Fudge Factors in Lessons on Crystallization, Rheology and
Morphology of Basalt Lava Flows
A.C. Rust
Department of Earth Sciences, University of Bristol, Wills Memorial Building,
Bristol BS8 1RJ, U.K., [email protected]
K.V. Cashman
Department of Geological Sciences, University of Oregon, U.S.A.,
[email protected]
H.M. Wright
School of Geosciences, Monash University, Australia,
[email protected]
ABSTRACT
Fudge is an excellent analog for basaltic lava and making
or tasting fudge leads to memorable lessons on the
importance of crystals in controlling the morphology of
basaltic lava flows. In particular, students learn why 'a'a
flows have rough broken surfaces, while pahoehoe flows
are smooth or folded. Furthermore, fudge provides an
interesting analog in lessons on the factors that control
crystal nucleation and growth as well as how crystals
affect magma rheology. Although the full process of
making fudge from scratch is too long for a lecture
demonstration, fudge can be incorporated into lessons
on basalt flows by way of taste-tests, photographs or
simplified experiments with pre-made fudge and syrup.
Advanced students can run experiments during a
laboratory period and examine the crystal textures under
a microscope, or do their own experiments in small
groups outside of the classroom. Evaluation with written
quizzes shows that fudge demonstrations can be an
effective aid for teaching the complex concepts of crystal
nucleation and growth and their effects on basalt lava
flows.
INTRODUCTION
"A close analogy exists in the making of fudge,
wherein if the candy is poured or otherwise
agitated after crystallization has advanced
beyond a certain stage there results a rough,
spinose, somewhat granular surface akin to the
surface of aa"
Macdonald (1953)
Crystals play a key role in controlling the overall shape,
surface textures and flow dynamics of lava flows.
However, explaining the kinetics of crystallization and
the effect of crystals on lava flow dynamics can be
challenging, particularly when opportunities to see lava
flows in action are limited. For this reason, we have
developed a set of classroom exercises using fudge as an
analogue for basaltic lava that allows students to explore
the effects of crystallization and shear rate on the
dynamics of flow in a safe and fun way. In our
experience, this approach not only improves student
understanding of lava flow dynamics, but also provides
them with basic concepts of crystallization and rheology
(flow properties including viscosity) that are broadly
applicable to many volcanological problems.
Like lavas, fudge contains crystals, and it is the
abundance of sugar crystals that gives fudge its strength
and firmness. However, for high quality fudge that feels
smooth and creamy in your mouth, the crystals must be
so small that you don't sense the individual crystals on
your tongue. Hence making great fudge comes down to
controlling crystal nucleation and growth. Traditional
fudge recipes are generally quite intricate and often
include warnings about when to stir and when not to stir
the mixture. This is because the abundance of tiny sugar
crystals in fudge is achieved by stirring a supersaturated
(undercooled) solution, and stirring at the wrong time
can have gritty consequences.
In many respects fudge is a good analog for basaltic
lava, and making fudge leads to memorable lessons on
both the fundamentals of crystal nucleation and growth
and the importance of crystals in controlling the
morphology of basaltic lava flows ('a'a vs. pahoehoe). In
this article we provide 1) background on the role of
crystals in basaltic lava flow rheology and morphology,
2) instructions and suggestions for experiments with
fudge, 3) a comparison of basalt and fudge crystallization
processes and textures, and 4) assessment of the
fudge-basalt analogy as a teaching tool. Moreover, as the
full fudge- making process is quite time-consuming and
thus not suitable as a lecture demonstration, we also
include simpler ideas for incorporating the essentials of
fudge-making into lessons on basaltic lava flows and
crystallization.
BASALT LAVA FLOWS
Basaltic lava flows cover much the Earth's surface as well
as the surfaces of the terrestrial planets. Although
emplaced under a wide range of conditions, many
basaltic lava flows may be classified by surface
morphology as either 'a'a or pahoehoe (Figure 1),
Hawaiian terms first used in the scientific literature by
Dana (1849) in his report of results from the U.S.
Exploring Expedition (see p. 162-163; available through
the Smithsonian Institution Library at http://www.
sil.si.edu/digitalcollections/usexex/).
'a'a
is
characterized by a rough broken surface whereas
pahoehoe has a smooth surface that is commonly folded
into a ropy texture as the lava continues to flow.
