Helium Diffusion Age of 6,000 Years Supports Accelerated Nuclear Decay
D. Russell Humphreys*, Steven A. Austin*, John R. Baumgardner**, and Andrew A. Snelling*†
CRSQ Vol 41 No 1 June 2004
AbstractExperiments co-sponsored by the Creation Research Society show that helium leakage deflates radioisotopic ages. In 1982 Robert Gentry found amazingly high retentions of nuclear-decay-generated helium in microscopic zircons (ZrSiO4 crystals) recovered from a borehole in hot Precambrian granitic rock at Fenton Hill, NM. We contracted with a high-precision laboratory to measure the rate of helium diffusion out of the zircons. The initial results were very encouraging. Here we report newer zircon diffusion data that extend to the lower temperatures (100º to 277º C) of Gentry's retention data. The measured rates resoundingly confirm a numerical prediction we made based on the reported retentions and a young age. Combining rates and retentions gives a helium diffusion age of 6,000 ± 2,000 years. This contradicts the uniformitarian age of 1.5 billion years based on nuclear decay products in the same zircons. These data strongly support our hypothesis of episodes of highly accelerated nuclear decay occurring within thousands of years ago. Such accelerations shrink the radioisotopic "billions of years" down to the 6,000-year timescale of the
Figure 1. Drilling rig for borehole GT-2 at
Fenton Hill, NM. Photo: courtesy of Los Alamos National Laboratory.
IntroductionUnder the deep blue skies of northern New Mexico in the fall of 1974, drillmen labored to extract cores from a borehole called GT-2 (Figure 1) nearly three miles deep. The site was Fenton Hill, on the west flank of the Valles volcanic caldera in the pine-covered Jemez Mountains. Two dozen miles to the east, geoscientists at Los Alamos National Laboratory analyzed the drill cores, investigating whether the hot, dry rock would be suitable for providing geothermal energy. The geoscientists identified the rock as biotite granodiorite, a granitic rock containing shiny flecks of a black mica called biotite. They crushed a core sample from a depth of 2,900 meters and extracted microscopic crystals of zirconium silicate (ZrSiO4) embedded in the biotite. These crystals, called zircons, were radioactive, containing high amounts of uranium and thorium relative to the rest of the rock, as is usual for that mineral. Comparing two isotopes of radiogenic(formed by nuclear decay) lead (206Pb from 238U and 207Pb from 235U), they determined that 1,500 ± 20 million years worth of nuclear decay had occurred in the zirconsassuming as usual that nuclear decay rates have always been constant (Zartman, 1979). The date is consistent with uniformitarian expectations for this Precambrian "basement" rock unit.
Figure 2. Uranium, lead, and helium in a schematic zircon. 238U decaying to 206Pb releases eight alpha particles (which become helium atoms) within the crystal.
Figure 3. Zircons 50 to 75 µm long extracted by Gentry et al. (1982a) from GT-2 core samples. Photo: courtesy of R. V. Gentry.
RATE gets involvedWhen creationists became aware of Gentry's data, many of us thought that it would have been impossible for the zircons to have retained that much helium for even a million years, much less over a billion years. Helium is a lightweight, fast-moving atom that does not attach itself to other atoms, so it diffuses (spreads out) through the atomic lattices of most minerals relatively fast. However, we knew of only one published measurement of diffusion rates of helium through zircon (Magomedov, 1970). That report was sketchy and ambiguous, leaving room for quite different ways to interpret the numbers. There were no published measurements for helium diffusion through biotite, the mineral surrounding the zircons. Until we had reliable numbers for these diffusion rates, we could not say for certain that the large retentions require a young earth.
