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RLumModel - Models and parameters

Sebastian Kreutzer (Earth Sciences and Geography, Abersytwyth University, UK) & Johannes Friedrich (University of Bayreuth, DE)

2022-02-20

1 Models and parameters

The table lists the parameters used in the different models implemented in 'RLumModel'. The tables are automatically extracted from the output of the function .set_pars() to provide a better human-readable output format.

It is common in the published literature to assign descriptive names to the energy levels. Obviously, this labelling is open to interpretation and has nothing carved in stone. Moreover, it depends partly on the model and the authors’ understanding.

Although different models are implemented in 'RLumModel', we did not assess whether they are meaningful but implemented them to allow direct comparison. Please remember that the main differences between models narrow down to the assumed concentration of specific levels (for instance, \(N\)). Sometimes models have different concentration levels underpinned by experiments that were or were not suitable to validate those changes. However, sometimes concentration levels differ because the authors modified them by try and error. Either way, we strongly recommend double-checking the underlying assumption of each model in the original article.

LEVEL LABEL DESCRIPTION
trap_1 110ºC TL Electron trap associated with the 110ºC TL peak
trap_2 230ºC TL Electron trap associated with the 230ºC TL peak
trap_3 OSL_fast Electron trap feeding the OSL fast component
trap_4 OSL_medium Electron trap linked to the OSL medium component
(trap_5) OSL_deep/OSL_slow1 Electron trap linked to the first OSL slow component or the deep OSL trap
(trap_6) OSL_slow2/TT-OSL Electron trap linked to the second OSL slow component or the TT-OSL trap
(trap_7) OSL_slow3/BT-OSL Electron trap linked to the third OSL slow component or the BT-OSL trap
(trap_8) OSL_deep Electron trap linked to the deep OSL trap
centre_1 R1 centre Reservoir centre 1, non-radiative, thermally unstable
centre_2 R2 centre Reservoir centre 2, non-radiative, thermally unstable
centre_3 K centre Killer centre, non-radiative recombination centre
centre_4 L centre Luminescence centre

The levels given in parentheses change according to the maximum number of levels in the model. For instance, if the model has only five electron traps, level trap_5 is associated with the deep OSL electron trap. However, if the model has traps associated with slow components, as in Bailey (2001), the OSL deep trap is associated with the trap_8 (cf. Friedrich, Kreutzer, and Schmidt 2016).

Please note that, unlike in the table above, the parameter tables below are generated automatically from the models implemented in 'RLumModel'. Therefore the labelling is kept very general.

1.1 Parameter: N

N (cm^-3)
concentration of electron traps
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 1.5e+07 1.42e+10 1.5e+07 5.1e+09 9.0e+09 1.5e+07 1.5e+07 1.50e+07
trap_2 2 1.0e+07 1.50e+09 1.0e+07 1.0e+07 1.0e+09 1.0e+07 1.0e+07 1.00e+07
trap_3 3 1.0e+09 2.05e+11 4.0e+07 1.0e+11 1.5e+11 1.0e+09 1.0e+09 1.00e+09
trap_4 4 2.5e+08 7.04e+10 2.5e+08 2.5e+08 5.0e+10 2.5e+08 2.5e+08 2.50e+08
trap_5 5 5.0e+10 1.77e+11 5.0e+10 5.0e+10 1.0e+11 5.0e+10 5.0e+10 5.00e+10
trap_6 6 NA 2.53e+11 5.0e+09 NA 1.5e+11 NA NA NA
trap_7 7 NA 3.58e+12 4.0e+09 NA 2.0e+12 NA NA NA
trap_8 8 NA 1.28e+13 NA NA 5.0e+12 NA NA NA
centre_1 9 3.0e+08 4.16e+12 3.0e+08 3.0e+08 1.2e+11 3.0e+09 1.0e+10 1.65e+08
centre_2 10 1.0e+10 4.20e+11 1.0e+10 1.0e+10 1.0e+12 1.0e+10 1.0e+10 5.00e+09
centre_3 11 5.0e+09 1.15e+14 1.2e+12 5.0e+09 5.0e+11 5.0e+09 5.0e+09 5.00e+09
centre_4 12 1.0e+11 8.83e+13 3.0e+10 1.0e+08 1.0e+13 1.0e+11 1.0e+11 1.00e+11

