LAMMPS-Tutorials-01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LAMMPS Tutorials 01. Running your first LAMMPS simulation!\n",
    "\n",
    "### Author: Mark Tschopp, mark.a.tschopp.civ at mail.mil\n",
    "\n",
    "Please contact me if you have a problem with this tutorial, so I can modify in Github.  I have added FAQs, and will update my versions of LAMMPS in the future to keep the scripts current.\n",
    "\n",
    "The latest version of this [Jupyter Notebook](http://ipython.org/notebook.html) tutorial is available at https://github.com/mrkllntschpp/lammps-tutorials.\n",
    "\n",
    "The original tutorials are given here: https://icme.hpc.msstate.edu/mediawiki/index.php/LAMMPS_tutorials.  A number of these tutorials are out of date and have been ported over into the current iPython Jupyter Notebook tutorials on github.\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Description:\n",
    "<a id=\"Sec1\"></a>\n",
    "This is a quick tutorial to running a LAMMPS simulation on a Windows machine. For this simple example, the molecular simulation calculates the equilibrium lattice constant and corresponding cohesive energy for aluminum in the face-centered cubic (fcc) lattice structure (see below).\n",
    "\n",
    "<img src=\"https://icme.hpc.msstate.edu/mediawiki/images/e/ef/Fcc_stereo.gif\" alt=\"Face-centered Cubic Lattice Structure\" title=\"FCC Lattice Structure\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Step 1: Download an Input File\n",
    "<a id=\"Step1\"></a>\n",
    "\n",
    "This input script was run using the Aug 2015 version of LAMMPS. Changes in some commands may require revision of the input script. To get the input file, you have a few options:\n",
    "\n",
    "*  Copy the text below and paste it into a text file, `calc_fcc.in`. Use the `Paste Special` command with unformatted text into the file. \n",
    "*  Or, I added the command `%%writefile calc_fcc.in` to the Jupyter Notebook which should just do everything for you!\n",
    "\n",
    "Obviously, if the second option worked, you are all set!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing calc_fcc.in\n"
     ]
    }
   ],
   "source": [
    "%%writefile calc_fcc.in\n",
    "######################################\n",
    "# LAMMPS INPUT SCRIPT\n",
    "# Find minimum energy fcc (face-centered cubic) atomic configuration\n",
    "# Mark Tschopp\n",
    "# Syntax, lmp_exe < calc_fcc.in\n",
    "\n",
    "######################################\n",
    "# INITIALIZATION\n",
    "clear \n",
    "units metal \n",
    "dimension 3 \n",
    "boundary p p p \n",
    "atom_style atomic \n",
    "atom_modify map array\n",
    "\n",
    "######################################\n",
    "# ATOM DEFINITION\n",
    "lattice fcc 4 orient x 1 1 0 orient y -1 1 0 orient z 0 0 1  \n",
    "region box block 0 1 0 1 0 1 units lattice\n",
    "create_box 1 box\n",
    "create_atoms 1 box\n",
    "replicate 1 1 1\n",
    "\n",
    "######################################\n",
    "# DEFINE INTERATOMIC POTENTIAL\n",
    "pair_style eam/alloy \n",
    "pair_coeff * * Al99.eam.alloy Al\n",
    "neighbor 2.0 bin \n",
    "neigh_modify delay 10 check yes \n",
    " \n",
    "######################################\n",
    "# DEFINE COMPUTES \n",
    "compute eng all pe/atom \n",
    "compute eatoms all reduce sum c_eng \n",
    "\n",
    "#####################################################\n",
    "# MINIMIZATION\n",
    "reset_timestep 0 \n",
    "fix 1 all box/relax iso 0.0 vmax 0.001\n",
    "thermo 10 \n",
    "thermo_style custom step pe lx ly lz press c_eatoms \n",
    "min_style cg \n",
    "minimize 1e-25 1e-25 5000 10000 \n",
    "\n",
    "variable natoms equal \"count(all)\" \n",
    "variable teng equal \"c_eatoms\"\n",
    "variable length equal \"lx\"\n",
