Young-Earth Creationist Helium Diffusion "Dates"

Appendices and References

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Appendix C Humphreys Feels the Pressure

APPENDIX A:  CALCULATION OF Q/Q₀ VALUES USING THE ASSUMPTIONS IN GENTRY ET AL. (1982a)

Q refers to the measured quantity of helium (presumably only radiogenic ⁴He) in a mineral.  From its crystallization to the present, Q₀ is the maximum amount of radiogenic helium (⁴He) that could accumulate in a mineral from the radioactive decay of its uranium and thorium (Humphreys et al., 2003a, p. 3).  Q₀ assumes that no diffusion ("leakage") has occurred except for "alpha ejection" (Farley et al., 1996; Tagami et al., 2003).  Q/Q₀ would then represent the fraction of radiogenic ⁴He (that is, presumably without any extraneous component) remaining in a sample since its crystallization.  The Q/Q₀ value of a zircon would not only depend on its age, but also its size, the number of fractures and metamict areas, subsurface pressures, its original uranium or thorium concentrations and a number of other factors.

By making several assumptions that are no doubt inaccurate, Gentry et al. (1982a, p. 1129) derived one Q₀ value for the zircons in all of their Precambrian samples and used this value to estimate the Q/Q₀ values of their zircons.  Gentry et al. (1982a, p. 1129) state their assumptions in the following paragraph:

"For the other zircons from the granite [sic, granodiorite] and gneiss cores [samples 1-6], we made the assumption that the radiogenic Pb concentration in zircons from all depths was, on the average, the same as that measured (Zartman, 1979) at 2900 m, i.e., ~80 ppm with ²⁰⁶Pb/²⁰⁷Pb and ²⁰⁶Pb/²⁰⁸Pb ratios of ten (Gentry et al., ...[1982b]; Zartman, 1979). Since every U and Th derived atom of ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb represents 8, 7 and 6 alpha-decays respectively, this means there should be ~7.7 atoms of He generated for every Pb atom in these zircons." [my emphasis, unlike Humphreys, 2005, Gentry et al., 1982a admit that the cores contain gneisses.]

First of all, they assumed that the radiogenic lead concentrations (total ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb) of the zircons from each of the six samples averaged 80 parts per million (ppm).  Based on the discussions in my Appendix B, this assumption is probably too low.  Nevertheless:

80 ppm = 80 micrograms radiogenic Pb/gram zircon = 0.00008 g radiogenic Pb/g zircon

Although the overall atomic mass of Pb (207.2 amu) includes non-radiogenic ²⁰⁴Pb, the atomic mass of radiogenic Pb is close to 207.2 amu.  Therefore:

0.00008 g/g divided by 207.2 g Pb/mole Pb = 3.9 x 10^-7 moles radiogenic Pb/g zircon

The concentrations of the various radiogenic lead isotopes are then represented by the following equation:

²⁰⁶Pb + ²⁰⁷Pb + ²⁰⁸Pb = 3.9 x 10^-7 moles total radiogenic Pb/gram zircon

Given:

²⁰⁶Pb/²⁰⁷Pb = 10. That is: ²⁰⁷Pb = ²⁰⁶Pb/10. Gentry et al.'s (1982a) assumption is reasonable here.  Actual values from Gentry et al. (1982b, p. 296) are about 9.6 to 11.2.

²⁰⁶Pb/²⁰⁸Pb = 10.  That is: ²⁰⁸Pb = ²⁰⁶Pb/10. This assumption by Gentry et al. (1982a) is more questionable.  Gentry et al. (1982b, p. 296) has actual values as low as 3.1 and as high as 14.

