Here I want to concentrate on another source of error, namely, processes that take place within magma chambers. To me it has been a real eye opener to see all the processes that are taking place and their potential influence on radiometric dating. Radiometric dating is largely done on rock that has formed from solidified lava. Lava (properly called magma before it erupts) fills large underground chambers called magma chambers. Most people are not aware of the many processes that take place in lava before it erupts and as it solidifies, processes that can have a tremendous influence on daughter to parent ratios. Such processes can cause the daughter product to be enriched relative to the parent, which would make the rock look older, or cause the parent to be enriched relative to the daughter, which would make the rock look younger. This calls the whole radiometric dating scheme into serious question.

Geologists assert that older dates are found deeper down in the geologic column, which they take as evidence that radiometric dating is giving true ages, since it is apparent that rocks that are deeper must be older. But even if it is true that older radiometric dates are found lower down in the geologic column, which is open to question, this can potentially be explained by processes occurring in magma chambers which cause the lava erupting earlier to appear older than the lava erupting later. Lava erupting earlier would come from the top of the magma chamber, and lava erupting later would come from lower down. A number of processes could cause the parent substance to be depleted at the top of the magma chamber, or the daughter product to be enriched, both of which would cause the lava erupting earlier to appear very old according to radiometric dating, and lava erupting later to appear younger.

Mechanisms that can alter daughter-to-parent ratios

The mineral makeup of an igneous rock is ultimately determined by the chemical composition of the magma from which it crystallized. Such a large variety of igneous rocks exists that it is logical to assume an equally large variety of magmas must also exist. However, geologists have found that various eruptive stages of the same volcano often extrude lavas exhibiting somewhat different mineral compositions, particularly if an extensive period of time separated the eruptions. Evidence of this type led them to look into the possibility that a single magma might produce rocks of varying mineral content.

A pioneering investigation into the crystallization of magma was carried out by N. L. Bowen in the first quarter of this century. Bowen discovered that as magma cools in the laboratory, certain minerals crystallize first. At successively lower temperature, other minerals begin to crystallize as shown in Figure 3.6. As the crystallization process continues, the composition of the melt (liquid portion of a magma, excluding any solid material continually changes. For example, at the stage when about 50 percent of the magma has solidified, the melt will be greatly depleted in iron, magnesium, and calcium, because these elements are found in the earliest formed minerals. But at the same time, it will be enriched in the elements contained in the later forming minerals, namely sodium and potassium. Further, the silicon content of the melt becomes enriched toward the latter stages of crystallization. Bowen also demonstrated that if a mineral remained in the melt after it had crystallized, it would react with the remaining melt and produce the next mineral in the sequence shown in Figure 3.6. For this reason, this arrangement of minerals became known as Bowen's reaction series. On the upper left branch of this reaction series, olivine, the first mineral to form, Ml] react with the remaining melt to become pyroxene. This reaction will continue until the last mineral in the series, biotite mica, is formed. This left branch is called a discontinuous reaction series because each mineral has a different crystalline structure. Recall that olivine is composed of a single tetrahedra and that the other minerals in this sequence are composed of single chains, double chains, and sheet structures, respectively. Ordinarily, these reactions are not complete so that various amounts of each of these minerals may exist at any given time.

The right branch of the reaction series is a continuum in which the earliest formed calcium-rich feldspar crystals react with the sodium ions contained in the melt to become progressively more sodium rich. Oftentimes the rate of cooling occurs rapidly enough to prohibit the complete transformation of calcium-rich feldspar into sodium-rich feldspar. In these instances, the feldspar crystals will have calcium-rich interiors surrounded by zones that are progressively richer in sodium. During the last stage of crystallization, after most of the magma has solidified, the remaining melt will form the minerals quartz, muscovite mica, and potassium feldspar. Although these minerals crystallize in the order shown, this sequence is not a true reaction series. Bowen demonstrated that minerals crystallize from magma in a systematic fashion. But how does Bowen's reaction series account for the great diversity of igneous rocks? It appears that at one or more stages in the crystallization process, a separation of the solid and liquid components of a magma frequently occurs. This can happen, for example, if the earlier formed minerals are heavier than the liquid portion and settle to the bottom of the magma chamber as shown in Figure 3.7A. This settling is thought to occur frequently with the dark silicates, such as olivine. When the remaining melt crystallizes, either in place or in a new location if it migrates out of the chamber, it will form a rock with a chemical composition much different from the original magma (Figure 3.7B). In many instances the melt which has migrated from the initial magma chamber will undergo further segregation. As crystallization progresses in the " new" magma, the solid particles may accumulate into rocklike masses surrounded by pockets of the still molten material. It is very likely that some of this melt will be squeezed from the mixture into the cracks which develop in the surrounding rock. This process will generate an igneous rock of yet another composition.

The process involving the segregation of minerals by differential crystallization an separation is called fractional crystallization. At any stage in the crystallization process the melt might be separated from the solid portion of the magma. Consequently, fractional crystallization can produce igneous rocks having a wide range of compositions. Bowen successfully demonstrated that through fractional crystallization one magma can generate several different igneous rocks. However, more recent work has indicated that this process cannot account for the relative quantities of the various rock types known to exist. Although more than one rock type can be generated from a single magma, apparently other mechanisms also exist to generate magmas of quite varied chemical compositions. We will examine some of these mechanisms at the end of the next chapter.

FIGURE 3.7

Separation of minerals by fractional crystallization. A. Illustration of how the earliest formed minerals can be separated from a magma by settling. B. The remaining melt could migrate to a number of different locations and, upon further crystallization, generate rocks having a composition much different from the parent magma.

Faure discusses fractional crystallization relating to U and Th in his book (p. 283) He says, "The abundances of U and Th in chondritic meteorites are 1 x 10^-2 and 4 x 10^-4 ppm, respectively. These values may be taken as an indication of the very low abundance of these elements in the mantle and crust of the Earth. In the course of partial melting and fractional crystallization of magma, U and Th are concentrated in the liquid phase and become incorporated into the more silica-rich products. For that reason, igneous rocks of granitic composition are strongly enriched in U and Th compared to rocks of basaltic or ultramafic composition. Progressive geochemical differentiation of the upper mantle of the Earth has resulted in the concentration of U and Th into the rocks of the continental crust compared to those of the upper mantle."

