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Chapter 8: Phase Diagrams


Example: Consider the system NaCl, KBr and H2O. ... H2O(s), KBr. H2O(s), and NaCl. H2O(s) Phases: P = 5 solid. Components: There are 8 constituents ... – PowerPoint PPT presentation

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Title: Chapter 8: Phase Diagrams

Chapter 8 Phase Diagrams
  • Homework
  • Exercises (a-only) 8.3,4, 6, 13, 15
  • Problems 8.2 8.4

  • Phase(P) -State matter which is uniform
    throughout not only in chemical composition but
    also in physical state J. Willard Gibbs
  • Solid
  • Various phases e.g. crystal structures (diamond
    graphite) or compositions (UCUC2)
  • Alloys (sometimes its difficult to tell this -
    microscopic examination may be necessary
    dispersions uniform on macroscopic scale)
  • Miscible one phase (P1)
  • Immisible multiple phases (Pgt1)
  • Liquid
  • Miscible liquids are one phase
  • Immiscible liquids are multiple phases (Pgt1)
  • Gas
  • Systems consisting of gases can have only one
  • Shape or degree of subdivision irrelevant

  • Heterogeneous and homogeneous systems
  • Systems with one phase are homogeneous
  • Systems with more than one phase are
  • Constituent- a chemical species (ion or molecule
    which is present
  • Component (C) - chemically independent
    constituents of a system
  • C of independent chemical constituents - of
    distinct chemical reactions
  • of independent chemical constituents total
    of constituents minus the number of any
    restrictive conditions (charge neutrality,
    material balance etc.)

Counting Components
  • Example CaCO3(s) CaO(s) CO2(g)
  • Phases P 2 solid 1 gas 3
  • Component C 3 consitiuents - 1 reaction 2
  • Example Consider the system NaCl, KBr and H2O.
    Suppose you can also isolate the following from
    it KCl(s), NaBr(s), NaBr. H2O(s), KBr. H2O(s),
    and NaCl. H2O(s)
  • Phases P 5 solid
  • Components
  • There are 8 constituents
  • You can write the following reactions four
  • NaCl KBr KCl NaBr NaCl H2O NaCl. H2O
  • KBr H2O KBr. H2O NaBr H2O NaBr. H2O
  • Conditions 1 -Material balance moles of KCl
    moles of NaBr NaBr. H2O
  • Components C (8 constituents -1 condition) - 4
    reactions 3

Counting Components (continued)
  • Remember you must count reactions which actually
    occur not those which could occur
  • Consider a system in which we has the following
    O2(g), H2(g), H2O(g)
  • If conditions are such O2(g) H2(g) H2O(g)
    does not occur, C3
  • If conditions are such (T, catalyst) O2(g), H2(g)
    H2O(g) occurs, then C3components -1reaction
  • If conditions are such (T, catalyst) O2(g), H2(g)
    H2O(g) occurs and you impose the condition
    that all the hydrogen and oxygen come from
    dissociation of water, then C3 constituents - 1
    condition -1 reaction 1
  • Identity of components is a matter of some
    choice, number isnt
  • Chose components that cannot be converted into
    one another by reactions
  • E.g. CaCO3(s) CaO(s) CO2(g)

Phase Rule
  • In discussing phase equilbria, you need only
    consider intensity factors (temperature,
    pressure, and concentration)
  • Only certain of these can be varied independently
  • Some are fixed by the values chosen for the
    independent variables and by the requirements of
    thermodynamic equilibrium
  • e.g. if you chose ? and T for a system P is fixed
  • Number of variables which can be varied
    independently without changing the number of
    phases is called the degrees of freedom of the
  • The number of degrees of freedom or variance of a
    system, F, is related to the number of
    components(C) and number of phases(P)
  • F C - P 2

Phase Rule Proof
  • In any system the number of intensive variables
    are pressure, temperature plus the mole
    fractions of each component of each phase.
  • Only C-1 mole fractions are needed since the ??xJ
  • Thus for P phase, the number of intensive
    variables P(C-1) 2
  • At equilibrium the chemical potential of phase
    must be equal,
  • i.e. µJP1 µJP2 µJP3 µJP4 µJP5.there are
    P-1 such equations
  • Since there are C components, equilibrium
    requires that there are C(P-1) equations linking
    the chemical potentials in all the phases of all
    the components
  • F total required variables - total restraining
  • F P(C-1) 2 - C(P-1) PC - P 2 -CP C
    C- P 2

One Component Systems
  • Phase rule says that you can have at most 3
  • F C- P 2 C1 so F3-P
  • If P3, F0 system is invariant
  • Specified by temperature and pressure and occurs
    at 1 point (called the triple point)
  • If one phase is present, F 2 that is P and T
    can be varied independently
  • This defines an area in a P,T diagram which only
    one phase is present
  • If two phases are present, F 1 so only P or T
    can be varied independently.
  • This defines a line in a P, T diagram

Single Component Phase Diagram
  • Point a only vapor present
  • Point b Liquid boils - 1 atm Tb but vapor and
    liquid co-exist along line(vapor pressure curve)
  • Point C Liquid freezes
  • Point D Only solid
  • Triple point 3 phases in equilibrium
  • Line Below triple point Vapor pressure above
  • Note You dont necessarily have to have 3 phases
    and they dont have to be solid liquid and gas

Cooling Curve
  • You can generate a cooling curve _at_ constant
    pressure (isobar) from previous phase diagram
  • Halts occur during 1st order phase transitions
    (e.g. freezing)

Experimental Measurements
  • Phase changes can be measured by performing DTA
    (differential thermal analysis) on samples
  • In DTA sample is heated vs. a reference
  • 1st order transitions can be measured even when
    they cant be observed
  • They will occur as peaks in DTA
  • High Pressures can be achieved with diamond anvil
  • See text descriptions

