Method of Hoogenstraaten as a tool for obtaining the trap parameters of general-order thermoluminescence glow peaks

The Hoogenstraaten method is a technique that uses various heating rates for obtaining the activation energy E (eV) in the case of first-order thermoluminescence glow peaks. This method can also be used for obtaining E (eV) for all types of glow peaks regardless of their kinetics order (b). The present work shows that the intercept of the Hoogenstraaten relation, which is usually used for obtaining the frequency factor S (s ^?1) of the first-order glow peak, can be used as a very good approximation to obtain the pre-exponential factor S ^{′ ′} (s ^?1) in the case of general-order glow peaks, when one uses Hoogenstraaten’s method to obtain E (eV). In addition, the present work suggests a numerical method for obtaining the kinetics order of the general-order glow peak. The method depends on the activation energy E (eV) obtained by the Hoogenstraaten method and the above-mentioned approximation for obtaining the pre-exponential factor S ^{′ ′} (s ^?1). An independent evaluation of the suggested methods for obtaining the trap parameters, the activation energy E (eV), the pre-exponential factor S ^{′ ′} (s ^?1) and the kinetics order (b) is illustrated here by taking a numerically computed glow peak and applying a one-trap and one-recombination-center model.     

The analysis of thermoluminescence glow curves

Information about the behavior of traps in a luminescent material is usually derived by fitting the glow curves in the thermoluminescence spectrum of the material to a general formula. From the fit one seeks to obtain values for the depth of the traps, the frequency factors governing the release of electrons from the traps, and some indication of the rates of trapping and retrapping. This study investigates how successful this fitting process is in providing reliable values for the trap parameters. The relevant rate equations are used to numerically generate simulated glow curves for specific values of trap parameters. These glow curves are then analyzed by the usual fitting process, and values for the trap parameters are derived from the fitting process. We comment on the comparison between the derived parameter values and the correct values. From these comparisons we attempt to obtain some useful insights to assist in the interpretation of experimentally observed thermoluminescence spectra.     

An algorithm for unified analysis on the thermoluminescence glow curve

An algorithm was developed to integrally handle excitation by radiation, relaxation and luminescence by thermal or optical stimulation in thermoluminescence (TL) and optically stimulated luminescence (OSL) processes. This algorithm reflects the mutual interaction between traps through a conduction band. Electrons and holes are created by radiation in the beginning, and these electrons move to the trap through the conduction band. These holes move to the recombination center through a valence band. The ratio of the electrons allocated to each trap differs with the recombination probability and these values also relevant to the process of luminescence. Accordingly, the glow curve can be interpreted by taking the rate of electron–hole pairs created by ionizing radiation as a unique initial condition. This method differs from the conventional method of interpreting the measured glow curve with the initial electron concentration allocated to each trap at the end of irradiation. A program using the Visual Studio's C# subsystem was made to realize such a developed algorithm. To verify this algorithm it was applied to LiF:Mg,Cu,Si. The TL glow curve was deconvoluted with a model of five traps, one deep trap and one recombination center (RC).     

Thermoluminescence glow curve deconvolution of LiF:Mg,Cu,Si with more realistic kinetic models

Thermoluminescence (TL) glow curves of LiF:Mg,Cu,Si were deconvoluted with the introduction of enhanced physical model which envisages that both electrons and holes, produced by ionization radiation and trapped at the respective traps, can be thermally released into the conduction and the valence band, respectively and the holes may also radiatively recombine with electrons at the electron recombination centers. The model is more generalized than the ordinary trap interaction model which only permits the traffic of electrons through the conduction band. An effective numerical analysis method was developed to calculate the glow curve to be compatible with the measured curves. The validity of the numerical method was verified through artificially generated TL glow curves for a wide range of trap parameters. In order to identify TL kinetics of LiF:Mg,Cu,Si with higher accuracy, its glow curves were deconvoluted for two more generalized models, namely, the Schön–Klasens model and the Chen–Pagonis–Lawless model as well as the ordinary trap interactive model. The parameters in the more generalized multi-trap multi-recombination center (MTMR) model were found to be consistent with the quasi-static approximation(QSA) method.     

