ElectronDiffraction.ipynb

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   "source": [
    "# Electron diffraction simulation computation tutorial\n",
    "\n",
    "_This is a step-by-step tutorial walking you through the numeric simulation, requiring minimal domain knowledge._\n",
    "\n",
    "\n",
    "### Electron wavelength\n",
    "\n",
    "Accelerated by a votage of $E_0$, the electron wavelength in vacuum is given by\n",
    "$$\n",
    "\\lambda_0 = \\frac{12.3984244}{\\sqrt{E_0 (E_0+1021.99812)}}\n",
    "$$\n",
    "\n",
    "That is to say, if the acceleration voltage is $120$ KeV, then the wave length is about $0.03349$ Å ($1.0 \\times 10^{-10}$ m).\n",
    "\n",
    "The electrons traveling through the specimen have a bit higher energy, but we ignore their impact in our calculation."
   ]
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     "name": "stdout",
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     "text": [
      "With an acceleration voltage of 120 KeV, the coresponding electron wave length is 0.03349216180963567 ångström.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "E_0 = 120 # in keV\n",
    "lambda_0 = 12.3984244/math.sqrt(E_0*(E_0+1021.99812)) # in Å\n",
    "print( f'With an acceleration voltage of {E_0} KeV, the coresponding electron wave length is {lambda_0} ångström.' )"
   ]
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    "### Select reflections\n",
    "\n",
    "We simulate the diffraction patterns of SrTiO3, thickness 40 nm, maximum tilt angle 40 mrad and orientation $(0, 0, 1)$, with an acceleration voltage of 120 KeV. The indexed diffraction discs (121 reflections) are demonstrated below\n",
    "\n",
    "----\n",
    "\n",
    "![srtio3](./images/SrTiO3_40_40.png)\n",
    "\n",
    "----\n"
   ]
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    "\n",
    "\n",
    "\n",
    "The diffraction image above shows 121 diffraction discs, most of which are weak and only 21 of them are visually strong.\n",
    "For ease of demonstration, we simulate the diffraction pattern only with 5 discs coresponding to reflections  $(\\bar{1}, 1, 0)$, $(1, 1, 0)$, $(0, 0, 0)$, $(\\bar{1}, \\bar{1}, 0)$ and $(1, \\bar{1}, 0)$. But it is easy to expand to arbitrary beam numbers.\n",
    "\n",
    "### Structure matrix\n",
    "\n",
    "We first constuct the structure factor matrix $\\mathcal{A}$. "
   ]
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   "source": [
    "We put the corresponding structure factors in the central column of the structure factor matrix $\\mathcal{A}$, as we only select 5 reflections, this matrix is a $5 \\times 5$ squared complex matrix:\n",
    "    \n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, 1, 0)} & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(1, 1, 0)} & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & ? & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & ? \\\\\n",
    "\\end{bmatrix}$$    \n",
    "    \n",
    "Please note that the mean inner potential $U_{(0, 0, 0)}$ is ommitted, as it serves as a pure phase factor to all reflections. \n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
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   "source": [
    "We continue to construct the structure factor matrix $\\mathcal{A}$, we set the rest diagonal elements to be $2\\,k_t \\, s_{(\\bar{1}, 1, 0)}$, $2\\,k_t \\, s_{(1, 1, 0)}$, $2\\,k_t \\, s_{(\\bar{1}, \\bar{1}, 0)}$ and $2\\,k_t \\, s_{(1, \\bar{1}, 0)}$. And we will discuss how to calculate these values later.\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & ? & \\mathbf{u}_{(\\bar{1}, 1, 0)} & ? & ? \\\\\n",
    " ? & 2\\,k_t \\, s_{(1, 1, 0)} & \\mathbf{u}_{(1, 1, 0)} & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$    \n",
    "    \n",
    "Please note, the subscriptions of $s$ are identical to the reflections in the central column.\n",
    "\n",
    " \n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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   "source": [
    "We determine $\\mathcal{A}[0][1]$ to be $\\mathbf{u}_{(\\bar{2}, 0, 0)}$, as $(\\bar{1}, 1, 0) - (1, 1, 0) = (\\bar{2}, 0, 0)$\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\underline{\\mathbf{u}_{(\\bar{2}, 0, 0)}} & \\boxed{ \\mathbf{u}_{(\\bar{1}, 1, 0)} } & ? & ? \\\\\n",
    " ? & 2\\,k_t \\, s_{(1, 1, 0)} & \\boxed{ \\mathbf{u}_{(1, 1, 0)} } & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n",
    "\n",
    "Please note the boxed positions where the reflections are selected to calcuate.\n",
    "\n",
    "\n"
   ]
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   "cell_type": "markdown",
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   "source": [
    "We determine $\\mathcal{A}[0][3]$ to be $\\mathbf{u}_{(0, \\bar{2}, 0)}$, as $(\\bar{1}, 1, 0) - (\\bar{1}, \\bar{1}, 0) = (0, \\bar{2},  0)$\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\boxed{ \\mathbf{u}_{(\\bar{1}, 1, 0)} } & \\underline{\\mathbf{u}_{(0, \\bar{2}, 0)}} & ? \\\\\n",
    " ? & 2\\,k_t \\, s_{(1, 1, 0)} & \\mathbf{u}_{(1, 1, 0)} & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\boxed{ \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} } & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n"
   ]
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   "source": [
    "We determine $\\mathcal{A}[0][4]$ to be $\\mathbf{u}_{(\\bar{2}, 2, 0)}$, as $(\\bar{1}, 1, 0) - (1, \\bar{1}, 0) = (\\bar{2}, 2, 0)$\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\boxed{ \\mathbf{u}_{(\\bar{1}, 1, 0)} } & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\underline{\\mathbf{u}_{(\\bar{2}, 2, 0)}} \\\\\n",
    " ? & 2\\,k_t \\, s_{(1, 1, 0)} & \\mathbf{u}_{(1, 1, 0)} & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)}  & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\boxed{ \\mathbf{u}_{(1, \\bar{1}, 0)} } & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We determine $\\mathcal{A}[1][0]$ to be $\\mathbf{u}_{(2, 0, 0)}$, as $(1, 1, 0) - (\\bar{1}, 1, 0) = ( 2, 0, 0)$\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\boxed{ \\mathbf{u}_{(\\bar{1}, 1, 0)} } & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, 2, 0)} \\\\\n",
    " \\underline{\\mathbf{u}_{(2, 0, 0)}} & 2\\,k_t \\, s_{(1, 1, 0)} & \\boxed{ \\mathbf{u}_{(1, 1, 0)} } & ? & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)}  & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n"
