Concordia-discordia dating provides a way to day rocks
that are open system. If one makes a naive application of
U-Pb dating one will get false results since lead (Pb) is quite
easily lost to the enviroment. This post will show how
geologists can get around this.
[sup]238[/sup]U decays into [sup]206[/sup]Pb
[sup]235[/sup]U decays into [sup]207[/sup]Pb
[sup]232[/sup]Th decays into [sup]208[/sup]Pb
(Those interested in detail should not that there are intermediate
steps in this decay. None of the three series has any steps
in common and the half-lives of the intermediates is far
smaller than the decay of the U or Th.)
Each of these three radioactive decay series has a different
rate of decay.
Now one get a radiometric date via the simple accumulation
methods usually protrayed in introductory textbooks and
in oversimplifed accounts for laymen. If all three clocks
agree with each other the date is almost certainly secure since
the odds of all three clocks agreeing by chance is quite small.
However most of the time they will not agree because of the
beforementioned fact that lead is often lost to the enviroment
since it is quite volitile. At first this might seem to be
an unsolvable problem. But it is not. And the point of this
post is to show how to solve this problem.
Lets make an assumption that there was no lead when the rock formed.
At first this seems like a bad assumption but fortune has been
good to geologists. There is a common mineral called a zircon.
When it is formed it excludes lead from its structure. Thus if
crystals of zircon are examined this can be done. There is also
an isotope of lead, decays into [sup]204[/sup]Pb that is not
the product of radioactive decay. If the zircon did form
with lead in it, the presence of [sup]204[/sup]Pb will alert
geologists to this fact.
The equation for the radioactive decay in this case is:
D[sub]t[/sub] = P[sub]t[/sub] ( e[sup]kt[/sup] - 1 )
D[sub]t[/sub] is simply daughter isotope at time t. This equation
is equivalent to one of the equations derived in my isochron post.
This equation assumes a closed system.
Now lets look at two of the radioactive decay series at once:
[sup]206[/sup]Pb/[sup]238[/sup]U = e[sup]k[sub]1[/sub]t[/sup] - 1
[sup]207[/sup]Pb/[sup]235[/sup]U = e[sup]k[sub]2[/sub]t[/sup] - 1
k[sub]1[/sub] being the decay constant for the decay of uranium-238
and k[sub]2[/sub] being the decay constant for uranium-235. They
have values of 1.55125 x 10[sup]-10[/sup] year[sup]-1[/sup] and
9.8485 x 10[sup]-10[/sup] year[sup]-1[/sup] respectively.
Now time to get out some graph paper. Lable the x-axis [sup]207[/sup]Pb/[sup]235[/sup]U
and lable the y-axis [sup]206[/sup]Pb/[sup]238[/sup]U. Plug
t=one billion years into the above two equations and plot the
result. Plug in t=two billion years, three billion, and four billion.
Then start plugging in intermediate values. When enough values are
plotted a curve will form. If all the assumptions we have made
are true then when the rock is formed (t=0) it will plot to the
origin (0, 0) of the graph. As time goes by the plot will follow
the curve that was plotted by the above procedure. This curve
is called the concordia.
So far this has been a lot of work for no information that was
not already implicate with the three simplistic clocks discussed
at the start of this post. Now lets see what happens when the
prior assumptions are violated. Lets look at loss of
lead which is the major problem that is the raison de etre
for this post. Lets say that a zircon lost 25% of its
[sup]207[/sup]Pb. If this happens we can say with confidence that
is also lost 25% of its [sup]206[/sup]Pb. The reason is that
two isotopes of lead act in an identical fashion. This little
fact of chemistry has some profound consequences. The percent
of lead lost for each isotope will always be the same. Now
the amounts of each of the isotopes involved are measured for
multiple zircon crystals. There is another useful fact. The
percent of lead lost by each crystal will vary those for all the
zircons the various isotopes of lead will lose the same percent.
(Actually there are other mineral that can be used, but to keep
things simple will just consider zircons.)
The end result of this is when the data for various zircon
crystals are plotted they will fall on a line that intersects
the concordia curve at two places. This line is called a
discordia. The top intersection of the concordia and the discordia
gives the age of the rock. If the lead was lost only in a single
event, the bottom intersection of the concordia and the discordia
will be when the lead loss occured. If the lead loss did not happen
at once then that will not be so. As in the case for the isochron
plots, if the assumptions made are not true, the line will be
destroyed and the geologist will have to try something else.
This method is self-checking.
In this method, t=0 is the last time the zircons were lead free.
Thus a severe heating incident might reset the clock. This
should not comfort YECs since this results in a too young of
a date. (It is always important in dating to keep in mind
what t=0 means.)
