4-circle kappa diffractometer example¶
The kappa geometry replaces the traditional \(\chi\)-ring on a 4-circle diffractometer with an alternative kappa stage that holds the phi stage. The kappa stage is tilted at angle \(\alpha\) (typically 50 degrees) from the \(\omega\) stage.
Note: This example is available as a Jupyter notebook from the hklpy source code website: https://github.com/bluesky/hklpy/tree/main/examples
Load the hklpy package (named ``hkl``)¶
Since the hklpy package is a thin interface to the hkl library (compiled C++ code), we need to first load the gobject-introspection package (named ``gi``) and name our required code and version.
This is needed every time before the hkl package is first imported.
import gi
gi.require_version('Hkl', '5.0')
Setup the K4CV diffractometer in hklpy¶
In hkl K4CV geometry (https://people.debian.org/~picca/hkl/hkl.html#org723c5b9):
K4CV geometry¶
For this geometry there is a special parameter \(\alpha\), the angle between the kappa rotation axis and the \(\vec{y}\) direction.
axis |
moves |
rotation axis |
vector |
|---|---|---|---|
komega |
sample |
\(-\vec{y}\) |
|
kappa |
sample |
\(\vec{x}\) |
|
kphi |
sample |
\(-\vec{y}\) |
|
tth |
detector |
\(-\vec{y}\) |
|
Define this diffractometer¶
Create a python class that specifies the names of the real-space
positioners. We call it KappaFourCircle here but that choice is
arbitrary. Pick any valid Python name not already in use.
The argument to the KappaFourCircle class tells which hklpy base
class will be used. This sets the geometry. See the hklpy
diffractometers
documentation
for a list of other choices.
In hklpy, the reciprocal-space axes are known as pseudo
positioners while the real-space axes are known as real positioners.
For the real positioners, it is possible to use different names than the
canonical names used internally by the hkl library. That is not
covered here.
note: The keyword argument kind="hinted" is an indication that this
signal may be plotted.
This demo uses simulated motors. To use EPICS motors, import that structure from ophyd:
from ophyd import EpicsMotor
Then, in the class, replace the real positioners with (substituting with the correct EPICS PV for each motor):
komega = Cpt(EpicsMotor, "pv_prefix:m41", kind="hinted")
kappa = Cpt(EpicsMotor, "pv_prefix:m22", kind="hinted")
kphi = Cpt(EpicsMotor, "pv_prefix:m35", kind="hinted")
tth = Cpt(EpicsMotor, "pv_prefix:m7", kind="hinted")
and, most important, remove the def __init__() method. It is
only needed to define an initial position for the simulators. Otherwise,
this will move these EPICS motors to zero.
from hkl.diffract import K4CV
from ophyd import PseudoSingle, SoftPositioner
from ophyd import Component as Cpt
class KappaFourCircle(K4CV):
"""
Our kappa 4-circle. Eulerian, vertical scattering orientation.
"""
# the reciprocal axes are called: pseudo in hklpy
h = Cpt(PseudoSingle, '', kind="hinted")
k = Cpt(PseudoSingle, '', kind="hinted")
l = Cpt(PseudoSingle, '', kind="hinted")
# the motor axes are called: real in hklpy
komega = Cpt(SoftPositioner, kind="hinted")
kappa = Cpt(SoftPositioner, kind="hinted")
kphi = Cpt(SoftPositioner, kind="hinted")
tth = Cpt(SoftPositioner, kind="hinted")
def __init__(self, *args, **kwargs):
"""Define an initial position for simulators."""