Faure does say that the Th/U and U/Pb ratios remain virtually constant in the different materials. The concentration of Pb is usually so much higher than U, that a 2- to 3-fold increase of U doesn't change the percent composition much ( e.g. 3.5ppm U/19.6ppm Pb in gneiss vs 1.6ppm U/18.7ppm Pb in granulite, and 4.8ppm U/23.0ppm Pb in granite shows some shifts in composition).

Finally, we have a third quotation from Elaine G. Kennedy in Geoscience Reports, Spring 1997, No. 22, p.8.:

Contamination and fractionation issues are frankly acknowledged by the geologic community.2 For example, if a magma chamber does not have homogeneously mixed isotopes, lighter daughter products could accumulate in the upper portion of the chamber. If this occurs, initial volcanic eruptions would have a preponderance of daughter products relative to the parent isotopes. Such a distribution would give the appearance of age. As the magma chamber is depleted in daughter products, subsequent lava flows and ash beds would have younger dates.

Such a scenario does not answer all of the questions or solve all of the problems that radiometric dating poses for those who believe the Genesis account of Creation and the Flood. It does suggest at least one aspect of the problem that could be researched more thoroughly.

2. G. Faure. 1986. Principles of Isotope Geology: John Wiley and Sons, Inc., NY, 589p.

So we have two kinds of processes taking place. There are those processes taking place when lava solidifies and various minerals crystallize out at different times. There are also processes taking place within a magma chamber that can cause differences in the composition of the magma from the top to the bottom of the chamber, since one might expect the temperature at the top to be cooler. Both kinds of processes can influence radiometric dates. In addition, the magma chamber would be expected to be cooler all around its borders, both at the top and the bottom as well as in the horizontal extremities, and these effects must also be taken into account.

For example, heavier substances will tend to sink to the bottom of a magma chamber. Also, substances with a higher melting point will tend to crystallize out at the top of a magma chamber and fall, since it will be cooler at the top. These substances will then fall to the lower portion of the magma chamber, where it is hotter, and remelt. This will make the composition of the magma different at the top and bottom of the chamber. This could influence radiometric dates. This mechanism was suggested by Jon Covey (and others). The solubility of various substances in the magma also could be a function of temperature, and have an influence on the composition of the magma at the top and bottom of the magma chamber. Finally, minerals that crystallize at the top of the chamber and fall may tend to incorporate other substances, and so these other substances will also tend to have a change in concentration from the top to the bottom of the magma chamber.

There are quite a number of mechanisms in operation in a magma chamber. I count at least three so far -- sorting by density, sorting by melting point, and sorting by how easily something is incorporated into minerals that form at the top of a magma chamber. Then you have to remember that sometimes one has repeated melting and solidification, introducing more complications. There is also a fourth mechanism -- differences in solubilities. How anyone can keep track of this all is a mystery to me, especially with the difficulties encountered in exploring magma chambers. These will be definite factors that will change relative concentrations of parent and daughter isotopes in some way, and call into question the reliability of radiometric dating. In fact, I think this is a very telling argument against radiometric dating.

Another possibility to keep in mind is that lead becomes gaseous at low temperatures, and would be gaseous in magma if it were not for the extreme pressures deep in the earth. It also becomes very mobile when hot. These processes could influence the distribution of lead in magma chambers.

Let me suggest how these processes could influence uranium-lead and thorium-lead dates:

The following is a quote from The Earth: An Introduction to Physical Geology by Tarbuck & Lutgens, pp. 55-57, (1987).

"For example, at the stage when about 50 percent of the magma has solidified, the melt will be greatly depleted in iron, magnesium, and calcium, because these elements are found in the earliest formed minerals. But at the same time, it will be enriched in the elements contained in the later forming minerals, namely sodium and potassium."

A geologist writes:

"Uranium and thorium ARE strongly fractionated during magmatic processes and tend to be concentrated in the silicic/felsic part of a magma hence granites and rhyolites tend to have a much higher average uranium and thorium concentration (3-5 ppm U) compared to basalts (less than 1 ppm U)."

From the above quotes and references, uranium is concentrated in granite, which is depleted in magnesium and iron. The magnesium and iron rich minerals come from the mantle (subducted oceanic plates), while granite comes from continental sediments (crustal rock). The mantle part solidifies first, and is rich in magnesium, iron, and calcium. The silicic/felsic part of a magma typically becomes granite and solidifies later, enriched in uranium, thorium, sodium, and potassium. So it is reasonable to expect that initially, the magma is rich in iron, magnesium, and calcium and poor in uranium, thorium, sodium, and potassium. Later on the magma is poor in iron, magnesium, and calcium and rich in uranium, thorium, sodium, and potassium. It doesn't say which class lead is in. But lead is a metal, and to me it looks more likely that lead would concentrate along with the iron. If this is so, the magma would initially be poor in thorium and uranium and rich in lead, and as it cooled it would become rich in thorium and uranium and poor in lead. Thus its radiometric age would tend to decrease rapidly with time, and lava emitted later would tend to look younger.

Another point is that of time. Suppose that the uranium does come to the top by whatever reason. Perhaps magma that is uranium rich tends to be lighter than other magma. Or maybe the uranium poor rocks crystallize out first and the remaining magma is enriched in uranium. Would this cause trouble for our explanation? Not necessarily. It depends how fast it happened. If it happened slowly with respect to the flood or whatever, then the uranium concentration could be rising with time, and this would tend to make the newer magma look younger since its U/Pb ratio would be higher.

Some information from the book Uranium Geochemistry, Mineralogy, Geology provided by Jon Covey gives us evidence that fractionation processes are making radiometric dates much, much too old. Geology contributing author Massimo Cortini cites a very interesting anomaly regarding the U 238 decay chain, which is U-238, U-234, Th-230, Ra-226, Rn-222, Po-218 Po-214, Po-210, Pb-210, Bi-210, Pb-206. The half life of U-238 is 4.47 x 10^9 years and that of Ra-226 is 1.6 x 10^3 years. Thus radium is decaying 3 million times as fast as U-238. At equilibrium, which should be attained in 500,000 years for this decay series, we should expect to have 3 million times as much U-238 as radium to equalize the amount of daughter produced. Cortini says geologists discovered that ten times more Ra-226 than the equilibrium value was present in rocks from Vesuvius. They found similar excess radium at Mount St. Helens, Vulcanello, and Lipari and other volcanic sites. The only place where radioactive equilibrium of the U-238 series exists in zero age lavas is in Hawiian rocks. Thus instead of having 1/(3 million) as much radium as uranium, which we should expect, there is ten times as much, or 1/(300,000) times as much radium as uranium.

