Partially reversible lithium plating

pybamm/CITATIONS.txt

@@ -296,6 +296,20 @@
   journal = {Journal of The Electrochemical Society}
 }
 
+@article{OKane2022,
+  author ="O{'}Kane, Simon E. J. and Ai, Weilong and Madabattula, Ganesh and Alonso-Alvarez, Diego and Timms, Robert and Sulzer, Valentin and Edge, Jacqueline Sophie and Wu, Billy and Offer, Gregory J. and Marinescu, Monica",
+  title  ="Lithium-ion battery degradation: how to model it",
+  journal  ="Phys. Chem. Chem. Phys.",
+  year  ="2022",
+  volume  ="24",
+  issue  ="13",
+  pages  ="7909-7922",
+  publisher  ="The Royal Society of Chemistry",
+  doi  ="10.1039/D2CP00417H",
+  url  ="http://dx.doi.org/10.1039/D2CP00417H",
+}
+
+
 @article{ORegan2021,
   author = {O'Regan, Kieran and Brosa Planella, Ferran and Widanage, W. Dhammika and Kendrick, Emma},
   title = {{Thermal-electrochemical parametrisation of a lithium-ion battery: mapping Li concentration and temperature dependencies}},

pybamm/input/parameters/lithium_ion/lithium_platings/okane2020_Li_plating/parameters.csv

@@ -8,3 +8,4 @@ Exchange-current density for plating [A.m-2],[function]plating_exchange_current_
 Exchange-current density for stripping [A.m-2],[function]stripping_exchange_current_density_OKane2020,,
 Initial plated lithium concentration [mol.m-3],0.00E+00,,
 Typical plated lithium concentration [mol.m-3],1000,1 molar,
+Lithium plating transfer coefficient,0.5,,

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/README.md

@@ -0,0 +1,7 @@
+# Lithium plating parameters
+
+Some example parameters for lithium plating from the paper:
+
+> O’Kane, S. E. J., Ai, W., Madabattula, G., Alonso-Alvarez, D., Timms, R, Sulzer, V., Edge, J. S., Wu, B., Offer, G. J., & Marinescu, M. (2022) Lithium-ion battery degradation: how to model it. Physical Chemistry: Chemical Physics, accepted.
+
+Note: this parameter set does not claim to be representative of the true parameter values. These are merely the parameter values that were used in the referenced papers.

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/SEI_limited_dead_lithium_OKane2022.py

@@ -0,0 +1,30 @@
+from pybamm import Parameter
+
+
+def SEI_limited_dead_lithium_OKane2022(L_sei):
+    """
+    Decay rate for dead lithium formation [s-1].
+    References
+    ----------
+    .. [1] Simon E. J. O'Kane, Weilong Ai, Ganesh Madabattula, Diega Alonso-Alvarez,
+    Robert Timms, Valentin Sulzer, Jaqueline Sophie Edge, Billy Wu, Gregory J. Offer
+    and Monica Marinescu. "Lithium-ion battery degradation: how to model it."
+    Physical Chemistry: Chemical Physics 24, no. 13 (2022): 7909-7922.
+    Parameters
+    ----------
+    L_sei : :class:`pybamm.Symbol`
+        Total SEI thickness [m]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Dead lithium decay rate [s-1]
+    """
+
+    gamma_0 = Parameter("Dead lithium decay constant [s-1]")
+    L_inner_0 = Parameter("Initial inner SEI thickness [m]")
+    L_outer_0 = Parameter("Initial outer SEI thickness [m]")
+    L_sei_0 = L_inner_0 + L_outer_0
+
+    gamma = gamma_0 * L_sei_0 / L_sei
+
+    return gamma

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/parameters.csv

@@ -0,0 +1,13 @@
+Name [units],Value,Reference,Notes
+,,,
+,,,
+# Lithium plating parameters,,,
+Lithium metal partial molar volume [m3.mol-1],1.30E-05,Yang2017,
+Lithium plating kinetic rate constant [m.s-1],1E-9,,
+Exchange-current density for plating [A.m-2],[function]plating_exchange_current_density_OKane2020,,
+Exchange-current density for stripping [A.m-2],[function]stripping_exchange_current_density_OKane2020,,
+Initial plated lithium concentration [mol.m-3],0.00E+00,,
+Typical plated lithium concentration [mol.m-3],1000,1 molar,
+Lithium plating transfer coefficient,0.65,,
+Dead lithium decay constant [s-1],1E-6,,
+Dead lithium decay rate [s-1],[function]SEI_limited_dead_lithium_OKane2022,,

