SEI on cracks

CHANGELOG.md

@@ -5,6 +5,9 @@
 
 -   Moved general code about submodels to `BaseModel` instead of `BaseBatteryModel`, making it easier to build custom models from submodels. ([#2169](https://github.com/pybamm-team/PyBaMM/pull/2169))
 -   Events can now be plotted as a regular variable (under the name "Event: event_name", e.g. "Event: Minimum voltage [V]") ([#2158](https://github.com/pybamm-team/PyBaMM/pull/2158))
+-   Added SEI growth on cracks ([#2104](https://github.com/pybamm-team/PyBaMM/pull/2104))
+-   Added Arrhenius temperature dependence of SEI growth ([#2104](https://github.com/pybamm-team/PyBaMM/pull/2104))
+-   The "Inner SEI reaction proportion" parameter actually gets used now ([#2104](https://github.com/pybamm-team/PyBaMM/pull/2104))
 
 ## Optimizations
 
@@ -23,6 +26,7 @@
 ## Breaking changes
 
 -   Exchange-current density functions (and some other functions) now take an additional argument, the maximum particle concentration for that phase ([#2134](https://github.com/pybamm-team/PyBaMM/pull/2134))
+-   Loss of lithium to SEI on cracks is now a degradation variable, so setting a particle mechanics submodel is now compulsory (NoMechanics will suffice)
 
 # [v22.6](https://github.com/pybamm-team/PyBaMM/tree/v22.6) - 2022-06-30
 

examples/notebooks/models/compare-ecker-data.ipynb

@@ -262,7 +262,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.0"
+   "version": "3.8.10"
   },
   "toc": {
    "base_numbering": 1,

examples/notebooks/models/using-submodels.ipynb

@@ -469,7 +469,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We don't want any SEI formation or lithium plating in this model"
+    "We don't want any particle mechanics, SEI formation or lithium plating in this model"
    ]
   },
   {
@@ -478,7 +478,14 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "model.submodels[\n",
+    "    \"Negative particle mechanics\"\n",
+    "] = pybamm.particle_mechanics.NoMechanics(model.param, \"Negative\")\n",
+    "model.submodels[\n",
+    "    \"Positive particle mechanics\"\n",
+    "] = pybamm.particle_mechanics.NoMechanics(model.param, \"Positive\")\n",
     "model.submodels[\"sei\"] = pybamm.sei.NoSEI(model.param)\n",
+    "model.submodels[\"sei on cracks\"] = pybamm.sei.NoSEI(model.param, cracks=True)\n",
     "model.submodels[\"lithium plating\"] = pybamm.lithium_plating.NoPlating(model.param)"
    ]
   },
@@ -603,7 +610,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.8.12 ('conda_jl')",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -617,7 +624,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.12"
+   "version": "3.8.10"
   },
   "toc": {
    "base_numbering": 1,

examples/scripts/custom_model.py

@@ -86,7 +86,14 @@
 ] = pybamm.electrolyte_conductivity.surface_potential_form.Explicit(
     model.param, "Positive"
 )
+model.submodels[
+    "Negative particle mechanics"
+] = pybamm.particle_mechanics.NoMechanics(model.param, "Negative")
+model.submodels[
+    "Positive particle mechanics"
+] = pybamm.particle_mechanics.NoMechanics(model.param, "Positive")
 model.submodels["sei"] = pybamm.sei.NoSEI(model.param)
+model.submodels["sei on cracks"] = pybamm.sei.NoSEI(model.param, cracks=True)
 model.submodels["lithium plating"] = pybamm.lithium_plating.NoPlating(model.param)
 
 # build model

pybamm/input/parameters/lithium_ion/cells/LGM50_Chen2020/parameters.csv

@@ -11,6 +11,7 @@ Electrode height [m],6.5E-2,Chen 2020,
 Electrode width [m],1.58,Chen 2020,accounts for both sides of unwound electrode (double-sided coating)
 Cell cooling surface area [m2],5.31E-3,Chen 2020,cylindrical
 Cell volume [m3],2.42E-5,Chen 2020,cylindrical
+Cell thermal expansion coefficient [m.K-1],1.1E-6,Ai2020,
 ,,,
 # Current collector properties ,,,
 Negative current collector conductivity [S.m-1],58411000,CRC Handbook,copper

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Chen2020_plating/graphite_cracking_rate_Ai2020.py

@@ -0,0 +1,35 @@
+from pybamm import Parameter, constants, exp
+
+
+def graphite_cracking_rate_Ai2020(T_dim):
+    """
+    graphite particle cracking rate as a function of temperature [1, 2].
+
+    References
+    ----------
+     .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+     Battery cycle life prediction with coupled chemical degradation and fatigue
+     mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    Parameters
+    ----------
+    T_dim: :class:`pybamm.Symbol`
+        temperature, [K]
+
+    Returns
+    -------
+    k_cr: :class:`pybamm.Symbol`
+        cracking rate, [m/(Pa.m0.5)^m_cr]
+        where m_cr is another Paris' law constant
+    """
+    k_cr = 3.9e-20
+    T_ref = Parameter("Reference temperature [K]")
+    Eac_cr = Parameter(
+        "Negative electrode activation energy for cracking rate [J.mol-1]"
+    )
+    arrhenius = exp(Eac_cr / constants.R * (1 / T_dim - 1 / T_ref))
+    return k_cr * arrhenius

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_Chen2020_plating/graphite_volume_change_Ai2020.py