Combining these equations and using some algebra:

²⁰⁶Pb + ²⁰⁶Pb/10 + ²⁰⁶Pb/10 = 3.9 × 10^-7 moles/g

Multiplying everything by 10:

10(²⁰⁶Pb) + ²⁰⁶Pb + ²⁰⁶Pb = 3.9 × 10^-6 moles/g

12 (²⁰⁶Pb) = 3.9 × 10^-6

²⁰⁶Pb = 3.25 × 10^-7 mole/g

Then:  ²⁰⁷Pb = ²⁰⁸Pb = 3.25 x 10^-8 mole/g

Gentry et al. (1982a, p. 1129) state:

"During the decay of uranium and thorium, every ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb atom has 8, 7, and 6 alpha-decays, respectively."

Therefore:

Total radiogenic ⁴He produced with the radiogenic Pb:

Total radiogenic ⁴He = 8(²⁰⁶Pb in moles) + 7(²⁰⁷Pb in moles) + 6(²⁰⁸Pb in moles)

Total radiogenic He = 8(3.25 × 10^-7) + 7(3.25 x 10^-8) + 6(3.25 × 10^-8) = 2.60 x 10^-6 + 2.275 × 10^-7 + 1.95 x 10^-7 = 3.02 × 10^-6 moles/g

There are 10⁹ nanomoles in one mole.

Total radiogenic He = 3.02 × 10^-6 moles/g x 10⁹ nanomoles/mole = 3020 nanomoles He/gram of zircon

Converting to Humphreys et al.'s scale of cubic centimeters (Standard Temperature and Presssure [STP]) of radiogenic He/microgram zircon requires the following steps:

Gas laws state that at standard atmospheric temperature and pressure (STP) 1 mole of every gas has a volume of 22.4 liters:

22.4 liters = 22,400 milliliters (ml)

1.0 ml = 1.0 cubic centimeter (cc)

Therefore: 22.4 liters = 22,400 cc

Total radiogenic He = 3020 × 10^-9 moles/g × 22,400 cc STP/mole = 6.8 x10^-2 cc STP/g

There are 10⁶ micrograms in one gram. Therefore:

6.8 × 10^-2 cc STP/g divided by 10⁶ micrograms/g = 6.8 × 10^-8 cc STP/microgram

Gentry et al. (1982a, p. 1129-1130) argue that up to 40% of the radiogenic helium is lost by alpha ejection:

60% of 6.8 × 10^-8 cc STP/microgram = 41 x 10^-9 cc STP radiogenic He/microgram zircon = Q₀

This value is more than twice as large as the Q₀ value of approximately 15 × 10^-9 cc STP radiogenic He/microgram zircon endorsed by Humphreys et al. (2004, p. 9).

Utilizing the measured helium concentrations (Q values) listed in Humphreys et al. (2003a, p. 3), Table A shows the Q/Q₀ values that Humphreys et al. (2003a) should have obtained by using the assumptions in Gentry et al. (1982a).  The use of alpha ejection percentages of 30% would lower these Q/Q₀ values even further.  Nevertheless, chemical data in Gentry et al. (1982a) and Zartman (1979) indicate that the values in Table A are probably not very reliable (compare with the diverse results in my Appendix B).  The assumptions in Gentry et al. (1982a) are no doubt inaccurate and it is improper to apply just one Q₀ value to all of the Precambrian Fenton Hill samples, especially when the chemical analyses in Gentry et al. (1982b) indicate highly variable uranium and thorium concentrations even within single zircons.

Rather than accepting that the assumptions in Gentry et al. (1982a) do not support a Q₀ value of 15 × 10^-9 cc STP radiogenic He/microgram zircon or his high Q/Q₀ values, Humphreys (2005) attempts to salvage his high Q/Q₀ values by claiming that there are additional "misstated" numbers in Gentry et al. (1982a) related to the alpha ejection percentages:

"In his Appendix A Henke derives his value for Q0, 41 ncc/µg (1 ncc = 1 "nano-cc" = 10^-9 cm³ at standard pressure and temperature, STP).  He is in the right ball park, but he is probably using too small a value for the percentage of alpha particles (helium nuclei emitted by the nuclear decay) escaping the zircons.  The percentage came from Gentry's paper, but Gentry may have misstated what he meant by the number."

