Stories of the Lithosphere

Gold, Pollution, and Farmland--Part 1, Partitioning and Mass Balance

Earth Science Essentials

by Russ Colson

Varie-colored stream stones in a colorado mountain stream

Lecture Recap

Although the Earth is made up of the whole periodic table of elements, the elements are not evenly distributed. Elements get combined in a variety of ways in different parts of the earth. The effect of this recombination of elements can be seen in all the different colors of rock seen in the picture of a mountain stream above. It's more than just differences in color. Some places have more copper, other places gold; someplaces have oil, and some places have great farmland.

This uneven distribution of resources has had a profound impact on development of human societies and the interaction between societies.

But, what causes that uneven distribution? How can we go from one homogeneous material to many materials with different composition?

The process of turning one homogeneous material into two or more new materials each with a different composition from the original is called geochemical differentiation.

Key ideas from the lecture include the following:

Value: 2

Phase change and elemental partitioning :

When ice partly melts, we get liquid water, and the liquid has the same composition as the solid. This is true for materials with only a single chemical component (in this case, H2O). However, if more components are involved, then the liquid will have a different composition from the solid. For example, if we partly freeze salt water, the salt will preferentially remain with the liquid, and the ice will have less salt than the original water.

You can think of this as follows. Suppose that you have 90 molecules of water with 10 salt "molecules" in it. With 'W' for water molecule and 'S' for a salt 'molecule' you get:

W W W W W W W W W S W W W W W W W W W S W W W W W W W W W S

W W W W W W W W W S

Value: 2

Suppose that the salt prefers the liquid over the solid by a factor of 9 (the partition coefficient D = concentration of salt in solid/concentration of salt in liquid = 0.11) (salt actually prefers the liquid to a much greater degree than this).

If you freeze half of the salt water (50 molecules total), while maintaining the chemical balance (partition coefficient), you get

Solid:

W W W W W W W W W W W W W W W W W W W W W W W W W W W W W S

W W W W W W W W W W W W W W W W W W W W

Liquid:

W W W W W W W W S S W W W W W W W W S S W W W W W W W W S S

W W W W W W W W S S W W W W W W W W W S

Value: 2

If this were a chemistry class instead of earth science, I would point out that when dissolved in water, salt doesn't really exist as a molecule, but rather as sodium and chlorine ions (that's why I put 'molecules' in quotes).

We're now going to do a puzzle somewhat like what happens in a basaltic magma chamber such as that below Hawaii. The mineral olivine crystallizes from the magma and, being more dense than the magma, sinks (this process is somewhat more complex in a real magma chamber).

We are going to think of a simplified olivine crystal with a composition of Mg₂SiO₄, which is 2 MgO 'units' and 1 SiO₂ 'units'.

Suppose we start with an original batch of magma as shown below (Blue for SiO₂, Red for FeO, and Green for MgO).

5 red, 6 green, and 7 blue Christmas tree balls

Value: 2

The next few questions address how the composition of the remaining melt will change if olivine crystallizes from it.

Now do a numerical simulation. Remove two Mg₂SiO₄ units from the melt (2 SiO₂ and 4 MgO) and calculate how the concentration of each of the components changes in the remaining melt.

5 red, 3 green, and 5 blue ornaments in the melt and 4 green plus 2 blue ornaments in the olivine crystals

Value: 2

Consider the graphs below. Which one portrays how we expect the composition of lave flows that erupt from a particular magma chamber to change through time if the process above is the main chemical process in the magma chamber.

001

graphs with %FeO on the Y axis, increasing upward, time on the X axis with later to the right. Slope in A is from upper left to lower right, in B is from lower left to upper right, C line is horizontal, D line is veritcal

Value: 2

Go through the same exercise, but change the starting amounts (below)

6 red, 6 green and 6 blue Christmas treen ornaments

Value: 2

Notice that if the partition coefficients is greater than 1 (with the solid on the top as is typically done), then the concentration in the melt decreases. We call this a compatible element or component--it is compatible in the primary solid phase. If the partition coefficient is less than 1, then the concentration in the melt increases. We call this an incompatible element or component. It is incompatible in the primary solid phase. If the partition coefficient equals one then the concentration in the melt doesn't change. This almost never occurs in nature.

Also notice that phases and chemical components are not the same thing! Olivine, for example, contained both MgO and SiO₂ (and in real life contains FeO and small amounts of other elements as well). Phases have many chemical components in them (essentially the whole periodic table of elements). Water is a phase, but in addition to H₂O, it can have salt, sugar, or the whole periodic table of elements dissolved in it.

Yttrium Puzzle :

MgO, FeO, and SiO₂ are major components of magma, meaning that they make up a substantial portion of most silicate magma as well as many important minerals. The partition coefficient is more often used for trace elements, those present at very low concentration in most natural systems.