Table I: Observed helium retentions for zircons recovered from various depths in borehole GT-2 and others nearby, Fenton Hill, NM. Samples 2002 and 2003 were recovered for the RATE project and named for the years we analyzed them. Samples 1-6 are those reported by Gentry et al. (1982a). Column 4 is the total helium yield (1 ncc = 10-9cm3 at standard temperature and pressure) per microgram of zircon. Column 5 is the corresponding fraction of the estimated amount of helium deposited in the zircons by nuclear decay. Column 6 is the estimated error in the fraction. All zircons were of length 50-75 µm, except for those from sample 2002, which were not sorted into size groups.In 1998, the Radioisotopes and the Age of the Earth (RATE) steering committee began planning to do experiments to measure helium diffusion in the relevant minerals. RATE (Vardiman et al., 2003) is a research initiative started in 1997 by seven scientists from three major creationist organizations: the Institute for Creation Research (ICR), Answers in Genesis (AiG), and the Creation Research Society (CRS). In 1998 a personnel transfer reduced the sponsoring organizations from three to two, ICR and CRS. Three board members of CRS have been on the RATE steering committee from the outset: Donald DeYoung, Eugene Chaffin, and Russell Humphreys. CRS members have supported the project by designating donations to the RATE research fund administered by ICR. The charter for RATE was to make a focused investigation of the problem posed by two large bodies of geoscience evidence for (A) large amounts of nuclear decay having occurred, and (B) a young world. From the start, several members of the steering committee were convinced that episodes of greatly accelerated nuclear decay rates had occurred within thousands of years ago. For the preservation of life, such episodes seem possible only under special circumstances: (1) before God created living things, (2) after the Fall but well beneath the biosphere, and (3) during the year of the Genesis Flood, when the occupants of Noah's ark would be safe from most radiation (Humphreys, 2000, pp. 340-341). Accordingly, the steering committee planned a research program to test the accelerated decay hypothesis, and they wrote a book (jointly published by ICR and CRS) outlining the various projects (Vardiman et al., 2000). In developing our plans for the helium experiments, we calculated what diffusion rates would be necessary to produce Gentry's reported helium retentions if the zircons were (a) 6,000 years old, or (b) 1.5 billion years old. Figure 4 shows the graph we published (Humphreys, 2000, p. 348, Figure 7) of the resulting two models. Figure 4, the prediction, is a typical Arrhenius plot. The vertical axis shows diffusivities (giving rates of diffusion) logarithmically. The horizontal axis shows inverse absolute temperature (1000 divided by degrees Kelvin) linearly. High temperatures are on the left and low temperatures are on the right. Diffusion data on such a plot usually fall into one or two straight lines (Humphreys et al., 2003a, § 3). Notice that the diffusion rates in the Uniformitarian model are over 100,000 times slower (to retain helium 1.5 billion years) than those in the Creation model (6,000 years). Such a large difference made it likely that experiments would be able to distinguish between the two models, so we began seeking ways to conduct or commission such measurements.
Experiments beginIn 2000, through an intermediary, we contracted with a well recognized expert (Humphreys et al., 2003a, § 5) to measure helium diffusion rates in biotite, the mineral we thought was the main restriction to helium loss from the zircons. We sent the experimenter biotite we had on hand, from the Beartooth Gneiss in Wyoming near Yellowstone National Park. In early 2001 he sent us data, the first ever reported on biotite. Also in 2001, we received a preprint of a paper reporting helium diffusion rates measured in zircons from Nevada (Reiners et al., 2002).
Figure 4. Predicted (Humphreys, 2000, p. 348, Figure 7) helium diffusion rates necessary to retain the observed amounts of helium (Table I) for (a) 6,000 years (Creation model), or (b) 1.5 billion years (Uniformitarian model).
Latest results arrive in mid-2003In the fall of 2002, we acquired new samples from borehole GT-2, this time from a depth of 1490 meters. That is between the depths of Gentry's samples 1 and 2 (see Table I). We sent them to Activation Laboratories, where Kapusta extracted both biotites and zircons. This time he sorted the zircons into several size groups, getting about 1200 crystals in the size range Gentry used, having lengths of 50-75 µm. Figure 5 shows a scanning electron microscope (SEM) image of one such zircon. Mark Armitage obtained the image in his newly established microscopy laboratory at ICR, where he also obtained SEM images of the HF-treated zircons the previous section mentioned. In the spring of 2003, we sent our experimenter the 5075 µm zircons, along with the biotites. This time we asked him (a) not to etch the crystals in HF (unnecessary because no sieving was needed) and (b) to get zircon diffusivities at lower temperatures. We also asked that he measure more precisely the total helium per unit mass in both the zircons and the biotites. In July 2003, one month before the conference, we received his results.
