fivec — Eulerian Five-Circle (Vlieg et al. 1987)

Five-circle diffractometer: a standard fourcv() (Eulerian four-circle) mounted on a vertical mu base stage. Sample and detector are coupled through mu.

Walko (2016) designation: (S3D1)1

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

Quick start

import ad_hoc_diffractometer as ahd

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

Pre-built geometry definition

This geometry is defined by the fivec() 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, shared base	base
omega	−transverse (−z)	left-handed	mu
chi	+longitudinal (+y)	right-handed	omega
phi	−transverse (−z)	left-handed	chi

Detector stages (base first):

Stage	Axis	Handedness	Parent
ttheta	−transverse (−z)	left-handed	mu

Shared stage: mu (base stage shared between sample and detector stacks)

Diffraction modes

Set the active mode with g.mode_name = "<mode>". Each mode is a ConstraintSet of 2 constraints (N − 3 = 2 for N = 5 DOF). With mu = 0, fivec() reduces identically to fourcv(). See Switch Diffraction Modes for usage and Work with Constraints and Diffraction Modes for changing constraint values at run time.

bisecting_4c (default)

SampleConstraint + BisectConstraint: mu = 0, omega = ttheta / 2. Reduces to standard four-circle bisecting geometry.

Computed	omega, chi, phi, ttheta
Constant during forward()	mu = 0

fixed_chi

SampleConstraint × 2: mu = 0. chi is held at the value declared in the constraint (factory default: 90°). The caller chooses the value by constructing a ConstraintSet; the constraint persists until replaced — see Work with Constraints and Diffraction Modes.

Computed	omega, phi, ttheta
Constant during forward()	mu = 0, chi

fixed_phi

SampleConstraint × 2: mu = 0. phi is held at the value declared in the constraint (factory default: 0°). The caller chooses the value by constructing a ConstraintSet.

Computed	omega, chi, ttheta
Constant during forward()	mu = 0, phi

fixed_mu

SampleConstraint + BisectConstraint: omega = ttheta / 2. mu is held at the value declared in the constraint (factory default: 0°). The caller chooses the value by constructing a ConstraintSet. Intended for non-zero mu once the tilted-plane solver is implemented.

Computed	omega, chi, phi, ttheta
Constant during forward()	mu

fixed_omega_noncoplanar

SampleConstraint × 2: mu = 0. omega is held at the value declared in the constraint (factory default: 0°). The caller chooses the value by constructing a ConstraintSet.

Computed	mu, chi, phi, ttheta
Constant during forward()	mu = 0, omega

API reference

• fivec()

• AdHocDiffractometer

• ConstraintSet

• BisectConstraint

• SampleConstraint

• DetectorConstraint

• EwaldSphereViolation

• ConstraintViolation

References

• Vlieg et al., J. Appl. Cryst. 20, 330–337 (1987). DOI: 10.1107/S0021889887087266

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