simqOTOR {tgcd} | R Documentation |
Simulating glow peaks according to the one trap-one recombination center (OTOR) model using the quasi-equilibrium approximation.
simqOTOR(temps, n0, Nn, Ah, An, ff, ae, hr, outfile = NULL, plot = TRUE)
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 |
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]β}
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 β 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: https://CRAN.R-project.org/package=deSolve).
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 |
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.
# 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)")