We need to consider the implications of this for radiometric dating. How is this excess of radium being produced? This radium cannot be the result of decay of uranium, since there is far too much of it. Either it is the result of an unknown decay process, or it is the result of fractionation which is greatly increasing the concentration of radium or greatly decreasing the concentration of uranium. Thus only a small fraction of the radium present in the lava (at most 10 percent) is the result of decay of the uranium in the lava.

This is interesting because both radium and lead are daughter products of uranium. If similar fractionation processes are operating for lead, this would mean that only a small fraction of the lead is the result of decay from the parent uranium, implying that the U-Pb radiometric dates are much, much too old. Cortini, in an article appearing in the Journal of Volcanology and Geothermal Research also suggests this possibility. He says:

"The invalidity of the Th-230 dating method is a consequence of the open-system behaviour of U and Th. By analogy with the behaviour of Ra, Th and U it can be suggested that Pb, owing to its large mobility, was also fed to the magma by fluids. This can and must be tested. The open-system behaviour of Pb, if true, would have dramatic consequences...." J Vol Geotherm Res 14 (1982) 247-260.

In fact, U-235 and Th-232 both have isotopes of radium in their decay chains with half lives of a week or two, and 6.7 years, respectively. Any process that is concentrating one isotope of radium will probably concentrate the others as well and invalidate these dating methods, too. Radium 226 has a low melting point (973 degrees K) which may account for its concentration at the top of magma chambers.

What radiometric dating needs to do to show its reliability is to demonstrate that no such fractionation could take place. Can this be done? With so many unknowns I don't think so.

How Uranium and Thorium are preferentially incorporated in various minerals

Concerning the distribution of parent and daughter isotopes in various substances, there are appreciable differences. Faure shows that in granite U is 4.8 ppm while Pb is 23 ppm, while in andesite U is 2.4 ppm and Pb is 5.8. Some process is causing the differences in the ratios of these magmatic rocks.

Depending on their oxidation state, according to Faure, uranium minerals can be very soluble in water while thorium compounds are, generally, very insoluble. These elements also show preferences for the minerals in which they are incorporated, so that they will tend to be "dissolved" in certain mineral "solutions" preferentially to one another. More U is found in carbonate rocks, while Th has a very strong preference for granites in comparison.

I saw a reference that uranium reacts strongly, and is never found pure in nature. So the question is what the melting points of its oxides or salts would be, I suppose. I also saw a statement that uranium is abundant in the crust, but never found in high concentrations. To me this indicates a high melting point for its minerals, as those with a low melting point might be expected to concentrate in the magma remaining after others crystallized out. (Such a high melting point would imply fractionation in the magma.) Thorium is close to uranium in the periodic table, so it may have similar properties, and similar remarks may apply to it.

It turns out that uranium in magma is typically found in the form of uranium dioxide, with a melting point of 2878 degrees centrigrade. (CRC Handbook of Chemistry and Physics 72 ed., 1992 (55th edition also)). This high melting point suggests that uranium would crystallize and fall to the bottom of magma chambers.

Geologists are aware of the problem of initial concentration of daughter elements, and attempt to take it into account. U-Pb dating attempts to get around the lack of information about initial daughter concentrations by the choice of minerals that are dated. For example, zircons are thought to accept little lead but much uranium. Thus geologists assume that the lead in zircons resulted from radioactive decay. But I don't know how they can be sure how much lead zircons accept, and even they admit that zircons accept some lead. Lead could easily reside in impurities and imperfections in the crystal structure. Also, John Woodmorappe's paper has some examples of anomalies involving zircons.

It is known that the crystal structure of zircons does not accept much lead. However, it is unrealistic to expect a pure crystal to form in nature. Perfect crystals are very rare. In reality, I would expect that crystal growth would be blocked locally by various things, possibly particles in the way. Then the surrounding crystal surface would continue to grow and close up the gap, incorporating a tiny amount of magma. I even read something about geologists trying to choose crystals without impurities (by visual examination) when doing radiometric dating. Thus we can assume that zircons would incorporate some lead in their impurities, potentially invalidating uranium-lead dates obtained from zircons.

Chemical fractionation, as we have seen, calls radiometric dates into question. But this cannot explain the distribution of lead isotopes. There are actually several isotopes of lead that are produced by different parent substances (uranium 238, uranium 235, and thorium). One would not expect there to be much difference in the concentration of lead isotopes due to fractionation, since isotopes have properties that are very similar. So one could argue that any variations in Pb ratios would have to result from radioactive decay. However, the composition of lead isotopes between magma chambers could still differ, and lead could be incorporated into lava as it traveled to the surface from surrounding materials. I also recall reading that geologists assume the initial Pb isotope ratios vary from place to place anyway. Later we will see that mixing of two kinds of magma, with different proportions of lead isotopes, could also lead to differences in concentrations.

Mechanism of uranium crystallization and falling through the magma

Tarbuck and Lutgens carefully explain the process of fractional crystallization in The Earth: An Introduction to Physical Geology. They show clear drawings of crystallized minerals falling through the magma and explain that the crystallized minerals do indeed fall through the magma chamber. Further, most minerals of uranium and thorium are denser than other minerals, especially when those minerals are in the liquid phase. Crystalline solids tend to be denser than liquids from which they came. But the degree to which they are incorporated in other minerals with high melting points might have a greater influence, since the concentrations of uranium and thorium are so low.

Now another issue is simply the atomic weight of uranium and thorium, which is high. Any compound containing them is also likely to be heavy and sink to the bottom relative to others, even in a liquid form. If there is significant convection in the magma, this would be minimized, however.

At any rate, there will be some effects of this nature that will produce some kinds of changes in concentration of uranium and thorium relative to lead from the top to the bottom of a magma chamber. Some of the patterns that are produced may appear to give valid radiometric dates. Others may not. The latter may be explained away due to various mechanisms.