Figure 5. Scanning electron microscopy photograph by Mark Armitage of zircon from group selected by size by Jakov Kapusta.
Table II: Latest (2003) helium diffusion data for 5075 µm length zircons from borehole GT-2 at a depth of 1490 meters. Column 3 is the amount of helium released (ncc defined in Table I) at the given temperature step. Column 4 is the time at each step. Column 5 is the cumulative fraction of the total helium yield (at bottom of table). Column 6 is the value of D/a2 estimated by the experimenter according to standard formulas, where D is the diffusivity and a is the average effective radius. Column 7 is the value of D assuming a = 30 µm, and omitting steps 1-9 according to advice from the experimenter (see below).
Figure 6. Recent (2003) zircon diffusion rate data compared with the Creation and Uniformitarian models shown in Figure 4.
Recent data also close loopholesAfter stepwise heating the 216 micrograms of zircons to get the diffusivity data, our experimenter raised the temperature to a high value, holding it there long enough to get the rest of the helium out of the crystals. The total yield of helium from the zircons was 1356 ncc (1 ncc = 10-9 cm3 at standard temperature and pressure = 0.4462 x 10-4 nanomole), or 6.05 x 10-2 nmol. Dividing by the mass gives us 6.28 ncc/µg, or 303 nmol/g. Multiplying the latter value by the density of zircon, 4.7 g/cm3, gives us the helium concentration in the zircon: 1320 nmol/cm3. For the 5.562 milligrams of biotite, the total yield of helium was 257 ncc, giving 2.06 nmol/g. Multiplying by the density of biotite, 3.2 grams/cm3, gives us the helium concentration in the biotite: 6.57 nmol/cm3. These data are quite useful in closing possible loopholes in our case. First, the 6.3 ncc/µg yield of these zircons is quite consistent with Gentry's retention data. Using Gentry's estimate of radiogenic helium deposited in the zircons, about 15 ncc/µg (which is consistent with our data on radiogenic lead in the zircons), gives us a retention fraction of 0.42 (42%). These zircons came from a depth of 1490 meters, nearly midway between Gentry's samples 1 and 2 in Table I. The interpolated temperature at that depth would be 124º C. Figure 7 shows that our new retention point fits quite well between Gentry's retentions for samples 1 and 2. This confirms the validity of Gentry's retention measurements. Second, the concentration of helium in the zircon, 1320 nmol/cm3, is about 200 times greater than the concentration in the surrounding biotite, 6.6 nmol/cm3. Because the laws of diffusion require flow from greater to lesser concentrations, these data mean that helium is moving from the zircons into the biotite, not the other way around. Third, because the average volume of the biotite flakes is hundreds of times greater than that of the zircons (Humphreys et al., 2003a, § 6), the amount of helium in the biotites is on the same order of magnitude as the amount of helium lost by the zircons. That rebuts a specious uniformitarian conjecture (Ross, 2003) that there could have been vast amounts (100,000 times greater than the already-large observed amounts) of non-radiogenic primordial helium in the zircons 1.5 billion years ago.
Table III: Estimates of age from Gentry's helium retentions (Table I) and our measurements of helium diffusivity in the same zircons (Table II). Diffusivities here come from best exponential fits to nearby measured points from Table II, column 7. Because our lowest measured value for D is at 175° C, we extrapolated 24° C down to the temperature of sample 2 but not 45° C further down to that of sample 1. Then we calculated ages as we did in our ICC03 paper (Humphreys et al., 2003a, §§ 6 and 8), putting the x-values of ICC03 Table 2 and the values of D above into ICC03 equation 17 to get the values for the age t we show above. See our comments on page 9 (related to Figure 8) about sample 3, which above has the greatest deviation from the average age. We report the average and sigma above as 6,000 ± 2,000 years.