    "variable ecoh equal \"v_teng/v_natoms\"\n",
    "\n",
    "print \"Total energy (eV) = ${teng};\"\n",
    "print \"Number of atoms = ${natoms};\"\n",
    "print \"Lattice constant (Angstoms) = ${length};\"\n",
    "print \"Cohesive energy (eV) = ${ecoh};\"\n",
    "\n",
    "print \"All done!\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Awesome!  That little script should have written the above text to the file `calc_fcc.in`.  To check, let's execute a command on the present directory listing all files that end in `*.in`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calc_fcc.in\r\n"
     ]
    }
   ],
   "source": [
    "!dir *.in"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Step 2: Running LAMMPS\n",
    "### Run this using LAMMPS in Jupyter Notebook\n",
    "We can actually run this from Jupyter Notebook.  Let's try it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAMMPS (3 Mar 2020)\r\n",
      "Lattice spacing in x,y,z = 5.65685 5.65685 4\r\n",
      "Created orthogonal box = (0 0 0) to (5.65685 5.65685 4)\r\n",
      "  1 by 1 by 1 MPI processor grid\r\n",
      "Created 8 atoms\r\n",
      "  create_atoms CPU = 0.000447035 secs\r\n",
      "Replicating atoms ...\r\n",
      "  orthogonal box = (0 0 0) to (5.65685 5.65685 4)\r\n",
      "  1 by 1 by 1 MPI processor grid\r\n",
      "  8 atoms\r\n",
      "  replicate CPU = 0.000544786 secs\r\n",
      "WARNING: Using 'neigh_modify every 1 delay 0 check yes' setting during minimization (src/min.cpp:190)\r\n",
      "Neighbor list info ...\r\n",
      "  update every 1 steps, delay 0 steps, check yes\r\n",
      "  max neighbors/atom: 2000, page size: 100000\r\n",
      "  master list distance cutoff = 8.28721\r\n",
      "  ghost atom cutoff = 8.28721\r\n",
      "  binsize = 4.1436, bins = 2 2 1\r\n",
      "  1 neighbor lists, perpetual/occasional/extra = 1 0 0\r\n",
      "  (1) pair eam/alloy, perpetual\r\n",
      "      attributes: half, newton on\r\n",
      "      pair build: half/bin/atomonly/newton\r\n",
      "      stencil: half/bin/3d/newton\r\n",
      "      bin: standard\r\n",
      "Setting up cg style minimization ...\r\n",
      "  Unit style    : metal\r\n",
      "  Current step  : 0\r\n",
      "WARNING: Energy due to 1 extra global DOFs will be included in minimizer energies\r\n",
      "Per MPI rank memory allocation (min/avg/max) = 4.474 | 4.474 | 4.474 Mbytes\r\n",
      "Step PotEng Lx Ly Lz Press c_eatoms \r\n",
      "       0   -26.835575    5.6568542    5.6568542            4     29590.11   -26.835575 \r\n",
      "      10   -26.878207    5.7134228    5.7134228         4.04    5853.9553   -26.878207 \r\n",
      "      16       -26.88    5.7275715    5.7275715    4.0500047 2.1489546e-10       -26.88 \r\n",
      "Loop time of 0.00125885 on 1 procs for 16 steps with 8 atoms\r\n",
      "\r\n",
      "80.0% CPU use with 1 MPI tasks x no OpenMP threads\r\n",
      "\r\n",
      "Minimization stats:\r\n",
      "  Stopping criterion = energy tolerance\r\n",
      "  Energy initial, next-to-last, final = \r\n",
      "        -26.8355745933     -26.8799999055     -26.8799999055\r\n",
      "  Force two-norm initial, final = 7.09198 5.69527e-14\r\n",
      "  Force max component initial, final = 7.09198 5.28006e-14\r\n",
      "  Final line search alpha, max atom move = 1 5.28006e-14\r\n",
      "  Iterations, force evaluations = 16 20\r\n",
      "\r\n",
      "MPI task timing breakdown:\r\n",
      "Section |  min time  |  avg time  |  max time  |%varavg| %total\r\n",
      "---------------------------------------------------------------\r\n",
      "Pair    | 0.0007658  | 0.0007658  | 0.0007658  |   0.0 | 60.83\r\n",
      "Neigh   | 0          | 0          | 0          |   0.0 |  0.00\r\n",
