystal diffractometer
Flat specimen application - texture
analysis 100 pole distribution in
polycrystalline sheet materials (cubic) use
stereographic projection representation Use
four-circle system to get pole density
distribution How??
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The four-circle single crystal diffractometer
Another preferred orientation application
drawn polymers (fiber texture) Pole
figure
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The four-circle single crystal diffractometer
Another preferred orientation application
drawn polymers (fiber texture) Pole
figure Use four-circle system to get pole
density distribution How??
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The four-circle single crystal diffractometer
Unknown crystal orientation initial reflection
search ? scans at various ?s for a sequence of
2?s Centre reflections w/ half shutters of
detector aperture Get ?, ?, ?, 2??for each
reflection
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The four-circle single crystal diffractometer
Unknown crystal orientation initial reflection
search ? scans at various ?s for a sequence of
2?s Centre reflections w/ half shutters of
detector aperture Get ?, ?, ?, 2??for each
reflection Need 25 reflections to index (get
(hkl)s and lattice params) Then get orientation
matrix
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The four-circle single crystal diffractometer
Unknown crystal orientation initial reflection
search Get orientation matrix Two coord.
Systems diffractometer xyz
(orthogonal) recip. lattice
abc(may be oblique)
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The four-circle single crystal diffractometer
Unknown crystal orientation initial reflection
search Get orientation matrix Two coord.
Systems diffractometer xyz
(orthogonal) recip. lattice
abc(may be oblique) Use orthogonal recip
lattice coord. System Horthog BH B is
matrix that transforms from oblique
to orthog. System and Hxyz UHorthog
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The four-circle single crystal diffractometer
To get reflection from a particular
reflection locate recip. Lattice pt. wrt
instrument coords. rotate crystal so that
recip. lattice vector is coincident w/
diffraction vector For the latter
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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer
To get reflection from a particular reflection
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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer

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The four-circle single crystal diffractometer