tgcd (version 2.0)

simqOTOR: Thermoluminescence glow peak simulation

Description

Simulating glow peaks according to the one trap-one recombination center (OTOR) model using the quasi-equilibrium approximation.

Usage

simqOTOR(temps, n0, Nn, Ah, An, ff, ae,  hr, outfile = NULL, plot = TRUE)

Arguments

temps

vector(required): temperature values (K) where the values of the thermoluminescence intensity will be computed, it needs to be sorted increasingly

n0

numeric(required): initial concentration of trapped electrons (1/cm^3)

Nn

numeric(required): total concentration of the traps in the crystal (1/cm^3)

Ah

numeric(optional): probability coefficient of electron recombining with holes in the recombination center (cm^3/s)

An

numeric(optional): probability coefficient of electron retrapping in the traps (cm^3/s)

ff

numeric(required): the frequency factor (1/s)

ae

numeric(required): the activation energy (eV)

hr

numeric(with default): the linear heating rate (K/s)

outfile

character(optional): if specified, simulated intensities of glow peaks will be written to a file named "outfile" in CSV format and saved to the current work directory

plot

logical(with default): draw a plot according to the simulated glow peak or not

Value

Return an invisible list containing the following elements:

Details

Function simqOTOR simulates a synthetic glow peak according to the OTOR model using the quasi-equilibrium approximation. This function may be used to simulating glow peaks of first-, second-, and general-order, depending on the given kinetic parameters. The approximate equation of the OTOR model derived using the quasi-equilibrium approximation can be described by (Pagonis et al., 2006):

$\frac{dn}{dT}=-Ah*n^2*S*e^{-E/(kT)}/((n*Ah+(Nn-n)*An)*hr)$

where $n$ is the concentration of trapped electrons, $\frac{dn}{dT}$ the rate of change of the concentration of trapped electrons, $S$ the frequency factor, $E$ the activation energy, $T$ the absolute temperature, $k$ the Boltzmann constant, $Nn$ the total concentration of the traps in the crystal, $Ah$ the probability coefficient of electron recombining with holes in the recombination center, $An$ the probability coefficient of electron retrapping in the traps, and $hr$ the linear heating rate.

The ordinary equation is solved by the Fortran 77 subroutine lsoda (original version written by Linda R. Petzold and Alan C. Hindmarsh available at Netlib: http://www.netlib.org/odepack/, modified version by R. Woodrow Setzer from the R package deSolve (Soetaert et al., 2010) available at CRAN: http://CRAN.R-project.org/package=deSolve).

References

Pagonis V, Kitis G, Furetta C, 2006. Numerical and practical exercises in thermoluminescence. Springer Science & Business Media.

Soetaert K, Petzoldt T, Setzer RW, 2010. Solving Differential Equations in R: Package deSolve. Journal of Statistical Software, 33(9): 1-25.

See Also

tgcd; simPeak

Examples

    # Synthesizing a glow curve consisting of five glow peaks.
     temps <- seq(330, 730, by=0.5)
     peak1 <- simqOTOR(temps, n0=0.7e10, Nn=1e10, Ah=1e-3, An=1e-7,
       ff=1e14, ae=1.5, hr=1, outfile = NULL, plot = TRUE)
     peak2 <- simqOTOR(temps, n0=0.5e10, Nn=1e10, Ah=1e-7, An=1e-7,
       ff=1e17, ae=1.9, hr=1, outfile = NULL, plot = TRUE)
     peak3 <- simqOTOR(temps, n0=0.2e10, Nn=1e10, Ah=1e-5, An=1e-7,
       ff=1e15, ae=1.45, hr=1, outfile = NULL, plot = TRUE)
     peak4 <- simqOTOR(temps, n0=0.2e10, Nn=1e10, Ah=1e-5, An=1e-7,
       ff=1e9, ae=0.85, hr=1, outfile = NULL, plot = TRUE)
     peak5 <- simqOTOR(temps, n0=0.3e10, Nn=1e10, Ah=1e-7, An=1e-7,
       ff=1e11, ae=1.4, hr=1, outfile = NULL, plot = TRUE)
     peaks <- cbind(peak1$tl, peak2$tl, peak3$tl, peak4$tl, peak5$tl, 
       peak1$tl+peak2$tl+peak3$tl+peak4$tl+peak5$tl)
     matplot(temps, y=peaks, type="l", lwd=2, lty="solid", 
       xlab="Temperature (K)", ylab="TL intensity (counts)")