From 92540ddced4e710bb03611effedec1ba30803a34 Mon Sep 17 00:00:00 2001
From: TM <taiminyang@gmail.com>
Date: Mon, 4 Jul 2022 10:57:01 +0200
Subject: [PATCH] Add simulations for dynamical scattering

---
 notebooks/diffraction_simulation/NaCl.cif     | 428 +++++++++++++++++
 .../simulate_dynamical_scattering.ipynb       | 434 ++++++++++++++++++
 2 files changed, 862 insertions(+)
 create mode 100644 notebooks/diffraction_simulation/NaCl.cif
 create mode 100644 notebooks/diffraction_simulation/simulate_dynamical_scattering.ipynb

diff --git a/notebooks/diffraction_simulation/NaCl.cif b/notebooks/diffraction_simulation/NaCl.cif
new file mode 100644
index 0000000..6525e88
--- /dev/null
+++ b/notebooks/diffraction_simulation/NaCl.cif
@@ -0,0 +1,428 @@
+ 
+data_sp1_225
+ 
+_audit_creation_method            'SHELXL-2018/3'
+_shelx_SHELXL_version_number      '2018/3'
+_chemical_name_systematic         ?
+_chemical_name_common             ?
+_chemical_melting_point           ?
+_chemical_formula_moiety          ?
+_chemical_formula_sum
+ 'Cl Na' 
+_chemical_formula_weight          58.44
+
+loop_
+ _atom_type_symbol
+ _atom_type_description
+ _atom_type_scat_dispersion_real
+ _atom_type_scat_dispersion_imag
+ _atom_type_scat_source
+ 'Na'  'Na'   0.0000   0.0000
+ 'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4'
+ 'Cl'  'Cl'   0.0000   0.0000
+ 'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4'
+ 
+_space_group_crystal_system       cubic
+_space_group_IT_number            225
+_space_group_name_H-M_alt         'F m -3 m'
+_space_group_name_Hall            '-F 4 2 3'
+ 
+_shelx_space_group_comment
+;
+The symmetry employed for this shelxl refinement is uniquely defined
+by the following loop, which should always be used as a source of
+symmetry information in preference to the above space-group names.
+They are only intended as comments.
+;
+ 
+loop_
+ _space_group_symop_operation_xyz
+ 'x, y, z'
+ '-x, -y, z'
+ '-x, y, -z'
+ 'x, -y, -z'
+ 'z, x, y'
+ 'z, -x, -y'
+ '-z, -x, y'
+ '-z, x, -y'
+ 'y, z, x'
+ '-y, z, -x'
+ 'y, -z, -x'
+ '-y, -z, x'
+ 'y, x, -z'
+ '-y, -x, -z'
+ 'y, -x, z'
+ '-y, x, z'
+ 'x, z, -y'
+ '-x, z, y'
+ '-x, -z, -y'
+ 'x, -z, y'
+ 'z, y, -x'
+ 'z, -y, x'
+ '-z, y, x'
+ '-z, -y, -x'
+ 'x, y+1/2, z+1/2'
+ '-x, -y+1/2, z+1/2'
+ '-x, y+1/2, -z+1/2'
+ 'x, -y+1/2, -z+1/2'
+ 'z, x+1/2, y+1/2'
+ 'z, -x+1/2, -y+1/2'
+ '-z, -x+1/2, y+1/2'
+ '-z, x+1/2, -y+1/2'
+ 'y, z+1/2, x+1/2'
+ '-y, z+1/2, -x+1/2'
+ 'y, -z+1/2, -x+1/2'
+ '-y, -z+1/2, x+1/2'
+ 'y, x+1/2, -z+1/2'
+ '-y, -x+1/2, -z+1/2'
+ 'y, -x+1/2, z+1/2'
+ '-y, x+1/2, z+1/2'
+ 'x, z+1/2, -y+1/2'
+ '-x, z+1/2, y+1/2'
+ '-x, -z+1/2, -y+1/2'
+ 'x, -z+1/2, y+1/2'
+ 'z, y+1/2, -x+1/2'
+ 'z, -y+1/2, x+1/2'
+ '-z, y+1/2, x+1/2'
+ '-z, -y+1/2, -x+1/2'
+ 'x+1/2, y, z+1/2'
+ '-x+1/2, -y, z+1/2'
+ '-x+1/2, y, -z+1/2'
+ 'x+1/2, -y, -z+1/2'
+ 'z+1/2, x, y+1/2'
+ 'z+1/2, -x, -y+1/2'
+ '-z+1/2, -x, y+1/2'
+ '-z+1/2, x, -y+1/2'
+ 'y+1/2, z, x+1/2'
+ '-y+1/2, z, -x+1/2'
+ 'y+1/2, -z, -x+1/2'
+ '-y+1/2, -z, x+1/2'
+ 'y+1/2, x, -z+1/2'
