Jökull - 01.12.1975, Page 23

that the emission of aparticles damages the
lattice, increasingly so with time. This means
that in a 1000 My old mineral, the present co-
efficient of diffusion, if measured, may be quite
different from the values of earlier times, and
could not be used for the whole life-time of
the mineral, e. g. with the aim of correcting
the ages.
The great influence of crystal size on dif-
fusion loss, immediately suggests tests of sucli
losses in dating work by single crystals: From
each rock sample in K/Ar-dating, at least 10
sanidine crystals are dated, from the largest to
the smallest ones, and of the most various
shapes. The same is done for biotite and other
potassium-bearing minerals in the sample. If
the age turns out to be independent of size
and shape for some mineral species, then dif-
fusion seems to be excluded as an error. And
if two or more mineral types have passed
this test, also washing by penetrating ground-
water seems excluded. Such dating would
seem to be reliable. If, on the other hand. the
ages increase regularly with mineral size, some
data have at least been obtained to aid in the
search for a correction of the age found for
the largest minerals. We shall return to the
problems of single crystals dating in another
connection, but only add here en passant the
phenomenon that during the grinding of large
crystals of potassium feldspars, loss of argon
from grains of diameter 10—80 microns is very
obvious (Dalrymple and Lanphere, 1969, p. 147).
The equation t2 = ti (r/R)2 explains this in all
essentials, even if the coefficient of diffusion is
found also to change from the macrocrystals to
grains in this micron-range. The latter effect
may in part be due to lattice dislocations or
lattice distortion in the grinding process.
To discuss further the importance of dimen-
sion, we mention whole-rock dating. For acid
rocks of fine grain, we only point out that
theoretically the diffusion from mm-size grains
is 100 times that from cm-size grains, if the
shape is the same. The escaped argon, say,
reaches the seams between crystals, and it is
then along these that groundwater is capable
of percolating and absorbing the argon.
As to basalts, the matter is very complicated.
The low content of potassium leads to the ex-
pectation that “from geochemical considera-
tions, most of the potassium . . . should reside
in the last components to solidify — for example,
in interstitial material, which is usually glass or
fine-grained feldspar. Observations with elec-
tron microprobes on potassium distribution in
basalts have confirmed this expectation” (Dal-
rymple and Lanphere, 1969, p. 181). “For this
reason, a careful evaluation of the condition
and composition of the interstitial material is
very important for whole-rock dating” (I. c., p.
182).
We have data (l.c.) on such interstitial potass-
ium feldspar lamellae (considered in b)) of a
thickness of 1—3 microns. If we expect inter-
stitial potassium feldspar grains also to be in
the micron range, we must expect their loss of
argon to be 108 to 108 times faster than the
loss from spherical crystals in the cm-range. And
as the minute grains in the basalts are inter-
stitial, as is the groundwater, loss of argon from
basalts would be expected, and is well known
to be very often far too serious and obvious to
allow K/Ar-dadng.
b) The plate. Here we use again the fact
that diffusion is mathematically analogous to
heat conduction, and consider an instructive
special case of the latter. A slab of thickness
2-1 is heated by a homogeneously distributed
source, A0 energy units per cm3. At the same
time its sides are kept constantly at the original
temperature of the slab, T0. This means that
there must be some cooling device at the sides,
to keep the temperature constant. Within the
slab, the temperature rises, and a temperature
gradient towards the sides is created at the
same time. This means that a heat flow goes
towards the cold sides, depending further on
the conductivity K and the thickness of the
slab.
As the temperature in the middle of the slab
rises, the gradient and the heat flow towards
the sides increases, until ultimately a state is
reached, when this loss of heat becomes equal
to the produced heat within the slab. The
central temperature then has reached a final
equilibrium value Tmax = A0-12/2K, when T0 is
taken to be zero (Carslaxu and Jaeger, 1959, p.
130-131).
This shows that by a given heat production
A0, and conductivity K, the final central tem-
JÖKULL 25. ÁR 2 1