Let us consider processes that could cause uranium and thorium to be incorporated into minerals with a high melting point. I read that zircons absorb uranium, but not much lead. Thus they are used for U-Pb dating. But many minerals take in a lot of uranium. It is also known that uranium is highly reactive. To me this suggests that it is eager to give up its 2 outer electrons. This would tend to produce compounds with a high dipole moment, with a positive charge on uranium and a negative charge on the other elements. This would in turn tend to produce a high melting point, since the atoms would attract one another electrostatically. (I'm guessing a little bit here.) There are a number of uranium compounds with different melting points, and in general it seems that the ones with the highest melting points are more stable. I would suppose that in magma, due to reactions, most of the uranium would end up in the most stable compounds with the highest melting points. These would also tend to have high dipole moments.

Now, this would also help the uranium to be incorporated into other minerals. The electric charge distribution would create an attraction between the uranium compound and a crystallizing mineral, enabling uranium to be incorporated. But this would be less so for lead, which reacts less strongly, and probably is not incorporated so easily into minerals. So in the minerals crystallizing at the top of the magma, uranium would be taken in more than lead. These minerals would then fall to the bottom of the magma chamber and thus uranium at the top would be depleted. It doesn't matter if these minerals are relatively lighter than others. The point is that they are heavier than the magma.

Two kinds of magma and implications for radiometric dating

Mantle material is very low in uranium and thorium, having only 0.004 ppm, while crustal rock has 1.4 ppm, according to Richard Arculus in a paper he presented at the Uranium Institute Mid-Term Meeting in Adelaide, 1996 (see http://www.uilondon.org for further information and the article). The source of magma for volcanic activity is subducted oceanic plates. Subduction means that these plates are pushed under the continents by motions of the earth's crust. While oceanic plates are basaltic (mafic) originating from the mid-oceanic ridges due to partial melting of mantle rock, the material that is magma is a combination of oceanic plate material and continental sediments. Subducted oceanic plates begin to melt when they reach depths of about 125 kilometers (See Tarbuck, The Earth, p. 102). In other words, mantle is not the direct source of magma.

Granite and rhyolite never arise from mantle even if granite has a magmatic origin because the upwelling melted mantle material produces basalts which are enriched in magnesium (Mg) and iron (Fe), which is why it is classified as mafic (MAgnesium + the F of Fe).

Further, Faure explains that uraninite (UO sub2) is a component of igneous rocks (Faure, p. 290), i.e., those rocks that form from cooling magma, the source of which is not mantle but subducted and melted oceanic plate and continental sediments eroded from all types of continental rocks. Uraninite is also known as pitchblende.

The following is taken from "WHAT HAPPENS WHEN ROCKS MELT?" by Elaine G. Kennedy.

According to plate tectonic theory, continental crust overrides oceanic crust when these plates collide because the continental crust is less dense than the ocean floor. As the ocean floor sinks, it encounters increasing pressures and temperatures within the crust. Ultimately, the pressures and temperatures are so high that the rocks in the subducted oceanic crust melt. Once the rocks melt, a plume of molten material begins to rise in the crust. As the plume rises it melts and incorporates other crustal rocks. This rising body of magma is an open system with respect to the surrounding crustal rocks.1 Convection currents stir the magma. Volatiles (e.g., water vapor and carbon dioxide) increase the pressure within the magma chamber and contribute to the mixing of the system.

It is possible that these physical processes have an impact on the determined radiometric age of the rock as it cools and crystallizes. Time is not a direct measurement. The actual data are the ratios of parent and daughter isotopes present in the sample. Time is one of the values that can be determined from the slope of the line representing the distribution of the isotopes. Isotope distributions are determined by the chemical and physical factors governing a given magma chamber.

A geologist writes, "Uranium and thorium ARE strongly fractionated during magmatic processes and tend to be concentrated in the silicic/felsic part of a magma hence granites and rhyolites tend to have a much higher average uranium and thorium concentration (3-5 ppm U) compared to basalts (less than 1 ppm U). Some granites in New Hampshire, Arizona, Washington State, Colorado, and Wyoming range from 10-30 ppm U. Rhyolites in Yellowstone N.P. average about 7 ppm U. Most genetic models for uranium deposits in sandstones in the U.S. require a granitic or silicic volcanic source rock to provide the uranium. Most of the uranium deposits in Wyoming are formed from uraniferous groundwaters derived from Precambrian granitic terranes. Uranium in the major uranium deposits in the San Juan basin of New Mexico is believed to have been derived from silicic volcanic ash from Jurassic island arcs at the edge of the continent. An excellent reference to hydrothermal uranium deposits and magmatic processes involving uranium is a book by Vladimir Ruzicka entitled `Hydrothermal Uranium Deposits'".

From the above sources, we see that another factor influencing radiometric dates is the proportion of the magma that comes from subducted oceanic plates and the proportion that comes from crustal rock. Initially, we would expect most of it to come from subducted oceanic plates, which are uranium and thorium poor and maybe lead rich. Later, more of the crustal rock would be incorporated by melting into the magma, and thus the magma would be richer in uranium and thorium and poorer in lead. So this factor would also make the age appear to become younger with time.

There are two kinds of magma, and the crustal material which is enriched in uranium also tends to be lighter. For our topic on radiometric dating and fractional crystallization, there is nothing that would prevent uranium and thorium ores from crystallizing within the upper, lighter portion of the magma chamber and descending to the lower boundaries of the sialic portion. The upper portion of the sialic magma would be cooler since its in contact with continental rock, and the high melting point of UO sub 2 (uranium dioxide, the common form in granite: mp = 2878 C) would assure that this mineral would crystallize as the magma body ascends into the cool lithosphere. The same kind of fractional crystallization would be true of non-granitic melts.

I think we can build a strong case for fictitious ages in magmatic rocks as a result of fractional cystallization and geochemical processes. As we have seen, we cannot ignore geochemical effects while we consider geophysical effects. Sialic (granitic) and mafic (basaltic) magma are separated from each other, with uranium and thorium chemically predestined to reside mainly in sialic magma and less in mafic rock.

Here is yet another mechanism that can cause trouble for radiometric dating: As lava rises through the crust, it will heat up surrounding rock. Lead has a low melting point, so it will melt early and enter the magma. This will cause an apparent large age. Uranium has a much higher melting point. It will enter later, probably due to melting of materials in which it is embedded. This will tend to lower the ages.