super().__init__(*args, **kwargs)
for p in self.real_positioners:
p._set_position(0) # give each a starting position
k4cv = KappaFourCircle("", name="k4cv")
Add a sample with a crystal structure¶
from hkl.util import Lattice
# add the sample to the calculation engine
a0 = 5.431
k4cv.calc.new_sample(
"silicon",
lattice=Lattice(a=a0, b=a0, c=a0, alpha=90, beta=90, gamma=90)
)
HklSample(name='silicon', lattice=LatticeTuple(a=5.431, b=5.431, c=5.431, alpha=90.0, beta=90.0, gamma=90.0), ux=Parameter(name='None (internally: ux)', limits=(min=-180.0, max=180.0), value=0.0, fit=True, inverted=False, units='Degree'), uy=Parameter(name='None (internally: uy)', limits=(min=-180.0, max=180.0), value=0.0, fit=True, inverted=False, units='Degree'), uz=Parameter(name='None (internally: uz)', limits=(min=-180.0, max=180.0), value=0.0, fit=True, inverted=False, units='Degree'), U=array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]]), UB=array([[ 1.15691131e+00, -7.08403864e-17, -7.08403864e-17],
[ 0.00000000e+00, 1.15691131e+00, -7.08403864e-17],
[ 0.00000000e+00, 0.00000000e+00, 1.15691131e+00]]), reflections=[])
Setup the UB orientation matrix using hklpy¶
Define the crystal’s orientation on the diffractometer using the 2-reflection method described by Busing & Levy, Acta Cryst 22 (1967) 457.
Choose the same wavelength X-rays for both reflections¶
k4cv.calc.wavelength = 1.54 # Angstrom (8.0509 keV)
Find the first reflection and identify its Miller indices: (hkl)¶
r1 = k4cv.calc.sample.add_reflection(
4, 0, 0,
position=k4cv.calc.Position(
tth=-69.0966,
komega=55.4507,
kappa=0,
kphi=-90,
)
)
Find the second reflection¶
r2 = k4cv.calc.sample.add_reflection(
0, 4, 0,
position=k4cv.calc.Position(
tth=-69.0966,
komega=-1.5950,
kappa=134.7568,
kphi=123.3554
)
)
Compute the UB orientation matrix¶
The compute_UB() method always returns 1. Ignore it.
k4cv.calc.sample.compute_UB(r1, r2)
1
Report what we have setup¶
import pyRestTable
tbl = pyRestTable.Table()
tbl.labels = "term value".split()
tbl.addRow(("energy, keV", k4cv.calc.energy))
tbl.addRow(("wavelength, angstrom", k4cv.calc.wavelength))
tbl.addRow(("position", k4cv.position))
tbl.addRow(("sample name", k4cv.sample_name.get()))
tbl.addRow(("[U]", k4cv.U.get()))
tbl.addRow(("[UB]", k4cv.UB.get()))
tbl.addRow(("lattice", k4cv.lattice.get()))
print(tbl)
print(f"sample\t{k4cv.calc.sample}")
==================== ===================================================
term value
==================== ===================================================
energy, keV 8.050922077922078
wavelength, angstrom 1.54
position KappaFourCirclePseudoPos(h=0.0, k=-0.0, l=0.0)
sample name silicon
[U] [[ 1.74532925e-05 -6.22695871e-06 -1.00000000e+00]
[ 0.00000000e+00 -1.00000000e+00 6.22695872e-06]
[-1.00000000e+00 -1.08680932e-10 -1.74532925e-05]]
[UB] [[ 2.01919115e-05 -7.20403894e-06 -1.15691131e+00]
[ 0.00000000e+00 -1.15691131e+00 7.20403894e-06]
[-1.15691131e+00 -1.25734128e-10 -2.01919115e-05]]
lattice [ 5.431 5.431 5.431 90. 90. 90. ]
==================== ===================================================
sample HklSample(name='silicon', lattice=LatticeTuple(a=5.431, b=5.431, c=5.431, alpha=90.0, beta=90.0, gamma=90.0), ux=Parameter(name='None (internally: ux)', limits=(min=-180.0, max=180.0), value=-160.36469500932463, fit=True, inverted=False, units='Degree'), uy=Parameter(name='None (internally: uy)', limits=(min=-180.0, max=180.0), value=-89.99893826046727, fit=True, inverted=False, units='Degree'), uz=Parameter(name='None (internally: uz)', limits=(min=-180.0, max=180.0), value=19.635304987561902, fit=True, inverted=False, units='Degree'), U=array([[ 1.74532925e-05, -6.22695871e-06, -1.00000000e+00],
[ 0.00000000e+00, -1.00000000e+00, 6.22695872e-06],
[-1.00000000e+00, -1.08680932e-10, -1.74532925e-05]]), UB=array([[ 2.01919115e-05, -7.20403894e-06, -1.15691131e+00],
[ 0.00000000e+00, -1.15691131e+00, 7.20403894e-06],
[-1.15691131e+00, -1.25734128e-10, -2.01919115e-05]]), reflections=[(h=4.0, k=0.0, l=0.0), (h=0.0, k=4.0, l=0.0)], reflection_measured_angles=array([[0. , 1.57081338],
[1.57081338, 0. ]]), reflection_theoretical_angles=array([[0. , 1.57079633],
[1.57079633, 0. ]]))
Check the orientation matrix¶
Perform checks with forward (hkl to angle) and inverse (angle to hkl) computations to verify the diffractometer will move to the same positions where the reflections were identified.