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/plating_exchange_current_density_OKane2020.py

@@ -0,0 +1,29 @@
+from pybamm import constants, Parameter
+
+
+def plating_exchange_current_density_OKane2020(c_e, c_Li, T):
+    """
+    Exchange-current density for Li plating reaction [A.m-2].
+    References
+    ----------
+    .. [1] O’Kane, Simon EJ, Ian D. Campbell, Mohamed WJ Marzook, Gregory J. Offer, and
+    Monica Marinescu. "Physical origin of the differential voltage minimum associated
+    with lithium plating in Li-ion batteries." Journal of The Electrochemical Society
+    167, no. 9 (2020): 090540.
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_Li : :class:`pybamm.Symbol`
+        Plated lithium concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+
+    k_plating = Parameter("Lithium plating kinetic rate constant [m.s-1]")
+
+    return constants.F * k_plating * c_e

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/stripping_exchange_current_density_OKane2020.py

@@ -0,0 +1,35 @@
+from pybamm import constants, Parameter
+
+
+def stripping_exchange_current_density_OKane2020(c_e, c_Li, T):
+    """
+    Exchange-current density for Li stripping reaction [A.m-2].
+
+    References
+    ----------
+
+    .. [1] O’Kane, Simon EJ, Ian D. Campbell, Mohamed WJ Marzook, Gregory J. Offer, and
+    Monica Marinescu. "Physical origin of the differential voltage minimum associated
+    with lithium plating in Li-ion batteries." Journal of The Electrochemical Society
+    167, no. 9 (2020): 090540.
+
+    Parameters
+    ----------
+
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_Li : :class:`pybamm.Symbol`
+        Plated lithium concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+
+    k_plating = Parameter("Lithium plating kinetic rate constant [m.s-1]")
+
+    return constants.F * k_plating * c_Li

pybamm/input/parameters/lithium_ion/lithium_platings/yang2017_Li_plating/parameters.csv

@@ -5,4 +5,5 @@ Name [units],Value,Reference,Notes
 Lithium metal partial molar volume [m3.mol-1],1.30E-05,Yang2017,6.94e-3/534
 Exchange-current density for plating [A.m-2],0.001,,
 Initial plated lithium concentration [mol.m-3],0.00E+00,,
-Typical plated lithium concentration [mol.m-3],1000,1 molar,
+Typical plated lithium concentration [mol.m-3],1000,1 molar,
+Lithium plating transfer coefficient,0.7,,

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Chen2020/graphite_LGM50_ocp_Chen2020.py

@@ -3,8 +3,9 @@
 
 def graphite_LGM50_ocp_Chen2020(sto):
     """
-    LG M50 graphite open circuit potential as a function of stochiometry, fit taken
-    from [1].
+    LG M50 Graphite open-circuit potential as a function of stochiometry. The fit is
+    taken from [1] with an extra term added by Simon O'Kane to capture behaviour in
+    the high stoichiometry range.
 
     References
     ----------

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Chen2020_plating/graphite_LGM50_ocp_Chen2020.py

@@ -0,0 +1,37 @@
+from pybamm import exp, tanh
+
+
+def graphite_LGM50_ocp_Chen2020(sto):
+    """
+    LG M50 Graphite open-circuit potential as a function of stochiometry. The fit is
+    taken from [1] with an extra term added by Simon O'Kane to capture behaviour in
+    the high stoichiometry range.
+
+    References
+    ----------
+    .. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
+    Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
+    Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
+    Electrochemical Society 167 (2020): 080534.
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Open circuit potential
+    """
+
+    u_eq = (
+        1.9793 * exp(-39.3631 * sto)
+        + 0.15561
+        - 0.0909 * tanh(29.8538 * (sto - 0.1234))
+        - 0.04478 * tanh(14.9159 * (sto - 0.2769))
+        - 0.0205 * tanh(30.4444 * (sto - 0.6103))
+        - 0.09259 * tanh(17.08 * (sto - 1))
+    )
+
+    return u_eq

