There are more than 20 particle form factors available in BornAgain GUI.
Detailed description of each form factor is available in BornAgain User Manual.
Particle position is a position of the local origin in the parent coordinate system.
The plot below shows a multi-layer with 3 layers: a semi-infinite ambient layer, a middle layer with a finite thickness and a semi-infinite substrate layer. For each of these 3 layers the $z$-axis is pointing up. For the ambient layer, the $z=0.0$ coordinate corresponds to the interface between ambient and a middle layer. To place a particle in the air layer, normally positive values $z>=0.0$ should be used. For any other layer $z=0.0$ corresponds to the top interface. To place a particle in one of such layers, normally negative values $z<=0.0$ should be used.
Particle coordinates:
See also BornAgain documentation on particle positioning.
BornAgain support following kinds of rotations:
Rotation around a single axis
Euler rotation
$\alpha$, $\beta$ and $\gamma$ are the Euler angles describing a rotation composed by three elemental rotations. The object is first rotated along the $z$ axis by $\alpha$. The following rotation is along the transformed $x$ axis (i.e. $X$ axis) by $\beta$, while the last rotation is along the transformed $z$ axis (i.e. $Z$ axis) by $\gamma$.
Warning: rotation may shift particles along $Z$ axis. Be sure to adjust the particle position after the rotation.
See also BornAgain documentation on particle rotation.
For example
Probability density function (PDF) of the Cosine distribution is
for $\mu - \pi\sigma \leq x \leq \mu + \pi\sigma$ and zero otherwise.
On the figure above, Mean$=\mu$, Sigma$=\sigma$, Number of samples is a number of sampling points and Sigma factor defines the range where samples are taken.
Distribution Gate is described with the following PDF:
In the figure above Min$=X_{min}$, Max$X_{max}=$ and Number of samples is a number of sampling points.
PDF of the Gaussian distribution is
$$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$where $\mu$ is the mean value and $\sigma$ describes the width of the distribution: FWHM$=2\sqrt{2\log 2}\sigma$.
In the figure above Mean$=\mu$, StdDev$=\sigma$, Number of samples is a number of sampling points and Sigma factor defines the range where samples are taken.
PDF of the Log-normal distribution is
$$f(x) = \frac{1}{x\sqrt{2\pi}\sigma}\cdot e^{-\frac{(\log x-\log\mu)^2}{2\sigma^2}}$$where $\mu$ is the median value and $\sigma$ describes the width of the distribution.
In the figure above Median$=\mu$, ScaleParameter$=\sigma$, Number of samples is a number of sampling points and Sigma factor defines the range where samples are taken.
PDF of the Lorentz distribution is
$$f(x) =\frac{\gamma}{\pi\left(\gamma^2 + (x - \mu)^2\right)}$$where $\mu$ is the mean value and $\gamma$ is the scale parameter which specifies the half-width at half-maximum (HWHM).
In the figure above Mean$=\mu$, HWHM$=\gamma$, Number of samples is a number of sampling points and Sigma factor defines the range where samples are taken.
PDF of the Trapezoidal distribution is
$$f(x) = \begin{cases} 0, \text{ for } x < \mu - \frac{m}{2} - l \\ \frac{h}{l}\cdot\left(x - \mu + \frac{m}{2} + l\right), \text{ for } \mu-\frac{m}{2}-l \leq x < \mu-\frac{m}{2}\\ h, \text{ for } \mu-\frac{m}{2} \leq x < \mu + \frac{m}{2} \\ \frac{h}{r}\cdot\left(x - \mu - \frac{m}{2}\right), \text{ for } \mu+\frac{m}{2} \leq x < \mu+\frac{m}{2} + r \end{cases}$$In the figure above Center$=\mu$, LeftWidth$=l$, MiddleWidth$=m$, RightWidth$=r$ and Number of samples is a number of sampling points.
To create size distribution for the particles, drag and drop the Distributed particle from the left panel to the sample design area. Connect it to particle layout and to the particle as shown above.
Parameters of supported distributions are described above. Parameter Limits sets the constraints for the distributed parameter. For example, in the figure above constraint Positive forces the radius and height of cylindrical particle be greater than zero.
Field Distributed parameter allows for choice of the parameter to distribute. For cylinder it can be radius or height. Field Linked parameter can be used to link another parameter to the distributed one if needed.
Core-shell particle accounts for the particles consisting of a core and a shell made of the different materials. The form factor $F_{cs}$ is calculated as follows
$$F_{cs} = \beta_c F_c + \Delta\beta F_s$$where $\beta$ is the scattering length density (SLD) of the material.
To create a core-shell particle in BornAgain, drag and drop the Core shell particle to the sample design area and attach it to the particle layout. Choose form factors for core and shell and attach them to the corresponding inputs of the core-shell particle.
Note: It is very important to set up properly size of the core and shell (shell must be larger!) to avoid unphysical constructions. It is also very important to set position of the core with respect to shell. Position offset field can be used for that. In the figure above core is positioned at $(0, 0, 0)$.
To make spheres concentric, one should set the core position to $(0,0,R_{shell} - R_{core})$, where $R$ stands for radius.
Particle composition accounts for a complex shapes consisting of various form factors and materials. In BornAgain form factor of the particle composition is calculated as a sum of the contributing form factors:
$$F = \sum_i\beta_i F_i$$To create a particle composition in BornAgain GUI, drag and drop the Particle Composition to the sample design area. Choose the contributing particles, set their sizes, materials and positions in a local coordinate system and connect them to the particle composition.
You can apply all the transformations to the whole particle composition like to a single particle.
See also BornAgain documentation on particle composition.
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