Helium Diffusion and Retention in Zircons

by Randy Isaac, Ph.D.

This page supplements an introductory paragraph in the author's essay review and a brief technical overview in a general reply that is part of a scientific examination of RATE.

        The objective of the RATE project was to examine issues of radioactivity in regards to the age of the earth.A short review of the RATE project has been published elsewhere2 as well as the RATE team’s response.This article seeks to elaborate in more detail the specific example of the RATE team’s analysis of dating zircons with helium. 
       The chapter on dating zircons with helium was authored by D. Russell Humphreys who has published numerous articles in creationist journals on this topic.  His chapter presents a “new creation model” and a “uniformitarian” model.  This article will assess the validity of three models: the standard model which is typically used by geochronologists but was not discussed by the RATE team, the RATE team’s “new creation model,” and the model the RATE team calls the “uniformitarian model.”

       The Standard Model
       The criteria for a valid dating technique include a physical model in which time is the only unknown and all other parameters can be measured experimentally.  It also requires a physical event that triggers the clock for a meaningful measurement of age.  Zircons are typically dated with radiometric techniques based on U and Th decay.  The helium content of zircons is not used to date the formation of the zircon but rather to garner clues to the thermal history.  At high temperatures, helium readily diffuses out of the zircon.  Any helium generated by alpha-emitting radioactive elements easily escapes from the mineral.  At low temperatures, helium remains trapped in the zircon and the concentration increases as the alpha emitters generate more helium.  The transition temperature is called the closure temperature and is typically on the order of 200oC but is dependent on the geometry as well as the diffusivity. 
       The helium clock in a zircon starts when a zircon cools to the closure temperature.  It may have had a varied thermal history prior to that but the high diffusivity above the closure temperature erases any record of it.  Below the closure temperature, the helium concentration grows from the continuous generation of alpha particles from radioactive members of the U-Th decay series.  The concentration and decay rate of these alpha-emitters can be measured as well as the current concentration of helium.  Using the simple equation Q = Pt where Q is the current helium concentration, P is the alpha generation rate and t is the time since the mineral cooled below the closure temperature, the time t is the only unknown and both Q and P can be measured.  The ratio Q/P has units of time and is known as the helium age of the zircon. 
       A more sophisticated mathematical treatment that fully accounts for both helium outdiffusion and helium generation as well as initial helium concentrations, is given by Wolf, et.al.,4 for the simplified case of spherical symmetry:


where 4He is Q , the current concentration of helium, and 4He* is Qo , the original concentration of helium at t=0 , P is the rate of helium generation, a is the radius of the sphere, and D is the diffusivity.  From this equation we can see that the time constant of the physical system is a2/Dp2.  For time periods of about 5 time constants or more, the system will be in steady state with a helium age of a2/15D.  The diffusivity is exponentially dependent on temperature and as the mineral cools, it will take a very long time for the crystal to achieve steady state. 
       The second term of the equation decreases over time so that the influence of any initial helium concentration will be negligible after about 5 time constants.  This quantifies the assumption made earlier that at high temperatures, any original helium will have escaped the crystal.  The first term of the equation will always increase with time until the steady state condition is reached.  This is physically consistent with a system where the sole source of helium is alpha production from radioactive decay and where outdiffusion is negligible.  The helium concentration will decrease in time only if equilibrium is affected in such a way that the concentration exceeds the steady state value.  This can happen if the temperature increases, causing the diffusivity to rise significantly and lowering the steady state value.  Another mechanism for altering the steady state value would be if the generation rate P were to rapidly decrease significantly.  If, for example, the alpha-emitters were quickly depleted or leached out of the system, the generation rate would drop and the helium concentration would be larger than its new steady state value and would subsequently decrease gradually.  Though zircons may have had a history of fluctuating temperatures, geological records indicate that the recent past has been a slow cooling mode.
       This equation also serves to bound the case in which the simplified model of Q=Pt can hold.  For systems with negligible initial concentration of helium, and for time short compared to the time constant, the equation reduces to a good approximation, Q=Pt
       Wolf, et.al., apply their model to apatite crystals and find values of helium ages on the order of 50 million years, in good correlation with other techniques.  Their work explores the usefulness of helium thermochronology and is also applicable to zircons.

       The New Creation Model
       In the RATE project, Humphreys takes a different approach.  Instead of the standard technique of using the helium retained by zircons, he uses a diffusion dating method based on the helium that is lost.  He assumes that at t=0 the zircon had a helium concentration of Qo which decreases over time to its current value of Q through outdiffusion, and assumes that helium generation from alpha-emitting radioactivity is negligible. 
       This model fails to meet the basic criteria for a good dating technique.  It is far more difficult to measure the helium that is missing than the helium that is present.  There is no direct measurement of Qo nor is there a physical mechanism that would start the clock for a determination of time.  This method also relies very sensitively on knowledge of the diffusivity and thermal history of the mineral.  Any calculation from this model would not be relevant for any physical parameter. 
       Undeterred, Humphreys proceeds to estimate all the unknowns.  To determine Q , he sent his own samples to a reputable experimenter to measure both helium content and diffusivity.  Most of his results, however, are based on samples obtained by Gentry.5  Humphreys takes Gentry’s published measurements of Q and adjusts them by a factor of 10 with no other explanation than it was done after private communication with Gentry.  With no knowledge of the reason for the adjustment, it is impossible to comment on its validity. 
       To determine Qo , Humphreys relies on Gentry’s calculation of the retention factor, Q/Qo .  Those values are given in the following table by Gentry:

