From: cust_ts@klaava.Helsinki.FI (Tero Sand)
Newsgroups: sfnet.keskustelu.evoluutio
Subject: Radioaktiiviset i{nm{{ritysmenetelm{t
Date: 13 Nov 92 08:28:35 GMT
Distribution: sfnet
Organization: University of Helsinki

T{ss{p{ taas vaihteeksi isochron FAQ. Lampolan sopii lukea ja sitten
kertoilla, miten i{nm{{ritysmenetelm{t ovat pieless{.

	Tero Sand

-----------------------------

========================================================================
Author:		Chris Stassen
Subject:	FAQ: Isochron Dating
Updated:	02/27/92
========================================================================

Outline:

	1. Generic Radiometric Dating
	2. What's wrong with non-isochron dating methods?
	3. Generic Isochron Dating
	4. What's NOT wrong with isochron dating methods?
	5. For further information (some things to read)

(1)  Generic Radiometric Dating

	Generally, radiometric dating is done by performing a simple
	calculation on a sample, involving three measurements:

    a)	The first "measurement" is actually a "known quantity" -- the
	half-life of the radioactive element used by the method.  This
	value can be experimentally measured in a lab -- but since many
	experiments have failed to effect a noticeable change in the
	rates relevant to radiometric dating, it is usually taken from a
	table.

    b)	The second measurement is the amount of "parent" element (the
	radioactive element used by the method).

    c)	The third measurement is the amount of "daughter" element (the
	element that the radioactive one decays into).

	Since each atom of the parent element decays into one atom of the
	daughter element, we calculate that the original quantity of the
	parent element is the sum of the current amounts of parent and
	daughter elements.  We then apply the following (frosh physics)
	equation (the infamous "radioactive decay" equation):

		P =	 P0 / (2 ^ (T / H) )

	   or	P = (P + D) / (2 ^ (T / H) )

	Where:
		P is the current amount of parent element
		P0 is the original amount of parent element (= P + D)
		T is time that has passed ("age" of the sample)
		H is the half-life of the element

	Solving for T, we calculate the sample's age as:

		T = H * log2 ( (P + D) / P)


(2)  What's wrong with non-isochron dating methods?

	Obviously, there are a few assumptions above which have been
	made for the sake of a simple expanation, but which will not
	always work in the real world.	These include:

    a)	The amount of daughter element at the time of formation of the
	sample is zero.  Possible ways to avoid this problem include:
	work on a mineral that can't incorporate any of the daughter
	compound when it forms; somehow calculate the amount of initial
	daughter product and subtract it out.

    b)	No parent element or daughter element has entered or left the
	sample since its time of formation.  Possible ways to avoid this
	problem include: only date samples whose geological history does
	not appear to include events which might cause this problem; date
	several different parts of the same sample and only accept the
	result if they all agree because contamination is not likely to
	affect all parts of a large sample in the same way.

	The invention of isochron methods solves both of these problems
	at once!  Read on...


(3) Generic Isochron Dating

	Isochron dating requires a fourth measurement to be taken, which
	is the amount of a _different_ isotope of the daughter element.
		In addition, it requires that the second through fourth
	measurements be taken from several different objects which all
	formed from a common pool of materials.  (Rocks which include
	several different minerals are perfect for this.)

	When any rock forms, minerals "choose" atoms for inclusion by
	their _chemical_ properties.  Since the two isotopes of the daughter
	element have identical chemical properties, they will be mixed
	evenly when the sample forms.
		However, the parent element, with different properties,
	will not be mixed evenly relative to the daughter elements.  So,
	at formation time, a sample would contain measurements like the
	following:

	Mineral No.	Parent		Daughter	Isotope
	---------	--------	--------	--------
	    1		 4 gm		 1 gm		 2 gm
	    2		 2 gm		 4 gm		 8 gm
	    3		 6 gm		 2 gm		 4 gm

	Note that (for this example) there is always twice as much of the
	"isotope" as there is of the "daughter" in every mineral.  Also
	note that the ratio of "parent" element to either one of the
	others varies (as the parent element has different chemical
	properties).  After one half-life's worth of time has passed, the
	values will have changed (as half of the parent atoms in each
	mineral will have decayed into daughter compounds):

	Mineral No.	Parent		Daughter	Isotope
	---------	--------	--------	--------
	    1		 2 gm		 3 gm		 2 gm
	    2		 1 gm		 5 gm		 8 gm
	    3		 3 gm		 5 gm		 4 gm

	Note that half of the amount in the Parent column has been
	taken away and added to the Daughter column for each mineral.
	Also note that the Isotope column, since it doesn't decay and
	isn't a decay product, doesn't change at all.