Analysis of the glow curve of KMgF3:Lu compounds without resorting to the quasi-equilibrium approximation

In this article we report an expression for the thermoluminescence light, which is derived from the set of differential equations by assuming negligible retrapping, but without resorting to the quasi-equilibrium approximation. The expression has been employed for analysing the glow curve of KMgF3:Lu fluoroperovskite compounds.     

Nanodosimetric kinetic model incorporating localized and delocalized recombination: Application to the prediction of the electron dose response of the peak 5a/5 ratio in the glow curve of LiF:Mg,Ti (TLD-100)

A kinetic model combining both localized and delocalized recombination is described which is based on different filling rates as a function of irradiation electron energy of a spatially correlated trapping center/luminescent center (TC/LC) complex. Following irradiation and thermal de-trapping the locally trapped electron-hole configuration is assumed to give rise to peak 5a and the e-only configuration to peak 5 in the glow curve of LiF:Mg,Ti (TLD-100). The model is capable of simulating the linear/supralinear dose response of composite peak 5, the dependence of the supralinearity on photon energy and the ratio of the intensities of peak 5a to peak 5 as a function of dose. However, this is achieved only by invoking the presence of band-tail states which allow thermally induced hopping leading to semi-localized recombination in the recombination mechanism of the e-only configuration.     

A novel algorithm to solve the differential equation describing the non-interactive multiple-trap system model in thermoluminescence

The analysis of glow curves in thermoluminescence requires finding a closed expression for the light emitted as a function of the temperature and the parameters characterizing trap and recombination centers. Since it is not possible to derive a closed expression from the set of coupled differential equations describing the thermoluminescence phenomenon, approximations are made even for the simplest models. All of them resort to an approximation known as the quasi-equilibrium approximation (QE), and to further approximations. In this article, an algorithm is reported that permit the derivation of a closed expression for the emitted light for the model known as the non-interactive multi-trap system (NMTS) model by resorting only to the QE approximation. It is shown that the integration of the first order differential equation related to the NMTS model can be replaced by finding the roots of an analytical expression.     

Afterglow mechanism and thermoluminescence of red-emitting CaS:Eu,Pr phosphor with incorporated Li ion upon visible light irradiation

This paper reports on the afterglow mechanism and thermoluminescence (TL) of a red-emitting CaS:Eu²⁺,Pr³⁺ phosphor with incorporated Li⁺ ion upon irradiation by visible light (D₆₅ lamp). In the TL glow curve of the CaS:Eu²⁺,Pr³⁺ phosphor, a TL peak was observed near 120 °C. The luminescence center of the CaS:Eu²⁺,Pr³⁺ phosphor was the Eu²⁺ ion and the trap depth of the CaS:Eu²⁺,Pr³⁺ phosphor with the cation vacancy (Trap 1) which formed by incorporation of the Pr³⁺ ion was 0.202 eV. A cation vacancy (Trap 2) was formed by incorporation of the Li⁺ ion in the CaS:Eu²⁺,Pr³⁺ phosphor. In the TL glow curve of the CaS:Eu²⁺,Pr³⁺ phosphor with incorporated Li⁺ ion, two TL peaks were observed near 120 and 200 °C. The TL luminance of the CaS:Eu²⁺,Pr³⁺ phosphor with incorporated Li⁺ ion increased with an increase in the initial Li/Ca atomic ratio. The two TL peaks moved to the high-temperature side with an increase in heating rate. The cation vacancy (Trap 2) calculated from the Hoogenstraaten method was 0.118 eV. The afterglow time of the CaS:Eu²⁺,Pr³⁺ phosphor with incorporated Li⁺ ion was prolonged by generation of a shallow trap.     

A generalised model of hydrogen diffusion in metals with multiple trap types

Continuum modelling of hydrogen diffusion in metals, which accounts for both trapping and an imposed force field, is revisited. A generalised model of hydrogen diffusion and trapping is developed as a continuous interpretation of the discrete random-walk theory. A system of nonlinear equations describing the phenomenon of diffusion with multiple types of traps is derived without the assumption of a local equilibrium among hydrogen populations in dissimilar positions. Lattice-trap interchange kinetics can degenerate into local equilibrium as a limit case. Moreover, certain terms in general equations may be negligible in specific situations. By removing these terms, known particularised models of hydrogen diffusion and trapping are recovered. Determining the terms, which are disregarded in reduced models, enables a straightforward assessment of the applicability of these models. The advantages and limitations of particularised models applied to hydrogen embrittlement analyses are discussed.     

