A python package for calculating XRD crystallite (grain) size
Install / Usage / Gauss / Voigt / Lorentzian / References / Contact
First, make sure you have a Python 3 environment installed. To install from github:
pip install -e git+https://github.com/amvro23/xrd/#egg=xrdNote: It might be useful to write "git+https://github.com/amvro23/xrd/#egg=xrd" if installing directly from a Python interpreter as # can be interpreted as a comment.
from xrd.models import ScherrerCreate an instance. Default optional values are instrument_defect = 0.0, shape_factor = 0.9, Cu_K_alpha = 1.54178.
xrd = Scherrer()Set inlet XRD values. Default parameter x represents the [eV] and optional parameter y represents the [counts/s].
xrd.set_inlet()Adjust the values of x and y parameters according to your xrd results (The model carries default values).
path = "xrd.txt"
df = pd.read_csv(path, delimiter = '\t')
x = df['eV'].values
y = df['counts/s'].values
xrd.set_inlet(x, y)Select the desired peak (e.g., 2θ = 43 to 2θ = 45.5).
xrd.zoom_area(43, 45.5)Choose the desired equation in order to fit the data and obtain the XRD crystallite (grain) size. Note that a fit analysis report alongside a residual plot is also printed.
xrd.gauss()
[[Model]]
(Model(gaussian, prefix='g_') + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 1833
# data points = 192
# variables = 5
chi-square = 0.08854927
reduced chi-square = 4.7353e-04
Akaike info crit = -1464.88477
Bayesian info crit = -1448.59729
R-squared = 0.99430169
[[Variables]]
exp_amplitude: 5.1616e-15 +/- 9.3517e-15 (181.18%) (init = 4.448869e-33)
exp_decay: -1.47171669 +/- 0.08725847 (5.93%) (init = -0.6143452)
g_amplitude: 0.40679699 +/- 0.00335422 (0.82%) (init = 1)
g_center: 44.6127722 +/- 0.00129809 (0.00%) (init = 44.61536)
g_sigma: 0.18233135 +/- 0.00143627 (0.79%) (init = 0.3693009)
g_fwhm: 0.42935752 +/- 0.00338216 (0.79%) == '2.3548200*g_sigma'
g_height: 0.89007471 +/- 0.00561759 (0.63%) == '0.3989423*g_amplitude/max(1e-15, g_sigma)'
[[Correlations]] (unreported correlations are < 0.250)
C(exp_amplitude, exp_decay) = -0.9999
C(g_amplitude, g_sigma) = +0.6944
C(exp_amplitude, g_amplitude) = -0.2829
C(exp_decay, g_amplitude) = +0.2731
Crystal size in nm with Gaussian fitting: 20
You can also draw fair comparisons regarding the best fit on occasion since R squared is also printed with the plot.
xrd.voigt()
[[Model]]
(Model(voigt, prefix='v_') + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 1284
# data points = 192
# variables = 5
chi-square = 0.03201933
reduced chi-square = 1.7123e-04
Akaike info crit = -1660.19086
Bayesian info crit = -1643.90338
R-squared = 0.99793950
[[Variables]]
exp_amplitude: 1.8677e-26 +/- 8.7869e-26 (470.47%) (init = 4.448869e-33)
exp_decay: -0.80057479 +/- 0.06648062 (8.30%) (init = -0.6143452)
v_amplitude: 0.53691781 +/- 0.00377304 (0.70%) (init = 1)
v_center: 44.6143955 +/- 7.6836e-04 (0.00%) (init = 44.61536)
v_sigma: 0.11663920 +/- 7.4103e-04 (0.64%) (init = 0.3693009)
v_gamma: 0.11663920 +/- 7.4103e-04 (0.64%) == 'v_sigma'
v_fwhm: 0.42005165 +/- 0.00266867 (0.64%) == '1.0692*v_gamma+sqrt(0.8664*v_gamma**2+5.545083*v_sigma**2)'
v_height: 0.96073817 +/- 0.00387211 (0.40%) == '(v_amplitude/(max(1e-15, v_sigma*sqrt(2*pi))))*wofz((1j*v_gamma)/(max(1e-15, v_sigma*sqrt(2)))).real'
[[Correlations]] (unreported correlations are < 0.250)
C(exp_amplitude, exp_decay) = -1.0000
C(v_amplitude, v_sigma) = +0.8232
C(exp_amplitude, v_amplitude) = -0.7420
C(exp_decay, v_amplitude) = +0.7388
C(exp_amplitude, v_sigma) = -0.5494
C(exp_decay, v_sigma) = +0.5465
Crystal size in nm with Voigt fitting: 20
xrd.lorentzian()
[[Model]]
(Model(lorentzian, prefix='l_') + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 5965
# data points = 192
# variables = 5
chi-square = 0.08446267
reduced chi-square = 4.5167e-04
Akaike info crit = -1473.95666
Bayesian info crit = -1457.66918
R-squared = 0.99456467
[[Variables]]
exp_amplitude: 1.4532e-84 +/- 7.2746e-83 (5005.89%) (init = 4.448869e-33)
exp_decay: -0.23895951 +/- 0.06247247 (26.14%) (init = -0.6143452)
l_amplitude: 0.63690019 +/- 0.00522466 (0.82%) (init = 1)
l_center: 44.6176801 +/- 0.00126901 (0.00%) (init = 44.61536)
l_sigma: 0.19730233 +/- 0.00197555 (1.00%) (init = 0.3693009)
l_fwhm: 0.39460467 +/- 0.00395110 (1.00%) == '2.0000000*l_sigma'
l_height: 1.02751767 +/- 0.00622355 (0.61%) == '0.3183099*l_amplitude/max(1e-15, l_sigma)'
[[Correlations]] (unreported correlations are < 0.250)
C(exp_amplitude, exp_decay) = -1.0000
C(l_amplitude, l_sigma) = +0.7966
C(exp_amplitude, l_amplitude) = -0.6326
C(exp_decay, l_amplitude) = +0.6321
C(exp_amplitude, l_sigma) = -0.4571
C(exp_decay, l_sigma) = +0.4566
C(exp_amplitude, l_center) = -0.3446
C(exp_decay, l_center) = +0.3443
Crystal size in nm with Lorentzian fitting: 22
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