pybamm-team#573 setup of the files needed for parametrisation

input/parameters/lithium-ion/electrolyte_conductivity_Petibon2016.py

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+import autograd.numpy as np
+
+
+def electrolyte_conductivity_Petibon2016(c_e, T, T_inf, E_k_e, R_g):
+    """
+    Conductivity of LiPF6 in EC:EMC as a function of ion concentration. The original
+    data and fit are from [1].
+
+    References
+    ----------
+    .. [1] R Petibon et al. Electrolyte System for High Voltage Li-Ion Cells. Journal
+    of the Electrochemical Society 163 (2016): A2571-A2578.
+
+    Parameters
+    ----------
+    c_e: :class: `numpy.Array`
+        Dimensional electrolyte concentration
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_k_e: double
+        Electrolyte conductivity activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    :`numpy.Array`
+        Electrolyte conductivity
+    """
+
+    sigma_e = 0.95 * c_e / 1000
+
+    return sigma_e

input/parameters/lithium-ion/electrolyte_diffusivity_Stewart2008.py

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+import autograd.numpy as np
+
+
+def electrolyte_diffusivity_Stewart2008(c_e, T, T_inf, E_D_e, R_g):
+    """
+    Diffusivity of LiPF6 in EC:DEC as a function of ion concentration. The original
+    data and fit are from [1].
+
+    References
+    ----------
+    .. [1] S G Stewart and J Newman. The Use of UV/vis Absorption to Measure Diffusion
+    Coefficients in LiPF6 Electrolytic Solutions. Journal of The Electrochemical
+    Society 155 (2008): F13-F16.
+
+    Parameters
+    ----------
+    c_e: :class: `numpy.Array`
+        Dimensional electrolyte concentration
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_D_e: double
+        Electrolyte diffusion activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    :`numpy.Array`
+        Electrolyte diffusivity
+    """
+
+    D_c_e = 2.582E-9 * np.exp(-2.85E-3 * c_e)
+
+    return D_c_e

input/parameters/lithium-ion/graphite_LGM50_diffusivity_CC3.py

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+import autograd.numpy as np
+
+
+def graphite_LGM50_diffusivity_CC3(sto, T, T_inf, E_D_s, R_g):
+    """
+      Graphite MCMB 2528 diffusivity as a function of stochiometry, in this case the
+      diffusivity is taken to be a constant. The value is taken from Dualfoil [1].
+
+      References
+      ----------
+      .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+
+      Parameters
+      ----------
+      sto: :class: `numpy.Array`
+         Electrode stochiometry
+      T: :class: `numpy.Array`
+         Dimensional temperature
+      T_inf: double
+         Reference temperature
+      E_D_s: double
+         Solid diffusion activation energy
+      R_g: double
+         The ideal gas constant
+
+      Returns
+      -------
+      : double
+         Solid diffusivity
+   """
+
+    D_ref = 3.9 * 10 ** (-14)
+    arrhenius = np.exp(E_D_s / R_g * (1 / T_inf - 1 / T))
+
+    correct_shape = 0 * sto
+
+    return D_ref * arrhenius + correct_shape
+

input/parameters/lithium-ion/graphite_LGM50_ocp_CC3.py

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+import autograd.numpy as np
+
+
+def graphite_LGM50_ocp_CC3(sto):
+    """
+       Graphite MCMB 2528 Open Circuit Potential (OCP) as a function of the
+       stochiometry. The fit is taken from Dualfoil [1]. Dualfoil states that the data
+       was measured by Chris Bogatu at Telcordia and PolyStor materials, 2000. However,
+       we could not find any other records of this measurment.
+
+       References
+       ----------
+       .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+       """
+
+    u_eq = (
+        0.194
+        + 1.5 * np.exp(-120.0 * sto)
+        + 0.0351 * np.tanh((sto - 0.286) / 0.083)
+        - 0.0045 * np.tanh((sto - 0.849) / 0.119)
+        - 0.035 * np.tanh((sto - 0.9233) / 0.05)
+        - 0.0147 * np.tanh((sto - 0.5) / 0.034)
+        - 0.102 * np.tanh((sto - 0.194) / 0.142)
+        - 0.022 * np.tanh((sto - 0.9) / 0.0164)
+        - 0.011 * np.tanh((sto - 0.124) / 0.0226)
+        + 0.0155 * np.tanh((sto - 0.105) / 0.029)
+    )
+
+    return u_eq

