s2d2 — S2D2 General-Inclination Four-Circle

S2D2 geometry with two independent sample axes (mu, Z) and two independent detector axes (nu, delta), all mechanically decoupled.

Walko (2016) designation: S2D2

Coordinate basis: You (1999) (BASIS_YOU): vertical=+x, longitudinal=+y, transverse=+z.

Quick start

import ad_hoc_diffractometer as ahd

g = ahd.presets.s2d2()
g.wavelength = 1.0  # Å
print(g.summary())

Pre-built geometry definition

This geometry is defined by the s2d2() factory function — see the source for the complete stage and mode configuration.

Stage layout

Static fallback (click to expand if the interactive figure above is blank)

Sample stages (base first):

Stage	Axis	Handedness	Parent
mu	+vertical (+x)	right-handed	base
Z	+longitudinal (+y)	right-handed	mu

Detector stages (base first):

Stage	Axis	Handedness	Parent
nu	+vertical (+x)	right-handed	base
delta	−transverse (−z)	left-handed	nu

Diffraction modes

Each mode is a ConstraintSet of 1 constraint (N − 3 = 1 for N = 4 DOF). See Work with Constraints and Diffraction Modes for the constraint framework.

fixed_mu

SampleConstraint: mu held at declared value (default 0°) — the incidence angle when the surface normal is aligned. The caller chooses the value by constructing a ConstraintSet — see Work with Constraints and Diffraction Modes.

Computed	Z, nu, delta
Constant during forward()	mu

reflectivity

ReferenceConstraint: symmetric reflection — incidence angle equals exit angle (alpha_i = beta_out). Requires g.surface_normal = (h, k, l) — see Surface Geometry and the Reference Vector.

Computed	mu, Z, nu, delta
Constant during forward()	—
Extras (input)	n̂ (surface normal)
Extras (output)	alpha_i, beta_out

API reference

• s2d2()

• AdHocDiffractometer

• ConstraintSet

• SampleConstraint

• ReferenceConstraint

• EwaldSphereViolation

• ConstraintViolation

References

• Evans-Lutterodt & Tang, J. Appl. Cryst. 28, 318–326 (1995). DOI: 10.1107/S0021889895001063

• Walko, Ref. Module Mater. Sci. Mater. Eng. (2016).