Solid Liquid Phase Diagrams

1
Solid - Liquid Phase Diagrams Consider a
2-component system in a region of temperatures
and pressures in which the liquids are partially
are partially miscible and the liquid and vapor
also form a low boiling azeotrope. If the upper
consulate temperature is below the azeotropic
temperature the following phase diagram results
2
If, on the other hand, the upper consulate
temperature is higher than the temperature of the
low boiling azeotrope, the two phases regions
grow into each other and we get the following
phase diagram
On the above phase diagram describe the phases
that are stable or in equilibrium in each region
of the diagram?
3
The binary liquid vapor phase diagram that we
have just considered, where the upper consulate
temperature is higher than the low boiling
azeotropic temperature, has a structure that is
characteristic of many binary solid liquid phase
diagrams
Rules for interpreting binary phase diagrams 1.
A binary phase diagram consists of one phase
regions, two phase regions, and horizontal lines
of three phase equilibrium. 2. A
horizontal line of three phase equilibrium is a
boundary for three two phase regions a. a
eutectic line has 2 two phase regions above the
line and 1 two phase region below the
line. b. a pertectic line has 1 two phase
region above the line and 2 two phase
regions below the line. 3. A horizontal traverse
must alternately encounter one and two phase
regions.
4
Consider the binary Ag - Mg phase diagram
1. Starting at the left of the above diagram
successively label each of the regions where
single solid phases are stable with the Greek
letters a, b, g, d, f, and q (you may not need
all of these letters). 2. Label the region
where the melt exists with an L 3. In each of
the regions where two phases are in equilibrium
use the appropriate Greek letters to indicate
what these phases are. 4. Identify any lines
of three phase equilibrium and label these lines
as eutectic or peritectic, indicating the phases
that are in equilibrium along these lines.
5
Some solids, Au and Si are an example, are
completely immiscible in each other over the
entire composition range. Consider the Au
- Si phase diagram developed at 1.000 bar total
pressure.
Note that liquidus curve that defines the
composition of the liquid in equilibrium with the
solid is also the curve of the depressed freezing
point of the pure solid that results from adding
a second solid into the melt. What phases are in
equilibrium along the eutectic line? In this
system are the eutectic temperature and
composition fixed or can they vary?
6
An equation can be developed to describe the
liquidus lines. Consider the equilibrium
between pure solid Au and a liquid solution of Si
in Au 1 bar Au (s) ------gt Au
(liquid Au solution containing Si) At equilibrium
the chemical potentials of Au in these two phases
are equal uAu (s) uAu
(soln) We will take the standard state of the
solid Au to be pure solid Au and the standard
state for the Au in solution to be pure liquid
Au uoAu (s) uoAu (liq) R T ln aAu(soln)
Rearranging and dividing through by T and then
differenting with respect to temperature at
constant pressure gives ? (uoAu (s) / T) / ? T
)P - ? (uoAu (liq) / T) / ? T P R ?
( ln aAu(soln) ) / ? T P which using the Gibbs
Helmholtz equation ? (Go / T) / ? TP ?
(uo / T) / ? T P - Ho / T2 can be
written HoAu (liq) - HoAu (s) D Homelt, Au
R T2 ? ( ln aAu(soln) ) / ? T P where D
Homelt, Au is the molar enthalpy of melting of
pure Au at standard pressure 1 bar
Au (s) ----------gt Au (liq)
Tom, Au
7
The variables in this equation can be separated
and integrated from pure liquid Au, where the
melting point is Tom, Au to a liquid Au solution
containing dissolved Si with a melting point of
Tm 0 ?ln aAu(soln) d ( ln aAu(soln) ) Tom,
Au ? Tm D Homelt, Au / ( R T2 ) dT Why is the
lower limit on the left integral zero? Making
the reasonable assumption that D Homelt, Au is
not a function of temperature and integrating
gives ln aAu(soln) - D Homelt, Au / R 1
/ Tm - 1 / Tom, Au If the liquid solution is
ideal, then we can write ln
XAu(soln) ln (1 - XSi(soln) ) - D
Homelt, Au / R 1 / Tm - 1 / Tom, Au This
expression can be solved for to give an equation
describing the Au liquidus or Au freezing point
depression curve XSi(soln) 1 - e - D
Homelt, Au / R 1 / Tm - 1 / Tom, Au Using
data in Chemical Rubber Company Handbook of
Chemistry and Physics determine the eutectic
temperature and composition in the Au - Si system.
8
Consider the changes that occur in cooling a Au
and Si containing melt that is 50 mole Si from
1400 oC
Initially the melt just cools. At 1000 oC the
melt becomes saturated in Si and pure solid Si
just begins to precipitate out of the melt. As
the temperature is further lowered more Si
precipiates from the melt. What happens to the
composition of the melt as this is occurring? At
any point in the two phase region the relative
amounts of melt and pure solid Si present are
given by the lever law nmelt ( XT - Xmelt )
n Si(s) (1 - XT )
9
50.0 grams of melt that is initially 50.0 mole
in Si is cooled to 650 oC, at which point
3.00 grams of Si have precipiated from the
solution. What is the composition of the melt at
this point in mole percent Si? At the
eutectic temperature the melt also becomes
saturated in Au and pure solid Au precipiates
from the melt along with the Si. The temperature
remains fixed (why?) during this eutectic halt,
until the melt is exhausted. Once the melt is
exhausted further cooling just cools a mixture of
pure solid Au and Si of composition, XT.
10

