This vignette describes the usage of the **R**-package
‘RLumModel’ for simulating Al_{2}O_{3} behaviour. In
literature a lot of parameters for describing the thermoluminescence
(TL) and/or optical stimulated luminescence (OSL) are given. We give
same examples for simulating different phenomena of luminescence in
Al_{2}O_{3}. Note that most of the model do not support
TL **and** OSL simulations. So please be careful when
creating sequences. The models presented in Sec. 2.1 and 2.2 support TL
simulations, but no OSL because parameters for `E_th`

(Thermal assistance energy) and `Th`

(Photo-eviction constant
or photoionisation cross section).

All examples need the **R** package RLumModel, so let’s
load it!

`library(RLumModel)`

Akselrod et al. (1998) presented
parameters for modelling the effect of quenching TL signals. This model
was built for Al_{2}O_{3}, but the rate equations are
identical with describing electron movements in quartz. Below is a
step-by-step introduction for involving these parameters in ‘RLumModel’
and re-calculating the simulationa from Figure 9 in Akselrod et al. (1998).

For a detailed introduction to own parameter sets in RLumModel, see vignette RLumModel - Using own parameter sets.

As a next step it is possible to set own starting-parameters, also called state parameters. In the case of Akselrod et al. (1998) they submitted initial concentrations of electrons and holes. This can be done via:

`<- c(0, 0, 1e11) own_state_parameters `

Here the first entry is the first electron trap, the second entry the
second electron trap and the third entry the luminescence centre
responsible for the TL signal. The vector
`own_state_parameters`

needs as much entries as energy levels
used in the model.

The effect of quenching luminescence signals will be simulated. In
RLumModel it is possible to submit the parameter `K`

as an
indicator for recognising thermal quenching or not. If the parameter is
set to `0`

thermal quenching will be neglected. Otherwise it
wil be calculated.

```
<- c(0, 1.05)
W
<- lapply(W, function(W){
TL_Akselrod_1998
<- list(
own_parameters N = c(1e18, 1e17, 1e18),
E = c(1.25, 0, 0),
s = c(1e13, 0, 0),
A = c(1e-16, 1e-16, 2e-17),
B = c(0, 0, 1e-16),
K = ifelse(W == 0, 0, 1e12),
W = W,
model = "customized",
R = 1e13)
<- list(
sequence IRR = c(20, 0.225, 0.01),
TL = c(20, 300, 1))
<- model_LuminescenceSignals(
model_output model = "customized",
sequence = sequence,
own_parameters = own_parameters,
own_state_parameters = own_state_parameters,
verbose = FALSE,
plot = FALSE)
return(get_RLum(model_output, recordType = "TL$", drop = FALSE))
})
<- merge_RLum.Analysis(TL_Akselrod_1998)
merge_results
plot_RLum.Analysis(
merge_results,legend.text = c("Unquenched", "Quenched"),
combine = T)
```

Pagonis, Chen, and Lawless (2007)
published three different parameter sets for Al_{2}O_{3}
chips. Here we analyse ‘Chip101’ and show how to re-calculate the
results presented in the publication.

```
<- list(
own_parameters N = c(2e15, 2e15, 2.4e16, 1e17),
E = c(1.3,0, 0, 0),
s = c(1e13, 0, 0, 0),
A = c(2e-8, 2e-9, 4e-9, 1e-8),
B = c(0, 0, 5e-11, 4e-8),
K = 1e11,
W = 1.1,
model = "customized",
R = 1.7e15)
<- c(0, 0, 0, 9.4e15) own_state_parameters
```

