Investigating signal evolution: A comparison of red and UV/blue TL,and UV OSL emissions from the same quartz sample

Samples from plutonic geological settings emit strong and stable UV, blue and red luminescence. These samples provide a unique opportunity to investigate the evolution of luminescence emissions by comparing their origin, intensity, trapping and recombination characteristics. In addition, the D_e derived from certain techniques can be used to investigate D_e consistency. Thus, UV and red signals emitted by the same sample of grantic quartz have been compared according to the strength and shape of the emissions, response to annealing and dose, growth characteristics and the resulting D_e derived from single-aliquot regeneration (SAR – UV emissions) and the dual-aliquot protocol for red TL (DAP – red emissions). This comparison of UV and red D_e values can be used as an alternative measure of accuracy for depositional situations where independent age control is not available. Furthermore, this comparison has been extended to a single-grain level to determine if UV and red signals are emitted by the same quartz grain. The resulting comparisons demonstrate that both signals are strong, reproducible, are suitable for dating, and a comparison of D_e is a valid internal check of consistency. The single-grain analysis demonstrates that the grains contain UV and red recombination centres rather than the typical characteristics of just beta or alpha quartz. Thus it has been suggested that the emissions relate to post-origin modifications of the signal rather than its thermal origin. This type of comparative analysis provides clues as to the source and evolution of the signals, provides a greater understanding of the complexities of the luminescence signal and a possible solution for accuracy testing in challenging depositional contexts.     

Bleaching of the post-IR IRSL signal from individual grains of K-feldspar: Implications for single-grain dating

Post-IR IRSL (pIRIR) signals from K-feldspar grains measured at elevated temperatures are increasingly being used for dating sediments. Unfortunately the pIRIR signal from K-feldspars bleaches more slowly than other signals (e.g. OSL from quartz) upon exposure to daylight, leading to concerns about residual signals remaining at deposition. However, earlier studies have not assessed whether the pIRIR signal bleaches at the same rate in all feldspar grains. In this study laboratory bleaching experiments have been conducted and for the first time the results show that the rate at which the pIRIR signal from individual K-feldspar grains bleach varies. To determine whether grain-to-grain variability in bleaching rate has a dominant control on equivalent dose (D_e) distributions determined using single grains, analysis was undertaken on three samples with independent age control from different depositional environments (two aeolian and one glaciofluvial). The D_e value determined from each grain was compared with the rate at which the pIRIR₂₂₅ signal from the grain bleaches. The bleaching rate of each grain was assessed by giving a 52 Gy dose and measuring the residual D_e after bleaching for an hour in a solar simulator. There is no clear relationship between the rate at which the pIRIR₂₂₅ signal of an individual grain bleaches and the magnitude of its D_e. It is concluded that variability in the bleaching rate of the pIRIR₂₂₅ signal from one grain to another does not appear to be a dominant control on single grain D_e distributions.     

Improving the accuracy and precision of equivalent doses determined using the optically stimulated luminescence signal from single grains of quartz

Optically stimulated luminescence (OSL) measurements of quartz are widely used to measure equivalent dose (D_e). At radiation doses above ～100 Gy, saturation of traps results in a decrease in the rate of growth of the OSL signal, and this makes calculation of D_e increasingly difficult. A series of dose recovery experiments was undertaken using single grains of quartz from Kalambo Falls, Zambia to explore saturation of single grains. When the OSL signal from many grains is averaged, the characteristic dose (D₀) is 47 Gy, typical of published values for quartz. However, D₀ for individual grains varies from ～10 to 100 Gy. Doses up to two times the average D₀ could be accurately recovered, but above this dose the D_e became increasingly underestimated. Overdispersion for this type of experiment should be zero, but was observed in all data sets; furthermore the value of overdispersion increased with D_e. An additional acceptance criterion, the Fast Ratio, is suggested for single grain OSL analysis. This criterion assesses the relative contribution of the fast component of the OSL signal. Including this as an additional acceptance criterion leads to an improved precision, with overdispersion reduced to zero, and improved accuracy in dose recovery at high doses.     