   ]
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   "source": [
    "We determine $\\mathcal{A}[1][3]$ to be $\\mathbf{u}_{(2, 2, 0)}$, as $(1, 1, 0) - (\\bar{1}, \\bar{1}, 0) = ( 2, 2, 0)$\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\mathbf{u}_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, 2, 0)} \\\\\n",
    "\\mathbf{u}_{(2, 0, 0)} & 2\\,k_t \\, s_{(1, 1, 0)} & \\boxed{ \\mathbf{u}_{(1, 1, 0)} } & \\underline{ \\mathbf{u}_{(\\bar{2}, \\bar{2}, 0)}} & ? \\\\\n",
    " ? & ? & 0 & ? & ? \\\\\n",
    " ? & ? & \\boxed{ \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} } & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & ? \\\\\n",
    "  ? & ? & \\mathbf{u}_{(1, \\bar{1}, 0)} & ? & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n"
   ]
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   "source": [
    "We finally determine all elements in the structure matrix $\\mathcal{A}$:\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\mathbf{u}_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, 2, 0)} \\\\\n",
    "\\mathbf{u}_{(2, 0, 0)} & 2\\,k_t \\, s_{(1, 1, 0)} & \\mathbf{u}_{(1, 1, 0) } & \\mathbf{u}_{(\\bar{2}, \\bar{2}, 0)} & \\mathbf{u}_{(0, 2, 0)} \\\\\n",
    " \\mathbf{u}_{(1, \\bar{1}, 0)} & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 0 & \\mathbf{u}_{(1, 1, 0)} & \\mathbf{u}_{(\\bar{1}, 1, 0)} \\\\\n",
    " \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} \\\\\n",
    " \\mathbf{u}_{(2, \\bar{2}, 0)} & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(1, \\bar{1}, 0)} & \\mathbf{u}_{(2, 0, 0)} & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix}$$  \n"
   ]
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   "source": [
    "### Structure factors\n",
    "\n",
    "We character SrTiO$_3$ crystal as follows:\n",
    "\n",
    "1. FCC structure, dimension 3.905 Å$^3$, vertex $(0, 0, 0)$, $(3.905, 0, 0)$ $(0, 3.905, 0)$ $(0, 0, 3.905)$\n",
    "2. Atoms\n",
    "    + Sr\n",
    "        - Z number: 38\n",
    "        - Pf (pengfactor): (1): 1.0127 (2): 2.9403 (3): 3.992 (4): 5.1441 (5): 0.4721 (6): 4.9802 (7): 26.8565 (8): 116.031\n",
    "        - position: $(0, 0, 0)$\n",
    "        - Debye-Waller factor: 0.410576\n",
    "    + Ti\n",
    "        - Z number: 22\n",
    "        - Pf: (1): 0.5398 (2): 2.1568 (3): 2.9961 (4): 3.0751 (5): 0.4281 (6): 4.2236 (7): 24.1928 (8): 90.6685 \n",
    "        - position: $(0.5, 0.5, 0.5)$\n",
    "        - Debye-Waller factor: 0.315827\n",
    "    + O\n",
    "        - Z number: 16\n",
    "        - Pf: (1): 0.1433 (2): 0.5103 (3): 0.937 (4): 0.3923 (5): 0.3055 (6): 2.2683 (7): 8.2625 (8): 25.6645\n",
    "        - positions: $(0, 0.5, 0.5)$, $(0.5, 0, 0.5)$, $(0.5, 0.5, 0)$\n",
    "        - Debye-Waller factor: 0\n",
    "\n",
    "It should be noticed that the scattering factor Pf are taken from _L.M. Peng, Micron 30 (1999) 625-648_.\n",
    "\n",
    "\n"
   ]
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   "source": [
    "Now lets calculate the structure factor $\\mathbf{u}_(0, 1, 0)$ on condition of a high tension 120 KeV.\n",
    "\n",
    "We calculate the contribution of the Oxygen atom at position $(0.5, 0.5, 0)$ as follows"
   ]
  },
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   "id": "1d039992-e9ae-4550-b237-db255469b49f",
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   "source": [
    "We calculate the coordinate in the reciprocal space\n",
    "$$\n",
    "\\mathbf{g}_{(0, 1, 0)} =\n",
    "\\begin{bmatrix}\n",
    "g_x \\\\\n",
    "g_y \\\\\n",
    "g_z \\\\\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "3.905, 0, 0 \\\\\n",
    "0, 3.905, 0 \\\\\n",
    "0, 0, 3.905 \\\\\n",
    "\\end{bmatrix}^{-1} \\cdot \n",
    "\\begin{bmatrix}\n",
    "0 \\\\\n",
    "1 \\\\\n",
    "0 \\\\\n",
    "\\end{bmatrix}\n",
    "= \n",
    "\\begin{bmatrix}\n",
    "0 \\\\\n",
    "0.256082 \\\\\n",
    "0 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc728ea9-7afa-449f-8e8c-5df44bfcfd15",
   "metadata": {},
   "source": [
    "We calculate the scattering factor of this Oxygen atom in the first Born approximation\n",
    "\n",
    "$$\n",
    "sf = Pf_{O, 1} \\, e^{-Pf_{O, 5}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{O, 2} \\, e^{-Pf_{O, 6}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{O, 3} \\, e^{-Pf_{O, 7}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} +  \\\\\n",
    "Pf_{O, 4} \\, e^{-Pf_{O, 8}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4}\n",
    "$$\n",
    "\n",
    "in which $Pf$ is taken from _L.M. Peng, Micron 30 (1999) 625-648_.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cb6937ac-988e-4fb5-9223-6e24d709edf1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The scattering factor for the Oxygen is 1.7101159496240943\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "sf_o = 0.0\n",
    "Pf_o = [0.0, 0.1433, 0.5103, 0.937, 0.3923, 0.3055, 2.2683, 8.2625, 25.6645]\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "for i in range(1, 5):\n",
    "    sf_o += Pf_o[i] * math.exp( -Pf_o[i+4] * s2 )\n",
    "print( f'The scattering factor for the Oxygen is {sf_o}' )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c05756df-fe31-4ace-a55b-21cc4862053d",
   "metadata": {},
   "source": [
    "We therefor obtain the contribution from this Oxygen atom \n",
    "\n",
    "$$\n",
    "U_{(0, 1, 0)}( O_{(0.5, 0.5, 0)} ) = sf_o  e^{-\\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} \\,dw_o}  e^{i \\, 2 \\pi  \\,  (0.5, 0.5, 0) \\cdot (0, 1, 0) } \n",
    "$$\n",
    "\n",
    "in whci $dw_o$ is the Debye-Waller factor for Oxygen\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fe2d638b-5c4e-4616-821f-9bf91e6fb1c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The contribution from the first Oxygen atom is (-1.7101159496240943-1.1941675850741058e-14j)\n"
     ]
    }
   ],
   "source": [
    "import cmath\n",
    "\n",
    "dw_o = 0\n",
    "_theta = 2.0 * 3.1415926535898 * ( 0.5 * 0 + 0.5 * 1 + 0 * 0 )\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "u_o1 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta), math.sin(_theta) )\n",
    "print( f'The contribution from the first Oxygen atom is {u_o1}' )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8717c98-f926-45d6-8a60-4c2dad1f23ce",
