Issue 836 add lithium plating

CHANGELOG.md

@@ -4,6 +4,7 @@ New SEI models, simplification of submodel structure, as well as optimisations a
 
 ## Features
 
+-   Added SEI reaction based on Yang et. al. 2017 and reduction in porosity ([#836](https://github.com/pybamm-team/PyBaMM/issues/836)) 
 -   Reformatted `Geometry` and `Mesh` classes ([#1032](https://github.com/pybamm-team/PyBaMM/pull/1032))
 -   Added arbitrary geometry to the lumped thermal model ([#718](https://github.com/pybamm-team/PyBaMM/issues/718))
 -   Allowed `ProcessedVariable` to handle cases where `len(solution.t)=1` ([#1020](https://github.com/pybamm-team/PyBaMM/pull/1020))

docs/source/models/submodels/interface/sei.rst

@@ -20,4 +20,7 @@ SEI models
     :members:
 
 .. autoclass:: pybamm.sei.SolventDiffusionLimited
+    :members:
+
+.. autoclass:: pybamm.sei.EcReactionLimited
     :members:

examples/scripts/cycling_ageing_yang.py

@@ -0,0 +1,51 @@
+import pybamm as pb
+options = {"sei": "ec reaction limited",
+           "porosity": "variable porosity"}
+param = pb.ParameterValues(chemistry=pb.parameter_sets.Ramadass2004)
+model = pb.lithium_ion.DFN(options)
+experiment = pb.Experiment((
+    [
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/10",
+        "Rest for 5 minutes",
+        "Discharge at 2 C until 2.8 V (1 seconds period)",
+        "Rest for 5 minutes",
+    ]
+    * 5 +
+    [
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at C/3 until 2.8 V(1 seconds period)",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 1 C until 2.8 V(1 seconds period)",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 2 C until 2.8 V(1 seconds period)",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 3 C until 2.8 V(1 seconds period)",
+    ]) * 2
+)
+sim = pb.Simulation(model, experiment=experiment,
+                    parameter_values=param)
+sim.solve(solver=pb.CasadiSolver(mode="safe"))
+sim.plot(
+    [
+        "Current [A]",
+        'Total current density [A.m-2]',
+        "Terminal voltage [V]",
+        "Discharge capacity [A.h]",
+        "Electrolyte potential [V]",
+        "Electrolyte concentration [mol.m-3]",
+        "Total negative electrode sei thickness",
+        "Negative electrode porosity",
+        "Negative electrode sei interfacial current density [A.m-2]",
+        "X-averaged total negative electrode sei thickness [m]",
+    ]
+)
+

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/README.md

@@ -0,0 +1,8 @@
+# Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, and S. Jon Chapman. "An asymptotic derivation of a single particle model with electrolyte." [arXiv preprint arXiv:1905.12553](https://arxiv.org/abs/1905.12553) (2019).
+> P. Ramadass, Bala Haran, Parthasarathy M. Gomadam, Ralph White, and Branko N. Popov.["Development of First Principles Capacity Fade Model for Li-Ion Cells."](https://scholarcommons.sc.edu/cgi/viewcontent.cgi?article=1161&context=eche_facpub) (2004)
+
+and references therein.

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_electrolyte_exchange_current_density_Ramadass2004.py

@@ -0,0 +1,35 @@
+from pybamm import exp, constants, standard_parameters_lithium_ion
+
+
+def graphite_electrolyte_exchange_current_density_Ramadass2004(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [2]
+
+    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 = 4.854 * 10 ** (-6)  # (A/m2)(mol/m3)**1.5
+    E_r = 37480
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    c_n_max = standard_parameters_lithium_ion.c_n_max
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_n_max - c_s_surf) ** 0.5
+    )

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_entropic_change_Moura2016.py

@@ -0,0 +1,33 @@
+from pybamm import exp, cosh
+
+
+def graphite_entropic_change_Moura2016(sto, c_n_max):
+    """
+        Graphite entropic change in open circuit potential (OCP) at a temperature of
+        298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code
+        [1].
+
+        References
+        ----------
+        .. [1] https://github.com/scott-moura/fastDFN
+
+          Parameters
+          ----------
+          sto : :class:`pybamm.Symbol`
+               Stochiometry of material (li-fraction)
+
+    """
+
+    du_dT = (
+        -1.5 * (120.0 / c_n_max) * exp(-120 * sto)
+        + (0.0351 / (0.083 * c_n_max)) * ((cosh((sto - 0.286) / 0.083)) ** (-2))
+        - (0.0045 / (0.119 * c_n_max)) * ((cosh((sto - 0.849) / 0.119)) ** (-2))
+        - (0.035 / (0.05 * c_n_max)) * ((cosh((sto - 0.9233) / 0.05)) ** (-2))
+        - (0.0147 / (0.034 * c_n_max)) * ((cosh((sto - 0.5) / 0.034)) ** (-2))
+        - (0.102 / (0.142 * c_n_max)) * ((cosh((sto - 0.194) / 0.142)) ** (-2))
+        - (0.022 / (0.0164 * c_n_max)) * ((cosh((sto - 0.9) / 0.0164)) ** (-2))
+        - (0.011 / (0.0226 * c_n_max)) * ((cosh((sto - 0.124) / 0.0226)) ** (-2))
+        + (0.0155 / (0.029 * c_n_max)) * ((cosh((sto - 0.105) / 0.029)) ** (-2))
+    )
+
+    return du_dT