Numerous observations and hypotheses about the origin
of these two lava types have filled the volcanological
literature for the subsequent 150 years.
The role of crystallization in producing these
distinctive flow surface textures was first intuited by
Alexander (1859) who recognized that although
pahoehoe was emplaced in a purely molten state, 'a'a
contained "solid points, or centers of cooling" and for this
reason "the aa stream grains like sugar." However, it was
not until Macdonald's (1953) summary paper that an
explicit link was made between flow surface
morphology and the mechanism of flow emplacement.
This link was formalized by Peterson and Tilling (1980),
who described the transition from pahoehoe to 'a'a as a
function of strain rate and apparent viscosity (Figure 2).
Rust et al. - Lessons on Crystallization, Rheology and Morphology of Basalt Lava Flows
73
Figure 1. Photographs of active lava flows: A) An ‘a’a Figure 2. Shear rate versus viscosity with ‘a’a,
flow at Mount Etna, Italy, taken at night. B) A pahoehoe and transitional regions based on figure of
pahoehoe lava lobe in Hawai`i. Scanning Electron Peterson and Tilling (1980)
Microscope (SEM) images of quenched samples of C)
‘a’a and D) pahoehoe from Hawai`i. In these SEM
images glass is light gray and crystals are darker gray
or black. Quenching (very rapid cooling) of these lava
samples converted the melt to glass and preserves
the crystals that were present when the hot lava
flowed.
Cashman et al. (1999) analyzed samples collected along
an active lava channel to show that the pahoehoe-'a'a
transition
represents
a
rheological
threshold,
specifically, that 'a'a forms when there is sufficient
interaction of crystals to continuously disrupt the surface
crust through development of yield strength. Katz and
Cashman (2003) generalized this model by quantifying
crystal textures in numerous Hawaiian lava flows, while
Soule and Cashman (2005) used analog materials (corn
syrup and rice) to investigate the physical mechanism by
which crystal interactions lead to flow surface textures.
Together these studies portray basaltic lava flow
dynamics as strongly controlled by both the flow (strain)
rate and the extent and timing of crystallization during
emplacement. Key to understanding this perspective on
lava flow surface morphologies is a basic understanding
of controls on crystal nucleation and growth.
Crystallization occurs when a solution becomes
over-saturated in one or more components. In lava flows,
supersaturation is caused by cooling of lava as it exits the
vent and flows down slope. Also important is the extent
of supersaturation (Figure 3) - large supersaturations
promote rapid crystal nucleation (producing numerous
small crystals) while small supersaturations inhibit
nucleation but allow rapid growth once nucleation
occurs (producing fewer but larger crystals).
FUDGE
Figure 3. Schematic illustration of the effect of
supersaturation on crystal nucleation and growth.
Low
supersaturation
promotes
growth
over
nucleation, resulting in fewer but larger crystals (A);
high supersaturation promotes nucleation over
growth, resulting in numerous tiny crystals (B);
extreme supersaturation forms glass (C).
the case for simpler recipes sometimes called "quick
fudge" or "easy fudge" that thicken the mixture with
ingredients such as condensed milk or melted
marshmallows. The steps for making fudge are listed
below and the ingredients and materials required are in
Tables 1 and 2, respectively.
The Basic Steps to Making Fudge -
1.
Before we experiment with 'a'a and pahoehoe versions of
fudge, we first review how traditional fudge is made and
discuss why it is made this way. As an example we use a 2.
chocolate fudge recipe but any recipe (e.g., other flavors)
will do as long as similar steps are involved. However, it 3.
is important is that the stiffness and texture of the fudge
be produced by numerous sugar crystals, which is not
74
Heat and stir sugar, cream, corn syrup, chocolate and
salt in a pot until the sugar is dissolved and the
mixture boils
Stop stirring and let it boil until it reaches 115°C
(235°F)
Remove the pot from the heat and leave it alone until
it has cooled to 45°C (110°F)
Journal of Geoscience Education, v. 56, n. 1, January, 2008, p. 73-80
Figure
4.
Water-sucrose
saturation
diagram
constructed from data compiled by Starzak and
Mathlouthi (2006). The water-sucrose system is a
good analog for understanding fudge-making
although
fudge
contains
more
phases
and
components. The liquidus (thin black line) separates
the field where liquid syrup is stable (white area) from
the field where (if in thermodynamic equilibrium)
liquid syrup coexists with sucrose crystals (gray area).
