Lecture 17: Binary and Ternary Phase Diagrams Read Chpt 8

Lecture 17:
Binary and Ternary Phase Diagrams
Read Chpt 8
Binary diagrams come in three types. We will look at each in turn.
(1) No Solid Solution
(2) Complete Solid Solution
(3) Partial Solid Solution
There are a number of tricks for understanding any of these binary (2 component)
phase diagrams, one is the concept of a:
Tie Line: a line on a phase diagram joining phases at equilibrium with one
another (dashed and dotted lines on diagrams below)
Liquidus: line that shows the composition of the liquid phase formed at a
given T

(1) NO SOLID SOLUTION (PURE A or PURE B)
Tieline: composition of the solid is given by the right hand side (pure An); composition
of the liquid is given by the intersection with the liquidus line (53% An, 47% Di)

Evenutally, you’ll reach the Eutectic composition: approximately 45%An, 55% Di
So farther from eutectic T, composition gets farther from eutectic composition,
closer to pure system composition

(2) INCOMPLETE SOLID SOLUTION
Now we have some miscibility (ability of one phase to dissolve in another)
Just like salt is miscible in water, up to the saturation limit.
Solvus: a line that shows the saturation limit of one solid component into another
Solidus: a line that gives the composition of a solid solution in equilibrium with a
liquid (analogous to liquidus in the no solid solution case)
1450°
Liquid
Liquidus
Solidus
T
T*
Di ss
+ L
An ss
+ L
Di ss
X 1 X 3 X 4
An ss
Solvus
Di ss
+ An ss
Di
X 2
An
Example: Orthoclase (KAlSi 3 O 8 ) – Albite (NaAlSi 3 O 8 )

1450°
Liquid
T
T*
Di ss
+ L
An ss
+ L
An ss
Di ss
+ An ss
Tielines:
Di
Di ss
X 1 X 3 X 4
X 2
An
At T*
From Di to X 1 : pure solid Di ss , composition evolves from Di to X 1
From X 1 to X 2 : pure solid Di ss + liquid; composition of Di ss => given by X 1 ;
composition of liquid given by X 2
From X 2 to X 3 : pure liquid; composition evolves from X 2 to X 3
From X 3 to X 4 : pure solid B ss + liquid; compositioin of B ss given by X 4 ; composition of
liquid given by X 3
From X 4 to An: pure solid B ss ; composition evolves from X 4 to An

(3) COMPLETE SOLID SOLUTION
Plagioclase Feldspars, for example,
NaAlSi 3 O 8 (albite) => CaAl 2 Si 2 O 8 (anorthite)
“melting loop”: solidus and liquidus lines join to form a loop
You can still use tielines to understand this diagram!!

(3) COMPLETE SOLID SOLUTION
At T*: At compositions from A to X*: pure solid solution with composition A to X*
At compositions from X* to Y*: liquid + solid solution; solid solution always has
composition X*; liquid always has composition Y*; as you move from X* to Y* you
change from mostly solid to mostly liquid
At compositions from Y* to B: pure liquid with composition from Y* to B

How can you use phase diagrams to understand something about petrology?
Well, what happens when you take a melt and cool it down? Depends on the type of
phase diagram and on how the magma forms:
(1) Perfect Equilibrium Crystallization: always at equilibrium, composition
of liquid and solid formed are constantly evolving; start with liquid of composition X,
end with solid of composition X

(1) Perfect Fractional Crystallization
• Crystals are removed from the melt (remember Bowen and differentiation of
magmas?), in other words, they sink to the bottom of the melt and stop reacting with
the remaining liquid
• So, first crystal to form has the same composition as in the perfect equilibrium
crystallization case, but subsequent crystals have solidus composition, so that the
AVERAGE composition of solids is very different
• The liquid becomes more and more pure (following the liquidus), and the liquid lasts
longer and goes through more compositions:

TERNARY PHASE DIAGRAMS
What if we add yet another component? Now we can’t draw the T-X phase diagram
in 2D, so we either need a 3D diagram or, we can use Projections
Binary eutectic point => ternary cotectic line
Ternary eutectic: 3 solids and liquid form