From b50e7fd9bfc8380a1fd2bc65da967dafe0a7a31e Mon Sep 17 00:00:00 2001 From: KulaginVladimir Date: Wed, 8 May 2024 12:57:58 +0300 Subject: [PATCH] upd DWO case --- Validation/DWO/Comparison.png | Bin 0 -> 63535 bytes Validation/DWO/D_in_WO.py | 207 ++ Validation/DWO/{exp.csv => exp_data/000O.csv} | 0 Validation/DWO/exp_data/050O.csv | 67 + Validation/DWO/exp_data/075O.csv | 67 + Validation/DWO/results/000O.csv | 951 +++++++++ Validation/DWO/results/050O.csv | 955 +++++++++ Validation/DWO/results/075O.csv | 955 +++++++++ Validation/DWO/test.py | 187 -- Validation/DWO/test/Clean_W.csv | 1698 ----------------- .../DWO/test/derived_quantities_expl_300.csv | 1417 -------------- 11 files changed, 3202 insertions(+), 3302 deletions(-) create mode 100644 Validation/DWO/Comparison.png create mode 100644 Validation/DWO/D_in_WO.py rename Validation/DWO/{exp.csv => exp_data/000O.csv} (100%) create mode 100644 Validation/DWO/exp_data/050O.csv create mode 100644 Validation/DWO/exp_data/075O.csv 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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() diff --git a/Validation/DWO/exp.csv b/Validation/DWO/exp_data/000O.csv similarity index 100% rename from Validation/DWO/exp.csv rename to Validation/DWO/exp_data/000O.csv diff --git a/Validation/DWO/exp_data/050O.csv b/Validation/DWO/exp_data/050O.csv new file mode 100644 index 000000000..99767acdf --- /dev/null +++ b/Validation/DWO/exp_data/050O.csv @@ -0,0 +1,67 @@ +x, y +307.1428843906948, -6060629413513603 +322.32142857142856, 0 +315.17861230032787, -3030256908311076.5 +329.4643129621233, 3030372505202311 +340.1785714285714, 18181888240540164 +340.1785714285714, 18181888240540164 +349.99998637608115, 54545433527838020 +346.42861230032787, 42424290297702480 +359.8214694431849, 90909094412026900 +362.5, 93939466917229420 +362.5, 93939466917229420 +369.64288439069475, 136363641618040450 +375.0000136239188, 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as sp -import warnings - -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 -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 -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 - - -################### FUNCTIONS ################### -def S0(T): - # the capturing coefficient - return f.exp(-E_diss / F.k_B / T) - - -def E_des(surf_conc): - theta_D = surf_conc / n_surf - theta_D0 = 0.253 - del_theta_D = 0.180 - E0 = 1.142 - dE = 0.346 - alpha = 0.303 - beta = 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 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 - - -################### MODEL ################### -W_model = F.Simulation(log_level=20) - -# 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 else 0.1, - 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 = "test/" - -derived_quantities = F.DerivedQuantities( - [F.AdsorbedHydrogen(surface=1), F.TotalSurface(field="T", surface=1)], - nb_iterations_between_compute=1, - filename=results_folder + "Clean_W.csv", -) - -W_model.exports = [derived_quantities] - -W_model.initialise() -W_model.run() - -results = pd.read_csv(results_folder + "Clean_W.csv", header=0) -results["Flux"] = results["Concentration of adsorbed H on surface 1"] -for i in range(len(results)): - surf_conc = results["Concentration of adsorbed H on surface 1"][i] - T = results["Total T surface 1"][i] - results["Flux"][i] = ( - 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, -) - -exp = pd.read_csv(f"./exp.csv", header=None, skiprows=1, sep=",") -plt.scatter(exp[0], exp[1], marker="x", s=75, linewidths=1.2) - -plt.ylabel(r"Desorption flux (m$^{-2}$ s$^{-1}$)") -plt.xlabel(r"Time (s)") -plt.xlim(300, 800) -plt.show() diff --git a/Validation/DWO/test/Clean_W.csv b/Validation/DWO/test/Clean_W.csv deleted file mode 100644 index 71552830f..000000000 --- a/Validation/DWO/test/Clean_W.csv +++ /dev/null @@ -1,1698 +0,0 @@ -t(s),Concentration of adsorbed H on surface 1,Total T surface 1 -1e-07,303999986946.8932,300.0 -2.25e-07,683999950235.0321,300.0 -3.8124999999999995e-07,1158999872477.275,300.0 -5.765624999999999e-07,1752749725486.4426,300.0 -8.207031249999999e-07,2494936963945.3584,300.0 -1.1258789062499999e-06,3422670890452.5503,300.0 -1.5073486328125e-06,4582338108639.002,300.0 -1.984185791015625e-06,6031921834579.126,300.0 -2.5802322387695313e-06,7843901028265.48,300.0 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