Mechanisms that can create isochrons giving meaningless ages:

The idea of isochrons is that one has a parent element, P, a daughter element, D, and another isotope, N, of the daughter that is not generated by decay. One would assume that initially, the concentration of N and D in different locations are proportional, since their chemical properties are very similar. Note that this assumption implies a thorough mixing and melting of the magma, which would also mix in the parent substances as well. Then we require some process to preferentially concentrate the parent substances in certain places. Radioactive decay would generate a concentration of D proportional to P. So after the passing of millions of years of assumed time, we would obtain an equation of the form

where p, d, and n are the concentrations of P, D, and N after some time period. The quantity c1*p represents the D generated by radioactive decay, and the c2*N representes the amount present originally. By taking enough measurements of the concentrations of P, D, and N, we can solve for c1 and c2, and from c1 we can determine the radiometric age of the sample. But we can only solve if the ratio p/n varies. Otherwise, the system is degenerate. Thus we need to have an uneven distribution of D relative to N at the start.

The ratios p/n and d/n have a linear relationship whose slope yields the age of the sample. If these ratios are observed to obey such a linear relationship in a series of rocks, then an age can be computed from them. The age will be the same as the age of a rock with d = c1*n, assuming that all of the daughter element D arose by radioactive decay from P. The bigger c1 is, the older the rock is. That is, the more daughter product relative to parent product, the greater the age. Thus we have the same general situation as with simiple parent-to-daughter computations, more daughter product implies an older age.

This is a very clever idea. However, there are some problems with it.

First, in order to have a meaningful isochron, it is necessary to have an unusual chain of events. Initially, one has to have a uniform ratio of lead isotopes in the magma. Usually the concentration of uranium and thorium varies in different places in rock. This will, over the assumed millions of years, produce uneven concentrations of lead isotopes. To even this out, one has to have a thorough mixing of the magma. Even this is problematical, unless the magma is very hot, and no external material enters. Now, after the magma is thoroughly mixed, the uranium and thorium will also be thoroughly mixed. If this condition remains, one gets an isochron in which all samples yield the same (p/n,d/n) values, and one gets just a single point, which does not yield an age. What has to happen next to get an isochron is that the uranium or thorium has to concentrate relative to the lead isotopes, more in some places than others. So this implies some kind of chemical fractionation. Then the system has to remain closed for a long time. This chemical fractionation will most likely arise by some minerals incorporating more or less uranium or thorium relative to lead.

Anyway, to me it seems unlikely that this chain of events would occur.

Another problem with isochrons is that they can occur by mixing and other processes that result in isochrons yielding meaningless ages. Sometimes, according to Faure, what seems to be an isochron is actually a mixing line, a leftover from differentiation in the magma. Fractionation followed by mixing can create isochrons giving too old ages, without any fractionation of daughter isotopes taking place. To get an isochron with a false age, all you need is (1) too much daughter element, due to some kind of fractionation and (2) mixing of this with something else that fractionated differently. Since fractionation and mixing are so common, we should expect to find isochrons often. How they correlate with the expected ages of their geologic period is an interesting question. There are at least some outstanding anomalies.

Faure states that chemical fractionation produces "fictitious isochrons whose slopes have no time significance." Faure explains how fictitious isochrons develop as a result of fractionation in lava flows. As an example, he uses Pliocene to Recent lava flows and from lava flows in historical times to illustrate the problem. He says, these flows should have slopes approaching zero(less than 1 million years), but they instead appear to be much older (773 million years). Steve Austin has found lava rocks on the Uinkeret Plateau at Grand Canyon with fictitious isochrons dating at 1.5 billion years, making them 0.5 to 1.0 billion years older than the deeply emplaced sediments. Faure explains that this situation actually represents a mixing line, the isotope ratios of Rb/Sr resulting from a mixing process, interpretable as evidence of long-term heterogeneity of the upper mantle (Faure, 145-147).

Suppose sample A has d = c1*p and a given concentration of N. Suppose sample B has no P or D but the same concentration of N as A. Then a mixing of A and B will have the same fixed concentration of N everywhere, but the amount of D will be proportional to the amount of P. This produces an isochron yielding the same age as sample A.

This is a reasonable scenario, since N is a non-radiogenic isotope (not produced by decay) such as lead 204, and it can be assumed to have similar concentrations in many magmas. Magma from the ocean floor has little U238 and little U235 and probably little lead byproducts lead 206 and lead 207. Magma from melted continental material probably has more of both U238 and U235 and lead 206 and lead 207. Thus we can get an isochron by mixing, that has the age of the younger-looking continental crust. The age will not even depend on how much crust is incorporated, as long as it is non-zero.

However, if the crust is enriched in lead or impoverished in uranium before the mixing, then the age of the isochron will be increased. If the reverse happens before mixing, the age of the isochron will be decreased. Any process that enriches or impoverishes part of the magma in lead or uranium before such a mixing will have a similar effect. So all of the scenarios given before can also yield spurious isochrons.

I hope that this discussion will dispel the idea that there is something magical about isochrons that prevents spurious dates from being obtained by enrichment or depletion of parent or daughter elements as one would expect by common sense reasoning. So all the mechanisms mentioned earlier are capable of producing isochrons with ages that are too old, or that decrease rapidly with time. The conclusion is the same, radiometric dating is in trouble.

I now describe this mixing in more detail. Suppose P(p) is the concentration of parent at a point p in a rock. The point p specifies x,y, and z co-ordinates. Let D(p) be the concentration of daughter at the point p. Let N(p) be the concentration of some non-radiogenic (not generated by radioactive decay) isotope of D at point p. For U-238 Pb-206 dating, P would be U-238 and D would be Pb-206 and N would be Pb-204.