+ '-y+1/2, -x, -z+1/2'
+ 'y+1/2, -x, z+1/2'
+ '-y+1/2, x, z+1/2'
+ 'x+1/2, z, -y+1/2'
+ '-x+1/2, z, y+1/2'
+ '-x+1/2, -z, -y+1/2'
+ 'x+1/2, -z, y+1/2'
+ 'z+1/2, y, -x+1/2'
+ 'z+1/2, -y, x+1/2'
+ '-z+1/2, y, x+1/2'
+ '-z+1/2, -y, -x+1/2'
+ 'x+1/2, y+1/2, z'
+ '-x+1/2, -y+1/2, z'
+ '-x+1/2, y+1/2, -z'
+ 'x+1/2, -y+1/2, -z'
+ 'z+1/2, x+1/2, y'
+ 'z+1/2, -x+1/2, -y'
+ '-z+1/2, -x+1/2, y'
+ '-z+1/2, x+1/2, -y'
+ 'y+1/2, z+1/2, x'
+ '-y+1/2, z+1/2, -x'
+ 'y+1/2, -z+1/2, -x'
+ '-y+1/2, -z+1/2, x'
+ 'y+1/2, x+1/2, -z'
+ '-y+1/2, -x+1/2, -z'
+ 'y+1/2, -x+1/2, z'
+ '-y+1/2, x+1/2, z'
+ 'x+1/2, z+1/2, -y'
+ '-x+1/2, z+1/2, y'
+ '-x+1/2, -z+1/2, -y'
+ 'x+1/2, -z+1/2, y'
+ 'z+1/2, y+1/2, -x'
+ 'z+1/2, -y+1/2, x'
+ '-z+1/2, y+1/2, x'
+ '-z+1/2, -y+1/2, -x'
+ '-x, -y, -z'
+ 'x, y, -z'
+ 'x, -y, z'
+ '-x, y, z'
+ '-z, -x, -y'
+ '-z, x, y'
+ 'z, x, -y'
+ 'z, -x, y'
+ '-y, -z, -x'
+ 'y, -z, x'
+ '-y, z, x'
+ 'y, z, -x'
+ '-y, -x, z'
+ 'y, x, z'
+ '-y, x, -z'
+ 'y, -x, -z'
+ '-x, -z, y'
+ 'x, -z, -y'
+ 'x, z, y'
+ '-x, z, -y'
+ '-z, -y, x'
+ '-z, y, -x'
+ 'z, -y, -x'
+ 'z, y, x'
+ '-x, -y+1/2, -z+1/2'
+ 'x, y+1/2, -z+1/2'
+ 'x, -y+1/2, z+1/2'
+ '-x, y+1/2, z+1/2'
+ '-z, -x+1/2, -y+1/2'
+ '-z, x+1/2, y+1/2'
+ 'z, x+1/2, -y+1/2'
+ 'z, -x+1/2, y+1/2'
+ '-y, -z+1/2, -x+1/2'
+ 'y, -z+1/2, x+1/2'
+ '-y, z+1/2, x+1/2'
+ 'y, z+1/2, -x+1/2'
+ '-y, -x+1/2, z+1/2'
+ 'y, x+1/2, z+1/2'
+ '-y, x+1/2, -z+1/2'
+ 'y, -x+1/2, -z+1/2'
+ '-x, -z+1/2, y+1/2'
+ 'x, -z+1/2, -y+1/2'
+ 'x, z+1/2, y+1/2'
+ '-x, z+1/2, -y+1/2'
+ '-z, -y+1/2, x+1/2'
+ '-z, y+1/2, -x+1/2'
+ 'z, -y+1/2, -x+1/2'
+ 'z, y+1/2, x+1/2'
+ '-x+1/2, -y, -z+1/2'
+ 'x+1/2, y, -z+1/2'
+ 'x+1/2, -y, z+1/2'
+ '-x+1/2, y, z+1/2'
+ '-z+1/2, -x, -y+1/2'
+ '-z+1/2, x, y+1/2'
+ 'z+1/2, x, -y+1/2'
+ 'z+1/2, -x, y+1/2'
+ '-y+1/2, -z, -x+1/2'
+ 'y+1/2, -z, x+1/2'
+ '-y+1/2, z, x+1/2'
+ 'y+1/2, z, -x+1/2'
+ '-y+1/2, -x, z+1/2'
+ 'y+1/2, x, z+1/2'
+ '-y+1/2, x, -z+1/2'
+ 'y+1/2, -x, -z+1/2'
+ '-x+1/2, -z, y+1/2'
+ 'x+1/2, -z, -y+1/2'
+ 'x+1/2, z, y+1/2'
+ '-x+1/2, z, -y+1/2'
+ '-z+1/2, -y, x+1/2'
+ '-z+1/2, y, -x+1/2'
+ 'z+1/2, -y, -x+1/2'
+ 'z+1/2, y, x+1/2'
+ '-x+1/2, -y+1/2, -z'
+ 'x+1/2, y+1/2, -z'
+ 'x+1/2, -y+1/2, z'
+ '-x+1/2, y+1/2, z'
+ '-z+1/2, -x+1/2, -y'
+ '-z+1/2, x+1/2, y'
+ 'z+1/2, x+1/2, -y'
+ 'z+1/2, -x+1/2, y'
+ '-y+1/2, -z+1/2, -x'
+ 'y+1/2, -z+1/2, x'
+ '-y+1/2, z+1/2, x'
+ 'y+1/2, z+1/2, -x'
+ '-y+1/2, -x+1/2, z'
+ 'y+1/2, x+1/2, z'
+ '-y+1/2, x+1/2, -z'
+ 'y+1/2, -x+1/2, -z'
+ '-x+1/2, -z+1/2, y'
+ 'x+1/2, -z+1/2, -y'
+ 'x+1/2, z+1/2, y'
+ '-x+1/2, z+1/2, -y'
+ '-z+1/2, -y+1/2, x'
+ '-z+1/2, y+1/2, -x'
+ 'z+1/2, -y+1/2, -x'
+ 'z+1/2, y+1/2, x'
+ 
+_cell_length_a                    5.6400(7)
+_cell_length_b                    5.6400(7)
+_cell_length_c                    5.6400(7)
+_cell_angle_alpha                 90
+_cell_angle_beta                  90
+_cell_angle_gamma                 90
+_cell_volume                      179.41(7)
+_cell_formula_units_Z             4
+_cell_measurement_temperature     293(2)
+_cell_measurement_reflns_used     ?