Dose dependence of thermally transferred optically stimulated luminescence signals in quartz

The thermally transferred optically stimulated luminescence (TT-OSL) responses of chemically purified fine-grained quartz from seven loess-like samples from Korea are presented. In particular, the experimental procedures used to separate the dose-dependent (recuperated OSL, ReOSL) and dose-independent parts of the signal were explored. The OSL signals used to monitor the sensitivity changes that take place during the measurement sequences used to determine the equivalent dose were investigated. A single aliquot procedure was used for the TT-OSL measurements and resulted in linear growth of the ReOSL with dose up to at least 2 kGy. For this suite of samples, a standardised growth curve (SGC) was constructed for the ReOSL, tested with dose recovery experiments, and was used to obtain D_e values for the seven samples.     

The estimation of basic experimental parameters in the fine-grained quartz multiple-aliquot regenerative-dose OSL dating of Chinese loess

The sensitivity-corrected multiple-aliquot regenerative-dose (MAR) protocol provides a reliable approach for fine-grained quartz optically stimulated luminescence (OSL) dating. For reliable estimation of the equivalent dose (D_e), we investigated certain basic experimental parameters in the fine-grained quartz MAR OSL dating of Chinese loess. (1) For suitable bleaching of the natural OSL signal of the regenerative-dose aliquots, the effect of bleaching duration using sunlight, SOL2 and blue LEDs on D_e was studied, and it is found that the appropriate method is a short-duration SOL2 (e.g. 5 min) or blue LEDs (e.g. 60 s) bleaching. (2) To select the appropriate test dose, the relationship between the test dose and D_e was investigated based on three samples having D_e values of approximately 11, 31 and 137 Gy respectively. It is suggested that the test dose for sensitivity correction may be limited to less than approximately 10–20 Gy. (3) Three commonly used fitting modes for quartz OSL growth curve were compared at three regenerative-dose scales. The results indicate that the mode of two saturating exponential functions plus a constant is appropriate and universal. (4) The comparison of D_e values derived using OSL approach with those obtained using the recuperated OSL (ReOSL) protocol shows that the reliable D_e estimation in the fine-grained quartz MAR OSL dating of Chinese loess may be limited to less than approximately 300 Gy. (5) The comparison of growth curves for 18 samples from the Weinan, Xifeng and Jingyuan sites shows that it is feasible to construct a standardized growth curve (SGC) for fine-grained quartz OSL signal in the Chinese Loess Plateau (CLP).     

Luminescence dating of quartz using an improved single-aliquot regenerative-dose protocol

Single aliquot protocols are now widely used as a means of measuring the equivalent dose (D_e) in quartz and feldspar optical stimulated luminescence (OSL) dating of both heated and sedimentary materials. The most recent of these is the single-aliquot regenerative-dose (SAR) protocol, first suggested by Murray and Roberts (Radiation Measurements 29, 503–515, 1998). In this approach, each natural or regenerated dose OSL measurement is corrected for changes in sensitivity using the OSL response to a subsequent test dose (10–20% of D_e). If the sensitivity correction is adequate, then the corrected OSL response should be independent of prior dose and thermal/optical treatment, i.e. there should be no change in the sensitivity-corrected dose–response curve on remeasurement. Here we examine the interpretation of the sensitivity corrected growth curve as a function of dose, and the effect of changing measurement conditions (e.g. preheat temperature, size of test dose, stimulation temperature) on the estimation of D_e. The dependence of the dose response on prior treatment is tested explicitly, and the significance of thermal transfer discussed. It is concluded that a robust SAR protocol is now available for quartz, and that it is applicable to a wide range of heated and unheated materials.     

Investigations of the post-IR IRSL protocol applied to single K-feldspar grains from fluvial sediment samples