   "metadata": {},
   "source": [
    "We calculate the contribution for the second Oxygen atom, whose position is (0.5, 0, 0.5):\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "U_{(0, 1, 0)}( O_{(0.5, 0, 0.5)} ) = sf_o  e^{-\\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} \\,dw_o}  e^{i \\, 2 \\pi  \\,  (0.5,0,  0.5) \\cdot (0, 1, 0) } \n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "41bd7192-94ed-48b7-adc0-a11e75ac0310",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The contribution from the second Oxygen atom is (1.7101159496240943+0j)\n"
     ]
    }
   ],
   "source": [
    "dw_o = 0\n",
    "_theta = 2.0 * 3.1415926535898 * ( 0.5 * 0 + 0 * 1 + 0.5 * 0 )\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "u_o2 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta), math.sin(_theta) )\n",
    "print( f'The contribution from the second Oxygen atom is {u_o2}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "753cab03-cbf8-4034-8e72-8e7ee109e8cf",
   "metadata": {},
   "source": [
    "We calculate the contribution for the third Oxygen atom, whose position is (0, 0.5 0.5):\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "U_{(0, 1, 0)}( O_{(0, 0.5, 0.5)} ) = sf_o  e^{-\\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} \\,dw_o}  e^{i \\, 2 \\pi  \\,  (0, 0.5,  0.5) \\cdot (0, 1, 0) } \n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b341fe2-4b79-4cbe-9562-4f0f076f1f92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The contribution from the third Oxygen atom is (-1.7101159496240943-1.1941675850741058e-14j)\n"
     ]
    }
   ],
   "source": [
    "dw_o = 0\n",
    "_theta = 2.0 * 3.1415926535898 * ( 0 * 0 + 0.5 * 1 + 0.5 * 0 )\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "u_o3 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta), math.sin(_theta) )\n",
    "print( f'The contribution from the third Oxygen atom is {u_o3}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cc8d6a8-a4e2-407f-af97-bc8e158ff963",
   "metadata": {},
   "source": [
    "We calculate the scattering factor of this Titanium atom in the first Born approximation\n",
    "\n",
    "$$\n",
    "sf = Pf_{Ti, 1} \\, e^{-Pf_{Ti, 5}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{Ti, 2} \\, e^{-Pf_{Ti, 6}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{Ti, 3} \\, e^{-Pf_{Ti, 7}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} +  \\\\\n",
    "Pf_{Ti, 4} \\, e^{-Pf_{Ti, 8}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c37cb62-0d90-4c94-a95b-2bc8c20ba1b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The scattering factor for the Titanium is 5.2591588390086565\n"
     ]
    }
   ],
   "source": [
    "sf_ti = 0.0\n",
    "Pf_ti = [ 0, 0.5398, 2.1568, 2.9961, 3.0751, 0.4281, 4.2236, 24.1928, 90.6685 ]\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "for i in range(1, 5):\n",
    "    sf_ti += Pf_ti[i] * math.exp( -Pf_ti[i+4] * s2 )\n",
    "print( f'The scattering factor for the Titanium is {sf_ti}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7d1e9eb-47ab-4769-a00f-dfc29f835214",
   "metadata": {},
   "source": [
    "We calculate the contribution for the Titanium atom, whose position is (0.5, 0.5 0.5):\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "U_{(0, 1, 0)}( Ti_{(0.5, 0.5, 0.5)} ) = sf_ti  e^{-\\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} \\,dw_{ti}}  e^{i \\, 2 \\pi  \\,  (0, 0.5,  0.5) \\cdot (0, 1, 0) } \n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a09e47bd-1a9b-45d8-bd83-27821fd4c1a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The contribution from the Titanium atom is (-5.231998211960813-3.653484824384364e-14j)\n"
     ]
    }
   ],
   "source": [
    "dw_ti = 0.315827\n",
    "_theta = 2.0 * 3.1415926535898 * ( 0.5 * 0 + 0.5 * 1 + 0.5 * 0 )\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "u_ti = sf_ti * math.exp(-s2*dw_ti) * complex( math.cos(_theta), math.sin(_theta) )\n",
    "print( f'The contribution from the Titanium atom is {u_ti}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7348d66f-0b72-4435-9653-c0fbbcfbea55",
   "metadata": {},
   "source": [
    "We calculate the scattering factor of this Strontium atom in the first Born approximation\n",
    "\n",
    "$$\n",
    "sf = Pf_{Sr, 1} \\, e^{-Pf_{Sr, 5}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{Sr, 2} \\, e^{-Pf_{Sr, 6}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} + \\\\\n",
    "Pf_{Sr, 3} \\, e^{-Pf_{Sr, 7}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} +  \\\\\n",
    "Pf_{Sr, 4} \\, e^{-Pf_{Sr, 8}}\\, \\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "27cd5d40-3974-45e9-b9f2-f75a0fad99a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The scattering factor for the Strontium is 7.0525387022144885\n"
     ]
    }
   ],
   "source": [
    "sf_sr = 0.0\n",
    "Pf_sr = [ 0,  1.0127, 2.9403, 3.992, 5.1441, 0.4721, 4.9802, 26.8565, 116.031 ]\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "for i in range(1, 5):\n",
    "    sf_sr += Pf_sr[i] * math.exp( -Pf_sr[i+4] * s2 )\n",
    "print( f'The scattering factor for the Strontium is {sf_sr}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc03cab4-95a0-45ec-9c69-3fea6c2adcf8",
   "metadata": {},
   "source": [
    "We calculate the contribution for the Strontium atom, whose position is (0, 0, 0):\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "U_{(0, 1, 0)}( Sr_{(0, 0, 0)} ) = sf_ti  e^{-\\frac{\\mathbf{g}_{(0, 1, 0)}^T \\cdot \\mathbf{g}_{(0, 1, 0)}}{4} \\,dw_{ti}}  e^{i \\, 2 \\pi  \\,  (0, 0,  0) \\cdot (0, 1, 0) } \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8cb5faf0-94f8-42dc-9979-332dd2382f76",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The contribution from the Strontium atom is (7.005226156852824+0j)\n"
     ]
    }
   ],
   "source": [
    "dw_sr = 0.410576\n",
    "_theta = 2.0 * 3.1415926535898 * ( 0 * 0 + 0 * 1 + 0 * 0 )\n",
    "s2 = 0.25 * (0*0 + 0.256082*0.256082 + 0*0)\n",
    "u_sr = sf_sr * math.exp(-s2*dw_sr) * complex( math.cos(_theta), math.sin(_theta) )\n",
    "print( f'The contribution from the Strontium atom is {u_sr}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0b0a9f3-30da-45d7-81c8-485a9c6bffac",
   "metadata": {},
   "source": [
    "Summing up all contributions, we get the structure factor $\\mathbf{u}_{(0, 1, 0)}$ with a factor\n",
    "\n",
    "$$\n",
