Run Monte-Carlo Simulation for TL (tunnelling transitions)

Source: R/run_MC_TL_TUN.R

Runs a Monte-Carlo (MC) simulation of thermoluminescence (TL) caused by tunnelling (TUN) transitions. Tunnelling refers to quantum mechanical tunnelling processes from the excited state of the trap into a recombination centre. The heating rate in this function is assumed to be 1 K/s.

run_MC_TL_TUN(
  s,
  E,
  rho,
  r_c = 0,
  times,
  b = 1,
  clusters = 10,
  N_e = 200,
  delta.r = 0.1,
  method = "par",
  output = "signal",
  ...
)

Arguments

s

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

E

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

rho

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

r_c

numeric (with default): Critical distance (>0) that is to be used 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.

times

numeric (required): The sequence of temperature steps within the simulation (s). The default heating rate is set to 1 K/s. The final temperature is max(times) * b

b

numeric (with default): the heating rate in K/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.

N_e

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

delta.r

numeric (with default): The increments of the dimensionless distance r'

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

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

Where in the function:
s := frequency for the tunnelling process (s^-1)
E := thermal activation energy (eV)
\(k_{B}\) := Boltzmann constant (8.617 x 10^-5 eV K^-1)
T := temperature (°C)
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 at distance r'

Function version

0.1.0

How to cite

Friedrich, J., Kreutzer, S., 2022. run_MC_TL_TUN(): Run Monte-Carlo Simulation for 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

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

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

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

Further reading

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

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.

Author

Johannes Friedrich, University of Bayreuth (Germany), Sebastian Kreutzer, Geography & Earth Sciences, Aberystwyth University (United Kingdom)

Examples

## the short example
run_MC_TL_TUN(
 s = 1e12,
 E = 0.9,
 rho = 1,
 r_c = 0.1,
 times = 80:120,
 b = 1,
 clusters = 50,
 method = 'seq',
 delta.r = 1e-1) %>%
plot_RLumCarlo()


if (FALSE) {
## the long (meaningful example)
results <- run_MC_TL_TUN(
 s = 1e12,
 E = 0.9,
 rho = 0.01,
 r_c = 0.1,
 times = 80:220,
 clusters = 100,
 method = 'par',
 delta.r = 1e-1)

## plot
plot_RLumCarlo(results)
}