@@ -0,0 +1,47 @@
+def graphite_volume_change_Ai2020(sto, c_s_max):
+    """
+    Graphite particle volume change as a function of stochiometry [1, 2].
+
+    References
+    ----------
+     .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016).
+     A new method to model the thickness change of a commercial pouch cell
+     during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry, dimensionless
+        should be R-averaged particle concentration
+    Returns
+    -------
+    t_change:class:`pybamm.Symbol`
+        volume change, dimensionless, normalised by particle volume
+    """
+    p1 = 145.907
+    p2 = -681.229
+    p3 = 1334.442
+    p4 = -1415.710
+    p5 = 873.906
+    p6 = -312.528
+    p7 = 60.641
+    p8 = -5.706
+    p9 = 0.386
+    p10 = -4.966e-05
+    t_change = (
+        p1 * sto ** 9
+        + p2 * sto ** 8
+        + p3 * sto ** 7
+        + p4 * sto ** 6
+        + p5 * sto ** 5
+        + p6 * sto ** 4
+        + p7 * sto ** 3
+        + p8 * sto ** 2
+        + p9 * sto
+        + p10
+    )
+    return t_change

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

@@ -29,6 +29,24 @@ Negative electrode specific heat capacity [J.kg-1.K-1],700,default,
 Negative electrode thermal conductivity [W.m-1.K-1],1.7,default,
 Negative electrode OCP entropic change [V.K-1],0,,
 ,,,
-,,,
-,,,
+# Mechanical properties,,,
+Negative electrode Poisson's ratio,0.3,,
+Negative electrode Young's modulus [Pa],15e9,,
+Negative electrode reference concentration for free of deformation [mol.m-3],0,,
+Negative electrode partial molar volume [m3.mol-1],3.1e-6,,
+Negative electrode volume change,[function]graphite_volume_change_Ai2020,Ai2020,
+,,,
+# Crack model,,,
+Negative electrode initial crack length [m],20e-9,,
+Negative electrode initial crack width [m],15e-9,,
+Negative electrode number of cracks per unit area [m-2],3.18e15,,
+Negative electrode Paris' law constant b,1.12,,
+Negative electrode Paris' law constant m,2.2,,
+Negative electrode cracking rate,[function]graphite_cracking_rate_Ai2020,Ai2020,
+Negative electrode activation energy for cracking rate [J.mol-1],0,,
+,,,
+# Loss of active materials (LAM) model,,,
+Negative electrode LAM constant proportional term [s-1],2.7778E-7,0.001/3600,
+Negative electrode LAM constant exponential term,2,,
+Negative electrode critical stress [Pa],60e6,,
 ,,,

pybamm/input/parameters/lithium_ion/positive_electrodes/nmc_OKane2022/README.md

@@ -0,0 +1,7 @@
+# NMC 811 positive electrode parameters
+
+Parameters for an LG M50 NMC 811 positive electrode, from the paper
+
+> 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."](https://iopscience.iop.org/article/10.1149/1945-7111/ab9050) Journal of the Electrochemical Society 167 (2020): 080534
+
+and references therein.

pybamm/input/parameters/lithium_ion/positive_electrodes/nmc_OKane2022/cracking_rate_Ai2020.py

@@ -0,0 +1,35 @@
+from pybamm import Parameter, constants, exp
+
+
+def cracking_rate_Ai2020(T_dim):
+    """
+    Particle cracking rate as a function of temperature [1, 2].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+     Battery cycle life prediction with coupled chemical degradation and fatigue
+     mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    Parameters
+    ----------
+    T: :class:`pybamm.Symbol`
+        temperature, [K]
+
+    Returns
+    -------
+    k_cr: :class:`pybamm.Symbol`
+        cracking rate, [m/(Pa.m0.5)^m_cr]
+        where m_cr is another Paris' law constant
+    """
+    k_cr = 3.9e-20
+    T_ref = Parameter("Reference temperature [K]")
+    Eac_cr = Parameter(
+        "Positive electrode activation energy for cracking rate [J.mol-1]"
+    )
+    arrhenius = exp(Eac_cr / constants.R * (1 / T_dim - 1 / T_ref))
+    return k_cr * arrhenius

pybamm/input/parameters/lithium_ion/positive_electrodes/nmc_OKane2022/nmc_LGM50_diffusivity_Chen2020.py

@@ -0,0 +1,33 @@
+from pybamm import exp, constants
+
+
+def nmc_LGM50_diffusivity_Chen2020(sto, T):
+    """
+     NMC diffusivity as a function of stoichiometry, in this case the
+     diffusivity is taken to be a constant. The value is taken from [1].
+
+     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
+     T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+     Returns
+     -------
+     :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    D_ref = 4e-15
+    E_D_s = 25000  # O'Kane et al. (2022), after Cabanero et al. (2018)
+    arrhenius = exp(E_D_s / constants.R * (1 / 298.15 - 1 / T))
+
+    return D_ref * arrhenius

pybamm/input/parameters/lithium_ion/positive_electrodes/nmc_OKane2022/nmc_LGM50_electrolyte_exchange_current_density_Chen2020.py

@@ -0,0 +1,36 @@
+from pybamm import exp, constants
+
+
+def nmc_LGM50_electrolyte_exchange_current_density_Chen2020(c_e, c_s_surf, c_s_max, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between NMC and LiPF6 in
+    EC:DMC.
+
+    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
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    m_ref = 3.42e-6  # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 17800
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_s_max - c_s_surf) ** 0.5
+    )