+_cell_measurement_theta_min       ?
+_cell_measurement_theta_max       ?
+ 
+_exptl_crystal_description        ?
+_exptl_crystal_colour             ?
+_exptl_crystal_density_meas       ?
+_exptl_crystal_density_method     ?
+_exptl_crystal_density_diffrn     2.164          
+_exptl_crystal_F_000              38
+_exptl_transmission_factor_min    ?
+_exptl_transmission_factor_max    ?
+_exptl_crystal_size_max           ?
+_exptl_crystal_size_mid           ?
+_exptl_crystal_size_min           ?
+_exptl_absorpt_coefficient_mu     0.000
+_shelx_estimated_absorpt_T_min    ?
+_shelx_estimated_absorpt_T_max    ?
+_exptl_absorpt_correction_type    ?
+_exptl_absorpt_correction_T_min   ?
+_exptl_absorpt_correction_T_max   ?
+_exptl_absorpt_process_details    ?
+_exptl_absorpt_special_details    ?
+_diffrn_ambient_temperature       293(2)
+_diffrn_radiation_wavelength      0.71073
+_diffrn_radiation_type            MoK\a
+_diffrn_source                    ?
+_diffrn_measurement_device_type   ?
+_diffrn_measurement_method        ?
+_diffrn_detector_area_resol_mean  ?
+_diffrn_reflns_number             229
+_diffrn_reflns_av_unetI/netI      0.0735
+_diffrn_reflns_av_R_equivalents   0.1938
+_diffrn_reflns_limit_h_min        -7
+_diffrn_reflns_limit_h_max        7
+_diffrn_reflns_limit_k_min        -7
+_diffrn_reflns_limit_k_max        7
+_diffrn_reflns_limit_l_min        -7
+_diffrn_reflns_limit_l_max        7
+_diffrn_reflns_theta_min          6.265
+_diffrn_reflns_theta_max          28.945
+_diffrn_reflns_theta_full         25.242
+_diffrn_measured_fraction_theta_max   1.000
+_diffrn_measured_fraction_theta_full  1.000
+_diffrn_reflns_Laue_measured_fraction_max    1.000
+_diffrn_reflns_Laue_measured_fraction_full   1.000
+_diffrn_reflns_point_group_measured_fraction_max   1.000
+_diffrn_reflns_point_group_measured_fraction_full  1.000
+_reflns_number_total              25
+_reflns_number_gt                 24
+_reflns_threshold_expression      'I > 2\s(I)'
+_reflns_Friedel_coverage          0.000
+_reflns_Friedel_fraction_max      .
+_reflns_Friedel_fraction_full     .
+ 
+_reflns_special_details
+;
+ Reflections were merged by SHELXL according to the crystal
+ class for the calculation of statistics and refinement.
+ 
+ _reflns_Friedel_fraction is defined as the number of unique
+ Friedel pairs measured divided by the number that would be
+ possible theoretically, ignoring centric projections and
+ systematic absences.
+;
+ 
+_computing_data_collection        ?
+_computing_cell_refinement        ?
+_computing_data_reduction         ?
+_computing_structure_solution     ?
+_computing_structure_refinement 'SHELXL-2018/3 (Sheldrick, 2018)'
+_computing_molecular_graphics     ?
+_computing_publication_material   ?
+_refine_special_details           ?
+_refine_ls_structure_factor_coef  Fsqd
+_refine_ls_matrix_type            full
+_refine_ls_weighting_scheme       calc
+_refine_ls_weighting_details
+'w=1/[\s^2^(Fo^2^)+(0.2000P)^2^] where P=(Fo^2^+2Fc^2^)/3'
+_atom_sites_solution_primary      ?
+_atom_sites_solution_secondary    ?
+_atom_sites_solution_hydrogens    .
+_refine_ls_hydrogen_treatment     undef
+_refine_ls_extinction_method      'SHELXL-2018/3 (Sheldrick 2018)'
+_refine_ls_extinction_coef        109(113)
+_refine_ls_extinction_expression
+ 'Fc^*^=kFc[1+0.001xFc^2^\l^3^/sin(2\q)]^-1/4^'
+_refine_ls_number_reflns          25
+_refine_ls_number_parameters      4
+_refine_ls_number_restraints      0
+_refine_ls_R_factor_all           0.1336
+_refine_ls_R_factor_gt            0.1328
+_refine_ls_wR_factor_ref          0.3412
+_refine_ls_wR_factor_gt           0.3402
+_refine_ls_goodness_of_fit_ref    1.704
+_refine_ls_restrained_S_all       1.704
+_refine_ls_shift/su_max           0.000
+_refine_ls_shift/su_mean          0.000
+ 
+loop_
+ _atom_site_label
+ _atom_site_type_symbol
+ _atom_site_fract_x
+ _atom_site_fract_y
+ _atom_site_fract_z
+ _atom_site_U_iso_or_equiv
+ _atom_site_adp_type
+ _atom_site_occupancy
+ _atom_site_site_symmetry_order  
+ _atom_site_calc_flag
+ _atom_site_refinement_flags_posn
+ _atom_site_refinement_flags_adp
+ _atom_site_refinement_flags_occupancy
+ _atom_site_disorder_assembly
+ _atom_site_disorder_group
+Cl01 Cl 1.000000 0.500000 0.500000 0.021(7) Uiso 1 48 d S . P . .
