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Young-Earth Creationist Helium Diffusion "Dates"

Appendices and References

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Main Article

Appendix C
Humphreys Feels the Pressure


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


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."


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?

Table A: Q/Q0 values for zircons in the Precambrian Fenton Hill, New Mexico well cores as they should appear in Humphreys et al. (2003a, p. 3) if all of the calculations using the assumptions in Gentry et al. (1982a) were done correctly.
No. Depth (m) Revised He concentrations (Q) in Humphreys et al., 2003a (cc STP/microgram) Humphreys et al.'s Q/Q0 ±30% (using Q0 = 15 × 10-9 cc STP/microgram) My calculated Q/Q0 using the assumptions in Gentry et al. (1982a)
1 960 8.6 × 10-9 0.58 0.21
2 2170 3.6 × 10-9 0.27 0.088
3 2900 2.8 × 10-9 0.17 0.068
4 3502 1.6 × 10-10 0.012 0.0039
5 3930 ~2 × 10-11 ~0.001 ~0.0005
6 4310 ~2 × 10-11 ~0.001 ~0.0005


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.

Table B1: Uranium and thorium concentrations on zircons from the Fenton Hill well cores, including ranges on seven zircons from Gentry et al. (1982b) and a single uranium and thorium analysis on an entire zircon from Zartman (1979).  The analyses for the different zircons are numbered according to the scheme in Gentry et al. (1982a).  Letters are used to distinguish different zircons from the same depth. The zircon in Zartman (1979) was collected near sample 3 of Gentry et al. (1982a) and Humphreys et al. (2003a).

Zircon ID

Depth (m)

U (parts per million)

Th (parts per million)



240 - 5300

800 - 2000



465 - 1130

220 - 750



1250 - 3300

100 - 275







83 - 220

63 - 120



90 - 110

60 - 90



110 - 550

63 - 175



125 - 210

40 - 85

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.

Table B2:  Concentrations of uranium and thorium in three zircons (A, B and C) from a depth of 960 meters (sample 1).
Zircon Element Current conc., ppm mole/g mole/g 238U mole/g, 235U N, atoms/g


U minimum










Th minimum






U maximum










Th maximum







U minimum










Th minimum






U maximum










Th maximum






U minimum










Th minimum






U maximum










Th maximum





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(eλt -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.

Table B3:  Further calculations for zircons from 960 meters deep.
Zircon Element Current concentration, ppm Isotope D* # He atoms


U min










Th min






U max










Th max







U min










Th min






U max










Th max






U min










Th min






U max










Th max





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).

Table B4: Further calculations for zircons from 960 meters deep.
Zircon Element Current conc., ppm Isotope mole He/g Total mole He/g He cc STP/g He cc STP/μg
1A U min 240 U-238 2.00E-06 3.69E-06 8.27E-02 8.27E-08
      U-235 1.59E-07      
1A Th min 800 Th-232 1.53E-06      
1A U max 5300 U-238 4.43E-05 5.16E-05 1.16 1.16E-06
      U-235 3.51E-06      
1A Th max 2000 Th-232 3.82E-06      
1B U min 465 U-238 3.88E-06 4.61E-06 0.103 1.03E-07
      U-235 3.08E-07      
1B Th min 220 Th-232 4.20E-07      
1B U max 1130 U-238 9.44E-06 1.16E-05 0.260 2.60E-07
      U-235 7.49E-07      
1B Th max 750 Th-232 1.43E-06      
1C U min 1250 U-238 1.04E-05 1.15E-05 0.257 2.57E-07
      U-235 8.28E-07      
1C Th min 100 Th-232 1.91E-07      
1C U max 3300 U-238 2.76E-05 3.03E-05 0.678 6.78E-07
      U-235 2.19E-06      
1C Th max 275 Th-232 5.25E-07      

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:

FT = 1 - 4.31β + 4.92β2

β = (4L + 2W)/LW


FT = 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.


Alpha ejection value = 1 - FT

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 FT 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.

Table B5.  Dimensions of Fenton Hill zircons (Heimlich, 1976, p. 7).  The samples were collected from the same sections of core as samples 1, 2, and 3 of Gentry et al. (1982a) and sample 2003 of Humphreys et al. (2004).
Depth (meters) Relevant Gentry et al. or Humphreys et al. Sample Mean Length
(2 std. dev.), microns
Mean Width
(2 std. dev.), microns
Mean Elongation
960 1 96.9 (57.4) 43.3 (24.2) 2.3071
960 (2nd sample) 1 70.7 (41.0) 38.3 (18.8) 1.8688
1492 ~2003 91.1 (60.2) 40.2 (23.6) 2.3464
2165 ~2 92.1 (64.0) 47.4 (28.8) 1.9845
2902 ~3 101.7 (76.0) 43.2 (26.4) 2.5015

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 FT values for samples 1 and 3.

Table B6.  Estimated alpha retention factors (Tagami et al., 2003, p. 59) for samples 1, 3, 5 and 6 from the Fenton Hill core.
Depth (meters) Relevant Gentry et al. or Humphreys et al. Sample Length, microns Mean elongation (Heimlich, 1976) Estimated Width, microns
(one significant digit)
FT, fraction alphas retained by zircon (one significant digit)
960 1 75 2.3071 30 0.5
    50 2.3071 20 0.3
960 (#2) 1 75 1.8688 40 0.5
    50 1.8688 30 0.3
2902 ~3 75 2.5015 30 0.4
    50 2.5015 20 0.2
3930 5 75 2.5 30 0.4
    50 2.5 20 0.2
4310 6 75 2 40 0.5
    50 2.5 20 0.2

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 FT 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 FT 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.

Table B7:  Calculation of Q0 values for three zircons from 960 meters.
Zircon ID Element Current ppm Total He, cc STP/μg FT alphas retained Q0 after boundary loss, cc STP/μg
1A U min 240 8.20E-08 0.30 2.46E-08
1A Th min 800      
1A U max 5300 1.15E-06 0.50 5.73E-07
1A Th max 2000      
1B U min 465 1.02E-07 0.30 3.07E-08
1B Th min 220      
1B U max 1130 2.58E-07 0.50 1.29E-07
1B Th max 750      
1C U min 1250 2.55E-07 0.30 7.64E-08
1C Th min 100      
1C U max 3300 6.73E-07 0.50 3.36E-07
1C Th max 275      
Table B8:  Range of possible Q/Q0 values for the zircons from 960 meters.
Zircon ID Depth (m) Element Current ppm Q0 in ncc STP/μg after 30 -50% boundary loss effects Measured He (Q) ncc STP/μg from Humphreys et al. (2003a) Rough Estimates of Q/Q0 for Individual Zircons
1A 960 U min 240 2.46E-08 8.60E-09 0.35
1A 960 Th min 800      
1A 960 U max 5300 5.73E-07 8.60E-09 0.015
1A 960 Th max 2000      
1B 960 U min 465 3.07E-08 8.60E-09 0.28
1B 960 Th min 220      
1B 960 U max 1130 1.29E-07 8.60E-09 0.067
1B 960 Th max 750      
1C 960 U min 1250 7.64E-08 8.60E-09 0.11
1C 960 Th min 100      
1C 960 U max 3300 3.36E-07 8.60E-09 0.026
1C 960 Th max 275      

Main Article

Appendix C
Humphreys Feels the Pressure

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Main Article

Appendix C
Humphreys Feels the Pressure

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