notebooks/2017-04-03-Slab generation and Wulff shape.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "This notebook demonstrates how to generate various slabs for a material using surface.py. In addition, it will also demonstrate how to obtain the Wulff shape with a set of surface energies associated with Miller indices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson, S. P. Ong, \"Surface Energies of Elemental Crystals\", Scientific Data, 2016, 3:160080, doi:10.1038/sdata.2016.80.\n",
    "\n",
    "Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs, Surface Science, 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uncomment the subsequent lines in this cell to install dependencies for Google Colab.\n",
    "# !pip install pymatgen==2022.7.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the necessary tools for making a Wulff shape\n",
    "from __future__ import annotations\n",
    "\n",
    "from pymatgen.analysis.wulff import WulffShape\n",
    "\n",
    "# Import the necessary tools to generate surfaces\n",
    "from pymatgen.core.surface import Lattice, SlabGenerator, Structure, generate_all_slabs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's start with fcc Ni\n",
    "lattice = Lattice.cubic(3.508)\n",
    "Ni = Structure(\n",
    "    lattice,\n",
    "    [\"Ni\", \"Ni\", \"Ni\", \"Ni\"],\n",
    "    [[0, 0, 0], [0, 0.5, 0], [0.5, 0, 0], [0, 0, 0.5]],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Ni(111) slab only has 1 termination.\n"
     ]
    }
   ],
   "source": [
    "# We'll use the SlabGenerator class to get a single slab. We'll start with the\n",
    "# (111) slab of Ni. Plug in the CONVENTIONAL unit cell of your structure, the\n",
    "# maximum Miller index value to generate the different slab orientations along\n",
    "# with the minimum slab and vacuum size in Angstroms\n",
    "slabgen = SlabGenerator(Ni, (1, 1, 1), 10, 10)\n",
    "\n",
    "# If we want to find all terminations for a particular Miller index orientation,\n",
    "# we use the get_slabs() method. This returns a LIST of slabs rather than a single\n",
    "# slab. When generating a slab for a particular orientation, there are sometimes\n",
    "# more than one location we can terminate or cut the structure to create a slab. The\n",
    "# simplest example of this would be the Si(Fd-3m) (111) slab which can be cut or\n",
    "# terminated in two different locations along the vector of the Miller index. For a\n",
    "# fcc structure such as Ni however, there should only be one way to cut a (111) slab.\n",
    "all_slabs = slabgen.get_slabs()\n",
    "print(\"The Ni(111) slab only has %s termination.\" % (len(all_slabs)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Notice now there are actually now 2 terminations that can be generated in the (111) direction for diamond Si\n",
      "18 unique slab structures have been found for a max Miller index of 3\n"
     ]
    }
   ],
   "source": [
    "# Let's try this for a diamond Silicon structure\n",
    "lattice = Lattice.cubic(5.46873)\n",
    "Si = Structure(\n",
    "    lattice,\n",
    "    [\"Si\", \"Si\", \"Si\", \"Si\", \"Si\", \"Si\", \"Si\", \"Si\"],\n",
    "    [\n",
    "        [0.00000, 0.00000, 0.50000],\n",
    "        [0.75000, 0.75000, 0.75000],\n",
    "        [0.00000, 0.50000, 0.00000],\n",
    "        [0.75000, 0.25000, 0.25000],\n",
    "        [0.50000, 0.00000, 0.00000],\n",
    "        [0.25000, 0.75000, 0.25000],\n",
    "        [0.50000, 0.50000, 0.50000],\n",
    "        [0.25000, 0.25000, 0.75000],\n",
    "    ],\n",
    ")\n",
    "\n",
    "slabgen = SlabGenerator(Si, (1, 1, 1), 10, 10)\n",
    "print(\n",
    "    \"Notice now there are actually now %s terminations that can be \\\n",
    "generated in the (111) direction for diamond Si\"\n",
    "    % (len(slabgen.get_slabs()))\n",
    ")\n",
    "\n",
    "# The simplest way to do this is to just use generate_all_slabs which finds all the unique\n",
    "# Miller indices for a structure and uses SlabGenerator to create all terminations for all of them.\n",
    "all_slabs = generate_all_slabs(Si, 3, 10, 10)\n",
    "print(\n",
    "    \"%s unique slab structures have been found for a max Miller index of 3\"\n",
    "    % (len(all_slabs))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 1, 1)\n",
      "(1, 1, 1)\n",
      "(1, 1, 0)\n",
      "(1, 0, 0)\n",
      "(2, 2, 1)\n",
      "(2, 2, 1)\n",
      "(2, 1, 1)\n",
      "(2, 1, 0)\n",
      "(3, 3, 2)\n",
      "(3, 3, 1)\n",
      "(3, 3, 1)\n",
      "(3, 2, 2)\n",
      "(3, 2, 2)\n",
      "(3, 2, 1)\n",
      "(3, 2, 0)\n",
      "(3, 1, 1)\n",
      "(3, 1, 1)\n",
      "(3, 1, 0)\n",