+Na02 Na 0.500000 0.500000 0.500000 0.027(7) Uiso 1 48 d S . P . .
+ 
+_geom_special_details
+;
+ All esds (except the esd in the dihedral angle between two l.s. planes)
+ are estimated using the full covariance matrix.  The cell esds are taken
+ into account individually in the estimation of esds in distances, angles
+ and torsion angles; correlations between esds in cell parameters are only
+ used when they are defined by crystal symmetry.  An approximate (isotropic)
+ treatment of cell esds is used for estimating esds involving l.s. planes.
+;
+ 
+loop_
+ _geom_bond_atom_site_label_1
+ _geom_bond_atom_site_label_2
+ _geom_bond_distance
+ _geom_bond_site_symmetry_2
+ _geom_bond_publ_flag
+Cl01 Na02 2.8200(4) 73 ?
+Cl01 Na02 2.8200(4) . ?
+Cl01 Na02 2.8200(4) 1_655 ?
+Cl01 Na02 2.8200(4) 49_554 ?
+Cl01 Na02 2.8200(4) 49 ?
+Cl01 Na02 2.8200(4) 73_545 ?
+ 
+loop_
+ _geom_angle_atom_site_label_1
+ _geom_angle_atom_site_label_2
+ _geom_angle_atom_site_label_3
+ _geom_angle
+ _geom_angle_site_symmetry_1
+ _geom_angle_site_symmetry_3
+ _geom_angle_publ_flag
+Na02 Cl01 Na02 90.0 73 . ?
+Na02 Cl01 Na02 90.0 73 1_655 ?
+Na02 Cl01 Na02 180.0 . 1_655 ?
+Na02 Cl01 Na02 90.0 73 49_554 ?
+Na02 Cl01 Na02 90.0 . 49_554 ?
+Na02 Cl01 Na02 90.0 1_655 49_554 ?
+Na02 Cl01 Na02 90.0 73 49 ?
+Na02 Cl01 Na02 90.0 . 49 ?
+Na02 Cl01 Na02 90.0 1_655 49 ?
+Na02 Cl01 Na02 180.0 49_554 49 ?
+Na02 Cl01 Na02 180.0 73 73_545 ?
+Na02 Cl01 Na02 90.0 . 73_545 ?
+Na02 Cl01 Na02 90.0 1_655 73_545 ?
+Na02 Cl01 Na02 90.0 49_554 73_545 ?
+Na02 Cl01 Na02 90.0 49 73_545 ?
+Cl01 Na02 Cl01 90.0 73_455 . ?
+Cl01 Na02 Cl01 90.0 73_455 1_455 ?
+Cl01 Na02 Cl01 180.0 . 1_455 ?
+Cl01 Na02 Cl01 90.0 73_455 49_454 ?
+Cl01 Na02 Cl01 90.0 . 49_454 ?
+Cl01 Na02 Cl01 90.0 1_455 49_454 ?
+Cl01 Na02 Cl01 90.0 73_455 49_455 ?
+Cl01 Na02 Cl01 90.0 . 49_455 ?
+Cl01 Na02 Cl01 90.0 1_455 49_455 ?
+Cl01 Na02 Cl01 180.0 49_454 49_455 ?
+Cl01 Na02 Cl01 180.0 73_455 73_445 ?
+Cl01 Na02 Cl01 90.0 . 73_445 ?
+Cl01 Na02 Cl01 90.0 1_455 73_445 ?
+Cl01 Na02 Cl01 90.0 49_454 73_445 ?
+Cl01 Na02 Cl01 90.0 49_455 73_445 ?
