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"This example shows a basic example of \"Feff fitting\" with larch for Cu metal at room temperature.\n",
"\n",
"We start with some import statements, then do a \"normal\" first-shell fit\n",
" 1. read in data for Cu metal, Cu K edge\n",
" 2. do background subtraction and plot $\\chi(k)$\n",
" 3. set the Fourier transform ranges\n",
" 4. define a Group of Parameters for the fit\n",
" 5. read in 1 Feff Path for Cu-Cu scattering\n",
" 6. run the fit and view the results\n",
" \n",
"Then we will expand that to include 2 more paths, and show one way to constrain the distances parameters"
]
},
{
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"execution_count": 1,
"id": "59499dc6",
"metadata": {},
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"source": [
"# step 0: imports\n",
"import numpy as np\n",
"from pathlib import Path\n",
"from larch.xafs import (pre_edge, autobk, xftf, xftr,\n",
" ff2chi, feffpath, feffit_transform, \n",
" feffit_dataset, feffit, feffit_report)\n",
"from larch.fitting import param, guess, param_group\n",
"from larch.io import read_ascii\n",
"from larch.plot.plotly_xafsplots import (plot_mu,plot_chik, plot_chir, plot_chifit, \n",
" multi_plot, plotlabels, set_label_weight)"
]
},
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"cell_type": "code",
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"radialaxis": {
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"scene": {
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"gridwidth": 2,
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"ticks": "",
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"yaxis": {
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"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
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"zaxis": {
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"showbackground": true,
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}
},
"shapedefaults": {
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},
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"title": {
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"xaxis": {
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"gridcolor": "white",
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"ticks": "",
"title": {
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},
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"zerolinewidth": 2
},
"yaxis": {
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},
"title": {
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},
"width": 650,
"xaxis": {
"color": "#004",
"gridcolor": "#D8D8D8",
"range": [
0,
null
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"showgrid": true,
"title": {
"text": "$k \\rm\\,(\\unicode{x212B}^{-1})$"
},
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},
"yaxis": {
"color": "#004",
"gridcolor": "#D8D8D8",
"showgrid": true,
"title": {
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},
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}
}
},
"text/html": [
""
]
},
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],
"source": [
"# step 2: do and check the background subtraction\n",
"autobk(cu_data, rbkg=1.0, kweight=2)\n",
"fig = plot_chik(cu_data, kweight=2)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "3c3c1148",
"metadata": {},
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"source": [
