calc_ThermalLifetime: Calculates the Thermal Lifetime using the Arrhenius equation

In Luminescence: Comprehensive Luminescence Dating Data Analysis

Calculates the Thermal Lifetime using the Arrhenius equation

Description

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:

Usage

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)

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).

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

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

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.

Author(s)

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

References

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

See Also

graphics::matplot, stats::rnorm, get_RLum

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"
)
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"
)

Luminescence documentation built on Nov. 3, 2023, 5:09 p.m.