A funny mistake by ICR and example of poor scholarship

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Originally posted by Joe Meert:
[B][QUOTE] Any thoughts on the units of Humphreys' "closure interval", Joe? Am I missing something?[/B][/QUOTE]

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JM: D/a^2 has units of 1/s (diffusivity is length^2/time) so everything is kosher with his units. The problem, as I see it, with Humphreys attempt to separate diffusion from closure temperature. Closure temperature is a function of diffusion and is defined as the temperature at which diffusion becomes negligible for the mineral. There is then some trickery in his math to come up with this tci thing. Look at it this way. Let's look, in a very simple way at how one would calculate an age in Humphreys world versus ours. Assume that retention is 100% at the closure temperature (but only for a short time). After that diffusion rate out equals production rate in (his tci concept). So, let's say that element A decays to element B with a characteristic half life of 1000 years. For simplicity, let's say that 100,000 A's were in the mineral at Tc. Decay then proceeds as follows (in the normal apostate decay world).

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Hello, all. I am new to this forum, but am a talk.origins regular.
I'm Chris Ho-Stuart; but am just using "cjhs" as my username here.
I've been fielding some questions about this in talk.origins, and
have found this forum to be a helpful reference.Just want to make some comments on the above.Closure temperature is not defined as a point of
negligible diffusion. In fact, at the point where a mineral
is at the closure temperature, there will still be substantial
amounts of diffusion. I think it is worth understanding this.Closure temperature is not actually defined in terms of diffusion
rates at all! The term can be misleading. Think of it as "The
temperature at the apparent date of closure".If you have a crystal that cooled very slowly after its original
formation (10 C / Mya is a typical figure for cooling rates) then
there will be a substantial loss of Helium during the cooling
phase, between being effectively completely open and unable to
retain any detectable amount of Helium and being completely closed
with negligible loss to diffusion.If we subsequently find and date the crystal, and calculate an "age"
based on the amount of Helium in the crystal, then this is called
the "apparent age" of the crystal. This age will indicate a date
somewhere older than the point at which diffusion became negligible
(because at that point there was already some Helium that accumulated
over the time of cooling) and somewhere younger than the point at
which the crystal was very hot. That is, the apparent age actually
gives the age to a point somewhere during the cooling phase of the
crystal. The calculations and definition of "closure temperature"
gives a way to describe the point at the "apparent age"; it is
the temperature inferred for that point in time given by the apparent
age.It is an odd definition, when you think about; but here is a
motivation... if you take a collection of different crystals
or minerals which have different closure temperatures, then a
plot of apparent age against closure temperature gives an
actual plot of the thermal history of the site being dated.
(Think about it.)Where this is possible, it provides a cross check on the results,
and also a confirmation of cooling rates that were assumed in
the calculation of closure temperatures. (One can iterate this
to a solution and actually measure the original cooling rates,
rather than make plausible assumptions.) This means that the
material has been dated, the thermal history of the site has
been discovered, and some stringent double checks on the
various assumptions have been made.Of course, in all of this we have the usual assumptions of
radiometric dating (constant decay rates, etc); and also
an assumption that over the rest of the life of the crystal
after the initial cooling, it was at temperatures were
diffusion really is negligible -- which means well below
the closure temperature. It is powerful evidence for those
assumptions that "apparent age"/"closure temperature" plots
tend to reveal sensible cooling curves.With respect to Humphreys "closure interval"; what he is
actually calculating there seems to be the "apparent age at
equilibrium", which is not the same thing at all! The
formula used by Humphreys is "tci = a^2 / D / 15". This formula is
derived and discussed by Wolf et al in:"Modeling of the temperature sensitivity of the Apatite (U-Th)/He
thermochronometer"by R.A. Wolf, K.A. Farley and D.M. KassChemical Geology 148 (1998) pp 105-114If you have a crystal in a state of equlibrium between diffusion
and production of helium, and apply a naive "apparent age"
calculation based on this steady state amount of Helium, then
what you get is the "equilibrium age". What Humphreys called the
"closure interval" is actually the amount of time it take to
get to equilbrium, which is not the same thing at all. Wolf et al
discuss this as well, and indicate that Humphreys' "closure
interval" is roughly one order of magnitude larger. If you
think about it, this makes sense; the paper gives the
mathematical justification.The above paper is on-line through ScienceDirect, but a
subscription is needed to access it.Other references I have found useful are as follows:
The original impact article by Humphreys
Further comment by Humphreys in reply to Jor Meert
The paper by Reiners, cited by Humphreys
The 1982 paper by Gentry et al, describing the Jemez zircons
Some lecture notes, which discuss closure temperature.
Very useful short conference paper on thermochronology, by James Lee.