Y (Ytrrium) is a trace element. It behaves much like Yb (Ytterbium), my favorite element that I mentioned in lecture.

Suppose that you do experiments in a laboratory to measure trace element partition coefficients (this is the kind of work that I did for my Ph.D. dissertation--on Yb!). Here is a simplified puzzle. Given the experimental results below, is the partition coefficient for Y (Partition coefficient calculated with the concentration of solid on top), less than one, equal to one, or greater than one?

Relative concentrations of Y in lava and solid under hot conditions and hotter conditions. There is more lava and less solid when hotter, with the Y atoms being diluted in more melt.

Value: 2

Temperature inside the Moon Puzzle :

Partition coefficients are not constant but vary as a function of temperature, pressure, and composition. Here is a conceptual example of the kinds of questions that geologists can answer using partition coefficients, taking into account how they vary with temperature. See if you can take all the information and figure out the answer to the puzzle! Take note that not all the experiments and measurements listed below will necessarily address the question!

There are many volcanic rocks on the Moon. Suppose we want to know the temperature at which the rocks melted that from that lava . The melting happened deep inside the Moon. We can't get to the inside of the Moon to measure the temperature! (We can't even get deep inside the Earth to measure the temperature there!). Even if we could measure the temperature inside the Moon today, the temperature there when the lava was formed long ago may have been very different!

Model for origin of lava on the Moon (or Earth):

volcano2

Experiment/Measurement #1: You measure the temperature for several weeks. You notice that the temperature starts out about -181ºC and increases to a maximum of about 101ºC two weeks later. Two weeks after that it is back down to -181ºC then back up to 101ºC in another two weeks. Why do you suppose it keeps getting hotter and colder?

Library research: The Origin of the Moon (1986) gives an estimate of the total average composition of the Moon. Let's consider for this problem that this composition is a good estimate of what exists in the Moon's interior where the partial melting we are interested in occurred. The concentration of Iron oxide (FeO) reported in Origin of the Moon is 13%, meaning that 13 percent of the Moon is Iron oxide (FeO). The rest of it is other chemical components, such as Silicon dioxide (SiO₂), Aluminum oxide (Al ₂O₃), Magnesium oxide (MgO), Calcium oxide (CaO), Sodium oxide (Na₂O).

Experiment/Measurement #2: Many samples of Lunar Maré were brought back by the Apollo missions from 1969 to 1972. You take one sample (sample # 12009) and measure its composition (for example, using X-ray fluorescence). That composition is (from Planetary Science, A Lunar Perspective, 1982) Silicon dioxide (SiO₂) = 45%, Aluminum oxide (Al₂O₃) = 8.6%, Iron oxide (FeO) = 21%, Magnesium oxide (MgO) = 11.6%, and Calcium oxide (CaO) = 9.4%. (The total does not add up to 100% because only a few components are given here for simplicity's sake).

Experiment/Measurement #3: You do experiments to measure the partition coefficient for FeO between solid and melt. Your results are shown symbolically below. HInt: you will need to calculate the partition coefficients at each temperature and you may want to draw a graph of the partition coefficient as a function of temperature

partitio

What was the temperature inside the Moon where the melting occurred that produced the lava on the surface?

Value: 2

The Problem at Gramma's Well :

One day you are out spraying Death-X to get rid of green bugs in the alfalfa field. The day is hot and long. You decide to get a drink of cool water from the cattle tank over by Gramma's Well. After skimming back the algae, you take a long, cool drink. Unfortunately, when you bend over, the tank of Death-X falls off your back and spills into the ground.

003

Oh my. The next rain might wash the poison right down through the sediment to the water table and contaminate Gramma's Well. The problem is, you don't want to have to own up to your blunder, and maybe the Death-X won't reach the water table. You know that if the Death-X partitions into sediment instead of into the water, then the sediment will act as a filter and remove the poison before it ever gets to the water table.

You scoop us some of the sediment for testing, and take the last little bit of Death-X left in the tank, and head back home to experiment.

You add 100 grams of water and 50 grams of sediment to a beaker, and to that you add 1 gram of Death-X. You stir the mixture to reach equilibrium and then measure the concentration of Death-X in the water. The concentration is 0.01%.

Value: 2

(A*) So, what is the partition coefficient for Death-X between the sediment and water (Concentration in the sediment on top) and do you have to tell Gramma?

a. D = about 0.02 and being a good grandchild, you will of course let Gramma know about the accident, but you can safely tell her that the Death-X probably won't reach the water table.
b. D = about 0.02 You have to tell Gramma what you did, and warn her that the well water probably won't be safe to drink.
c. D= about 200 and being a good grandchild, you will of course let Gramma know about the accident, but you can safely tell her that the Death-X probably won't reach the water table.
d. D = about 200, You have to tell Gramma what you did, and warn her that the well water probably won't be safe to drink.

Last updated 11/21/2016. All text and pictures are the property of Russ Colson.