tgcd(Sigdata, npeak, inis = NULL, mwt = 90, mdt = 3, nstart = 30, model=c("g", "lw"), elim = NULL, logy = FALSE, hr = NULL, outfile = NULL, plot = TRUE)two-column matrix, temperature values and thermoluminescence signal values are stored in the first and second column, respectivelynpeak-row 4-column matrix used for storing starting parameters Im, E, Tm, b (or R).
If inis=NULL, the user has to click with a mouse on a plot to locate each glow peak maximummwt prevents
the appearance of glow peaks with large total half-width. A conservative mwt is adopted by defaultmdt prevents
the appearance of strongly overlapping peaks. A conservative mdt is adopted by defaultnstart>1, a "try-and-error" protocol will be performed, the upper limit for
nstart is set equal to 10000"g" means fitting a general-order model, "lw" means fitting the Lambert W (Wright Omega) function, default model="g"elim=c(0.5, 5) "outfile" in CSV format and
saved to the current work directoryThe general-order empirical expression for a glow peak is:
I(T)=Im*b^(b/(b-1))*expv*((b-1)*(1-xa)*(T/Tm)^2*expv+Zm)^(-b/(b-1))
xa=2*k*T/E
xb=2*k*Tm/E
expv=exp(E/(k*T)*(T-Tm)/Tm)
Zm=1+(b-1)*xb
where b is the kinetic parameter (lies between 1 and 2), I is the glow peak intensity,
E the activation energyin ev, k the Boltzmann constant in eV/k, T the temperature in K with constant heating rate K/s,
Tm the temperature at maximum thermoluminescence intensity in K, and Im the maximum intensity.
The four parameters for this model are: Im, E, Tm, and b.
The semi-analytical expression derived from the one trap-one recombination (OTOR) model is (with the assumption of An where The procedure minimizes the objective: $fcn=\sum_{i=1}^n |y_i^o-y_i^f|, i=1,...,n$ where $y_i^o$ and $y_i^f$ denote the i-th observed and fitted signal value, respectively,
and $n$ indicates the number of data points. Starting parameters ( Parameters can be interactively constrained and fixed by modifying the following elements in a automatically
generated Dialog Table if I(T)=Im*exp(-E/(k*T)*(Tm-T)/Tm)*(W(Zm)+W(Zm)^2)/(W(Z)+W(Z)^2)
Zm=R/(1-R)-log((1-R)/R)+E*exp(E/(k*Tm))/(k*Tm^2*(1-1.05*R^1.26))*F(Tm,E)
Z=R/(1-R)-log((1-R)/R)+E*exp(E/(k*Tm))/(k*Tm^2*(1-1.05*R^1.26))*F(T,E)
F(Tm,E)=Tm*exp(-E/(k*Tm))+E/k*Ei(-E/(k*Tm))
F(T,E)=T*exp(-E/(k*T))+E/k*Ei(-E/(k*T))W(x) is the wright Omega function for variable x, Ei(x) is the exponential integral function for variable x,
I is the glow peak intensity, E the activation energy in eV, k the Boltzmann constant in eV/K,
T the temperature in K with constant heating rate in K/s, Tm the temperature at maximum thermoluminescence intensity in K,
and Im the maximum intensity. The four parameters for this model are: Im, E, Tm, and R.
The Fortran 90 subroutine used for evaluating the Wright Omega function is transformed from the Matlab code
provided by Andrew Horchler available at https://github.com/horchler/wrightOmegaq. Here the Wright Omega
function suggested by Singh and Gartia (2013, 2014, 2015) was used instead of the Lambert's W function proposed
by Kitis and Vlachos (2013) to avoid unnecessary overflow.inis) can be specified by the user through argument inis or by clicking with a mouse on
the plot of the thermoluminescence glow curve showing peak maxima if inis=NULL.The Levenberg-Marquardt algorithm
(More, 1978) (minpack: http://netlib.org/minpack/, original Fortran 77 version by Jorge More, Burton Garbow, Kenneth Hillstrom.