• The slope of the cooling curve is determined by
  the heat capacity of the system and the rate of
  cooling.
• Differentiating the heat capacity
• dT dq / C
• with respect to time
• dT/dt (1 / C) dq/dt
• Do systems with higher heat capacities cool
  faster or slower?
• Where only the melt is present this expression
  can be written
• dT/dt dq/dt 1 / (nAu nSi) (XAu Cp, Au(l)
  XSi Cp, Si(l)
• When solid Si begins to precipitate, the rate of
  cooling changes and in fact becomes non-linear
  (but not noticeably) because
• The relative number of moles of Si in the
  melt and solid Si is constantly changing as
  solid Si precipitates from the melt, resulting
  in a constantly changing heat capacity.
• The precipitation of Si from the melt is
  exothermic, thus changing the rate of heat
  removal.

rate of cooling
rate of heat removal (experimentally designed to
be constant)
11
The length of the eutectic halt is proportional
to the moles of the liquid melt that are present
when the eutectic temperature is reached
time of halt nmelt DHoe / (dq/dt)
ntotal (1 - XT ) / (1 - Xe ) DHoe / (dq/dt) At
what overall composition would you expect to
observe the longest halt, at what composition the
shortest halt? Plots of the length of the
eutectic halt versus overall composition can be
used to determine the eutectic composition
12
The p-toluidine phenol binary solid liquid phase
diagram exhibits compound formation between
p-toluidine and phenol
liquid melt
When a solid that is 50 mole phenol is heated
to 30 oC, the solid melts to form a liquid that
is also 50 mole in phenol. Congruent melting
in which a solid melts to form a liquid of the
same composition is indicative of compound
formation. Since the compound is 50 mole
phenol, it would have an empirical formula
of T1.0-0.5 P0.5 T0.5 P0.5 T1 P1
TP Label the above regions according to the
phases that are stable or in equilibrium in each
region. Indicate any eutectic or peritectic
lines and the phases in equilibrium along these
lines? Note that compound formation divides the
more complicated phase diagram into simpler
diagrams that resemble phase diagrams associated
with simple eutectic behavior.
13
Incongruent melting in which an unstable compound
rather than melting on heating decomposes to give
another solid and a liquid of a composition
different than the original compound is
illustrated in the Mg and Ni binary solid -
liquid phase diagram
What are the empirical formulas of compounds A
and B? Label the phase diagram according to the
phases that are present or are stable? Describe
the changes that occur as a melt that is 50 mole
Ni is cooled from 1300 oC to 400 oC. For the
above cooling write the reaction that occurs at
the peritectic line. What is the limiting
reactant?
14
The phase diagram for the sulfuric acid water
system, which exhibits compound or hydrate
formation between sulfuric acid and water, is
shown below
What are the empirical formulas of the sulfuric
acid water hydrates present in this phase
diagram? Which of them melt congruently and
which decompose on heating? If you live in a cold
climate and allow your car battery acid to reach
a level of 85 by weight sulfuric acid, should
you be concerned?
15
For the TiO2 and MnO binary solid - liquid phase
diagram
Label all the regions according to the phases
present. For any compounds determine ? their
empirical formulas ? whether they are stable
or unstable ? the temperatures at which they
melt or decompose Label all eutectic and
peritectic lines, indicating the phases that are
in equilibrium along these lines. Construct a
cooling curve for a 45.0 weight MnO melt that
is initially at 1500 oC and cools to 1000 oC (see
the red isopleth on the diagram). Describe the
changes that occur along this isopleth. 100.0
grams of the melt described above is cooled to
1200 oC, where the composition of the melt is
39.0 weight MnO. Calculate the grams of all
phases present and the grams of TiO2 and MnO that
are present in the melt.
16
Mo and W are examples of two solids that are
completely miscible with each other over the
entire composition range
17
Au and Fe exhibit limited miscisbility and an
upper consulate temperature that is higher than
the solidus temperature, giving rise to the
following phase diagram
Describe and label the phases on this phase
diagram. Construct a cooling curve for the
isopleth shown on the diagram and describe the
changes that occur as a melt of this composition
is cooled along this curve. Write an equation
describing the reaction that occurs at the
peritectic.
18

• Given the following information construct a
  semi-quantitative binary solid - liquid phase
  diagram for Al and Co with a mole Co axis (use
  decent ruled graph paper to do this problem)
• pure Al melts at 658 oC
• pure Co melts at 1480 oC
• AlCo melts congruently at 1630 oC
• Al5Co2 decomposes at 1170 oC to give a liquid
  that is 24 mole Co.
• Al4Co decomposes at 945 oC to give a liquid
  that is 19 mole Co.
• At 1375 oC solid solutions that are 84 and 92
  mole in Co are in equilibrium with a melt that
  is 89 mole in Co.
• At 500 oC a eutectic that is 12 mole in Co
  is formed.
• An extensive on line collection of binary phase
  diagrams can be found at
• http//cyberbuzz.gatech.edu/asm_tms/phase_diagrams
  /
• A good complilation of both binary and ternary
  (primarily) phase diagrams can be found
• Phase Diagrams for Ceramists, The American
  Ceramic Society, Westerville, Ohio, Volumes I -
  XIV.