D. RUSSELL HUMPHREYS, PH.D.
STEVEN A. AUSTIN, PH.D.
ANDREW A. SNELLING, PH.D.
INSTITUTE FOR CREATION RESEARCH
JOHN R. BAUMGARDNER, PH.D.
LOS ALAMOS
NATIONAL LABORATORY^{**}
KEYWORDS
ABSTRACT
Two decades
ago, Robert Gentry and his colleagues at Oak Ridge National Laboratory
reported surprisingly high amounts of nucleardecaygenerated helium
in tiny radioactive zircons recovered from Precambrian crystalline rock,
the Jemez Granodiorite on the west flank of the volcanic Valles Caldera
near Los Alamos, New Mexico [9]. Up
to 58% of the helium (that radioactivity would have generated during
the alleged 1.5 billion year age of the granodiorite) was still in the
zircons. Yet the zircons were so small that they should not have retained
the helium for even a tiny fraction of that time. The high helium retention
levels suggested to us and many other creationists that the helium simply
had not had enough time to diffuse out of the zircons, and that recent
accelerated nuclear decay had produced over a billion years worth of
helium within only the last few thousand years, during Creation and/or
the Flood. Such acceleration would reduce the radioisotopic
time scale from megayears down to months.
However, until a few years ago nobody had done the experimental
and theoretical studies necessary to confirm this conclusion quantitatively.
There was only one (ambiguously reported) measurement of helium
diffusion through zircon [18]. There
were no measurements of helium diffusion through biotite, the black
mica surrounding the zircons. In 2000 the RATE project [14] began experiments
to measure the diffusion rates of helium in zircon and biotite specifically
from the Jemez Granodiorite. The
data, reported here, are consistent with data for a mica related to
biotite [17], with recently reported data for zircon [19] and with a
reasonable interpretation of the earlier zircon data [18]. We show that these data limit the age of these rocks to between
4,000 and 14,000 years.
These results support our hypothesis of accelerated nuclear decay
and represent strong scientific evidence for the young world of Scripture.
Figure 1  Zircons from the Jemez Granodiorite. Photo by R.V.
Gentry
1. INTRODUCTION
A significant fraction of the earth's radioactive elements,
particularly uranium and thorium, appear to be in the granitic rock
of the upper continental crust. Uranium
and thorium tend to be localized in the granites inside special minerals
such as zircon
(zirconium silicate, ZrSiO_{4}).
Zircon has high hardness, high density, and high melting point,
often forming microscopic, stubby, prismatic crystals with dipyramidal
terminations (Fig. 1, commonly grayish, yellowish, or reddish brown.
Atoms of uranium and thorium within cooling magma replace up
to 4% of the normal zirconium atoms within the lattice structure of
zircon as it is crystallizing. The
radioactive zircon crystals often become embedded in larger crystals,
such as mica, as magma cools and solidifies.
As the uranium
and thorium nuclei in a zircon decay, they produce helium. For example, uranium238 (^{238}U)
emits eight alpha particles as it decays through various intermediate
elements to lead206 (^{206}Pb).
Each alpha particle is a helium4 nucleus (^{4}He), consisting
of two protons and two neutrons. Each
explosively expelled ^{4}He nucleus eventually comes to a stop,
either within the zircon or in the surrounding material. There it quickly gathers two electrons and becomes a neutral helium
atom.
Helium is
a lightweight, fastmoving atom that does not form chemical bonds with
other atoms. It can diffuse through solids relatively
fast, meaning that helium atoms wiggle through the spaces between atoms
in a crystal lattice and spread themselves out as far from one another
as possible. For the same reason
it can leak rapidly through tiny holes and cracks, making it ideal for
leak detection in laboratory vacuum systems.
The diffusion and leakage rates are so great that believers in
the billions of years had expected most of the helium produced during
the alleged 4.5 billion years of the earth's existence to have worked
its way out of the crust and into the earth's atmosphere long ago.
But the helium
is not in the earth's atmosphere! When
nonspecialists hear that, they usually assume that (A) helium has risen
to the top of the atmosphere as it would in a balloon, and (B) most
of the helium has then leaked from the top of the atmosphere into space. However, assumption (A) is wrong, because unconfined
helium spreads throughout the atmosphere from top to bottom, like any
other gas.
On assumption
(B), the simple kinetic theory of gases says the loss of neutral helium
atoms into space would be much too small to account for the missing
helium. In 1957 Melvin Cook,
a creationist chemist, pointed out this problem in the prestigious journal
Nature [4]. In 1990 Larry Vardiman, a creationist atmospheric
scientist, calculated that even
after accounting for such slow leakage into space, the earth's
atmosphere has only about 0.04% of the helium it should have if the
earth were billions of years old [23].
Until the
1970’s, uniformitarians (see next section) had no good answer. However in recent decades they have been trying
to evolve one. Satellite data
[1,13] show that ions (electrically charged atoms) of helium
(and other gases) move back and forth along the earth’s magnetic lines
of force above much of the atmosphere.
Some space plasma physicists theorize that storms of particles
from the sun blow the helium ions loose from the lines of force outward
into space frequently enough “to balance the [assumed] outgassing from
the earth’s crust” [16]. The theory is very complex, and no creationist
expert in the field has yet reviewed it to see whether it is well founded.
Rapid helium
leaks into space are essential to uniformitarians, but slow leaks are
not essential to creationists. If
the leakage turns out to be slow, it would bolster our case here. But fast leakage would not damage our case.
The next section offers evidence for a much simpler explanation
of the missing atmospheric helium: most of the radiogenic (nuclear decay
generated) helium has not entered the earth’s atmosphere.
It is still in the earth’s crust and mantle—much of it still
in the zircons. In this paper we argue that the helium has not had enough time
(less than 14,000 years) to escape the zircons, much less the crust.
2. THE HELIUM IS STILL IN THE ZIRCONS
In the 1970's, geoscientists from Los Alamos National
Laboratory began drilling core samples at Fenton Hill, a potential geothermal
energy site just west of the volcanic Valles Caldera in the Jemez Mountains
near Los Alamos, New Mexico (Fig. 2).
There, in borehole GT2, they sampled the granitic Precambrian
basement rock, which we will refer to as the Jemez Granodiorite. It has a radioisotopic age of about 1.5 billion
years, as measured by various methods using the uranium, thorium, and
lead isotopes in the zircons themselves [25].
The depths of the samples varied from near the surface down to
4.3 kilometers, with temperatures from 20°C to 313°C. The Los Alamos team sent some of these core samples to Oak Ridge
National Laboratory for isotopic analysis.
Most of the zircons were in biotite [10], a black mica
common in granitic rock. At
Oak Ridge, Robert Gentry, a creationist physicist, crushed the samples
(without breaking the much harder zircon grains), extracted a highdensity
residue (because zircons have a density of 4.7 grams/cm^{3}),
and isolated the zircons by microscopic examination, choosing crystals
about 5075 μm long. The zircon masses were typically on the order
of micrograms. The Oak Ridge
team then heated the zircons to 1000°C in a mass spectrometer and measured
the amount of helium 4 liberated. In
1982 they published the data in Geophysical Research Letters
[9]. Table 1 details their results.
Table
1. Helium Retentions in Zircons from the Jemez
Granodiorite

Depth (m)

Temperature (°C)

He (10^{}^{9} cm^{3}/mg)