Figure 7. Recent (2003) measurement of percentage helium retained for zircons from 1490 meters depth and 124º C, compared with percent retentions (points 1 and 2) measured by Gentry et al. (1982a) shown in Table I.Our conference paper answers other commonly raised objections, including (1) a nearly automatic response among uniformitarians involving the geoscience concept of "closure temperature" (Humphreys et al., 2003a, § 10), and (2) the possibility that the rock unit was much cooler for most of its history. Two short answers are that (1) the closure temperature for these zircons happens to be relatively low, 128º C, permitting the zircons above that temperature to leak helium freely, and (2) the zircons would have to have been refrigerated cooler than minus 100º C in order to retain the helium for the alleged eons (Humphreys et al., 2003b, see poster and extended temperature range Arrhenius plot at its bottom). Our conference paper clarifies these points and adds other answers (Humphreys et al., 2003a, §§ 9, 10). Our new helium retention fraction (0.42 at 124º C) can be treated the same way as we treated Gentry's retention data to make a prediction of diffusion rates. That is, we can use our retention figure to calculate what value of D at 124º C would be required if the zircons were 6,000 years old. Figure 8 shows how this "retrodiction" point fits very well with the diffusion rate data and the Creation model prediction. In Figure 8, we have redrawn the lines in accord with the new data. The largest outlier from the lines is the model point at 197º C. The difference suggests the true retention fraction for that sample might have been about half the fraction Gentry et al. reported (Table 1, sample 3). Whatever the cause, a two-fold discrepancy for one point pales into insignificance in light of the whopping 100,000-fold discrepancy between the observed diffusivities and all points of the Uniformitarian model!
Figure 8. Figure 6 with lines redrawn in accordance with the new (2003) data. Squares with temperatures below them are the diffusivities we predicted in 2000 on the basis of Gentry's reported retentions (Table I, samples 1-5) and an age of 6,000 years. The star with "124º C" above it is the diffusivity required by our new retention datum (Table I, sample 2003, and page 9) and a 6,000-year age.
Lead diffusion supports our caseLead also diffuses out of zircon, although much more slowly than helium does. In addition to studying helium, Gentry and his team (1982b) at Oak Ridge also studied lead retention in 50-75 µm zircons from the same rock unit. The deepest sample was from a depth of 4310 meters and a temperature of 313º C. The paper reports, "there was little or no differential Pb loss which can be attributed to the higher temperatures at greater depths." Judging from their experimental error, their results mean that more than 90% of the lead generated by "1.5 billion years" worth of nuclear decay has remained in even the deepest, hottest zircons. The diffusion rates for lead in zircon are known, and the article reports that at 200º C, it would take 50 billion years for 1% of the lead to diffuse out of a 50-µm zircon. However, the article does not report such times for higher temperatures. Using the same equation and data (Gentry et al., 1982b, note 16; Magomedov, 1970), we calculate that at the highest borehole temperature, 313º C, a zircon 60 µm long (a = 30 µm) would lose about 50% of its lead in 1.5 billion years. Because the observations show that those zircons did not lose anywhere near that much lead, these data imply an age much less than 1.5 billion years. Thus the lead diffusion data support the young helium diffusion age of the zircons.
Conclusion: a tale of two hourglassesExperiments have strongly vindicated what creationists felt when Gentry reported the high helium retentions over twenty years ago. The helium indeed could not have remained in the zircons for even a million years, much less the alleged 1.5 billion years. Even more exciting, the most recent experiments give a helium diffusion age of 6,000 ± 2,000 years, which resonates strongly with the date of creation we get from a straightforward Biblical chronology. Figure 9 illustrates the contrast between this helium age and the radioisotopic age. It shows two different "hourglasses," representing helium diffusion and uranium-to-lead nuclear decay. These hourglasses give drastically different dates.
Figure 9. Two hourglasses representing dating by (a) helium diffusion and (b) uranium-lead decay. "Valve" represents possible nuclear decay acceleration.