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Originally posted by edge:
Has anyone here figured out where Humphreys thinks we are on his [He] vs. time graph? It would seem to me that this graph (which has absolutely no data on it, by the way) cannot be used to tell any kind of age for anything. Helium concentration is clearly not a function of time after an unspecified interval. This looks like another one of Humphreys' graphs that we have puzzled over before... completely irrelevant.

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His graph is a tolerably sensible representation of what would happen if a zircon cooled to a temperature where there is still some diffusion, and than eventually reached an equilibrium as Helium builds up in the crystal. This is quite plausible for hot zircons, and of course no one tries to apply the U-Th/He dating method to such hot zircons.Minor defects exist in the fine detail of shape of the curve, but to a first approximation it is not bad. The major problem is labelling of "closure temperature"; closure temperature really only makes sense for zircons that have passed through a cooling phase all the way to a point of negligible diffusion. A zircon which has only cooled to a point where there is enough diffusion to allow equilibrium to be reached within the age of the earth arguably does not have a sensible closure temperature. (See the definition of "closure temperature" I have given in another post.)

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Originally posted by wj:
Chris, it appears that Humphreys postualtes a "reopening" of zircon crystals to helium diffusion some time after closure temperature is reached.

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Is it accurate to say that the term closure temperature is the temperature at which the rate of diffusion is equal to the rate of production by radioactive decay?

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You imply that there is a temperature at which diffusion becomes negligible, presumably at a lower temperature than the diffusion rate. What term could be used to identify this temperature?

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Humphreys asserts that the accumulation of radiogenic helium in the crystals would eventually cause the helium to "reopen". Is there any evidence that this occurs after crystals have cooled to the temperature at which diffusion becomes negligible?

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Could it be that Humphreys is using the confusion of the term "closure temperature" to model a process which happens just below the closure temperature of zircon but which does not occur when the zircon cools further to a temperature at whcih diffusion becomes negligible?

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Reopening, as Humphreys describes it, is simply when a zircon reaches equilibrium. This can happen at any temperature; though for cool zircons this typically requires much more time than the age of the universe. For hot zircons, it can happen very quickly. But there is no one temperature that can be defined in this way.Reiners' zircons, from Fish canyon, were dated at roughly 21 million years old (raw apparent age). Closure temperatures were calculated at around 150 to 190 C (probably low estimates). At those temperatures, the equilibrium age is only about 3 to 4 million years. What that means is that if Fish Canyon zircons cooled to about 190C, and then remaining at that temperature, they would tend to be approaching equilibrium about now! Of course, they were actually found at much lower temperatures than this, which is why they could be dated.For the hot Jemez zircons, equilibrium is probably reached quite quickly. Humphreys' mention of a few dozen to a few thousand years sounds about right, for zircons at 313C. The last paragraph of his reply to Meert is as follows:

If the closure interval is long compared to the age of the zircon, then the zircon would indeed be a closed system. But would that be the case in the uniformitarian view of the Jemez zircons? Using the effective radius of the zircons, 30 m, and the measured values of D (Figure 7) in eq. (22) gives us tci values between a few dozen years and a few thousand years, depending on the temperature of the sample in the borehole. Those times are very small compared to the uniformitarian age of 1.5 billion years.

Well of course the equilibrium age is much less than the actual age for a hot zircon in equilibrium. There is no conflict here with any uniformitarian assumptions, since uniformitarians do not attempt to date hot zircons. This is misleading to the point of deliberate dishonesty. 1.5Gya is sufficiently long that it is plausible for zircons even at 150C (well below literature cited closure temperatures) to reach equilibrium.It really only makes sense to speak of a closure temperature for a zircon that has cooled from hot down to a point of negligible diffusion. You can't really get a reliable date from old zircons found at the published closure temperatures. That is too hot, and allows for too much diffusion. But if zircons drop down to (for example) 70C then the amount of diffusion is sufficiently small that it would take substantially more than the age of the Universe to get to equilibrium, and so dating can be applied quite sensibly.Closure temperature has nothing to do with balancing rates; it is rather the temperature at the time given by the crystal's apparent age. The descriptions of closure temperature as being a point of negligible diffusion (Meert), or as a point of balancing diffusion with production (Humphreys), are simply wrong. It is true to say that diffusion drops off very rapidly below closure temperature (it is an exponential function, after all).The functions involved here are nice smooth differentiable functions and so there is no well defined cut off point at which diffusion is negligible. What is negligible will depend on other sources of error in your calculations. But basically, if a zircon is sufficiently cool that only 1% of produced Helium has been lost by diffusion over the life of the crystal, then that should be negligible, and trying to compensate for it in calculations will make no difference.Remember, the function is exponential, so every twenty degrees less probably gives you are order of magnitude less diffusion! 70C would be as safe as houses for zircons, using Reiners' data.It is certainly possible for a zircon to cool a little bit, and then have sufficient Helium build up inside to bring it back to equilibrium again at the cooler temperature, without ever getting anywhere near published closure temperatures. This may well be the case for some of the Jemez zircons. They could also have been heated up at some point after having reached equilibrium at one temperature, after which they will again approach equilibrium but from a point of elevated Helium concentrations! The data is not sufficient to tell.

