What Are Isochrons?

1. What Are Isochrons? Christopher Chui, PhD Acknowledgment: I am indebted to numerous sources in the Internet, and especially William Overn’s paper on “Isochron Rock Dating Is Fatally Flawed.” http://ChristCenterGospel.org ckchui1@yahoo.com 8/14/2014 1

2. A Decay Equation with Two Unknowns D = D0 + N(t) (eλt − 1) where t is age of the sample, D is number of atoms of the daughter isotope in the sample, D0 is number of atoms of the daughter isotope in the original composition, N is number of atoms of the parent isotope in the sample at time t (the present), given by N(t) = Noe-λt, and λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2.

3. Isochron Dating where D is the initial concentration of the daughter isotope, Di is the concentration of the non-radiogenic isotope of the daughter element (assumed constant), P is the initial concentration of the parent isotope, and ΔPt is the total amount of the parent isotope which has decayed by time t.

4. The Rb-Sr Isochron Method Rubidium and strontium occur as trace elements in many common rock types. Rubidium has 25 isotopes. 85Rb (stable, abundance 72.15%) and 87Rb (radioactive). 87Rb decays to 87Sr with a half-life of approximately 47 billion years. Strontium is stable in all natural forms, and in addition to the radiogenic 87Sr (7%), has isotopes  88Sr (82%), 86Sr (10%), and 84Sr (<1%).

5. The Rb-Sr Isochron Method The general method of dating is to take several samples of the rock, to determine the ratios of the Rb-Sr isotopes in each, and by simultaneous equations determine the probable beginning points for each, from which the age may be determined. For the sake of compatibility with the available laboratory instruments, the specific ratios chosen are 87Rb-86Sr and 87Sr-86Sr. The algebra is equivalent to a simple straight-line diagram.

7. Here is graphically represented the fact that the amount of daughter isotope increases as the amount of parent increases in the sample. The magnitude of that increase (i.e. the slope of the line) depends on the time allowed for the decay process to transpire, or the age of the rock. If we extrapolate down the line to the zero intercept, we have a representation of a sample with no parent isotope to contribute to the daughter concentration. This must represent the initial daughter concentration. The Rb-Sr Isochron Method

8. The Rb-Sr Isochron Method • For a problem to be solvable by simultaneous equations there must be as many independent equations as there are unknowns. The unknowns are the original 87Sr-86Sr ratio for each sample and the age of each sample. Each sample gives one equation, but introduces two additional unknowns. Regardless of the number of samples, there are never enough equations to cover all the unknowns. These problems must be resolved by the assumptions. 8/14/2014 8

9. If all initial 87Sr-86Sr ratios in the system are assumed to be the same, the scheme can be made to work, as the unknowns are reduced to two, the common age, and the common strontium ratio. Any two samples may now introduce the required two equations, and any more beyond that will simply improve the accuracy and the confidence level. This assumption is outside the experience based on field data, however, where the general case is that every sample has its own unique ratio. However, it can be rationally assumed that each sample we find has its own age and its particular rubidium concentration, which over time may have imparted a unique portion of daughter isotope. The assumed uniform strontium ratios should certainly be valid when applied to a rock system solidifying from a uniform homogenized melt. We must emphasize, however, that this enabling assumption must fail in the absence of an initial homogenized melt. Assumption 1: The same initial strontium ratio TheBig Bang Never Happened! - Christopher Chui, PhD

10. If isotopes have migrated in or out of the sample during the aging period, the resulting data have no time significance. Isochrons are thought to be self checking in this regard, since with several samples an open system with random migration should scatter the points off of the straight line. Indeed, it often happens that there is a scatter of data, rendering the isochron worthless. But there are many occurrences of isochrons having acceptably straight-line form that are also rejected. Often "metamorphism" is cited as the probable cause, the system having opened, either partially or completely resetting the clock. In order to assure an acceptably closed system, samples as large as 1 meter cubes have been suggested. The assumption of a closed system for many of the isochrons, if they have not been questioned by the geochronologists, will not be challenged here. We note that these are generally obtained on the samples of larger dimensions, that is the whole-rock isochrons. Assumption 2: A "closed" system 8/14/2014 10

11. Independent equations If the equations are not independent, the problem cannot be solved. This would be the case where all samples on the diagram plot on a single point. Although the single point on the diagram is valid, there is no way of finding a slope or intercept. If the melt were initially homogeneous and remained closed, it could be expected still to be homogeneous, and yield that single-point isochron. This should be the general case of the whole-rock isochron. 8/14/2014 11

12. The mineral isochron solves the dilemma. The mineral crystals have done the job in an elegant way. Crystals naturally form around a specific chemical composition, each atom occupying its naturally-assigned site. Foreign atoms just don't fit, either electrochemically or physically, and are strongly rejected. Depending on its concentration in the melt, a foreign element may have more or less acceptance in a crystal, based on its chemical and physical resemblance to one or another of the normal host elements. As the crystals form, each different mineral type accepts a different trace level of rubidium and of strontium. Because of their individual unique chemistry they each extract a different amount of rubidium and of strontium from the melt. The crystals of the individual minerals are used as the rock samples in the mineral isochrons. 8/14/2014 12

13. Modern Rocks Sit on a 4.5 Billion Year Isochron 8/14/2014 13