| simqOTOR {tgcd} | R Documentation |
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 |
plot |
logical(with default): draw a plot according to the simulated glow peak or not |
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{d_n}{d_T}=\frac{-A_hn^2Sexp(-\frac{E}{kT})}{[nA_h+(N_n-n)A_n]\beta}
where n is the concentration of trapped electrons, \frac{d_n}{d_T} 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, N_n the total concentration of the traps in the crystal, A_h the probability
coefficient of electron recombining with holes in the recombination center, A_n the probability coefficient of
electron retrapping in the traps, and \beta 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: https://www.netlib.org/odepack/, modified version by R. Woodrow Setzer from the R package deSolve (Soetaert et al., 2010) available at CRAN: https://CRAN.R-project.org/package=deSolve).
Value
Return an invisible list containing the following elements:
temps |
a vector of temperature values |
tl |
values of the thermoluminescence intensity |
n |
variation of concentration of trapped electrons with temperature |
sp |
parameters used for describing the shape of a glow peak, see function simPeak for details |
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
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)")