The post-IR IRSL protocol with single K-feldspar grains was applied to three samples taken from a fluvial sedimentary sequence at the archaeological site of the Dali Man, Shaanxi Province, China. K-feldspar coarse grains were extracted for measurement. Approximately 30–40% of the grains were sufficiently bright to measure, and after application of rejection criteria based on signal strength, recuperation, recycling ratio and saturation dose, ～10–15% of the grains were used for D_e calculation. The relationship of signal decay rate and form of D_e(t) with the recovery dose were investigated. The dose recovery ratios of the samples after initial bleaching with the four different light sources were within uncertainties of unity. No anomalous fading was observed. The over-dispersion of the recovered dose and D_e values were similar, suggesting neither incomplete resetting of the post-IR IRSL signals nor spatially heterogeneous dose rates significantly affected the natural dose estimates. The values of D_e obtained with the single K-feldspar grain post-IR IRSL protocol were in the range ～400–490 Gy. Combining all of the measured single-grain signals for each of the individual samples (into a ‘synthetic single aliquot’) increased the D_e estimates to the range ～700–900 Gy, suggesting that the grains screened-out by the rejection criteria may have the potential to cause palaeodose over-estimation, although this finding requires a more extensive investigation. Thermally transferred signals were found in the single K-feldspar grains post-IR IRSL protocol, and the proportion of thermally transferred signal to test-dose OSL signal (stimulation at 290 °C) from the natural dose was higher than from regenerative doses, and the proportion was grain- and dose-dependent. As such, TT-post-IR IRSL signals at 290 °C have the potential to cause dose underestimation, although this may be reduced by using larger test-dose irradiations. Our study demonstrates considerable potential in the post-IR IRSL method in providing chronological control in studies relevant to human evolution in the later-Pleistocene.     

Empirical insights into multi-grain averaging effects from ‘pseudo’ single-grain OSL measurements

In this study we assess the signatures of multi-grain averaging effects for a series of sedimentary samples taken from the archaeological site of Hotel California, Atapuerca, Spain. We focus on the special case of equivalent dose (D_e) measurements made on single-grain discs that contain more than one quartz grain in each of the individual grain-hole positions with the aims of (i) providing insight into the nature and extent of averaging effects in very small multi-grain aliquots of sedimentary quartz, and (ii) assessing the suitability of ‘pseudo’ single-grain D_e measurements for this particular dating application. Pseudo single-grain OSL measurements made on standard discs loaded with 90–100 μm grains (equivalent to ～30 grains per hole) yield significantly different D_e distribution characteristics and finite mixture model (FMM) burial dose estimates compared with single-grain OSL measurements. Grains with aberrant luminescence behaviours, which are routinely rejected during single-grain analysis, exert strong averaging effects on the pseudo single-grain and multi-grain aliquot D_e distributions. Grain-hole averaging effects arising from pseudo single-grain measurements also give rise to ‘phantom’ dose components and are apt to provide bias assessments of quartz signal characteristics and grain type classifications. Though this is a site-specific study, it serves as a cautionary note for interpretations of other pseudo single-grain OSL and D_e datasets – particularly those obtained from measurements of discs containing several tens of grains per hole and those derived from complex depositional environments. The use of custom single-grain discs drilled with smaller sized grain holes is recommended as a means of limiting grain-hole averaging effects when dealing with very fine (<180 μm) sediments.     

Developing a single-aliquot protocol for measuring equivalent dose in biogenic carbonates

Exploiting biogenic carbonates as thermoluminescence dosimeters requires an understanding of trap kinetics and an appropriate sequence with which to measure equivalent dose. The trap kinetics of two high temperature peaks (peaks II and III) from calcitic snail opercula have been investigated resulting in the calculation of lifetimes of 7.4 × 10⁷ and 1.4 × 10¹¹ years for the two peaks respectively. Two measurement sequences, based upon changes in the application and measurement of a test dose, have been applied to peaks II and III, and though both methods were equally successful in dose recovery and production of a dose response curve some differences were observed. Primarily, the use of method 1 lead to dose dependant sensitivity change implying competition effects occurring during irradiation; method 2 did not experience this phenomenon. As a consequence method 2 was chosen as the most appropriate protocol for single-aliquot dating of this material.When assessing the TL behaviour of the two peaks, peak II performed poorly in dose recovery experiments recovering a dose 60–100% larger than that applied. Disproportionate growth of peak II in response to a beta dose applied prior to measurement, compared to growth following regeneration doses indicated that peak II was not suitable for use in single-aliquot protocols. However, dose recovery results for peak III were all within errors of unity of the given dose, and peak III was therefore chosen as the most appropriate peak for TL dosimetry in these single-aliquot procedures. The lifetime of charge in peak III is sufficient to date over many millions of years, and furthermore using the chosen method 2 the dose response curve has a D₀ of 3,250 ± 163 Gy allowing dating to over 3 million years.     