      "Comm    | 0.00012136 | 0.00012136 | 0.00012136 |   0.0 |  9.64\r\n",
      "Output  | 2.0027e-05 | 2.0027e-05 | 2.0027e-05 |   0.0 |  1.59\r\n",
      "Modify  | 0          | 0          | 0          |   0.0 |  0.00\r\n",
      "Other   |            | 0.0003517  |            |       | 27.94\r\n",
      "\r\n",
      "Nlocal:    8 ave 8 max 8 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "Nghost:    606 ave 606 max 606 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "Neighs:    560 ave 560 max 560 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "\r\n",
      "Total # of neighbors = 560\r\n",
      "Ave neighs/atom = 70\r\n",
      "Neighbor list builds = 0\r\n",
      "Dangerous builds = 0\r\n",
      "Total energy (eV) = -26.8799999054703;\r\n",
      "Number of atoms = 8;\r\n",
      "Lattice constant (Angstoms) = 5.72757152037121;\r\n",
      "Cohesive energy (eV) = -3.35999998818379;\r\n",
      "All done!\r\n",
      "Total wall time: 0:00:00\r\n"
     ]
    }
   ],
   "source": [
    "!lmp_serial < calc_fcc.in"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sweet!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to view the entire file (opening `log.lammps` in Notepad), then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAMMPS (3 Mar 2020)\r\n",
      "######################################\r\n",
      "# LAMMPS INPUT SCRIPT\r\n",
      "# Find minimum energy fcc (face-centered cubic) atomic configuration\r\n",
      "# Mark Tschopp\r\n",
      "# Syntax, lmp_exe < calc_fcc.in\r\n",
      "\r\n",
      "######################################\r\n",
      "# INITIALIZATION\r\n",
      "clear\r\n",
      "units metal\r\n",
      "dimension 3\r\n",
      "boundary p p p\r\n",
      "atom_style atomic\r\n",
      "atom_modify map array\r\n",
      "\r\n",
      "######################################\r\n",
      "# ATOM DEFINITION\r\n",
      "lattice fcc 4 orient x 1 1 0 orient y -1 1 0 orient z 0 0 1\r\n",
      "Lattice spacing in x,y,z = 5.65685 5.65685 4\r\n",
      "region box block 0 1 0 1 0 1 units lattice\r\n",
      "create_box 1 box\r\n",
      "Created orthogonal box = (0 0 0) to (5.65685 5.65685 4)\r\n",
      "  1 by 1 by 1 MPI processor grid\r\n",
      "create_atoms 1 box\r\n",
      "Created 8 atoms\r\n",
      "  create_atoms CPU = 0.000447035 secs\r\n",
      "replicate 1 1 1\r\n",
      "  orthogonal box = (0 0 0) to (5.65685 5.65685 4)\r\n",
      "  1 by 1 by 1 MPI processor grid\r\n",
      "  8 atoms\r\n",
      "  replicate CPU = 0.000544786 secs\r\n",
      "\r\n",
      "######################################\r\n",
      "# DEFINE INTERATOMIC POTENTIAL\r\n",
      "pair_style eam/alloy\r\n",
      "pair_coeff * * Al99.eam.alloy Al\r\n",
      "neighbor 2.0 bin\r\n",
      "neigh_modify delay 10 check yes\r\n",
      "\r\n",
      "######################################\r\n",
      "# DEFINE COMPUTES\r\n",
      "compute eng all pe/atom\r\n",
      "compute eatoms all reduce sum c_eng\r\n",
      "\r\n",
      "#####################################################\r\n",
      "# MINIMIZATION\r\n",
      "reset_timestep 0\r\n",
      "fix 1 all box/relax iso 0.0 vmax 0.001\r\n",
      "thermo 10\r\n",
      "thermo_style custom step pe lx ly lz press c_eatoms\r\n",
      "min_style cg\r\n",
      "minimize 1e-25 1e-25 5000 10000\r\n",
      "WARNING: Using 'neigh_modify every 1 delay 0 check yes' setting during minimization (src/min.cpp:190)\r\n",
      "Neighbor list info ...\r\n",
      "  update every 1 steps, delay 0 steps, check yes\r\n",
      "  max neighbors/atom: 2000, page size: 100000\r\n",
      "  master list distance cutoff = 8.28721\r\n",
      "  ghost atom cutoff = 8.28721\r\n",
      "  binsize = 4.1436, bins = 2 2 1\r\n",
      "  1 neighbor lists, perpetual/occasional/extra = 1 0 0\r\n",