Certainly, there are plenty of questionable assumptions and unreliable numbers in Gentry et al. (1982a).  However, if the 30-40% alpha ejection values of Gentry et al. (1982a) are too small as Humphreys (2005) claims, why should we accept any other statements in Gentry et al. (1982a)?  Why is Dr. Humphreys still willing to trust the Q/Q₀ values in Gentry et al. (1982a) after he's admitted that almost every other datum in this paper is a "typo" or "misstated" number?   When will the list of errors in Gentry et al. (1982a) end?

APPENDIX B:  CALCULATION OF MORE REALISTIC Q₀ VALUES AND ESTIMATIONS OF Q/Q₀ VALUES FOR INDIVIDUAL ZIRCONS FROM SAMPLES 1, 3, 5 AND 6 USING CHEMICAL DATA FROM GENTRY ET AL. (1982b) AND Zartman (1979) (No Response from Humphreys, 2005)

Gentry et al. (1982b) list chemical data for individual zircons taken from depths of 960, 3930 and 4310 meters in the Fenton Hill cores (samples 1, 5 and 6 in Gentry et al., 1982a).  Zartman (1979) also contains a uranium and thorium analysis on a zircon that was collected within four meters of sample 3 and within the same lithology (a biotite granodiorite).  These data allow the Q₀ values at the four depths to be better estimated than simply utilizing the generic values that were calculated for samples 1-6 by Gentry et al. (15 ncc STP/μg according to Humphreys et al., 2004, p. 9) or in Appendix A of this report (41 ncc STP/μg).  The Q₀ values calculated in this appendix may then be used to roughly estimate the range of possible Q/Q₀ values for the four samples.

Table B1 shows the range of uranium and thorium concentrations for seven different zircons from samples 1, 5 and 6 of Gentry et al., (1982b, p. 296) and the zircon from Zartman (1979).  The letters associated with the Gentry et al. (1982b) sample numbers in Table B1 represent different zircon specimens that were analyzed from each depth.

Typically, Gentry et al. (1982b) performed four pairs of uranium and thorium analyzes on each zircon.  Gentry et al. (1982b) noticed that the uranium and thorium concentrations varied considerably even at different locations on the same zircon grain.  When calculating the concentrations, Gentry et al. (1982b) assumed that the zircons were pure ZrSiO₄.  Although zircons typically contain 1-4% hafnium (Klein, 2002, p. 498), this assumption is probably reasonable.  Zartman (1979, p. 6) dissolved and analyzed his entire zircon for uranium, thorium and lead isotopes.

The calculations in this appendix were performed on a Microsoft Excel™ spreadsheet.   These calculations assume no uranium or thorium addition or loss in the zircons over time.  To obtain a maximum possible range of helium Q₀ values for each of the Gentry et al. (1982b) zircons in Table B1, the calculations paired up the highest uranium concentration for each zircon with its highest concentration of thorium and the lowest uranium concentration with the lowest thorium value.

Table B2 shows the current maximum and minimum uranium and thorium concentrations for each zircon from the Precambrian gneiss at a depth of 960 meters (sample 1).  Parts-per-million (ppm) values are the same as micrograms/gram.  The micrograms/gram concentrations may be divided by 1 x 10⁶ micrograms/gram to convert them into grams of element/gram of zircon.  Concentrations in moles element/gram zircon are obtained by dividing the grams/gram concentrations by the atomic weights of uranium and thorium (238.03 and 232.038 g/mole, respectively).  Now, 99.2743% of modern natural uranium is ²³⁸U and only 0.7200% is ²³⁵U (Faure, 1998, p. 284). These percentages are used to determine the concentrations in moles/g of each uranium isotope as shown in Table B2. Next, the moles/g of ²³⁸U, ²³⁵U, and ²³²Th are multiplied by Avogadro's number (6.022 x 10²³ atoms/mole) to obtain the total number of atoms (N) of each isotope in every gram of zircon.