AcknowledgementsWe express our appreciation to Los Alamos National Laboratory for giving us the Fenton Hill samples, to Jakov Kapusta and Activation Laboratories, Ltd., for processing them, to Robert Gentry for his advice and help, to Mark Armitage for his microscope work, to Zodiac Mining and Manufacturing, Inc., for its services as intermediary, and especially to the donors whose generosity made this work possible.
Appendix: Responding to a CriticRecently a critic sought very hard to find loopholes in our arguments. While none of his points had any significant impact on our conclusions, it is worthwhile to review the specifics of his critique and answer them here. The critic felt a crucial issue was the possibility that the interface between zircon and biotite might slow or stop helium diffusion because of helium having different chemical potentials or solubilities in those two minerals, or because of interface resistance between them due to other causes. In the next three sections we will explain those terms and quantify their effects.
DIFFERENCES IN CHEMICAL POTENTIALA diffusion theorist (Manning, 1968, § 5-3, p. 180, equation 5-36) expresses the chemical potential, µ, for helium atoms constituting a fraction N of all the atoms in a crystal at temperature T as the sum of two parts:
where k is the Boltzmann constant. The first term on the right, the "entropy of mixing," contains no information related to the forces between atoms. The second term, µ', is of interest. It is the contribution from all other factors, particularly the interaction energy between helium and the other atoms of the crystal.
The same theorist (Manning, 1968, § 5-3, p. 180, equations 5-37 and 5-39) then expresses the flux J of helium atoms in the x-direction through a region with diffusivity D as:
The first term on the right represents ordinary diffusion. It is the second term that represents an additional flux due to a driving force, the gradient of µ'. This force originates in whatever chemical attraction the helium atom might have for the atoms of the crystal in which it resides. Inside the crystal, these forces average to zero, but at the interface with another crystal, there may be a jump in µ'. If a helium atom were to have greater chemical attraction for the atoms of zircon than for the atoms of biotite, that would result in a force at the interface hindering its outward motion into the biotite. The question we need to address is, "Just how great is the effect?"
Because helium is one of the noble gases, we might suspect that it would have very little chemical attraction for any other atoms. In fact, helium is the least chemically active of all the noble gases (Holloway, 1968, p. 45, Table 2.1). Nevertheless it does exhibit a faint attraction for other atoms. Theory and experiments (Wilson et al., p. 936, Table XI) show that helium atoms adhere very slightly to the surfaces of alkali halide crystals, with interaction potentials on the order of a few hundred calories per mole of helium. The largest estimated potential is 293.4 cal/mol, at the "saddle point" between the sodium and fluorine ions at the surface of NaF. The smallest potential listed is beside a chlorine ion at the surface of NaCl, 111.7 cal/mol.
The difference of those potentials provides an estimate of the difference of µ' at an interface between NaF and NaCl: 181.7 cal/mol, or 0.00788 eV per helium atom. Because noble gases have a greater chemical affinity for halides (Holloway, 1968, p. 89) than for most other ions, the above number is almost certainly greater than the corresponding number for the silicate minerals we are considering. So at the interface between zircon and biotite, we can take the following value as a generous upper bound on the magnitude (absolute value) of the difference in µ':
Now we need to quantify the effect of that difference on the flux of helium atoms in equation A2. As we did in our ICC paper (Humphreys et al., 2003a, § 6, after equation 9), we assume for simplicity that the diffusivity D is the same for biotite as for zircon, and therefore constant across the interface. Because the observed value of C in the biotite is hundreds of times smaller than in the zircon (this paper, § 5), the magnitude of the change in concentration, ΔC, across the interface is nearly equal to the concentration C in the zircon:
Assuming that the changes ΔC and Δµ' both occur within roughly the same small distance δx, the width of the interface, the helium flux J in equation (A2) becomes:
To make this mechanism a viable possibility for rescuing the uniformitarian scenario, the second term on the right-hand side must be: (1) of opposite sign to the first (Δµ' must be negative, meaning helium is more attracted to zircon than biotite), and (2) large enough to reduce J to a level about 100,000 times lower than what the first term alone would give. That could reduce the helium flow enough to let the zircon retain the helium for 1.5 billion years. In the coolest sample we analyzed, at 100° C, the average thermal energy kT of the atoms was 0.0321 eV. Then |Δµ'/kT| would be less than 0.246 for that sample, and even smaller for the hotter samples. That makes the magnitude of the second term less than 25% of that of the first term for all the samples we analyzed. However, our upper bound on the value of Δµ' based on the chemical affinity of helium with alkali halides is likely at least an order of magnitude larger than the actual value. So a magnitude of the second term less than 2.5% of the first term is probably more realistic. The second term obviously does not provide the large reduction of helium flow the uniformitarian scenario requires.