1.2 Parameter: E

E (eV)
depth below conduction or valence band
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97
trap_2 2 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55
trap_3 3 1.70 1.70 1.73 1.73 1.70 1.70 1.70 1.70
trap_4 4 1.72 1.72 1.80 1.80 1.72 1.72 1.72 1.72
trap_5 5 2.00 1.80 2.00 2.00 1.80 1.95 1.95 2.00
trap_6 6 NA 1.65 1.65 NA 1.65 NA NA NA
trap_7 7 NA 2.60 1.60 NA 2.60 NA NA NA
trap_8 8 NA 2.00 NA NA 2.00 NA NA NA
centre_1 9 1.43 1.75 1.43 1.43 1.43 1.80 1.80 1.41
centre_2 10 1.75 1.43 1.75 1.75 1.75 1.75 1.75 1.65
centre_3 11 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
centre_4 12 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00

1.3 Parameter: s

s (s^-1)
frequency factor
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 5e+12 5e+12 5.0e+12 5.0e+12 5e+12 5e+12 5e+12 5e+12
trap_2 2 5e+14 5e+14 5.0e+14 5.0e+14 5e+14 5e+14 5e+14 5e+14
trap_3 3 5e+13 5e+12 6.5e+13 3.6e+14 5e+12 5e+13 5e+13 1e+13
trap_4 4 5e+14 5e+13 1.5e+13 1.5e+13 5e+13 5e+14 5e+14 1e+14
trap_5 5 1e+10 5e+13 1.0e+10 1.0e+10 5e+13 1e+10 1e+10 1e+10
trap_6 6 NA 5e+13 6.5e+13 NA 5e+13 NA NA NA
trap_7 7 NA 5e+13 5.0e+12 NA 5e+13 NA NA NA
trap_8 8 NA 1e+10 NA NA 1e+10 NA NA NA
centre_1 9 5e+13 5e+14 5.0e+13 5.0e+13 5e+13 5e+13 5e+13 5e+13
centre_2 10 5e+14 5e+13 5.0e+14 5.0e+14 5e+14 5e+14 5e+14 5e+14
centre_3 11 1e+13 1e+13 1.0e+13 1.0e+13 1e+13 1e+13 1e+13 1e+13
centre_4 12 1e+13 1e+13 1.0e+13 1.0e+13 1e+13 1e+13 1e+13 1e+13

1.4 Parameter: A

A (cm^3 s^-1)
transiation probability to conduction or valence band
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 1e-08 1e-08 1e-08 1e-08 1e-08 1e-08 1e-08 1.00e-08
trap_2 2 1e-08 1e-08 1e-08 1e-09 1e-08 1e-08 1e-08 1.00e-08
trap_3 3 1e-09 1e-09 5e-09 5e-10 1e-09 1e-09 1e-09 1.00e-09
trap_4 4 5e-10 8e-10 5e-10 5e-10 8e-10 5e-10 5e-10 5.00e-10
trap_5 5 1e-10 8e-10 1e-10 1e-10 8e-10 1e-10 1e-10 3.33e-11
trap_6 6 NA 5e-10 1e-11 NA 5e-10 NA NA NA
trap_7 7 NA 2e-10 6e-12 NA 2e-10 NA NA NA
trap_8 8 NA 1e-10 NA NA 1e-10 NA NA NA
centre_1 9 5e-07 1e-09 5e-07 5e-07 5e-08 5e-07 5e-07 5.00e-07
centre_2 10 1e-09 5e-08 1e-09 1e-09 1e-09 1e-09 1e-09 1.00e-09
centre_3 11 1e-10 1e-10 1e-14 1e-10 1e-10 1e-10 1e-10 1.00e-10
centre_4 12 1e-09 1e-09 1e-10 1e-09 1e-09 1e-09 1e-09 1.00e-09

1.5 Parameter: B

B (cm^3 s^-1)
conduction band to hole centre transition probability
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
trap_2 2 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
trap_3 3 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
trap_4 4 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
trap_5 5 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00 0e+00
trap_6 6 NA 0e+00 0e+00 NA 0e+00 NA NA NA
trap_7 7 NA 0e+00 0e+00 NA 0e+00 NA NA NA
trap_8 8 NA 0e+00 NA NA 0e+00 NA NA NA
centre_1 9 5e-09 5e-10 5e-09 5e-09 5e-09 5e-09 5e-09 5e-09
centre_2 10 5e-10 5e-09 5e-10 5e-10 5e-10 5e-10 5e-10 5e-10
centre_3 11 1e-10 1e-10 3e-10 1e-10 1e-10 1e-10 1e-10 1e-10
centre_4 12 1e-10 1e-10 1e-10 1e-10 1e-10 1e-10 5e-10 1e-10

