# mixscatter
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## Table of Contents
* [Overview](#overview)
* [Installation](#installation)
* [Documentation](#documentation)
* [Example Showcase](#example-showcase)
* [Contributing](#contributing)
* [License](#license)
## Overview
**mixscatter** is a pure python package for the calculation of scattering functions of
multi-component mixtures of interacting spherical scatterers in the Born approximation
([Rayleigh-Gans-Debye scattering](https://en.wikipedia.org/wiki/Rayleigh-Gans_approximation)).
Key Features:
* Calculation of scattering amplitudes, measurable intensities, form factors, structure factors, and diffusion coefficients.
* Flexible construction of systems with arbitrary compositions and complex scattering length density profiles.
* Suitable for researchers and developers working on particulate systems characterization.
Take a look at these publications if you are interested:
- P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and
scattering", [Adv. Colloid Interface Sci. 43, 169-288 (1993)](
https://doi.org/10.1016/0001-8686(93)80017-6)
- A. Vrij, "Mixtures of hard spheres in the Percus–Yevick approximation. Light scattering at
finite angles", [J. Chem. Phys. 71, 3267-3270 (1979)](https://doi.org/10.1063/1.438756)
- R. Botet, S. Kwok and B. Cabane, "Percus-Yevick structure factors made simple",
[J. Appl. Cryst. 53, 1570-1582 (2020)](https://doi.org/10.1107/S1600576720014041)
- J. Diaz Maier, K. Gaus and J. Wagner, "Measurable structure factors of dense dispersions
containing polydisperse, optically inhomogeneous particles",
[arXiv:2404.03470 [cond-mat.soft]](https://doi.org/10.48550/arXiv.2404.03470)
## Installation
**mixscatter** is available on the [Python Package Index (PyPI)](
https://pypi.org/project/mixscatter).
### Prerequisites
Ensure you have Python 3.10 or higher installed.
### Using pip
Install the package via pip:
```shell
pip install mixscatter
```
The source code is currently hosted on GitHub at: https://github.com/joelmaier/mixscatter
## Documentation
Find the documentation on GitHub Pages: https://joelmaier.github.io/mixscatter/
## Example Showcase
This example demonstrates the fundamental capabilities of **mixscatter**. For a comprehensive
walk-through, refer to the
[Getting Started Guide](
https://joelmaier.github.io/mixscatter/getting_started/getting-started).
Run this code to
produce the figure below.
```python
import numpy as np
import matplotlib.pyplot as plt
from mixscatter.mixture import Mixture
from mixscatter.scatteringmodel import SimpleCoreShell
from mixscatter.liquidstructure import PercusYevick
from mixscatter import (
measurable_intensity,
measurable_structure_factor,
measurable_diffusion_coefficient
)
if __name__ == "__main__":
plt.ion()
plt.close("all")
fig, ax = plt.subplots(3, 2, figsize=(6, 8), layout="constrained")
# Initialize a particle mixture
mixture = Mixture(radius=[100, 250], number_fraction=[0.4, 0.6])
# Visualize mixture composition
ax[0, 0].stem(mixture.radius, mixture.number_fraction)
ax[0, 0].set_xlim(0, 300)
ax[0, 0].set_ylim(-0.05, 1.05)
ax[0, 0].set_xlabel("particle radius")
ax[0, 0].set_ylabel("number fraction")
# Provide a model for the optical properties of the system
wavevector = np.linspace(1e-3, 7e-2, 1000)
scattering_model = SimpleCoreShell(
wavevector=wavevector,
mixture=mixture,
core_to_total_ratio=0.5,
core_contrast=1.0,
shell_contrast=0.5
)
# Visualize SLD profile
distance = np.linspace(0, 350, 1000)
for i, particle in enumerate(scattering_model.particles):
profile = particle.get_profile(distance)
ax[0, 1].plot(distance, profile, label=f"particle {i + 1}")
ax[0, 1].set_xlim(0, 400)
ax[0, 1].set_xlabel("distance from particle center")
ax[0, 1].set_ylabel("scattering contrast")
ax[0, 1].legend()
# Visualize individual and average form factor(s)
for i, form_factor in enumerate(scattering_model.single_form_factor):
ax[1, 0].plot(wavevector, form_factor, label=f"particle {i + 1}")
ax[1, 0].plot(
wavevector, scattering_model.average_form_factor, label="average"
)
ax[1, 0].set_yscale("log")
ax[1, 0].set_ylim(1e-6, 3e0)
ax[1, 0].legend()
ax[1, 0].set_xlabel("wavevector")
