Glossary

Italics

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

axis:

Either a pseudo, real, or extra.

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.

crystal:

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

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).

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".

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 as 3 sample axes (omega, chi, phi) and 1 detector axis (tth). In some shorthand reference, this is 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.

operator:

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.

orientation:

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

pseudo:

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

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.

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.

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.