1.6 Parameter: Th

Th (s^-1)
photo-ionisation cross-section
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 0.75 1e-19 0.75 0.75 1e-19 0.75 0.75 0.75
trap_2 2 0.00 0e+00 0.00 0.00 0e+00 0.00 0.00 0.00
trap_3 3 6.00 1e-16 6.00 6.00 1e-16 6.00 6.00 6.00
trap_4 4 4.50 3e-17 4.50 4.50 3e-17 4.50 4.50 4.50
trap_5 5 0.00 4e-18 0.00 0.00 4e-18 0.00 0.00 0.00
trap_6 6 NA 3e-19 0.01 NA 3e-19 NA NA NA
trap_7 7 NA 2e-21 0.00 NA 2e-21 NA NA NA
trap_8 8 NA 0e+00 NA NA 0e+00 NA NA NA

1.7 Parameter: E_th

E_th (eV)
thermal assistance energy
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
trap_2 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
trap_3 3 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
trap_4 4 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13
trap_5 5 0.00 0.20 0.00 0.00 0.20 0.00 0.00 0.00
trap_6 6 NA 0.20 0.20 NA 0.20 NA NA NA
trap_7 7 NA 0.20 0.00 NA 0.20 NA NA NA
trap_8 8 NA 0.00 NA NA 0.00 NA NA NA

1.8 Parameter: k_B

k_B (eV K^-1)
Boltzmann constant
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 8.617e-05 8.617e-05 8.617e-05 8.617e-05 8.617e-05 8.617e-05 8.617e-05 8.617e-05

1.9 Parameter: W

W (eV)
activation energy
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

1.10 Parameter: K

K ()
dimensionlss constant after Wintle (1975)
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 2.8e+07 2.8e+07 2.8e+07 2.8e+07 2.8e+07 2.8e+07 2.8e+07 2.8e+07

1.11 Parameter: n

n (cm^-3)
concentration of trapped charges
# Bailey2001 Bailey2004 Pagonis2008 Pagonis2007 Bailey2002 Friedrich2017 Friedrich2018 Peng2022
trap_1 1 9.169767e-03 5.150601e+02 3.401581e-03 3.788751e+00 1.304051e+01 4.282981e-02 2.025417e-02 9.169767e-03
trap_2 2 7.619894e+04 1.164635e+09 5.718477e+04 1.931482e+03 2.474416e+07 2.165932e+06 1.048967e+06 7.619894e+04
trap_3 3 1.291564e+08 4.270964e+10 2.879822e+07 7.322346e+08 3.791273e+10 1.464513e+08 2.789634e+07 1.291564e+08
trap_4 4 7.432290e+06 1.201018e+10 1.235043e+08 3.233415e+06 9.871927e+09 1.898261e+07 3.508166e+06 7.432290e+06
trap_5 5 2.690423e+10 5.712265e+10 2.556071e+10 1.902026e+10 2.088693e+10 1.372718e+10 8.606323e+09 2.690423e+10
trap_6 6 NA 2.065021e+11 3.881049e+06 NA 1.506005e+10 NA NA NA
trap_7 7 NA 3.573812e+12 7.550608e+06 NA 1.989412e+12 NA NA NA
trap_8 8 NA 1.280000e+13 NA NA 4.962146e+12 NA NA NA
centre_1 9 5.741230e+06 1.496238e+11 1.734105e+08 3.000000e+08 2.696001e+09 2.215388e+09 5.796382e+09 5.741230e+06
centre_2 10 6.779304e+07 1.214026e+10 3.332680e+09 1.000000e+10 5.054229e+10 4.107361e+07 5.274192e+06 6.779304e+07
centre_3 11 1.591234e+08 2.194172e+12 1.294818e+08 5.000000e+09 8.974516e+10 6.146246e+07 1.648926e+07 1.591234e+08
centre_4 12 2.680824e+10 1.433739e+13 2.208893e+10 1.000000e+08 6.892331e+12 1.157685e+10 2.820631e+09 2.680824e+10
n_c 13 2.450977e-07 2.450977e-07 2.450977e-07 2.450977e-07 2.450977e-07 2.450977e-07 2.450977e-07 2.450977e-07
n_v 14 4.263486e-07 4.263486e-07 4.263486e-07 4.263486e-07 4.263486e-07 4.263486e-07 4.263486e-07 4.263486e-07

References

Bailey, R M. 2001. “Towards a General Kinetic Model for Optically and Thermally Stimulated Luminescence of Quartz.” Radiation Measurements 33: 17–45.
Friedrich, Johannes, Sebastian Kreutzer, and Christoph Schmidt. 2016. Solving ordinary differential equations to understand luminescence: ’RLumModel’, an advanced research tool for simulating luminescence in quartz using R .” Quaternary Geochronology 35: 88–100.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.