ax[1, 0].set_ylabel("form factor")
# Provide a model for the liquid structure
liquid_structure = PercusYevick(
wavevector=wavevector, mixture=mixture, volume_fraction_total=0.45
)
# Calculate the scattered intensity of the system
intensity = measurable_intensity(liquid_structure, scattering_model)
ax[1, 1].plot(wavevector, intensity)
ax[1, 1].set_yscale("log")
ax[1, 1].set_xlabel("wavevector")
ax[1, 1].set_ylabel("intensity")
# Calculate the experimentally obtainable, measurable structure factor
structure_factor = measurable_structure_factor(
liquid_structure, scattering_model
)
ax[2, 0].plot(wavevector, structure_factor)
ax[2, 0].set_xlabel("wavevector")
ax[2, 0].set_ylabel("structure factor")
# Calculate the effective Stokes-Einstein diffusion coefficient
# which would be obtained from a cumulant analysis in
# dynamic light scattering
diffusion_coefficient = measurable_diffusion_coefficient(
scattering_model, thermal_energy=1.0, viscosity=1.0 / (6.0 * np.pi)
)
# Visualize the apparent hydrodynamic radius, which is
# proportional to 1/diffusion_coefficient
ax[2, 1].plot(wavevector, 1 / diffusion_coefficient)
ax[2, 1].set_xlabel("wavevector")
ax[2, 1].set_ylabel("apparent hydrodynamic radius")
fig.savefig("simple_example_figure.png", dpi=300)
```
## Contributing
Contributions are welcome! If you find any bugs or want to request features,
feel free to get in touch or create an issue.
## License
This project is licensed under the MIT License - see the [LICENSE](
https://raw.githubusercontent.com/joelmaier/mixscatter/main/LICENSE) file for details.
Raw data
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"description": "# mixscatter\n\n[](https://badge.fury.io/py/mixscatter)\n[](https://badge.fury.io/py/mixscatter)\n[](https://opensource.org/licenses/MIT)\n[](https://github.com/joelmaier/mixscatter/actions/workflows/test.yml)\n[](https://github.com/joelmaier/mixscatter/actions/workflows/lint.yml)\n[](https://github.com/joelmaier/mixscatter/actions/workflows/type_check.yml)\n[](https://github.com/joelmaier/mixscatter/actions/workflows/docs.yml)\n[](https://github.com/wntrblm/nox)\n\n\n## Table of Contents\n* [Overview](#overview)\n* [Installation](#installation)\n* [Documentation](#documentation)\n* [Example Showcase](#example-showcase)\n* [Contributing](#contributing)\n* [License](#license)\n\n## Overview\n\n**mixscatter** is a pure python package for the calculation of scattering functions of\nmulti-component mixtures of interacting spherical scatterers in the Born approximation\n([Rayleigh-Gans-Debye scattering](https://en.wikipedia.org/wiki/Rayleigh-Gans_approximation)).\n\nKey Features:\n* Calculation of scattering amplitudes, measurable intensities, form factors, structure factors, and diffusion coefficients.\n* Flexible construction of systems with arbitrary compositions and complex scattering length density profiles.\n* Suitable for researchers and developers working on particulate systems characterization.\n\nTake a look at these publications if you are interested:\n\n - P. Salgi and R. Rajagopalan, \"Polydispersity in colloids: implications to static structure and\n scattering\", [Adv. Colloid Interface Sci. 43, 169-288 (1993)](\n https://doi.org/10.1016/0001-8686(93)80017-6)\n - A. Vrij, \"Mixtures of hard spheres in the Percus\u2013Yevick approximation. Light scattering at\n finite angles\", [J. Chem. Phys. 71, 3267-3270 (1979)](https://doi.org/10.1063/1.438756)\n - R. Botet, S. Kwok and B. Cabane, \"Percus-Yevick structure factors made simple\",\n [J. Appl. Cryst. 53, 1570-1582 (2020)](https://doi.org/10.1107/S1600576720014041)\n - J. Diaz Maier, K. Gaus and J. Wagner, \"Measurable structure factors of dense dispersions\n containing polydisperse, optically inhomogeneous particles\",\n [arXiv:2404.03470 [cond-mat.soft]](https://doi.org/10.48550/arXiv.2404.03470)\n\n## Installation\n\n**mixscatter** is available on the [Python Package Index (PyPI)](\nhttps://pypi.org/project/mixscatter).\n\n### Prerequisites\n\nEnsure you have Python 3.10 or higher installed.