      "Notice some Miller indices are repeated. Again, this is due to there being more than one termination\n"
     ]
    }
   ],
   "source": [
    "# What are the Miller indices of these slabs?\n",
    "for slab in all_slabs:\n",
    "    print(slab.miller_index)\n",
    "print(\n",
    "    \"Notice some Miller indices are repeated. Again, this is due to there being more than one termination\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating the surface energy\n",
    "To do this, we actually need to calculate (from first principles) the total energy of two structures. The total energy of the bulk ($E_{bulk}$) (preferably the oriented unit cell corresponding to the slab) and the total energy of the slab($E_{slab}$) which is several layers of atoms interfaced with a vacuum. Using the following equation, we can get the surface energy $\\gamma = \\frac{E_{slab}-E_{bulk}}{2A}$ where both slab and bulk systems have the same number of atoms and species (you can multiply $E_{bulk}$ where n is the number of oriented unit cell layers contained in your slab system relative ot your bulk system). The factor of 1/2 accounts for the two surfaces in our slab model so $\\gamma$ is the surface energy of one surface.\n",
    "\n",
    "# Some basic properties of the Wulff shape\n",
    "\n",
    "Using the WulffShape class, there are a couple of properties we can get. Here we will explain what some of them are.\n",
    "\n",
    "weighted_surface_energy:\n",
    "\n",
    "Surface Gibbs free energy for a crystal is given by $\\Delta G=\\sum\\limits_{hkl}\\gamma_{hkl}A_{hkl}$. Where $\\gamma_{hkl}$ is the surface energy of facet (hkl) and $A_{hkl}$ is the surface area of that particular facet that occupies the Wulff shape. We can normalize this value with the total surface area of the Wulff shape to get the weighted (average) surface energy for a particular material $\\bar{\\gamma}=\\frac{\\Delta G}{\\sum\\limits_{hkl}A_{hkl}}$\n",
    "\n",
    "anisotropy:\n",
    "\n",
    "Typically in the literature when discussing surface anisotropy, we would only look at the ratios of 2 surface energies when talking about anisotropy. eg. the ratio of a generic fcc (111) to (100) surface energy should be less than 1 as the (111) facet is the closest packed surface of an fcc structure and should have the lowest surface energy. However this method of determining surface anisotropy does not allow us to determine an overall anisotropy of a material, ie. how different are all the surface energies for a material. As such, we used the Coefficient of Variation from the weighted surface energy. For reference, an ideal sphere Wulff shape (eg. completely isotropic) has a anisotropy of 0.\n",
    "\n",
    "shape_factor:\n",
    "\n",
    "An alternative to anisotropy. This is useful for determining the critical nucleus size. A large shape factor indicates great anisotropy.\n",
    "See Ballufi, R. W., Allen, S. M. & Carter, W. C. Kinetics of Materials. (John Wiley & Sons, 2005), p.461"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape factor: 5.178, anisotropy: 0.070, weighted surface energy: 2.035 J/m^2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes3D: xlabel='x', ylabel='y', zlabel='z'>"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now let's assume that we then calculated the surface energies for these slabs\n",
    "\n",
    "# Surface energy values in J/m^2\n",
    "surface_energies_Ni = {\n",
    "    (3, 2, 0): 2.3869,\n",
    "    (1, 1, 0): 2.2862,\n",
    "    (3, 1, 0): 2.3964,\n",
    "    (2, 1, 0): 2.3969,\n",
    "    (3, 3, 2): 2.0944,\n",
    "    (1, 0, 0): 2.2084,\n",
    "    (2, 1, 1): 2.2353,\n",
    "    (3, 2, 2): 2.1242,\n",
    "    (3, 2, 1): 2.3183,\n",
    "    (2, 2, 1): 2.1732,\n",
    "    (3, 3, 1): 2.2288,\n",
    "    (3, 1, 1): 2.3039,\n",
    "    (1, 1, 1): 1.9235,\n",
    "}\n",
    "miller_list = surface_energies_Ni.keys()\n",
    "e_surf_list = surface_energies_Ni.values()\n",
    "\n",
    "# We can now construct a Wulff shape with an accuracy up to a max Miller index of 3\n",
    "wulffshape = WulffShape(Ni.lattice, miller_list, e_surf_list)\n",
    "\n",
    "# Let's get some useful information from our wulffshape object\n",
    "print(\n",
    "    \"shape factor: %.3f, anisotropy: \\\n",
    "%.3f, weighted surface energy: %.3f J/m^2\"\n",
    "    % (\n",
    "        wulffshape.shape_factor,\n",
    "        wulffshape.anisotropy,\n",
    "        wulffshape.weighted_surface_energy,\n",
    "    )\n",
    ")\n",
    "\n",
    "\n",
    "# If we want to see what our Wulff shape looks like\n",
    "wulffshape.get_plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets try something a little more complicated, say LiFePO4\n",