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_mcmb2528_diffusivity_Dualfoil1998.py

@@ -0,0 +1,30 @@
+from pybamm import exp, constants
+
+
+def graphite_mcmb2528_diffusivity_Dualfoil1998(sto, T):
+    """
+    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:`pybamm.Symbol`
+        Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+   """
+
+    D_ref = 3.9 * 10 ** (-14)
+    E_D_s = 42770
+    arrhenius = exp(E_D_s / constants.R * (1 / 298.15 - 1 / T))
+
+    return D_ref * arrhenius

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_ocp_Ramadass2004.py

@@ -0,0 +1,22 @@
+from pybamm import exp
+
+
+def graphite_ocp_Ramadass2004(sto):
+    """
+       Graphite Open Circuit Potential (OCP) as a function of the
+       stochiometry (theta?). The fit is taken from Ramadass 2004.
+
+       References
+       ----------
+       .. [1]
+       """
+
+    u_eq = (
+        0.7222 + 0.1387 * sto
+        + 0.029 * (sto ** 0.5) - 0.0172 / sto
+        + 0.0019 / (sto ** 1.5)
+        + 0.2808 * exp(0.9 - 15 * sto)
+        - 0.7984 * exp(0.4465 * sto - 0.4108)
+    )
+
+    return u_eq

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv

@@ -0,0 +1,33 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrode properties,,,
+Negative electrode conductivity [S.m-1],100,Ramadass,graphite
+Maximum concentration in negative electrode [mol.m-3],30555,Ramadass,
+Negative electrode diffusivity [m2.s-1],[function]graphite_mcmb2528_diffusivity_Dualfoil1998,Also valid for Ramadass,
+Negative electrode OCP [V],[function]graphite_ocp_Ramadass2004,
+,,,
+# Microstructure,,,
+Negative electrode porosity,0.485,Ramadass,electrolyte volume fraction
+Negative electrode active material volume fraction,0.49,Ramadass,
+Negative particle radius [m],2e-06,Ramadass,
+Negative particle distribution in x,1,,
+Negative electrode surface area to volume ratio [m-1],735000, 3eps.radi-1,
+Negative electrode Bruggeman coefficient (electrolyte),4,Guess,
+Negative electrode Bruggeman coefficient (electrode),4,Ramadass,
+,,,
+# Interfacial reactions,,,
+Negative electrode cation signed stoichiometry,-1,,
+Negative electrode electrons in reaction,1,,
+Reference OCP vs SHE in the negative electrode [V],,,
+Negative electrode charge transfer coefficient,0.5,Ramadass,
+Negative electrode double-layer capacity [F.m-2],0.2,,
+Negative electrode exchange-current density [A.m-2],[function]graphite_electrolyte_exchange_current_density_Ramadass2004,,
+,,,
+# Density,,,
+Negative electrode density [kg.m-3],1657,,
+,,,
+# Thermal parameters,,,
+Negative electrode specific heat capacity [J.kg-1.K-1],700,,
+Negative electrode thermal conductivity [W.m-1.K-1],1.7,,
+Negative electrode OCP entropic change [V.K-1],[function]graphite_entropic_change_Moura2016,,

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/README.md

@@ -0,0 +1,9 @@
+# Lithium Cobalt Oxide cathode parameters
+
+Parameters for a lithium Cobalt Oxide cathode, from the paper
+
+> Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, and S. Jon Chapman. "An asymptotic derivation of a single particle model with electrolyte." [arXiv preprint arXiv:1905.12553](https://arxiv.org/abs/1905.12553) (2019).
+> P. Ramadass, Bala Haran, Parthasarathy M. Gomadam, Ralph White, and Branko N. Popov.
+"Development of First Principles Capacity Fade Model for Li-Ion Cells." (2004)
+
+and references therein.