Q / Q_{0}

Error

0

0

20

82

—

—

1

960

105

86

0.58

± 0.17

2

2170

151

36

0.27

± 0.08

3

2900

197

28

0.17

± 0.05

4

3502

239

0.76

0.012

± 0.004

5

3930

277

~0.2

~0.001

—

6

4310

313

~0.2

~0.001

—

The first column itemizes the samples analyzed. The second and third columns show the depth
and temperature of each sample in situ.
The fourth column shows the volume (at standard temperature and
pressure) of helium liberated in the lab per microgram of zircon.
The fifth
column is the ratio of the observed quantity of helium Q (total number of helium atoms in the crystal) to the calculated
quantity Q_{0} that the
zircons would have accumulated and retained if there had been no diffusion.
The Los Alamos team measured the amount of radiogenic lead in
zircons 2.9 km deep in the same borehole and same granodiorite [25],
and the Oak Ridge team confirmed those figures with their ion microprobe
[10]. Because the various decay
chains generate an average of 7.7 helium atoms per lead atom produced,
Gentry and his colleagues were able to calculate Q_{0} from the
amount of lead in the zircons. In
doing so, they compensated for the estimated loss of alpha particles
emitted from near the edges of the zircons out into the surrounding
material.
The Oak Ridge
team estimated that uncertainties in calculating Q_{0} might limit
the accuracy of the ratio Q/Q_{0} to ±30%.
The sixth column of the table shows the resulting estimated errors
in the ratios.
Samples 1
through 6 came from the granodiorite, but sample zero came from larger
zircons in a surface outcrop of an entirely different rock unit. For that rock unit U/Th/Pb information was
not available, making an estimate of Q_{0} not feasible. Lacking a ratio, we cannot use sample zero
in the calculations.
Samples 5
and 6 had the same amount of helium.
Gentry and his colleagues noted that helium emerged from those
samples in shorter bursts than the other samples, indicating a different
distribution of helium within those zircons.
In section 6, we will show that the amount of helium from sample
5 is just about what would be expected from the trend in the cooler
samples. But we allow for the possibility of its error
being considerably larger than the cooler samples.
According
to the thermal behavior outlined in the next section, we would ordinarily
expect that the hotter sample 6 would have much less helium than sample
5. The fact that the helium content did not decrease
suggests that some additional effect may have occurred which limited
the outflow of helium from the zircon.
In section 6 we suggest a likely explanation.
The above
considerations suggest that we can use samples 1 through 5 in a theoretical
analysis with ordinary diffusion. We
will treat sample 6 as a special case.
Samples 1
through 3 had helium retentions of 58, 27, and 17 percent. The fact
that these percentages are high confirms that a
large amount of nuclear decay did
indeed occur in the zircons.
Other evidence strongly supports much nuclear decay having occurred
in the past [14, pp. 335337]. We
emphasize this point because many creationists have assumed that "old"
radioisotopic ages are merely an artifact of analysis, not really indicating
the occurrence of large amounts of nuclear decay. But according to the measured amount of lead physically present
in the zircons, approximately 1.5 billion years worth — at today’s rates
— of nuclear decay occurred. Supporting
that, sample 1 still retains 58% of all the alpha particles (the helium)
that would have been emitted during this decay of uranium and thorium
to lead.
It is the
uniformitarian assumption of invariant decay rates, of course, that
leads to the usual conclusion that this much decay required 1.5 billion
years. Uniformitarianism is the prevalent belief
of this age that “all things continue as they were from the beginning”
[II Peter 3:4], denying the possibility of any physical interventions
by God into the natural realm. Uniformitarians
interpret scientific data to support their idea of cosmic and biological
evolution during billions of years of imagined time. We maintain that their interpretations are a distortion of observational
data all around us. As the Bible
predicted [II Peter 3:56], uniformitarians willingly ignore “elephant
in the living room” evidence for a recent creation and a worldwide catastrophic
flood. In this paper we will include their assumption
of billions of years of time and solely natural processes in the uniformitarian
model we construct for diffusion.
Getting back
to the helium data, notice that the retention levels decrease as the
temperatures increase. That
is consistent with ordinary diffusion: a high concentration of helium
in the zircons diffusing outward into a much lower concentration in
the surrounding minerals, and diffusing faster in hotter rock.
As the next section shows, diffusion rates increase strongly
with temperature.
In later
sections, we will show that these large retentions are quite consistent
with diffusion taking place over thousands
of years, not billions of years.
3. HOW DIFFUSION WORKS
If the reader is not very familiar with diffusion and
wants to know more, we recommend a very clear little book, Atomic Migration in Crystals, written for nonexperts
[11]. Figure 3, adapted from
that book [11, p. 39, Fig. 23], illustrates how an atom diffuses through
a solid crystal lattice of other atoms. Figure 3(a) shows a helium atom initially
at position A, surrounded
by a cell of lattice atoms. The
lattice atoms repel the helium atom, tending to confine it to the center
of the cell, where the repulsion balances out in all directions. Heat keeps the atoms of the lattice vibrating
at its various resonant frequencies. The vibrating atoms continually
bump into the helium atom, jostling it from all sides.
The higher the temperature, the more vigorous the jostling.
Every now
and then, the lattice atoms will bump the helium atom hard enough to
push it into the "activated" position B,
midway between cells. The lattice
atoms must give the helium enough kinetic energy to overcome the repulsive
potential energy barrier between the cells, which we have shown in Figure
3(b). This required amount of kinetic energy, E, is called the activation
energy. If the lattice
atoms have given any more energy than E to the helium
atom, it will not stop at position B. Instead, it will continue
on to position C at
the center of the adjacent cell. The
helium atom has thus moved from one cell to the next.
If there
is an initially high concentration of helium atoms in one part of the
crystal, these random motions will eventually spread — i.e., diffuse
— the helium more uniformly though the crystal and out of it.
Let us define C(x, y, z, t) as the concentration,
the number of helium atoms per unit volume, at position (x, y, z) at time t. Many textbooks show
that when diffusion occurs, the time rate of change of C is proportional to the “sharpness” of the edges of the distribution
of helium, or more mathematically, proportional to the Laplacian of
C, Ñ^{2}C :
_{} (1a, b)
Equation
(1a), called the "diffusion equation", occurs frequently in
many branches of physics, for example to describe heat conduction in
solids. Specialists in the diffusion of atoms through
materials call it "Fick's Second Law of Diffusion". The factor D, the diffusion coefficient (or “diffusivity”), has dimensions of
cm^{2} (or m^{2}) per second.
(Most of the diffusion literature still uses centimeters and
calories instead of meters and joules).
Very often it turns out that at high temperatures, the diffusion
coefficient depends exponentially on the absolute temperature T (degrees
kelvin above absolute zero):
_{}
(2)
where R is the universal gas constant, 1.986 calories
per molekelvin (8.314 joules per molekelvin). The constant D_{0} is independent
of temperature. The “intrinsic”
activation energy E_{0} typically
is between 10 and 100 kilocalories per mole (about 40 and 400 kilojoules
per mole). Section 10 discusses
how these quantities are related to the geoscience concept of closure
temperature, and it shows why the concept is irrelevant to our conclusions.
If the crystal
has defects such as vacancies in the crystal lattice, impurities, dislocations,
or grain boundaries, then the diffusion coefficient equation will have
a second term related to the defects:
_{}
(3)
The defect
parameters (D_{1} and E_{1}) are almost always smaller than
the intrinsic parameters (D_{0} and E_{0}):
_{}
(4)
The typical
Arrhenius plot in Figure 4(a) shows how the diffusion coefficient
D of eq. (3)
depends on the inverse of the absolute temperature, 1/T. Because the plot uses a logarithmic
scale for D and a linear scale for 1/T, each term of eq. (3) manifests
itself as a straight line in the temperature region where it is dominant. (Plotting with T instead
of 1/T would make
the lines curved instead of straight.) The slopes are proportional to
the activation energies E_{0} and E_{1}.
The intercepts with the vertical axis, where 1/T is zero,
are the parameters D_{0} and D_{1}.
The intrinsic line has a steep slope and a high intercept,
while the defect line has a shallow slope and a low intercept. Starting on the righthand side of the graph,
at low temperatures, let us increase the temperature, moving to the
left. When the temperature
is high enough, we reach a region, the “knee”, where the two terms of
eq. (3) are about equal. To
the left of that region, at high temperatures, the intrinsic properties
of the crystal dominate the diffusion.
To the right of the knee, at lower temperatures, the defects
dominate. Because defects are
very common in natural crystals, this twoslope character is typical
[11, pp. 102, 126].
For a given type of
mineral, the location of the knee can vary greatly. It depends on the value of D_{1}, which depends on the amount
of defects in the particular crystal.
The more defects there are, the higher D_{1} is. If we increase
the number of defects, the defect line moves upward (keeping its slope
constant) on the graph, as Figure 4(b) illustrates.
In the case of zircons
containing radioisotopes, the main cause of defects is radiation damage,
so highly radioactive (“metamict”) zircons will have a large value of
D_{1}, causing the defect line
to be higher on the graph than for a lowradioactivity zircon.
4. EARLY ZIRCON
DATA WERE AMBIGUOUS
In 1970 Sh. A. Magomedov, a researcher in Dagestan (then
part of the Soviet Union) published diffusion data for radiogenic lead
and helium in highly metamict (radiationdamaged) zircons from the Ural
Mountains [18]. These were the
only heliuminzircon diffusion data we could find during an extensive
literature search we did in 1999.