On the intrinsic accuracy and precision of the standardised growth curve (SGC) and global-SGC (gSGC) methods for equivalent dose determination: A simulation study

In optically stimulated luminescence (OSL) dating, the single aliquot regenerative-dose (SAR) method has been used extensively for determining equivalent doses (D_e) in quartz. A variation of the SAR method is the “standardised growth curve” (SGC) method, which has been used as an efficient procedure to save measurement time during dating studies. During the application of the SGC method one establishes the SGC and calculation of the D_e of an aliquot requires only measurement of the standardised natural dose signal. Recently, a “global standardised growth curve” (gSGC) method was developed as an improved version of the SGC procedure. During the application of the gSGC method, the growth curves are re-normalised using sensitivity-corrected signal corresponding to one of the regenerative doses. Subsequently the D_e of an aliquot is estimated using the sensitivity-corrected natural dose signal and an additional sensitivity-corrected regenerative dose signal as well as the established gSGC. In the present study, simulations are performed to assess the intrinsic accuracy and precision of the SGC and gSGC D_e estimates. The results of our simulations validate that the gSGC method is intrinsically more precise than the SGC method and is also more accurate for doses greater than 210 Gy. Several factors which affect the reliability of the two methods are investigated.     

Yellow stimulated luminescence from potassium feldspar: Observations on its suitability for dating

Yellow stimulated luminescence (Y-OSL) is the light detected from potassium-rich feldspars at 410 nm under stimulation by a yellow light source emitting 590 nm. The investigation of this study aimed at understanding basic luminescence physics of Y-OSL in order to assess the suitability of the technique for dating. The Y-OSL signal properties tested were signal intensity, thermal assistance, thermal stability, sensitivity to daylight and the suitability of a single aliquot regenerative (SAR) protocol to be employed for equivalent dose (D_e) estimation. D_e measurements were conducted on samples of Holocene, last glacial and Tertiary age. The tests were undertaken on sedimentary feldspar separates extracted from aeolian, fluvial and coastal deposits.Results from experiments show that the signal intensity increases by measuring Y-OSL at elevated temperature suggesting thermal assistance characteristics similar to infrared stimulated luminescence (IRSL). The yellow stimulated signal remains unaffected by preheat temperatures up to ～200 °C suggesting higher thermal stability than the IRSL signal. The Y-OSL signal is less light sensitive than the IRSL signal and D_e residuals obtained from modern samples are up to 7 Gy indicating suitability of the technique for ‘older’ and well-bleached sediments. The dose recovery tests successfully recovered the given dose if the specific light sensitivity of Y-OSL is taken into account. For every sample Y-OSL D_e values obtained by a single aliquot regenerative dose protocol (SAR) are higher than those obtained by an IRSL SAR approach. From these results we infer high thermal stability and a minimal anomalous fading of the Y-OSL signal. We conclude that Y-OSL has a high potential to date Quaternary sediments that were sufficiently bleached in nature.     

Investigations into the reliability of SAR-OSL equivalent doses obtained for quartz samples displaying dose response curves with more than one component

Fast component dominated quartz single aliquot regenerative dose optically stimulated luminescence (SAR-OSL) dose response curves that display continuing growth at high doses are increasingly reported in literature. This behaviour would result in higher equivalent doses being obtained. Here we document the characteristics of OSL signals from fine (4–11 μm) and coarse (63–90 μm) quartz extracted from Romanian loess that display such behaviour. For very high doses (>1 kGy up to 5–15 kGy) the data could be closely fitted to a double saturating exponential regression model. Nonetheless, the saturation charcteristics of these fine and coarse quartz grains are very different, with average saturation chracteristic doses of D₀₁ ≈ 175 Gy and D₀₂ ≈ 1800 Gy in the case of the fine material, while in the case of the coarse material values of D₀₁ ≈ 55 Gy and D₀₂ ≈ 600 Gy have been obtained. Our results imply a hitherto unexplained mechanism in OSL production at high doses and question the reliability of obtaining SAR-OSL equivalent doses in the high dose region when a second function is needed to describe the dose response.     