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Originally posted by Joe Meert:

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Closure temperature has nothing to do with balancing rates; it is rather the temperature at the time given by the crystal's apparent age. The descriptions of closure temperature as being a point of negligible diffusion (Meert), or as a point of balancing diffusion with production (Humphreys), are simply wrong. It is true to say that diffusion drops off very rapidly below closure temperature (it is an exponential function, after all).

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JM: Well, of course I want to argue a bit on this point. Negligible diffusion does not mean NO diffusion. Diffusion can still take place at and below the closure temperature, but it such diffusion will not significantly affect the age of the zircons so much as to make them only 1000's of years old. What Humphreys wants is for the zircons to reflect a very young age for the earth, closure temperature does not help him in this regard.

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Cheers

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Joe Meert

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Thanks for responding, Joe.I am concerned to give accurate information. The statement that diffusion at the closure temperature is negligible is wrong. It is, in fact, an error widely repeated even in technical literature; but it is still wrong.What is correct is that diffusion at the closure temperature is still significant. This is a necessary consequence of the definition of closure temperature.Closure temperature is defined as the temperature at the time given by the apparent age of the crystal. This is only really useful for a crystal which has cooled gradually from a point of high diffusion to a point of negligible diffusion, and which has remained with negligible diffusion since then. The apparent age will indicate a time somewhere between high diffusion and neglible diffusion; it therefore requires that diffusion at that point is NOT negligible.The temperature at that time is called a closure temperature, which is rather misleading for amateur readers. In this thread, people are getting into a bit of detail, and so the correct definitions should really be used.I have not read the RATE book. It looks a bit like Humphrey's problems include some technical errors, dependance on outdated results from the 70s on diffusion rates, and dependance on some figures by Gentry in 1982 which even at the time of original publication were identified as unreliable in various ways by the original authors. The model of Humphreys is not about diffusion at closure temperature being high enough to give ages in the thousands of years.For the technically minded, we can demonstrate just how significant diffusion is at the closure temperature. It is sufficiently high that zircons can reach an equilibrium in a few million years; and of course that is way too much diffusion to allow the zircons to be dated.Consider Reiner's data (which was cited by Humphreys). Reiner's paper is on-line atTable 1 gives the first sample (FCT1) with the following figures.

• Ea (Activation energy) 37.1 kcal/mol (up steps) and 44.1 kcal/mol (down steps)
• D0/a^2 9491 s^-1 (up steps) and 43670 s^-1 (down steps)
  

People can read the paper for more discussion of what this means. The paper uses the down step measurements to infer a closure temperature of 189C. I've done the up step case for myself, just for comparison, and obtained 149.4 C. In both cases I assumed a cooling rate of 10K/Mya. In both cases, the inferred time to reach equilibrium is about 3.5 Mya. All the other zircons in the table also show that between 3 and 4 Mya is enough to reach equilibrium at the closure temperature. Assuming greater cooling rates gives faster times to equilibrium.Reiner's zircons, however, were nowhere near equilibrium, and so they were able to be dated. They dated to around 28 Mya.I suspect Joe is aware of much of this. I look forward to his updated RATE page sometime soon. But please; when putting up a web page don't talk down to people too much. Try for something which is readable by a novice, but still acceptable to someone who is reading up on more technical stuff. This is not easy, I know.Closure temperature is not defined by its diffusion rate. It is not a point of negligible diffusion. By all means show that diffusion at the closure temperature is very low, if this is relevant. But when refuting Humphreys try to engage his written argument, which is not simply about the rate of diffusion at closure temperatures.Cheers -- Chris