Jökull - 01.12.1975, Page 22

still less possibility o£ measuring an equilibrium
in argon concentration between sanidine or
other potassium-bearing mineral on one hand,
and water on the other. But without this know-
ledge, it seeems impossible to have such a
physical insight into the processes in the na-
tural environment, that one could state whether
argon — or other daugther elements of a radio-
active process — would tend to diffuse into the
groundwater or the reverse way. If the argon
equilibrium were reached rapidly, in a geo-
logical sense, by diffusion into the mineral,
then for the rest of the time, the addition of
40Ar could lead to an outward diffusion of an
argon mixture steadily enriched in 40Ar, re-
sulting in too low an age.
To these problems must be added the pos-
sibility that groundwater is capable of penetrat-
ing minerals due to a hydrostatic gradient, cf.
Section 1, and in that way wash out radiogenic
elements in a significant amount. The physical
processes here mentioned would tend to affect
in a comparable way the measured age of
single minerals of the same type and similar
size in a certain rock. The near-equality of ages,
based on such single minerals of the same type,
would then be no guarantee of correct dating.
The samples from a certain rock would simply
have a common history of temperature, depth,
groundwater, and diffusion effects. Physical
understanding of the processes in nature which
can influence a radiometric clock are clearly
most essential. In the next section we continue
this study by considering the role of dimension,
or crystal sizes, in diffusion frorn or into rniner-
als.
4. THE ROLE OF DIMENSION IN
DIFFUSION LOSSES FROM MINERALS.
Diffusion in isotropic solids is mathematical-
ly analogous to heat conduction; the tempera-
ture diffusivity k has only to be replaced by
the material diffusivity D. We can, therefore,
use exactly treated cases of thermal losses to
clucidate diffusion losses, and for the present
purposes it is sufficient to consider two simple
cases of heat loss.
a) The sphere. A compact homogeneous
sphere of radius R and the initial temperature
T cools by conduction while the surface is kept
at a constant lower temperature, which is call-
20 JÖKULL 25. ÁR
ed zero temperature. After a time ti, the heat
content in the sphere has been lowered by
50%, say. Another sphere of radius r, but other-
wise equal conditions, looses 50% of its lieat in
the time t2. Then t2 =ti ■ (r/R)2. Hence, i£ a
spherical mineral of radius 1 cm looses by dif-
fusion 50% of a certain element in ten times
the age of the earth, i. e. 4.5 X 1010 years, then
by otherwise unaltered conditions, a mineral
of radius 1 micron (10~4 cm) will loose 50%
in 450 years. (For r = 100 microns, cf. zircon
grains used for U/Pb-dating, the corresponding
time of 50% loss would be 4.5 My).
The choice r = 1 micron was not used here
only to demonstrate the very great influence
of mineral size on diffusion in minerals, it is
not at all an unrealistic choice in connection
with at least certain cases of radiometric dating.
As a provisory example, we mention that
"crystals of biotite and other minerals in
granitic or metamorphic rocks commonly en-
close minute specs of crystals (sphene, monazite,
xenotime, zircon, and so on) containing uran-
ium or thorium” (Verhoogen et al., 1970, p.
206). Such specs are the explanation of pleo-
chroic halos. These are formed of concentric
circles with radii of a few microns, which proves
that the specs must be even smaller. What this
case shows is that e. g. the lead produced by
the U- and Th-radioactive series might diffuse
rather easily from the specs, and so influence
the ratio of U or Th to their stable end pro-
ducts within the specs. The loss of lead is a
well-known assumption in dating work. It leads
to ages lying on a straight line in a Concordia
diagram — if the duration of loss is relatively
short and comes at the end of a long time of
undisturbed lead accumulation — and so to the
correct age. But we might add the theoretical
possibility that individual internal radioactive
members of the two U- and the Th-series are
partially lost by diffusion, not least from
micron-size specs. Such escaped members are
first caught in mm- to cm-size crystals, contain-
ing the specs. Here, such radioactive members
of the chains carry on their production, but
both here and within the specs the element
concentrations would be different from those
of radioactive equilibrium, and the effects of
this process on the quantity of the stable end
products are not quite obvious. Add to this