    "\\mathbf{u}_{(0, 1, 0)} = ( \\mathbf{u}_{O1} + \\mathbf{u}_{O1} + \\mathbf{u}_{O1} + \\mathbf{u}_{Ti} + \\mathbf{u}_{Sr} ) \\frac{511+V}{511 \\, \\Omega \\, \\pi}\n",
    "$$\n",
    "\n",
    "in which $V$ is high tension in KeV, and $\\Omega$ is the volume of the unit cell.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "34b22509-14ab-41bd-969d-f8d6cd4a650a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The structure factor for reflection (0, 1, 0) is (0.00041658860144866427-3.988074423954121e-16j)\n"
     ]
    }
   ],
   "source": [
    "u_0_1_0 = (u_o1+u_o2+u_o3+u_ti+u_sr) * (511.0+120.0)/(511.0*3.14159265*3.905*3.905*3.905)\n",
    "print( f'The structure factor for reflection (0, 1, 0) is {u_0_1_0}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a5d62ec-e4e4-4573-87ae-39be256844a6",
   "metadata": {},
   "source": [
    "In a same way, we calculate the structure factor coresponding to reflection $(0, 2, 0)$.\n",
    "We calculate the coordinate in the reciprocal space\n",
    "$$\n",
    "\\mathbf{g}_{(0, 2, 0)} =\n",
    "\\begin{bmatrix}\n",
    "g_x \\\\\n",
    "g_y \\\\\n",
    "g_z \\\\\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "3.905, 0, 0 \\\\\n",
    "0, 3.905, 0 \\\\\n",
    "0, 0, 3.905 \\\\\n",
    "\\end{bmatrix}^{-1} \\cdot \n",
    "\\begin{bmatrix}\n",
    "0 \\\\\n",
    "2 \\\\\n",
    "0 \\\\\n",
    "\\end{bmatrix}\n",
    "= \n",
    "\\begin{bmatrix}\n",
    "0 \\\\\n",
    "0.512164 \\\\\n",
    "0 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "866f8b74-dd39-4201-b7d0-6ec295f561b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The scattering factor for the Oxygen is 1.1981522073765374\n",
      "get s2: 0.06557796318125257\n",
      "The contribution from the first Oxygen atom is (1.1981522073765374+1.6733304292595553e-14j)\n",
      "The contribution from the second Oxygen atom is (1.1981522073765374+0j)\n",
      "The contribution from the third Oxygen atom is (1.1981522073765374+1.6733304292595553e-14j)\n",
      "The scattering factor for the Titanium is 2.781030400418762\n",
      "The contribution from the Titanium atom is (2.724024044847086+3.804351647657437e-14j)\n",
      "The scattering factor for the Strontium is 3.7914311616948275\n",
      "The contribution from the Strontium atom is (3.690709903154659+0j)\n",
      "The structure factor for reflection [0, 2, 0] is (0.06606849749470538+4.720228359511909e-16j)\n"
     ]
    }
   ],
   "source": [
    "g = [0, 2, 0]\n",
    "\n",
    "\n",
    "xyz = [ g[0]/3.905+g[1]*0+g[2]*0, g[0]*0+g[1]/3.905+g[2]*0, g[0]*0+g[1]*0+g[2]/3.905 ]\n",
    "s2 = 0.25 * (xyz[0]*xyz[0]+xyz[1]*xyz[1]+xyz[2]*xyz[2])\n",
    "\n",
    "sf_o = 0.0\n",
    "Pf_o = [0.0, 0.1433, 0.5103, 0.937, 0.3923, 0.3055, 2.2683, 8.2625, 25.6645]\n",
    "for i in range(1, 5):\n",
    "    sf_o += Pf_o[i] * math.exp( -Pf_o[i+4] * s2 )\n",
    "print( f'The scattering factor for the Oxygen is {sf_o}' )\n",
    "\n",
    "dw_o\n",
    "_theta_o1 = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0.5 * g[1] + 0 * g[2] )\n",
    "print( f'get s2: {s2}' )\n",
    "u_o1 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o1), math.sin(_theta_o1) )\n",
    "print( f'The contribution from the first Oxygen atom is {u_o1}' )\n",
    "\n",
    "_theta_o2 = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0 * g[1] + 0.5 * g[2] )\n",
    "u_o2 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o2), math.sin(_theta_o2) )\n",
    "print( f'The contribution from the second Oxygen atom is {u_o2}' )\n",
    "\n",
    "_theta_o3 = 2.0 * 3.1415926535898 * ( 0 * g[0] + 0.5 * g[1] + 0.5 * g[2] )\n",
    "u_o3 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o3), math.sin(_theta_o3) )\n",
    "print( f'The contribution from the third Oxygen atom is {u_o3}' )\n",
    "\n",
    "\n",
    "sf_ti = 0.0\n",
    "Pf_ti = [ 0, 0.5398, 2.1568, 2.9961, 3.0751, 0.4281, 4.2236, 24.1928, 90.6685 ]\n",
    "for i in range(1, 5):\n",
    "    sf_ti += Pf_ti[i] * math.exp( -Pf_ti[i+4] * s2 )\n",
    "print( f'The scattering factor for the Titanium is {sf_ti}' )\n",
    "\n",
    "dw_ti = 0.315827\n",
    "_theta_ti = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0.5 * g[1] + 0.5 * g[2] )\n",
    "u_ti = sf_ti * math.exp(-s2*dw_ti) * complex( math.cos(_theta_ti), math.sin(_theta_ti) )\n",
    "print( f'The contribution from the Titanium atom is {u_ti}' )\n",
    "\n",
    "sf_sr = 0.0\n",
    "Pf_sr = [ 0,  1.0127, 2.9403, 3.992, 5.1441, 0.4721, 4.9802, 26.8565, 116.031 ]\n",
    "for i in range(1, 5):\n",
    "    sf_sr += Pf_sr[i] * math.exp( -Pf_sr[i+4] * s2 )\n",
    "print( f'The scattering factor for the Strontium is {sf_sr}' )\n",
    "\n",
    "dw_sr = 0.410576\n",
    "_theta_sr = 2.0 * 3.1415926535898 * ( 0 * g[0] + 0 * g[1] + 0 * g[2] )\n",
    "u_sr = sf_sr * math.exp(-s2*dw_sr) * complex( math.cos(_theta_sr), math.sin(_theta_sr) )\n",
    "print( f'The contribution from the Strontium atom is {u_sr}' )\n",
    "      \n",
    "      \n",
    "ans = (u_o1+u_o2+u_o3+u_ti+u_sr) * (511.0+120.0)/(511.0*3.14159265*3.905*3.905*3.905)\n",
    "print( f'The structure factor for reflection {g} is {ans}' )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b626972b-9c12-41b3-984d-fc9950fc6597",
   "metadata": {},
   "source": [
    "Rewriting the subroutine above as a function that takes $\\mathbf{g}$ as input, we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "47ad6da7-545f-4d44-ba16-2fcbcbe20d2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_ug( g ):\n",
    "    xyz = [ g[0]/3.905+g[1]*0+g[2]*0, g[0]*0+g[1]/3.905+g[2]*0, g[0]*0+g[1]*0+g[2]/3.905 ]\n",
    "    s2 = 0.25 * (xyz[0]*xyz[0]+xyz[1]*xyz[1]+xyz[2]*xyz[2])\n",
    "\n",
    "    sf_o = 0.0\n",
    "    Pf_o = [0.0, 0.1433, 0.5103, 0.937, 0.3923, 0.3055, 2.2683, 8.2625, 25.6645]\n",
    "    for i in range(1, 5):\n",
    "        sf_o += Pf_o[i] * math.exp( -Pf_o[i+4] * s2 )\n",
    "    #print( f'The scattering factor for the Oxygen is {sf_o}' )\n",
    "\n",
    "    dw_o\n",
    "    _theta_o1 = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0.5 * g[1] + 0 * g[2] )\n",
    "    #print( f'get s2: {s2}' )\n",
    "    u_o1 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o1), math.sin(_theta_o1) )\n",
    "    #print( f'The contribution from the first Oxygen atom is {u_o1}' )\n",
    "\n",
    "    _theta_o2 = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0 * g[1] + 0.5 * g[2] )\n",
