Wirth – Magmatic Differentiation Using M&M’s®
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USING AN M&M® MAGMA CHAMBER TO ILLUSTRATE
MAGMATIC DIFFERENTIATION
Karl R. Wirth
Geology Department
Macalester College
St. Paul, MN 55105
wirth@macalester.edu
BACKGROUND AND NOTES FOR INSTRUCTORS
Purpose:
 improve student understanding of fractional crystallization and magmatic differentiation
 provide students an opportunity to utilize concepts (e.g., stoichiometry) learned in the
mineralogy course
 reinforce concepts (e.g., classification and chemical variation diagrams) learned in the
petrology course
 provide students with practical experience designing and using spreadsheets
 enhance student knowledge and appreciation of the historical origins of an important
concept in geology
Introduction
An understanding of the process of magmatic differentiation is essential to the study of the
petrology of igneous rocks. Students at Macalester College typically first encounter this concept
in the introductory geology course when they learn about Bowen’s reaction series and fractional
crystallization. After a brief introduction to phase diagrams in the mineralogy course, students
generally receive a thorough treatment of magmatic differentiation in the petrology course.
Despite trying several different approaches to “teaching” the concepts of element
incompatibility, fractional crystallization, and magmatic differentiation in the petrology course, it
was clear that many students still did not have a firm understanding of the details of
differentiation. In retrospect, this made sense; the students didn’t have any real-world
experience with fractional crystallization, they had only heard or read about. Although it would
be possible to have students conduct a phase diagram experiment to illustrate the differentiation
process, this would likely require specialized equipment and would be time-intensive. The
M&M® magma chamber exercise was developed to provide students first-hand experience with
the process of magmatic differentiation by fractional crystallization using a simple experiment.
This experiment is currently being used in both the petrology and introductory geology courses
at Macalester College. Most students indicate that the exercise is both enjoyable and
informative. Student knowledge of fractional crystallization and magmatic differentiation, as
indicated by exam results and course projects, has increased significantly since incorporating this
exercise into the curriculum.
A Brief History of the Theory of Magmatic Differentiation
The origin and evolution of the theory of magmatic differentiation is rich with history.
However, the history of this important concept is rarely examined in detail in most textbooks;
many currently available petrology textbooks only trace the theory of differentiation back to N.L.
Wirth – Magmatic Differentiation Using M&M’s®
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Bowen. This contrasts with many biology textbooks and curricula in which there is much greater
emphasis on the historical development of key concepts. It is important to reveal some history to
students, not only to deepen their understanding of the important concepts, but also to help them
understand the process of science itself. Several recent publications (Pearson, 1996; Young,
1998; Estes et al., 2000) describe key aspects of the history of the theory of differentiation and
are the basis of the summary provided below.
Prior to the development of the idea of magmatic differentiation in the late nineteenth
century, magmas were generally regarded as originating from two distinct sources, one silica rich
and the other silica-poor. Intermediate lavas were explained as being a mixture of these two
sources. At the time, some geologists suggested these different magma sources originated from
concentrically distributed zones within the earth and others argued for a secular change in
erupted magma compositions. Early ideas about differentiation began to emerge in the mid to
late-1800’s with the recognition of mineralogical and chemical similarities among suites of
igneous rocks (Young, 1998). However, it was Charles Darwin who first integrated field
observations with available experimental data into a coherent model of differentiation (e.g.,
Pearson, 1996). Darwin’s notes suggest that he began contemplating the relationships among
different igneous rock types while traveling along the coast of South America (Pearson, 1996).
However, it wasn’t until arriving in the Galapagos Islands (Figure 1) that he recognized the
importance of crystallization and gravitational settling. The following description is from
Darwin’s 1844 Geological Observations on Volcanic Islands (available online from Project
Gutenberg at: http://onlinebooks.library.upenn.edu/):
One side of Freshwater Bay [sic; this is an error in Darwin’s publication and should be Buccaneer
Cove], in James Island, is formed by the wreck of a large crater, mentioned in the last chapter, of which the
interior has been filled up by a pool of basalt, about two hundred feet in thickness. This basalt is of grey
colour, and contains many crystals of glassy albite, which become much more numerous in the lower,
scoriaceous part.... At James Island, the crystals of albite, though no doubt of less weight than the grey
basalt, in the parts where compact, might easily be of greater specific gravity than the scoriaceous mass,
formed of melted lava and bubbles of heated gas.
Darwin, 1844; p. 244.
