Concordia plot

Figure 9. U, Th and Pa isotopic data and ages for speleothems (Beck et al. 2001 Mnsgrove et al. 2001, Dorale et al. 2003). A.) vs. concordia plot. Evolntion cnrves for different 5 " U(0)...

Because the second derivative d yfdx ) of a function y = f x)) determines whether the curve of the function is concave upward or down, to answer the question of this section, we need to derive the second derivatives of the Tera-Wasserburg Concordia plot. 

For the Tera-Wasserburg plot and conventional Concordia plot, we measure a mineral (e.g., zircon) that is enriched in U and initially contains little unradiogenic (conunon) Pb. 

All terms on the right hand side of Eq. (12.34) is positive and thus dy/dx > 0 everywhere, as displayed by the positive relationship between (230rh/238u) and ( Pa/ U) in the U-Th-Pa Concordia plot (Fig. 12.5). To obtain the second derivative of y with respect to x, or d yfdx, we need to first obtain the derivative of dy/dx with respect to t from Eq. (12.34) ... 

I230-/I231 <0. The second derivative d yjdx [Pg.260]

Figure 1 concordia plot. The full concordia plot is shown in the inset of the left diagram. The curves... 

Concordia plots allow the interpretation of the geological histories of uranium/lead systems and provide information on the past disturbances of these systems. Several concordia models have been developed in order to interpret the discordancy of the U/Pb dates of uranium-bearing minerals. 

Application of the Tera and Wasserburg Concordia plot is the only procedure to apply to young zircons because conunon-Pb can easily exceed the radiogenic Pb content and the Pb/ Pb ratio cannot be measured. In very young zircons, the ratio should be constant... 

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). 

Fig. 2. Concordia plot for zircons from the Precambrian Johnny Lyon Granodiorite (Silver and Deutsch, 1963). Triangles are two samples of uranothorite washes. Squares are four size fractions of zircons from one sample. Circles indicate various partial fusions and an average value of the intermediate zone of the retained 200-mesh fraction. The diamonds indicate a separate sample of zircon collected about 3 miles from the first sample. The inset is a photographic enlargement (5x) (from Silver and Deutsch Uranium Lead Isotopic Variations in Zircons. The Journal of Geology, Vol. 71, No. 6, pp. 721-758. Copyright by the University of Chicago 1963).

Fig. 5. Effects of loss of lead from Ceylon zircon (6,500) (-100 to -1-200 mesh) as a result of hydrothermal experiments at 500° C in 2 molal NaCl at 1,000 bars fluid pressure A, Concordia plot showing episodic lead loss B, change of lead content in zircon with time (from Pidgeon, O Neil and Silver Uranium and Lead Isotopic Stability in a Metamict Zircon under Experimental Hydrothermal Conditions. Science 154, 1538—1540. Copyright 1966 by the American Association for the Advancement of Science)...

Edwards et al. (1997) demonstrate that for samples with similar " U(O), such as corals that grew in open marine water, and remained closed system since time of formation, isotopic data plot on or close to an ideal concordia in vs. °Th/ U... 

A unique strength of concordia diagrams is their ability to reveal modes of diagenetic disturbance. If U-Th-Pa isotopic data for numerous co-eval sub-samples that have experienced different degrees of the same diagenetic process are plotted in or vs. space, they should fall on a curve or straight line... 

Figure 10. Modified Tera-Wasseibuig f° Pb/ ° Pb-2 U/2 Pb) plot with disequilibrium concordia (after Wendt and Carl 1985). The curvilinear trajectories (dotted lines), or concordia, show the change in 23 U/ 06p ) 207p y206p ggg incrcascs for different values of 8234u(0) and Pao = orh = 226Ra = q.

Figure 13. Tera-Wasserbnrg style three-dimensional concoidia plot for the WHCl stalactite (Richards et al. 1988). Shown is the projection onto the U/ ° Pb- ° Pb/ ° Pb plane (see Fig. 10 caption). The intercept of the three-dimensional fit with this plane is shown by the shaded error ellipse. A) Three-dimensional regression, disequilibrium concordia (5 " U(0) = 320 dashed line], and plane intercept. B) Detail of intercept with 2 U/ ° Pb- ° Pb/ Pb plane, disequilibrium concordia (2o error), regression line, and the secular equilibrium concordia.

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,... 

Figure 1 U-Pb Concordia diagram showing the results of an analysis of a detrital zircon crystal by ion microprobe (SHRIMP) followed by analysis of the same crystal using TIMS. Both error ellipses are plotted at 2a. The best estimate of the age of crystallization of the zircon is identical for both techniques however, the TIMS analysis is an order of magnitude more precise than that obtained using the ion microprobe (source Samson et aL, 2003).

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