upd DWO case

Validation/DWO/D_in_WO.py

@@ -0,0 +1,207 @@
+import festim as F
+import fenics as f
+import numpy as np
+import matplotlib.pyplot as plt
+import pandas as pd
+import sympy as sp
+import warnings
+global n_surf
+
+warnings.filterwarnings("ignore")
+
+################### PARAMETERS ###################
+N_A_const = 6.022e23  # Avogadro, mol^-1
+e = 1.602e-19
+M_D2 = 4.028e-3 / N_A_const  # the H2 mass, kg mol^-1
+
+# Exposure conditions
+P_D2 = 2e-5  # Pa
+T0 = 300  # K
+ramp = 5  # K/s
+t_imp = 3000  # exposure duration, s
+t_storage = 3600  # storage time, s
+t_TDS = 100  # s
+L = 2e-3 / 2  # half thickness, m
+
+# W properties
+rho_W = 6.3382e28  # W atomic concentration, m^-3
+n_IS = 6 * rho_W  # concentration of interstitial sites, m^-3
+n_surf = 1.416e19  # concentration of adsorption sites, m^-2
+
+nu0 = 1e13  # attempt frequency, s^-1
+
+D0 = 1.9e-7 / np.sqrt(2)  # diffusivity pre-factor, m^2 s^-1
+E_diff = 0.2  # diffusion activation energy, eV
+
+# Transitions
+E_bs = E_diff  # energy barrier from bulk to surface, eV
+E_diss = 0  # energy barrier for D2 dissociation, eV
+Q_sol = 1  # heat of solution, eV
+
+# Fitting parameters
+fits = {
+    "E0": [1.142, 1.111, 1.066],
+    "dE": [0.346, 0.289, 0.234],
+    "theta_D0": [0.253, 0.113, 0.161],
+    "dtheta_D": [0.180, 0.082, 0.057],
+    "alpha": [0.303, 0.460, 0.437],
+    "beta": [8.902, 7.240, 4.144]
+}
+################### FUNCTIONS ###################
+
+
+
+################### MODEL ###################
+colors = ["tab:blue", "tab:red", "tab:green"]
+names = ["000O", "050O", "075O"]
+labels = ["Clean", "0.5ML of O", "0.75ML of O"]
+n_surfs = [n_surf, n_surf*(1-0.5), n_surf*(1-0.75)]
+for i in range(3):
+    n_surf = n_surfs[i]
+    lamda_des = 1 / np.sqrt(n_surf)  # average distance between adsorption sites, m
+    lambda_abs = n_surf / n_IS  # distance between subsurface IS and adsorption sites, m
+
+    def E_des(surf_conc):
+        theta_D = surf_conc / n_surf
+        theta_D0 = fits["theta_D0"][i] #0.253
+        del_theta_D = fits["dtheta_D"][i] #0.180
+        E0 = fits["E0"][i] #1.142
+        dE = fits["dE"][i] #0.346
+        alpha = fits['alpha'][i] #0.303
+        beta = fits['beta'][i] #8.902
+
+        E_FD = E0 + dE / (1 + f.exp((theta_D - theta_D0) / del_theta_D))
+        E_des = E_FD * (1 - alpha * f.exp(-beta * (1 - theta_D)))
+        return E_des
+
+    def S0(T):
+        # the capturing coefficient
+        return f.exp(-E_diss / F.k_B / T)
+
+
+    def E_sb(surf_conc):
+        # energy barrier from surface to bulk, eV
+        return (E_des(surf_conc) - E_diss) / 2 + E_bs + Q_sol
+
+
+    def J_vs(surf_conc, T, t):
+        J_ads = (
+            2
+            * S0(T)
+            * (1 - surf_conc / n_surf) ** 2
+            * f.conditional(t <= t_imp, 1.52e18, 0)
+        )
+
+        J_des = (
+            2 * nu0 * (lamda_des * surf_conc) ** 2 * f.exp(-E_des(surf_conc) / F.k_B / T)
+        )
+        return J_ads - J_des
+
+    W_model = F.Simulation(log_level=40)
+
+    # Mesh
+    vertices = np.linspace(0, L, num=500)
+    W_model.mesh = F.MeshFromVertices(np.sort(vertices))
