{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This cell is added by sphinx-gallery\n\n%matplotlib inline\n\nimport mrsimulator\nprint(f'You are using mrsimulator v{mrsimulator.__version__}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n# Czjzek distribution, 27Al (I=5/2) 3QMAS\n\n27Al (I=5/2) 3QMAS simulation of amorphous material.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we illustrate the simulation of a quadrupolar MQMAS spectrum arising\nfrom a distribution of the electric field gradient (EFG) tensors from amorphous\nmaterial. We proceed by employing the Czjzek distribution model.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib as mpl\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom mrsimulator import Simulator\nfrom mrsimulator.methods import ThreeQ_VAS\nfrom mrsimulator.models import CzjzekDistribution\nfrom mrsimulator.utils.collection import single_site_system_generator\nfrom scipy.stats import multivariate_normal\n\n# global plot configuration\nmpl.rcParams[\"figure.figsize\"] = [4.5, 3.0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate probability distribution\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# The range of isotropic chemical shifts, the quadrupolar coupling constant, and\n# asymmetry parameters used in generating a 3D grid.\niso_r = np.arange(101) / 1.5 + 30 # in ppm\nCq_r = np.arange(100) / 4 # in MHz\neta_r = np.arange(10) / 9\n\n# The 3D mesh grid over which the distribution amplitudes are evaluated.\niso, Cq, eta = np.meshgrid(iso_r, Cq_r, eta_r, indexing=\"ij\")\n\n# The 2D amplitude grid of Cq and eta is sampled from the Czjzek distribution model.\nCq_dist, e_dist, amp = CzjzekDistribution(sigma=1).pdf(pos=[Cq_r, eta_r])\n\n# The 1D amplitude grid of isotropic chemical shifts is sampled from a Gaussian model.\niso_amp = multivariate_normal(mean=58, cov=[4]).pdf(iso_r)\n\n# The 3D amplitude grid is generated as an uncorrelated distribution of the above two\n# distribution, which is the product of the two distributions.\npdf = np.repeat(amp, iso_r.size).reshape(eta_r.size, Cq_r.size, iso_r.size)\npdf *= iso_amp\npdf = pdf.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two-dimensional projections from this three-dimensional distribution are shown\nbelow.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "_, ax = plt.subplots(1, 3, figsize=(9, 3))\n\n# isotropic shift v.s. quadrupolar coupling constant\nax[0].contourf(Cq_r, iso_r, pdf.sum(axis=2))\nax[0].set_xlabel(\"Cq / MHz\")\nax[0].set_ylabel(\"isotropic chemical shift / ppm\")\n\n# isotropic shift v.s. quadrupolar asymmetry\nax[1].contourf(eta_r, iso_r, pdf.sum(axis=1))\nax[1].set_xlabel(r\"quadrupolar asymmetry, $\\eta$\")\nax[1].set_ylabel(\"isotropic chemical shift / ppm\")\n\n# quadrupolar coupling constant v.s. quadrupolar asymmetry\nax[2].contourf(eta_r, Cq_r, pdf.sum(axis=0))\nax[2].set_xlabel(r\"quadrupolar asymmetry, $\\eta$\")\nax[2].set_ylabel(\"Cq / MHz\")\n\nplt.tight_layout()\nplt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation setup\nLet's create the site and spin system objects from these parameters. Use the\n:func:`~mrsimulator.utils.collection.single_site_system_generator` utility function to\ngenerate single-site spin systems.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spin_systems = single_site_system_generator(\n isotopes=\"27Al\",\n isotropic_chemical_shifts=iso,\n quadrupolar={\"Cq\": Cq * 1e6, \"eta\": eta}, # Cq in Hz\n abundance=pdf,\n)\nlen(spin_systems)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate a $^{27}\\text{Al}$ 3Q-MAS spectrum by using the `ThreeQ_MAS` method.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mqvas = ThreeQ_VAS(\n channels=[\"27Al\"],\n spectral_dimensions=[\n {\n \"count\": 512,\n \"spectral_width\": 26718.475776, # in Hz\n \"reference_offset\": -4174.76184, # in Hz\n \"label\": \"Isotropic dimension\",\n },\n {\n \"count\": 512,\n \"spectral_width\": 2e4, # in Hz\n \"reference_offset\": 2e3, # in Hz\n \"label\": \"MAS dimension\",\n },\n ],\n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create the simulator object, add the spin systems and method, and run the simulation.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sim = Simulator()\nsim.spin_systems = spin_systems # add the spin systems\nsim.methods = [mqvas] # add the method\nsim.config.number_of_sidebands = 1\nsim.run()\n\ndata = sim.methods[0].simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot of the corresponding spectrum.\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ax = plt.subplot(projection=\"csdm\")\ncb = ax.imshow(data / data.max(), cmap=\"gist_ncar_r\", aspect=\"auto\")\nplt.colorbar(cb)\nax.set_ylim(-20, -50)\nax.set_xlim(80, 20)\nplt.tight_layout()\nplt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 0 }