The dashed gray line marks the boiling temperature
of sucrose syrup at a pressure of 1 atmosphere. As
syrup boils it loses water and the boiling temperature
rises.
The
two
black
arrows
show
the
temperature-composition path for boiling until the
solution reaches 110°C (similar to step 2 of fudge
recipe), followed by cooling to 45°C (step 3 of fudge
recipe). In this scenario, if the equilibrium is
maintained then sucrose crystals would begin to form
when the liquidus is reached at about 85°C. However,
if the solution is not agitated while cooling, it may
become supersaturated and crystallization may be
delayed to a temperature well below the liquidus. This
is what happens when making fudge.
4.
5.
Add butter and stir for several minutes until it starts
to look dull and lighter in color and feels stiffer
Transfer to the dish and flatten the top surface by
pressing with hands.
sugar:water ratio of the solution is appropriate for fudge;
at this point the mixture is removed from the source of
heat.
The solution should begin to crystallize sugar as it
cools (step 3) and crosses the saturation curve (liquidus;
Figure 4), if thermodynamic equilibrium is maintained.
However, if the pot is left undisturbed, crystal nucleation
is delayed (i.e., the solution does not remain in
thermodynamic
equilibrium),
thus
delaying
crystallization
and
causing
supersaturation
(undercooling) of the solution. Professionals usually
pour the hot solution onto a marble slab rather than
leaving it to cool in a pot. This causes the solution to cool
more quickly and more evenly, which is particularly
important if making a large volume of fudge. As
supersaturation is critical to the process of making fudge,
it is important not to stir the mixture while it cools in step
3 (whether cooling in a pot or on a marble slab). Many
recipes also advise wiping the sides of the pot with a wet
pastry brush in step 2 to prevent crystals from building
up. This is because sugar crystals will form along the
cooler sides of the pot. Any crystals that fall into the
solution in step 3 will provide easy sites for sugar crystal
growth, thus aiding crystallization and preventing
attainment of a supersaturated solution.
When the solution has cooled to 45°C without
crystallizing, it is far from equilibrium and there is a large
thermodynamic driving force for crystallization. Because
the supersaturated solution is quite unstable, the
agitation and further cooling caused by sudden stirring
(step 4) leads to rapid crystal nucleation (Figure 3).
Continued stirring also helps to promote further
nucleation of new crystals (rather than growth of existing
crystals) by aiding heat and mass transfer. Stirring
disturbs and shears the adsorption layer around crystals,
that is, the transition zone between sucrose molecules in
solution and sucrose molecules in the sugar crystal
lattice. The result is a large number of small crystals that
give the fudge the dull and light-colored appearance
(late in step 4), which signals that it is time to put the
fudge into a dish (step 5) where crystallization will be
completed. If the fudge is stirred too long the crystals will
be so abundant that the fudge will be too stiff to easily
press into a dish.
The high supersaturation of the solution provides
the thermodynamic driving force for rapid
crystallization. So why not boil the solution longer in
step 2 to increase the sugar concentration or let the
solution cool to refrigerator temperature before stirring
in step 4? Either of these changes to the recipe would
increase the degree of supersaturation but it would also
increase the viscosity of the solution. Increasing the
viscosity decreases the mobility of the sugar and other
molecules. This inhibits crystallization because
molecules must move around and rearrange to produce
crystals. Thus despite being far from equilibrium a very
viscous solution will have low crystal nucleation and
growth rates (Figure 3), which are properties that are not
conducive to making good fudge. In fact, at sufficiently
high viscosities crystal nucleation is prevented and sugar
solutions can form a glass (a non-crystalline solid such as
a lollipop). This is exactly what happens in silicic lava
flows, which form obsidian (glass).
What's Happening? - In short, making fudge involves
first boiling then cooling a sugary solution so that it is
supersaturated, followed by stirring to induce rapid
nucleation of sugar crystals. The result is a large number
of small sugar crystals that give the fudge its
characteristic firm but smooth texture. In contrast,
gradual nucleation of crystals over a long time interval
would result in fewer crystals, but a larger mean crystal
size and a broader distribution of crystal sizes, and thus
gritty fudge. The steps in making fudge are discussed in
much greater detail below. For further reading we
suggest Hartel (2001) and http://www.exploratorium.
edu/cooking/candy/recipe-fudge.html.