+ 
+_refine_diff_density_max    0.167
+_refine_diff_density_min   -0.247
+_refine_diff_density_rms    0.097
+
+
+
+
diff --git a/notebooks/diffraction_simulation/simulate_dynamical_scattering.ipynb b/notebooks/diffraction_simulation/simulate_dynamical_scattering.ipynb
new file mode 100644
index 0000000..a44cf3c
--- /dev/null
+++ b/notebooks/diffraction_simulation/simulate_dynamical_scattering.ipynb
@@ -0,0 +1,434 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import py4DSTEM\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Load cif files in py4DSTEM"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "structure = py4DSTEM.process.diffraction.Crystal.from_CIF('NaCl.cif')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "resolution = 1.0 # in reciprocal A\n",
+    "thickness = 2000 # in A\n",
+    "thermal_sigma = 0.2 # in A (square root of Uiso ADP)\n",
+    "zone_axis = [0, 1, 1]\n",
+    "voltage = 300000\n",
+    "structure.setup_diffraction(accelerating_voltage=voltage)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Calculate kinamatical structure factors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "structure.calculate_structure_factors(k_max=resolution)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Generate inamatical diffraction pattern at a certain zone axis"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bragg_peaks = structure.generate_diffraction_pattern(zone_axis_lattice=zone_axis, accel_voltage=voltage)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A point list will be generated, with qx, qy intensity and h,k,l inside"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([(-5.01494171e-01,  7.09219858e-01, 0.00170754, -4, -2,  2),\n",
+       "       (-6.14153231e-17,  7.09219858e-01, 0.00303301, -4,  0,  0),\n",
+       "       ( 5.01494171e-01,  7.09219858e-01, 0.00170754, -4,  2, -2),\n",
+       "       (-2.50747086e-01,  5.31914894e-01, 0.00040371, -3, -1,  1),\n",
+       "       ( 2.50747086e-01,  5.31914894e-01, 0.00040371, -3,  1, -1),\n",
+       "       (-5.01494171e-01,  3.54609929e-01, 0.00435453, -2, -2,  2),\n",
+       "       (-3.07076616e-17,  3.54609929e-01, 0.01279031, -2,  0,  0),\n",
+       "       ( 5.01494171e-01,  3.54609929e-01, 0.00435453, -2,  2, -2),\n",
+       "       (-7.52241257e-01,  1.77304965e-01, 0.00013431, -1, -3,  3),\n",
+       "       (-2.50747086e-01,  1.77304965e-01, 0.00117659, -1, -1,  1),\n",
+       "       ( 2.50747086e-01,  1.77304965e-01, 0.00117659, -1,  1, -1),\n",
+       "       ( 7.52241257e-01,  1.77304965e-01, 0.00013431, -1,  3, -3),\n",
+       "       (-5.01494171e-01, -4.34271915e-17, 0.00683318,  0, -2,  2),\n",
+       "       ( 0.00000000e+00,  0.00000000e+00, 0.04662113,  0,  0,  0),\n",
+       "       ( 5.01494171e-01,  4.34271915e-17, 0.00683318,  0,  2, -2),\n",
+       "       (-7.52241257e-01, -1.77304965e-01, 0.00013431,  1, -3,  3),\n",
+       "       (-2.50747086e-01, -1.77304965e-01, 0.00117659,  1, -1,  1),\n",
+       "       ( 2.50747086e-01, -1.77304965e-01, 0.00117659,  1,  1, -1),\n",
+       "       ( 7.52241257e-01, -1.77304965e-01, 0.00013431,  1,  3, -3),\n",
+       "       (-5.01494171e-01, -3.54609929e-01, 0.00435453,  2, -2,  2),\n",
+       "       ( 3.07076616e-17, -3.54609929e-01, 0.01279031,  2,  0,  0),\n",
+       "       ( 5.01494171e-01, -3.54609929e-01, 0.00435453,  2,  2, -2),\n",
+       "       (-2.50747086e-01, -5.31914894e-01, 0.00040371,  3, -1,  1),\n",
+       "       ( 2.50747086e-01, -5.31914894e-01, 0.00040371,  3,  1, -1),\n",
+       "       (-5.01494171e-01, -7.09219858e-01, 0.00170754,  4, -2,  2),\n",
+       "       ( 6.14153231e-17, -7.09219858e-01, 0.00303301,  4,  0,  0),\n",
+       "       ( 5.01494171e-01, -7.09219858e-01, 0.00170754,  4,  2, -2)],\n",
+       "      dtype=[('qx', '<f8'), ('qy', '<f8'), ('intensity', '<f8'), ('h', '<i4'), ('k', '<i4'), ('l', '<i4')])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# check what's inside the box\n",
+    "bragg_peaks.data"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "##  Calculate dynamical structure factors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Computing WK-CP lookup table: 100%|███████████████| 739/739 [00:00<00:00, 4998.69it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "structure.calculate_dynamical_structure_factors(accelerating_voltage=voltage, k_max=resolution, thermal_sigma=thermal_sigma)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Generate dynamical diffraction pattern from its kinamatical counterpart"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dyn_bragg_peaks = structure.generate_dynamical_diffraction_pattern(beams=bragg_peaks, thickness=thickness, zone_axis=zone_axis)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([(-5.01494171e-01,  7.09219858e-01, 7.41930743e-06, -4, -2,  2),\n",
+       "       (-6.14153231e-17,  7.09219858e-01, 1.61563211e-04, -4,  0,  0),\n",
+       "       ( 5.01494171e-01,  7.09219858e-01, 7.41930743e-06, -4,  2, -2),\n",
+       "       (-2.50747086e-01,  5.31914894e-01, 1.14033830e-04, -3, -1,  1),\n",