Check the inverse calculation: (400)¶
sol = k4cv.inverse((55.4507, 0, -90, -69.0966))
print("(4 0 0) ?", f"{sol.h:.2f}", f"{sol.k:.2f}", f"{sol.l:.2f}")
(4 0 0) ? 4.00 -0.00 -0.00
Check the inverse calculation: (040)¶
sol = k4cv.inverse((-1.5950, 134.7568, 123.3554, -69.0966))
print("(0 4 0) ?", f"{sol.h:.2f}", f"{sol.k:.2f}", f"{sol.l:.2f}")
(0 4 0) ? -0.00 4.00 0.00
Check the forward calculation: (400)¶
sol = k4cv.forward((4, 0, 0))
print(
"(400) :",
f"tth={sol.tth:.4f}",
f"komega={sol.komega:.4f}",
f"kappa={sol.kappa:.4f}",
f"kphi={sol.kphi:.4f}"
)
(400) : tth=-69.0985 komega=55.4507 kappa=0.0000 kphi=-90.0010
Check the forward calculation: (040)¶
sol = k4cv.forward((0, 4, 0))
print(
"(040) :",
f"tth={sol.tth:.4f}",
f"komega={sol.komega:.4f}",
f"kappa={sol.kappa:.4f}",
f"kphi={sol.kphi:.4f}"
)
(040) : tth=-69.0985 komega=-1.5939 kappa=134.7551 kphi=-57.3291
Check the forward calculation: (440)¶
sol = k4cv.forward((4, 4, 0))
print(
"(440) :",
f"tth={sol.tth:.4f}",
f"komega={sol.komega:.4f}",
f"kappa={sol.kappa:.4f}",
f"kphi={sol.kphi:.4f}"
)
(440) : tth=-106.6471 komega=16.3379 kappa=59.9415 kphi=-110.3392
Scan in reciprocal space using Bluesky¶
To scan with Bluesky, we need more setup.
%matplotlib inline
from bluesky import RunEngine
from bluesky import SupplementalData
from bluesky.callbacks.best_effort import BestEffortCallback
import bluesky.plans as bp
import bluesky.plan_stubs as bps
import databroker
import matplotlib.pyplot as plt
plt.ion()
bec = BestEffortCallback()
db = databroker.temp().v1
sd = SupplementalData()
RE = RunEngine({})
RE.md = {}
RE.preprocessors.append(sd)
RE.subscribe(db.insert)
RE.subscribe(bec)
1
(h00) scan near (400)¶
RE(bp.scan([], k4cv.h, 3.9, 4.1, 5))
Transient Scan ID: 1 Time: 2020-12-09 01:26:09
Persistent Unique Scan ID: 'c4e101a0-4519-49db-b018-95f85a207b89'
New stream: 'primary'
+-----------+------------+------------+
| seq_num | time | k4cv_h |
+-----------+------------+------------+
| 1 | 01:26:09.1 | 3.900 |
| 2 | 01:26:09.2 | 3.950 |
| 3 | 01:26:09.3 | 4.000 |
| 4 | 01:26:09.4 | 4.050 |
| 5 | 01:26:09.4 | 4.100 |
+-----------+------------+------------+
generator scan ['c4e101a0'] (scan num: 1)
('c4e101a0-4519-49db-b018-95f85a207b89',)
chi scan from (400) to (040)¶
RE(bp.scan([k4cv.komega,k4cv.kappa,k4cv.kphi, k4cv.tth, k4cv.h, k4cv.k, k4cv.l], k4cv.h, 4, 0, k4cv.k, 0, 4, 10))
Transient Scan ID: 2 Time: 2020-12-09 01:26:09
Persistent Unique Scan ID: '9a06c68b-aa82-489d-90ae-533c6049218b'
New stream: 'primary'
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
| seq_num | time | k4cv_h | k4cv_k | k4cv_l | k4cv_komega | k4cv_kappa | k4cv_kphi | k4cv_tth |