      "  (1) pair eam/alloy, perpetual\r\n",
      "      attributes: half, newton on\r\n",
      "      pair build: half/bin/atomonly/newton\r\n",
      "      stencil: half/bin/3d/newton\r\n",
      "      bin: standard\r\n",
      "Per MPI rank memory allocation (min/avg/max) = 4.474 | 4.474 | 4.474 Mbytes\r\n",
      "Step PotEng Lx Ly Lz Press c_eatoms \r\n",
      "       0   -26.835575    5.6568542    5.6568542            4     29590.11   -26.835575 \r\n",
      "      10   -26.878207    5.7134228    5.7134228         4.04    5853.9553   -26.878207 \r\n",
      "      16       -26.88    5.7275715    5.7275715    4.0500047 2.1489546e-10       -26.88 \r\n",
      "Loop time of 0.00125885 on 1 procs for 16 steps with 8 atoms\r\n",
      "\r\n",
      "80.0% CPU use with 1 MPI tasks x no OpenMP threads\r\n",
      "\r\n",
      "Minimization stats:\r\n",
      "  Stopping criterion = energy tolerance\r\n",
      "  Energy initial, next-to-last, final = \r\n",
      "        -26.8355745933     -26.8799999055     -26.8799999055\r\n",
      "  Force two-norm initial, final = 7.09198 5.69527e-14\r\n",
      "  Force max component initial, final = 7.09198 5.28006e-14\r\n",
      "  Final line search alpha, max atom move = 1 5.28006e-14\r\n",
      "  Iterations, force evaluations = 16 20\r\n",
      "\r\n",
      "MPI task timing breakdown:\r\n",
      "Section |  min time  |  avg time  |  max time  |%varavg| %total\r\n",
      "---------------------------------------------------------------\r\n",
      "Pair    | 0.0007658  | 0.0007658  | 0.0007658  |   0.0 | 60.83\r\n",
      "Neigh   | 0          | 0          | 0          |   0.0 |  0.00\r\n",
      "Comm    | 0.00012136 | 0.00012136 | 0.00012136 |   0.0 |  9.64\r\n",
      "Output  | 2.0027e-05 | 2.0027e-05 | 2.0027e-05 |   0.0 |  1.59\r\n",
      "Modify  | 0          | 0          | 0          |   0.0 |  0.00\r\n",
      "Other   |            | 0.0003517  |            |       | 27.94\r\n",
      "\r\n",
      "Nlocal:    8 ave 8 max 8 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "Nghost:    606 ave 606 max 606 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "Neighs:    560 ave 560 max 560 min\r\n",
      "Histogram: 1 0 0 0 0 0 0 0 0 0\r\n",
      "\r\n",
      "Total # of neighbors = 560\r\n",
      "Ave neighs/atom = 70\r\n",
      "Neighbor list builds = 0\r\n",
      "Dangerous builds = 0\r\n",
      "\r\n",
      "variable natoms equal \"count(all)\"\r\n",
      "variable teng equal \"c_eatoms\"\r\n",
      "variable length equal \"lx\"\r\n",
      "variable ecoh equal \"v_teng/v_natoms\"\r\n",
      "\r\n",
      "print \"Total energy (eV) = ${teng};\"\r\n",
      "Total energy (eV) = -26.8799999054703;\r\n",
      "print \"Number of atoms = ${natoms};\"\r\n",
      "Number of atoms = 8;\r\n",
      "print \"Lattice constant (Angstoms) = ${length};\"\r\n",
      "Lattice constant (Angstoms) = 5.72757152037121;\r\n",
      "print \"Cohesive energy (eV) = ${ecoh};\"\r\n",
      "Cohesive energy (eV) = -3.35999998818379;\r\n",
      "\r\n",
      "print \"All done!\"\r\n",
      "All done!\r\n",
      "Total wall time: 0:00:00\r\n"
     ]
    }
   ],
   "source": [
    "!cat log.lammps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## LAMMPS Input Script Explained\n",
    "\n",
    "In this section, we will break down what LAMMPS is doing for each step. The easy way to do this on your own is to consult the LAMMPS manual for each command or go to the Internet LAMMPS manual, *i.e.*, at https://lammps.sandia.gov\n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    # Find minimum energy fcc configuration  <br>\n",
    "# Mark Tschopp </div>\n",
    "\n",