Magomedov
was mainly interested in lead diffusion, so he did not list his helium
data explicitly in a table. Instead
he showed them in a small graph, along with data for lead diffusion
and electrical conductivity, s. His label for the ordinate was ambiguous: “ln(D, s)”. In scientific literature “ln” with no
further note usually means the natural logarithm (base e). The common logarithm (base 10) is usually shown
as “log”. If we assume Magomedov was reporting ln_{e}D, the resulting
diffusion coefficients would be very high, as the triangles and dotted
line near the top of Figure 5 show.
The RATE book shows that interpretation [14, p. 347, Fig. 6]. Another interpretation is that Magomedov was
reporting ln_{e}(D/a^{2}), where a is the effective
radius of his zircons, about 75 μm. As Figure 5 shows (circles and thin solid line near middle), that
still gives rather high diffusion rates in the temperature range of
interest to us.
Based
on those supposed high rates, we assumed in our first theoretical model
[14, pp. 346 –348] that the zircons were a negligible impediment to
helium outflow, compared to the minerals around them.
But in 2001 we received a preprint of a paper [19] listing new
helium diffusion data in zircons from several sites in Nevada.
Figure 5 shows some of that data (Fish Canyon Tuff sample FCT1)
as a line of solid dots. These
data were many orders of magnitude lower than our interpretation of
Magomedov’s graph. The Russian
data would agree with the Nevada data if we reinterpret Magomedov’s
label as meaning “log_{10}D”, the common logarithm of D. Figure 5 shows
that interpretation near the bottom (squares and thick solid line). The small difference between the highslope
“intrinsic” parts of the Russian and Nevada data is easily attributable
to sitetosite differences in composition.
The nearly horizontal part of the Russian data is probably a
“defect” line due to much radiation damage (see end of previous section).
The new data and our new interpretation of the old data
imply that zircon is not a negligible impediment to helium diffusion. In this paper we have changed our theoretical
model to account for that fact. As
we will show in later sections, our new interpretation of the Russian
data is still five orders of magnitude too high for uniformitarian models. But it is quite compatible with creationist
models and time scales.
5. DATA FOR MINERALS FROM THE JEMEZ GRANODIORITE
Measurements of noble gas diffusion in a given type
of naturally occurring mineral often show significant differences from
site to site, caused by variations in composition.
For that reason it is important to get helium diffusion data
on zircon and biotite from the same rock unit (the Jemez Granodiorite)
which was the source of Gentry’s samples.
Accordingly, in 2000 the RATE project commissioned such experimental
studies.
Los Alamos
National Laboratory was kind enough to give us core samples of granodiorite
from the same borehole, GT2, and from a similar depth, about 750 meters. The geology laboratory at the Institute for
Creation Research extracted the biotite using heavy liquids and magnetic
separation. Using similar methods,
Activation Laboratories, Ltd., in Ontario, Canada, extracted the zircons
and chose three of them for isotopic analysis.
Appendix A gives those results, which agreed fairly well with
the leadlead dates published by Los Alamos National Laboratory for
the same site [25]. We reserved
the rest of the zircons, about 0.35 milligrams, for diffusion measurements.
Through a small mining company, Zodiac Minerals and
Manufacturing, we contracted with Kenneth A. Farley of the California
Institute of Technology (Division of Geological and Planetary Sciences)
to measure the diffusion coefficients of the zircon and biotite from
the Jemez site. He is a recognized expert on helium diffusion
measurements in minerals, having many publications related to that field.
As we wished, Zodiac did not tell Farley they were under contract
to us, the goals of the project, or the sites of the samples.
We have encouraged him to publish his measurements and offered
to send him the geologic site information if he does so.
Appendices B and C list his data in detail.
Figures 6(a) and 6(b) are Arrhenius
plots of the most relevant data for zircon and biotite, respectively.
The zircon data are from the Jemez Granodiorite in New Mexico,
the Fish Canyon Tuff in Nevada, and the Ural Mountains in Russia (the
reinterpreted Magomedov data). The first two studies are for essentially the
same size crystals (average length ~60 μm, a @
30 μm, sect. 6). The Russian
study was for crystals ~150 μm long.
The biotite data are
from the Jemez Granodiorite. Those,
and similar data we obtained (see Appendix B) for biotite from the Beartooth
Gneiss in Wyoming, are the only data for that mineral we know of.
For comparison to the biotite data, we have also included published
data for muscovite, a different mica [17].
Notice that all the sets of zircon
data agree fairly well with each other at high temperatures. At 390ºC (abscissa = 1.5), the Russian data
have a knee, breaking off to the right into a more horizontal slope
for lower temperatures. That
implies a high number of defects (see sect. 4), consistent with the
high radiation damage Magomedov reported.
The Nevada and New Mexico data go down to 300ºC
(abscissa = 1.745) with no strong knee, implying that the data
are on the intrinsic part of the curve.
A leastsquares fit of eq. (2) to the New Mexico (Jemez Granodiorite)
zircon data gives the following diffusion parameters:
_{}(5a)
However, there appears to be a slight decrease of slope
in the data below 450ºC. Later
on we will need a fit at temperatures below that.
The bestfit parameters from 440ºC down to 300ºC are:
_{}
(5b)
Because the
New Mexico zircons are radioactive, they must have some defects and
should have a knee at some lower temperature than 300ºC. We have recently requested that Farley get additional data from
100ºC to 300ºC. But as of February
2003, we do not have reliable data for that range.
The muscovite
and biotite data are consistent with each other. In the low temperature range of interest, the
New Mexico biotite has a somewhat higher diffusion coefficient than
the zircons. That means the
biotite, while not being negligible, did not impede the helium outflow
as much as the zircon did.
6. A NEW CREATION
MODEL
We need a theoretical framework in which we can interpret
the diffusion data of the previous section. As we mentioned at the end of section 4, in our first creation model
we wrongly assumed that the zircons were a negligible impediment to
the helium diffusion. In this
section we construct a new creation model.
As before,
the creation model starts with a brief burst of accelerated nuclear
decay generating a high concentration C_{0} of helium uniformly throughout the
zircon (like the distribution of U and Th atoms), but not in the surrounding
biotite. After that the helium
diffuses out of the zircon into the biotite for a time t. As in our previous model, we chose t = 6000 years.
The time is short enough that the additional amount of helium
generated by normal nuclear decay would be small compared to the initial
amount. We assume the temperatures
to have been constant at today’s values. We will show in section 7 that this assumption
is generous to uniformitarians.


