Glossary

Tip

Italics are used in these definitions to identify other glossary entries.

auxiliary

Axes that are not pseudos or reals.

axis

Either a pseudo, real, extra.

physical:

Axis (either pseudo or real) which is not computed from other axes (except by the solver). “Physical” for a real implies a direct connection to hardware,

virtual:

Axis (either pseudo and real) which is computed from one or more other axes.

extra:

See below for definition of extra.

backend

Synonym for solver.

configuration

Complete description of a diffractometer’s settings. Includes solver, geometry (& engine, if applicable), ordered lists of the axis names, dictionaries of samples (with lattice & reflection(s)).

constraint

Limitations on acceptable positions for a diffractometer’s computed forward() solutions (from \(hkl\) to angles). A solver’s forward() computation returns a list of solutions, where a solution is the set of real-space angles that position the diffractometer to the desired \(hkl\) value. A constraint can be used to reject solutions for undesired angles.

core

The hklpy2 intermediate software adapter layer between DiffractometerBase (user-facing code) and a SolverBase.

Connects a diffractometer with a Solver library and one of its geometries.

crystal

A homogeneous substance composed from a repeating three-dimensional pattern. The pattern (unit cell) is characterized by its lattice.

crystal analyzer

A passive crystal mounted on the detector arm that selects a specific scattered wavelength by Bragg diffraction, acting as a narrow bandpass filter. The Bragg angle (often called atheta) positions the crystal; the detector relocates to the analyzer arm (often attheta) and points at the analyzer. Treated by hklpy2 as auxiliary positioners; does not affect crystallography calculations. See Crystal Analyzer on the Detector Arm.

cut point

The angle at which a motor’s reported position “wraps around.” It sets the start of the 360-degree window used to express the angle — the physics is unchanged, only how the number is written.

Two common choices:

• cut_point = -180 (default): angles reported in −180 up to (but not including) +180.

• cut_point = 0: angles reported in 0 up to (but not including) 360.

Any finite number is acceptable. inf, -inf, and nan raise ConstraintsError. The cut point does not need to fall within the axis limits — it is independent of low_limit and high_limit.

Applied before constraint checking in the forward() pipeline — controls representation, not whether a solution is accepted or rejected.

Equivalent to SPEC cuts and diffcalc setcut.

See also: constraint.

detector

Measures the intensity of diffracted radiation from the sample.

diffractometer

Diffractometers, mechanical systems of real space rotation axes, are used in studies of the stucture of crystalline samples. The structural features of interest are usually expressed in terms of reciprocal space (pseudo) axes.

A diffractometer is a type of goniometer. Generally, a diffractometer consists of two stacks of rotation axes, used to control the orientation of a crystalline sample and a detector. In a study, while the sample is oriented and exposed to a controlled radiation source, the detector is oriented to measure the intensity of radiation diffracted by the sample in specific directions.

engine

Some Solver libraries provide coordinate transformations between real axes and different types of pseudo axes, such as for reflectometry or surface scattering. The Solver may provide an engine for each separate type of transformation (and related pseudos).

entry point

A Python packaging mechanism that allows a package to advertise a named object (such as a class or function) so other packages can discover and load it without a hard-coded import. hklpy2 uses the "hklpy2.solver" entry point group to locate installed Solver plugins.

extra

An additional axis used by a Solver for operation of a diffractometer. For example, when rotating by angle \(\psi\) around some arbitrary diffraction vector, \((h_2,k_2,l_2)\), the extra axes are: "h2", "k2", "l2", "psi".

An extra axis is not defined as a diffractometer Component.

geometry

The set of reals (stacked rotation angles) which define a specific diffractometer. A common distinguishing feature is the number of axes in each stack. For example, the E4CV geometry has 3 sample axes (omega, chi, phi) and 1 detector axis (tth). In some shorthand reference, this could be called “S3D1”.

goniometer

Mechanical system which allows an object to be rotated to a precise angular position.

lattice

Characteristic dimensions of the parallelepiped representing the sample crystal structure. For a three-dimensional crystal, the lengths of each side of the lattice are \(a\), \(b\), & \(c\), the angles between the sides are \(\alpha\), \(\beta\), & \(\gamma\)

mode

Diffractometer geometry operation mode for forward().

A mode (implemented by a Solver), defines which axes will be modified by the forward() computation.

monochromatic

Radiation of a single wavelength (or sufficiently narrow range), such that it may be characterized by a single floating point value.

OR

Orienting Reflection, a reflection used to define the sample orientation (and compute the \(UB\) matrix).

orientation

Positioning of a crystalline sample’s atomic planes (identified by a set of pseudos) within the laboratory reference frame (described by the reals).

polarization analyzer

A passive crystal mounted on the detector arm whose Bragg angle is close to 45° (so the scattering angle 2θ is near 90°), suppressing radiation polarized in the diffraction plane. Rotation around the beam selects which polarization direction is suppressed, allowing the beam polarization state to be probed. Treated by hklpy2 as auxiliary positioners; does not affect crystallography calculations. See Polarization Analyzer on the Detector Arm.

preset

A value assigned to a constant (read-only) real axis for use during forward() computations, in place of the current motor position. Presets do not move any motor. Each mode stores its own independent preset dictionary, defaulting to {}.

See also

Presets, How to Use Presets

pseudo

Reciprocal-space axis, such as \(h\), \(k\), and \(l\). The engineering units (rarely examined for crystalline work) are reciprocal of the wavelength units.

Note: pseudo axes are virtual axes, computed by the solver from real axes.

real

Real-space axis (typically a rotation stage), such as omega (\(\omega\)). The engineering units are expected to be in degrees.

reflection

User-identified coordinates serving as a fiducial reference associating crystal orientation (reciprocal space, pseudos) and rotational axes (real space, reals). Reflections are used to orient a sample with a specific diffractometer geometry. In hklpy2, a reflection has a name, a set of pseudos, a set of reals, and a wavelength.

sample

The named substance to be explored with the diffractometer. In hklpy2, a sample has a name, a lattice, and a list of reflections.

The axes in a sample’s reflections are specific to the diffractometer geometry.

Consequently, the sample is defined for a specific Solver and geometry. The same sample cannot be used for other geometries.

solver

The hklpy2 interface layer to a backend Solver library, such as Hkl/Soleil. The library provides computations to transform coordinates between pseudo and real axes for a defined diffractometer geometry. The library also provides one or more diffractometer geometries.

stale UB

State of a sample whose stored UB matrix no longer reflects the current orienting reflections (the first two entries of Sample.reflections.order). Detected via UB_is_stale; cleared by running calc_UB() again or by direct assignment to U / UB (user takes ownership).

U

UB

Orientation matrix (3 x 3).

\(U\) Orientation matrix

of the crystal lattice as mounted on the diffractometer sample holder.

\(B\) Transition matrix

of a non-orthonormal (the reciprocal of the crystal) in an orthonormal system.

\(UB\) Orientation matrix

of the crystal lattice in the laboratory reference frame.

unit cell

The parallelepiped representing the smallest repeating structural pattern of the crystal, characterized by its lattice parameters.

virtual

Virtual (computed) diffractometer axis (either pseudo or real), computed from one or more additional diffractometer axes.

wavelength

The numerical value of the wavelength of the incident radiation. The radiation is expected to be monochromatic neutrons or X-rays. The engineering units of wavelength must be identical to those of the crystalline lattice length parameters.

zone

A set of lattice planes which are all parallel to one line, called the zone axis.