In the same style that would became his hallmark in the Origin of Species, Darwin integrates
his observations from the Galapagos with those of other localities, the results of melting
experiments on natural rock systems, and observations from the metallurgical sciences, into a
hypothesis of gravity settling to explain the diversity of igneous rocks:
In a body of liquified volcanic rocks, left for some time without any violent disturbance, we might
expect, in accordance with the above facts, that if one of the constituent minerals became aggregated into
crystals or granules, or had been enveloped in this state from some previously existing mass, such crystals
or granules would rise or sink, according to their specific gravity. Now we have plain evidence of crystals
being embedded in many lavas, whilst the past or basis has continued fluid. I need only refer, as instances,
to the several, great, pseudo-porphyritic streams in the Galapagos Islands, and to the trachytic streams in
many parts of the world, in which we find crystals of feldspar bent and broken by the movement of the
surrounding, semi-fluid matter. Lavas are chiefly composed of three varieties of feldspar, varying in
specific gravity from 2.4 to 2.74; of hornblende and augite, varying from 3.0 to 3.4; of olivine, varying
from 3.3 to 3.4; and lastly, of oxides of iron, with specific gravities from 4.8 to 5.2. Hence crystals of
feldspar, enveloped in a mass of liquified, but not highly vesicular lava, would tend to rise to the upper
parts; and crystals or granules of the other minerals, thus enveloped, would tend to sink. We ought not,
however, to expect any perfect degree of separation in such viscid materials. Trachyte, which consists
chiefly of feldspar, with some hornblende and oxide of iron, has a specific gravity of about 2.45; whilst
basalt, composed chiefly of augite and feldspar, often with much iron and olivine, has a gravity of about
Wirth – Magmatic Differentiation Using M&M’s®
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3.0. Accordingly, we find, that where both trachytic and basaltic streams have proceeded from the same
orifice, the trachytic streams have generally been first erupted owing, as we must suppose, to the molten
lava of this series having accumulated in the upper parts of the volcanic focus.
Darwin, 1844, p. 244-245.
Elsewhere Darwin also proposes an explanation that is the basis of the mechanism of “filter
pressing.” The remarkable parallels between Darwin’s theories of differentiation and evolution
are also explored by Pearson (1996). Although the role of differentiation was widely recognize
by the time of N.L. Bowen, the mechanisms had not yet been quantitatively studied. Young
(1998) provides an excellent review of the debate surrounding the origins of igneous rocks
during the twentieth century. Young (1998) also explores some of the influences that Darwin’s
Origin of Species may have had on Bowen, including the choice of title for Bowen’s book (The
Evolution of the Igneous Rock) and the use of terms such as ‘rock species.’ No discussion of
magmatic differentiation would be complete without mention of Wager and Deer (1939) whose
work in the Skaergaard intrusion figured heavily into the debate in the mid-twentieth century. A
recent summary of the mechanisms of differentiation in layered intrusions is provided by
Naslund and McBirney (1996).
Figure 1. Photograph of the northern portion of Buccaneer Cove, Santiago Island (formerly James Island)
where Darwin described porphyritic flows that contributed to his theory of density segregation.
The bay is formed in a partially eroded volcanic cone consisting of alternating basalt flows and
scoria; the center of the cone is located just to the right of the view. The resistant rocks along
the ridge in the central part of the photograph exhibit variations in feldspar phenocryst content
and formed as a series of ponded lavas in a volcanic crater (Estes et al., 2000; G. Estes; personal
communication, 2003).
Materials and Procedures
Relatively few materials are needed for this experiment. At a minimum you need a number
of small colored pieces with 8 different colors. I use M&M’s® because they are widely
available, relatively inexpensive, and edible. A 22 oz bag of plain M&M’s® contains more than
Wirth – Magmatic Differentiation Using M&M’s®
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700 pieces. Because there are only six different colored pieces of plain M&M’s®, I usually
supplement these with a small (3 oz) bag of peanut, almond, or crispy M&M’s® to use for the
remaining two cations (e.g., Ti, K). It is also possible to order a custom selection from the more
than 21 colors that are available from the M&M/Mars® website (http://www.colorworks.com).
Other kinds of small pieces (plastic, wood, metal) with different shapes or colors would probably
work just as well. The magma chamber exercise can be conducted on any tabletop. However, I
have found that the exercise works better if you use a large sheet of paper (approximately 36” x
24”). This not only provides a clean surface, but also enables students to label different parts of
the magma chamber system (see Figure 2) and to note the fractionating mineral assemblages in
each of the cumulus layers.
