# Modeling U-Series Concordia/Discordia Using STELLA

Kirsten Menking

, Vassar College, Dept. of Geology and Geography

Author Profile#### Summary

U-Series dating techniques are widely used to determine the absolute ages of some of Earth's oldest rocks, but the concordia/discordia diagram can be quite difficult for students to grasp. I have produced a STELLA-based lab exercise to develop students' understanding of this important chronologic technique. Students create models of the two isotopic decay systems and run these models to create the concordia diagram. They then carry out experiments in which they "add" or "remove" varying amounts of lead or uranium in simulation of metamorphism. In the course of the lab, students are introduced to the concepts of exponential decay and secular equilibrium as well as modeling concepts such as the creation of if-then statements.

## Context

**Audience**:

undergraduate geology majors

**Skills and concepts that students must have mastered**:

The student needs a basic introduction to the STELLA modeling software.

**How the activity is situated in the course**:

This exercise is one of several that I do in my Computer Methods and Modeling in Geology course. This is senior-seminar level course, though it has been taken by students as young as sophomores, who have done fine. Other modeling exercises in the course cover the global phosphorus cycle, Earth's energy balance and radiative equilibrium temperature, the impact of climate change on a chain of lakes in eastern California, the flow of ice in glaciers, scarp retreat, and James Lovelock's Daisyworld.

## Goals

**Content/concepts goals for this activity**:

Students learn about U-Pb decay series, secular equilibrium, and how the concordia-discordia diagram is constructed.

**Geologic skills**:

**Higher order thinking skills goals for this activity**:

**Other skills goals for this activity**:

The Radioactive Decay exercise has several additional purposes:

1) To convey concepts necessary in modeling a system involving exponential growth and decay

2) To introduce elementary differential equations

3) To convey the difference between closed and open systems

4) To introduce if-then-else logical statements in modeling

1) To convey concepts necessary in modeling a system involving exponential growth and decay

2) To introduce elementary differential equations

3) To convey the difference between closed and open systems

4) To introduce if-then-else logical statements in modeling

## Description of the activity/assignment

U-Series dating techniques are widely used to determine the absolute ages of some of Earth's oldest rocks, but the concordia/discordia diagram can be quite difficult for students to grasp. In particular, the fact that differing amounts of lead and uranium loss from minerals such as zircon can be used to determine not only the original formation age, but also the time of metamorphism of a rock like granite, is a challenging concept. Making use of previous workers' web-published excercises on radiometric decay, I have produced a STELLA-based lab exercise to develop students' understanding of this important chronologic technique. Students create models of the two isotopic decay systems, 238U --> 206Pb and 235U --> 207Pb, and run these models for 4.5 billion years to create the concordia diagram. They then carry out experiments in which they "add" or "remove" varying amounts of lead or uranium in simulation of metamorphism. The uranium-lead ratios at the end of the simulation allow the discordia line to be plotted on top of the concordia diagram and the ages of original crystallization and metamorphism to be determined from the points of intersection of the two lines. In the course of the lab, students are introduced to the concepts of exponential decay and secular equilibrium as well as modeling concepts such as the creation of if-then statements.

## Evaluation

I'm always interested in improving my exercises, so if anyone uses this and finds problem spots, I hope they will contact me. I have used graded lab assignments and a student attitudinal questionnaire to gauge students' understanding of this exercise.

## Logistics

The STELLA box modeling software from isee systems. No major logistical challenges as long as one has a lab license for STELLA.