A comparison of natural- and laboratory-generated dose response curves for quartz optically stimulated luminescence signals from Chinese Loess

It has previously been observed that laboratory-generated quartz optically stimulated luminescence (OSL) signals from different samples have similar dose response curves (DRCs) after they are normalized using a test dose. It therefore seems likely that growth of the normalized signal due to natural irradiation of quartz may also follow a general dose response curve. The existence of such a curve is investigated by constructing a natural DRC from the test dose-normalized natural OSL signals of seven samples from the Luochuan section of the Chinese Loess Plateau. The same aliquots are then used to build single aliquot regenerative (SAR) DRCs, making it possible to compare the natural and laboratory constructed curves. Two main differences are observed. Firstly, the laboratory-generated DRCs are best fitted with double saturating exponential functions whereas the natural DRC is equally well fitted with a single saturating function. Secondly, in the laboratory-generated DRCs the normalized OSL signal continues to increase at high laboratory doses (>500 Gy), whereas no growth is seen at these doses in the equivalent natural DRC. These differences between natural- and laboratory-generated DRCs are still apparent even if data are manipulated to isolate the fast component, or if a sensitivity corrected multiple aliquot regenerative (SC-MAR) dose procedure is used. This suggests that the observed differences are not due to the influence of different components or inter-regenerative dose cycle sensitivity changes. The divergence between the natural- and laboratory-generated DRC means that the current maximum limit of quartz OSL dating at the Luochuan section is 150 Gy, as D_e estimates above this value are likely to be underestimations.     

The interpretation of quartz optically stimulated luminescence equivalent dose versus time plots

Numerical modelling has shown that the form of the quartz OSL shine plateau (hereafter ‘D_e(t)-plot’) is influenced by the effects of phototransferred TL in the ∼110°C region. It is suggested also that the presence of multiple OSL components (as described by Bailey, Smith and Rhodes, 1997. Partial bleaching and the decay form characteristics of quartz OSL. Radiat. Meas., 27, 123–136; Bailey, 1998. The form of the optically stimulated luminescence signal of quartz: implications of dating. Unpublished PhD thesis, University of London) affects the form of the D_e(t)-plot. Laboratory measurements of a fully reset and artificially dosed sample yielded non-flat D_e(t)-plots, the deviation being greater for the larger of the two simulated palaeodoses, in accordance with theoretical predictions. It is suggested that the so-called ‘shine plateau’ test is of limited use in assessing the bleaching history of quartz sediments.     

Development of a personal dosimeter badge system using sintered LiF:Mg,Cu,Na,Si TL detectors for photon fields

The badge system of personal thermoluminescence (TL) dosimeter for photon fields using LiF:Mg,Cu,Na,Si TL material, which was developed by Korea Atomic Energy Research Institute (KAERI) a few years ago, was developed by taking advantage of its dosimetric properties including energy dependencies. A badge filter system was designed by practical irradiation experiments supported by computational modeling using Monte Carlo simulation. Design properties and dosimetric characteristics such as photon energy response and angular dependence of new TL dosimeter system examined through the irradiation experiments are presented. Based on the experiments for the developed dosimeter, it is demonstrated that the deep dose response of dosimeter provided the value between 0.78 and 1.08, which is within the design limit by ISO standard. This multi-element TL dosimeter badge system allows the discrimination of the incident radiation type between photon and beta by using the ratios of the four TL detectors. Personal TL dosimeter using sintered LiF:Mg,Cu,Na,Si TL detectors has the ability to measure a personal dose equivalent H_p(d) for a wide range of photon energies.     

Noble gas halides: The B → X and D → X systems of 136Xe35Cl

The B → X (2870–3100 Å) and D → X (2250–2370 Å) band systems of ¹³⁶Xe³⁵Cl are photographed and vibrationally analyzed. A simultaneous least-squares fit of 41 band-heads in the B-X system and 35 in D-X yields, in part, the following constants (in cm^?1): T_eB = 32 405.8, T_eD = 42 347.9, ω_eB = 194.75, ω_eD = 204.34, ω_eX = 26.22. The ground state dissociation energy ($\text{D}$″_e) is estimated to be 281 ± 10 cm^?1. Potential curves are derived for all three states through Franck-Condon calculations. From these curves the D-state internuclear distance is 0.09 ± .02 Å smaller than the B-state distance.     