Thus secure dates can be obtained using U-Pb clocks were
the system is not closed. And thus one of the YECs
pet objections is again shown to be without merit.
that are open system. If one makes a naive application of
U-Pb dating one will get false results since lead (Pb) is quite
easily lost to the enviroment. This post will show how
geologists can get around this.
[sup]238[/sup]U decays into [sup]206[/sup]Pb
[sup]235[/sup]U decays into [sup]207[/sup]Pb
[sup]232[/sup]Th decays into [sup]208[/sup]Pb
(Those interested in detail should not that there are intermediate
steps in this decay. None of the three series has any steps
in common and the half-lives of the intermediates is far
smaller than the decay of the U or Th.)
Each of these three radioactive decay series has a different
rate of decay.
Now one get a radiometric date via the simple accumulation
methods usually protrayed in introductory textbooks and
in oversimplifed accounts for laymen. If all three clocks
agree with each other the date is almost certainly secure since
the odds of all three clocks agreeing by chance is quite small.
However most of the time they will not agree because of the
beforementioned fact that lead is often lost to the enviroment
since it is quite volitile. At first this might seem to be
an unsolvable problem. But it is not. And the point of this
post is to show how to solve this problem.
Lets make an assumption that there was no lead when the rock formed.
At first this seems like a bad assumption but fortune has been
good to geologists. There is a common mineral called a zircon.
When it is formed it excludes lead from its structure. Thus if
crystals of zircon are examined this can be done. There is also
an isotope of lead, decays into [sup]204[/sup]Pb that is not
the product of radioactive decay. If the zircon did form
with lead in it, the presence of [sup]204[/sup]Pb will alert
geologists to this fact.
The equation for the radioactive decay in this case is:
D[sub]t[/sub] = P[sub]t[/sub] ( e[sup]kt[/sup] - 1 )
D[sub]t[/sub] is simply daughter isotope at time t. This equation
is equivalent to one of the equations derived in my isochron post.
This equation assumes a closed system.
Now lets look at two of the radioactive decay series at once:
[sup]206[/sup]Pb/[sup]238[/sup]U = e[sup]k[sub]1[/sub]t[/sup] - 1
[sup]207[/sup]Pb/[sup]235[/sup]U = e[sup]k[sub]2[/sub]t[/sup] - 1
k[sub]1[/sub] being the decay constant for the decay of uranium-238
and k[sub]2[/sub] being the decay constant for uranium-235. They
have values of 1.55125 x 10[sup]-10[/sup] year[sup]-1[/sup] and
9.8485 x 10[sup]-10[/sup] year[sup]-1[/sup] respectively.
Now time to get out some graph paper. Lable the x-axis [sup]207[/sup]Pb/[sup]235[/sup]U
and lable the y-axis [sup]206[/sup]Pb/[sup]238[/sup]U. Plug
t=one billion years into the above two equations and plot the
result. Plug in t=two billion years, three billion, and four billion.
Then start plugging in intermediate values. When enough values are
plotted a curve will form. If all the assumptions we have made
are true then when the rock is formed (t=0) it will plot to the
origin (0, 0) of the graph. As time goes by the plot will follow
the curve that was plotted by the above procedure. This curve
is called the concordia.
So far this has been a lot of work for no information that was
not already implicate with the three simplistic clocks discussed
at the start of this post. Now lets see what happens when the
prior assumptions are violated. Lets look at loss of
lead which is the major problem that is the raison de etre
for this post. Lets say that a zircon lost 25% of its
[sup]207[/sup]Pb. If this happens we can say with confidence that
is also lost 25% of its [sup]206[/sup]Pb. The reason is that
two isotopes of lead act in an identical fashion. This little
fact of chemistry has some profound consequences. The percent
of lead lost for each isotope will always be the same. Now
the amounts of each of the isotopes involved are measured for
multiple zircon crystals. There is another useful fact. The
percent of lead lost by each crystal will vary those for all the
zircons the various isotopes of lead will lose the same percent.
(Actually there are other mineral that can be used, but to keep
things simple will just consider zircons.)
The end result of this is when the data for various zircon
crystals are plotted they will fall on a line that intersects
the concordia curve at two places. This line is called a
discordia. The top intersection of the concordia and the discordia
gives the age of the rock. If the lead was lost only in a single
event, the bottom intersection of the concordia and the discordia
will be when the lead loss occured. If the lead loss did not happen
at once then that will not be so. As in the case for the isochron
plots, if the assumptions made are not true, the line will be
destroyed and the geologist will have to try something else.
This method is self-checking.
In this method, t=0 is the last time the zircons were lead free.
Thus a severe heating incident might reset the clock. This
should not comfort YECs since this results in a too young of
a date. (It is always important in dating to keep in mind
what t=0 means.)
Thus secure dates can be obtained using U-Pb clocks were
the system is not closed. And thus one of the YECs
pet objections is again shown to be without merit.