Fortran 90 version by John Burkardt was modified so as to supports constraints and fixes of parameters. If argument nstart>1,
a "try-and-error" protocol with starting values generated uniformly around the given starting values inis will be performed
repeatedly to search the optimal parameters that give a minimum Figure Of Merit (FOM) value.inis=NULL:
(1) INTENS(min, max, ini, fix): lower and upper bounds, starting and fixing values of Im
(2) ENERGY(min, max, ini, fix): lower and upper bounds, starting and fixing values of E
(3) TEMPER(min, max, ini, fix): lower and upper bounds, starting and fixing values of Tm
(4) bValue(min, max, ini, fix): lower and upper bounds, starting and fixing values of b
Kitis G, Polymeris GS, Sfampa IK, Prokic M, Meric N, Pagonis V, 2016. Prompt isothermal decay of thermoluminescence in MgB4O7:Dy, Na and LiB4O7:Cu, In dosimeters. Radiation Measurements, 84: 15-25.
Kitis G, Vlachos ND, 2013. General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert W-function. Radiation Measurements, 48: 47-54.
More JJ, 1978. "The Levenberg-Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics: Numerical Analysis, Springer-Verlag: Berlin. 105-116.
Pagonis V, Kitis G, Furetta C, 2006. Numerical and practical exercises in thermoluminescence. Springer Science & Business Media.
Sadek AM, Eissa HM, Basha AM, Carinou E, Askounis P, Kitis G, 2015. The deconvolution of thermoluminescence glow-curves using general expressions derived from the one trap-one recombination (OTOR) level model. Applied Radiation and Isotopes, 95: 214-221.
Singh LL, Gartia RK, 2013. Theoretical derivation of a simplified form of the OTOR/GOT differential equation. Radiation Measurements, 59: 160-164.
Singh LL, Gartia RK, 2014. Glow-curve deconvolution of thermoluminescence curves in the simplified OTOR equation using the Hybrid Genetic Algorithm. Nuclear Instruments and Methods in Physics Research B, 319: 39-43.
Singh LL, Gartia RK, 2015. Derivation of a simplified OSL OTOR equation using Wright Omega function and its application. Nuclear Instruments and Methods in Physics Research B, 346: 45-52.
Further reading
Bos AJJ, Piters TM, Gomez Ros JM, Delgado A, 1993. An intercomparison of glow curve analysis computer programs: I. Synthetic glow curves. Radiation Protection Dosimetry, 47(1-4), 473-477.
Chung KS, Choe HS, Lee JI, Kim JL, Chang SY, 2005. A computer program for the deconvolution of thermoluminescence glow curves. Radiation Protection Dosimetry, 115(1-4): 345-349. Software is freely available at http://physica.gsnu.ac.kr/TLanal.
Harvey JA, Rodrigues ML, Kearfott JK, 2011. A computerized glow curve analysis (GCA) method for WinREMS thermoluminescent dosimeter data using MATLAB. Applied Radiation and Isotopes, 69(9):1282-1286. Source codes are freely available at http://www.sciencedirect.com/science/article/pii/S0969804311002685.
Kiisk V, 2013. Deconvolution and simulation of thermoluminescence glow curves with Mathcad. Radiation Protection Dosimetry, 156(3): 261-267. Software is freely available at http://www.physic.ut.ee/~kiisk/mcadapps.htm.
Puchalska M, Bilski P, 2006. GlowFit-a new tool for thermoluminescence glow-curve deconvolution. Radiation Measurements, 41(6): 659-664. Software is freely available at http://www.ifj.edu.pl/dept/no5/nz58/deconvolution.htm.
# Load the data.
data(Refglow)
# Deconvolve Refglow002 with 4 peaks using the semi-analytical expression
# derived from the one trap-one recombination (OTOR) model.
startingPars <-
cbind(c(400, 550, 850, 1600), # Im
c(1.4, 1.5, 1.6, 2), # E
c(420, 460, 480, 510), # Tm
c(0.1, 0.1, 0.1, 0.1)) # R
tgcd(Refglow$Refglow002, npeak=4, model="lw",
inis=startingPars, nstart=10)
# Do not run.
# Deconvolve Refglow009 with 9 peaks using the general-order equation.
# startingPars <-
# cbind(c(9824, 21009, 27792, 50520, 7153, 5496, 6080, 1641, 2316), # Im
# c(1.24, 1.36, 2.10, 2.65, 1.43, 1.16, 2.48, 2.98, 2.25), # E
# c(387, 428, 462, 488, 493, 528, 559, 585, 602), # Tm
# c(1.02, 1.15, 1.99, 1.20, 1.28, 1.19, 1.40, 1.01, 1.18)) # b
# tgcd(Refglow$Refglow009, npeak=9, model="g",
# inis=startingPars, nstart=10)
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