    "    u_o2 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o2), math.sin(_theta_o2) )\n",
    "    #print( f'The contribution from the second Oxygen atom is {u_o2}' )\n",
    "\n",
    "    _theta_o3 = 2.0 * 3.1415926535898 * ( 0 * g[0] + 0.5 * g[1] + 0.5 * g[2] )\n",
    "    u_o3 = sf_o * math.exp(-s2*dw_o) * complex( math.cos(_theta_o3), math.sin(_theta_o3) )\n",
    "    #print( f'The contribution from the third Oxygen atom is {u_o3}' )\n",
    "\n",
    "\n",
    "    sf_ti = 0.0\n",
    "    Pf_ti = [ 0, 0.5398, 2.1568, 2.9961, 3.0751, 0.4281, 4.2236, 24.1928, 90.6685 ]\n",
    "    for i in range(1, 5):\n",
    "        sf_ti += Pf_ti[i] * math.exp( -Pf_ti[i+4] * s2 )\n",
    "    #print( f'The scattering factor for the Titanium is {sf_ti}' )\n",
    "\n",
    "    dw_ti = 0.315827\n",
    "    _theta_ti = 2.0 * 3.1415926535898 * ( 0.5 * g[0] + 0.5 * g[1] + 0.5 * g[2] )\n",
    "    u_ti = sf_ti * math.exp(-s2*dw_ti) * complex( math.cos(_theta_ti), math.sin(_theta_ti) )\n",
    "    #print( f'The contribution from the Titanium atom is {u_ti}' )\n",
    "\n",
    "    sf_sr = 0.0\n",
    "    Pf_sr = [ 0,  1.0127, 2.9403, 3.992, 5.1441, 0.4721, 4.9802, 26.8565, 116.031 ]\n",
    "    for i in range(1, 5):\n",
    "        sf_sr += Pf_sr[i] * math.exp( -Pf_sr[i+4] * s2 )\n",
    "    #print( f'The scattering factor for the Strontium is {sf_sr}' )\n",
    "\n",
    "    dw_sr = 0.410576\n",
    "    _theta_sr = 2.0 * 3.1415926535898 * ( 0 * g[0] + 0 * g[1] + 0 * g[2] )\n",
    "    u_sr = sf_sr * math.exp(-s2*dw_sr) * complex( math.cos(_theta_sr), math.sin(_theta_sr) )\n",
    "    #print( f'The contribution from the Strontium atom is {u_sr}' )\n",
    "\n",
    "\n",
    "    ans = (u_o1+u_o2+u_o3+u_ti+u_sr) * (511.0+120.0)/(511.0*3.14159265*3.905*3.905*3.905)\n",
    "    #print( f'The structure factor for reflection {g} is {ans}' )\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba631b5d-443d-4c93-90bb-647cc162739b",
   "metadata": {},
   "source": [
    "And we are able to work out all the structure factors in the structure matrix $\\mathcal{A}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b3f66646-4dbe-4776-bbb4-1480a259f1d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u_(-2, -2, 0) = (0.04491475729167272-6.441319249171e-16j)\n",
      "u_(-2, -1, 0) = (-0.0014912349996597481+4.31843585050379e-16j)\n",
      "u_(-2, 0, 0) = (0.06606849749470538-4.720228359511909e-16j)\n",
      "u_(-2, 1, 0) = (-0.0014912349996597481+1.0300970716402575e-17j)\n",
      "u_(-2, 2, 0) = (0.04491475729167272+0j)\n",
      "u_(-1, -2, 0) = (-0.0014912349996597481+4.31843585050379e-16j)\n",
      "u_(-1, -1, 0) = (0.05001082596051881-3.579009236898845e-16j)\n",
      "u_(-1, 0, 0) = (0.00041659031445320305+3.988074902030808e-16j)\n",
      "u_(-1, 1, 0) = (0.05001082596051881+0j)\n",
      "u_(-1, 2, 0) = (-0.0014912349996597481-1.0300970716402575e-17j)\n",
      "u_(0, -2, 0) = (0.06606849749470538-4.720228359511909e-16j)\n",
      "u_(0, -1, 0) = (0.00041659031445320305+3.988074902030808e-16j)\n",
      "u_(0, 0, 0) = (0.1835387388287753+0j)\n",
      "u_(0, 1, 0) = (0.00041659031445320305-3.988074902030808e-16j)\n",
      "u_(0, 2, 0) = (0.06606849749470538+4.720228359511909e-16j)\n",
      "u_(1, -2, 0) = (-0.0014912349996597481+1.0300970716402575e-17j)\n",
      "u_(1, -1, 0) = (0.05001082596051881+0j)\n",
      "u_(1, 0, 0) = (0.00041659031445320305-3.988074902030808e-16j)\n",
      "u_(1, 1, 0) = (0.05001082596051881+3.579009236898845e-16j)\n",
      "u_(1, 2, 0) = (-0.0014912349996597481-4.31843585050379e-16j)\n",
      "u_(2, -2, 0) = (0.04491475729167272+0j)\n",
      "u_(2, -1, 0) = (-0.0014912349996597481-1.0300970716402575e-17j)\n",
      "u_(2, 0, 0) = (0.06606849749470538+4.720228359511909e-16j)\n",
      "u_(2, 1, 0) = (-0.0014912349996597481-4.31843585050379e-16j)\n",
      "u_(2, 2, 0) = (0.04491475729167272+6.441319249171e-16j)\n"
     ]
    }
   ],
   "source": [
    "for h in [-2, -1, 0, 1, 2]:\n",
    "    for k in [-2, -1, 0, 1, 2]:\n",
    "        u = (h, k, 0)\n",
    "        ug = calculate_ug( u )\n",
    "        print( f'u_{u} = {ug}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbd87b80-49a7-4741-8de4-865c1e9883f5",
   "metadata": {},
   "source": [
    "### Excitation errors\n",
    "\n",
    "We calculate the diagonal elements in the structure matrix $\\mathcal{A}$. $2\\,k_t \\, s_{(1, 1, 0)}$ can be approximated to\n",
    "\n",
    "$$\n",
    "2\\,k_t \\, s_{(1, 1, 0)} = - 1*1 - 1*1 - 2.0*1*\\frac{\\sin(\\theta_x * 0.001)}{\\lambda} - 2.0*1*\\frac{\\sin(\\theta_y * 0.001)}{\\lambda}\n",
    "$$\n",
    "\n",
    "in which $\\theta_x$ and $\\theta_y$ are incident beam tilt angles in x and y direction, and $\\lambda$ is the wave length. \n",
    "\n",
    "Given a tilt angle of (3 mrad, 10 mrad), we have\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1198b43a-357d-451c-90ef-2dcac4cd376c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For (1, 1, 0), the coresponding diagonal element is -0.3299499897220892\n"
     ]
    }
   ],
   "source": [
    "t_x, t_y = 3.0, 10.0\n",
    "g = (1, 1, 0)\n",
    "xyz = [ g[0]/3.905+g[1]*0+g[2]*0, g[0]*0+g[1]/3.905+g[2]*0, g[0]*0+g[1]*0+g[2]/3.905 ]\n",
    "ans = -xyz[0]*xyz[0] - xyz[1]*xyz[1] - 2.0*xyz[0]*math.sin(t_x*0.001)/lambda_0  - 2.0*xyz[1]*math.sin(t_y*0.001)/lambda_0\n",
    "print( f'For {g}, the coresponding diagonal element is {ans}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab1e4780-48d5-4a18-a788-4d7645170a75",
   "metadata": {},
   "source": [
    "Rewriting as a function taking reflection $g$ and tilt angle $\\theta$ as inputs, we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ef1f4a98-e1f7-446b-a30a-01b142a83236",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_diag( g, theta ):\n",
    "    t_x, t_y, _ = theta\n",
    "    xyz = [ g[0]/3.905+g[1]*0+g[2]*0, g[0]*0+g[1]/3.905+g[2]*0, g[0]*0+g[1]*0+g[2]/3.905 ]\n",
    "    ans = -xyz[0]*xyz[0] - xyz[1]*xyz[1] - 2.0*xyz[0]*math.sin(t_x*0.001)/lambda_0  - 2.0*xyz[1]*math.sin(t_y*0.001)/lambda_0\n",
    "    return ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "805a443b-33e5-40c4-a733-9362a84b5d9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diag_(-1, -1, 0) = 0.480485390528094\n",
      "Diag_(-1, 1, 0) = -0.13115592636250514\n",
      "Diag_(1, -1, 0) = -0.13115592636250517\n",