Suppose this rock is obtained by mixing of two other rocks, A and B. Suppose that A has a (for the sake of argument, uniform) concentration of P1 of parent, D1 of daughter, and N1 of non-radiogenic isotope of the daughter. Thus P1, D1, and N1 are numbers between 0 and 1 whose sum adds to less than 1. Suppose B has concentrations P2, D2, and N2. Let r(p) be the fraction of A at any given point p in the mixture. Thus if r(p) is 1/3, the mixture has 1/3 A and 2/3 B at point p. Then

Now, to have an isochron we need to have constants c1 and c2 independent of p such that for all p,

This can happen if P2 = 0 and N1 = N2 and D1 > D2. Then we have

We can choose c1 = (D1-D2)/P1 and c2 = D2/N2 and the formula D(p) = c1*P(p) + c2*N(p) works out (if I didn't make any errors).

So this is a mixing that yields an isochron giving an age corresponding to a daughter to parent ratio of (D1-D2)/P1, which is less than the daughter to parent ratio of rock A, which is D1/P1. However, it is still positive, since D1 > D2, and it still increases as D1 increases and decreases as P1 increases. So the usual methods for augmenting and depleting parent and daughter substances still work to influence the age of this isochron. More daughter product means an older age, and less daughter product (relative to parent) means a younger age. And I think the assumptions P2 = 0 and N1 = N2 and D1 > D2 are reasonable, since the substance N, lead 204, is probably of nearly constant concentration in many magmas. This corresponds to the condition N1=N2. It's also reasonable to think that the crustal material from continents is enriched in both parent and daughter product relative to the ocean floor, corresponding to the condition D1 > D2, and we know that the ocean floor is very poor in parent material (uranium in this case). This corresponds to the condition P2 = 0.

In fact, more is true. Any isochron whatever with a positive age and a constant concentration of N can be constructed by such a mixing. It is only necessary to choose r(p) and P1, N1, and N2 so as to make P(p) and D(p) agree with the observed values, and there is enough freedom to do this.

Anyway, to sum up, there are many processes that can produce a rock or magma A having a spurious parent-to-daughter ratio. Then from mixing, one can produce an isochron having a spurious age. This shows that computed radiometric ages, even isochrons, do not have any necessary relation to true geologic ages.

Mixing can produce isochrons giving false ages. This can be detected _sometimes_. But anyway, let's suppose we only consider isochrons for which mixing cannot be detected. How do their ages agree with the assumed ages of their geologic periods? As far as I know, it's anyone's guess, but I'd appreciate more information on this. I believe that the same considerations apply to concordia and discordia, but am not as familiar with them.

It's interesting that isochrons depend on chemical fractionation for their validity. They assume that initially the magma was well mixed to assure an even concentration of lead isotopes, but that uranium or thorium were unevenly distributed initially. So this assumes at the start that chemical fractionation is operating. But these same chemical fractionation processes call radiometric dating into question.

The relative concentrations of lead isotopes are measured in the vicinity of a rock. The amount of radiogenic lead is measured by seeing how the lead in the rock differs in isotope composition from the lead around the rock. This is actually a good argument. But, is this test always done? How often is it done? And what does one mean by the vicinity of the rock? How big is a vicinity? One could say that some of the radiogenic lead has diffused into neighboring rocks, too. Some of the neighboring rocks may have uranium and thorium as well (although this can be factored in in an isochron-type manner). Furthermore, I believe that mixing can also invalidate this test, since it is essentially an isochron. Finally, if one only considers U-Pb and Th-Pb dates for which this test is done, and for which mixing cannot be detected. how do they correlate with other dates and with conventional ages?

The above two-source mixing scenario is limited, because it can only produce isochrons having a fixed concentration of N(p). To produce isochrons having a variable N(p), a mixing of three sources would suffice. This could produce an arbitrary isochron, so this mixing could not be detected.

Also, it seems unrealistic to say that a geologist would discard any isochron with a constant value of N(p), as it seems to be a very natural condition (at least for whole rock isochrons), and not necessarily to indicate mixing. And it's not clear to me in any case that just because an isochron gives evidence that it _could_ have been produced by a mixing of two sources, that it would always be discarded.

I now show that the mixing of three sources can produce an isochron that could not be detected by the mixing test. First let me note that there is a lot more going on than just mixing. There can also be fractionation that might treat the parent and daughter products identically, and thus preserve the isochron, while changing the concentrations so as to cause the mixing test to fail. It is not even necessary for the fractionation to treat parent and daughter equally, as long as it has the same preference for one over the other in all minerals examined; this will also preserve the isochron.

Now, suppose we have an arbitrary isochron with concentrations of parent, daughter, and non-radiogenic isotope of the daughter as P(p), D(p), and N(p) at point p. Then we have the relationship

which guarantees that an isochron exists. Suppose that the rock is then diluted with another source which does not contain any of D, P, or N. Then these concentrations would be reduced by a factor of say r'(p) at point p, and so the new concentrations would be P(p)r'(p), D(p)r'(p), and N(p)r'(p) at point p. These still satisfy the isochron relationship at each point, since

Thus one again obtains an isochron, but the concentration of N(p) has been changed at each point.

Now, earlier I stated that an arbitrary isochron with a fixed concentration of N(p) could be obtained by mixing of two sources, both having a fixed concentration of N(p). With mixing from a third source as indicated above, we obtain an isochron with a variable concentration of N(p), and in fact an arbitrary isochron can be obtained in this manner.

So we see that it is actually not much harder to get an isochron yielding a given age than it is to get a single rock yielding a given age. This can happen by mixing scenarios as indicated above. Thus all of our scenarios for producing spurious parent-to-daughter ratios can be extended to yield spurious isochrons.

The condition that one of the sources have no P, D, or N is fairly natural, I think, because of the various fractionations that can produce very different kinds of magma, and because of crustal materials of various kinds melting and entering the magma. In fact, considering all of the processes going on in magma, it would seem that such mixing processes and pseudo-isochrons would be guaranteed to occur. Even if one of the sources has only tiny amounts of P, D, and N, it would still produce a reasonably good isochron as indicated above, and this isochron could not be detected by the mixing test.

I now give a more natural three-source mixing scenario that can produce an arbitrary isochron, which could not be detected by a mixing test. Suppose we have three sources with concentrations of parent, daughter, and non-radiogenic isotope of daughter of Pi, Di, Ni, respectively, for i = 1,2,3. Suppose

This is plausible, since we generally assume the isotopes of lead (say) have a roughly constant ratio everywhere. For sample 1, with more parent, we expect more daughter, so D1/N1 > D2/N2. P2 and P3 are small, since some rocks will have little parent substance. Suppose also that N2 and N3 differ significantly.

