Monte-Carlo Simulation for ISO-TL (tunnelling transitions)

Runs a Monte-Carlo (MC) simulation of isothermally stimulated luminescence (ISO-TL or ITL) using the tunnelling (TUN) model. Tunnelling refers to quantum mechanical tunnelling processes from the excited state of the trapped charge, into the recombination centre.

run_MC_ISO_TUN(
  E,
  s,
  T = 200,
  rho,
  times,
  clusters = 10,
  r_c = 0,
  delta.r = 0.1,
  N_e = 200,
  method = "par",
  output = "signal",
  ...
)

Arguments

E

numeric (required): Thermal activation energy of the trap (eV).

s

numeric (required): The effective frequency factor for the tunnelling process (s^-1).

T

numeric (with default): Constant stimulation temperature (°C).

rho

numeric (required): The dimensionless density of recombination centres (defined as \(\rho\)' in Huntley 2006) (dimensionless).

times

numeric (required): The sequence of time steps within the simulation (s).

clusters

numeric (with default): The number of created clusters for the MC runs. The input can be the output of create_ClusterSystem. In that case n_filled indicate absolute numbers of a system.

r_c

numeric (with default): Critical distance (>0) that must be provided if the sample has been thermally and/or optically pretreated. This parameter expresses the fact that electron-hole pairs within a critical radius r_c have already recombined.

delta.r

numeric (with default): Fractional change of the dimensionless distance of nearest recombination centres (r')

N_e

numeric (width default): The total number of electron traps available (dimensionless). Can be a vector of length(clusters), shorter values are recycled.

method

character (with default): Sequential 'seq' or parallel 'par'processing. In the parallel mode the function tries to run the simulation on multiple CPU cores (if available) with a positive effect on the computation time.

output

character (with default): output is either the 'signal' (the default) or 'remaining_e' (the remaining charges/electrons in the trap)

...

further arguments, such as cores to control the number of used CPU cores or verbose to silence the terminal

Value

This function returns an object of class RLumCarlo_Model_Output which is a list consisting of an array with dimension length(times) x length(r) x clusters and a numeric time vector.

Details

The model

$$ I_{TUN}(r',t) = -dn/dt = (s * exp(-E/(k_{B}*T_{ISO}))) * exp(-(\rho')^{-1/3} * r') * n (r',t) $$

Where in the function:
E := thermal activation energy (eV)
s := the effective frequency factor for the tunnelling process (s^-1)
\(T_{ISO}\) := the temperature of the isothermal experiment (°C)
\(k_{B}\) := Boltzmann constant (8.617 x 10^-5 eV K^-1)
r' := the dimensionless tunnelling radius
\(\rho\)' := rho the dimensionless density of recombination centres see Huntley (2006)
t := time (s)
n := the instantaneous number of electrons corresponding to the radius r'

Function version

0.1.0

How to cite

Friedrich, J., Kreutzer, S., 2022. run_MC_ISO_TUN(): Monte-Carlo Simulation for ISO-TL (tunnelling transitions). Function version 0.1.0. In: Friedrich, J., Kreutzer, S., Pagonis, V., Schmidt, C., 2022. RLumCarlo: Monte-Carlo Methods for Simulating Luminescence Phenomena. R package version 0.1.9. https://CRAN.R-project.org/package=RLumCarlo

References

Pagonis, V. and Kulp, C., 2017. Monte Carlo simulations of tunneling phenomena and nearest neighbor hopping mechanism in feldspars. Journal of Luminescence 181, 114–120. doi:10.1016/j.jlumin.2016.09.014

Further reading Aitken, M.J., 1985. Thermoluminescence dating. Academic Press.

Huntley, D.J., 2006. An explanation of the power-law decay of luminescence. Journal of Physics: Condensed Matter, 18(4), 1359.

Jain, M., Guralnik, B., Andersen, M.T., 2012. Stimulated luminescence emission from localized recombination in randomly distributed defects. Journal of Physics: Condensed Matter 24, 385402.

Pagonis, V., Friedrich, J., Discher, M., Müller-Kirschbaum, A., Schlosser, V., Kreutzer, S., Chen, R. and Schmidt, C., 2019. Excited state luminescence signals from a random distribution of defects: A new Monte Carlo simulation approach for feldspar. Journal of Luminescence 207, 266–272. doi:10.1016/j.jlumin.2018.11.024

Author

Johannes Friedrich, University of Bayreuth (Germany), Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany)

Examples

## short example
run_MC_ISO_TUN(
 E = .8,
 s = 1e16,
 T = 50,
 rho = 1e-4,
 times = 0:100,
 clusters = 10,
 N_e = 100,
 r_c = 0.2,
 delta.r = 0.5,
 method = "seq") %>%
 plot_RLumCarlo(legend = TRUE)


if (FALSE) {
## long (meaningful) example
results <- run_MC_ISO_TUN(
 E = .8,
 s = 1e16,
 T = 50,
 rho = 1e-4,
 times = 0:100,
 clusters = 1000,
 N_e = 200,
 r_c = 0.1,
 delta.r = 0.05,
 method = "par")

plot_RLumCarlo(results, legend = TRUE)
}