      "Diag_(1, 1, 0) = -0.7427972432531044\n"
     ]
    }
   ],
   "source": [
    "for h in [-1, 1]:\n",
    "    for k in [-1, 1]:\n",
    "        g = (h, k, 0)\n",
    "        theta = (20, 20, 0)\n",
    "        diag = calculate_diag( g, theta )\n",
    "        print( f'Diag_{g} = {diag}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a379ab3b-7438-45a1-87ba-ee7eef74a4ab",
   "metadata": {},
   "source": [
    "In case of tilt angle of (20 mrad, 20mrad), we determine the structure matrix $\\mathcal{A}$:\n",
    "\n",
    "$$\\mathcal{A} = \\begin{bmatrix}\n",
    " 2\\,k_t \\, s_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} & \\mathbf{u}_{(\\bar{1}, 1, 0)} & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, 2, 0)} \\\\\n",
    "\\mathbf{u}_{(2, 0, 0)} & 2\\,k_t \\, s_{(1, 1, 0)} & \\mathbf{u}_{(1, 1, 0) } & \\mathbf{u}_{(\\bar{2}, \\bar{2}, 0)} & \\mathbf{u}_{(0, 2, 0)} \\\\\n",
    " \\mathbf{u}_{(1, \\bar{1}, 0)} & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 0 & \\mathbf{u}_{(1, 1, 0)} & \\mathbf{u}_{(\\bar{1}, 1, 0)} \\\\\n",
    " \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{2}, \\bar{2}, 0)} & \\mathbf{u}_{(\\bar{1}, \\bar{1}, 0)} & 2\\,s_t \\, s_{(\\bar{1}, \\bar{1}, 0)} & \\mathbf{u}_{(\\bar{2}, 0, 0)} \\\\\n",
    " \\mathbf{u}_{(2, \\bar{2}, 0)} & \\mathbf{u}_{(0, \\bar{2}, 0)} & \\mathbf{u}_{(1, \\bar{1}, 0)} & \\mathbf{u}_{(2, 0, 0)} & 2\\,k_t \\, s_{(1, \\bar{1}, 0)} \\\\\n",
    "\\end{bmatrix} \\\\\n",
    "= \\begin{bmatrix}\n",
    "-0.1311559  & 0.06606849749470538 & 0.05001082596051881 & 0.06606849749470538 & 0.06606849749470538 \\\\\n",
    "0.06606849749470538 & -0.742797 & 0.05001082596051881 & 0.04491475729167272 & 0.06606849749470538 \\\\\n",
    " 0.05001082596051881 & 0.05001082596051881 & 0 & 0.05001082596051881 & 0.05001082596051881 \\\\\n",
    " 0.06606849749470538 & 0.04491475729167272 & 0.05001082596051881 & 0.48048539 & 0.06606849749470538 \\\\\n",
    "0.04491475729167272 & 0.06606849749470538 & 0.05001082596051881 & 0.06606849749470538 & -0.1311559 \\\\\n",
    "\\end{bmatrix}\n",
    "$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "898d794d-79e1-4190-be94-4b88e2b98609",
   "metadata": {},
   "source": [
    "### Scattering matrix\n",
    "\n",
    "\n",
    "We can use the numpy package to calculate the scattering matrix $\\mathcal{S}$, which can be approximated by\n",
    "\n",
    "$$\n",
    "\\mathcal{S} = e^{i \\, \\pi \\lambda  t \\mathcal{A}}\n",
    "$$\n",
    "\n",
    "in which $t$ is the thickness of the specimen, and $\\lambda$ is the wavelength\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b4f962bb-de9b-4204-841f-2cc9ba7af3b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With a tilt angle of (10, -10, 0), we get the structure matrix A\n",
      "[[ 0.17468002+0.00000000e+00j  0.0660685 -4.72022836e-16j\n",
      "   0.05001083+0.00000000e+00j  0.0660685 -4.72022836e-16j\n",
      "   0.04491476+0.00000000e+00j]\n",
      " [ 0.0660685 +4.72022836e-16j -0.13115593+0.00000000e+00j\n",
      "   0.05001083+3.57900924e-16j  0.04491476-6.44131925e-16j\n",
      "   0.0660685 +4.72022836e-16j]\n",
      " [ 0.05001083+0.00000000e+00j  0.05001083-3.57900924e-16j\n",
      "   0.        +0.00000000e+00j  0.05001083+3.57900924e-16j\n",
      "   0.05001083+0.00000000e+00j]\n",
      " [ 0.0660685 -4.72022836e-16j  0.04491476-6.44131925e-16j\n",
      "   0.05001083-3.57900924e-16j -0.13115593+0.00000000e+00j\n",
      "   0.0660685 -4.72022836e-16j]\n",
      " [ 0.04491476+0.00000000e+00j  0.0660685 -4.72022836e-16j\n",
      "   0.05001083+0.00000000e+00j  0.0660685 +4.72022836e-16j\n",
      "  -0.43699188+0.00000000e+00j]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = np.zeros((5,5),dtype=np.complex_)\n",
    "theta = (10, -10, 0)\n",
    "\n",
    "\n",
    "A[0][0] = calculate_diag( (-1, 1, 0), theta )\n",
    "A[0][1] = calculate_ug( (-2, 0, 0) )\n",
    "A[0][2] = calculate_ug( (-1, 1, 0) )\n",
    "A[0][3] = calculate_ug( (0, -2, 0) )\n",
    "A[0][4] = calculate_ug( (-2, 2, 0) )\n",
    "\n",
    "A[1][0] = calculate_ug( (2, 0, 0) )\n",
    "A[1][1] = calculate_diag( (1, 1, 0), theta )\n",
    "A[1][2] = calculate_ug( (1, 1, 0) )\n",
    "A[1][3] = calculate_ug( (-2, -2, 0) )\n",
    "A[1][4] = calculate_ug( (0, 2, 0) )\n",
    "\n",
    "A[2][0] = calculate_ug( (1, -1, 0) )\n",
    "A[2][1] = calculate_ug( (-1, -1, 0) )\n",
    "A[2][2] = 0\n",
    "A[2][3] = calculate_ug( (1, 1, 0) )\n",
    "A[2][4] = calculate_ug( (-1, 1, 0) )\n",
    "\n",
    "A[3][0] = calculate_ug( (0, -2, 0) )\n",
    "A[3][1] = calculate_ug( (-2, -2, 0) ) \n",
    "A[3][2] = calculate_ug( (-1, -1, 0) )\n",
    "A[3][3] = calculate_diag( (-1, -1, 0), theta )\n",
    "A[3][4] = calculate_ug( (-2, 0, 0) )\n",
    "\n",
    "A[4][0] = calculate_ug( (2, -2, 0) )\n",
    "A[4][1] = calculate_ug( (0, -2, 0) ) \n",
    "A[4][2] = calculate_ug( (1, -1, 0) )\n",
    "A[4][3] = calculate_ug( (2, 0, 0) )\n",
    "A[4][4] = calculate_diag( (1, -1, 0), theta )\n",
    "\n",
    "print( f'With a tilt angle of {theta}, we get the structure matrix A' )\n",
    "print( A )\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c117a396-ac80-4494-a8d6-27c2720f0a73",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i \\pi \\lambda t A is \n",
      "[[ 0.00000000e+00 +7.35184406j  1.98662572e-14 +2.78065734j\n",
      "   0.00000000e+00 +2.10483022j  1.98662572e-14 +2.78065734j\n",
      "   0.00000000e+00 +1.89034948j]\n",
      " [-1.98662572e-14 +2.78065734j -0.00000000e+00 -5.52002397j\n",
      "  -1.50631522e-14 +2.10483022j  2.71098971e-14 +1.89034948j\n",
      "  -1.98662572e-14 +2.78065734j]\n",
      " [ 0.00000000e+00 +2.10483022j  1.50631522e-14 +2.10483022j\n",
      "   0.00000000e+00 +0.j         -1.50631522e-14 +2.10483022j\n",
      "   0.00000000e+00 +2.10483022j]\n",
      " [ 1.98662572e-14 +2.78065734j  2.71098971e-14 +1.89034948j\n",
      "   1.50631522e-14 +2.10483022j -0.00000000e+00 -5.52002397j\n",
      "   1.98662572e-14 +2.78065734j]\n",
      " [ 0.00000000e+00 +1.89034948j  1.98662572e-14 +2.78065734j\n",
      "   0.00000000e+00 +2.10483022j -1.98662572e-14 +2.78065734j\n",
      "  -0.00000000e+00-18.391892j  ]]\n"
     ]
    }
   ],
   "source": [
    "t = 400 # 40 nm\n",
    "\n",
    "_A =  1j * 3.14159265 * lambda_0 * t * A\n",
    "\n",