    "from pymatgen.util.testing import PymatgenTest\n",
    "\n",
    "# Get the LiFePO4 structure\n",
    "LiFePO4 = PymatgenTest.get_structure(\"LiFePO4\")\n",
    "\n",
    "# Let's add some oxidation states to LiFePO4, this will be\n",
    "# important when we want to take surface polarity into consideration\n",
    "LiFePO4.add_oxidation_state_by_element({\"Fe\": 2, \"Li\": 1, \"P\": 5, \"O\": -2})\n",
    "slabgen = SlabGenerator(LiFePO4, (0, 0, 1), 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When generating a slab of LiFePO4, we also want to be careful \n",
    "not break any of the P-O bonds. These bonds are strong \n",
    "enough that they will result in a significantly high surface \n",
    "energy when broken so its reasonable to say that any terminations \n",
    "with such broken bonds will not yield the lowest surface energy. To\n",
    "implement this, we add the bonds parameter to get_slabs, a dictionary \n",
    "where the key will be two atoms whose bonds we do not want to break \n",
    "and the element of that value would be their maximum bond length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the (001) slab of LiFePO4, there are 2 terminations.\n"
     ]
    }
   ],
   "source": [
    "all_slabs = slabgen.get_slabs(bonds={(\"P\", \"O\"): 2})\n",
    "# any bond between P and O less than 2 Angstroms cannot be broken when generating slabs\n",
    "print(\"For the (001) slab of LiFePO4, there are %s terminations.\" % (len(all_slabs)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a couple of rules before we actually run calculations on some of these \n",
    "slab models. First off, we need to ensure that all slabs we will be calculating have \n",
    "the same surface on both sides. To do this, we need to ensure the slab model has Laue \n",
    "point group symmetry ie. contains inversion symmetry. We use the is_symmetric() \n",
    "property of our slab object to check this. It's important that both surfaces are the \n",
    "same as the above equation for surface energy is used to get the energy of one surface, \n",
    "hence the 1/2 factor in the equation. If the surfaces are different (the slab is not \n",
    "symmetric), we would be calculating the average surface energy of two different surfaces \n",
    "in our slab rather than the surface energy for one slab in our calculation. Secondly, \n",
    "for structures containing oxidation states, we need to ensure that our surfaces are \n",
    "nonpolar. A polar termination will lead to a very high surface energy, so we can skip \n",
    "those particular structures. We can check polarity using the is_polar() property of \n",
    "our slab object. Both these criterias (nonpolar and symmetric) should be satisfied \n",
    "before calculating a particular slab model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True False\n",
      "False True\n"
     ]
    }
   ],
   "source": [
    "for slab in all_slabs:\n",
    "    print(slab.is_polar(), slab.is_symmetric())\n",
    "# Notice that none of the terminations in the (001) direction do not simultaneously satisfy\n",
    "# our two criteria so a (001) surface with a reasonable surface energy cannot be calculated.\n",
    "# In such cases, we need to modify the surfaces of our slabs. A future release of surface.py\n",
    "# will implement such modification techniques for these cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now let's generate all possible slabs for a max Miller index of 2 for LiFePO4 and see if\n",
    "# any of these surfaces can be calculated to yield reasonable and accurate surface energy\n",
    "# values. This may take a while.\n",
    "all_slabs = generate_all_slabs(LiFePO4, 2, 10, 10, bonds={(\"P\", \"O\"): 2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a total of 5 slabs generated including polar, asymmetric, and P-O terminated slabs\n",
      "(0, 0, 1)\n",
      "Number of slabs that are nonpolar, symmetric and do not terminate P-O bonds: 1\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    \"There is a total of %s slabs generated including polar, asymmetric, and \\\n",
    "P-O terminated slabs\"\n",
    "    % (len(all_slabs))\n",
    ")\n",
    "\n",
    "# store any slabs for calculation that satisfies our criterias\n",
    "valid_slabs = []\n",
    "for slab in all_slabs:\n",
    "    if not slab.is_polar() and slab.is_symmetric():\n",
    "        print(slab.miller_index)\n",
    "        valid_slabs.append(slab)\n",
    "\n",
    "print(\n",
    "    \"Number of slabs that are nonpolar, symmetric and do not terminate P-O bonds: %s\"\n",
    "    % (len(valid_slabs))\n",
    ")"
   ]
  }
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