All Isochrons can be explained by Mixing

1. All Isochrons can be explained by Mixing 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 1/3/2020 1

2. 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. 1/3/2020 2

3. 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. 1/3/2020 3

4. Mixing -1 • Often an isochron yields an unacceptable slope, indicating an age much too young or much too old to be compatible with the accepted model. Frequently the slope is negative. A common explanation for these cases is "mixing". It has always been recognized that the same straight-line plot as the isochron can be achieved if the original melt were a mixture of two original homogenized pools. If points a and c are the compositions of the two original pools that partially merged to form the melt, any sample from the melt will occupy a place on a straight line between them, such as point b. No sample will be found above a or below c. Such a "mixing line" has no time significance, and the textbook warns to be wary of accepting such mixing as a true isochron.

5. Mixing -2 • Faure's text also proposes a test for mixing. If a plot of 87Sr-86Sr vs 1/Sr (the concentration of strontium) shows a linear relationship, then mixing is indicated. A brief study conducted in 1981 showed a high degree of correlation to this mixing test in the isochrons being published. A subsequent public dialog between Dalrymple and Arndts & Overn concluded that although the mixing test is strongly indicative of mixing, there are circumstances under which mixing would not be detected by such a test, and others wherein the test could give a false indication of mixing. The caution for the geochronologist would be to suspect any isochron, since there is no way to rule out mixing.

6. Mixing -3 • It is now clear, however, that there is at least one positive test for mixing. It is the whole-rock isochron itself. If the whole rock yields samples that give a linear plot, whether the slope is positive or negative, or whether the slope signifies an age that fits a preconceived model or not, there is no other known mechanism outside of mixing to which the data may be rationally ascribed.

7. Mixing -4 • Mixing is an unfortunate misnomer that has become popular for describing rocks formed from two or more original melts, or from a melt becoming contaminated by isolated incorporation of local rock. Understand it to mean partial mixing, with resulting heterogeneity. Complete mixing would result in homogeneity, and would give only a single point to plot. No curve of any kind, nor even a scattering of points would occur.

8. Mixing -5 • This homogeneity is the assumed starting point in the history of the rock being dated. It then solidifies. But now, years later, we dig up 6 adjacent meter cubes of the rock, and discover that the normalized ratio of the parent (and incidentally of the daughter) is different in each cube, sufficient to plot as an "isochron". How can we rationally accept the assumed initial homogeneity? We can not.

9. Mixing -6 • The whole-rock isochron is justified on the basis that migration of the isotopes in a metamorphic event may be confined to distances of perhaps 1 cm. This is much larger than the average crystal size. Thus the original constituents of each crystal will lie nearby. By taking samples of 100-cm dimensions, one could assure that the entire content of the original crystals are well represented by the sample, with very small error. However, this matrix is the original melt that was theorized to be homogeneous. The ability to find differences in the rubidium content among the samples violates the assumption of original homogeneity. Original inhomogeneity is the only possible explanation: in other words, mixing.

10. Mixing -7 • It is claimed that fractional crystallization of magmas and separation of crystals from the remaining liquid result in suites of comagmatic rocks of differing composition. This may be true, but there is no experimental evidence that this can generally be applied to trace elements that are foreign to the crystals. Add the fact that trace elements are not securely held by crystals until temperatures are well below the melting points, and this postulate falls far short of explaining the variation in rubidium in whole-rock isochrons. Mixing is much preferred, particularly when it is noted that many data sets have negative slope, where mixing is always the accepted explanation. Often the negative-slope data pertain to large formations that particularly fit the hypothesis of slow cooling from a melt.

11. Mixing -8 • The ability to obtain a whole-rock diagram, straight-line or not, can be considered proof that the data represent a "mixing line" rather than an "isochron". If mixing has not occurred, and the system has remained closed, then the whole-rock data must all lie on a single point. In fact, even if the whole-rock data show scatter, either mixing is indicated -- but of a complex nature, with more than two components -- or there have been subsequent alterations described as the system being open, or both. 1/3/2020 11

12. Mixing -9 • Has any legitimate isochron ever been formed? It is improbable. There is ample evidence for mixing. Any "isochron" could be mixing. There is no way to rule it out. All whole-rock "isochrons" are mixing, and they are approximately 90% of all published. Many of the remaining (mineral) "isochrons" have a whole-rock point located close enough to the straight line to discredit them. Why should we expect any of the others to be "true isochrons", since mixing has the strongest probability? 1/3/2020 12