Effects of thermally transferred signals in the post-IR IRSL SAR protocol

The recently developed post-IR IRSL SAR protocol is promising to isolate more stable IRSL signals of feldspars. However, the high temperature thermal treatments used will inevitably induce thermally transferred post-IR IRSL₂₉₅ (TT-post-IR IRSL₂₉₅) signal, which would contribute to the measured post-IR IRSL₂₉₅ signal of the test dose and may lead to inaccurate sensitivity correction. In this study, the effects of TT-post-IR IRSL₂₉₅ signal in the post-IR IRSL₂₉₅ SAR protocol are investigated using medium polyminerals from a loess section at Caoxian, northwestern Loess Plateau in China. The sensitivity changes of the IRSL₅₀ and the post-IR IRSL₂₉₅ signals are different from natural cycle to regenerative cycles, which can be attributed to the interference of the TT-post-IR IRSL₂₉₅ signal. Such difference is dependent on the test dose and the post-IR IR stimulation time. The TT-post-IR IRSL₂₉₅ signal is also shown to affect the post-IR IRSL₂₉₅ D_o and D_e values and to cause overestimation of the fading rates. Our study therefore highlights the need of serious consideration on the effects of TT-post-IR IRSL signal when the post-IR IRSL SAR protocol is employed for dating.     

The Effect of TiO2 and MgO on the Thermoluminescence Properties of a Lithium Potassium Borate Glass System

The influence of dopant TiO₂ and co-dopant MgO on the thermoluminescence (TL) properties of lithium potassium borate glass (LKB) is reported in this paper. The glow curve exhibits a prominent peak (T_m) at 230 °C. The TL intensity was enhanced by a factor of ~3 due to the incorporation of MgO, and this was attributed to the creation of extra electron traps mediated by radiative recombination energy transfer. We achieved good linearity of the TL yield with dose, low fading, excellent reproducibility and a promising effective atomic number (Z_eff=8.89), all of which are highly suitable for dosimetry. The effect of heating rate, sunlight and dose rate on the TL are also examined. These attractive features demonstrate that our dosimeter is useful in medical radiation therapy.     

Theoretical studies of the bonding of sulfur to models of the (100) surface of nickel

Electronic wavefunctions have been obtained as a function of geometry for a S atom bonded to Ni clusters consisting of 1 to 4 atoms designed to model bonding to the Ni(100) surface. Electron correlation effects were included using the generalized valence bond and configuration interaction methods. Modeling the (100) surface with four Ni atoms, we find the optimum S position to be 1.33 Å above the surface, in good agreement with the value (1.30 ± 0.10 Å) from dynamic LEED intensity calculations. The bonding is qualitatively like that in H₂S with two covalent bonds to one diagonal pair of Ni atoms. There is a S pπ pair overlapping the other diagonal pair of Ni atoms. [Deleting this pair the S moves in to a position 1.04 Å from the surface.] There are two equivalent such structures, the resonance leading to equivalent S atoms and a c(2 × 2) structure for the S overlayer. The Ni in the layer beneath the surface seems to have little effect (~0.03 Å) on the calculated geometry. Bonding the S directly above a single Ni atom leads to a much weaker bond (D_e = 3.32 eV) than does bonding in a bridge position (D_e = 5.37 eV).     

Standardised growth curves for optical dating of sediment using multiple-grain aliquots

The single aliquot regenerative dose (SAR) protocol offers the opportunity of exploring, relatively simply, the existence of a ‘universal’ growth curve for use in dating using optically stimulated luminescence (OSL). A test dose is used in the SAR procedure to monitor and correct for sensitivity change occurring either over the burial period, or as a result of thermal pretreatments during the measurement procedure. However, this test dose can also be used to correct for variations in signal intensity between individual aliquots, thus enabling the comparison of growth response with dose for many different aliquots and samples, even for measurements made using different instruments.In this paper, the growth characteristics of coarse-grained quartz and polymineral fine-grains are examined using data obtained as part of the SAR procedure. Following standardisation of these data for differences in the test dose response and the magnitude of the test dose used, distinct and reproducible patterns of growth are observed and mineral-specific standardised growth curves (SGCs) are defined for multiple-grain aliquots. An equivalent dose for a sample can then be determined based only on measurements of the natural luminescence signal intensity (L_n) and the response to an artificial irradiation dose (T_n). This equivalent dose, determined using the SGCs defined for quartz and polymineral fine-grains, is compared to that determined using a conventional SAR measurement procedure, for a large number of samples and aliquots. Using an SGC, accurate estimates of equivalent dose may be made based solely on measurements of L_n and T_n, thus potentially speeding up the measurement process. This has obvious benefits where it is necessary to examine a large number of aliquots.