    "The `#` denotes a comment. Hence LAMMPS does not do anything for these lines. \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "# ---------- Initialize Simulation ---------------------  <br>\n",
    "clear  <br>\n",
    "units metal  <br>\n",
    "dimension 3  <br>\n",
    "boundary p p p  <br>\n",
    "atom_style atomic  <br>\n",
    "atom_modify map array <br>\n",
    "</div>\n",
    "\n",
    "This section initializes the simulations. The `clear` command clears all memory. The `units` command specifies the units that will be used for the remainder of the simulation; `metal` uses Angstroms and eV, among other units. The `dimension 3` command specifies a 3-dimensional simulation cell will be used (2-D is also an option). The `boundary p p p` specifies periodic boundaries in the x-, y-, and z-directions. \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "# ---------- Create Atoms ---------------------  <br>\n",
    "lattice \tfcc 4 <br>\n",
    "region\tbox block 0 1 0 1 0 1 units lattice <br>\n",
    "create_box\t1 box <br> <br>\n",
    "lattice\tfcc 4 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1   <br>\n",
    "create_atoms 1 box <br>\n",
    "replicate 1 1 1 <br></div>\n",
    "\n",
    "The `lattice` command specifies what type of lattice is used (fcc, bcc, hcp, etc.) and the number following this specifies the lattice constant. The `region` command specifies the simulation cell. Here, we have used lattice units and specified that the simulation cell box is to be 1 lattice unit in each direction. The `create_box` command following this will use the parameters outlined in the `region` command to actually create the box. The `replicate` command can be used to replicate the periodic cell in each direction. \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "# ---------- Define Interatomic Potential --------------------- <br>\n",
    "pair_style eam/alloy  <br>\n",
    "pair_coeff * * Al99.eam.alloy Al <br>\n",
    "neighbor 2.0 bin  <br>\n",
    "neigh_modify delay 10 check yes  <br>\n",
    "</div>\n",
    "\n",
    "The `pair_style` command specifies what kind of interatomic potential will be used, while the `pair_coeff` specifies the file that the pair potential coefficients are stored in. The file extension for the interatomic potential file can sometimes give a clue as to which format is being used (eam.alloy = eam/alloy).\n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "# ---------- Define Settings --------------------- <br>\n",
    "compute eng all pe/atom <br>\n",
    "compute eatoms all reduce sum c_eng <br>\n",
    "</div>\n",
    "\n",
    "Here, two computes are defined. In the first `compute` command, a variable named `eng` is defined to store the potential energy for each atom. In the second `compute` command, a variable named `eatoms` is defined to store the sum of all `eng` values. This is just to show how to use computes with user-defined variables.  Notice that the `pe` energy column during minimization is equivalent to the `c_eatoms` column, as expected.\n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "# ---------- Run Minimization --------------------- <br> \n",
    "reset_timestep 0  <br>\n",
    "fix 1 all box/relax iso 0.0 vmax 0.001 <br>\n",
    "thermo 10  <br>\n",
    "thermo_style custom step pe lx ly lz press c_eatoms  <br>\n",
    "min_style cg  <br>\n",
    "minimize 1e-25 1e-25 5000 10000   <br>\n",
    "</div>\n",
    "\n",
