Isochronal plots

Figure 4. Osmond type II isochron plot for sub-samples from single growth layer in stalagmite SVC-98-3.B from Spring Valley Caverns Morale et al. 2003).

Figure 12. Uranium-lead ( U/ Pb- ° Pb/ °" Pb) isochron plot for the WHCl stalactite from Peak District, England (Richards et al. 1998).

Figure 10. Single-crystal internal isochron plot of the 26A l-26Mg evolution diagram for different areas with distinct 27Al/24Mg ratios within individual anorthite crystals from TS-21 (9) and TS-23 ( A. V-...

In the isochron plot, the horizontal axis is the atomic ratio of " Sm/ " " Nd, but measurements are often reported as Sm and Nd weight concentrations. The atomic ratio of two nuclides may be calculated from the weight concentrations of the two elements as follows ... 

One drawback of the Pb-Pb system is that two-stage or three-stage evolution of the U-Pb isotopic system can produce linear arrays on a Pb-Pb isochron plot (Gale and Mussett, 1973). If these arrays are interpreted as single-stage isochrons, incorrect dates may be obtained. In some cases, measurements of the U/Pb ratio can help identify multistage samples. But if several events occurred sufficiently early in solar system history, even a concordia approach may not be able to identify a multistage system (Tera and Carlson,... 

Fig. 12.3 Isochrones plotted on a 36Cl-Cl composition diagram. Calculation of the age for samples A and B is discussed in the text.

Variable fractionation of uranium and thorium generates a horizontal array of samples (Figure 7(a)). If the melt and residue remain in chemical equilibrium, this flat array can persist indefinitely (Section 3.14.2.2.2). However, if the melts and residues become chemically separated, the array rotates with age, pivoting around a point on the equiline, until it ultimately returns to equilibrium with a slope of 1. As in any isochron plot, a linear array may have age significance, or it may simply reflect mixing between two unrelated samples. 

Similarly, the application of isochronal analysis to transient data (20) assumes that the time dependence of the transient response is independent of the parameter being varied. For example, plotting current at a particular time against temperature yields useful data only if the transient proceeds at a rate independent of temperature. However, the example of Figure 1 and transients calculated from the model have features which would appear as peaks in an isochronal plot, yet are intrinsic to the conduction mechanism. 

Isochron A set of data points on an isochron plot that all fall on a single line and represent a single radiometric age. 

The slope is CR, the product of the initial iodine isotope ratio and the conversion factor. The real point of the experiment is to determine R, the initial iodine isotogm composition. To do so, however, it is necessary to know C, the efficiency with which is converted to Xe. This is normally done by including an irradiation monitor in the nuclear irradiation, a sample with a known ( 1/ I)o ratio. The data from the monitor are then plotted on the same type of isochron plot, but for the monitor, the unknown is C, the conversion factor for that particular experiment. Then, knowing the conversion factor, R can be determined for the other samples irradiated at the same time. 

Ar/ Ar ratios are not constant, and are generally achieved using an isochron plot. Cosmogenic contributions are considered elsewhere in this volume (Wieler 2002 Niedermann 2002). 

Figure 18. Sm-Nd isochron plot from coeval samples from different sectors of the sectorally zoned apatite in Figure 17. The isochron yields an age of ciystalhzation of 43.8 4.7 Ma. [Modified after Rakovan et al. 1997.]...

An isochron plot of vs Sm/ Nd for volcanic rocks from the Onverwacht... 

Since only one point of an isochronous plot is obtained from each creep test, it is usually necessary to run at least three stress levels (preferably more) to obtain an isochronous plot. 

Fig. 35. Typical djaiamic mechanical behavior for viscoelastic functions and G and G" and log damping decrement = tt tan S (isochronal plot, constant frequency = 1 Hz) for a styrene-butadiene copolymer (78). To convert Pa to dynes/cm, multiply by 10.

Figure 6.19. Comparison of DRS and TSC data of PMMA selected isochronal dielectric loss spectra and the typical (global) TSC spectrum (Kalogeras and Vassilikou-Dova, unpublished results). Arrows indicate the location of the main signals in the case of the isochronal plot at 10 Hz. The inset shows a comparative plot of the temperature dependence of the dielectric loss (e") and the mechanical loss modulus E") for PMMA [DMA data taken from de Deus et al. (2004)].

FIG. 12-19. Isochronal plots of storage and loss Young s modulus (with a logarithmic scale) at a frequency of 110 Hz against temperature for styrene-butadiene triblock copolymers. Decreasing values of E correspond to decreasing styrene/butadiene ratio (West and Cooper, after Matsuo reproduced by permission of the publishers, IPC Business Press Ltd." )... 

FIG. 18-18. Isochronal plots of bulk longitudinal wave attenuation at 2 X 10 Hz against temperature for mixtures of poly(vinyl chloride) and di- -butyl phthalate. Figures denote weight fraction of polymer. (Thurn and Wflrstlin. )... 

Stieff and Stern (1961) and Stieff et al. (1963) considered plots of data similar to the concordia plot wherein the common lead was not first removed in the age calculation. These plots allow calculation of the initial ° Pb/ ° Pb. Also valuable are plots of ° Pb/ Pb versus U/ Pb and ° Pb/ Pb versus U/ Pb, similar to the strontium isochron plot (or Bernard Price Institute plots), which also allow the initial values of ° Pb/ Pb and Pb/ ° Pb to be determined. These plots are best suited to situations in which there is not great radiogenic enrichment. One good example of this application is given by Mirkina and Makarochkin (1966). 

Because many geotextile reinforcement design codes specify a limit to allowable creep strain, it is convenient to present the loads at which these strain limits are reached. In this context, the creep data may be presented in an isochronous plot consisting of an array of load—strain curves, similar to the one from a tensile test, but with each curve representing a different duration. Each isochronous (ie, constant time) curve is created by taking load and strain levels from each creep curve at a given constant time and plotting them to form an isochronous curve. Isochronous curves are not an extrapolation tool, but instead are an interpolation tool. 

In order to illustrate the general relaxation behavior, Figure 2 shows isochronal plots of e" and e as a function of temperature at different frequencies for a PBT-P04 copolymer [12] with 50 wt% PBT and a polymerization degree... 

The contribution of the asphalt binder to permanent deformation of asphalt mixtures is considered in terms of the minimum value for the stiffness parameter, G /sln5, at a maximum pavement design temperature (i. e., 1000 Pa 10 rad/s). This parameter correlates to that portion of the accumulated, non-recoverable deformation occurring In a pavement that Is attributable to the asphalt binder. The higher the value, the less deformable Is the pavement. Isochronal plots of GVsin 5 reveal distinct differences in the contribution of the additives to the mixture stiffness. In Figure 5, It is clear that the base asphalt would qualify for a maximum use... 

Figure 5. Isochronal plots of G7sin 6 for neat, polymer and rubber modified paving grade AC10-3 binders. Reference material Novaphalt acIO.

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