The recipe begins (step 1) by combining ingredients
and heating the mixture so that all the sugar crystals
dissolve. As the fudge solution boils (step 2) water
evaporates, which concentrates the sugar content of the
remaining solution and consequently increases its
boiling temperature (Figure 4). This is different from a FUDGE EXPERIMENTS
pot of boiling water, which has only one component
(H2O) and remains at 100°C until it evaporates Slight modifications to the fudge recipe outlined above
completely. At a boiling temperature of about 115°C the can be used to experiment with the role of crystals in
Rust et al. - Lessons on Crystallization, Rheology and Morphology of Basalt Lava Flows
75
the recipe. Instead tilt the pot (e.g., hold the pot so that
base is 45° from horizontal). The down-slope flow of
liquid will cause the skin on top to fold into a ropey
texture (Figure 5). Students can experiment with both the
angle of the pot and the length of time allowed for skin
cooling to explore controls on wrinkling behavior of the
flow surface.
225 g (3 cups) sugar
240 ml (1 cup) cream
15 ml (1 tablespoon) corn syrup
85 g (3 ounces) unsweetened chocolate
pinch of salt
45 ml (3 tablespoons) butter
'A'a Fudge - The rough and spiny surfaces that
characterize 'a'a are easily created in our fudge analogue
system, as making 'a'a fudge is very similar to making
normal fudge. As described above, fudge contains lots of
little crystals, with the final bit of crystallization and
stiffening occurring after the fudge is pressed into a dish
(step 5). To make 'a'a fudge, simply continue stirring in
step 4 until the fudge becomes so crystalline and stiff that
stirring causes it to break into pieces and the surface of
these blocks is rough, spinose and granular (Figure 5).
'a'a! Students can also experiment with the rate of stirring
to determine the effect of shear rate on the surface texture
of the fudge.
Table 1. Ingredients of fudge.
wooden (or similar) spoon
large saucepan
stove top or hotplate
candy thermometer
dish (20x20 cm or similar size)1
baking sheet2
1
2
for regular fudge but not `a`a or pahoehoe
for smooth pahoehoe fudge flow only
Table 2. Materials for fudge.
controlling the flow behavior of the mixture. Specifically,
we outline below methods by which students may create
'a'a or ropey pahoehoe textures or a thin smooth
pahoehoe fudge flow, thereby exploring relationships
among cooling, stirring (shear rate) and final flow
morphology. These variants require the same
ingredients (Table 1) and materials (Table 2) as the
regular fudge recipe except replicating flows requires
that the dish be replaced by a baking sheet covered with
aluminum foil for easy clean-up. Making the fudge is not
difficult but it is time-consuming. For ideas on simpler
and quicker experiments to create 'a'a and pahoehoe
textures, see the section "Incorporating fudge into the
classroom".
Smooth Pahoehoe - To make smooth pahoehoe fudge
flows, ignore steps 4 and 5 of the fudge recipe. Instead
pour a portion of the warm (e.g., 45°C) liquid (e.g., 1/2 to
1 cup) onto a baking sheet. A student may taste a
spoonful of the warm solution from the pot to confirm
that it feels like a simple liquid without crystals. On a
horizontal surface, the poured fudge liquid will spread
and form a thin, smooth, round flow. Tilting the baking
sheet will allow the fudge to flow down slope in addition
to spreading radially. The fudge will eventually
crystallize and harden in the shape of the flow.
It is not necessary to wait for the fudge liquid to cool
all the way to 45°C (end of step 3) before pouring it. If you
use hot liquid fudge then it will flow and spread faster
and produce a thinner flow. This will affect cooling rates
and the resulting crystals. However, be careful not to
accidentally burn your skin and certainly do not taste the
hotter liquid. Additional experiments on the flow of
viscous fluids are provided in a later section.
Ropey Pahoehoe - To make pahoehoe, the fudge recipe
must be modified at the end of the undisturbed cooling
in step 3. At this point, the pot of warm liquid will have a
skin on top that is cooler and dryer than the fluid below.