However, an even more basic consideration shows our measurement procedures have already accounted for such differences. We note that the magnitude of Δµ' is several times greater for a zircon-vacuum interface than for a zircon-biotite interface. That is, the attraction of a helium atom for the biotite it is entering partly cancels its attraction for the zircon it is leaving. But our experimenter measured the diffusivities of zircons in a vacuum. So the zircon diffusivities we report in Table II already include the effect of a stronger interface reflection than would exist for the zircons in their natural biotite setting. So however strong or weak the "chemical potential" interface effect may be, our measured diffusivities already account for it in a way that is generous to the uniformitarian model.
Solubility in this context corresponds to the maximum number of helium atoms one gram of crystal can absorb per bar of pressure (Weast, 1986, p. 101). The critic used the term as a measure of the difficulty with which a helium atom could enter biotite. As a hypothetical example, if all the spaces between atoms in biotite were much smaller than the diameter of a helium atom, then helium could never enter the crystal, so helium would be completely insoluble in biotite. If an alpha-decaying nucleus inside the biotite were to generate a helium atom therein, then the atom could distort the lattice and push its way out. The crystal would have a small but non-zero helium diffusivity and zero solubility.
However, real minerals have non-zero solubilities. The solubilities of helium in obsidian and basaltic glass between 200 and 300° C, for example, are on the order of 50 nmol/g per bar (Jambon and Shelby, 1980, Fig 2c) and on the same order in other minerals (Broadhurst et al., 1992). The solubility of helium in biotite has not been measured (we were the first to measure even diffusivity for that pair of substances), so we must find a way to estimate its effect in this case.
One way is to consider the interaction potential part µ' of the chemical potential we mentioned in the previous section. For a helium atom near the surface of a crystal, the gradient of the potential is negative, making the force attractive. But the force can become repulsive for a helium atom entering a tightly packed crystal. For example, imagine that a helium atom has to come very close to an oxygen atom. If their nuclei are closer together than 2.94 Å (1 Å = 1 angstrom = 1 x 10-8 cm ≈ diameter of a neutral hydrogen atom), the force between the two atoms is repulsive (Kar and Chakravarty, 2001, Table I σos column and gradient of their equation 2).
However the space between silicate sheets in biotite is much larger than that (Deer et al., 1962, Vol. 3, pp. 1-3, 55; Dahl, 1996, Figure 1 and Table 4). The large spacing is the reason the diffusivity of helium in biotite (Humphreys et al., 2003a, Figure 6b) is about ten times higher than in zircon, which has tighter spacing (Deer et al., 1962, Vol. I, pp. 59-68). The relative spacings and diffusivities imply the solubility of helium in biotite is greater than in zircon, so the force related to solubility, included in the gradient of µ', would tend to push helium atoms out of zircon and into biotite. Hence their respective solubilities would not hinder helium outflow from the zircon but rather enhance it.
Our critic also postulated some type of interface resistance arising from special distortion of the crystalline lattices at the interface between zircon and biotite. We can model such hypothetical interface resistance (Crank, 1975, p. 40, § 3.4.1) as a very thin layer of very low diffusivity between the zircon and biotite. The concentration of helium would drop rapidly across the layer, approximating a discontinuous change of concentration between zircon and biotite. Such a layer might consist of physically or chemically altered zircon or biotite, and it would be at most a few dozen angstroms thick.