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Chen2020_plating/parameters.csv

@@ -5,7 +5,7 @@ Name [units],Value,Reference,Notes
 Negative electrode conductivity [S.m-1],215,Chen 2020,graphite
 Maximum concentration in negative electrode [mol.m-3],33133,Chen 2020,tuned for 1C
 Negative electrode diffusivity [m2.s-1],[function]graphite_LGM50_diffusivity_Chen2020,Chen 2020,tuned for 1C
-Negative electrode OCP [V],[data]graphite_LGM50_ocp_Chen2020,Chen 2020,
+Negative electrode OCP [V],[function]graphite_LGM50_ocp_Chen2020,Chen 2020,
 ,,,
 # Microstructure,,,
 Negative electrode porosity,0.25,Chen 2020,

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Ecker2015/graphite_electrolyte_exchange_current_density_Ecker2015.py

@@ -33,7 +33,7 @@ def graphite_electrolyte_exchange_current_density_Ecker2015(c_e, c_s_surf, T):
         Exchange-current density [A.m-2]
     """
 
-    k_ref = 1.995 * 1e-10
+    k_ref = 1.11 * 1e-10
 
     # multiply by Faraday's constant to get correct units
     m_ref = constants.F * k_ref  # (A/m2)(mol/m3)**1.5 - includes ref concentrations

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_ORegan2021/graphite_LGM50_ocp_Chen2020.py

@@ -4,7 +4,8 @@
 def graphite_LGM50_ocp_Chen2020(sto):
     """
     LG M50 Graphite open-circuit potential as a function of stochiometry. The fit is
-    taken from [1].
+    taken from [1] with an extra term added by Simon O'Kane to capture behaviour in
+    the high stoichiometry range.
 
     References
     ----------

pybamm/input/parameters/lithium_ion/positive_electrodes/LiNiCoO2_Ecker2015/nco_electrolyte_exchange_current_density_Ecker2015.py

@@ -33,7 +33,7 @@ def nco_electrolyte_exchange_current_density_Ecker2015(c_e, c_s_surf, T):
         Exchange-current density [A.m-2]
     """
 
-    k_ref = 5.196e-11
+    k_ref = 3.01e-11
 
     # multiply by Faraday's constant to get correct units
     m_ref = constants.F * k_ref  # (A/m2)(mol/m3)**1.5 - includes ref concentrations

pybamm/input/parameters/lithium_ion/positive_electrodes/LiNiCoO2_Ecker2015/nco_ocp_Ecker2015_function.py

@@ -26,6 +26,7 @@ def nco_ocp_Ecker2015_function(sto):
 
     # LiNiCo from Ecker, Kabitz, Laresgoiti et al.
     # Analytical fit (WebPlotDigitizer + gnuplot)
+    # Parameter m modified by Simon O'Kane to improve fit
     a = -2.35211
     c = 0.0747061
     d = 31.886

pybamm/models/full_battery_models/base_battery_model.py

@@ -67,7 +67,7 @@ class BatteryModelOptions(pybamm.FuzzyDict):
                 Can be "full" (default), "constant", or "current-driven".
             * "lithium plating" : str
                 Sets the model for lithium plating. Can be "none" (default),
-                "reversible" or "irreversible".
+                "reversible", "partially reversible", or "irreversible".
             * "loss of active material" : str
                 Sets the model for loss of active material. Can be "none" (default),
                 "stress-driven", "reaction-driven", or "stress and reaction-driven".
@@ -198,7 +198,12 @@ def __init__(self, extra_options):
                 "Marcus-Hush-Chidsey",
             ],
             "interface utilisation": ["full", "constant", "current-driven"],
-            "lithium plating": ["none", "reversible", "irreversible"],
+            "lithium plating": [
+                "none",
+                "reversible",
+                "partially reversible",
+                "irreversible",
+            ],
             "lithium plating porosity change": ["false", "true"],
             "loss of active material": [
                 "none",
@@ -300,6 +305,15 @@ def __init__(self, extra_options):
         # The "stress-induced diffusion" option will still be overridden by
         # extra_options if provided
 
