Calculates the Thermal Lifetime using the Arrhenius equation

The function calculates the thermal lifetime of charges for given E (in eV), s (in 1/s) and T (in deg. C.) parameters. The function can be used in two operational modes:

calc_ThermalLifetime(
  E,
  s,
  T = 20,
  output_unit = "Ma",
  profiling = FALSE,
  profiling_config = NULL,
  verbose = TRUE,
  plot = TRUE,
  ...
)

Arguments

E

numeric (required): vector of trap depths in eV, if profiling = TRUE only the first two elements are considered

s

numeric (required): vector of frequency factor in 1/s, if profiling = TRUE only the first two elements are considered

T

numeric (with default): temperature in deg. C for which the lifetime(s) will be calculated. A vector can be provided.

output_unit

character (with default): output unit of the calculated lifetimes, accepted entries are: "Ma", "ka", "a", "d", "h", "min", "s"

profiling

logical (with default): this option allows to estimate uncertainties based on given E and s parameters and their corresponding standard error (cf. details and examples section)

profiling_config

list (optional): allows to set configuration parameters used for the profiling (and only have an effect here). Supported parameters are:

• n (number of MC runs),

• E.distribution (distribution used for the re-sampling for E) and

• s.distribution (distribution used for the re-sampling for s).

Currently only the normal distribution is supported (e.g., profiling_config = list(E.distribution = "norm")

verbose

logical: enables/disables verbose mode

plot

logical: enables/disables output plot, currently only in combination with profiling = TRUE.

...

further arguments that can be passed in combination with the plot output. Standard plot parameters are supported (plot.default)

Value

A RLum.Results object is returned a along with a plot (for profiling = TRUE). The output object contain the following slots:

@data

Object	Type	Description
lifetimes	array or numeric	calculated lifetimes
profiling_matrix	matrix	profiling matrix used for the MC runs

@info

Object	Type	Description
call	call	the original function call

Details

Mode 1 (profiling = FALSE)

An arbitrary set of input parameters (E, s, T) can be provided and the function calculates the thermal lifetimes using the Arrhenius equation for all possible combinations of these input parameters. An array with 3-dimensions is returned that can be used for further analyses or graphical output (see example 1)

Mode 2 (profiling = TRUE)

This mode tries to profile the variation of the thermal lifetime for a chosen temperature by accounting for the provided E and s parameters and their corresponding standard errors, e.g., E = c(1.600, 0.001) The calculation based on a Monte Carlo simulation, where values are sampled from a normal distribution (for E and s).

Used equation (Arrhenius equation)

$$\tau = 1/s exp(E/kT)$$ where: \(\tau\) in s as the mean time an electron spends in the trap for a given \(T\), \(E\) trap depth in eV, \(s\) the frequency factor in 1/s, \(T\) the temperature in K and \(k\) the Boltzmann constant in eV/K (cf. Furetta, 2010).

Note

The profiling is currently based on re-sampling from a normal distribution, this distribution assumption might be, however, not valid for given E and s parameters.

Function version

0.1.0

How to cite

Kreutzer, S., 2023. calc_ThermalLifetime(): Calculates the Thermal Lifetime using the Arrhenius equation. Function version 0.1.0. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., 2023. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.23. https://CRAN.R-project.org/package=Luminescence

References

Furetta, C., 2010. Handbook of Thermoluminescence, Second Edition. World Scientific.

See also

graphics::matplot, stats::rnorm, get_RLum

Author

Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany) , RLum Developer Team

Examples

##EXAMPLE 1
##calculation for two trap-depths with similar frequency factor for different temperatures
E <- c(1.66, 1.70)
s <- 1e+13
T <- 10:20
temp <- calc_ThermalLifetime(
  E = E,
  s = s,
  T = T,
  output_unit = "Ma"
)
#> 
#> [calc_ThermalLifetime()]
#> 
#> 	mean:	 1.355559e+03 Ma
#> 	sd:	 1.51684e+03 Ma
#> 	min:	 1.095458e+02 Ma (@20 °C)
#> 	max:	 5.747042e+03 Ma (@10 °C)
#> 	--------------------------
#> 	(22 lifetimes calculated in total)
contour(x = E, y = T, z = temp$lifetimes[1,,],
        ylab = "Temperature [\u00B0C]",
        xlab = "Trap depth [eV]",
        main = "Thermal Lifetime Contour Plot"
)
mtext(side = 3, "(values quoted in Ma)")


##EXAMPLE 2
##profiling of thermal life time for E and s and their standard error
E <- c(1.600, 0.003)
s <- c(1e+13,1e+011)
T <- 20
calc_ThermalLifetime(
  E = E,
  s = s,
  T = T,
  profiling = TRUE,
  output_unit = "Ma"
)
#> 
#> [calc_ThermalLifetime()]
#> 
#> 	profiling = TRUE
#> 	--------------------------
#> 	mean:	 1.027227e+01 Ma
#> 	sd:	 1.233001e+00 Ma
#> 	min:	 6.99807e+00 Ma
#> 	max:	 1.497807e+01 Ma
#> 	--------------------------
#> 	(1000 lifetimes calculated in total)

#> 
#>  [RLum.Results-class]
#> 	 originator: calc_ThermalLifetime()
#> 	 data: 2
#>  	 .. $lifetimes : numeric
#> 	 .. $profiling_matrix : matrix
#> 	 additional info elements:  1