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_data_example.csv

@@ -0,0 +1,50 @@
+0.000000000000000000e+00, 4.714135898019971016e+00
+2.040816326530612082e-02, 4.708899441575220557e+00
+4.081632653061224164e-02, 4.702448345762175741e+00
+6.122448979591836593e-02, 4.694558534379876136e+00
+8.163265306122448328e-02, 4.684994372928071193e+00
+1.020408163265306006e-01, 4.673523893805322516e+00
+1.224489795918367319e-01, 4.659941254449398329e+00
+1.428571428571428492e-01, 4.644096031712390271e+00
+1.632653061224489666e-01, 4.625926611260677390e+00
+1.836734693877550839e-01, 4.605491824833229053e+00
+2.040816326530612013e-01, 4.582992038370575116e+00
+2.244897959183673186e-01, 4.558769704421606228e+00
+2.448979591836734637e-01, 4.533281647154224103e+00
+2.653061224489795533e-01, 4.507041620859735254e+00
+2.857142857142856984e-01, 4.480540404981123714e+00
+3.061224489795917880e-01, 4.454158468368703439e+00
+3.265306122448979331e-01, 4.428089899175588151e+00
+3.469387755102040782e-01, 4.402295604083254155e+00
+3.673469387755101678e-01, 4.376502631465185367e+00
+3.877551020408163129e-01, 4.350272100879827519e+00
+4.081632653061224025e-01, 4.323179536958428493e+00
+4.285714285714285476e-01, 4.295195829713853719e+00
+4.489795918367346372e-01, 4.267407675466301065e+00
+4.693877551020407823e-01, 4.243081968022011985e+00
+4.897959183673469274e-01, 4.220583168834260768e+00
+5.102040816326530726e-01, 4.177032236370062712e+00
+5.306122448979591066e-01, 4.134943568540559333e+00
+5.510204081632652517e-01, 4.075402582839823928e+00
+5.714285714285713969e-01, 4.055407164381796825e+00
+5.918367346938775420e-01, 4.036052896449991323e+00
+6.122448979591835760e-01, 4.012970397550268409e+00
+6.326530612244897211e-01, 3.990385577539371287e+00
+6.530612244897958663e-01, 3.970744780585252709e+00
+6.734693877551020114e-01, 3.954753574690877738e+00
+6.938775510204081565e-01, 3.942237451863396025e+00
+7.142857142857141906e-01, 3.932683425747200534e+00
+7.346938775510203357e-01, 3.925509771581312979e+00
+7.551020408163264808e-01, 3.920182838859009422e+00
+7.755102040816326259e-01, 3.916256861206461881e+00
+7.959183673469386600e-01, 3.913378070528176877e+00
+8.163265306122448051e-01, 3.911274218446639583e+00
+8.367346938775509502e-01, 3.909739285381772067e+00
+8.571428571428570953e-01, 3.908613829807601192e+00
+8.775510204081632404e-01, 3.907726324580658162e+00
+8.979591836734692745e-01, 3.906474088522892796e+00
+9.183673469387754196e-01, 3.900204875423951556e+00
+9.387755102040815647e-01, 3.848912814816038974e+00
+9.591836734693877098e-01, 3.445226042113884724e+00
+9.795918367346938549e-01, 1.687177743081021308e+00
+1.000000000000000000e+00, 6.378908986260003328e-03

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_diffusivity_Ramadass2004.py

@@ -0,0 +1,29 @@
+from pybamm import exp, constants
+
+
+def lico2_diffusivity_Ramadass2004(sto, T):
+    """
+    LiCo2 diffusivity as a function of stochiometry, in this case the
+    diffusivity is taken to be a constant. The value is taken from Ramadass 2004.
+
+    References
+    ----------
+    .. [1]
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+    D_ref = 1 * 10 ** (-14)
+    E_D_s = 18550
+    arrhenius = exp(E_D_s / constants.R * (1 / 298.15 - 1 / T))
+
+    return D_ref * arrhenius

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_electrolyte_exchange_current_density_Ramadass2004.py

@@ -0,0 +1,35 @@
+from pybamm import exp, constants, standard_parameters_lithium_ion
+
+
+def lico2_electrolyte_exchange_current_density_Ramadass2004(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between lico2 and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [2]
+
+    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 = 2.252 * 10 ** (-6)  # (A/m2)(mol/m3)**1.5
+    E_r = 39570
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    c_p_max = standard_parameters_lithium_ion.c_p_max
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_p_max - c_s_surf) ** 0.5
+    )

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_entropic_change_Moura2016.py

@@ -0,0 +1,35 @@
+from pybamm import cosh
+
+
+def lico2_entropic_change_Moura2016(sto, c_p_max):
+    """
+        Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
+        a temperature of 298.15K as a function of the stochiometry. The fit is taken
+        from Scott Moura's FastDFN code [1].
+
+        References
+        ----------
+        .. [1] https://github.com/scott-moura/fastDFN
+
+          Parameters
+          ----------
+          sto : :class:`pybamm.Symbol`
+               Stochiometry of material (li-fraction)
+
+    """
+
+    # Since the equation for LiCo2 from this ref. has the stretch factor,
+    # should this too? If not, the "bumps" in the OCV don't line up.
+    stretch = 1.062
+    sto = stretch * sto
+
+    du_dT = (
+        0.07645 * (-54.4806 / c_p_max) * ((1.0 / cosh(30.834 - 54.4806 * sto)) ** 2)
+        + 2.1581 * (-50.294 / c_p_max) * ((cosh(52.294 - 50.294 * sto)) ** (-2))
+        + 0.14169 * (19.854 / c_p_max) * ((cosh(11.0923 - 19.8543 * sto)) ** (-2))
+        - 0.2051 * (5.4888 / c_p_max) * ((cosh(1.4684 - 5.4888 * sto)) ** (-2))
+        - (0.2531 / 0.1316 / c_p_max) * ((cosh((-sto + 0.56478) / 0.1316)) ** (-2))
+        - (0.02167 / 0.006 / c_p_max) * ((cosh((sto - 0.525) / 0.006)) ** (-2))
+    )
+
+    return du_dT