According to the information in Appendix A of Humphreys et al. (2003a), the zircons at 750 meters depth are about 1.43 billion years old.  Zartman (1979) found the zircon at 2903.8 meters depth (near Gentry et al.'s sample 3) to be 1.500 billion years old.  For the samples at 3930 and 4310 meters (samples 5 and 6), I'll agree with Humphreys et al. (2003a, p. 11) and assume an age of 1.5 billion years.

The following equations and data from Faure (1998, p. 281-284) are used to calculate the number of moles of radiogenic lead and helium produced from the decay of ²³⁸U, ²³⁵U and ²³²Th over 1.43 or 1.5 billion years.

D^* = N(e^λt -1)

D^* = number of radiogenic Pb atoms

N = number of uranium and thorium atoms currently present in the sample.

λ = decay constants:

λ for ²³⁸U = 1.55125 × 10^-10 1/year

λ for ²³⁵U = 9.8485 × 10^-10 1/year

λ for ²³²Th = 4.9475 × 10^-11 1/year

t = age of the sample

The number of daughter atoms (a D^* value for ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb) can now be calculated, as shown in Table B3.  For every ²⁰⁶Pb atom produced by the decay of ²³⁸U, 8 ⁴He atoms form.  The formation of a ²⁰⁷Pb atom results in the formation of 7 ⁴He atoms and 6 ⁴He atoms are associated with every ²⁰⁸Pb atom (Gentry et al., 1982a, p. 1129).  Table B3 lists the number of radiogenic helium atoms that would be produced by 1.43 billion years worth of radioactive decay of ²³²Th, ²³⁵U, and ²³⁸U.

Avogadro's number is used to convert the number of radiogenic helium atoms into moles (Table B4).  For each minimum and maximum zircon calculation, the helium concentrations in moles associated with the decay of ²³⁸U, ²³⁵U, and ²³²Th are summed (Table B4).  Following the usage in Gentry et al. (1982a), Humphreys et al. (2003a), and Appendix A in this document, the moles of radiogenic helium are then converted into cubic centimeters of helium per microgram of zircon at standard temperature and pressure (STP) (Table B4).

Gentry et al. (1982a, p. 1129-1130) assumed an alpha ejection value of 30-40% for their 40-50 micron zircons:

"Knowledge of the zircon mass and the appropriate compensation factor (to account for differences in initial He loss via near-surface α-emission) enabled us to calculate the theoretical amount of He which could have accumulated assuming negligible diffusion loss.  This compensating factor is necessary because the larger (150-250 µm) zircons lost a smaller proportion of the total He generated with the crystal via near-surface α-emission than did the smaller (40-50 µm) zircons.  For the smaller zircons we estimate as many as 30-40% of the α-particles (He) emitted within the crystal could have escaped initially whereas for the larger zircons we studied only 5-10% of the total He could have been lost via this mechanism."

Of course, Humphreys (2005) says that these values have been "misstated."  To settle this dispute, Tagami et al. (2003) contains several equations that might be useful in estimating the alpha ejections of the Fenton Hill zircons.  Tagami et al. (2003, p. 59) lists the following equations for calculating the fraction of alphas retained by a zircon immediately after their formation from radioactive decay:

F_T = 1 - 4.31β + 4.92β²

β = (4L + 2W)/LW

where:

F_T = fraction of alphas (⁴He) retained by the mineral

L = length of the zircon in microns or cm.

            W = width of the zircon in the same units as the length.

Therefore:

Alpha ejection value = 1 - F_T

Although Gentry et al. (1982a) described the "sizes" of their analyzed zircons as 40-50 µm, the following description in Humphreys et al. (2003a, p. 3), which is probably based on a personal communication with R. Gentry, indicates that the zircons of samples 1, 3, 5 and 6 were somewhat larger, at least in length:

"At Oak Ridge, Robert Gentry, a creationist physicist, crushed the [rock] samples (without breaking the much harder zircon grains), extracted a high-density residue (because zircons have a density of 4.7 grams/cm³), and isolated the zircons by microscopic examinations, choosing crystals about 50-75 μm long."