To make ropey pahoehoe fudge ignore steps 4 and 5 of
76
Taste Test for Crystal Sizes - Each student, or a lucky
representative, should taste a piece of the 'a'a and smooth
pahoehoe fudge when cooled to room temperature. Our
tongues are quite sensitive to grain size and we have yet
to come across a person that could not feel the difference
between 'a'a and pahoehoe fudge when eating them. The
'a'a fudge feels like regular fudge: firm and smooth
(internally) due to the abundance of tiny crystals. On the
other hand, pahoehoe fudge feels gritty. The gritty
texture is produced by the growth of relatively large
crystals after pouring. This is in contrast to its almost
crystal-free state when it was poured. The cause of the
variations in crystal textures is a good topic for students
to discuss using the nucleation and growth curves shown
in Figure 3. Explanations are given in the subsequent
section "Comparing basalt and fudge".
More advanced students who are familiar with
studying rocks in thin sections can go beyond the taste
test and look at the crystal microtextures of 'a'a and
pahoehoe fudge and basalt under a microscope. Fudge
thin sections can be prepared by cutting slivers of fudge
as thin as possible with a razor blade and then pressing
them or smearing them on a glass slide. Alternatively,
students can compare photomicrographs of crystals in
'a'a and pahoehoe lava and fudge (e.g., Figure 6).
COMPARISON OF BASALT AND FUDGE
The similarities between basalt and fudge are much more
significant than the superficial resemblances between
photographs in Figures 1 and 5. Whether it is fudge or
lava, the rheology of the fluid (liquid +/- crystals)
depends on the abundance of crystals as well as the
temperature and water content of the residual liquid.
Furthermore, it is the effect of crystals on the fluid
rheology that is the most important factor controlling
whether the sheared fluid will have an 'a'a or pahoehoe
surface morphology. Also important is the rate at which
the fluid is sheared, as shear rate controls the ways in
which crystals interact (e.g., Peterson and Tilling, 1980;
Soule and Cashman, 2005).
'A'a lava and fudge both contain numerous crystals,
enough that the crystals touch each other and give the
fluid strength (a yield strength; Barnes, 2000). Because
the crystals resist flow past each other, the crystal-rich
lava (fudge) breaks rather than flowing when it is
Journal of Geoscience Education, v. 56, n. 1, January, 2008, p. 73-80
Figure 5. Photographs of ‘a’a (A) and pahoehoe fudge (B).
Figure 6. Optical photomicrographs of ‘a’a (A) and pahoehoe (B) fudge after slow cooling, and Scanning Electron
Microscope images of the interiors of ‘a’a (C) and pahoehoe (D) basalt flows. Both basalt samples are highly
crystalline because in the interior of the flows, where cooling is slow, crystal growth dominates over crystal
nucleation. However, the crystals in the pahoehoe sample are larger and less numerous because there were fewer
crystals in the pahoehoe lava when it stopped flowing. Note the contrast between the pahoehoe basalt image from
the interior of a flow (D) and the SEM image of pahoehoe basalt in Figure 1D which has a low crystallinity because
quenching prevented further crystal growth. The fudge samples are also highly crystalline when fully cooled (A and
B), and like their basalt counterparts, the `a`a sample contains more and smaller crystals because agitation
promoted high nucleation rates.
Figure 7. Ropey pahoehoe texture produced with golden syrup and plastic wrap. A) Syrup flowing under a
plastic film that is taped to the baking sheet along sides marked with white rectangles. The arrow indicates
the down-slope flow direction. B) Ropey pâhoehoe forming in a flowing lava in Hawai`i. C) A square of plastic
film is folded as the underlying syrup flows up against and around a solid cube that obstructs flow. D) Ropey
pahoehoe lava in Hawai`i with folded and twisted skin. Photograph B was taken by D. Swanson, courtesy of
the USGS.
sheared. So it is the effect of crystals on lava and fudge
rheology that causes flows to form rough, broken
surfaces when sheared with enough force.
In contrast, while they are flowing, pahoehoe lava
and molten fudge have such low crystal contents that the
crystals hardly interfere with each other. Thus
low-crystallinity lava (<25% crystals by volume) or
fudge flows much like syrup, which is a simple viscous
fluid that forms thin smooth flows. One difference
between pahoehoe and syrup, however, is the rapid
surface cooling of pahoehoe as the hot (1150-1200°C) lava
interacts with cool air. This causes the outside of a
pahoehoe lava lobe to cool quickly and form a thin skin
that resists flow (and is too viscous for crystal nucleation
and growth). Fudge also forms a skin as it cools in the pot
(step 3) and dehydrates, although it develops more
slowly than for basalt. When this skin (lava or fudge)
sticks to the ground at the flow margins (or to the edge of
the pot) and can't be carried along by the fluid flowing
beneath, the skin buckles to form multiple folds that
often resemble ropes (giving rise to 'ropey' pahoehoe).
