GEMOC ARC National Key Centre
The
conventional, 3D concordia diagram
A three dimensional view of the classical concordia diagram is shown here. An ancient zircon which has suffered neither lead loss nor contamination with common lead will plot on a line in space (the ì3D concordiaî ñ green curve), which is curved in both 206Pb/238U-207Pb/235U (i.e. the classical U-Pb concordia) and 206Pb/238U-208Pb/232Th projections. A zircon of age t1 and with no common lead, which has lost lead in a subsequent event (at t2) will plot on the straight line connecting the two points C1 and C2, corresponding to concordant lead compositions at t1 and t2, respectively.
A zircon of age t1 which has picked up common lead at the time of crystallization will plot on a line from C1 towards the composition of common lead, which lies at infinity. A zircon of age C1 with a given fraction, fc, of common lead will plot at A; lead loss at t2 will displace its composition along a straight line (AC2) towards concordant lead composition at age t2 (i.e. point C2), to an intermediate composition at Aí. The lines C1A, C1C2 and AC2 define a plane in 206Pb/238U-207Pb/235U-208Pb/232Th space.
Correcting a zircon which contains common lead and which has lost part of its total lead content in a later event is is equivalent to moving its composition along the line from its measured composition (at Aí), along the broken line AíB, until intersection with the common lead free lead loss line C1C2 at B, which is the radiogenic lead component in the zircon. Since common lead is situated at infinity, this line is fixed in space, parallel with C1A, and confined to the plane C1C2A. For a given t2, there is only one such plane, and hence only one pair of points C1 and B. The initial age (t1, i.e. point C1), the fraction of lead lost (fl, representing the relative displacement from A to Aí or from C1 to B) and the fraction of common lead (fc, corresponding to the distance from Aí to B) are therefore interdependent, and can in principle be determined in a single operation. The 206Pb/238U, 207Pb/235U and 208Pb/232Th ratios of a zircon at point B is uniquely given by the composition of concordant lead of age t1, the age of lead loss (t2), and the amount of lead lost at t2.
In geometrical terms, determining the amount of common lead in a zircon which has lost lead amounts to determining the orientation of the plane C1AC2. This can be done by making an initial guess of t1 (as, for example, indicated by the intersection between the concordia and the plane outlined by a broken, red line), and rotating this plane with the line AC2 as a hinge, by reducing t1, until coincident with the line AíB.
To explore the features of the 3D concordia in more detail, go to an interactive, 3D view