The trap parameters of electrons in intermediate energy levels in quartz

The trap parameters (thermal activation energy E_t and frequency factor s) of the glow peaks of quartz, occurring in the temperature range 420–520 K and corresponding to intermediate energy levels, were evaluated using different and complementary methods of analysis: peak shift, isothermal decay and fractional glow curve. The values of E_t and of s derived with the isothermal decay method and with the peak shift technique agree quite well, within the error limits. The corresponding values obtained using the fractional glow curve analysis proved to be underestimated, probably as a consequence of the thermal quenching. Proper corrections were therefore applied to take into account this phenomenon.     

Energy dependence of electron-induced radiation damage in tungsten

Abstract

The energy dependence of low dose damage production in commercial and high purity polycrystalline tungsten wires was studied near 350 K with 1.6 to 2.4 MeV electrons. From resistivity measurements at 291 K the threshold energy for the onset of observable damage was determined as 50 × 2 eV. An ‘effective’ threshold of 52 ±2 eV was also determined by directly fitting the energy dependence of the damage rates to theoretical displacement cross sections calculated from step-function displacement probabilities. A decrease of two orders of magnitude in impurity content reduced damage rates by about a factor of two but did not affect threshold. These results combined with current defect recovery models for tungsten, low temperature threshold data, and computer-calculated bcc damage theory suggest: (1) Observed damage consisted of equal concentrations of vacancies and impurity-trapped Stage I free interstitials. (2) Across Stage II (100 K to 600 K) onset threshold should be within 50 ±2 eV. (3) Minimum recoil energy required for free interstitial production near 0 K is 53 ± 5 eV. (4) Threshold has little dependence on crystal direction. An empirical method is presented for predicting threshold energies in the bcc transition metals by assuming the directional dependence of threshold is directly proportional to that of Young's modulus. By the use of one universal proportionality constant (1.2 × 10^?11 eV.cm²/dyne), thresholds for a number of metals and directions are calculated and shown to have significantly better agreement with experiment than the best available theoretical estimates.     

Dose response of F center optical absorption in LiF:Mg,Ti (TLD-100)

Optical absorption (OA) of nominally pure single crystal LiF following beta irradiation was measured in order to estimate, the energy and width of the dominant F-band with minimum interference from dopant-related bands. The OA dose response of LiF:Mg,Ti was measured to 30,000 Gy, a level of dose sufficiently high to observe total saturation of the F band, which, we believe, reduces uncertainty in the estimation of the dose filling constant. The dose filling constants for the OA bands associated with the trapping center (4 eV) and competitive center (5.45 eV) responsible for the major dosimetric TL glow peak 5 were also determined. The results of these studies will be used in the framework of a kinetic model which includes the effects of radiation created defects and which will aid in the investigation of the capability of Track Structure Theory to predict OA heavy charged particle (HCP) relative efficiencies.     

Interatomic potentials for simulating radiation damage effects in metals

We critically review the recent developments in the field of semi-empirical interatomic potentials for molecular dynamics simulations, with particular emphasis on the requirements and criteria associated with the simulations of radiation damage effects in metals. We address a range of issues including the suitability of potentials for large-scale simulations, the role of electronic excitations and electron energy losses, and the part played by the dynamics of internal degrees of freedom of atoms, for example magnetic excitations. To cite this article: K. Nordlund, S.L. Dudarev, C. R. Physique 9 (2008).     