Because the
biotite diffusion coefficients are not too different from the zircon
coefficients, we should have a model accounting for two materials. Diffusion in zircon is isotropic, with helium
flowing essentially at the same rate in all three directions. Diffusion in biotite is not isotropic, because
most of the helium flows twodimensionally along the cleavage planes
of the mica. But accounting
for anisotropy in the biotite would be quite difficult, so we leave
that refinement to the next generation of analysts. To keep the mathematics
tractable, we will assume spherical symmetry, with a sphere of zircon
of effective radius a inside a
spherical shell of material having an outer radius b, as Figure
7 shows. Then the concentration
C will depend
only on time and the distance r from the center
Let us consider
the values we should assign to a and b. Magomedov’s zircons were between 100 and 200
μm long [18, p. 263], for an average length of about 150 μm. He assigned the crystals an effective radius
of half the average length, or 75 μm.
Gentry selected zircons between about 50 μm and 75 μm,
for an average that we will round off to 60 μm.
Half of that gives us an effective radius for our analysis of
the Jemez zircons:
_{}
(6)
Biotite in
the Jemez Granodiorite is in the form of flakes averaging about 0.2
mm in thickness and about 2 millimeters in diameter.
Because the cleavage planes are in the long direction, and diffusion
is mainly along the planes, the diameter is the relevant dimension for
diffusion. That gives us an
outer radius of:
_{}
(7)
Because b is more
than 32 times larger than a, the disklike (not spherical) volume of biotite the helium
enters is more than 1000 (~32 squared) times the volume of the zircon. This consideration affects the boundary conditions
we choose for r
= b, and how we might interpret sample 6 (see sect. 2), as follows.
Suppose that
helium could not escape the biotite at all. Then as diffusion proceeds, C would decrease in the zircon and
increase in the biotite, until the concentration was the same throughout
the two materials. After that
C would remain
essentially constant, at about 0.001 C_{0}.
The fraction Q/Q_{0} remaining in the zircon would be about 0.001, which is just
what Gentry observed in sample 6.
So a possible
explanation for sample 6 is that diffusion into the surrounding materials
(feldspar, quartz), and leakage (along grain boundaries) was slow enough
(during the relatively short time t) to make the outflow of helium from
the biotite negligible. For
that sample, the temperature and diffusion coefficient were high enough
for helium to spread uniformly through both zircon and biotite during
that time.
Our measurements
(see Appendix B) showed that the helium concentration in the Jemez biotite
at a depth of 750 meters was small, only about 0.32 ´ 10^{9}
cm^{3} (at STP) per microgram.
Taking into account the difference in density of biotite and
zircon (3.2 g/cm^{3} and 4.7 g/cm^{3}), that corresponds
to almost exactly the same amount of helium per unit volume as sample
6 contained. That suggests the zircon and biotite were near
equilibrium in sample 6, thus supporting our hypothesis.
At lower
temperatures, for helium retentions greater than 0.001, C in the biotite
would be lower than C in the zircon. In
that case the boundary at r
= b would not significantly affect the outflow of helium from
the zircon. We will assume this
was approximately true for sample 5 also, but not for sample 6. To simplify our analysis for samples 1 through
5, we will assume the usual boundary condition, that the concentration
C(r) falls to
zero at radius r = b:
_{}
(8)
For the initial
conditions, we assume that the concentration is a constant, C_{0}, inside
the zircon, and zero outside it:
_{}
(9a, b)
After time
zero, there also must be continuity of both C and helium flow at r = a. We need a solution to the diffusion equation,
(1), in its radial form, for the above boundary conditions. In 1945, R. P. Bell published such a solution
for the corresponding problem in heat flow [2, p. 46, eq. (4B)]. His solution, which is mathematically complex,
allows for different diffusion coefficients in the two regions. We will simplify the solution considerably
by making the diffusion coefficients the same in both regions. Because the diffusion coefficient of biotite
is somewhat higher than that of zircon at the temperatures of interest,
our solution will have slightly slower (no more than 30% slower) helium
outflows and correspondingly longer times than the real situation. But because uniformitarians need to increase
the time anyhow, they should not object to this approximation.
With the
above simplification, Bell’s equation reduces to one given by Carslaw
and Jaeger [3, p. 236, eq. (19)]. After
making the simple changes required to go from heat flow to atomic diffusion
[5, p. 8, eq. (1.21)], and accounting for notation differences (note
meanings of a and b), we get
the following solution:
_{}
(10)
where D is the diffusion
coefficient of zircon. Next
we need to determine the fraction Q/Q_{0} of helium retained in the zircon
after diffusion takes place for time t.
First, note that Q(t) and Q_{0} are the
volume integrals of C(r,
t) and C_{0} in the zircon:
_{}
(11a, b)
Volume integrating
eq. (10) as required by eq. (11a) and dividing by eq. (11b) gives the
fraction of helium retained in the zircon after time t elapses:
_{}
(12)
where we
define the function S_{n} as follows:
_{}
(13)
To solve
eq. (12), let us rewrite it in terms of a new variable, x, and a new
function F(x) as follows:
_{}
(14a, b, c,)
Now we can
use software like Mathematica [24] to find the roots of eq. (14a),
that is, to find the values of x for which F(x) will give us particular values
of the retention fraction Q/Q_{0}. When the latter and
b/a are large,
the series in eq. (14b) does not converge rapidly. For our value of b/a, 33.3, it
was necessary to go out to N = 300 to get good accuracy. Table 2 lists the resulting values of x, and the
values of D necessary
to get those values from eq. (14c) using a time of 6000 years, t = 1.892
´ 10^{11}
seconds. The estimated errors
in D result from
the reported errors in Q/Q_{0}.
Table 2. New
Creation Model

T (ºC)

Q/Q_{0}

x

D (cm^{2}/sec)

Error (%)

1

105

0.58 ± 0.17

5.9973 ´10^{4}

3.2103 ´ 10^{18}

+122

 67

2

151

0.27 ± 0.08

2.4612 ´10^{3}

1.3175 ´ 10^{17}

+ 49

 30

3

197

0.17 ± 0.05

4.0982 ´10^{3}

2.1937 ´ 10^{17}

+ 39

 24

4

239

0.012 ± 0.004

3.3250 ´10^{2}

1.7798 ´ 10^{16}

+ 33

 18

5

277

~0.001

1.8190
´10^{1}

9.7368
´ 10^{16}

—

—

In summary, the fifth column shows the zircon diffusion
coefficients that would be necessary for the Jemez zircons to retain
the observed fractions of helium (third column) for 6000 years at the
temperatures listed in the second column.
This new
model turns out to be amazingly close to our previous creation model
— within 0.5% for sample 1 and 0.05% for the others — despite the different
assumptions and equations. This
strongly suggests there is an underlying (but not obvious) physical
equivalence between the two models, and that the small differences are
merely due to the numerical error of the calculations. Thus our previously
published predictions [14, p. 348, Fig. 7] of diffusion coefficients
are valid, but they should be reinterpreted to apply to zircon, not
biotite.
We will compare
the data not only to this new model, but also to a uniformitarian model,
which we describe in the next section.
7. UNIFORMITARIAN
MODEL
In the RATE
book [14, p. 346], we outlined a simple model appropriate for the uniformitarian
view, with its billions of years, of the history of the rock unit:
…
steady lowrate radioactive decay, He production, and He diffusion for
1.5 billion years at today’s temperatures in the formation.
Our assumption
of constant temperatures is generous to uniformitarians. Two geoscientists from Los Alamos National
Laboratory constructed a theoretical model of the thermal history of
the particular borehole (GT2) we are concerned with [15, p. 213, Fig.
11]. They started by assuming “a background vertical
geothermal gradient of 25ºC/km.” That
means initial conditions with absolute temperatures 16% to 31% lower
than today for samples 1 through 6, putting them in the lowslope “defect”
range of diffusion. Their model
then has an episode of PliocenePleistocene volcanism starting to increase
the temperature several megayears ago. It would peak about 0.6 Myr ago at temperatures roughly 50 to 120ºC
above today’s values, depending on depth. After the peak, temperatures would decline steadily until 0.1 Myr
ago, and then level off at today’s values.
Later studies [12, 20] add a more recent pulse of heat
and have past temperatures being higher, 110ºC to 190ºC more than today’s
levels just 24,000 years ago, and higher before that [12, p. 1906, Fig.
9]. This would put the samples
well into the highslope “intrinsic” range of diffusion.
The effect of such heat pulses would be great. For several million years, the diffusion coefficients
would have been about two to three orders of magnitude higher than today’s
values. During the previous
1.5 billion years, supposedly at lower temperatures than today, the
diffusion rates would have been on the “defect” line [Figure 4(a]) and
therefore not much below today’s levels.
Thus the long time at lower temperatures would not compensate
for high losses during the few million years at higher temperatures.
This makes our assumption of constant temperatures at today’s
values quite favorable to the uniformitarian scenario.
As we will see, the long uniformitarian time scale requires
zircon diffusion coefficients to be about a million times slower than
the measured biotite coefficients.
That means the biotite would not be a significant hindrance to
the helium flow in the uniformitarian model, and the results would not
be much different than those for a bare zircon.
For continuous production of helium, the concentration C in the zircon would reach its steadystate level relatively quickly (see
sect. 10) and remain at that level for most of the alleged 1.5 billion
years. Again we assume a spherical
zircon of radius a. Carslaw and Jaeger give the corresponding solution for heat flow
[3, p. 232, case VIII)]. Converting
to the notation for atomic diffusion shows us how the steadystate concentration
C in the zircon depends on the radius r from the center:
_{}
(15)
Here Q_{0} is the total
amount of helium that would be produced in time t. That is, Q_{0}_{ }/ t is the helium
production rate. As before,
D is the diffusion
coefficient of zircon, and a is the effective radius. Using eq. (11a) to integrate eq. (15) and dividing
by Q_{0} gives us
the fraction of helium Q/Q_{0} in the zircon
in the steadystate condition:
_{
}
(16)
Table 3 gives
us the zircon diffusion coefficients required to give the observed retentions
for a = 30 mm and t = 1.5 billion
years = 4.73 ´ 10^{16}
seconds.
Table 3. Uniformitarian
Model

T (ºC)

