The four-circle single crystal diffractometer
The four-circle single crystal diffractometer
The four-circle single crystal diffractometer
The four-circle single crystal diffractometer
The four-circle single crystal diffractometer
(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to plane
Counter rotated to appropriate Bragg angle
Crystal rotated into reflecting position
The four-circle single crystal diffractometer
(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to plane
Counter rotated to appropriate Bragg angle
Crystal rotated into reflecting position
The four-circle single crystal diffractometer
(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to plane
Counter rotated to appropriate Bragg angle
Crystal rotated into reflecting position
The four-circle single crystal diffractometer
(see Arndt & Willis, Single Crystal Diffractometry)
Counter restricted to plane
Counter rotated to appropriate Bragg angle
Crystal rotated into reflecting position
The four-circle single crystal diffractometer
Detect reflections one at a time (conventional counter)
Thus, need to know where reflections are
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
s
so
S = so – s
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
so
s
S = so – s
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
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
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
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
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
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
The four-circle single crystal diffractometer
(see 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
The four-circle single crystal diffractometer
(see 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
The four-circle single crystal diffractometer
(see 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
The four-circle single crystal diffractometer
Instrument alignment
1. Adjust tube to instrument - pinhole collimator sees
tube focal spot
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 (< 0.3 mm)
stable
strong reflections
low mosaicity
minimum fluorescence
ACA ruby crystals
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 (< 0.3 mm)
stable
strong reflections
low mosaicity
minimum fluorescence
ACA ruby crystals
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
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
The four-circle single crystal diffractometer
Crystal alignment
Use nearly same procedure - adjust goniometer head arcs
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
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
The four-circle single crystal diffractometer
Flat specimen application - texture analysis
What is texture (preferred orientation)?
The four-circle single crystal diffractometer
Flat specimen application - texture analysis
What is texture (preferred orientation)?
1st – the stereographic projection
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
oriented
crystals all aligned
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
oriented
crystals all aligned
For real textured matl, pole figure is somewhere betwn these
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
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??
The four-circle single crystal diffractometer
Another preferred orientation application –
drawn polymers (fiber texture)
FA
Pole figure
The four-circle single crystal diffractometer
Another preferred orientation application –
drawn polymers (fiber texture)
FA
Pole figure
Use four-circle system to get pole density distribution
How??
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
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
The four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer
recip. lattice
–
–
xyz (orthogonal)
a*b*c*(may be oblique)
The four-circle single crystal diffractometer
Unknown crystal orientation – initial reflection search
Get orientation matrix
Two coord. Systems:
diffractometer
recip. lattice
–
–
xyz (orthogonal)
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 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:
The four-circle single crystal diffractometer
1
2
3
The four-circle single crystal diffractometer
To get reflection from a particular reflection:
The four-circle single crystal diffractometer
The four-circle single crystal diffractometer
The four-circle single crystal diffractometer