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The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Detect reflections one at a time (conventional counter)
Thus, need to know where reflections are
Detect reflections one at a time (conventional counter)
Thus, need to know where reflections are
The four-circle single crystal diffractometerThe 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
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
sos
S = so – s
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
sso
S = so – s
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Here, counter in position to receive reflectionbut crystal not in position to reflect
Crystal is rotated around the axes to bring it to correct position
for reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
= 0 when -axis along z= 0 when -axis along z
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
= 0 when -axis along z
= 0 when -circle normal to x
= 0 when -axis along z
= 0 when -circle normal to x
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
= 0 when -axis along z
0 when l x
2 = 0 when counter at beam position
= 0 when -axis along z
0 when l x
2 = 0 when counter at beam position
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
The four-circle single crystal diffractometer(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
Counter restricted to planeCounter rotated to appropriate Bragg angleCrystal rotated into reflecting position
= 0 when -axis along z
0 when l x
2 = 0 when counter at beam position
arbitrary
= 0 when -axis along z
0 when l x
2 = 0 when counter at beam position
arbitrary
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Instrument alignment
1. Adjust tube to instrument - pinhole collimator sees tube focal spot
Instrument alignment
1. Adjust tube to instrument - pinhole collimator sees tube focal spot
The four-circle single crystal diffractometerThe 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 (< 0.3 mm)stablestrong reflectionslow mosaicityminimum fluorescence
ACA ruby crystals
Instrument alignment
1. Adjust tube to instrument - pinhole collimator sees tube focal spot
2. Align goniometer using alignment crystal
small sphere (< 0.3 mm)stablestrong reflectionslow mosaicityminimum fluorescence
ACA ruby crystals
The four-circle single crystal diffractometerThe 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 (< 0.3 mm)stablestrong reflectionslow mosaicityminimum fluorescence
ACA ruby crystals
Instrument alignment
1. Adjust tube to instrument - pinhole collimator sees tube focal spot
2. Align goniometer using alignment crystal
small sphere (< 0.3 mm)stablestrong reflectionslow mosaicityminimum fluorescence
ACA ruby crystals
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Crystal alignment
Use nearly same procedure - adjust goniometer head arcs
Crystal alignment
Use nearly same procedure - adjust goniometer head arcs
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Flat specimen application - texture analysis
What is texture (preferred orientation)?
Flat specimen application - texture analysis
What is texture (preferred orientation)?
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Flat specimen application - texture analysis
What is texture (preferred orientation)?
1st – the stereographic projection
Flat specimen application - texture analysis
What is texture (preferred orientation)?
1st – the stereographic projection
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe 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
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
The four-circle single crystal diffractometerThe 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??
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??
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Another preferred orientation application –drawn polymers (fiber texture)
Pole figure
Another preferred orientation application –drawn polymers (fiber texture)
Pole figure
FA
The four-circle single crystal diffractometerThe 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??
Another preferred orientation application –drawn polymers (fiber texture)
Pole figure
Use four-circle system to get pole density distribution
How??
FA
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
scans at various s for a sequence of 2s
Centre reflections w/ half shutters of detector aperture
Get , , , 2for each reflection
Unknown crystal orientation – initial reflection search
scans at various s for a sequence of 2s
Centre reflections w/ half shutters of detector aperture
Get , , , 2for each reflection
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
scans at various s for a sequence of 2s
Centre reflections w/ half shutters of detector aperture
Get , , , 2for each reflection
Need ~25 reflections to index (get (hkl)s and lattice params)
Then get orientation matrix
Unknown crystal orientation – initial reflection search
scans at various s for a sequence of 2s
Centre reflections w/ half shutters of detector aperture
Get , , , 2for each reflection
Need ~25 reflections to index (get (hkl)s and lattice params)
Then get orientation matrix
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer – xyz (orthogonal)recip. lattice – a*b*c*(may be oblique)
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer – xyz (orthogonal)recip. lattice – a*b*c*(may be oblique)
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer – xyz (orthogonal)recip. lattice – a*b*c*(may be oblique)
Use orthogonal recip lattice coord. System
Horthog = BH B is matrix that transforms from oblique to orthog. System
and
Hxyz = UHorthog
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer – xyz (orthogonal)recip. lattice – a*b*c*(may be oblique)
Use orthogonal recip lattice coord. System
Horthog = BH B is matrix that transforms from oblique to orthog. System
and
Hxyz = UHorthog
The four-circle single crystal diffractometerThe 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:
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:
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
1
2
3
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
To get reflection from a particular reflection:To get reflection from a particular reflection:
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
The four-circle single crystal diffractometerThe four-circle single crystal diffractometer
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