Q/Q_{0}

D (cm^{2}/sec)

Error (%)

1

105

0.58 ± 0.17

2.1871 ´ 10^{23}

± 30

2

151

0.27 ± 0.08

4.6981 ´ 10^{23}

± 30

3

197

0.17 ± 0.05

7.4618 ´ 10^{23}

± 30

4

239

0.012 ± 0.004

1.0571 ´ 10^{21}

± 30

5

277

~0.001

1.2685
´ 10^{20}

—

The same
reasoning on sample 6 applies for this model as for the creation model,
except that it is less likely the helium could remain totally sealed
in the biotite for over a billion years.
For the other samples, this model is exactly the same as our
previously published “evolution” model [14, p. 348, Fig. 7].
8. COMPARING DATA AND MODELS
Figure 8 shows the zircon data from the Jemez Granodiorite,
along with the two models. The
zircon data are fully consistent with the creation model. These new data are also quite consistent with
all published zircon data, as Figure 6(a) shows. As of this writing (February, 2003) we do not
have reliable data on the Jemez zircons below 300ºC. But notice that the data have the same slope as the creation model
points for samples 3, 4, and 5, and the data nearly touch point 5. That allows us to use eq. (14c) to roughly
estimate values for the time t for those three points:
_{}
(17)
Using a/b = 0.03,
the values of D/a^{2} xtrapolated
down from the bestfit experimental parameters of eq. (5b), and the
values of x and errors
from Table 2 gives us the following times for diffusion to have occurred:
Table 4. Time
For Diffusion

x

D^{
}/^{ }b^{2} (sec^{1})

Time t (years)

Error (years)

3

4.0982 ´10^{3}

1.2672 ´ 10^{15}

10389

+ 4050

 2490

4

3.3250 ´10^{2}

1.6738 ´ 10^{14}

6392

+ 2110

 1150

5

1.8190
´10^{1}

1.2311
´ 10^{13}

4747

—

—

The errors above do not include the statistical errors
in extrapolating the fit to the zircon diffusion coefficient data down
to the lower temperatures required.
Actual data for temperatures below 300ºC would eliminate the
extrapolation error.
In the meantime
we can say the data of Table 4, considering the estimates of error,
indicate an age between 4,000 and 14,000 years. This is far short of the 1.5 billion year uniformitarian
age!
It looks as if the retention data require points 1 and
2 of the creation model to be on a “defect” line, similar to the Russian
data for radiationdamaged zircons.
The similarity gives us good reason to hope that the lowtemperature
zircon data, when they come in, will come close to those model points
as well.
The data
offer no hope for the uniformitarian model.
It is unlikely that the zircon data will continue down on the
intrinsic line for five more orders of magnitude.
It is certain (because all natural zircons have defects) that
at some lower temperature there will be a knee, where the data will
break off horizontally to the right into a shallowslope defect line. But even if that were not to be the case, the
intrinsic line would pass well above the uniformitarian model.
We can also
use these observed data to estimate what helium retentions Gentry should
have found if the zircons were really 1.5 billion years old. If no helium could leak out of the biotite
during that time, then all of the samples would have had retentions
of about 0.001, much less than samples 1 through 4 [see sect. 6 between
eqs. (7) and (8)]. However,
we know that helium can diffuse through the surrounding materials, quartz
and feldspar. By assuming those are negligible hindrances,
we can use the extrapolated data in eq. (16) to get lower bounds on
the retentions. Table 5 shows the results:
Table 5. Billionyear
lower bounds versus observed retentions
Sample

T

Observed
D^{ }/^{ }a^{2 }(sec^{1})

Helium Retentions Q^{ }/^{ }Q_{0}


(ºC)