+       "       ( 2.50747086e-01,  5.31914894e-01, 1.14033830e-04, -3,  1, -1),\n",
+       "       (-5.01494171e-01,  3.54609929e-01, 4.53889481e-04, -2, -2,  2),\n",
+       "       (-3.07076616e-17,  3.54609929e-01, 2.98183191e-02, -2,  0,  0),\n",
+       "       ( 5.01494171e-01,  3.54609929e-01, 4.53889481e-04, -2,  2, -2),\n",
+       "       (-7.52241257e-01,  1.77304965e-01, 3.02618725e-05, -1, -3,  3),\n",
+       "       (-2.50747086e-01,  1.77304965e-01, 4.12178889e-03, -1, -1,  1),\n",
+       "       ( 2.50747086e-01,  1.77304965e-01, 4.12178889e-03, -1,  1, -1),\n",
+       "       ( 7.52241257e-01,  1.77304965e-01, 3.02618725e-05, -1,  3, -3),\n",
+       "       (-5.01494171e-01, -4.34271915e-17, 7.03385115e-05,  0, -2,  2),\n",
+       "       ( 0.00000000e+00,  0.00000000e+00, 5.55325044e-03,  0,  0,  0),\n",
+       "       ( 5.01494171e-01,  4.34271915e-17, 7.03385115e-05,  0,  2, -2),\n",
+       "       (-7.52241257e-01, -1.77304965e-01, 3.02618725e-05,  1, -3,  3),\n",
+       "       (-2.50747086e-01, -1.77304965e-01, 4.12178889e-03,  1, -1,  1),\n",
+       "       ( 2.50747086e-01, -1.77304965e-01, 4.12178889e-03,  1,  1, -1),\n",
+       "       ( 7.52241257e-01, -1.77304965e-01, 3.02618725e-05,  1,  3, -3),\n",
+       "       (-5.01494171e-01, -3.54609929e-01, 4.53889481e-04,  2, -2,  2),\n",
+       "       ( 3.07076616e-17, -3.54609929e-01, 2.98183191e-02,  2,  0,  0),\n",
+       "       ( 5.01494171e-01, -3.54609929e-01, 4.53889481e-04,  2,  2, -2),\n",
+       "       (-2.50747086e-01, -5.31914894e-01, 1.14033830e-04,  3, -1,  1),\n",
+       "       ( 2.50747086e-01, -5.31914894e-01, 1.14033830e-04,  3,  1, -1),\n",
+       "       (-5.01494171e-01, -7.09219858e-01, 7.41930743e-06,  4, -2,  2),\n",
+       "       ( 6.14153231e-17, -7.09219858e-01, 1.61563211e-04,  4,  0,  0),\n",
+       "       ( 5.01494171e-01, -7.09219858e-01, 7.41930743e-06,  4,  2, -2)],\n",
+       "      dtype=[('qx', '<f8'), ('qy', '<f8'), ('intensity', '<f8'), ('h', '<i4'), ('k', '<i4'), ('l', '<i4')])"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dyn_bragg_peaks.data"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It is also possible to check the values of the calculated dynamical scattering factors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(-5.0, -1.0, -1.0): (0.00201757289249767+0.0004305498246690356j),\n",
+       " (-5.0, -1.0, 1.0): (0.0020175728924976704+0.00043054982466903533j),\n",
+       " (-5.0, 1.0, -1.0): (0.0020175728924976704+0.00043054982466903533j),\n",
+       " (-5.0, 1.0, 1.0): (0.0020175728924976704+0.0004305498246690351j),\n",
+       " (-4.0, -2.0, -2.0): (0.011895468279764962+0.0013792100394537593j),\n",
+       " (-4.0, -2.0, 0.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (-4.0, -2.0, 2.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (-4.0, 0.0, -2.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (-4.0, 0.0, 0.0): (0.01819633424049186+0.0019795641914175013j),\n",
+       " (-4.0, 0.0, 2.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (-4.0, 2.0, -2.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (-4.0, 2.0, 0.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (-4.0, 2.0, 2.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (-3.0, -3.0, -3.0): (0.00201757289249767+0.0004305498246690358j),\n",
+       " (-3.0, -3.0, -1.0): (0.003737104886272656+0.0006446750106240256j),\n",
+       " (-3.0, -3.0, 1.0): (0.003737104886272656+0.0006446750106240251j),\n",
+       " (-3.0, -3.0, 3.0): (0.002017572892497669+0.00043054982466903457j),\n",
+       " (-3.0, -1.0, -3.0): (0.003737104886272656+0.0006446750106240256j),\n",
+       " (-3.0, -1.0, -1.0): (0.008296467071262187+0.0009834275810407399j),\n",
+       " (-3.0, -1.0, 1.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (-3.0, -1.0, 3.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (-3.0, 1.0, -3.0): (0.003737104886272656+0.0006446750106240251j),\n",
+       " (-3.0, 1.0, -1.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (-3.0, 1.0, 1.0): (0.008296467071262185+0.0009834275810407384j),\n",
+       " (-3.0, 1.0, 3.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (-3.0, 3.0, -3.0): (0.002017572892497669+0.00043054982466903457j),\n",
+       " (-3.0, 3.0, -1.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (-3.0, 3.0, 1.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (-3.0, 3.0, 3.0): (0.002017572892497669+0.0004305498246690338j),\n",
+       " (-2.0, -4.0, -2.0): (0.011895468279764962+0.0013792100394537593j),\n",
+       " (-2.0, -4.0, 0.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (-2.0, -4.0, 2.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (-2.0, -2.0, -4.0): (0.011895468279764962+0.0013792100394537593j),\n",
+       " (-2.0, -2.0, -2.0): (0.024450662632080105+0.0023935721927523935j),\n",
+       " (-2.0, -2.0, 0.0): (0.0340072541399737+0.0029318044770577476j),\n",
+       " (-2.0, -2.0, 2.0): (0.024450662632080105+0.002393572192752388j),\n",
