simPeak {tgcd} | R Documentation |
Simulating first-order, second-order, or general-order glow peaks.
simPeak(temps, n0, Nn = NULL, bv = NULL, ff, ae, hr, typ = c("f", "s", "g"), 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. A vector of temperature values may be generated using the internal function seq |
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) |
bv |
numeric(required): order number for the general order glow peak |
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) |
typ |
character(with default): the type of a glow peak, |
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 simPeak simulates glow peaks of various orders. The first-, second-, and general-order glow peak can be simulated using the following three ordinary equations, respectively (Pagonis et al., 2006):
\frac{d_n}{d_T}=\frac{-nSexp(-\frac{E}{kT})}{β}
\frac{d_n}{d_T}=\frac{-n^{2}Sexp(-\frac{E}{kT})}{N_nβ}
\frac{d_n}{d_T}=\frac{-n^{b}Sexp(-\frac{E}{kT})}{N_nβ}
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, b the b value (kinetic order), 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 (Pagonis et al., 2006): |
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.
# Simulate second-order glow peaks with various # initial electron trap concentration (n0). temps <- seq(400, 600, by=0.5) peak1 <- simPeak(temps, n0=0.2e10, Nn=1e10, ff=1e19, ae=2.0, hr=1, typ="s") peak2 <- simPeak(temps, n0=0.4e10, Nn=1e10, ff=1e19, ae=2.0, hr=1, typ="s") peak3 <- simPeak(temps, n0=0.6e10, Nn=1e10, ff=1e19, ae=2.0, hr=1, typ="s") peak4 <- simPeak(temps, n0=0.8e10, Nn=1e10, ff=1e19, ae=2.0, hr=1, typ="s") peak5 <- simPeak(temps, n0=1.0e10, Nn=1e10, ff=1e19, ae=2.0, hr=1, typ="s") peaks <- cbind(peak1$tl, peak2$tl, peak3$tl, peak4$tl, peak5$tl) matplot(temps, peaks, type="l", lwd=2, lty="solid", xlab="Temperature (K)", ylab="TL intensity (counts)")