Overview

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Functional forms

Depth laws attached to DepthProfile. Any _FieldBase form (Spline, Polynomial, Diffusion, SecondOrderTransition, CallableField, …) can drive any supported channel — not only Mix volume fraction \(\phi\) or orientation \(\gamma\) / \(\langle\cos^2\gamma\rangle\).

Channels

Channel kwargs Typical use
phi Volume fraction of materials[0] in a Mix
gamma, cos2_gamma Orientation / order parameter on a uniaxial material
density Density scale on the material
delta_o, delta_e, beta_o, beta_e Free laboratory optical diagonals (no Mix required)

Attach the same form class to different kwargs:

# Mix composition
DepthProfile(material=Mix([mat_a, mat_b], rule="linear"), thickness=200.0, phi=field)

# Free optical diagonals (δ + iβ packing)
DepthProfile(
    material=mat,
    thickness=240.0,
    delta_o=field_o,
    delta_e=field_e,
    beta_o=4e-4,
    beta_e=6e-4,
)

Depth panels annotate the controlling constants. Figure builders live in build_figures.py; conventions are on the Building structures overview.

For interfacial orientation / composition transitions see Phase transitions. For Fick couple / exponential profiles see Diffusion.

Pages

Page Role
Splines Knotted \(\phi(z)\) (order / knot count) and free \(\delta_o\)/\(\delta_e\) Splines
Polynomials Polynomial \(\phi(z)\) and free \(\delta_o\)/\(\delta_e\) channels
Callable profiles User CallableField / CallableDepthProfile escape hatches

Shared preamble:

from refloxide.model import MaterialSLD, FreeUniTensor, Mix, ReflectModel
from refloxide.profiles import (
    Diffusion,
    SecondOrderTransition,
    DepthProfile,
    Spline,
    Polynomial,
    CallableField,
    CallableDepthProfile,
)

vac = MaterialSLD("", 0, name="vacuum")(0, 0)
si = MaterialSLD("Si", 2.33, name="si")(0, 3.0)
mat = FreeUniTensor(energies=[284.4], name="film")
mat_a = FreeUniTensor(energies=[284.4], name="a")
mat_b = FreeUniTensor(energies=[284.4], name="b")
mat_c = FreeUniTensor(energies=[284.4], name="c")

Typical Mix composition pattern:

phi = Spline(
    knots=[0.0, 30.0, 70.0, 110.0, 150.0, 200.0],
    values=[0.20, 0.95, 0.25, 0.80, 0.15, 0.55],
)
layer = DepthProfile(
    material=Mix([mat_a, mat_b], rule="linear"),
    thickness=200.0,
    phi=phi,
)
stack = vac | layer | si
Mixed slabs Splines