Extrapolated from data

After 1.5
billion years

Observed

3

197

1.4080 ´ 10^{12}

1.0007 ´ 10^{6}

0.170

4

239

1.8597 ´ 10^{11}

7.5764 ´ 10^{8}

0.012

5

277

1.3679
´ 10^{10}

1.0368
´ 10^{8}

0.001

In summary,
the observed diffusion rates are so high that if the zircons had existed
for 1.5 billion years at the observed temperatures, samples 1 through
5 would have retained much less helium than we observe. That strongly implies they have not existed
nearly so long a time.
9. CLOSING SOME LOOPHOLES
One response
to these data from uniformitarians might be this: assert that temperatures
in the Jemez Granodiorite before the PliocenePleistocene volcanism
were low enough to make the diffusion coefficients small enough to retain
the helium. We discussed that
possibility in section 7, but here we point out how low such temperatures
are likely to be.
Until we
have reliable lowtemperature data for the Jemez Granodiorite zircons,
we must reason indirectly from the other data we have.
The only published lowtemperature zircon data, the Russian data
by Magomedov [18], show a defect line [Figure 6(a)]. The line is rather high, probably because those zircons had many
defects due to the high radiation damage Magomedov reported. But the slope of the defect line is similar
to the slope of points 1, 2, and 3 in both the creation and uniformitarian
models of the retention data (Figure 8).
Since the hightemperature Jemez zircon data agree well with
the creation model, there is good reason to suppose the lowtemperature
data will also conform to that model.
In that case, the parameters of the zircon defect line would
be: _{
}
_{
}
(18)
Because E_{1} is small,
the slope of the defect line is small.
These numbers would mean that to get the diffusion coefficients
low enough to meet uniformitarian needs, say on the order of 10^{23}
cm^{2}/sec, the prePliocene temperature in the granodiorite
would have to have been about –190°C, near that of liquid nitrogen.
No uniformitarian we know would advocate an earth that was cryogenic
for billions of years! Of course
these values are only preliminary estimates, and perhaps the actual
defect line of the Jemez zircons would require less severe cooling. But it demonstrates how zircons would need unrealistically low temperatures
to retain large amounts of helium for uniformitarian eons of time.
A second
uniformitarian line of defense might be to claim that the helium 4 concentration
in the biotite or surrounding rock is presently about the same as it
is in the zircons. (Such a scenario
would be very unusual, because the major source of ^{4}He is
U or Th series radioactivity in zircons or a few other minerals like
titanite or apatite, but not biotite.)
The scenario would mean that essentially no diffusion into or
out of the zircons is taking place.
However, our measurements (Appendix B) show that except
for possibly samples 5 and 6, the concentration of helium in the biotite
[sect. 6, between eqs. (7) and (8)] is much lower than in the zircons.
Diffusion always flows from greater to lesser concentrations.
Thus helium must be diffusing out of the zircons and into the
surrounding biotite. Moreover,
the Los Alamos geothermal project made no reports of large amounts of
helium (commercially valuable) emerging from the boreholes, thus indicating
that there is not much free helium in the formation as a whole.
A third uniformitarian
defense could be that the Oak Ridge team somehow made a huge mistake,
that the actual amounts of helium were really many orders of magnitude
smaller than they reported. But
as Appendix C reports, our experimenter Kenneth Farley, not knowing
how much he should find and going up to only 500°C, got a partial (not
exhaustive) yield of 540 nanomoles of helium per gram of zircon, or
in Gentry’s units, 11 × 10^{9} cm^{3}/μg.
That is on the same order of magnitude as Gentry’s results in
Table 2, which reports the total (exhaustive) amount liberated after
heating to 1000°C until no more helium would emerge.
Thus our experiments support Gentry’s data.
10. “CLOSURE
TEMPERATURE” DOESN’T HELP UNIFORMITARIANS
Some uniformitarians
try to use the geoscience concept of closure temperature to claim
that zircons below that temperature are permanently closed systems,
losing no significant helium by diffusion.
They fail to understand that even well below that temperature,
zircons can reopen and lose large amounts of helium. Here we explain closure temperature and reopening, and show that
in the uniformitarian scenario, the Jemez Granodiorite zircons would
reopen early in their history.
Consider
a hot zircon cooling down in newly formed granite. If the cooling rate is constant, then the seminal article by Martin
Dodson [6] on closure temperature shows that the diffusion coefficient
D (of helium
moving out of the zircon) decreases exponentially with a time constant
t given by:
_{
}
(19)
where T is the absolute
temperature, dT/dt is the cooling
rate, R is the gas
constant, and E_{0} is the activation
energy in the “intrinsic” region (sect. 3).
In the uniformitarian
scenario, nuclear decay produces helium at a nearly constant rate.
At the beginning, when the zircon is very hot, helium diffuses
out of the crystal as fast as nuclear decay produces it.
But as the zircon cools, it will eventually reach a temperature
below which the loss rate becomes less than the production rate.
That point is essentially what Dodson meant by the “closure”
temperature. He showed that for a constant cooling rate
the closure temperature T_{c} is
_{
}
(20)
where
A is a dimensionless constant
(55 for a sphere), D_{0}
is the “intrinsic” intercept in Figure 4(a), a is the effective radius of the crystal, and t is the diffusion time constant given by eq. (19).
Since t depends on the cooling rate, hence affecting T_{c} somewhat, geoscientists imply some conventional cooling
rate when they specify a closure temperature. In Appendix C Kenneth Farley assumes a cooling rate of 10ºC per
million years and finds that the closure temperature of the Jemez Granodiorite
zircons is 128ºC.
That
temperature is below the borehole temperatures of samples 2 through
5 (Table 1). Most of our samples
were above the closure temperature, so they would always have
been open systems, losing helium. However,
even if they had reached closure temperature, the analysis below shows
they would not have remained closed for long.
After
the zircon cools below the closure temperature, helium begins to accumulate
in it, as Figure 9 shows.
Later,
as the temperature levels off to that of the surrounding rock, the diffusion
coefficient D becomes
constant. (The case of changing longterm temperatures
is harder to analyze, but there will still be a time of reopening.)
As the amount of helium in the zircon increases, Fick’s laws
of diffusion (sect. 3) say the loss rate also increases.
Eventually, even well below the closure temperature, the loss
rate approaches the production rate, an event we call the “reopening”
of the zircon. Then the amount of helium in the zircon will level off at a steadystate
value, which we called Q in eq. (16). After that, the zircon
will again lose helium as fast as nuclear decay produces it.
Let us estimate the closure interval, the length
of time t_{ci}
the zircon remains closed before reopening.
As we remarked just below eq. (15), the helium production rate
is Q_{0}_{ }/^{ }t, where t
is the uniformitarian age of the zircon, 1.5 billion years. Assuming a linear rise as a first approximation,
the production rate multiplied by t_{ci} is roughly equal to the steadystate value of Q, which is the righthand side of our eq. (16) multiplied
by Q_{0}:
_{
}
(21)
Solving for t_{ci} gives us the approximate closure interval:
_{
}
(22)
If the closure interval were 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 µm, and the measured values
of D (Figure 8) in eq.
(22) gives us t_{ci}
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.
So even if the zircons had cooled rapidly and reached
closure temperature early in their history, our measured diffusion rates
say they would have reopened shortly after that.
During most of the alleged eons the zircons would have been an
open system. They would be losing
as much helium as the nuclear decay produced.
Thus closure temperature does not help uniformitarians
in this case, because the closure interval is brief.
11. CONCLUSION
The experiments
the RATE project commissioned in 2000 have clearly confirmed the numerical
predictions of our creation model (updated slightly in sect. 6), which
we published beforehand [14, p. 348, Fig. 7]. Other experimental data published since 2000 agree with our data.
The data also clearly reject the uniformitarian model.
The data and our analysis show that over a billion years worth
of nuclear decay have occurred very recently, between 4,000 and 14,000
years ago. This strongly supports our hypothesis of recent episodes of highly
accelerated nuclear decay.
These diffusion
data are not precise enough to reveal details about the acceleration
episodes. Were there one, two,
or three? Were they during early
Creation week, after the Fall, or during the Flood?
Were there only 500 to 600 million years worth of acceleration
during the year of the Flood, with the rest of the acceleration occurring
before that? We cannot say from
this analysis. However, the
fact that these zircons are from a Precambrian rock unit sheds some
light on various creationist models about when strata below the Cambrian
formed. We can say that the “diffusion clock” requires
a large amount of nuclear decay to have taken place within thousands
of years ago, after the zircons became solid.
At whatever time in Biblical history Precambrian rocks came into
existence, these data suggest that “1.5 billion years” worth of nuclear
decay took place after the rocks solidified not long ago.
Our most
important result is this: Helium diffusion casts doubt on uniformitarian
longage interpretations of nuclear data and strongly supports the young
world of Scripture.
ACKNOWLEDGMENTS
Many people
and institutions have contributed to collecting and interpreting these
data. In particular, we would
like to thank Robert Gentry, Bill Hoesch, Yakov Kapusta, Roger Lenard,
Majdah alQuhtani, and Phil Legate.
We would also like to thank supporters of the RATE project for
their generous contributions and prayers.
REFERENCES
[1] Anonymous, Physics update, Physics Today, 53(8, Pt 1):9, August 2000.
[2] Bell, R. P., A problem of heat conduction with spherical
symmetry, Proceedings of the Physical
Society (London), 57:4548,1945.
[3] Carslaw, H. S., and Jaeger, J. C., Conduction of
Heat in Solids, 2^{nd} edition, Clarendon
Press, Oxford, 1959.
[4] Cook, M. A., Where is the earth's radiogenic helium? Nature,
179:213, 1957.
[5] Crank, J., The Mathematics of Diffusion,
2^{nd} edition, Oxford University Press, Oxford, 1975.
[6] Dodson, M. H., Closure temperature in cooling geochronological
and petrological systems, Contributions to Mineralogy
and Petrology, 40:259274, 1973.
[7] Farley, K. A., Helium diffusion from apatite: general behavior
as illustrated by Durango Fluorapatite, Journal of
Geophysical Research, 105(B2):29032914, February 10,
2000.
[8] Fechtig, H., and Kalblitzer, S., The diffusion of argon in
potassiumbearing solids, in Potassium Argon Dating,
O. A. Schaeffer and J. Zähringer, editors, SpringerVerlag, New York,
1966.
[9] Gentry, R. V., Glish, G. J., and McBay, E. H., Differential
helium retention in zircons: implications for nuclear waste management,
Geophysical Research Letters 9(10): 11291130,
October, 1982.
[10] Gentry, R. V., private communication, December 31, 1995.
[11] Girifalco, L. A., Atomic Migration in Crystals,
Blaisdell Publishing Company, New York. pp. 39, 89, 1964.
[12] Harrison,
T. M., Morgan, P., and Blackwell, D.D., Constraints on the age of
heating at the Fenton Hill site, Valles Caldera, New Mexico, Journal
of Geophysical Research, 91(B2):18991908, February
10, 1986.
[13] Hoffman,
J. H., and Dodson, W. H., Light ion concentrations and fluxes in
the polar regions during magnetically quiet times, Journal
of Geophysical Research, 85(A2):626632, February
1, 1980.
[14] Humphreys,
D.R., Accelerated nuclear decay: a viable hypothesis? in Radioisotopes
and the Age of the Earth:
A YoungEarth Creationist Research Initiative,
L. Vardiman, A. A. Snelling, and E. F. Chaffin, editors, Institute for
Creation Research and the Creation Research Society, San Diego, CA,
pp. 333379, 2000.
[15] Kolstad,
C. D., and McGetchin, T. R., Thermal evolution models for the Valles
Caldera with reference to a hotdryrock geothermal experiment,
Journal of Volcanology and Geothermal
Research, 3:197218, 1978.
[16] LieSvendsen,
Ø., and Rees, M. H., Helium escape from the terrestrial atmosphere:
the ion outflow, Journal of Geophysical Research,
101(A2):24352443, February 1, 1996.
[17] Lippolt,
H. J., and Weigel, E., ^{4}He diffusion in ^{40}Arretentive
minerals, Geochimica et Cosmochimica Acta,
52:14491458, 1988.
[18] Magomedov,
Sh. A., Migration of radiogenic products in zircon, Geokhimiya,
1970, No. 2, pp. 263267 (in Russian).
English abstract in Geochemistry International
7(1):203, 1970. English translation
available from D. R. Humphreys.
[19] Reiners,
P. W., Farley, K. A., and Hickes, H. J., He diffusion and (UTh)/He
thermochronometry of zircon: initial results from Fish Canyon Tuff and
Gold Butte, Nevada, Tectonophysics 349(14):297308, 2002.
[20] Sakada,
M., Fluid inclusion evidence for recent temperature increases at
Fenton Hill hot dry rock test site west of the Valles Caldera, New Mexico,
U.S. A., Journal of Volcanology and
Geothermal Research, 36:257266, 1989.
[21] Stacey,
J. S., and Kramers, J. D., Approximation of terrestrial lead isotope
evolution by a twostage model, Earth and Planetary
Science Letters, 26:201221, 1975.
[22] Steiger,
R. H., and Jäger, E., Subcommission on geochronology: convention
on the use of decay constants in geo and cosmochronology, Earth
and Planetary Science Letters, 36:359362
1977.
[23] Vardiman,
L., The Age of the Earth's
Atmosphere: A study of the Helium
Flux through the Atmosphere, Institute
for Creation Research, P.O. Box 2667, El Cajon, CA
92021, p. 28, 1990.
[24] Wolfram,
S., Mathematica, 2^{nd} edition, AddisonWesley, New
York, 1991.
[25] Zartman,
R. E., Uranium, thorium, and lead isotopic composition of biotite
granodiorite (Sample 95272b) from LASL Drill Hole GT2, Los Alamos Scientific Laboratory Report LA7923MS,1979.
APPENDIX A: ISOTOPIC
ANALYSIS OF JEMEZ ZIRCONS
Here we summarize a report by Dr. Yakov Kapusta (Activation
Laboratories, Ltd., in Ontario, Canada) on an isotopic analysis he made
on three zircons from Los Alamos National Laboratories core sample GT2480
from borehole GT2 in the Jemez Granodiorite at a depth of 750 meters.
Dr. Kapusta separated zircons from the core sample using
heavy liquids and magnetic separation.
He picked three crystals from the concentrate for analysis. Table A1 shows his results and notes.
Table A1. Uraniumlead
analysis of three zircons


