Diffractometer “Parameters”

Some of the diffractometer modes use additional parameters. The E4CV geometry, for example, has a double_diffraction mode which requires a reference \(hkl_2\) vector. The vector is set and accessed by a Python command that calls directly the corresponding libhkl function:

action	E4CV method
read names	e4cv.calc.engine._engine.parameters_names_get(units_code)
read values	e4cv.calc.engine._engine.parameters_values_get(units_code)
write names	Names are pre-defined by libhkl and cannot be changed.
write values	e4cv.calc.engine._engine.parameters_values_set(values, units_code)

Objective

Show how to use the double_diffraction mode in the E4CV geometry.

First, we start by importing the constant, A_KEV (product of Planck’s constant and speed of light in a vacuum). The value of this constant is obtained from the 2019 NIST publication of 2018 CODATA Fundamental Physical Constants.

from hkl import A_KEV

E4CV, hkl, double_diffraction

term	value
geometry	E4CV
engine	hkl
mode	double_diffraction

Using the standard E4CV geometry with simulated motors, we copy the E4CV setup for the LNO_LAO sample. Using a kwarg, we can automatically compute the UB matrix once we define the second reflection. (This means we do not have to call compute_UB() on a separate line.)

from hkl import SimulatedE4CV
e4cv = SimulatedE4CV("", name="e4cv")

# order:  a b c  alpha beta gamma
lattice = (3.781726143, 3.791444574, 3.79890313, 90.2546203, 90.01815424, 89.89967858)
e4cv.calc.new_sample("LNO_LAO", lattice=lattice)

wavelength = 1.239424258
e4cv.energy.put(A_KEV / wavelength)

# order:   omega    chi      phi  tth
p_002 = (19.1335, 90.0135, 0.0, 38.09875)
r_002 = e4cv.calc.sample.add_reflection(0, 0, 2, p_002)

p_113 = (32.82125, 115.23625, 48.1315, 65.644)
r_113 = e4cv.calc.sample.add_reflection(1, 1, 3, p_113, compute_ub=True)

# e4cv.calc.sample.compute_UB(r_002, r_113)

Set the double_diffraction mode.

print(f"{e4cv.calc.engine.mode = }")
e4cv.calc.engine.mode = "double_diffraction"
print(f"{e4cv.calc.engine.mode = }")

e4cv.calc.engine.mode = 'bissector'
e4cv.calc.engine.mode = 'double_diffraction'

To read and write the \(hkl_2\) parameters (h2, k2, l2), we must use (at least for now) the low-level libhkl interface. Expect this code to become easier in a future hklpy release.

First, there is a shortcut property in the calc module. It simplifies a more complicated path to the lower level support.

e4cv.calc.parameters

['h2', 'k2', 'l2']

This is the lower-level call simplified by the above:

e4cv.calc.engine._engine.parameters_names_get()

['h2', 'k2', 'l2']

Read the parameters. The supplied argument is either 0 or 1, pick 1 for user units. (libhkl: Hkl.UnitEnum.USER == 1) although either might give the same result. This units feature of libhkl is not used at this time.

e4cv.calc.engine._engine.parameters_values_get(1)

[1.0, 1.0, 1.0]

Set the parameters. First are the values, then the 0 or 1.

# no shortcut to this one.  Yet.
e4cv.calc.engine._engine.parameters_values_set((2,2,0), 1)

1

Calculate (002) with (220) as second diffracting plane

print(f"{e4cv.calc.engine._engine.parameters_values_get(1) = }")
print("(002) :", e4cv.forward((0, 0, 2)))

e4cv.calc.engine._engine.parameters_values_get(1) = [2.0, 2.0, 0.0]
(002) : PosCalcE4CV(omega=19.125954018919902, chi=89.98529317061232, phi=19.05658549375111, tth=38.084063171155435)

Calculate (002) with (222) as second diffracting plane

e4cv.calc.engine._engine.parameters_values_set((2,2,2), 1)
print(f"{e4cv.calc.engine._engine.parameters_values_get(1) = }")
print("(002) :", e4cv.forward((0, 0, 2)))

e4cv.calc.engine._engine.parameters_values_get(1) = [2.0, 2.0, 2.0]
(002) : PosCalcE4CV(omega=19.125992826777857, chi=89.98551636715716, phi=18.904239486428196, tth=38.08406317115545)