Hi，
I’m working on thermo-desorption spectra of hydrogen in tungsten with FESTIM.However,there’s a question that troubles me:
Why does FESTIM’s TDS simulation for a single trap have a second peak after the first main peak?
Thanks!
Hi @Jellycarrot and welcome to FESTIM!
Do you have an example that you could share with us? A minimal working example that we could run.
A few ideas:
- a peak of mobile particles
- a desorption peak of the right hand side
But again it’s hard to tell without having a script
Thank you for your prompt attention!
Here is my code as an example
import festim as F
my_model = F.Simulation()
import numpy as np
vertices = np.concatenate([
np.linspace(0, 30e-9, num=200),
np.linspace(30e-9, 49.97e-6, num=500),
np.linspace(49.97e-6, 50e-6, num=200),
])
my_model.mesh = F.MeshFromVertices(vertices)
tungsten = F.Material(
id=1,
D_0=4.1e-07, # m2/s
E_D=0.39, # eV
)
my_model.materials = tungsten
import sympy as sp
implantation_time = 400 # s
ion_flux = sp.Piecewise((2.5e19, F.t <= implantation_time), (0, True))
source_term = F.ImplantationFlux(
flux=ion_flux, # H/m2/s
imp_depth=4.5e-9, # m
width=2.5e-9, # m
volume=1
)
my_model.sources = [source_term]
w_atom_density = 6.3e28 # atom/m3
trap_1 = F.Trap(
k_0=4.1e-7/(1.1e-10**2*6*w_atom_density),
E_k=0.39,
p_0=2e13,
E_p=1.25,
density=2e-4*w_atom_density,
materials=tungsten
)
my_model.traps = [trap_1]
my_model.boundary_conditions = [
F.DirichletBC(surfaces=[1, 2], value=0, field=0)
]
#Temperature
implantation_temp = 300 # K
temperature_ramp = 1 # K/s
start_tds = implantation_time + 50 # s
my_model.T = F.Temperature(
value=sp.Piecewise(
(implantation_temp, F.t < start_tds),
(implantation_temp + temperature_ramp*(F.t-start_tds), True))
)
#Stepsize
my_model.dt = F.Stepsize(
initial_value=0.5,
stepsize_change_ratio=1.1,
max_stepsize=lambda t: 0.5 if t > start_tds else None,
dt_min=1e-05,
milestones=[implantation_time, start_tds],
)
#Settings
my_model.settings = F.Settings(
absolute_tolerance=1e10,
relative_tolerance=1e-09,
final_time=1000
)
list_of_derived_quantities = [
F.TotalVolume("solute", volume=1),
F.TotalVolume("retention", volume=1),
F.TotalVolume("1", volume=1),
F.HydrogenFlux(surface=1),
F.HydrogenFlux(surface=2)
]
derived_quantities = F.DerivedQuantities(
list_of_derived_quantities,
# filename="tds/derived_quantities.csv" # optional set a filename to export the data to csv
)
my_model.exports = [derived_quantities]
my_model.initialise()
my_model.run()
t = derived_quantities.t
flux_left = derived_quantities.filter(fields="solute", surfaces=1).data
flux_right = derived_quantities.filter(fields="solute", surfaces=2).data
flux_total = -np.array(flux_left) - np.array(flux_right)
import matplotlib.pyplot as plt
plt.plot(t, flux_total, linewidth=3)
plt.ylabel(r"Desorption flux (m$^{-2}$ s$^{-1}$)")
plt.xlabel(r"Time (s)")
plt.savefig('1.png')
trap_1 = derived_quantities.filter(fields="1").data
contribution_trap_1 = -np.diff(trap_1)/np.diff(t)
plt.plot(t, flux_total, linewidth=3)
plt.plot(t[1:], contribution_trap_1, linestyle="--", color="grey")
plt.fill_between(t[1:], 0, contribution_trap_1, facecolor='grey', alpha=0.1)
plt.xlim(450, 1000)
plt.ylim(bottom=-0.05e18, top=0.6e18)
plt.ylabel(r"Desorption flux (m$^{-2}$ s$^{-1}$)")
plt.xlabel(r"Time (s)")
plt.ylabel(r"Desorption flux (m$^{-2}$ s$^{-1}$)")
plt.xlabel(r"Time (s)")
plt.savefig("2.png",dpi=600)
In the code above (which is slightly modified from your Task 02 in FESTIM-workshop)，I try to run a system of 50μm with single trap.
Then I’ve got two graphs like this:
So I wonder how did the second peak appear.
Thanks again for answering me!
Instead of plotting contribution_trap_1 can you plot flux_left and flux_right instead?
@Jellycarrot I confirm this is the desorption from the right hand side
plt.plot(t, flux_total, linewidth=3, color="black")
plt.stackplot(
t,
-np.array(flux_left),
-np.array(flux_right),
colors=["tab:blue", "tab:orange"],
labels=["Left", "Right"],
)
If you increase the sample size to say 1 mm then this peak disappears:
This is because when you have a thin sample, after detrapping, hydrogen diffuses to both sides and there is a small delay after which it has reached the right side. This also happens with thicker samples except there is a much larger distance to diffuse through and therefore H only desorbs from the left.