Figure 2. Schematic diagram showing the M&M® magma chamber at four stages of evolution. Cations
grouped in the rounded rectangle at the top of each panel represent the melt portion of the
magma chamber. Cations arranged between the dashed lines in the lower part of each panel
represent cumulus layers. The numbers of cations in the cumulus layers are correctly
represented but those in the magma chamber are schematic.
Notes for Instructors
Considerable effort was made to make the M&M® magma chamber as realistic as possible.
The parental magma composition was created by re-calculating the average compositions (in
cation %) of several parental magmas in the Duluth Complex of the Midcontinent Rift (Miller
and Ripley, 1996; Wirth, unpublished data.). Initially I considered modeling the M&M® magma
chamber after the evolutionary path indicated by MELTS software (Ghiorso and Sack, 1995;
http://penmelts.ess.washington.edu/). However, this model required a large number of phases
and cations and proved too complex for a short classroom activity. In order to simplify the
model I decided to omit some phases (e.g., orthopyoxene, accessory minerals) and include only
Wirth – Magmatic Differentiation Using M&M’s®
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two minerals that exhibit solid-solution (olivine and plagioclase). Another variable that had to
be constrained was the number of cations in the magma chamber. The minimum size of the
system is determined by the smallest number of low-concentration cations (e.g., Ti, K) that are
needed to realistically model the differentiation process. Using eight elements I found that a
chamber consisting of about 400 cations gave good results and was not too large for a classroom
activity. I use a slightly smaller system (~350 cations) for a six-element model in introductory
geology classes. The sequence of fractionating minerals and their relative proportions were
chosen to approximate those of Duluth Complex intrusions (e.g., Sonju Lake Intrusion). The
composition of the parental liquid and the proportions of fractionating phases were adjusted to
yield realistic cumulate assemblages and residual liquid compositions. Obviously, there is more
than one solution to the problem and the example provided here should be considered one of
many possible solutions.
Several aspects of the model M&M® magma chamber approximate those of natural systems,
including: 1) the sequence of fractionating minerals and their relative proportions, 2) the
changing proportions of end-member minerals of solid solution series, 3) the rock types
consisting of cumulus minerals, 4) the evolutionary trends of the residual liquids on Harker
diagrams (Figure 3), 5) the composition of the residual liquid with increasing degree of
fractionation (e.g., basalt, basaltic andesite, rhyolite). Student should recognize several
shortcomings in the model, including: 1) the exclusion of several important rock-forming
minerals (e.g., orthopyroxene, low-Ca pyroxene, accessory minerals), 2) the absence of an ironrich end-member in the clinopyroxene group; 3) the lack of any hydrous phases (e.g., amphibole,
biotite, muscovite), and 4) the unrealistically large amounts of fractionating oxide minerals (as
high as 23% in step 6). In many natural and experimental systems the concentration of Si in the
residual liquid remains relatively constant until the late stages of differentiation (F < 0.3); the
concentration of Si in the model increases throughout the crystallization sequence.
Depending on the background of the students and the time available I have used several
different versions of this activity. It takes about three hours to complete the activity making it
ideal for a laboratory exercise. However, this activity can also be adapted for the lecture setting.
It takes just a little over one hour to construct and fractionate the magma chamber so one can
conduct this portion of the activity in a one-hour lecture meeting. The length of the exercise can
be shortened considerably by counting out the M&M’s® beforehand; this step is facilitated by
purchasing M&M’s® that are sorted by color and using an electronic balance that has a
“counting” function. After conducting the experiment in the classroom, students can work
individually or in groups after class to enter the data, generate plots, and answer the questions.
The length of the lab can also be reduced considerably by providing students with a spreadsheet
template, but this deprives the students of gaining experience in the design of spreadsheets. I use
a version of this exercise during lecture class in Physical Geology, but I provide students with
blank hardcopies of Harker diagrams and they do the plotting by hand. I have found that using
the experiment in the introductory course in this abbreviated format has resulted in dramatic
improvements in student understanding of fractional crystallization, Bowen’s reactions series,
and magmatic differentiation.
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Figure 3. Harker variation diagrams for the M&M magma chamber exercise.