    "print( f'i \\pi \\lambda t A is ' )\n",
    "print(  _A )\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b5536c3-6edc-436b-ab19-dc7096c20c41",
   "metadata": {},
   "source": [
    "Due to the fact that \n",
    "\n",
    "$$\n",
    "e^A = e^{A/2} e^{A/2} = \\big( e^{A/2} \\big)^2 = \\big( e^{A/4} \\big)^4 = \\big( e^{A/8} \\big)^8 = \\big( e^{A/16} \\big)^{16} \\ldots\n",
    "$$\n",
    "\n",
    "As all elements in matrix $i\\pi \\lambda t \\mathcal{A}$ are not very large, \n",
    "We approximate the S matrix directly when $||\\mathcal{A}||_2$ is mall\n",
    "\n",
    "$$\n",
    "e^A \\simeq I + A + \\frac{A^2}{2!} + \\frac{A^3}{3!} + \\frac{A^4}{4!}+ \\frac{A^5}{5!} + \\ldots\n",
    "$$\n",
    "\n",
    "\n",
    "And when $||\\mathcal{A}||_2$ is large, we scale it, calculate the exponential and then square back\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "401058a9-c8c6-4994-9c3f-0766ad417782",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The scattering matrix S is\n",
      "[[-0.40425601-0.34053538j -0.35663335-0.24448523j -0.52391433-0.17441914j\n",
      "  -0.35663335-0.24448523j -0.19138644-0.08344857j]\n",
      " [-0.35663335-0.24448523j  0.47125649-0.21711702j -0.06291532-0.20818557j\n",
      "   0.04189212+0.68623795j -0.0725352 +0.14413899j]\n",
      " [-0.52391433-0.17441914j -0.06291532-0.20818557j  0.72900587+0.25935033j\n",
      "  -0.06291532-0.20818557j -0.04646589-0.01450244j]\n",
      " [-0.35663335-0.24448523j  0.04189212+0.68623795j -0.06291532-0.20818557j\n",
      "   0.47125649-0.21711702j -0.0725352 +0.14413899j]\n",
      " [-0.19138644-0.08344857j -0.0725352 +0.14413899j -0.04646589-0.01450244j\n",
      "  -0.0725352 +0.14413899j  0.83471844-0.52546471j]]\n"
     ]
    }
   ],
   "source": [
    "n = 5\n",
    "B = [_A/16.0,]\n",
    "for i in range(n):\n",
    "    B.append( np.dot( B[0], B[-1] ) )# [A, A^2, A^3, A^4, A^5, ...]\n",
    "    \n",
    "I = np.zeros((5,5),dtype=np.complex_)\n",
    "for idx in range(5):\n",
    "    I[idx][idx] = 1.0+0j\n",
    "\n",
    "    \n",
    "# e^A = I + A + A^2/2! + A^3/3! + A^4/4! + A^5/5!    \n",
    "factor = 1.0\n",
    "S = I\n",
    "for i in range( n ):\n",
    "    S += B[i] / factor\n",
    "    factor *= i+2\n",
    "\n",
    "#e^A = (e^{A/16})^16    \n",
    "for i in range( 4 ):\n",
    "    S = np.dot( S, S )\n",
    "    \n",
    "    \n",
    "print( 'The scattering matrix S is' )\n",
    "print( S )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3678b325-89a0-4a51-9cfe-adb86e0babf5",
   "metadata": {},
   "source": [
    "### Simulate the intensity\n",
    "\n",
    "As we put the selected beams/reflections  $(\\bar{1}, 1, 0)$, $(1, 1, 0)$, $(0, 0, 0)$, $(\\bar{1}, \\bar{1}, 0)$ and $(1, \\bar{1}, 0)$ in the central column of the structure matrix $\\mathcal{A}$,\n",
    "we extract the diffraction intensities for these discs from the central colum as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5136c098-afd2-4413-9e21-ad4e9ef02644",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.30490826383309777, 0.04729956976719501, 0.5987121567016085, 0.047299569767194065, 0.0023693994288727814]\n"
     ]
    }
   ],
   "source": [
    "I = [abs(S[i, 2])**2 for i in range(5)]\n",
    "print( I )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d642ec59-3a10-475d-99d3-1d2e78fa7ad5",
   "metadata": {},
   "source": [
    "As we are assume elastic diffraction, in which no energy loss is expected. We check the total energy after diffraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "07e71a68-c560-4850-b42f-c4a3890567e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total_energy=1.000588959497968\n"
     ]
    }
   ],
   "source": [
    "total_energy = np.sum( np.asarray(I) )\n",
    "print( f'{total_energy=}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57ea0b27-7933-44b6-9b79-0ad482d2b531",
   "metadata": {},
   "source": [
    "Putting the intensity simulation subroutine together, we have a function taking the tilt angle $\\theta$ as argument"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3b68a03b-ac6b-4183-b4b0-146f6280df32",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_intensity(theta):\n",
    "    A[0][0] = calculate_diag( (-1, 1, 0), theta )\n",
    "    A[0][1] = calculate_ug( (-2, 0, 0) )\n",
    "    A[0][2] = calculate_ug( (-1, 1, 0) )\n",
    "    A[0][3] = calculate_ug( (0, -2, 0) )\n",
    "    A[0][4] = calculate_ug( (-2, 2, 0) )\n",
    "\n",
    "    A[1][0] = calculate_ug( (2, 0, 0) )\n",
    "    A[1][1] = calculate_diag( (1, 1, 0), theta )\n",
    "    A[1][2] = calculate_ug( (1, 1, 0) )\n",
    "    A[1][3] = calculate_ug( (-2, -2, 0) )\n",
    "    A[1][4] = calculate_ug( (0, 2, 0) )\n",
    "\n",
    "    A[2][0] = calculate_ug( (1, -1, 0) )\n",
    "    A[2][1] = calculate_ug( (-1, -1, 0) )\n",
    "    A[2][2] = 0\n",
    "    A[2][3] = calculate_ug( (1, 1, 0) )\n",
    "    A[2][4] = calculate_ug( (-1, 1, 0) )\n",
    "\n",
    "    A[3][0] = calculate_ug( (0, -2, 0) )\n",
    "    A[3][1] = calculate_ug( (-2, -2, 0) ) \n",
    "    A[3][2] = calculate_ug( (-1, -1, 0) )\n",
    "    A[3][3] = calculate_diag( (-1, -1, 0), theta )\n",
    "    A[3][4] = calculate_ug( (-2, 0, 0) )\n",
    "\n",
    "    A[4][0] = calculate_ug( (2, -2, 0) )\n",
    "    A[4][1] = calculate_ug( (0, -2, 0) ) \n",
    "    A[4][2] = calculate_ug( (1, -1, 0) )\n",
    "    A[4][3] = calculate_ug( (2, 0, 0) )\n",
    "    A[4][4] = calculate_diag( (1, -1, 0), theta )\n",
    "\n",
    "    t = 400 \n",
    "    _A =  1j * 3.14159265 * lambda_0 * t * A\n",
    "\n",
    "    n = 5\n",
    "    B = [_A/16.0,]\n",
    "    for i in range(n):\n",
    "        B.append( np.dot( B[0], B[-1] ) )# [A, A^2, A^3, A^4, A^5, ...]\n",
    "\n",
    "    I = np.zeros((5,5),dtype=np.complex_)\n",
    "    for idx in range(5):\n",
    "        I[idx][idx] = 1.0+0j\n",
    " \n",
    "    factor = 1.0\n",
    "    S = I\n",
    "    for i in range( n ):\n",
    "        S += B[i] / factor\n",
    "        factor *= i+2\n",
    "   \n",
    "    for i in range( 4 ):\n",
    "        S = np.dot( S, S )    \n",
    "        \n",
    "    I = [abs(S[i, 2])**2 for i in range(5)] \n",
    "    return I"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e32e24f8-61fc-46db-a0c0-be7cc26d57f0",
   "metadata": {},
   "source": [
    "### All intensities in a disk\n",
    "\n",