Moreover, the planform shape of the folds indicates the
direction in which the fluid flowed.
78
It may seem a contradiction that the overall smooth
appearance of the pahoehoe fudge flow is due to its lack
of crystals, yet in the taste test it feels gritty (crystalline),
with larger crystals than the 'a'a fudge. The explanation
is that the pahoehoe fudge crystallizes as it sits on the
baking sheet and, due to relatively low nucleation rates
compared to growth rates (Figure 3), the crystals grow
bigger than in their 'a'a counterparts. This is similar to
what happens in the interior of real pahoehoe flows.
Pahoehoe flow margins contain few crystals and are
glassy because they cool quickly and become too viscous
to nucleate crystals. For this reason, examining the
crystal content of the margins is quite a good indicator of
the crystal content while it was flowing. However in
flows thicker than about 0.2m, the flow interior cools
sufficiently slowly to crystallize completely, although at
lower supersaturations (fewer but larger crystals) than in
'a'a flows (Katz and Cashman, 2003; Figure 6). In
contrast, 'a'a flows are fine-grained and crystal-rich
throughout the flow, regardless of the flow thickness
(Katz and Cashman, 2003; Figure 6). This uniform texture
results from extensive crystal nucleation and stirring
while the flow is traveling through lava channels. The
Journal of Geoscience Education, v. 56, n. 1, January, 2008, p. 73-80
high number density of crystal nuclei formed before the
flow came to rest limits the growth of any individual
crystal, producing finely crystalline lava. Similarly, in
'a'a fudge the crystals don't grow very large because
there are so many crystal nuclei growing and competing
for the dissolved sugar.
We have seen that in both fudge and basalt flow
interiors, 'a'a has smaller crystals and more crystals per
unit volume than pahoehoe (Figure 6). The fudge
experiments show that stirring is key to forming this
texture. Experiments by Kouchi et al. (1986) show that
shearing during crystallization also increases the
number of nuclei and decreases the size of crystals in
basalts. However there is an important difference
between fudge and basalt: In the fudge recipe, nucleation
occurs suddenly from a supersaturated solution,
whereas the basalt melt in an 'a'a flow would at most be
only slightly supersaturated. The key to the small
crystals in 'a'a basalt flows is the mixing, recycling and
shearing, which aid mass and heat transfer and may even
break small protrusions from crystal margins to form
new nucleation sites (a process known as secondary
nucleation). Note 'a'a fudge can be made in the same
manner if, rather than leaving the solution undisturbed
and waiting for it to cool to 45°C in step 3, it is stirred
continuously until it is sufficiently crystalline to break.
The result will be a wider range in crystal sizes than in
'a'a fudge made following the recipe earlier in this paper.
However the crystals will still be considerably smaller
(and the fudge taste will be smoother) than in the
pahoehoe fudge with the smooth surface.
INCORPORATING FUDGE INTO THE
CLASSROOM
Making
fudge
from
scratch
is
sufficiently
time-consuming that it is not feasible as a lecture
demonstration. However, there are shortcuts by which
fudge can be used to enhance a lesson on magma
rheology or lava flows without taking up extensive
lecture time. For instance, the instructor could make the
'a'a and pahoehoe fudges in advance and have the
students participate in a taste test. This would lead to a
discussion of both why the 'a'a and pahoehoe fudge
samples look and feel different from each other and how
this difference relates to basaltic lava flows. The lesson
could be augmented with short videos of the making of
'a'a and pahoehoe fudges as well photographs and
photomicrographs of basalt lavas (e.g., Figures 1, 5, 6).
There are also classroom demonstrations that are
much quicker than making fudge from scratch. For
instance, to save time and mess one can start with fudge
purchased from a shop or made in advance by the
instructor. Students (or a demonstrator) can quickly
make 'a'a fudge by heating fudge in a beaker or small
saucepan on a hotplate. To help it heat evenly, break the
fudge into small pieces and mix it with a spoon. When it
is all hot enough that the solution can be stirred and
appears homogeneous (e.g., 45°C), remove it from the
heat and stir vigorously and continuously until an 'a'a
texture develops.
