import escape as esc
import numpy as np

esc.require("0.9.8")

Loading material database from /home/dkor/Data/Development/workspace_escape/escape-core/python/src/escape/scattering/../data/mdb/materials.db

q = esc.var("Q")

SAXS. Form-factors. CoreShell

Original: https://www.ncnr.nist.gov/resources/sansmodels/CoreShell.html

Author: Denis Korolkov

Calculates the form factor, $P(q)$, for a monodisperse spherical particle with a core-shell structure. The form factor is normalized by the total particle volume.

Parameters

Parameter	Variable	Value
0	Scale	1.0
1	Core Radius (Å)	60.0
2	Shell Thickness (Å)	10.0
3	Core SLD ($Å^{-2}$)	1.0e-6
4	Shell SLD ($Å^{-2}$)	2.0e-6
5	Solvent SLD ($Å^{-2}$)	3.0e-6
6	incoherent Background(cm^{-1})	0.000

Usage notes

The function calculated is:

where and equation 4 The returned value is scaled to units of $cm^{-1}$.

Parameter[0] (scale) and the SLD's are multiplicative factors in the model and are perfectly correlated. No more than one of these parameters can be free during the model fitting.

Reference

Guinier, A. and G. Fournet, "Small-Angle Scattering of X-Rays", John Wiley and Sons, New York, (1955).

# Definition of parameters
I0 = esc.par("Scale", 1, scale=1e8, fixed=True)
Rc = esc.par("Core Radius", 60, units=esc.angstr)
S = esc.par("Shell thickness", 10, units=esc.angstr)
rho_c = esc.par("Core SLD", 1, scale=1e-6, units=f"{esc.angstr}⁻²")
rho_s = esc.par("Shell SLD", 2, scale=1e-6, units=f"{esc.angstr}⁻²")
rho_solv = esc.par("Solvent SLD", 3, scale=1e-6, units=f"{esc.angstr}⁻²")
bkgr = esc.par("Background", 0.0, userlim=[0, 0.03])

# Model equations

Rs = Rc + S

Vc = 4 / 3 * np.pi * Rc**3
Vs = 4 / 3 * np.pi * Rs**3

QRc = q * Rc
QRs = q * Rs

jc = (esc.sin(QRc) - QRc * esc.cos(QRc)) / QRc**3
js = (esc.sin(QRs) - QRs * esc.cos(QRs)) / QRs**3

P = (
    I0 / Vs * (3 * Vc * (rho_c - rho_s) * jc + 3 * Vs * (rho_s - rho_solv) * js) ** 2
    + bkgr
)

P.show(coordinates=np.linspace(0.001, 0.7, 256)).config(
    title="CoreShell",
    xlog=True,
    ylog=True,
    xlabel=f"Q [{esc.angstr}⁻¹]",
    ylabel="P(q)[cm⁻¹]",
)