input/parameters/lithium-ion/nmc_LGM50_diffusivity_CC3.py

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+import autograd.numpy as np
+
+
+def nmc_LGM50_diffusivity_CC3(sto, T, T_inf, E_D_s, R_g):
+    """
+       LiCo2 diffusivity as a function of stochiometry, in this case the
+       diffusivity is taken to be a constant. The value is taken from Dualfoil [1].
+
+       References
+       ----------
+       .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+
+       Parameters
+       ----------
+       sto: :class: `numpy.Array`
+         Electrode stochiometry
+       T: :class: `numpy.Array`
+          Dimensional temperature
+       T_inf: double
+          Reference temperature
+       E_D_s: double
+          Solid diffusion activation energy
+       R_g: double
+          The ideal gas constant
+
+       Returns
+       -------
+       : double
+          Solid diffusivity
+    """
+
+    D_ref = 1 * 10 ** (-13)
+    arrhenius = np.exp(E_D_s / R_g * (1 / T_inf - 1 / T))
+
+    correct_shape = 0 * sto
+
+    return D_ref * arrhenius + correct_shape

input/parameters/lithium-ion/nmc_LGM50_ocp_CC3.py

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+import autograd.numpy as np
+
+
+def nmc_LGM50_ocp_CC3(sto):
+    """
+        Lithium Cobalt Oxide (LiCO2) Open Circuit Potential (OCP) as a a function of the
+        stochiometry. The fit is taken from Dualfoil [1]. Dualfoil states that the data
+        was measured by Oscar Garcia 2001 using Quallion electrodes for 0.5 < sto < 0.99
+        and by Marc Doyle for sto<0.4 (for unstated electrodes). We could not find any
+        other records of the Garcia measurements. Doyles fits can be found in his
+        thesis [2] but we could not find any other record of his measurments.
+
+        References
+        ----------
+        .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+        .. [2] CM Doyle. Design and simulation of lithium rechargeable batteries,
+               1995.
+
+          Parameters
+          ----------
+          sto: double
+               Stochiometry of material (li-fraction)
+
+    """
+
+    stretch = 1.062
+    sto = stretch * sto
+
+    u_eq = (
+        2.16216
+        + 0.07645 * np.tanh(30.834 - 54.4806 * sto)
+        + 2.1581 * np.tanh(52.294 - 50.294 * sto)
+        - 0.14169 * np.tanh(11.0923 - 19.8543 * sto)
+        + 0.2051 * np.tanh(1.4684 - 5.4888 * sto)
+        + 0.2531 * np.tanh((-sto + 0.56478) / 0.1316)
+        - 0.02167 * np.tanh((sto - 0.525) / 0.006)
+    )
+
+    return u_eq

results/LGM50/DFN.py

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+import pybamm
+import numpy as np
+
+# load model
+model = pybamm.lithium_ion.DFN()
+
+# create geometry
+geometry = model.default_geometry
+
+# load parameter values and process model and geometry
+param = pybamm.ParameterValues("input/parameters/lithium-ion/LGM50_parameters.csv")
+param.update({
+    "Electrolyte conductivity": "electrolyte_conductivity_Petibon2016.py",
+    "Electrolyte diffusivity": "electrolyte_diffusivity_Stewart2008.py",
+    "Negative electrode OCV": "graphite_LGM50_ocp_CC3.py",
+    "Positive electrode OCV": "nmc_LGM50_ocp_CC3.py",
+    "Negative electrode diffusivity": "graphite_LGM50_diffusivity_CC3.py",
+    "Positive electrode diffusivity": "nmc_LGM50_diffusivity_CC3.py",
+    "Negative electrode OCV entropic change": "graphite_entropic_change_Moura.py",
+    "Positive electrode OCV entropic change": "lico2_entropic_change_Moura.py",
+    "Negative electrode reaction rate": "graphite_electrolyte_reaction_rate.py",
+    "Positive electrode reaction rate": "lico2_electrolyte_reaction_rate.py",
+    "Typical current [A]": 5,
+    "Current function": pybamm.GetConstantCurrent(current=5)
+})
+param.process_model(model)
+param.process_geometry(geometry)
+
+# set mesh
+mesh = pybamm.Mesh(geometry, model.default_submesh_types, model.default_var_pts)
+
+# discretise model
+disc = pybamm.Discretisation(mesh, model.default_spatial_methods)
+disc.process_model(model)
+
+# solve model
+t_eval = np.linspace(0, 0.2, 100)
+solution = model.default_solver.solve(model, t_eval)
+
+# plot
+plot = pybamm.QuickPlot(model, mesh, solution)
+plot.dynamic_plot()