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The tutorial 5th

Shows how to calculate atomic distances based on the radial distribution function derived from diffraction patterns.

coding

1. Save your diffraction data to the root directory and rename the file to intensity.csv.

# import PyXplore package
from PyXplore import WPEM
import pandas as pd

2. Parse your diffraction data (2θ, intensity) and perform background processing.

intensity_csv = pd.read_csv(r'intensity.csv',header=None )
var = WPEM.BackgroundFit(intensity_csv,lowAngleRange=3.8,poly_n=12,bac_split=8,bac_num=100)

3. After running the code, a new folder named ConvertedDocuments will be created in the root directory. This folder contains the background information.

Copy the two important files — bac.csv and no_bac_intensity.csv — from ConvertedDocuments into the root directory, as they are required for the next steps.

Parse the .cif file as demonstrated in the crystal fitting section, and generate the peak0.csv file.

# The wavelength is set according to the actual light source
wavelength = [1.03]
# The file name of non-background data (2theta-intensity data)
no_bac_intensity_file = "no_bac_intensity.csv" 
# The file name of raw/original data (2theta-intensity data)
original_file = "intensity.csv"  
# The file name of background data (2theta-intensity data)
bacground_file = "bac.csv"  


# Input the initial lattice constants {a, b, c, α, β, γ}, whose values need to be assumed at initialization.
Lattice_constants = [[17.53,17.53,6.47,90,90,120],]

# Execute the model

WPEM.XRDfit(
    wavelength, var, Lattice_constants,no_bac_intensity_file, original_file, bacground_file, 
    subset_number=3,low_bound=6,up_bound=16,bta = 0.78,iter_max = 50, asy_C = 0,InitializationEpoch=0, 
    )

After processing the crystalline signals, the remaining signals corresponding to the amorphous phase are saved.

Fit the amorphous signal using the following code:

WPEM.Amorphous_fit(mix_component=3, sigma2_coef = 0.5, max_iter = 5000,peak_location = None,Wavelength=1.03
                )

After coverage, the amorphous components (referred to as "holes") are derived. You can visualize each amorphous hole using the provided plotting functions. The results are saved in the DecomposedComponents folder.

WPEM.Plot_Components(lowboundary = 4, upboundary = 19, wavelength = wavelength, Macromolecule = True,phase = 1)

The relative bulk crystallinity can be estimated from the diffraction intensity ratio

after subtracting the amorphous signal, which is saved in the 'DecomposedComponents' folder as 'Amorphous.csv'.

Additionally, the radial distribution function (RDF) can be applied to the remaining signal to calculate the nearest-neighbor atomic distance based on features within the diffraction pattern.

WPEM.AmorphousRDFun( r_max = 4,density_zero=None,Nf2=1,highlight= 6,)

The peak positions at 0.42, 0.93, 1.36, 1.80, 2.23, and 2.68 correspond to a series of atomic clusters.