+       " (-2.0, -2.0, 4.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (-2.0, 0.0, -4.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (-2.0, 0.0, -2.0): (0.0340072541399737+0.0029318044770577476j),\n",
+       " (-2.0, 0.0, 0.0): (0.049619020307736995+0.0037018329915546612j),\n",
+       " (-2.0, 0.0, 2.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (-2.0, 0.0, 4.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (-2.0, 2.0, -4.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (-2.0, 2.0, -2.0): (0.024450662632080105+0.002393572192752388j),\n",
+       " (-2.0, 2.0, 0.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (-2.0, 2.0, 2.0): (0.024450662632080105+0.0023935721927523814j),\n",
+       " (-2.0, 2.0, 4.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (-2.0, 4.0, -2.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (-2.0, 4.0, 0.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (-2.0, 4.0, 2.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (-1.0, -5.0, -1.0): (0.00201757289249767+0.0004305498246690356j),\n",
+       " (-1.0, -5.0, 1.0): (0.0020175728924976704+0.00043054982466903533j),\n",
+       " (-1.0, -3.0, -3.0): (0.0037371048862726575+0.0006446750106240248j),\n",
+       " (-1.0, -3.0, -1.0): (0.008296467071262192+0.0009834275810407446j),\n",
+       " (-1.0, -3.0, 1.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (-1.0, -3.0, 3.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (-1.0, -1.0, -5.0): (0.00201757289249767+0.0004305498246690356j),\n",
+       " (-1.0, -1.0, -3.0): (0.008296467071262192+0.0009834275810407446j),\n",
+       " (-1.0, -1.0, -1.0): (0.015135112521336735+0.001548151937054946j),\n",
+       " (-1.0, -1.0, 1.0): (0.015135112521336735+0.001548151937054944j),\n",
+       " (-1.0, -1.0, 3.0): (0.008296467071262187+0.0009834275810407368j),\n",
+       " (-1.0, -1.0, 5.0): (0.002017572892497669+0.0004305498246690338j),\n",
+       " (-1.0, 1.0, -5.0): (0.0020175728924976704+0.00043054982466903533j),\n",
+       " (-1.0, 1.0, -3.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (-1.0, 1.0, -1.0): (0.015135112521336735+0.001548151937054944j),\n",
+       " (-1.0, 1.0, 1.0): (0.015135112521336735+0.001548151937054942j),\n",
+       " (-1.0, 1.0, 3.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (-1.0, 1.0, 5.0): (0.0020175728924976704+0.0004305498246690341j),\n",
+       " (-1.0, 3.0, -3.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (-1.0, 3.0, -1.0): (0.008296467071262185+0.0009834275810407375j),\n",
+       " (-1.0, 3.0, 1.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (-1.0, 3.0, 3.0): (0.003737104886272656+0.0006446750106240228j),\n",
+       " (-1.0, 5.0, -1.0): (0.002017572892497669+0.0004305498246690338j),\n",
+       " (-1.0, 5.0, 1.0): (0.002017572892497669+0.00043054982466903354j),\n",
+       " (0.0, -4.0, -2.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (0.0, -4.0, 0.0): (0.01819633424049186+0.0019795641914175013j),\n",
+       " (0.0, -4.0, 2.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (0.0, -2.0, -4.0): (0.01489576013862339+0.0016487988186157832j),\n",
+       " (0.0, -2.0, -2.0): (0.0340072541399737+0.0029318044770577476j),\n",
+       " (0.0, -2.0, 0.0): (0.049619020307736995+0.0037018329915546612j),\n",
+       " (0.0, -2.0, 2.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (0.0, -2.0, 4.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (0.0, 0.0, -4.0): (0.01819633424049186+0.0019795641914175013j),\n",
+       " (0.0, 0.0, -2.0): (0.049619020307736995+0.0037018329915546612j),\n",
+       " (0.0, 0.0, 0.0): (0.10823935029268598+0.007551932079682521j),\n",
+       " (0.0, 0.0, 2.0): (0.049619020307736995+0.003701832991554649j),\n",
+       " (0.0, 0.0, 4.0): (0.01819633424049186+0.0019795641914174926j),\n",
+       " (0.0, 2.0, -4.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (0.0, 2.0, -2.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (0.0, 2.0, 0.0): (0.049619020307736995+0.003701832991554649j),\n",
+       " (0.0, 2.0, 2.0): (0.0340072541399737+0.0029318044770577315j),\n",
+       " (0.0, 2.0, 4.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (0.0, 4.0, -2.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (0.0, 4.0, 0.0): (0.01819633424049186+0.0019795641914174926j),\n",
+       " (0.0, 4.0, 2.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (1.0, -5.0, -1.0): (0.002017572892497669+0.0004305498246690348j),\n",
+       " (1.0, -5.0, 1.0): (0.002017572892497669+0.00043054982466903457j),\n",
+       " (1.0, -3.0, -3.0): (0.003737104886272656+0.0006446750106240251j),\n",
+       " (1.0, -3.0, -1.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (1.0, -3.0, 1.0): (0.008296467071262185+0.0009834275810407384j),\n",
+       " (1.0, -3.0, 3.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (1.0, -1.0, -5.0): (0.0020175728924976704+0.00043054982466903533j),\n",
+       " (1.0, -1.0, -3.0): (0.008296467071262187+0.0009834275810407388j),\n",
+       " (1.0, -1.0, -1.0): (0.015135112521336735+0.001548151937054944j),\n",
+       " (1.0, -1.0, 1.0): (0.015135112521336735+0.001548151937054942j),\n",