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
| 1 | 01:26:10.0 | 4.000 | -0.000 | -0.000 | 55.451 | -0.000 | -90.001 | -69.099 |
| 2 | 01:26:10.7 | 3.556 | 0.444 | -0.000 | 56.473 | 9.305 | -92.995 | -61.065 |
| 3 | 01:26:11.4 | 3.111 | 0.889 | 0.000 | 55.945 | 20.863 | -96.750 | -54.612 |
| 4 | 01:26:12.0 | 2.667 | 1.333 | 0.000 | 53.570 | 34.906 | -101.426 | -50.011 |
| 5 | 01:26:12.8 | 2.222 | 1.778 | -0.000 | 49.086 | 51.202 | -107.119 | -47.592 |
| 6 | 01:26:13.5 | 1.778 | 2.222 | -0.000 | 42.420 | 68.872 | -113.785 | -47.592 |
| 7 | 01:26:14.1 | 1.333 | 2.667 | 0.000 | 33.757 | 86.675 | -121.238 | -50.011 |
| 8 | 01:26:14.7 | 0.889 | 3.111 | 0.000 | 23.427 | 103.647 | -129.267 | -54.612 |
| 9 | 01:26:15.3 | 0.444 | 3.556 | 0.000 | 11.673 | 119.520 | -137.793 | -61.065 |
| 10 | 01:26:16.0 | -0.000 | 4.000 | 0.000 | -1.595 | 134.757 | 122.954 | -69.099 |
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
generator scan ['9a06c68b'] (scan num: 2)
('9a06c68b-aa82-489d-90ae-533c6049218b',)
(0k0) scan near (040)¶
RE(bp.scan([], k4cv.k, 3.9, 4.1, 5))
Transient Scan ID: 3 Time: 2020-12-09 01:26:18
Persistent Unique Scan ID: 'b0b83e7f-d8b3-4cb9-95e4-83d6ddce81b5'
New stream: 'primary'
+-----------+------------+------------+
| seq_num | time | k4cv_k |
+-----------+------------+------------+
| 1 | 01:26:18.3 | 3.900 |
| 2 | 01:26:18.3 | 3.950 |
| 3 | 01:26:18.3 | 4.000 |
| 4 | 01:26:18.3 | 4.050 |
| 5 | 01:26:18.4 | 4.100 |
+-----------+------------+------------+
generator scan ['b0b83e7f'] (scan num: 3)
('b0b83e7f-d8b3-4cb9-95e4-83d6ddce81b5',)
(hk0) scan near (440)¶
RE(bp.scan([], k4cv.h, 3.9, 4.1, k4cv.k, 3.9, 4.1, 5))
Transient Scan ID: 4 Time: 2020-12-09 01:26:18
Persistent Unique Scan ID: '0b2d4091-081d-4583-8f81-fe8871f35840'
New stream: 'primary'
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
| seq_num | time | k4cv_h | k4cv_k | k4cv_l | k4cv_komega | k4cv_kappa | k4cv_kphi | k4cv_tth |
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
| 1 | 01:26:18.9 | 3.900 | 3.900 | 0.000 | -121.103 | -59.941 | 110.338 | -102.883 |
| 2 | 01:26:19.5 | 3.950 | 3.950 | -0.000 | -122.034 | -59.941 | 110.338 | -104.745 |
| 3 | 01:26:20.2 | 4.000 | 4.000 | 0.000 | -122.985 | -59.941 | 110.338 | -106.647 |
| 4 | 01:26:20.9 | 4.050 | 4.050 | 0.000 | -123.958 | -59.941 | 110.338 | -108.593 |
| 5 | 01:26:21.6 | 4.100 | 4.100 | 0.000 | -124.954 | -59.941 | 110.338 | -110.585 |
+-----------+------------+------------+------------+------------+-------------+------------+------------+------------+
generator scan ['0b2d4091'] (scan num: 4)
('0b2d4091-081d-4583-8f81-fe8871f35840',)