Such mixings can produce arbitrary isochrons, so these cannot be detected by any mixing test.

Also, if P1 is reduced by fractionation prior to mixing, this will make the age larger. If P1 is increased, it will make the age smaller. If P1 is not changed, the age will at least have geological significance. But it could be measuring the apparent age of the ocean floor or crustal material rather than the time of the lava flow.

I believe that the above shows the 3 source mixing to be natural and likely.

We now show in more detail that we can get an arbitrary isochron by a mixing of three sources. Thus such mixings cannot be detected by a mixing test.

We want to create an arbitrary isochron with

Suppose D1 = c1*P1, both chosen as large as possible.

Suppose D2 = c2*N2, both chosen as large as possible.

Thus D1 + P1 = 1, and D2 + N2 = 1.

Thus c1*P1 + P1 = 1, so P1 = 1/(1+c1) and D1 = c1/(1+c1). (2)

Also, c2*N2 + N2 = 1, so N2 = 1/(1+c2) and D2 = c2/(1+c2). (3)

This scenario is unrealistic, since the concentrations are large, but makes the math simpler. One can get this mixing to work with smaller concentrations, too.

To get the mixing, dilute source 1 by P(p)/P1 at point p, and dilute source 2 by N(p)/N2 at point p. All the rest of the mixing comes from source 3.

This produces a mixing with concentration of P at point p of (P(p)/P1) * P1 = P(p), and similarly for N(p) and D(p). Thus we produce the desired isochron.

Claim: P(p)/P1 + N(p)/N2 is at most 1, so this is a valid mixing.

Proof: P(p)/P1 = P(p)*(1+c1) by (2). N(p)/N2 = N(p)*(1+c2) by (3).

Their sum is P(p) + c1*P(p) + N(p) + c2*N(p), which equals P(p) + N(p) + D(p) by (1), which is less than or equal to one.

So this is a valid mixing, and we are done.

We can get more realistic mixings of three sources with the same result by choosing the sources to be linear combinations of sources 1, 2, and 3 above, with more natural concentrations of D, P, and N. For example, let m be the maximum value of D(p) + P(p) + N(p) for any p in the sample. Then we can choose

P1 = m/(1+c1) and D1 = c1*m/(1+c1)

N2 = m/(1+c2) and D2 = c2*m/(1+c2).

The two sources can then still mix to produce the original isochron, with the concentration of source 1 at a point p being P(p)/P1 and the concentration of source 2 at the point p being N(p)/N2. The rest of the mixing comes from source 3. This mixing is more realistic because P1, N1, D2, and N2 are not so large.

I did see in one reference the statement that some parent-to-daughter ratio yielded more accurate dates than isochrons. To me, this suggests the possibility that geologists themselves recognize the problems with isochrons, and are looking for a better method. The impression I have is that geologists are continually looking for new methods, hoping to find something that will avoid problems with existing methods. But then problems also arise with the new methods, and so the search goes on.

Furthermore, here is a brief excerpt from a recent article which also indicates that isochrons often have severe problems. If all of these isochrons indicated mixing, one would think that this would have been mentioned:

The geological literature is filled with references to Rb-Sr isochron ages that are questionable, and even impossible. Woodmorappe (1979, pp. 125-129) cites about 65 references to the problem. Faure (1977, pp. 97-105) devotes this chapter to seven possible causes for "fictitious" isochrons. Zheng (1989, pp. 15-16) also cites 42 references.

Zheng (pp. 2-3, 5) also discusses the frequent occurrence of a variable Sr-86 (another non-radioactive isotope of strontium) that is critical to the situation. He comes closest to recognizing the fact that the Sr-86 concentration is a third or confounding variable in the isochron simple linear regression. Austin (1994, 1992, 1988), Butler (1982), and Dodson (1982) also discuss the discordant and long ages given by the Rb/Sr isochron. Snelling (1994) discusses numerous false ages in the U-Pb system where isochrons are also used. However, the U-Th-Pb method uses a different procedure that I have not examined and for which I have no data. Many of the above authors attempt to explain these "fictitious" ages by resorting to the mixing of several sources of magma containing different amounts of Rb-87, Sr-87, and Sr-86 immediately before the formation hardens. Akridge (1982), Armstrong (1983), Arndts (1983), Brown (1986, 1994), Helmick and Baumann (1989) all discuss this factor in detail.

Anyway, if isochrons producing meaningless ages can be produced by mixing, and this mixing cannot be detected if three (or maybe even two, with fractionation) sources are involved, and if mixing frequently occurs, and if simple parent-to-daughter dating also has severe problems, as mentioned earlier, then I would conclude that the reliability of radiometric dating is open to serious question. The many acknowledged anomalies in radiometric dating only add weight to this argument. I would also mention that there are some parent-to-daughter ratios and some isochrons that yield ages in the thousands of years for the geologic column, as one would expect if it is in fact very young.

One might question why we do not have more isochrons with negative slopes if so many isochrons were caused by mixing. This depends on the nature of the samples that mix. It is not necessarily true that one will get the same number of negative as positive slopes. If I have a rock X with lots of uranium and lead daughter isotope, and rock Y with less of both (relative to non-radiogenic lead), then one will get an isochron with a positive slope. If rock X has lots of uranium and little daughter product, and rock Y has little uranium and lots of lead daughter product (relative to non-radiogenic lead), then one will get a negative slope. This last case may be very rare because of the relative concentrations of uranium and lead in crustal material and subducted oceanic plates. I note that there are _some_ isochrons with negative slopes.

Another interesting fact is that isochrons can be inherited from magma into minerals. Earlier, I indicated how crystals can have defects or imperfections in which small amounts of magma can be trapped. This can result in dates being inherited from magma into minerals. This can also result in isochrons being inherited in the same way. So the isochron can be measuring an older age than the time at which the magma solidified.

This can happen also if the magma is not thoroughly mixed when it erupts. If this happens, the isochron can be measuring an age older than the date of the eruption. This is how geologists explain away the old isochron at the top of the Grand Canyon.