+       " (1.0, -1.0, 3.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (1.0, -1.0, 5.0): (0.0020175728924976704+0.0004305498246690341j),\n",
+       " (1.0, 1.0, -5.0): (0.002017572892497669+0.00043054982466903457j),\n",
+       " (1.0, 1.0, -3.0): (0.008296467071262187+0.0009834275810407377j),\n",
+       " (1.0, 1.0, -1.0): (0.015135112521336735+0.001548151937054942j),\n",
+       " (1.0, 1.0, 1.0): (0.015135112521336735+0.0015481519370549404j),\n",
+       " (1.0, 1.0, 3.0): (0.008296467071262192+0.0009834275810407397j),\n",
+       " (1.0, 1.0, 5.0): (0.0020175728924976704+0.00043054982466903387j),\n",
+       " (1.0, 3.0, -3.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (1.0, 3.0, -1.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (1.0, 3.0, 1.0): (0.008296467071262192+0.0009834275810407397j),\n",
+       " (1.0, 3.0, 3.0): (0.0037371048862726575+0.0006446750106240216j),\n",
+       " (1.0, 5.0, -1.0): (0.0020175728924976704+0.0004305498246690341j),\n",
+       " (1.0, 5.0, 1.0): (0.0020175728924976704+0.00043054982466903387j),\n",
+       " (2.0, -4.0, -2.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (2.0, -4.0, 0.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (2.0, -4.0, 2.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (2.0, -2.0, -4.0): (0.011895468279764962+0.0013792100394537565j),\n",
+       " (2.0, -2.0, -2.0): (0.024450662632080105+0.002393572192752388j),\n",
+       " (2.0, -2.0, 0.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (2.0, -2.0, 2.0): (0.024450662632080105+0.0023935721927523814j),\n",
+       " (2.0, -2.0, 4.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (2.0, 0.0, -4.0): (0.01489576013862339+0.0016487988186157795j),\n",
+       " (2.0, 0.0, -2.0): (0.0340072541399737+0.0029318044770577398j),\n",
+       " (2.0, 0.0, 0.0): (0.049619020307736995+0.003701832991554649j),\n",
+       " (2.0, 0.0, 2.0): (0.0340072541399737+0.0029318044770577315j),\n",
+       " (2.0, 0.0, 4.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (2.0, 2.0, -4.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (2.0, 2.0, -2.0): (0.024450662632080105+0.0023935721927523814j),\n",
+       " (2.0, 2.0, 0.0): (0.0340072541399737+0.0029318044770577315j),\n",
+       " (2.0, 2.0, 2.0): (0.024450662632080105+0.0023935721927523758j),\n",
+       " (2.0, 2.0, 4.0): (0.011895468279764962+0.0013792100394537476j),\n",
+       " (2.0, 4.0, -2.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (2.0, 4.0, 0.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (2.0, 4.0, 2.0): (0.011895468279764962+0.0013792100394537476j),\n",
+       " (3.0, -3.0, -3.0): (0.002017572892497669+0.00043054982466903457j),\n",
+       " (3.0, -3.0, -1.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (3.0, -3.0, 1.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (3.0, -3.0, 3.0): (0.002017572892497669+0.0004305498246690338j),\n",
+       " (3.0, -1.0, -3.0): (0.003737104886272656+0.0006446750106240242j),\n",
+       " (3.0, -1.0, -1.0): (0.008296467071262185+0.0009834275810407375j),\n",
+       " (3.0, -1.0, 1.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (3.0, -1.0, 3.0): (0.003737104886272656+0.0006446750106240228j),\n",
+       " (3.0, 1.0, -3.0): (0.003737104886272656+0.0006446750106240237j),\n",
+       " (3.0, 1.0, -1.0): (0.008296467071262187+0.0009834275810407358j),\n",
+       " (3.0, 1.0, 1.0): (0.008296467071262187+0.0009834275810407349j),\n",
+       " (3.0, 1.0, 3.0): (0.003737104886272656+0.0006446750106240223j),\n",
+       " (3.0, 3.0, -3.0): (0.002017572892497669+0.0004305498246690338j),\n",
+       " (3.0, 3.0, -1.0): (0.003737104886272656+0.0006446750106240228j),\n",
+       " (3.0, 3.0, 1.0): (0.003737104886272656+0.0006446750106240223j),\n",
+       " (3.0, 3.0, 3.0): (0.0020175728924976704+0.00043054982466903365j),\n",
+       " (4.0, -2.0, -2.0): (0.011895468279764962+0.0013792100394537535j),\n",
+       " (4.0, -2.0, 0.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (4.0, -2.0, 2.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (4.0, 0.0, -2.0): (0.01489576013862339+0.0016487988186157758j),\n",
+       " (4.0, 0.0, 0.0): (0.01819633424049186+0.0019795641914174926j),\n",
+       " (4.0, 0.0, 2.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (4.0, 2.0, -2.0): (0.011895468279764962+0.0013792100394537507j),\n",
+       " (4.0, 2.0, 0.0): (0.01489576013862339+0.001648798818615772j),\n",
+       " (4.0, 2.0, 2.0): (0.011895468279764962+0.0013792100394537476j),\n",
+       " (5.0, -1.0, -1.0): (0.0020175728924976704+0.00043054982466903436j),\n",
+       " (5.0, -1.0, 1.0): (0.0020175728924976704+0.0004305498246690341j),\n",
+       " (5.0, 1.0, -1.0): (0.0020175728924976704+0.0004305498246690341j),\n",
+       " (5.0, 1.0, 1.0): (0.0020175728924976704+0.00043054982466903387j)}"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "structure.Ug_dict"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.8"
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+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}