Humphreys interpolates those numbers for his own samples.  No clear explanation is given for the way in which Gentry obtained these retention factors nor their meaning.  The only comment in this regard is Gentry’s note that:
       “Knowledge of the zircon mass and the appropriate compensation factor (to account for differences in initial He loss via near-surface a-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 mm) zircons lost a smaller proportion of the total He generated within the crystal via near-surface a-emission than did the smaller (40-50 mm) zircons.  For the smaller zircons we estimate as many as 30-40% of the a-particles (He) emitted within the crystal could have escaped initially whereas for the larger zircons we studied only 5-10% of the total He would have been lost via this mechanism.  The ratio of the measured to the theoretical amount of He is shown in the last column of Table 1.  The uncertainties in our estimates of the zircon masses and compensation factors probably mean these last values are good only to ±30%.”
       It is not at all clear that Gentry’s theoretical concentration of helium can correctly be interpreted as an initial concentration Qo of helium.  If so, how did Gentry make that calculation?  What were his assumptions?  If Gentry’s calculation is based on an estimate of all possible helium generated by alpha-emitters in the 1.5 billion year age of the zircon, corrected for near-surface losses, then the RATE team’s assumption that at some time in the past the zircon contained a helium concentration of Qo cannot be supported.  That amount of helium was never concentrated in the zircon at the same time.
       The physical mechanism that Humphreys proposes to explain an initial value of Qo with a subsequent decrease in concentration is that accelerated nuclear decay during Noah’s flood caused a very large alpha generation rate which then dropped to its current value.  Subsequent discussion by the RATE team shows that the justification for speculating that accelerated nuclear decay occurred is based largely on a young earth as determined by helium diffusion in zircons.  This is circular reasoning at best.  Nuclear decay rates have long been shown to be constant and there is no independent evidence to support any deviation.
       Humphreys uses diffusion data from the experimenter to which he sent his own samples and also the diffusivity data that Gentry provided.  As is typical, these data are taken at higher temperatures and extrapolated down to the regime close to the closure temperatures and ambient temperatures at which the samples were found.  He makes the approximation that the diffusivity is constant over time to simplify the calculation.  In this temperature range, the diffusivity is highly uncertain and strongly dependent on the physical environment and structure.6
        At this point, Humphreys takes two directions.  First, he assumes that t=6,000 years and calculates the diffusivity that would be required to lose the amount of helium indicated by Gentry’s retention factor.  Amazingly, the answer is close to the measured diffusivities.  Then, he assumes the measured diffusivity and calculates the time required to lose that helium.  The answer is on the order of 6,000 years.  On this basis, the RATE team concludes that helium diffusion provides evidence for a young earth.
        The model proposed by the RATE team fails to meet the basic criteria for a dating technique and any values calculated from the model have no relationship to any physical parameter.  The team speculates on the physical system and possible values of the physical constants and then performs a complex numerical solution that doesn’t converge easily, according to their report.

       The Uniformitarian Model
       The RATE team then turns to assessing what they call the uniformitarian model.  The name is intended to imply an assessment of how geologists normally date zircons.  But the model has no relationship to the standard model.  Instead, Humphreys notes without calculation that with so much time, the crystals would surely be in steady state.  He then derives the steady state equation to be Q/Qo=a2/15Dt.  He notes that Qo/t is the alpha generation rate which is essentially constant but then he fails to note that the parameter t cancels out of the equation as it should for a steady state condition.  In that case, the equation is identical to that discussed in the standard model.  However, Humphreys chooses to identify Q/Qo as Gentry’s retention factor and arbitrarily inserts 1.5 billion years for the value of t on the right hand side.  He then calculates a value of D that is five orders of magnitude lower than his measured values and derisively concludes that the uniformitarian model is hopelessly flawed.  It is indeed true that the model he presents is hopelessly flawed.  There is no reason to believe that the steady-state condition has any relationship to Gentry’s retention factor nor is there justification for using 1.5 billion years.  {comment, added 2-24-08: In essence, the RATE team’s version of the solid-state condition equates Gentry’s retention factor to the ratio of the helium age to the age of the zircon as determined from standard dating techniques based on U, Th, and Pb. Though there is not sufficient information about how Gentry derived his retention factors, the typical values of helium ages in zircons are in the tens of millions of years, in good harmony with the typical ages of zircons of 1.5 billion years. There is no fundamental discrepancy.}  More importantly, a steady state equation should not have time as a parameter.  There would be no change over time in a steady state mode.  This model has no relationship to any model used in thermochronology.

       In summary, when we consider three models for using helium to date minerals, we find that only the standard model meets the criteria for a useful dating technique.  The RATE team uses models that do not relate to what is known physically about zircon formation.  No amount of fine-tuning of the parameters would correct the fatal flaws of the models.  Neither the new creation model nor the so-called uniformitarian model provide any insight to the history of a real zircon. 
       We conclude therefore that helium dating of zircons leads convincingly to dates that are consistent with standard zircon dating methods.  Helium ages on the order of tens of millions of years are consistent with measured zircon ages of a billion or more years.  Helium diffusion in zircons provides evidence that the earth cannot be thousands but must be billions of years old.



1)  L Vardiman, et.al., Radioisotopes and the Age of the Earth, Vol. 2, Institute for Creation Research, 2005.
2)  R Isaac, Perspectives on Science and Christian Faith, Vol. 59, No. 2, p. 143. {full text}
3)  L Vardiman, et.al., Perspectives on Science and Christian Faith, Vol. 60, No. 1, pp. 35-36. {full text}
4)  RA Wolf, KA Farley, and DM Kass, Modeling of the temperature sensitivity of the apatite (U-Th)/He thermochronometer: Chemical Geology, Vol. 148, pp 105–114 (1998). {abstract}
5)  RV Gentry, Geophysical Research Letters, Vol. 9, No. 10, pp 1129-1130, Oct 1982. {full text}
6)  R Whitefield, The RATE Project Claims [about accelerated decay, and helium in zircons] {full text}



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