Let us estimate how low the diffusivity D of the interface would have to be in order to retain the helium in the zircon for 1.5 billion years. Since D is supposed to be much lower than the diffusivities of both zircon and biotite, we can approximate the situation as a hollow sphere with a wall of diffusivity D having an inner radius a and outer radius b. A source (representing nuclear decay) inside the sphere generates helium at a steady rate q0, and the helium diffuses through the wall out into a vacuum outside the sphere. Textbooks show (Carslaw and Jaeger, 1959, §9.2, p. 231, example IV, Q0 → q0, K → D, v1 → C, v2 → 0) that the steady-state helium outflow q0 is
where C is the steady-state concentration of helium inside the sphere. Taking the wall thickness δ (b = a + δ) to be small compared to a (δ << a), integrating q0 for time t and C over the sphere volume (Humphreys et al., 2003a, § 7, equation 16) gives us the ratio of helium retained, Q, to total helium generated, Q0:
Turning this around gives us the interface diffusivity D required to retain a fraction Q/Q0 of helium for time t in a zircon of effective radius a surrounded by an interface of thickness δ:
For example, with an interface thickness of 30 angstroms, a = 30 µm, and a time of 1.5 billion years, the 17% retention of sample 3 requires an interface diffusivity of
|D ≈ 3.8 x 10-26 cm2/second||(A9)|
This is over ten billion times lower than the diffusivities we measured in biotite (Humphreys et al., 2003, Figure 6b) and zircon (this paper, Figure 8) at the same temperature, 197° C. To see whether this is an achievable value or not, let us examine an example the critic gave for physical alteration of the minerals at the zircon-biotite interface.
The critic suggested that when biotite crystallizes around a zircon, it possibly forms with its silicate sheets (along which are the cleavage planes) everywhere parallel to the surface of the zircon, so that the biotite wraps up the zircon like layers of cellophane. But in the thousands of zircon-containing biotite flakes that we ourselves have observed under the microscope (Snelling and Armitage, 2003; Snelling et al., 2003b), the silicate sheets remain parallel all the way to the edge of the zircon crystal and do not wrap around the included zircons. A Los Alamos report has a photo of a radiohalo in biotite from borehole GT-2 showing the biotite cleavage staying parallel to itself, running right up against the zircon, and not becoming parallel to the zircon surface (Laughlin and Eddy, 1977, Figure 6, p. 18). There is simply no observational support for the critic's hypothesis that layers of biotite envelop an included zircon.
However, for the sake of having a specific illustration of interface resistance, let us indulge the critic and imagine that a few of the biotite layers closest to the zircon wrap around it. We will even imagine that there are no openings in the biotite wrapping at the edges and corners of the zircon faces. In that case, diffusion in the interface would have to take place in the harder direction, perpendicular to the silicate sheets rather than parallel to them.
Let us estimate the diffusivity in that harder direction. Measurements show that in biotite, "Ar diffusion is ~500 times faster parallel to the silicate sheets than perpendicular to the silicate sheets" (Onstott et al., 1991, § 7, p. 166). Because a helium atom has a smaller diameter, 2.28 Å, than an argon atom, 3.35 Å (Kar and Chakravarty, 2001, Table I sss column), then for helium there should not be as great a difference between "parallel" diffusivity D | | and "perpendicular" diffusivity D⊥. So for helium in biotite, the ratio D | | / D⊥ should be less than 500. Our measurements for helium in biotite (Humphreys et al, 2003, Figure 6b) gave, for example, D | | = 8.6 x 10-15 cm2/s at 200° C. Dividing that diffusivity by 500 gives us a lower bound on the diffusivity in the difficult direction:
|D⊥ > 1.7 x 10-17 cm2/second||(A10)|
That is over 400 million times greater than the maximum diffusivity, equation (A9), that a 30 Å interface could have to retain the helium for 1.5 Gyr. Hence such a hypothetical mechanism fails to account for the high helium retention we document. Moreover, as we have already indicated, there is no observational support for the sort of interface crystallographic structure our critic speculates might exist.
