TL-kinetics 0.0.1

Python tools for simulation of Thermoluminescence (TL) glow curves

Tools for simulate TL Glow Curves

This library provides functions to simulate thermoluminescence (TL) glow curves using three kinetic models:

• First-order kinetics
• Second-order kinetics
• General-order kinetics (with the kinetic order b)

It is intended for research and modeling of thermoluminescence phenomena.

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Installation

Once the package is available on PyPI:

pip install mi_libreria_TL

Or if you are using the raw tl_models.py file, simply place it in your project and import the functions:

from tl_models import TL_first_order, TL_second_order, TL_general_order

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Function Descriptions

TL_first_order(E, s, k, beta, n0, Npoints, T0, Tfinal) Simulates a first-order TL glow peak.

TL_second_order(E, s, k, beta, N, n0, Npoints, T0, Tfinal) Simulates a second-order TL glow peak.

TL_general_order(E, s, k, beta, n0, Npoints, T0, Tfinal, b=1.5) Simulates a general-order TL glow peak.

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Parameter Meaning

Parameter	Units	Description
E	eV	Activation energy of the trap (depth below conduction band).
s	s⁻¹	Frequency factor (attempt-to-escape frequency).
k	eV/K	Boltzmann constant (≈ 8.617 × 10⁻⁵ eV/K).
beta	K/s	Heating rate (temperature increase per second).
n0	carriers	Initial number of trapped carriers at T0.
N	carriers	Total trap concentration (used in second-order kinetics).
Npoints	—	Number of temperature steps in the simulation.
T0	K	Initial temperature (Kelvin).
Tfinal	K	Final temperature (Kelvin).
b	—	Kinetic order parameter (b=1 → first order, b=2 → second order, etc.).

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Example Usage

import matplotlib.pyplot as plt
from tl_models import TL_first_order, TL_second_order, TL_general_order

# Example parameters
E = 1.0          # eV, trap depth
s = 1e12         # s^-1, frequency factor
k = 8.617e-5     # eV/K, Boltzmann constant
beta = 1         # K/s, heating rate
N = 1e10         # total traps
n0 = N           # assume all traps are filled initially
Npoints = 500
T0 = 273.15 + 25     # Initial temperature (298 K = 25 °C)
Tfinal = 273.15 + 250  # Final temperature (523 K = 250 °C)

# First-order TL
T1, I1 = TL_first_order(E, s, k, beta, n0, Npoints, T0, Tfinal)

# Second-order TL
T2, I2 = TL_second_order(E, s, k, beta, N, n0, Npoints, T0, Tfinal)

# General-order TL
Tg, Ig = TL_general_order(E, s, k, beta, n0, Npoints, T0, Tfinal, b=1.5)

# Plotting
plt.plot(T1 - 273.15, I1, label="First-order")
plt.plot(T2 - 273.15, I2, label="Second-order")
plt.plot(Tg - 273.15, Ig, label="General-order (b=1.5)")
plt.xlabel("Temperature (°C)")
plt.ylabel("TL Intensity (a.u.)")
plt.legend()
plt.show()

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Output

Each function returns:

• T_eval: array of temperature values (K).
• I: array of simulated TL intensity values (arbitrary units).

You can directly plot T_eval vs I to visualize the TL glow peak.