# calc_ThermalLifetime

##### 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:

- Keywords
- datagen

##### 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 calculted. 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 configurate 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 resampling for E) and`s.distribution`

(distribution used for the resampling 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, currenlty 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 |

`@info`

Object |
Type |
Description |

##### Note

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

##### Function version

0.1.0 (2018-02-08 18:09:55)

##### How to cite

Kreutzer, S. (2018). 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. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
##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"
)
# }
```

*Documentation reproduced from package Luminescence, version 0.8.6, License: GPL-3*