80
3.0
Ti (cation %)
Si (cation %)
70
60
2.0
1.0
50
40
0.0
0.0
0.2
0.4
0.6
0.8
1.0
45
50
55
F (liquid fraction)
Fe (cation %)
Al (cation %)
70
75
65
70
75
65
70
75
65
70
75
10
18
16
14
8
6
4
2
12
0
10
45
50
55
60
65
Si (cation %)
70
45
75
12
10
10
8
8
6
4
50
55
60
Si (cation %)
Ca (cation %)
Mg (cation %)
65
12
20
6
4
2
2
0
0
45
50
55
60
65
70
75
45
50
55
Si (cation %)
60
Si (cation %)
12
10
10
8
8
K (cation %)
Na (cation %)
60
Si (cation %)
6
4
6
4
2
2
0
0
45
50
55
60
Si (cation %)
65
70
75
45
50
55
60
Si (cation %)
Wirth – Magmatic Differentiation Using M&M’s®
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References Cited
Bowen, N.L., 1928, The Evolution of igneous Rocks: Princeton University Press, Princeton, NJ,
332 p.
Darwin, Charles, 1844, Geological observations on the volcanic islands visited during the
voyage of the HMS Beagle, together with some notes on the geology of Australia and the
Cape of Good Hope, being the second part of the geology of the voyage of the Beagle,
under the command of Capt. Fitzroy, R.N., during the years 1832 to 1836: Smith Elder,
London.
Estes, Gregory, K., Grant, Thalia, and Grant, Peter, R., FRS, 2000, Darwin in Galapagos: His
footsteps through the archipelago: Notes Records of the Royal Society of London, v. 54, p.
343-368.
Ghiorso, M.S., and Sack, R.O., 1995, Chemical mass transfer in magmatic processes IV: A
revised and internally consistent thermodynamic model for the interpolation and
extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and
pressures: Contributions to Mineralogy and Petrology, v. 119, p. 197-2132.
Miller, J.G., Jr., and Ripley, E.M., 1996, Layered intrusions of the Duluth Complex, Minnesota,
USA: in Layered Intrusions, Cawthorn R.G., editor, Developments in Petrology 15, p. 257301.
Naslund, H.R., and McBirney, A.R., 1996, Mechanism of formation of igneous layering: in
Layered Intrusions, Cawthorn R.G., editor, Developments in Petrology 15, p. 1-43.
Pearson, Paul, N., 1996, Charles Darwin on the origin and diversity of igneous rocks: Earth
Sciences History, v. 15, no. 1, p. 49-67.
Wager, L.R., and Deer, W.A., 1939, Geological investigations in East Greenland: Part III. The
petrology of the Skaergaard intrusion, Kangerdluqssuaq, East Greenland: Meddeleser om
Grønland, v. 105, p. 1-352.
Young, D.A. 1998, N.L. Bowen and Crystallization-Differentiation: The Evolution of a Theory:
Mineralogical Society of America, Monograph 4, Washington, DC, 276 p.
Wirth – Magmatic Differentiation Using M&M’s®
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HANDOUT
Differentiation of Magmas By Fractional Crystallization
Objective
The objective of this exercise is to gain first-hand knowledge of the process of magmatic
differentiation by fractional crystallization. The activity also provides an opportunity to utilize
your knowledge of mineral stoichiometry, the IUGS classification system, and spreadsheets.
A Bit of History and Terminology
In the introductory geology course you learned about Bowen’s reaction series and the
importance of crystal-melt fractionation in generating the spectrum of observed igneous rock
compositions (e.g., basalt, andesite, rhyolite). Magmatic differentiation is the process by which
diverse rock types are generated from a single magma. Differentiation is accomplished by
crystal-melt fractionation, a two-stage process that involves the formation and mechanical
separation of compositionally distinct phases. In 1844 Charles Darwin described flows from the
Galápagos Islands in which the lowest flows contained greater proportions of feldspar crystals.
These observations led Darwin to propose that density differences between crystals and melt
would result in mechanical separation of these two phases and the formation of different magma
types. This process, known today as gravity settling, was the focus of detailed experimental
studies by N.L. Bowen. Today, several additional mechanisms of crystal-melt fractionation are
also recognized, including: flow segregation, filter pressing, and convective melt fractionation.
Constructing the Magma Chamber
1.
In this exercise each major cation (e.g., Si, Ti, Al) will be represented by a different colored
M&M® (e.g., brown, purple, red, respectively). Count out the appropriate number of
M&M’s® for each cation (refer to data sheet). Mix the M&M’s® and pile them in the
magma chamber (circled area on large white sheet of paper).
Crystallization and Fractionation of the Magma
1.
Before you begin, note the general proportions of the different cations (colors) in the
magma chamber. Determine the composition and stoichiometry of each of the minerals
involved in the crystallization process. For the first increment of crystallization, move the
appropriate number of M&M’s® from the magma chamber to the “floor” of the magma
chamber. For each cation, record the number that remains in the magma chamber.
2.
