Jökull - 01.12.1975, Side 25

Tmax = T0 + A0 • 13/2K. This sliows that if the
original temperature of the slab and the con-
stant temperature at its sides (temperature of
“surroundings”) is raised by a certain amount,
Tmax rises by the same amount.
The above solution for heat flow can be used
directly for the diffusion from a mineral plate,
of a stable element which is a daughter ele-
ment in a radioactive process, taking place
evenly within the plate. We have only to re-
place k by the respective coefficient of diffu-
sion, D, and the temperature T by the con-
centration C of the element. The letter A0 now
means the rate of production of the respective
element within the plate.
Only in the case D = 0, we have C = A0 • t
everywhere in the plate. This would leacl to an
infinite concentration gradient for x/1 = 1,
which is not always easy to accept from a
physical point of view. When D t 0, Fig. 2
shows the rise of C as a function of x and t.
And there is an upper level for the concentra-
tion in the middle plane, only reached in in-
finite time: Cmax = C0 + A0 • l2/2Dk, where k
is a constant for each mineral type and C0
corresponds to T0.
We see from this formula how important it
is in radiometric dating to know D, and we see
the importance of the dimension: If the thick-
ness falls from 1 cm to 1 mm, Cmax — C0 drops
by a factor of 100.
As groundwater is generally capable of flow-
ing along the linings between the minerals,
even in such a dense rock as granite, and ab-
sorbs many elements, the condition C0 = 0
could very well be realistic. (For the moment
we shall assume that the groundwater does not
otherwise contain an element under study). At
the surface of every mineral, containing a radio-
active daughter element, the concentration is
then zero. Fig. 2 then gives a realistic idea of
the loss of the element frorn the mineral plate.
If D, A0, and 1 are known, the measured age of
the plate can be corrected to give the true age,
unless the concentration in the central plane
is too close to Cmax. But obviously it need not
be true, that if 10 similar mineral plates from
the same rock give similar measured ages, then
the average is the true age. Instead, the ages
for various sizes and shapes of the same type of
radioactive mineral must be compared, and the
test of reliability follows the same lines as given
in a).
c) Whole-rock dating of basalts, and the sites
of the potassium.
We can now come back to Iv/Ar-dating of
basalts. If the potassium is essentially found in
interstitial potassium feldspar lamellae of a
thickness of, say, 2 microns, then Cmax in such
lamellae is a factor of 10e less than for 2 mm
thick mineral plates. This means that even if
there is no sign that a 2 mm plate has lost a
significant amount in 1000 My, a 2 micron
lamella might still have lost a very serious
amount (1000 times more) in 1 My.
With this in mind, it is hardly surprising
that basalts are, as a rule, extremely difficult
to date by the K/Ar-method, the only method
which is applicable for ages below about 50 My.
But it happens, nevertheless, that fresh, or even
somewhat altered holocrystalline basalts give
ages which seern significant. Firstly, the mea-
sured ages for two or a few more samples from
the same lava flow turn out to be very similar.
This either means that there was no loss of
argon, or the argon loss was the same because
the rock was the same, and had an identical
geological history. Secondly, when dating lava
sequences, ancl selecting the most promising
lavas, it turns out that the ages in the main
agree with the known stratigraphic order of
the lavas.
Again there are two possible interpretations.
Either there was no serious loss of argon or,
because of the close similarity of the retention
capacity of the selected lavas, their stratigraphic
order was preserved, in accordance with the
rule presented in Fig. 2 — in spite of a possible
serious argon loss in all cases. Fig. 2 shows most
clearly that measured ages can be in keeping
with the stratigraphic order and yet far below
the true ages. Such measured ages of basalts
cannot be considered to be reliable, unless in
every dating a special study of the micron-size
interstitial potassium-bearing grains or lamellae
proves that these minute crystals, or sometimes
glass lamellae, cannot have lost serious amounts
of argon at temperatures indicated by second-
ary minerals — during times of 30—50 My, even
though we know that 10—80 micron grains loose
argon very clearly during laboratory work.
JÖKULL 25. ÁR 23