{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Example of XANES convolution\n", "\n", "- Author: Mauro Rovezzi \n", "- Date: 2023-05\n", "\n", "This notebook shows how to perform an energy-dependent convolution of XANES simulated data with the [FDMNES](https://fdmnes.neel.cnrs.fr/) code." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We load an example of experimental data from the [SSHADE/FAME database](https://www.sshade.eu/db/fame):\n", "\n", "- [Zn K-edge XAS spectrum of ZnO](https://doi.org/10.26302/SSHADE/EXPERIMENT_ST_20180418_001)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from larch.io import read_ascii\n", "from larch.xafs import pre_edge\n", "\n", "dat = read_ascii(\"../fdmnes/ZnO_SSHADE.data.txt\", labels=(\"energy\", \"mu\"))\n", "pre_edge(dat)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "A corresponding XAS simulation of Zn K-edge ZnO wurtzite is performed with FDMNES. We load both the non-convoluted data and the automatically convoluted one by FDMNES in order to compare with the convolution performed in Python here, that is, to show they are equivalent." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def read_fdmnes(path, labels=None):\n", " g = read_ascii(path, labels=labels)\n", " with open(path) as f:\n", " header = f.readline().split()\n", " g.e_edge = float(header[0])\n", " g.Z = header[1]\n", " g.e_fermi = float(header[6])\n", " return g\n", "\n", "sim = read_fdmnes(\"../fdmnes/ZnO_FDMNES.txt\", labels=(\"energy\", \"mu\"))\n", "sim_conv = read_ascii(\"../fdmnes/ZnO_FDMNES_conv.txt\", labels=(\"energy\", \"mu\"))\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We do a convolution with a Lorentzian kernel. Need to create an array of energy dependent broadening parameters, starting from the XAS core-hole $\\Gamma_{hole}$. *NOTE* all the parameters are described in the FDMNES manual." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from larch.math.convolution1D import atan_gamma, conv_fast\n", "\n", "gamma_hole = 1.67 #from tabulated data\n", "\n", "agammas = atan_gamma(sim.energy, e_cut=sim.e_fermi, gamma_hole=gamma_hole)\n", "\n", "myconv_a = conv_fast(sim.energy, sim.mu, e_cut=sim.e_fermi, kernel=\"lorentzian\", gammas=agammas)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "To further simulate the experimental broadening, we may do an additional convolution with a Gaussian kernel" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from larch.math.convolution1D import lin_gamma\n", "\n", "lgammas = lin_gamma(sim.energy, gamma_hole=1)\n", "\n", "myconv_b = conv_fast(sim.energy, myconv_a, e_cut=-10, kernel=\"gaussian\", gammas=lgammas)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "A simple plot to show that the FDMNES and Larch convoluted spectra are identical (**NOTE**: click on the plot legend to hide/show a curve)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "black", "width": 3 }, "name": "exp data", "type": "scatter", "uid": "93ab822c-e702-4f94-8951-5887a740cbed", "x": [ -145.83978500000012, -145.33978500000012, -144.83978500000012, -144.33978500000012, -143.83978500000012, -143.33978500000012, -142.83978500000012, -142.33978500000012, -141.83978500000012, -141.33978500000012, -140.83978500000012, -140.33978500000012, -139.83978500000012, 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