+        # Change default SEI model based on which lithium plating option is provided
+        # return "none" if option not given
+        plating_option = extra_options.get("lithium plating", "none")
+        if plating_option == "partially reversible":
+            default_options["SEI"] = "constant"
+        else:
+            default_options["SEI"] = "none"
+        # The "SEI" option will still be overridden by extra_options if provided
+
         options = pybamm.FuzzyDict(default_options)
         # any extra options overwrite the default options
         for name, opt in extra_options.items():

pybamm/models/submodels/interface/lithium_plating/base_plating.py

@@ -19,7 +19,10 @@ class BasePlating(BaseInterface):
     .. [1] SEJ O'Kane, ID Campbell, MWJ Marzook, GJ Offer and M Marinescu. "Physical
            Origin of the Differential Voltage Minimum Associated with Li Plating in
            Lithium-Ion Batteries". Journal of The Electrochemical Society,
-           167:090540, 2019
+           167:090540, 2020
+    .. [2] SEJ O'Kane, W Ai, G Madabattula, D Alonso-Alvarez, R Timms, V Sulzer,
+           JS Edge, B Wu, GJ Offer and M Marinescu. "Lithium-ion battery degradation:
+           how to model it". Physical Chemistry: Chemical Physics, 24:7909, 2022
 
     **Extends:** :class:`pybamm.interface.BaseInterface`
     """
@@ -53,7 +56,7 @@ def get_coupled_variables(self, variables):
 
         return variables
 
-    def _get_standard_concentration_variables(self, c_plated_Li):
+    def _get_standard_concentration_variables(self, c_plated_Li, c_dead_Li):
         """
         A private function to obtain the standard variables which
         can be derived from the local plated lithium concentration.
@@ -82,20 +85,32 @@ def _get_standard_concentration_variables(self, c_plated_Li):
         L_plated_Li_av = pybamm.x_average(L_plated_Li)
         Q_plated_Li = c_plated_Li_av * param.n.L * param.L_y * param.L_z
 
+        c_dead_Li_av = pybamm.x_average(c_dead_Li)
+        L_dead_Li = c_dead_Li  # dead Li "thickness", required by porosity submodel
+        L_dead_Li_av = pybamm.x_average(L_dead_Li)
+        Q_dead_Li = c_dead_Li_av * param.n.L * param.L_y * param.L_z
+
         variables = {
             "Lithium plating concentration": c_plated_Li,
             "Lithium plating concentration [mol.m-3]": c_plated_Li * c_scale,
             "X-averaged lithium plating concentration": c_plated_Li_av,
             "X-averaged lithium plating concentration"
             " [mol.m-3]": c_plated_Li_av * c_scale,
+            "Dead lithium concentration": c_dead_Li,
+            "Dead lithium concentration [mol.m-3]": c_dead_Li * c_scale,
+            "X-averaged dead lithium concentration": c_dead_Li_av,
+            "X-averaged dead lithium concentration"
+            " [mol.m-3]": c_dead_Li_av * c_scale,
             "Lithium plating thickness": L_plated_Li,
             "Lithium plating thickness [m]": L_plated_Li * L_scale,
             "X-averaged lithium plating thickness [m]": L_plated_Li_av * L_scale,
-            "Loss of lithium to lithium plating [mol]": Q_plated_Li * c_scale,
-            "Loss of capacity to lithium plating [A.h]": Q_plated_Li
-            * c_scale
-            * param.F
-            / 3600,
+            "Dead lithium thickness": L_dead_Li,
+            "Dead lithium thickness [m]": L_dead_Li * L_scale,
+            "X-averaged dead lithium thickness [m]": L_dead_Li_av * L_scale,
+            "Loss of lithium to lithium plating [mol]": (Q_plated_Li + Q_dead_Li)
+            * c_scale,
+            "Loss of capacity to lithium plating [A.h]":
+            (Q_plated_Li + Q_dead_Li) * c_scale * param.F / 3600,
         }
 
         return variables

pybamm/models/submodels/interface/lithium_plating/no_plating.py

@@ -25,7 +25,7 @@ def get_fundamental_variables(self):
         zero = pybamm.FullBroadcast(
             pybamm.Scalar(0), "negative electrode", "current collector"
         )
-        variables = self._get_standard_concentration_variables(zero)
+        variables = self._get_standard_concentration_variables(zero, zero)
         variables.update(self._get_standard_overpotential_variables(zero))
         variables.update(self._get_standard_reaction_variables(zero))
         return variables