Off-Specular simulation

Off-specular simulation is a technique developed to study roughness or micromagnetism at micrometric scale [1]. For the moment BornAgain has only the limited support for off-specular simulation. User feedback is required to continue development.

Off-specular Geometry [1]

The term off-specular scattering is typically ised for experiment geometries where $\mathbf{q}$ is not strictly perpendicular to the sample surface. Following features can be encountered in off-specular scattering experiment: Yoneda peaks, Bragg sheets, diffuse scattering, magnetic spin-flip scattering, and correlated and uncorrelated roughness [2].

Create an off-specular simulation in BornAgain GUI

Start a new project Welcome view->New project
Go to the Instrument view and add an Offspec instrument.
Set the instrument parameters as follows.
Switch to the Sample view. Create a sample as shown below:
Create 4 layers (from bottom to top):
- Si substrate, $\delta=7.6\cdot 10^{-6}$, $\beta=1.7\cdot 10^{-7}$. Assign roughness with Sigma 0.46 nm, Hurst parameter 0.5 and CorrelationLength 100 nm.
- Nb layer of thickness 5.8 nm, $\delta=2.4\cdot 10^{-5}$, $\beta=1.5\cdot 10^{-6}$. No roughness.
- Si layer of thickness 3 nm. No roughness.
- Air layer.
Switch to Simulation view. Set option Include specular peak to Yes.

Run simulation. Vary the intensity scale. You should be able to see the specular line and Yonedas. To see the Bragg sheets we need to increase a number of [Si/Nb] double-layers to at least 10. Let's do it in Python.

Off-specular simulation with BornAgain Python API

Go to Simulation View and click button Export to Python script. Save the script somewhere. The script should look as shown below.

Exercise: Change the script to add layer_2 and layer_3 10 times. Hint: use for loop, take care of indentations.

Exercise (Advanced)

Add exponentially decreasing roughness to all Si layers (except of substrate). The RMS roughness of the layer $n$ should be calculated as

$$\sigma_n = \sigma_0\cdot e^{-0.01n}$$

where $\sigma_0=0.46$nm

Set the roughness of all the layers to be fully correlated.



In [2]:

    
%matplotlib inline



In [9]:

    
# %load offspec_ex.py
import numpy as np
import bornagain as ba
from bornagain import deg, angstrom, nm, kvector_t

def get_sample():
    # Defining Materials
    material_1 = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    material_2 = ba.HomogeneousMaterial("Si", 7.6e-06, 1.7e-07)
    material_3 = ba.HomogeneousMaterial("Nb", 2.4e-05, 1.5e-06)

    # Defining Layers
    layer_1 = ba.Layer(material_1)
    layer_2 = ba.Layer(material_2, 3)
    layer_3 = ba.Layer(material_3, 5.8)
    layer_4 = ba.Layer(material_2)

    # Defining Roughness Parameters
    layerRoughness_1 = ba.LayerRoughness(0.46, 0.5, 10.0*nm)

    # Defining Multilayers
    multiLayer_1 = ba.MultiLayer()
    # uncomment the line below to add vertical cross correlation length
    # multiLayer_1.setCrossCorrLength(200)
    multiLayer_1.addLayer(layer_1)
    #=================================
    # put your code here 
    multiLayer_1.addLayer(layer_2)
    multiLayer_1.addLayer(layer_3)
    #==================================
    multiLayer_1.addLayerWithTopRoughness(layer_4, layerRoughness_1)
    return multiLayer_1


def get_simulation():
    simulation = ba.OffSpecSimulation()
    simulation.setDetectorParameters(10, -1.0*deg, 1.0*deg, 100, 0.0*deg, 5*deg)
    
    simulation.setDetectorResolutionFunction(ba.ResolutionFunction2DGaussian(0.005*deg, 0.005*deg))
    alpha_i_axis = ba.FixedBinAxis("alpha_i", 100, 0.0*deg, 5*deg)
    simulation.setBeamParameters(0.154*nm, alpha_i_axis, 0.0*deg)
    simulation.setBeamIntensity(1.0e+08)
    simulation.getOptions().setIncludeSpecular(True)
    return simulation


def run_simulation():
    sample = get_sample()
    simulation = get_simulation()
    simulation.setSample(sample)
    simulation.runSimulation()
    return simulation.result()


if __name__ == '__main__': 
    result = run_simulation()
    ba.plot_simulation_result(result, intensity_max=10.0)

Solution

Run the line below to see the solution.



In [12]:

    
%load offspec.py









    












    





<Figure size 432x288 with 0 Axes>

References

[1] Daillant, J., Gibaud, A. (Eds.), X-ray and Neutron Reflectivity: Principles and Applications, Lect. Notes Phys. 770 (Springer, Berlin Heidelberg 2009), DOI 10.1007978-3-540-88588-7

[2] Ott, F. & Kozhevnikov, S. (2011). J. Appl. Cryst. 44, 359-369.



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