# Practice Problems

```Practice Problems
Problem W4.1. Plutonic Equivalents of Surface Igneous Rocks. Igneous rocks that form
when lava cools on the surface correspond to equivalent rocks that form when magma
cools underground.
WQ4.1. What is the plutonic equivalent of rhyolite?
WQ4.2. What is the plutonic equivalent of basalt?
Problem W4.2. Identifying Plutonic Rocks. Imagine examining a plutonic rock that
contains visible quartz, potassium feldspar, and plagioclase.
WQ4.3. What is this rock, most likely?
Problem W4.3. How Composition Varies with Temperature. This problem requires
Magmas crystallize (solidify), not at a single temperature, but over a range of
temperatures. This is different from your daily experience with the crystallization
(freezing) of water, which occurs at a single temperature, not over a range. At normal
pressure, water crystallizes to ice at its single crystallization temperature of 0ºC (32ºF).
Why should a liquid like magma behave differently, with a range of crystallization
temperatures?
The short answer is that water is a simple substance, with the simple formula H2O,
whereas magmas are very complex substances with complex chemical formulas. Let us
amplify this.
An ice crystal grows from a tiny nucleus of frozen water, adding more water particles as
it grows. Thus, an ice crystal is essentially pure frozen water, all the way through. From
the earliest-formed center of the crystal to its last-formed outer rim, the ice crystal has a
uniform composition, entirely of H2O molecules (Figure WS4.1A).
Water-freezing-into-ice is a single-component system because only one type of
molecule, H2O, is involved in the crystallization. We can show this by drawing a simple
phase diagram (Figure WS4.1B). It shows water changing from its liquid phase to its
solid phase at 0ºC.
Figure WS4.1 (A) Ice crystal. (B) Water phase diagram at 1 atmosphere of
pressure. The phase diagram shows water changing from its liquid phase to its
solid phase at 0°C (32°F).
Magmas are far more complex. In the melt are numerous elements, such as sodium,
calcium, potassium, aluminum, silicon, oxygen, carbon, and so on. As a result, several
different minerals crystallize from the melt as it cools. One of these, plagioclase
feldspar, actually varies in composition within a single crystal. We often find plagioclase
crystals that contain zones of different compositions (Figure WS4.2A).
Consequently, the phase diagram for plagioclase is more complex than the phase diagram
for ice (Figure WS4.2B). Plagioclase is a two-component system, which grades from a
sodium-rich formula to a calcium-rich formula (see bottom of Figure WS4.2B). It is this
complexity of composition that allows plagioclase to crystallize over a range of
temperatures, as shown in the figure. (This is true even at any single pressure.) In the
figure, the curve represents the composition of plagioclase crystals as they form at
different temperatures.
Looking deeper, consider a magma having a composition indicated by the sample at
temperature point T1. As this magma cools to temperature T1, a calcium-rich plagioclase
crystal will grow in the melt. This first little bit of crystal will be 80% calcium and 20%
sodium. But as the magma cools further, a more sodium-rich plagioclase will solidify
from the melt. At temperature point T2, plagioclase crystals then forming will be half
calcium and half sodium.
Even later-forming (cooler) sodium-rich plagioclase will grow around and encase the
earlier-formed calcium-rich plagioclase crystals. Eventually, when the magma has cooled
to temperature T3, pure sodium plagioclase will crystallize, forming the last layer of
zoned plagioclase crystals, like that shown in Figure WS4.2A.
This phenomenon is so dependable that the composition of plagioclase can be read
directly from temperature in the phase diagram. For example, a crystal forming at 1200°C
(2,150°F) will be 75% sodium and 25% calcium.
And this is just one example. Plutonic rocks are made up of many different minerals, not
just plagioclase. Each mineral and its range of composition contributes to the overall
temperature range over which a magma crystallizes. The net result is a large variation in
mineral content among plutonic igneous rocks.
Figure WS4.2 (A) Plagioclase crystal in cross-section. (B) Phase diagram
of plagioclase at fixed pressure.
The full phase diagram for plagioclase feldspar at a given pressure is shown in Figure
WS4.3. The solid curve indicates temperatures at which different compositions of
plagioclase crystallize in the melt, and is called the solidus. The dashed line indicates
temperatures of different liquid compositions, and is called the liquidus. The liquidus and
solidus divide the phase diagram into three areas:
 all-liquid melt
 liquid plus some solid crystals of plagioclase
 all solid plagioclase crystals
Let us interpret this diagram, using the sample magma indicated. As our magma cools, it
doesn’t initially change composition; it simply lowers in temperature (indicated by the
straight line downward). The composition of the liquid is shown by the x-axis: in this
case, 30% calcium feldspar.
As the magma cools to the temperature of the liquidus (reaches T1), plagioclase crystals
begin to form. You can read their composition from the horizontal line drawn to C1.
Thus, at T1, there is a liquid having the composition of about 30% calcium feldspar, plus
a few individual crystals of plagioclase having the composition 70% calcium feldspar.
To keep this simple, assume that once a crystal of plagioclase forms, it will not
chemically react with the magma around it. This isolation from the melt means that
different layers of crystalline material will surround the initial “seed” of high-calcium
plagioclase. This whole process is called fractional crystallization, and it results in highly
zoned plagioclase crystals.
Figure WS4.3 Full phase diagram for plagioclase feldspar.
WQ4.4. In Figure WS4.3, use a ruler to determine the various compositions at T1, T2, T3,
and T4.
At temperature T1:
composition of the melt is ______ % calcium feldspar.
composition of the plagioclase just formed is ______ % calcium feldspar.
At temperature T2:
composition of the melt is ______ % calcium feldspar.
composition of the plagioclase just formed is ______ % calcium feldspar.
At temperature T3:
composition of the liquid material is ______ % calcium feldspar.
composition of the plagioclase just formed is ____ % calcium feldspar.
At temperature T4:
composition of the last drop of liquid and the final rim of the plagioclase crystal is ____
% calcium feldspar.
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Pennine Alps

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