    "We enumerate all possible integer tilt angles with in range 40 mrad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b3faa3bf-dfd7-4129-ac2b-db2b91962497",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generate 5023 tilt angles, the first one is [-40, 0, 0] and the last one is [39, 8, 0]\n"
     ]
    }
   ],
   "source": [
    "angles = []\n",
    "for ax in range(-40, 40):\n",
    "    for ay in range(-40, 40):\n",
    "        if (ax*ax+ay*ay) <= 40*40:\n",
    "            angles.append( [ax, ay, 0] )\n",
    "            \n",
    "print( f'Generate {len(angles)} tilt angles, the first one is {angles[0]} and the last one is {angles[-1]}' )            "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e22df8d-6175-4f78-8b03-d525ecf10510",
   "metadata": {},
   "source": [
    "We simulate the scattering intensities for all these tilt angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c856f4da-f5e4-40ff-ba0f-1d4af101abee",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 5023/5023 [00:00<00:00, 5150.47it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the tilt angle [-40, 0, 0], we have intensities [0.01558523292693548, 0.015996941424102216, 0.9400348861824537, 0.015585232926935502, 0.01599694142410225].\n",
      "For the tilt angle [39, 8, 0], we have intensities [0.03290924099388043, 0.001609544350978326, 0.9641860728148215, 0.0022243853494005876, 0.0011212318730355194].\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import tqdm\n",
    "intensities = []\n",
    "for angle in tqdm.tqdm(angles):\n",
    "    intensities.append( simulate_intensity( angle ) )\n",
    "    \n",
    "print( f'For the tilt angle {angles[0]}, we have intensities {intensities[0]}.' )     \n",
    "print( f'For the tilt angle {angles[-1]}, we have intensities {intensities[-1]}.' )    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d94b94d-9f37-4065-99cb-c1f72e057ed1",
   "metadata": {},
   "source": [
    "### Visualize simulated intensity\n",
    "\n",
    "We only simulate inteisities for $(\\bar{1}, 1, 0)$, $(1, 1, 0)$, $(0, 0, 0)$, $(\\bar{1}, \\bar{1}, 0)$ and $(1, \\bar{1}, 0)$. We can put all these intensities together to generate a diffraction image. We assume each disk only occupies a dimension of $81 \\times 81$ pixels, and the whole image then occupies $3 \\times 81 \\times 3 \\times 81$ pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "05eaa4fb-caf0-41dd-8715-52e3bf1d6890",
   "metadata": {},
   "outputs": [],
   "source": [
    "image = np.zeros( (3*81, 3*81) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "124fd08e-63bf-4e6e-a46b-6d7fa6b48d4d",
   "metadata": {},
   "source": [
    "We put the intensities for reflection $(\\bar{1}, 1, 0)$ on the top-left of this image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e92a9c95-e922-40da-ad59-7dc612386d0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "for angle, intensity in zip(angles, intensities):\n",
    "    ax, ay, _ = angle\n",
    "    i = intensity[0]\n",
    "    image[ax+40, ay+40+2*81] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e2be70-c6a8-4da4-bf8f-add6df8a28ea",
   "metadata": {},
   "source": [
    "We put the intensities for reflection $(1, 1, 0)$ on the top-right of this image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "64c42d60-faf7-4bdc-b84f-ca2cb2ca005a",
   "metadata": {},
   "outputs": [],
   "source": [
    "for angle, intensity in zip(angles, intensities):\n",
    "    ax, ay, _ = angle\n",
    "    i = intensity[1]\n",
    "    image[ax+40+2*81, ay+40+2*81] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8557aeae-9ba0-4e57-ba28-d059e3532456",
   "metadata": {},
   "source": [
    "We put the intensities for reflection $(0, 0, 0)$ on the center of this image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a5c79474-71a2-4edd-9a9f-215901cb4fb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "for angle, intensity in zip(angles, intensities):\n",
    "    ax, ay, _ = angle\n",
    "    i = intensity[2]\n",
    "    image[ax+40+1*81, ay+40+1*81] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ef58d7a-83eb-4c6c-b2a9-897022885b8b",
   "metadata": {},
   "source": [
    "We put the intensities for reflection $(\\bar{1}, \\bar{1}, 0)$ on the bottom-left of the image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9ed0601f-f6f7-470a-b001-c980682238f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "for angle, intensity in zip(angles, intensities):\n",
    "    ax, ay, _ = angle\n",
    "    i = intensity[3]\n",
    "    image[ax+40, ay+40] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "683ac57a-75c9-44f5-ac67-145afe5dffd7",
   "metadata": {},
   "source": [
    "And we put the intensities for reflection $(1, \\bar{1}, 0)$ on the bottom-right of the image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a128cf60-2bb0-40a2-ab17-e548e9806355",
   "metadata": {},
   "outputs": [],
   "source": [
    "for angle, intensity in zip(angles, intensities):\n",
    "    ax, ay, _ = angle\n",
    "    i = intensity[4]\n",
    "    image[ax+40+2*81, ay+40] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "695b6a1a-ec94-4d73-bb0b-facea2e8571b",
   "metadata": {},
   "source": [
    "We visualize our image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "143a8a34-7a51-41bf-8098-4839feb516d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "imgplot = plt.imshow(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24feaedd-7b22-4cbc-9842-8a129427ea57",
   "metadata": {},
   "source": [
    "### Notes\n",
    "\n",
    "- Please find most recent version from here\n",
    "    - <https://github.com/fengwang/electron_diffraction_simulation>\n",
    "    \n",
    "- Other versions (maybe out of date)\n",
    "    - web: <https://fengwang.github.io/blogs/electron_diffraction_simulation/index.html>\n",
    "    - notebook: <https://colab.research.google.com/drive/1Gt4sjrgKio53sYptBvJUOyuQ7I3rbVgJ?usp=sharing>\n",
    "    - pdf: <https://github.com/fengwang/electron_diffraction_simulation/raw/main/ElectronDiffraction.pdf>\n",
    "    \n",
    "- Please submit your questions, suggestions and error reports to\n",
    "    + <https://github.com/fengwang/electron_diffraction_simulation/issues>\n",
    "    \n",
    "- Last edit\n",
    "    + Sun Jan 15 2023\n",
    "    + <wang_feng@live.com>\n"
   ]
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}