EFFECTS OF MODEL ASSUMPTIONS
The critic also explored the effects of several changes in the assumptions of our models: (1) inserting a large interface resistance, (2) greatly increasing the creation model D for biotite, (3) decreasing the uniformitarian model D for biotite from infinity to that of zircon, (4) accounting for anisotropy of biotite and zircon, and (5) changing the effective radius a from our early value of 22 µm (Humphreys, 2000, p. 347) to our more recent and more appropriate value of 30 µm (Humphreys et al., 2003a, § 6, after equation 9).
We have discussed change (1) in the preceding section, showing that it is unrealistic. Change (2) increases the helium loss rate from the zircons by a factor of six, making it less realistic than our assumption, which had a worst-case effect of 30% (Humphreys et al., 2003a, § 6, after equation 9). Change (3) decreases the loss rate from zircons by a factor of six, but we think it is unrealistic for uniformitarians to demand an extremely low value of D for the biotite as well as the zircon.
Regarding mineral anisotropies (4), we point out two things: (a) switching from sphere to cylinder geometry (roughly approximating anisotropy effects) for the most important mineral (zircon) would alter the results by less than a factor of two, and (b) even a factor-of-ten reduction in the modeled diffusivity of the surrounding mineral (biotite) would change our results by less than 30% (Humphreys et al., 2003a, § 6 after equation 9). Thus, accounting for biotite anisotropy would affect our results by much less than 30%. As for zircon, anisotropy in it is probably just as negligible as it is in many other similarly shaped crystals, such as quartz. Both our experimenter and other diffusion experts have not assigned a high priority to investigating that possibility.
Change (5), the increase in effective radius a required by our better knowledge of zircons, by itself would have increased the model-required D's by a factor of about two. But our better knowledge also required another model change, from a "bubble" in biotite to a solid in biotite. This second change reduced the D's by about a factor of two. Because the two effects nearly cancelled each other out, the net change in predicted D was less than 0.5%. We explained these things in our ICC paper (Humphreys et al., 2003a, § 6), but perhaps not clearly enough.
The critic acknowledged that changes (2-5) would not come anywhere close to eliminating the 100,000-fold discrepancy between our data and any reasonable uniformitarian scenario. But he asserted that the several-fold sensitivity to changes in assumptions means that the close agreement between the creation model and the data was merely accidental. That may be a possibility, but it may also mean we exercised good theoretical judgment in choosing the simplifying assumptions for our prediction.
Finally, the critic proposed we postpone publication until (a) further theoretical and experimental investigations would close all alleged loopholes, and (b) until we have much more data supporting our case from boreholes all over the world. We disagree with him. On point (a), detractors can allege loopholes eternally, and we think we have addressed all the so-far-alleged loopholes well enough to place the burden of proof on the detractors.
On point (b), the critic was laboring under a misunderstanding. He reasoned that the possible scarcity of sites with what uniformitarians call "excess helium" meant that sites with high retentions and short helium diffusion ages are rare. As we explained at the ends of the introduction and the "Latest results arrive in mid-2003"section in this paper, those two concepts (excess helium and diffusion age) are fundamentally different. But even if he were correct, we feel that the data in this paper are so well established that immediate publication is warranted.
We thank Roger Lenard, a physicist at Sandia National Laboratories in Albuquerque, NM, for his expert advice on chemical thermodynamics, which helped us to prepare the "Solubility" and "Interface resistance" sections above.
References and Notes
CRSQ: Creation Research Society Quarterly
ICC03: Proceedings of the Fifth International Conference on Creationism
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——. 2003b. The enigma of the ubiquity of 14C in organic samples older than 100 ka, Eos, Transactions of the American Geophysical Union 84(46), Fall Meeting Supplement, Abstract V32C-1045. Poster at http://www.icr.org/research/AGUC-14_Poster_Baumgardner.pdf .
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