To make pahoehoe fudge from pre-made fudge
requires more time and higher temperatures than the 'a'a
version. The process is the same (and takes as long) as for
making pahoehoe fudge from scratch. To save time we
suggest an alternative demonstration with viscous syrup
(e.g., golden syrup or corn syrup) or honey that involves
pouring syrup (~ 1/2 cup) onto a baking sheet or dish.
The viscous fluid will spread to form a smooth circular
shape similar to the smooth fudge experiment. To create
surface textures similar to pahoehoe, the syrup flow can
be covered with a large rectangle of plastic wrap that
simulates the crust or surface skin. Tape two edges of the
plastic film to the baking sheet without stretching the
plastic (in fact a little slack helps) and then tilt the sheet so
that the syrup flows parallel to the taped edges (Figure
7A; compare with lava in Figure 7B). Alternatively, place
a piece of plastic film on the syrup without covering the
entire syrup flow and then press an object (or just a
finger) on the plastic. The stresses caused by pressing on
the plastic cause it to wrinkle but of more interest are the
folds that develop if the baking sheet is tilted to that the
syrup flows around and builds up against the obstacle
(Figure 7C; compare with lava in Figure 7D).
If there is time available, students really enjoy and
learn a lot from making fudge from scratch. An
alternative to the entire class spending a laboratory
period working with fudge is for a group of students to
make fudge on their own time and present their results to
the rest of the class. As part of a group-project in an
undergraduate volcanology course at the University of
British Columbia, four students studied literature on
crystallization of fudge and basalt, ran the fudge
experiments, examined fudge thin sections with a
microscope, wrote a report about their findings and
presented their research (and fudge) to their classmates
during lecture period. At this level students can design
their own extra experiments. These students decided to
examine how the addition of nuts and marshmallows
affects the microtexture and rheology of fudge. Other
possibilities include measuring latent heat of
crystallization or examining how the timing of stirring
affects crystal sizes and shapes.
ASSESSMENT
To assess the effectiveness of fudge demonstrations for
teaching concepts related crystallization and flow of
lavas, we used a written quiz about the lessons learned
after an initial lecture, and compared results with the
same evaluation after demonstration and discussion.
The 42 student participants were attending a regular
session of a year 3 undergraduate course in volcanology
at the University of Bristol. Many graduate students sit in
on the course and the day of the fudge demonstration
there were 34 undergraduates and 8 graduate students.
Less than ten minutes was spent discussing fudge and
thus we are evaluating the effectiveness of a minor
interruption of a lecture to incorporate fudge into the
lesson. As discussed in the previous section, we have also
used the fudge-basalt analogy for more in-depth,
self-directed learning with students at the University of
British Columbia. However, in that case we did not do a
formal assessment of the effectiveness of the activity for
student learning.
The initial lecture introduced the University of
Bristol students to 1) the effects of crystals and
temperature on the viscosity of lava, 2) the effects of
supersaturation on crystal growth and nucleation in
silicate melts, 3) the roles of crystallization and shear rate
on the generation of 'a'a and pahoehoe surface
morphologies. Students then wrote a quiz about these
topics. The quiz included several short-answer questions
as well as a diagram similar to Figure 3 on which
students were asked to label conditions for the formation
of glass, lots of fine crystals, and fewer coarse crystals.
Rust et al. - Lessons on Crystallization, Rheology and Morphology of Basalt Lava Flows
79
After the quiz each student examined and tasted a cube
of fudge. The lecturer then explained 1) the importance
of the abundance and small size of crystals for the firm
and smooth texture of good fudge, and 2) how
traditional fudge is made. Students were asked to predict
what would happen if the fudge recipe was altered by
stirring too early, too late, too long or not at all. The
lecturer then explained how 'a'a vs. Pahoehoe fudge are
made and showed photographs of the resulting fudges
(e.g., Figure 5). As a group discussion, students
considered how the crystal textures in hot and cooled 'a'a
and pahoehoe fudge would differ. Students then saw
photomicrographs of 'a'a and pahoehoe fudge and lava.
The class ended with the students writing the quiz about
crystallization, viscosity and morphology of basalt lavas
for a second time. The instructor evaluated all quizzes
after the class ended.