This account suggests that the zircons were recovered by float-sink methods and "grain picking" under a microscope.  There is no indication of whether or not the samples were sieved.   Unfortunately, no width data on the zircons are listed anywhere in Gentry et al. (1982a) or in any of the Humphreys et al. documents.  Without width data, a F_T cannot be accurately calculated.  Although far from ideal, the only present method of estimating the widths of the zircons in Humphreys et al. (2003a, 2004) and Gentry et al. (1982a) is to use information from Heimlich (1976).  Heimlich (1976) performed a detailed zircon study on nine samples from the Fenton Hill GT-2 core, which included average lengths and widths of zircons that were collected close to samples 1, 2003, 2, and 3 (my Table 1).   Some relevant parameters from Heimlich (1976) are shown in Table B5.

For each sample, the width of any 50-75 μm long zircon can be estimated with the mean elongation; that is, the average of the length to width ratios of all of the zircons of a sample.  The information in Table B5 suggests that if sample 1 contained 50-75 μm long zircons, their widths should be roughly 20-40 μm.  Because the mean elongation is larger, any 50-75 μm zircons in sample 3 would have widths of about 20-30 μm.   Using the equations from Tagami et al. (2003, p. 59), Table B6 includes the likely F_T values for samples 1 and 3.

Estimating the widths for samples 5 and 6 are very uncertain.  Sample 5 (like 3) is a biotite granodiorite (Laughlin et al., 1983, p. 26).  I will assume that the mean elongation for sample 5 is similar to sample 3 (another biotite granodiorite), or 2.5.   Sample 6 is a gneiss that has been intruded by a fine-grained granodiorite (Laney et al., 1981, p. 4).  The mean elongation probably ranges from 2 to 2.5.  To obtain a maximum range of possible F_T values for sample 6, the mean elongation of any 75 micron long zircons would be 2 and a value of 2.5 would be used with the 50 micron long zircons.  The results are shown in Table B6.

In Table B7, the F_T values are used to calculate the likely range of Q₀ values for the sample 1 zircons. To obtain highly accurate Q/Q₀ values for every zircon, the helium concentration (Q) of each individual zircon must be known.  Unfortunately, this information is not available. Because the uranium, thorium and Q₀ values of the individual zircons are highly variable (Tables B1 and B7), large variations in the Q values are also expected for the different zircons.  Until the critical Q data become available, only educated guesses can be made about the possible ranges of Q/Q₀ values for any of the samples.  An individual might estimate the range of possible Q/Q₀ values for each sample by dividing the maximum and minimum Q₀ values for each zircon into Humphreys et al.'s revised Q value for each sample (from my Table 1).  For example, as shown in Table B8, the overall Q of 8.60 ncc STP/μg zircon may divided by the various Q₀ values for zircons 1A-1C to obtain a series of Q/Q₀ values for sample 1.  They range from 0.015 to 0.35.  The maximum and minimum Q/Q₀ values for the zircons at depths of 3930 and 4310 meters were calculated in the same way and are shown as approximations in Table 2.

Unfortunately, the data in Gentry et al. (1982a,b) and Humphreys et al. (2003a; 2004) are too inadequate and poorly defined to obtain any definitive Q/Q₀ values for the Fenton Hill core samples.  The actual Q/Q₀ values could easily be one or more orders of magnitude different than the values used by Gentry et al. (1982a) and Humphreys et al. (2003a, 2004).  Without suitable data, the "modeling" efforts and helium diffusion "dates" in Humphreys et al. (2003a,b; 2004) and Humphreys (2003) are unreliable and even deceptive.

Main Article

Appendix C Humphreys Feels the Pressure

REFERENCES (including Internet links, where available)

Main Article

Appendix C Humphreys Feels the Pressure

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