Dependence of peak height of glow curves on heating rate in thermoluminescence

The area under the glow curve (no thermal quenching and same dose) is conserved only in TL-time plots and is not conserved (scales by a factor by which heating rate is increased) in TL-temperature plots. This increase in area under TL-temperature glow curves with increase in heating rate at a constant dose should not be interpreted as increase in sensitivity of the dosimeter and is the consequence of transformation of time to temperature scale (temperature scale obtained from time scale by multiplying with β, T=T₀+βt). This is further supported by the fact that the light output or integrated counts seen by the PMT do not change (ignoring statistical fluctuations) with increase in heating rate at a constant dose. Further for a given heating rate, the glow peak height is similar in time and temperature plots and the glow peak height increases with increase in heating rate. However to conserve area in TL-temperature plots, the TL intensity should be divided by the respective heating rate, which will lead to the decrease of glow peak height in I/β-temperature plots and is the artifact of the normalization process. However for normalized glow curves (I/β-temperature), the glow peak height decreases with increase in heating rate, which is actually true for I/β or TL/β versus temperature plots. Hence it is recommended that in such cases where normalized glow curves (I/β versus temperature) are presented, the obtained peak height must be multiplied by β. By doing so, glow peak height increases with increase in heating rate. In addition to the above, studies are also carried out by considering thermal quenching effect and it is found that a logical way to measure thermal quenching quantitatively is to record the decrease of integrated counts (PMT current) with increase in heating rate at a constant dose, i.e. the integrated peak area (PMT current or TL-time or TL/β-temperature) must be plotted against the heating rate and the same should be used for interpretation of thermal quenching effect. Only this proves the fact whether the decrease of TL intensity (TL/β-temperature) is due to thermal quenching or not.     

四阳极直流辉光放电正柱区数值分析

分析了具有中间开窗电极四阳极直流辉光放电装置的氦气放电中阴极与较近阳极间放电正柱区的电子密度、电子温度和等离子体碰撞频率, 及其空间分布随放电气压变化规律。结果表明电子密度在径向上呈类似于抛物线的分布, 而碰撞频率和电子温度在整个放电管内近似均匀分布。探讨了不锈钢阳极座和矩形窗口对这些参数的影响, 为进一步进行装置仿真和实验研究提供参考。     

Systematic underestimation of the age of samples with saturating exponential behaviour and inhomogeneous dose distribution

In luminescence and ESR studies, a systematic underestimate of the (average) equivalent dose, and thus also the age, of a sample can occur when there is significant variation of the natural dose within the sample and some regions approach saturation. This is demonstrated explicitly for a material that exhibits a single-saturating-exponential growth of signal with dose. The result is valid for any geometry (e.g. a plain layer, spherical grain, etc.) and some illustrative cases are modelled, with the age bias exceeding 10% in extreme cases. If the dose distribution within the sample can be modelled accurately, it is possible to correct for the bias in the estimates of equivalent dose estimate and age. While quantifying the effect would be more difficult, similar systematic biases in dose and age estimates are likely in other situations more complex than the one modelled.     

The study of radiation damage in metals with the field-ion and atom-probe microscopes

The application of the field-ion microscope (FIM) and the atom-probe FIM techniques to the study of radiation damage in metals is reviewed. The FIM research in the following three areas is discussed: (1) the defect structure of the primary state of irradiated metals; (2) the recovery behavior in Stages I, II and III of irradiated body-centered and face-centered cubic metals (tungsten and platinum); and (3) the recovery behavior in Stages I, II and III of irradiated body-centered and face-centered cubic alloys [tungsten (carbon), tungsten (rhenium) and platinum (gold)]. The data obtained in each of these three categories provide fundamental structural, kinetic and thermodynamic information about the properties of point defects and point-defect clusters. The atom-probe FIM research on the direct measurement of the range of 300 eV He⁺ ions and the mobility of interstitial helium atoms in tungsten is also presented and compared with the theoretical predictions of Wilson, Haggmark and Bisson.     

Relevance of the displacement damage concept for the evaluation of radiation effects in metals

Abstract

Changes in dimensions, mechanical properties and chemical composition due to irradiation by different particles at elevated temperatures are compared on the basis of atomic displacements derived from low temperature resistivity damage rates. The available data on void swelling, irradiation creep and room temperature hardening correlate reasonably well on this basis. The correlation seems poor for hardening at high temperatures and even worse for fracture properties and chemical effects (solute segregation, precipitate growth). The results are discussed in terms of the basic damage processes.