From my reading, isochrons are generally not done, as they are expensive. Isochrons require more measurements than single parent-to-daughter ratios, so most dates are based on parent-to-daughter ratios. So all of the scenarios given apply to this large class of dates. Another thing to keep in mind is that it is not always possible to do an isochron. Often one does not get a straight line for the values. This is taken to imply re-melting after the initial solidification, or some other disturbing event. Anyway, this also reduces the number of data points obtained from isochrons.

Anyway, suppose we throw out all isochrons for which mixing seems to be a possibility. What is the distribution of the _remaining_ dates? Due to some published anomalies, I don't think we know that they have any clear relationship to the assumed dates.

It is also interesting that the points for isochrons are sometimes selected so as to obtain the isochron property, according to John Woodmorappe's paper.

Do the various methods correlate with one another?

We all seem to have this image in our mind of the various dating methods agreeing with each other and also with the accepted age of their geologic periods. So we are investing a lot of time and energy to explain how this marvelous agreement of the various methods can arise in a creationist framework.

The really funny thing to me is that it is very possible that we are trying to explain a phantom of our imagination. The real radiomatric dating methods are often very badly behaved, and often disagree with one another as well as with the assumed ages of their geological periods. It would really be nice if geologists would just do a double blind study sometime to find out what the distributions of the ages are. In practice, geologists carefully select what rocks they will date, and have many explanations for discordant dates, so it's not clear how such a study could be done, but it might be a good project for creationists. There is also evidence that many anomalies are never reported.

Concerning the geologic time scale, Brown writes:

"The construction of this time scale was based on about 380 radioisotope ages that were selected because of their agreement with the presumed fossil and geological sequences found in the rocks. Radioisotope ages that did not meet these requirements were rejected on the basis of presumed chemical and/or physical modifications that made the "ages" unreliable indicators of real time. About 85% of the selections were K-Ar date s, 8% rubidium-strontium dates, and 4% uranium-lead dates."

So we see that only a tiny proportion of these dates on which geologic time was based, were uranium-lead dates. Maybe only 15 in all. Why is this? It is possible that the reason is that uranium-lead dates so rarely agree with the correct dates. So there may not be anything to explain.

For example, it's not clear to me that we need to worry about isochrons or whether U238 and U235 dates etc. agree with each other. I'd like to know how often this happens, in any case, especially on the geologic column of Cambrian and above. People should read John Woodmorappe's articles on radiometric dating to see some of the anomalies.

One might say that if there were problems, then geologists wouldn't use these methods. I think we need something more solid than that.

John W. did have an example of a correlation study for K-Ar and Rb-Sr dating in precambrian rocks. The correlation was not very good. I assume he would have mentioned if any others had been done. Maybe since then?

What we really need is the raw data on how these dates correlate, especially on the geologic column of Cambrian and above. We need to see the data to know if there is really any need to explain anything away. Many anomalies never get published, according to John Woodmorappe's references; other quotes indicate that the various methods typically disagree with each other.

There appears to be an increase in K/Ar ages with depth, but there are a number of explanations for that.

A friend related one example of serious anomalies in K/Ar dating that has been reported and that also indicates that there are serious problems.

A few years ago I took a course in the "Evolution of Desert Environments". We were standing on the Simi Volcanic flow, about 80 miles south of the south end of Death Valley. The instructor was a well known geologist and evolutionist from Cal. State Long Beach. He told us that the upper end of the flow was dated at 100,000 years, the middle of the flow was dated at 50,000 years, and the toe of the flow was dated at 20,000 years. He then noted that the whole flow probably occured and solidified (the surface at least) within weeks. He then said, based on his observation of the rates of evolution of desert environments he thought the flow was less than 10,000 years of age. He then said "radiometric dating is the cornerstone of modern historical geology and we get this kind of variation?" Clearly he was not happy with the published dates on the Simi flow.

He was also not happy with the published dates on the flows in the Nevada Atomic Bomb Test site where one of the volcanic flows showed a reversal of isotope ratios and gave a value of 20,000 years in the future! These data were, in fact, published in Science magazine in about November of 1988. Please note, these were not MY ideas but the statements of a convinced, tenured, evolutionary geologist who apparently really wanted to beleive in the credibility of radiometric dating. I am just reporting what HE said!

Thus, there apparently ARE some problems in that kind of radiometric dating.

Furthermore, if there are special circumstances that invalidate the method, then this raises questions about the method in general. It's been an eye opener to me to see all the processes that lead to segregation of different minerals in the magma. We have gold appearing pure at times, silver pure at times, etc., and no one says this is due to radiometric decay. The geological processes at work have a tremendous ability to separate different kinds of elements and minerals. And yet we expect that uranium-lead ratios are determined by radiometeric decay alone (or at least sometimes)!

There are so many complicated phenomena to consider like this that it calls the whole radiometric dating scheme into question.

We haven't even considered the fact that uranium is highly water soluble and lead is not, which could make the dates too old, too. Another factor to consider.

We now have so many things that can make radiometric dating go wrong, and isochrons don't remedy the situation at all, that I think the weight of evidence of radiometric dating is nullified.

I really feel ``bullish'' about the creationist model now. Evolution has always been in trouble. I now have a good explanation for where the flood water came from and where it went, based on water trapped inside the crust (however the planet formed or was created). And now radiometric dating has had its foundation removed from under it. I suspect that a number of geologists now realize the implications of what they know about the lead and uranium content of subducted oceanic plate versus crustal material and the mechanics of magma solidification. What it means is that radiometric dates have no necessary relation to true ages! (For this I'm mainly concerned with the geologic column of Cambrian and above.) At least, there are so many variables to consider that the relationship between radiometric ages and true ages is too complicated to disentangle at present, isochrons or no isochrons.

We have seen many ways in which radiometric dates can be affected by what is going on in the magma. I think this is really the weak spot of radiometric dating. It takes a long time to get to the bottom of things, and I think we have finally hit it.

Still, the creationist task is not finished by proposing all of these mechanisms for invalidating radiometric dating. We can explain many dates away, but a question creationists need to face is which is the best explanation of the data. Can we find evidence that shows that an explanation of radiometric dates in terms of a young geologic column is more plausible than an explanation in terms of an old geologic column? I'm not speaking of evidences based on erosion or the lack of it, or other kinds of evidence, but rather on evidences relating to the radiometric dates and the concenrations of isotopes themselves.

I thank Jon Covey for much of the source material cited in this article, and for some other contributions as well.

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