"# step 3: Fourier transform ranges ranges\n",
"xftf(cu_data, kmin=3, kmax=17, kweight=2, dk=4, window='kaiser')\n",
"xftr(cu_data, rmin=1.2, rmax=3, window='hanning', dr=0)\n",
"\n",
"plot_chir(cu_data, show_window=True, rmax=7)\n",
"\n",
"\n",
"# we can then definte Fourier tranform and fit ranges (first shell only: out to 3.0 Ang)\n",
"trans = feffit_transform(kmin=3, kmax=17, kweight=2, dk=4, window='kaiser', rmin=1.2, rmax=3.0)"
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"source": [
"# step 4: setup fitting Parameters: we will vary \n",
"# amplitude, e0, sigma2, and delta_R, and a third cumulant C3\n",
"\n",
"pars = param_group(amp=param(1, vary=True),\n",
" de0=param(3, vary=True),\n",
" c3=param(.0002, vary=True),\n",
" sig2=param(.005, vary=True),\n",
" delr=param(0.01, vary=True) )\n"
]
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"source": [
"# step 5: define a Feff Path for Cu-Cu scattering\n",
"\n",
"# using a Path file from a previous Feff calculation for Zn-Se (shown elsewhere)\n",
"# here we give math expressions using the Parameters named in the Parameter group \n",
"# to set the values for the Path Parameters in the EXAFS equation\n",
"path1 = feffpath(Path('..', 'feffit','feff0001.dat'), label='Cu R=2.56Ang',\n",
" s02='amp', e0='de0', sigma2='sig2', deltar='delr', third='c3')\n",
"\n",
"tmpsum = ff2chi([path1], params=pars)\n",
"fig = plot_chik(tmpsum, kweight=2, label='initial Feff Model', show=False)\n",
"fig.add_plot(cu_data.k, cu_data.chi*cu_data.k**2, label='data')\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "2a63b3c7",
"metadata": {},
"outputs": [
{
"name": "stdout",
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"text": [
"=================== FEFFIT RESULTS ====================\n",
"[[Statistics]]\n",
" n_function_calls = 31\n",
" n_variables = 5\n",
" n_data_points = 116\n",
" n_independent = 17.0428183\n",
" chi_square = 73.9433580\n",
" reduced chi_square = 6.14003769\n",
" r-factor = 0.00177931\n",
" Akaike info crit = 35.0115368\n",
" Bayesian info crit = 39.1901813\n",
" \n",
"[[Variables]]\n",
" amp = 0.9435343 +/- 0.0312676 (init= 1.0000000)\n",
" c3 = 2.0191e-4 +/- 7.6522e-5 (init= 2.0000e-4)\n",
" de0 = 6.0481828 +/- 0.7342104 (init= 3.0000000)\n",
" delr = 0.0118328 +/- 0.0069547 (init= 0.0100000)\n",
" sig2 = 0.0087457 +/- 2.4353e-4 (init= 0.0050000)\n",
" \n",
"[[Correlations]] (unreported correlations are < 0.100)\n",
" c3, delr = 0.957\n",
" de0, delr = 0.951\n",
" amp, sig2 = 0.929\n",
" c3, de0 = 0.846\n",
" amp, delr = 0.184\n",
" delr, sig2 = 0.171\n",
" amp, c3 = 0.151\n",
" amp, de0 = 0.141\n",
" de0, sig2 = 0.136\n",
" c3, sig2 = 0.130\n",
" \n",
"[[Dataset]]\n",
" unique_id = 'dc5vezx7'\n",
" fit space = 'r'\n",
" r-range = 1.200, 3.000\n",
" k-range = 3.000, 17.000\n",
" k window, dk = 'kaiser', 4.000\n",
" paths used in fit = [PosixPath('../feffit/feff0001.dat')]\n",
" k-weight = 2\n",
" epsilon_k = Array(mean=6.1910e-4, std=0.0016545)\n",
" epsilon_r = 0.0208085\n",
" n_independent = 17.043\n",
" \n",
"[[Paths]]\n",
" = Path 'Cu R=2.56Ang' = Cu K Edge\n",
" feffdat file = ../feffit/feff0001.dat, from feff run 'feffit'\n",
" geometry atom x y z ipot\n",
" Cu 0.0000, 0.0000, 0.0000 0 (absorber)\n",
" Cu 0.0000, -1.8016, 1.8016 1\n",
" reff = 2.5478000\n",
" degen = 12.000000\n",
" n*s02 = 0.9435343 +/- 0.0312676 := 'amp'\n",
" e0 = 6.0481828 +/- 0.7342104 := 'de0'\n",
" r = 2.5596328 +/- 0.0069547 := 'reff + delr'\n",
" deltar = 0.0118328 +/- 0.0069547 := 'delr'\n",