We now have to define the sequence for simulating the TL behaviour.
For that purpose different doses are given before the TL measurement. To
handle this a `lapply`

command was used. The result is the
combined plot of all simulated TL measurements.

```
<- 10^seq(-1, 3.5, 0.5)
dose
<- lapply(dose, function(dose){
Pagonis_2007
<- list(
sequence IRR = c(20, dose, 1),
PAUSE = c(20, 60),
TL = c(20, 250, 1))
<- model_LuminescenceSignals(
model_output model = "customized",
sequence = sequence,
own_parameters = own_parameters,
own_state_parameters = own_state_parameters,
verbose = FALSE,
plot = FALSE)
return(Luminescence::get_RLum(model_output, recordType = "TL", drop = FALSE))
})
<- Luminescence::merge_RLum.Analysis(Pagonis_2007)
merge_results
::plot_RLum.Analysis(
Luminescence
merge_results,subset = list(recordType = "TL$"),
xlim = c(100, 250),
legend.text = paste0(round(dose, digits = 2), " Gy"),
combine = T)
```

Figure 2 in the original publiction by Pagonis, Chen, and Lawless (2007) will be plotted with the following commands. The following code commands are able to calculate the maximum of the TL signal of all curves.

```
<- vapply(1:length(Pagonis_2007), function(x){
TL_max
<- get_RLum(get_RLum(Pagonis_2007[[x]], recordType = "TL$"))
TL
return(max(TL[,2]))
FUN.VALUE = 1) },
```

Now the calculation of the concentration:

```
<- vapply(1:length(Pagonis_2007), function(x){
m1_max
<- get_RLum(get_RLum(Pagonis_2007[[x]], recordType = "conc. level 4"))
m1
return(m1[1,2])
FUN.VALUE = 1) },
```

When plotting L-centre concentration vs. dose or TL_{max}
vs. dose the same results as presented in Fig. 2 in Pagonis, Chen, and Lawless (2007) are
reached.

```
<- seq(1,400, 1)
dose
<- lapply(dose, function(dose){
Fig_5
<- list(
sequence RF = c(20, dose, 1))
<- model_LuminescenceSignals(
model_output model = "customized",
sequence = sequence,
own_parameters = own_parameters,
own_state_parameters = own_state_parameters,
verbose = FALSE,
plot = FALSE)
})
```

```
<- vapply(1:length(Fig_5), function(x){
n1
<- get_RLum(get_RLum(Fig_5[[x]], recordType = "conc. level 1"))
temp
return(temp[nrow(temp),2])
FUN.VALUE = 1)
},
<- vapply(1:length(Fig_5), function(x){
n2
<- get_RLum(get_RLum(Fig_5[[x]], recordType = "conc. level 2"))
temp
return(temp[nrow(temp),2])
FUN.VALUE = 1)
},
<- vapply(1:length(Fig_5), function(x){
m1
<- get_RLum(get_RLum(Fig_5[[x]], recordType = "conc. level 4"))
temp
return(temp[nrow(temp),2])
FUN.VALUE = 1)
},
<- vapply(1:length(Fig_5), function(x){
m2
<- get_RLum(get_RLum(Fig_5[[x]], recordType = "conc. level 3"))
temp
return(temp[nrow(temp),2])
FUN.VALUE = 1) },
```

```
plot(dose, m2, type = "l", ylim = c(0, 1.5e16), xlim = c(0, 500), xlab= "Dose [Gy]", ylab = "Concentration [a.u.]")
lines(dose, n2, col = "red")
lines(dose, m1, col = "green")
lines(dose, n1, col = "blue")
legend("topright", legend = c("n1", "n2", "m1", "m2"), col = c("blue", "red", "green", "black"), lwd = 1, bty = "n")
grid()
```

This vignette showed the potential of the **R** package
‘RLumModel’ to simulate Al_{2}O_{3} behaviour. Two
different models known from literature were re-compiled in the framework
of RLumModel.

Akselrod, MS, N Agersnap Larsen, V Whitley, and SWS McKeever. 1998.
“Thermal Quenching of F-Center Luminescence in
Al\({_2}\)O\({_3}\):C.” *Journal of
Applied Physics* 84 (6): 3364–73.

Pagonis, V, R Chen, and J L Lawless. 2007. “A Quantitative Kinetic
Model for Al\({_2}\)O\({_3}\):C: TL Response to Ionizing
Radiation.” *Radiation Measurements* 42 (2): 198–204.