+
+    # Materials
+    tungsten = F.Material(id=1, D_0=D0, E_D=E_diff)
+    W_model.materials = tungsten
+
+    surf_conc = F.SurfaceConcentration(
+        k_sb=nu0,
+        E_sb=E_sb,
+        k_bs=nu0,
+        E_bs=E_bs,
+        l_abs=lambda_abs,
+        N_s=n_surf,
+        N_b=n_IS,
+        J_vs=J_vs,
+        surfaces=1,
+        initial_condition=F.InitialCondition(field="adsorbed", value=0),
+        t=F.t,
+    )
+
+    W_model.surface_concentrations = [surf_conc]
+
+    traps = F.Traps(
+        [
+            F.Trap(
+                k_0=nu0 / n_IS,
+                E_k=E_diff,
+                p_0=nu0,
+                E_p=0.912,
+                density=7.7e-6,
+                materials=tungsten,
+            ),
+            F.Trap(
+                k_0=nu0 / n_IS,
+                E_k=E_diff,
+                p_0=nu0,
+                E_p=1.176,
+                density=7.9e-7,
+                materials=tungsten,
+            ),
+        ]
+    )
+    W_model.traps = traps
+
+    W_model.T = F.Temperature(
+        value=sp.Piecewise(
+            (T0, F.t < t_imp + t_storage), (T0 + ramp * (F.t - t_imp - t_storage), True)
+        )
+    )
+
+    W_model.dt = F.Stepsize(
+        initial_value=1e-7,
+        stepsize_change_ratio=1.25,
+        max_stepsize=lambda t: 10 if t < t_imp + t_storage-10 else 0.5,
+        dt_min=1e-9,
+    )
+
+    W_model.settings = F.Settings(
+        absolute_tolerance=1e8,
+        relative_tolerance=1e-7,
+        maximum_iterations=50,
+        final_time=t_imp + t_storage + t_TDS,
+    )
+
+    # Exports
+    results_folder = "./results/"
+
+    derived_quantities = F.DerivedQuantities(
+        [F.AdsorbedHydrogen(surface=1), F.TotalSurface(field="T", surface=1)],
+        nb_iterations_between_compute=1,
+        filename=results_folder + names[i] + ".csv",
+    )
+
+    W_model.exports = [derived_quantities]
+
+    W_model.initialise()
+    W_model.run()
+
+    results = pd.read_csv(results_folder + names[i] + ".csv", header=0)
+    results["Flux"] = results["Concentration of adsorbed H on surface 1"]
+    for j in range(len(results)):
+        surf_conc = results["Concentration of adsorbed H on surface 1"][j]
+        T = results["Total T surface 1"][j]
+        results["Flux"][j] = (
+            2 * nu0 * (lamda_des * surf_conc) ** 2 * np.exp(-E_des(surf_conc) / F.k_B / T)
+        )
+
+
+    plt.plot(
+        results["Total T surface 1"][results["t(s)"] >= t_imp + t_storage],
+        results["Flux"][results["t(s)"] >= t_imp + t_storage],
+        linewidth=3,
+        label='FESTIM: '+labels[i],
+    )
+
+    exp = pd.read_csv(f"./exp_data/"+names[i]+".csv", header=None, skiprows=1, sep=",")
+    plt.scatter(exp[0], exp[1], marker="x", s=75, linewidths=1.2, label = "exp. "+labels[i])
+
+plt.ylabel(r"Desorption flux (m$^{-2}$ s$^{-1}$)")
+plt.xlabel(r"Temperature (K)")
+plt.legend()
+plt.xlim(300, 800)
+plt.savefig("Comparison.png")
+plt.show()

Validation/DWO/exp_data/050O.csv

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Validation/DWO/exp_data/075O.csv

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