" sigma2 = 0.0087457 +/- 2.4353e-4 := 'sig2'\n",
" third = 2.0191e-4 +/- 7.6522e-5 := 'c3'\n",
"\n",
"=======================================================\n"
]
}
],
"source": [
"# step 6: run and view the fit\n",
"\n",
"# now that we have data, a set of paths, and Fourier transform values, we can\n",
"# set up a \"Feffit Dataset\" and then fit that with the group of Parameters\n",
"\n",
"# define dataset to include data, pathlist, transform\n",
"dset = feffit_dataset(data=cu_data, pathlist=[path1], transform=trans)\n",
"\n",
"# do the fit...\n",
"result = feffit(pars, dset)\n",
"\n",
"# print out the fit report\n",
"print(feffit_report(result))"
]
},
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"# finally, plot the results\n",
"fig6, fig7 = plot_chifit(result.datasets[0])"
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"From the fit report,we see that the third cumulant, $C_3$ is ever-so-slightly above 0 for room temperature Cu, and that this is highly correlated with $R$. In another notebook, we'll explore those correlations and uncertainties\n",
"in more detail.\n",
"\n",
"Now we can add two more Paths for Cu scattering, and extend the R-range of the fit range to 3.5 Ang"
]
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"# we will just change the Rmax to 3.5:\n",
"trans.rmax = 3.5\n",
"\n",
"# and we will update the parameters to \n",
"# include a separate sigma2 for each path, \n",
"# but we'll change 'delr' to 'alpha' and use this as fractional change in distance for each path.\n",
"pars = param_group(amp=param(1,vary=True),\n",
" de0 = param(3, vary=True),\n",
" c3 = param(.002, vary=True),\n",
" sig2 = param(.002, vary=True),\n",
" sig2_p2 = param(.002, vary=True),\n",
" sig2_p3 = param(.002, vary=True),\n",
" alpha= param(0.001, vary=True) )\n",
"\n",
"\n",
"# and we will define 3 paths to use use these:\n",
"path1.deltar = 'alpha*reff'\n",
"\n",
"path2 = feffpath('../feffit/feff0002.dat', s02='amp', e0='de0',\n",
" sigma2='sig2_p2', deltar='alpha*reff')\n",
"\n",
"path3 = feffpath('../feffit/feff0003.dat', s02='amp', e0='de0',\n",
" sigma2='sig2_p3', deltar='alpha*reff')\n",
"\n",
"# note that all 3 expressions for 'deltar' are the same 'alpha*reff'. \n",
"# The value of 'reff' will be nominal Path distance"
]
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"text": [
"=================== FEFFIT RESULTS ====================\n",
"[[Statistics]]\n",
" n_function_calls = 107\n",
" n_variables = 7\n",
" n_data_points = 150\n",
" n_independent = 21.4991567\n",
" chi_square = 105.154005\n",
" reduced chi_square = 7.25242215\n",
" r-factor = 0.00253915\n",
" Akaike info crit = 48.1280253\n",
" Bayesian info crit = 55.6041213\n",
" \n",
"[[Variables]]\n",
" alpha = 0.0027937 +/- 0.0027987 (init= 1.0000e-3)\n",
" amp = 0.9365027 +/- 0.0340717 (init= 1.0000000)\n",
" c3 = 1.4437e-4 +/- 7.7277e-5 (init= 0.0020000)\n",
" de0 = 5.6958140 +/- 0.7689779 (init= 3.0000000)\n",
" sig2 = 0.0086826 +/- 2.6711e-4 (init= 0.0020000)\n",
" sig2_p2 = 0.0131224 +/- 0.0010719 (init= 0.0020000)\n",
" sig2_p3 = 0.0062715 +/- 0.0028923 (init= 0.0020000)\n",
" \n",
"[[Correlations]] (unreported correlations are < 0.100)\n",
" alpha, c3 = 0.952\n",
" alpha, de0 = 0.950\n",
" amp, sig2 = 0.929\n",
" c3, de0 = 0.836\n",
" amp, sig2_p2 = 0.297\n",
" sig2, sig2_p2 = 0.276\n",
" sig2, sig2_p3 = 0.214\n",
" amp, sig2_p3 = 0.213\n",
" c3, sig2_p3 = -0.188\n",
" alpha, amp = 0.186\n",
