psic — Eulerian Six-Circle, 4S+2D (You 1999)#

You (1999) 4S+2D six-circle diffractometer. Four sample stages (mu, eta, chi, and phi) and two detector stages (nu, delta). Transverse detector, vertical scattering plane. Standard synchrotron six-circle.

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

Quick start#

import ad_hoc_diffractometer as ahd

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

Pre-built geometry definition#

This geometry is defined by the psic() 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)

psic stage layout

Sample stages (base first):

Stage	Axis	Handedness	Parent
`mu`	+vertical (+x)	right-handed	base
`eta`	−transverse (−z)	left-handed	`mu`
`chi`	+longitudinal (+y)	right-handed	`eta`
`phi`	−transverse (−z)	left-handed	`chi`

Detector stages (base first):

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

Diffraction modes#

Set the active mode with g.mode_name = "<mode>". Each mode is a ConstraintSet of 3 constraints (N − 3 = 3 for N = 6 DOF). See Switch Diffraction Modes for usage and Work with Constraints and Diffraction Modes for changing constraint values at run time.

Bisect pairs:

Vertical plane: eta (transverse) ↔ delta (transverse) → eta = delta/2
Horizontal plane: mu (vertical) ↔ nu (vertical) → mu = nu/2

`bisecting_vertical` (default)#

BisectConstraint + SampleConstraint + DetectorConstraint: eta = delta/2, mu = 0, nu = 0. Vertical scattering plane bisecting condition (You 1999, §5.3).


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0

`fixed_phi_vertical`#

phi held at declared value (default 0°), eta = delta/2, nu = 0.


Computed	eta, chi, delta
Constant during `forward()`	phi, mu = 0, nu = 0

`fixed_chi_vertical`#

chi held at declared value (default 90°), eta = delta/2, nu = 0. The caller chooses the chi value by constructing a ConstraintSet — see Work with Constraints and Diffraction Modes.


Computed	eta, phi, delta
Constant during `forward()`	chi, mu = 0, nu = 0

`fixed_mu_vertical`#

mu held at declared value (default 0°), eta = delta/2, nu = 0.


Computed	eta, chi, phi, delta
Constant during `forward()`	mu, nu = 0

`fixed_nu_vertical`#

nu held at declared value (default 0°), eta = delta/2, mu = 0.


Computed	eta, chi, phi, delta
Constant during `forward()`	nu, mu = 0

`fixed_alpha_i_vertical`#

Incidence angle α_i fixed at declared value (default 0°) in the vertical scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0
Extras (input)	n̂ (surface normal)

`fixed_beta_out_vertical`#

Exit angle β_out fixed at declared value (default 0°) in the vertical scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0
Extras (input)	n̂ (surface normal)

`alpha_eq_beta_vertical`#

Symmetric reflection: α_i = β_out in the vertical scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0
Extras (input)	n̂ (surface normal)

`fixed_psi_vertical`#

Vertical bisecting with azimuthal angle ψ validation. Set g.azimuthal_reference = (h, k, l) before calling forward(). The solver returns bisecting solutions only when the natural ψ for the requested (h,k,l) matches the stored target. See Surface Geometry and the Reference Vector.


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0
Extras (input)	n̂ (reference vector), ψ (target azimuth, degrees)
Extras (output)	psi (computed azimuth)

`double_diffraction_vertical`#

Full 4D simultaneous solver in the vertical scattering plane: finds motor angles where both the primary (h₁,k₁,l₁) and secondary (h₂,k₂,l₂) reflections satisfy the Ewald sphere condition. Set mode.extras['h2'], ['k2'], ['l2'] before calling forward().


Computed	eta, chi, phi, delta
Constant during `forward()`	mu = 0, nu = 0
Extras (input)	h₂, k₂, l₂ (secondary reflection Miller indices)

`bisecting_horizontal`#

BisectConstraint + SampleConstraint + DetectorConstraint: mu = nu/2, eta = 0, delta = 0. Horizontal scattering plane bisecting condition (You 1999, §5.1).


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0

`fixed_phi_horizontal`#

phi held at declared value (default 0°), mu = nu/2, delta = 0.


Computed	mu, chi, nu
Constant during `forward()`	phi, eta = 0, delta = 0

`fixed_chi_horizontal`#

chi held at declared value (default 90°), mu = nu/2, delta = 0.


Computed	mu, phi, nu
Constant during `forward()`	chi, eta = 0, delta = 0

`fixed_eta_horizontal`#

eta held at declared value (default 0°), mu = nu/2, delta = 0.


Computed	mu, chi, phi, nu
Constant during `forward()`	eta, delta = 0

`fixed_delta_horizontal`#

delta held at declared value (default 0°), mu = nu/2, eta = 0.


Computed	mu, chi, phi, nu
Constant during `forward()`	delta, eta = 0

`fixed_alpha_i_horizontal`#

Incidence angle α_i fixed at declared value (default 0°) in the horizontal scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0
Extras (input)	n̂ (surface normal)

`fixed_beta_out_horizontal`#

Exit angle β_out fixed at declared value (default 0°) in the horizontal scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0
Extras (input)	n̂ (surface normal)

`alpha_eq_beta_horizontal`#

Symmetric reflection: α_i = β_out in the horizontal scattering plane. Set g.surface_normal = (h, k, l) before calling forward().


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0
Extras (input)	n̂ (surface normal)

`fixed_psi_horizontal`#

Horizontal bisecting with azimuthal angle ψ validation. Set g.azimuthal_reference = (h, k, l) before calling forward().


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0
Extras (input)	n̂, ψ
Extras (output)	psi

`double_diffraction_horizontal`#

Full 4D simultaneous solver in the horizontal scattering plane.


Computed	mu, chi, phi, nu
Constant during `forward()`	eta = 0, delta = 0
Extras (input)	h₂, k₂, l₂ (secondary reflection Miller indices)

`lifting_detector_phi`#

Out-of-plane mode: phi and mu frozen, nu and delta solved via the qaz constraint (tan(qaz) = tan(delta) / sin(nu), You 1999 eq. 18). qaz = 90° constrains the scattering to the vertical plane.


Computed	phi, nu, delta
Constant during `forward()`	phi = 0, mu = 0

`lifting_detector_mu`#

Out-of-plane mode: mu and eta frozen, nu and delta solved via the qaz constraint (tan(qaz) = tan(delta) / sin(nu), You 1999 eq. 18). qaz = 90° constrains the scattering to the vertical plane.


Computed	mu, nu, delta
Constant during `forward()`	mu = 0, eta = 0

API reference#

References#

You, J. Appl. Cryst. 32, 614–623 (1999). DOI: 10.1107/S0021889899001223
Walko, Ref. Module Mater. Sci. Mater. Eng. (2016).

psic — Eulerian Six-Circle, 4S+2D (You 1999)#

Quick start#

Pre-built geometry definition#

Stage layout#

Diffraction modes#

bisecting_vertical (default)#

fixed_phi_vertical#

fixed_chi_vertical#

fixed_mu_vertical#

fixed_nu_vertical#

fixed_alpha_i_vertical#

fixed_beta_out_vertical#

alpha_eq_beta_vertical#

fixed_psi_vertical#

double_diffraction_vertical#

bisecting_horizontal#

fixed_phi_horizontal#

fixed_chi_horizontal#

fixed_eta_horizontal#

fixed_delta_horizontal#

fixed_alpha_i_horizontal#

fixed_beta_out_horizontal#

alpha_eq_beta_horizontal#

fixed_psi_horizontal#

double_diffraction_horizontal#

lifting_detector_phi#

lifting_detector_mu#