For each increment of crystallization, move the appropriate number of cations (M&M’s®)
from the chamber to the floor of the chamber. Note: it is helpful to group the cations that
were removed in each crystallization step in separate layers. In other words, move the
M&M’s® that were crystallized during the first step the furthest away from the magma
chamber; cations from each additional crystallization step will be successively closer to the
magma chamber.
3.
After each crystallization step, you should observe the proportions of the cations (colored
M&M’s®) in the remaining liquid and in the cumulus layers. Record the number of
remaining M&M’s® in each step.
Wirth – Magmatic Differentiation Using M&M’s®
4.
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Before your experiment is dismantled (or consumed), describe the general trends that you
observed during the fractional crystallization of the magma?
Analyzing the Results
1.
Enter your data into the Excel spreadsheet that has been provided.
2.
For each crystallization step, complete the calculations of the:
(a)
modes of the minerals being removed to the chamber floor (cumulus minerals),
(b) normalized modes of the minerals used for IUGS classification,
(c)
number of cations remaining and the cation composition of the remaining liquid,
(d) fraction of liquid remaining (F), and
(e)
Mg# = ([Mg]/[Mg+Fe]).
3.
Next, use your data to determine the following:
(a)
IUGS rock name for the cumulus layer formed during each crystallization event, and
(b) the rock name for the residual liquid remaining after each crystallization event.
4.
Generate x-y plots of the following:
(a)
fraction of liquid remaining (F) and Mg# versus Si,
(b) Si versus Ti, Al, Fe, Mg, Ca, Na, K, and
(c)
indicate the arrival of minerals on the liquidus on each of the plots
Reflecting on What You Have Learned
1.
Describe the effect each mineral has on the liquid line of descent.
2.
How are the terms compatible and incompatible defined (both mathematically and
qualitatively)? From your results, which elements behaved compatibly during
crystallization of this magma? Which behaved incompatibly? Do all of the elements
exhibit the same behavior throughout the duration of crystallization? Explain.
3.
Describe the changes in rock composition (proportions of cumulus minerals) that result
from each increment of crystallization. Use IUGS rock terms and plots in your answer.
4.
Describe the chemical changes that result in the residual magma after each increment of
crystallization.
5.
At what melt fraction (F) does the magma approximate andesite composition? Rhyolite
composition?
6.
Is the parental basaltic magma in this experiment also a “primitive liquid?” Explain.
7.
Which aspects of this model magma chamber are realistic? Which are not? Discuss the
ways that the model might be made more realistic.
8.
Contrast the results of this model (fractional crystallization) with those of a model
involving equilibrium crystallization.
Wirth – Magmatic Differentiation Using M&M’s®
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M&M® Magma Chamber Data Sheet
M odes of Fractionated Minerals
Cation
Parent
M &M®
M elt
Color
Si
Ti
Al
Fe
Mg
Ca
Na
K
184
5
71
38
40
33
23
6
Total
400
Forsterite
Fayalite
Diopside
2
3
3
4
1
1
2
4
3
1
1
3
M inerals on Liquidus
M inerals
1
2
Fo
Fa
Di
Anorthite
Albite
K-spar
Quartz
Ilmenite
M agnetite
Fractionating M inerals
Anorthite
Albite
K-feldspar
Crystallization Step
5
6
2
1
1
1
4
3
4
1
1
Cumulus M ineral M odes
M inerals
1
3
Quartz
Ilmenite
Magnetite
7
8
9
10
2
3
3
2
3
6
1
1
2
1
1
1
5
2
1
1
1
1
1
7
2
4
1
1
3
4
Crystallization Step
5
6
7
8
9
10
2
3
4
Crystallization Step
5
6
7
8
9
10
2
3
4
Crystallization Step
5
6
7
8
9
10
2
3
4
Crystallization Step
5
6
7
8
9
10
2
Fo
Fa
Di
Anorthite
Albite
K-spar
Quartz
Ilmenite
M agnetite
Normalized M ineral M odes for IUGS Classification
Classification Mineral
1
ol
pyx
plag
alk
qtz
Cations Remaining in Liquid
Elements
Parent
M elt
1
Si
184
Ti
5
Al
71
Fe
38
Mg
40
Ca
33
Na
23
K
6
Total
% Liq
400
1.00
Liquid Composition (Cation %)
Elements
Parent
M elt
1
Si
46.00
Ti
1.25
Al
17.75
Fe
9.50
Mg
10.00
Ca
8.25
Na
5.75
K
1.50
Total
F (Liq. fract.)
M g#
TAS Classif.
100.00
1.00
0.51