    "The `reset_timestep` does just that. The `fix` command uses the `box/relax` setting, whereby all directions (`iso`) are relaxed to 0.0 Pa pressure for all atoms (`all`). The `thermo` specifies the output during minimization. The `thermo_style` specifies what type of output is shown to screen. Here I have used a `custom` list of metrics, including the time`step`, the potential energy (`pe`), the length of the box in x, y, and z (`lx`, `ly`, `lz`, respectively), the `press`ure, and the computed variable `eatoms`. The `min_style` specifies that conjugate gradient will be used for minimization and the `minimize` starts the minimization, *i.e.*, the simulation cell boundaries are relaxed from the specified lattice constant (4 Angstroms) to the actual lattice constant (4.05 Angstroms). \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "variable natoms equal \"count(all)\" <br>\n",
    "variable teng equal \"c_eatoms\" <br>\n",
    "variable length equal \"lx\" <br>\n",
    "variable ecoh equal \"v_teng/v_natoms\" \n",
    "</div>\n",
    "\n",
    "This section defines some variables, such as `natoms` for the number of atoms, `teng` for the total potential energy, `length` for the length of the simulation cell, and `ecoh` for the cohesive energy of Al.\n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "print \"Total energy (eV) = \\${teng};\" <br>\n",
    "print \"Number of atoms = \\${natoms};\" <br>\n",
    "print \"Lattice constant (Angstoms) = \\${length};\" <br>\n",
    "print \"Cohesive energy (eV) = \\${ecoh};\" <br>\n",
    "print \"All done!\"\n",
    "</div>\n",
    "\n",
    "This section prints these values to screen and to the logfile. The `${}` is used to insert the variables defined earlier. "
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    "***\n",
    "## FAQs \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-danger\">\n",
    "<strong>Question 1</strong>: But I wanted a simulation cell with <110> directions.  How would I change this?\n",
    "</div>\n",
    "\n",
    "Aha!  Yes, it is relatively easy to start changing the directions in the x, y, and z directions.  For instance, if you change this line: <br>\n",
    "`lattice fcc 4 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1`\n",
    "\n",
    "to this one: <br>\n",
    "`lattice fcc 4 orient x 1 1 0 orient y -1 1 0 orient z 0 0 1`\n",
    "\n",
    "then you get a simulation cell that is oriented in the $<110>$ directions in the x- and y- directions.  If you mess up on the math, i.e., try 110 and 110 for the x and y directions (without the '-1'), then LAMMPS will return: <br>\n",
    "`ERROR: Lattice orient vectors are not orthogonal`\n",
    "\n",
    "So, if you try the $<110>$-oriented single crystal cell, LAMMPS automatically scales the x- and y-direction periodic lengths to 5.6568542 Angstroms (i.e., $4\\sqrt{2}$).  After minimization, the cohesive energy per atom is `-3.35999998818379` ev, th\n",
    "    \n",
    "<br>\n",
    "<div class=\"alert alert-danger\">\n",
    "<strong>Question 2</strong>: I typed in the above line and nothing happened.\n",
    "</div>\n",
    "\n",
    "Make sure that you are in the same directory as the LAMMPS executable. Make sure that you are typing in the correct filename. \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-danger\">\n",
    "<strong>Question 3</strong>: I keep getting an error with the potential, i.e., potential file not found.\n",
    "</div>\n",
    "\n",
    "First, check that the potential file is in the directory that you are running out of. Although, you can insert paths, if you want to store the potentials in another directory. Second, make sure that the potential file name is the same as that given in the input script. For instance, Windows has the habit of saving text files (like the potential files) with .txt extensions. If you happen to be running from a Windows operating system, I would change the settings so that you can see the extensions of the files as well. "
   ]
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    "***\n",
    "## Tutorial Links\n",
    "\n",
    "[Click here to open the next tutorial](LAMMPS-Tutorials-02.ipynb)"
   ]
  }
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