	I can do some math here, but it's easier to see it on a graph.
	The isochron graph is drawn by graphing D/I vs. P/I.  The
	first set of measurements results in:


    D/I    1 -
	     |
	     |
	     |
	     -	   (2)................................(3)...........(1)
	     |
	     |
	     |
	     +-------------|-------------|-------------|-------------|
	    0		  0.5		 1	      1.5	     2

					P/I


	Note that all of the samples lie on a straight, flat line.  This
	is what we expect: they all have the same D/I ratio,  and hence
	the same Y-value.
		Note that, if the sample were homogeneously distributed
	with respect to parent and daughter, then all of the data points
	fall on the same point and no line can be derived.

	The graph for the second set of measurements is:

	   2 -
	     |
	     |
	     |
	     -			      .(1)
	     |			    ..
	     |		       ..(3)
	     |		    ...
    D/I    1 -		 ...
	     |	       ..
	     |	     ..
	     |	  (2)
	     -
	     |
	     |
	     |
	     +-------------|-------------|-------------|-------------|
	    0		  0.5		 1	      1.5	     2

					P/I

	Once again, all the points lie on a straight line.  And the slope
	of the line is 1.  (I know it doesn't look like it on the screen,
	but that's because I used different units for X and Y -- you can
	calculate it for yourself from the table above.)

	We can make a simple table of slope of line versus age:

		Slope			Age
		--------		-------------------
		   0			 0
		   1			 1 half-life
		   3	  		 2 half-lives
		   7			 3 half-lives
		  ...			 ...
		   N			 log2( N + 1 ) half-lives


(4) What's NOT wrong with isochron dating methods?

	Now that the mechanics of plotting an isochron have been
	described, we will return to address the problems that were
	mentioned before and describe why isochron methods don't fall
	prey to them.

    a)	Initial daughter compound.

	Any amount of initial daughter compound is compensated by the
	isochron method.  If one of the minerals happened to have none
	of the parent element (the Y-intercept of the line), then its
	amount of daughter compound wouldn't change over time -- because
	it has no parent atoms to produce daughter atoms.
		Regardless of whether there's a data point there or not,
	the Y-intercept of the line doesn't change as the slope of the
	line does.  (You can verify this for yourself; the Y-intercept
	of both lines above is 0.5.)  The Y-intercept of the isochron
	line actually gives the ratio of daughter to the other isotope
	at the time of formation.
		For each mineral, we can then measure the amount of the
	other isotope and calculate the amount of daughter product that
	was present when the sample formed.  If we then subtract it out,
	we could derive a "traditional" age for each mineral by the
	equations described in the first section.  Each such age would
	match the result given by the isochron.

    b)	Random contamination (parent or daughter entering or leaving the
	system)

	For the sake of brevity, our example only included three data
	points.  While isochrons are performed with that few data points,
	their value is not treated as seriously as those which have tens
	of points.
		Any non-systematic contamination is _extremely_ unlikely
	to leave all of the data points on the line.  Even in our little
	example, any contamination of one of the minerals would require
	a specific contamination of one of the other two in order to keep
	all three points on the same line.

	When we get to an isochron with tens of data points, the suggestion
	that contamination "just happened to place the points on a (fake)
	isochron line" can be discarded out of hand.  It's too unlikely.
	[Now, there is a form of isochron contamination, known as "mixing,"
	which basically amounts to a _partial_ resetting of the isochron
	clock.	However, there are tests to detect it.]

    c)	General dating assumptions

	All radiometric dating methods must assume certain initial
	conditions and lack of contamination over time.  The wonderful
	property of isochron methods is that *if one of these assumptions
	is violated*, it is nearly *certain* that the data will show that
	by the points not plotting on a line.


(5) For further information, see:

	G. Faure, _Principles of Isotope Geology_  (a textbook/handbook;
		very technical, but very good.)

	G. B. Dalrymple, _Radiometric Dating, Geologic Time, and the Age of
		the Earth_  (Email Chris Stassen if you want a copy.)

	A. N. Strahler, _Science and Earth History_, pp. 130-135

========================================================================
-- 
Chris Stassen			408-943-0630			stassen@alc.com


-- 
	EMail: cust_ts@cc.helsinki.fi   or   custts@cc.helsinki.fi
   "I feel most ministers who claim they've heard God's voice are eating
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intestinal disorder, not a revelation." - Reverend Jerry Falwell
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