Concentrations

Ratios

#

Mass

U

Pb

Pb(c)

^{206}Pb

^{208}Pb

^{206}Pb

Error


(µg)

(ppm)

(ppm)

(pg)

^{204}Pb

^{206}Pb

^{238}U

(2s %)


(a)



(b)

(c)

(d)

(e)


z1

0.8

612

106.1

13.6

241.2

0.633

0.102828

.50

z2

1.0

218

59.6

1.4

2365.1

0.253

0.236433

.23

z3

1.7

324

62.7

1.7

3503.6

0.218

0.172059

.11


Ratios

Ages

#

^{207}Pb

Error

^{207}Pb

Error

^{206}Pb

^{207}Pb

^{207}Pb

Corr.


^{235}U

(2s %)

^{206}Pb

(2s %)

^{238}U

^{235}U

^{206}Pb

coef.


(e)


(e)






z1

1.2744

.56

0.08989

.23

631.0

834.4

1423.2

0.912

z2

2.9535

.26

0.09060

.12

1368.1

1395.7

1438.2

0.887

z3

2.1456

.13

0.09044

.07

1023.4

1163.6

1434.9

0.828

Notes:
(a) Sample weights
are estimated by using a video monitor and are known to within 40%.
(b) Total commonPb
in analyses
(c) Measured ratio
corrected for spike and fractionation only.
(d) Radiogenic
Pb.
(e) Corrected
for fractionation, spike, blank, and initial common Pb.
Mass fractionation correction of 0.15%/amu ± 0.04%/amu
(atomic mass unit) was applied to singlecollector Daly analyses and
0.12%/amu ± 0.04% for dynamic FaradayDaly analyses. Total procedural blank less than 0.6 pg for Pb and less than 0.1
pg for U. Blank isotopic composition:
^{206}Pb/^{204}Pb = 19.10 ± 0.1, ^{207}Pb/^{204}Pb
= 15.71 ± 0.1, ^{208}Pb/^{204}Pb = 38.65 ± 0.1.
Age calculations are based on the decay constants of Steiger and Jäger
(1977) [22]. CommonPb corrections
were calculated by using the model of Stacey and Kramers (1975) [21]
and the interpreted age of the sample.
The upper intercept of the concordia plot of the ^{206}Pb/^{238}U
and ^{207}Pb/^{238}U data was 1439.3 Ma ± 1.8 Ma. (The published Los Alamos radioisotope date
for zircons from a different depth, 2900 meters, was 1500 ± 20 Ma [25].)
APPENDIX
B: DIFFUSION RATES IN BIOTITE
Below are
two reports by Kenneth Farley (with our comments in brackets) on his
measurements of helium diffusion in biotite from two locations. As far as we know, these are the only heliuminbiotite
diffusion data that have been reported. The first sample, BT1B, was from the Beartooth
Gneiss near Yellowstone National Park. The second sample, GT2, was from the Jemez Granodiorite, borehole
GT2, from a depth of 750 meters. The
geology laboratory at the Institute for Creation Research extracted
the biotite for from both rock samples by crushing, magnetic separation,
and density separation with heavy liquids.
Farley sieved both samples to get flakes between 75 and 100 microns
in diameter. Taking half of
the average diameter to get an effective radius of 44 microns, we plotted
the resulting diffusion coefficients for the GT2 sample in Figure 6(b). We plotted the muscovite data in Figure 6(b)
using the effective radius recommended in the report [17], 130 microns.
Results of He Diffusion on Zodiac biotite, BT1B
[Beartooth Gneiss] October 18,
2000
Kenneth A. Farley
Experiment:
Approximately
10 mg of biotite BT1B, sieved to be between 75 and 100µm, was subjected
to step heating. Steps ranged
in temperature from 50ºC to 500ºC in 50ºC increments, with an estimated
uncertainty on T of <
3ºC. Durations ranged from 6
to 60 minutes, with longer durations at lower temperatures; uncertainty
on time is < 1% for all steps. After
the ten steps the partially degassed biotite was fused to establish
the total amount of He in the sample.
He was measured by isotope dilution quadrupole mass spectrometry,
with an estimated precision of 2%.
He diffusion coefficients were computed using the equations of
Fechtig and Kalbitzer (1966) [8] assuming spherical geometry.
Data:
Table
B1. Diffusion of helium from
Biotite sample BT1B
Step

Temp ºC

Minutes

Cumulative fraction

ln_{e}(D/a^{2})

1

50

61

3.45E06

35.80

2

100

61

1.16E04

28.76

3

150

61

1.37E03

23.83

4

200

61

6.34E03

20.81

5

250

30

1.76E02

18.15

6

300

30

5.33E02

15.88

7

350

16

1.02E02

14.11

8

400

16

2.11E01

12.54

9

450

10

3.38E01

11.25

10

500

6

4.74E01

10.11

Remainder Fusion

5.26E01


Total

1.00000


[In a later
addendum to this report, Farley told us that the total amount of helium
liberated was about 0.13 ´ 10^{9} cm^{3} (at STP) per microgram of biotite.]
Interpretation:
He diffusion
from this biotite defines a remarkably linear Arrhenius profile, fully
consistent with thermally activated volume diffusion from this mineral.
The first two data points lie slightly below the array; this
is a common feature of He release during step heating of minerals and
has been attributed to “edge effects” on the He concentration profile
[7, 8]. Ignoring those two data
points, the activation energy and diffusivity at infinite T based on these data are 25.7 kcal/mol and 752
respectively. At a cooling rate
of 10ºC/Myr, these parameters correspond to a closure temperature of
39ºC.
[After this
Farley added a “Recommendations” section wherein he discussed the possibility
of vacuum breakdown of the biotite at high temperatures, the relevant
effective radius for biotite (probably half the sieved flake diameter),
and the source of helium in the biotite (probably uranium and thorium
in zircons that had been in the flakes before separation). We decided none of these questions were important
enough to investigate in detail for now, since this sample was not from
a site we were interested in at the time.
It merely happened to be on hand at the ICR geology laboratory,
making it ideal for an initial run to look for possible difficulties
in experimental technique.]
Results of Helium Diffusion experiment on Zodiac biotite, GT2
[Jemez Granodiorite] March 24,
2001
Kenneth A. Farley
Experiment:
Approximately
10 mg of biotite GT2, sieved to be between 75 and 100µm, was subjected
to step heating. Steps ranged
in temperature from 50ºC to 500ºC in 50ºC increments, with an estimated
uncertainty on T of < 3ºC.
Durations ranged from 7 to 132 minutes, with longer durations
at lower temperatures; uncertainty on time is < 1% for all steps. After 11 steps of increasing T, the sample was brought back to lower temperature,
and then heated in 6 more Tincreasing steps. After the 17
steps the partially degassed biotite was fused to establish the total
amount of He in the sample. He
was measured by isotope dilution quadrupole mass spectrometry, with
an estimated precision of 2% (steps 12 and 13 are much more uncertain
owing to low gas yield). He diffusion coefficients were computed using
the equations of Fechtig and Kalbitzer (1966) assuming spherical geometry.
Data:
Table B2. Diffusion of helium from
biotite sample GT2
Step

