GEO1003 Spring2007 Introduction to Phase Diagrams

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GEO1003 Spring2007 Introduction to Phase Diagrams
Introduction to Phase Diagrams
Phase diagrams can be complex. it is vital you
read ch6 in textbook for these classes and for
Exam 2!
In this class, we will look at terminology,
definitions and some simple phase diagrams. In
next class, we will look at more complex and
geologically relevant diagrams
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Proportions of phases in lava lake samples of
cooling basaltic magma
Note that the compositions of phases also changes
with time (on cooling)
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Why We Need Phase Diagrams!

• Several phases crystallize sequentially over T
  and P range
• Minerals that are solid solutions change
  composition during crystallization sequence
• Melt (magma) composition clearly also changes
  during this time
• Minerals that form and their sequence of
  crystallization depend on composition
• of magma, T, P etc
• P and presence/nature of volatiles can affect the
  temperature range of crystallization
• All of the above applies in reverse for melting
  of a rock (and generation of magma)
• Remember that a rock can form by cooling
  (quenching) at any time during
• crystallization and we need to understand which
  crystals are present, in what
• proportions, and their compositions
• Clearly the above is complicatedhence PHASE
  DIAGRAMS!!!

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• Phase diagrams are used by many scientists
  (geologists, chemists, materials scientists)
• They are a shorthand simplified way of
  illustrating what phases are stable under
• what conditions
• Igneous petrologists use them to illustrate what
  phases are present when a magma
• crystallizes or when a rock melts (usually at a
  particular fixed P or T)
• Phase diagrams simplify magma chemistry to a
  small number of components (ie
• some of the chemistry is ignored)

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Basic Definitions

• Phase diagram illustrates stability fields of
  phases in a system (system is some
• part of Universe you have selected for study)
• A phase is any substance that is physically
  separable from the system
• Physically separable means without breaking
  bonds
• Phases include solids, liquids, vapors, solid
  solution series (but not end-members of a
• solid solution series as these are not physically
  separable)
• A component is distinct from a phase, and often
  causes some confusion. It can
• be defined as a chemical constituent. For
  phases diagrams components are minimized
• (by convention).
• For example a beaker of melting ice, has two
  phases (ice and water) but only one
• component (H2O), not H2 and O.
• A variable can be subdivided into extensive
  variables and intensive variables.

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• Liquidus Temp above which all of system is
  liquid
• Solidus Temp below which all of system is solid
• Betweem solidus and liquidus is crystallization
  interval
• (ie solidliquid)
• Changes that effect system after it has
  completely solidified
• are called sub-solidus (eg. exsolution)

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The Phase Rule and Degrees of Freedom (F)

• There are a large number of intensive variables
  and many are interdependent
• The phase rule is used to determine how many
  intensive variables we must specify
• to constrain the others (and hence illustrate
  stability fields on a phase diagram)
• Minimum number of intensive variables that need
  to be described to define the system
• (ie draw a phase diagram) is called degrees of
  freedom (F)
• F can also be thought as number of intensive
  variables we can change for a
• particular phase (but only change within the
  stability field for that phase)
• without destroying the phase
• PHASE RULE FC-P2 (C is minimum number of
  components and P is number of phases)
• Use reduced phase rule FC-P1 if one of
  variables is fixed (often P in our examples)
• The phase rule can only be used with systems in
  chemical equilibrium, hence phase

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Application of Phase Rule to H2O system

• C is 1
• If water is solid (ice), then P 1 also. Hence
  from phase rule, F2. Hence in other
• words to fully specify the system we must
  specify 2 intensive variables. In this
• (and many other cases), this is P and T
• If we specify P and T then all other intensive
  variables (heat capacity, density etc
• are fixed (measurable) values.
• Remember that F can also be thought of as number
  of intensive variables that can be
• changed independently (until number of phases
  changes). In this case, P or T can be changed
• independently and we still have only ice (until
  either liquid water or steam is produced,
• i.e. we have crossed into another stability
  field)
• If we heat the ice (at constant P), eventually a
  new phase (liquid water) appears, so
• P is now 2, and F is now only 1.
• When new phase appears, we need to specify only
  one intensive variable (could be P or T)
• to define the system

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Simple One-Component Geological System

• Systems can be subdivided into one, two, three or
  more component systems.
• To describe magmas as fully as possible we
  usually need three or more components
• Lets start by looking at a simple one-component
  system that is geologically relevant,
• that of silica (SiO2)
• Note stability fields of various phases
• Each field is a divariant field (P and T can be
  varied within them independently)
• Lines separating fields are univariant lines
  (curves)
• Note that there are also invariant points on this
  1 component phase diagram
• Note also this diagram illustrates two phases of
  quartz (these are the polymorphs
• alpha-quartz and beta quartz)

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Two-Component System With Solid Solution Series

• Now we add a second component. This complicates
  matters, but the easiest 2-component
• diagram to follow is one with complete solid
  solution
• Now we have two components, and so in a binary
  plot one of the axes has to reflect
• compositional change (referred to as X)
• Other axis is an intensive variable (P or T
  usually). We now must fix one of the variables
• (eg P for a T-X plot, or T for a P-X plot)
• We will look at a very relevant 2 component
  system with complete solid solution,
• that of plagioclase feldspar (which has the two
  components Ab (albite) and
• anorthite (An)
• We will look at this diagram in some detail and
  follow what happens during crystallization
• and melting

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Lets follow crystallization of liquid a on this
diagram.

• On all phase diagrams
• Solidus Temperature below which everything is
  solid
• Liquidus Temperature above which everything is
  liquid
• Between liquidus and solidus curves is a field of
  solid(s)liquid(s)
• Lines bc, df, gh are called tie-lines. They are
  isothermal and join (tie)
• co-existing liquid and solid compositions

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The Lever Rule

• Lever Rule is used to work out proportions of
  crystals and liquid at any instant
• (eg particular T).
• Use intersection of bulk composition line and
  compositional tie lines
• E.g. on plagioclase diagram. Proportion of
  crystals (plag) at point b is de/df.
• Proportion of liquid at same point is ef/df