Approximately a third (12 of 34 undergraduate
students and 3 of 8 graduate students) answered all
questions well on the first quiz and thus understood all
the major concepts of the lesson before fudge was
introduced. However, many of these students
demonstrated more in-depth knowledge on the second
quiz. Of the students who had difficulties with the first
quiz, 74% improved their answers on the second quiz
after learning about the crystallization of fudge. The
most common problem in the initial quiz was not
understanding that the disequilibrium crystallization in
basalt lava flows is related to cooling and cooling rate.
Several students confused the crystallization of basalt
flows driven by cooling with the decompression-driven
crystallization of water-saturated silicic magmas, which
was also discussed in the lecture. However, the fudge
interlude clarified this issue for ten of the students who
had not previously understood. The fudge discussion
also helped six students to learn the importance of
crystals in controlling basalt lava flow morphologies,
and three students learned why shearing and mixing
affect crystallization of lava.
Although the discussion of fudge crystallization
lasted only a few minutes, it improved most students
understanding of the processes of silicate crystal
nucleation and growth and the effects of these crystals on
lava flow morphology. We suggest that the use of
multiple representations along with directive help and
post-demonstration discussion increases student
comprehension of these complex topics. Unsolicited
comments from students in the week following the
lecture indicate that they enjoyed learning about fudge,
and several of them talked about crystallization with
acquaintances outside of the course. The exercise could
be further extended to include student design of fudge
experiments and evaluation of results in the context of
lava flows as we did with a group of students at the
University of British Columbia. Such design-based
learning may be more effective as it allows students to
create, debate, and evaluate models, as opposed to
simple absorption of transmitted material (e.g. Penner et
al., 1998).
80
ACKNOWLEDGEMENTS
We thank the many enthusiastic taste-testers including
the undergraduate volcanology students at the
University of British Columbia and the University of
Bristol. The manuscript benefited from reviews from J.
Brady, J. Wenner and D. Perkins. We particularly want to
thank J. Brady for the suggestion to add a phase diagram.
A. Rust was supported by a Royal Society URF. NSF
grant EAR EAR0510437 funded K. Cashman and H.
Wright for this work.
REFERENCES
Cashman, K.V., Thornber, C.R., and Kauahikaua, J.P.,
1999, Cooling and crystallization of lava in open
channels, and the transition of pahoehoe lava to 'a'a,
Bulletin of Volcanology v. 61, p. 306-323.
Dana, J.D., 1849, Geology, Report of results from the U.S.
Exploring Expedition during the years 1838 to 1842,
v. 10, New York, Putnam, 756 p.
Hartel, R.W., 2001, Crystallization in Foods, Maryland,
Aspen Publishers, 325 p.
Katz, M.G., and Cashman, K.V., 2003, Hawaiian lava
flows in the third dimension: Identification and
interpretation of pahoehoe and 'a'a distribution in
the KP-1 and SOH-4 cores: Geochemistry,
Geophysics, Geosystems (G3), v. 4, 8705, doi:
10.1029/2001GC000209.
Kouchi, A. Tsuchiyama, and A. Sunagawa, I., 1986, Effect
of stirring on crystallization kinetics of basalt: texture
and element partitioning, Contributions to
Mineralogy and Petrology, v. 93 , p. 429-438.
Macdonald, G.A., 1953, Pahoehoe, ‘a’a, and block lava,
American Journal of Science v. 251, p. 169-191.
Penner, D.E., Lehrer, R., and Schauble, L., 1998, From
physcial models to biomechanics: a design-based
modeling approach: The Journal of the Learning
Sciences, v. 7, p. 429-449.
Peterson, D.W., and Tilling, R.I., 1980, Transition of
basaltic lava from pahoehoe to 'a'a, Kilauea volcano
Hawaii: Field observations and key factors, Journal
of Volcanology and Geothermal Research, v. 7, p.
271-293.
Starzak, M., and Mathlouthi, M., 2006, Temperature
dependence of water activity in aqueous solutions of
sucrose, Food Chemistry, v. 96, p.346-370.
Soule, S.A., and Cashman, K.V., 2005, Shear rate
dependence of the pahoehoe-to-'a'a transition:
Analog experiments, Geology, v. 33, p. 361-364.
Journal of Geoscience Education, v. 56, n. 1, January, 2008, p. 73-80