Temp ºC

Minutes

Cumulative fraction

ln_{e}(D/a^{2})

1

50

61

1.61E05

32.72

2

50

60

2.79E05

32.01

3

100

60

2.39E04

27.32

4

150

61

1.91E03

23.18

5

200

61

4.70E03

21.54

6

250

31

6.81E03

20.59

7

300

31

9.69E03

19.92

8

350

16

1.35E02

18.63

9

400

15

2.44E02

17.03

10

450

9

4.90E02

15.05

11

500

7

1.07E01

13.13

12

225

132

1.07E01

22.12

13

275

61

1.07E01

21.07

14

325

61

1.07E01

19.70

15

375

60

1.10E01

18.07

16

425

55

1.24E01

16.15

17

475

61

1.99E01

14.22

Fusion

8.00E01


Total

1.00000


[In a later
addendum to this report, Farley told us that the total amount of helium
liberated was about 0.32 ´ 10^{9} cm^{3} (at STP) per microgram of biotite.]
Interpretation:
He diffusion
in this sample follows a rather strange pattern, with a noticeable curve
at intermediate temperatures. I
have no obvious explanation for this phenomenon. Because biotite BT1B did not show this curve, I doubt it is vacuum
breakdown. I ran more steps,
with a drop in temperature after the 500ºC step, to see if the phenomenon
is reversible. It appears to
be, i.e., the curve appears again after the highest T step, but the two steps (12, 13) that define this curve had very low gas
yield and high uncertainties. It
is possible that we are dealing with more than one He source (multiple
grain sizes or multiple minerals?).
[We think it is likely there were some very small heliumbearing
zircons still embedded in the biotite flakes, which would be one source.
The other source would be the helium diffused out of larger zircons
no longer attached to the flakes.]
This sample had about twice as much helium as BT1B. Note that despite the strange curvature in GT2, the two biotite
samples have generally similar He diffusivity overall.
[The similarity
Farley remarks upon made us decide that the biotite data were approximately
correct. Because these data
below 300ºC were also about an order of magnitude higher than our creation
model, we supposed that zircon might be a more significant hindrance
to helium loss than biotite, so we turned our attention to zircon. It turned out that our supposition was correct,
which makes it less important to have exact biotite data.]
APPENDIX
C: DIFFUSION RATES IN ZIRCON
Below is a report by Kenneth
Farley (again with our comments in brackets) on his measurements of
helium diffusion in zircons extracted by Yakov Kapusta from Los Alamos National Laboratories core sample GT2480
from borehole GT2 in the Jemez Granodiorite at a depth of 750 meters. Appendix A gives Kapusta’s radioisotopic analysis
of three of the zircons. The
rest, unsorted by size and labeled as sample YK511, were forwarded
to Farley for diffusion analysis. In
Figure 8, we have assumed an effective radius of 30 microns (or length
60 microns) and plotted the points (numbers 1544) which Farley concludes
below are the most reliable. These
points only go down to 300ºC. In
later publications we hope to report similar measurements down to 100ºC.
Report
on Sample YK511
[Jemez Granodiorite] May 14, 2002,
Kenneth A. Farley
We step heated
0.35 mg of zircons from the large vial supplied by Zodiac. We verified
that the separate was of high purity and was indeed zircon. The step
heat consisted of 45 steps so as to better define the He release behavior.
The first 15 steps were monotonically increasing in temperature, after
that the temperature was cycled up and down several times.
Results
[See Table
C1 on next page]. The first
14 steps lie on a linear array corresponding to an activation energy
of ~ 46 kcal/mol and a closure temperature of ~183ºC assuming a cooling
rate of 10ºC/Myr. However steps 15 to 44 [shown in Figures 6(a) and
8], which were cycled from low to high temperature and back, lie on
a shallower slope, corresponding to E_{a }= 34.5 kcal/mol
and T_{c
}= 128ºC. This change
in slope from the initial runup to the main body of the experiment
is occasionally observed and attributed to either:
1) A rounded He concentration profile in the zircons, such
that the initial He release is anomalously retarded. In other words,
the He concentration profile is shallower than the computational model
used to estimate diffusivities assumes. This effect goes away as the
experiment proceeds and the effects of the initial concentration profile
become less significant. This rounding could be due to slow cooling
or possibly to recent reheating.
2) The change
in slope might be due to changes in the zircons during the heating experiment.
For example, it is possible that annealing of radiation damage has occurred.
This sample has a very high He yield (540 nmol/g) so radiation
damage is likely. However the zircons were only marginally within the window where
radiation damage is thought to anneal in zircons, so this hypothesis
is deemed less likely.
Consideration of geologic history
and/or further experiments are necessary to firmly distinguish between
these possibilities.
Conclusion
The most reasonable conclusion from the data is that
the main body of the experiment, steps 1544, yields the best estimate
of the closure temperature, about 130ºC.
This is somewhat cooler than we have observed before in zircons
though the database is not large. Radiation damage may be important
in the He release kinetics from this Herich sample.
Table C1. Diffusion
data for sample YK511
Step

Temp

Helium
4

Time

Fraction

Cumulative

D/a^{2}


ºC

(nmol/g)

(sec)


Fraction

(sec^{1})

1

300

5.337083

3660

0.001259

0.001259

3.78E11

2

300

1.316732

3660

0.000311

0.001570

2.10E11

3

300

0.935963

3660

0.000221

0.001791

1.77E11

4

325

3.719775

3660

0.000878

0.002669

9.34E11

5

350

7.910044

3660

0.001867

0.004536

3.21E10

6

375

18.12294

3660

0.004278

0.008815

1.36E09

7

400

36

3660

0.008498

0.017313

5.29E09

8

425

73.10049

3660

0.017256

0.034569

2.13E08

9

450

106.0761

3660

0.025040

0.059609

5.85E08

10

460

78.89137

1860

0.018623

0.078232

1.27E07

11

470

96.99925

1860

0.022897

0.101130

2.08E07

12

480

117.2479

1800

0.027677

0.128807

3.40E07

13

490

146.8782

1860

0.034671

0.163479

5.38E07

14

500

171.5538

1800

0.040496

0.203976

8.46E07

15

453

149.5962

7200

0.035313

0.239290

2.31E07

16

445

66.45767

7260

0.015687

0.254978

1.16E07

17

400

9.589814

6840

0.002263

0.257241

1.86E08

18

420

10.64711

3600

0.002513

0.259755

3.98E08

19

440

23.19366

3660

0.005475

0.265230

8.69E08

20

460

52.3035

3660

0.012346

0.277577

2.05E07

21

480

102.7062

3660

0.024244

0.301821

4.38E07

22

325

0.357828

3660

8.45E05

0.301906

1.61E09

23

350

0.718240

3660

0.000170

0.302075

3.23E09

24

375

1.690889

3660

0.000399

0.302475

7.62E09

25

400

4.246082

3660

0.001002

0.303477

1.92E08

26

425

8

3660

0.001888

0.305365

3.64E08

27

450

21

3660

0.004957

0.310323

9.70E08

28

460

22.0839

1860

0.005213

0.315536

2.05E07

29

470

33

1800

0.007789

0.323326

3.26E07

30

480

45

1860

0.010622

0.333948

4.47E07

31

490

62.39899

1800

0.014729

0.348678

6.75E07

32

500

82.65262

1800

0.019510

0.368189

9.59E07

33

475

120.222

7260

0.028379

0.396569

3.80E07

34

445

45

7260

0.010622

0.407191

1.53E07

35

400

5.879406

7260

0.001387

0.408579

2.05E08

36

300

0.075983

3660

1.79E05

0.408597

5.26E10

37

320

0.685076

21660

0.000162

0.408759

8.02E10

38

340

1.122111

18060

0.000265

0.409024

1.58E09

39

360

1.986425

14460

0.000469

0.409493

3.49E09

40

380

3.413768

10860

0.000806

0.410299

8.01E09

41

400

5.752365

7260

0.001357

0.411657

2.03E08

42

420

6.126626

3660

0.001446

0.413103

4.30E08

43

440

13.67016

3600

0.003226

0.416330

9.85E08

44

460

30.37821

3660

0.007171

0.423501

2.19E07

[End of report by Kenneth A. Farley.]