" alpha, sig2 = 0.172\n",
" c3, sig2_p2 = 0.170\n",
" alpha, sig2_p2 = 0.153\n",
" amp, de0 = 0.148\n",
" alpha, sig2_p3 = -0.148\n",
" amp, c3 = 0.146\n",
" de0, sig2 = 0.143\n",
" c3, sig2 = 0.125\n",
" \n",
"[[Dataset]]\n",
" unique_id = 'dc5vezx7'\n",
" fit space = 'r'\n",
" r-range = 1.200, 3.500\n",
" k-range = 3.000, 17.000\n",
" k window, dk = 'kaiser', 4.000\n",
" paths used in fit = [PosixPath('../feffit/feff0001.dat'), '../feffit/feff0002.dat', '../feffit/feff0003.dat']\n",
" k-weight = 2\n",
" epsilon_k = Array(mean=6.1910e-4, std=0.0016545)\n",
" epsilon_r = 0.0208085\n",
" n_independent = 21.499\n",
" \n",
"[[Paths]]\n",
" = Path 'Cu R=2.56Ang' = Cu K Edge\n",
" feffdat file = ../feffit/feff0001.dat, from feff run 'feffit'\n",
" geometry atom x y z ipot\n",
" Cu 0.0000, 0.0000, 0.0000 0 (absorber)\n",
" Cu 0.0000, -1.8016, 1.8016 1\n",
" reff = 2.5478000\n",
" degen = 12.000000\n",
" n*s02 = 0.9365027 +/- 0.0340717 := 'amp'\n",
" e0 = 5.6958140 +/- 0.7689779 := 'de0'\n",
" r = 2.5549177 +/- 0.0071304 := 'reff + alpha*reff'\n",
" deltar = 0.0071177 +/- 0.0071304 := 'alpha*reff'\n",
" sigma2 = 0.0086826 +/- 2.6711e-4 := 'sig2'\n",
" third = 1.4437e-4 +/- 7.7277e-5 := 'c3'\n",
"\n",
" = Path 'pj3m4qvfy' = Cu K Edge\n",
" feffdat file = ../feffit/feff0002.dat, from feff run 'feffit'\n",
" geometry atom x y z ipot\n",
" Cu 0.0000, 0.0000, 0.0000 0 (absorber)\n",
" Cu -3.6032, 0.0000, 0.0000 1\n",
" reff = 3.6032000\n",
" degen = 6.0000000\n",
" n*s02 = 0.9365027 +/- 0.0340717 := 'amp'\n",
" e0 = 5.6958140 +/- 0.7689779 := 'de0'\n",
" r = 3.6132661 +/- 0.0100842 := 'reff + alpha*reff'\n",
" deltar = 0.0100661 +/- 0.0100842 := 'alpha*reff'\n",
" sigma2 = 0.0131224 +/- 0.0010719 := 'sig2_p2'\n",
"\n",
" = Path 'pibakl7xe' = Cu K Edge\n",
" feffdat file = ../feffit/feff0003.dat, from feff run 'feffit'\n",
" geometry atom x y z ipot\n",
" Cu 0.0000, 0.0000, 0.0000 0 (absorber)\n",
" Cu 1.8016, -1.8016, 0.0000 1\n",
" Cu 1.8016, 0.0000, -1.8016 1\n",
" reff = 3.8218000\n",
" degen = 48.000000\n",
" n*s02 = 0.9365027 +/- 0.0340717 := 'amp'\n",
" e0 = 5.6958140 +/- 0.7689779 := 'de0'\n",
" r = 3.8324768 +/- 0.0106959 := 'reff + alpha*reff'\n",
" deltar = 0.0106768 +/- 0.0106959 := 'alpha*reff'\n",
" sigma2 = 0.0062715 +/- 0.0028923 := 'sig2_p3'\n",
"\n",
"=======================================================\n"
]
}
],
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"# now we can run that fit and view the results\n",
"\n",
"dset = feffit_dataset(data=cu_data, pathlist=[path1, path2, path3], transform=trans)\n",
"\n",
"result = feffit(pars, dset)\n",
"\n",
"print(feffit_report(result))"
]
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"source": [
"from larch.plot.plotly_xafsplots import plot_paths_k, plot_paths_r\n",
"\n",
"f = plot_paths_k(result.datasets[0], offset=-0.25)"
]
},
{
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"id": "9884ffdf",
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"gridcolor": "#D8D8D8",
"showgrid": true,
"title": {
"text": "$R \\rm\\,(\\unicode{x212B})$"
},
"zerolinecolor": "#DDD"
},
"yaxis": {
"color": "#004",
"gridcolor": "#D8D8D8",
"showgrid": true,
"title": {
"text": "$|\\chi(R)| \\rm\\,(\\unicode{x212B}^{{-3}})$"
},
"zerolinecolor": "#DDD"
}
}
},
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f = plot_paths_r(result.datasets[0], offset=-0.25)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5e10b611",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}