\n\n### Using pip\n\nInstall the package via pip:\n```shell\npip install mixscatter\n```\nThe source code is currently hosted on GitHub at: https://github.com/joelmaier/mixscatter\n\n## Documentation\n\nFind the documentation on GitHub Pages: https://joelmaier.github.io/mixscatter/\n\n## Example Showcase\n\nThis example demonstrates the fundamental capabilities of **mixscatter**. For a comprehensive \nwalk-through, refer to the\n[Getting Started Guide](\nhttps://joelmaier.github.io/mixscatter/getting_started/getting-started). \n\nRun this code to\nproduce the figure below.\n\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom mixscatter.mixture import Mixture\nfrom mixscatter.scatteringmodel import SimpleCoreShell\nfrom mixscatter.liquidstructure import PercusYevick\nfrom mixscatter import (\n measurable_intensity,\n measurable_structure_factor,\n measurable_diffusion_coefficient\n)\n\nif __name__ == \"__main__\":\n plt.ion()\n plt.close(\"all\")\n fig, ax = plt.subplots(3, 2, figsize=(6, 8), layout=\"constrained\")\n\n # Initialize a particle mixture\n mixture = Mixture(radius=[100, 250], number_fraction=[0.4, 0.6])\n\n # Visualize mixture composition\n ax[0, 0].stem(mixture.radius, mixture.number_fraction)\n ax[0, 0].set_xlim(0, 300)\n ax[0, 0].set_ylim(-0.05, 1.05)\n ax[0, 0].set_xlabel(\"particle radius\")\n ax[0, 0].set_ylabel(\"number fraction\")\n\n # Provide a model for the optical properties of the system\n wavevector = np.linspace(1e-3, 7e-2, 1000)\n scattering_model = SimpleCoreShell(\n wavevector=wavevector,\n mixture=mixture,\n core_to_total_ratio=0.5,\n core_contrast=1.0,\n shell_contrast=0.5\n )\n\n # Visualize SLD profile\n distance = np.linspace(0, 350, 1000)\n for i, particle in enumerate(scattering_model.particles):\n profile = particle.get_profile(distance)\n ax[0, 1].plot(distance, profile, label=f\"particle {i + 1}\")\n ax[0, 1].set_xlim(0, 400)\n ax[0, 1].set_xlabel(\"distance from particle center\")\n ax[0, 1].set_ylabel(\"scattering contrast\")\n ax[0, 1].legend()\n\n # Visualize individual and average form factor(s)\n for i, form_factor in enumerate(scattering_model.single_form_factor):\n ax[1, 0].plot(wavevector, form_factor, label=f\"particle {i + 1}\")\n ax[1, 0].plot(\n wavevector, scattering_model.average_form_factor, label=\"average\"\n )\n ax[1, 0].set_yscale(\"log\")\n ax[1, 0].set_ylim(1e-6, 3e0)\n ax[1, 0].legend()\n ax[1, 0].set_xlabel(\"wavevector\")\n ax[1, 0].set_ylabel(\"form factor\")\n\n # Provide a model for the liquid structure\n liquid_structure = PercusYevick(\n wavevector=wavevector, mixture=mixture, volume_fraction_total=0.45\n )\n\n # Calculate the scattered intensity of the system\n intensity = measurable_intensity(liquid_structure, scattering_model)\n ax[1, 1].plot(wavevector, intensity)\n ax[1, 1].set_yscale(\"log\")\n ax[1, 1].set_xlabel(\"wavevector\")\n ax[1, 1].set_ylabel(\"intensity\")\n\n # Calculate the experimentally obtainable, measurable structure factor\n structure_factor = measurable_structure_factor(\n liquid_structure, scattering_model\n )\n ax[2, 0].plot(wavevector, structure_factor)\n ax[2, 0].set_xlabel(\"wavevector\")\n ax[2, 0].set_ylabel(\"structure factor\")\n\n # Calculate the effective Stokes-Einstein diffusion coefficient\n # which would be obtained from a cumulant analysis in\n # dynamic light scattering\n diffusion_coefficient = measurable_diffusion_coefficient(\n scattering_model, thermal_energy=1.0, viscosity=1.0 / (6.0 * np.pi)\n )\n # Visualize the apparent hydrodynamic radius, which is\n # proportional to 1/diffusion_coefficient\n ax[2, 1].plot(wavevector, 1 / diffusion_coefficient)\n ax[2, 1].set_xlabel(\"wavevector\")\n ax[2, 1].set_ylabel(\"apparent hydrodynamic radius\")\n\n fig.savefig(\"simple_example_figure.png\", dpi=300)\n```\n\n![Example Figure](https://raw.githubusercontent.com/joelmaier/mixscatter/main/examples/simple_example_figure.png \"Example figure\")\n\n## Contributing\n\nContributions are welcome! If you find any bugs or want to request features, \nfeel free to get in touch or create an issue.\n\n## License\n\nThis project is licensed under the MIT License - see the [LICENSE](\nhttps://raw.githubusercontent.com/joelmaier/mixscatter/main/LICENSE) file for details.\n",
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