Two Component Systems
  • For two component systems, F 2-P2 4-P
  • If P or T is held constant, F 3-P ( indicates
    something is constant)
  • Maximum value for F is 2
  • If T is constant one degree of freedom is
    pressure and the other is mole fraction
  • Phase diagram (Constant T) is map of pressure
    and compositions at which each phase is stable
  • If P is constant one degree of freedom is
    temperature and the other is mole fraction
  • Phase diagram (Constant P) is map of temperature
    and compositions at which each phase is stable
  • Both Useful

Vapor Pressure Diagrams
  • By Raoults law (pA xApA pB xBpB ), the
    total pressure p is
  • p pA pB xApA xBpB
  • But xB (1-xA)so xApA xBpB xApA
    (1-xA) pB pB xA(pA -pB )
  • _at_ Constant T, total vapor pressure is
    proportional to xA (or xB )
  • The composition of the vapor is given by Raoults
    law so the mole fraction in the gas phase, yA and
    yB is
  • yA pA/p and yB pB/p also yA 1-yA)
  • From above yA xApA /pB xA(pA -pA )
  • If pA /pB pA/B then yA (xA pA/B) /(1
    (xA pA/B) - xA )
  • Or yA (xA pA/B) /(1 (xA ( pA/B - 1) )

Effect of Ratio of Vapor Pressure on Mole
Fraction in Vapor
  • This shows the vapor is richer in the more
    volatile component
  • If B is non volatile then yB 0

Pressure Composition Diagrams
  • Assume the composition on the x axis is the
    overall composition, zA (as mole fraction)
  • In Liquid region zA xA
  • In vapor Region region zA yA
  • In between two phases present
  • F1 so at given pressure compositions are fixed
    by tie lines

Isopleth Compositions in Each Phase
  • A vertical line represents a line of constant
    composition or isopleth
  • Until pressure p1sample is liquid vapor phase
    composition is a1
  • At p1, vapor composition is given by tie line to
    vapor curve
  • At p2 vapor composition is a2, liquid
    composition is a2 and overall composition is a
  • At p3 vitually all the liquid is vapor and trace
    of liquid has composition given by tie line to

Determining proportions of Phases (lever rule)
  • The composition of each phase is given by the
    each end of the tie line
  • The relative proportion of each phase is given by
    the length of the tie line
  • n?l? n?l? or n? n?l? / l?

  • Assume A more volatile than B
  • Region between two curves is 2-phase region
  • F1 (pressure is fixed)
  • At given temperature compositions are fixed by
    tie lines
  • Region outside lines composition temperature
  • Heat liquid with composition a1
  • Hits boiling curve, vapor has composition a2,
    liquid a2 (a1)
  • vapor is richer in more volatile component
  • Distillation
  • Vapor condensed (a2-a3)
  • New vapor _at_ concentration a3 (richer still)
  • New condensate _at_a4 etc until nearly pure liquid

Distillation/Theoretical Plates
  • A theoretical plate is a vaporization-condensation
  • Previous example has 3 theortetical plates
  • If the two curves move closer together, more
    theoretical plates are required to achieve same
    degree of separation
  • Curves more together if components have similar
    vapor pressures

Non-Ideal T-C Diagrams - High Boiling Azeotropes
  • Maximum in phase diagram occurs when interactions
    in liquid between A B stabilize the liquid
  • GE is more negative
  • If such a liquid is boiled, as vapor is removed,
    composition of liquid is richer in B (less A)
  • As vapor is removed you move to right up the
    curve until you reach point b
  • At b liquid boils with constant composition
  • Called an azeotrope (unchanging Gr.)
  • Example HCl-water boils _at_80 wt water at 108.6C

Non-Ideal T-C Diagrams - Low Boiling Azeotropes
  • Minimum in phase diagram occurs when interactions
    in liquid between A B destabilize the liquid
  • GE is more positive
  • If such a liquid is boiled, vapor is condensed
    , composition of vapor is richer in B (less A)
  • As vapor is removed you move to right down the
    curve until you reach point b
  • At b liquid boils with constant composition
  • Example ethanol-water boils at constant water
    content of 4 wt _at_ 78C

Non-Ideal T-C Diagrams - Immisicble Liquids
  • If two liquids immiscible and in intimate contact
    then p is nearly the sum of vapor pressures of
    pure components (p pA pB)
  • mixture will boil when p atmospheric pressure
  • intimate contact ( trace level saturation
  • If two liquids immiscible and not in intimate
    contact then p for each is the vapor pressures of
    pure components (p pA and p pB)
  • Each will boil separately when respective pA
    atmospheric pressure and/or pB atmospheric

Liquid-Solid Phase Diagrams
  • Liquids miscible solids immiscible
  • Consider Cooling along isopleth from a1
  • At a2 pure B starts to come out of solution
  • At a3 solution is mixture of B Liquid with
    composition b3 (ratio by lever rule)
  • At a4 liquid has composition e and freezes
  • In solid region there are two phases pure A and
    pure B
  • Composition given by tie line, ratio by lever
  • e is called a eutectic

Examples of Simple Eutectic Systems
  • In previous diagram, the eutectic (easily melted,
    Gr.) point is a temperature at which a mixture
    freezes without first depositing pure A or B
  • Like a melting point in that it it is a definite
  • Thats because, since C2 and P3, by Phase rule,
  • A cooling (or heating) curve will have a halt at
    the eutectic temperature
  • If pure A and pure B are in contact a liquid will
    form at the eutectic temperature
  • Examples
  • solder lead/tin (67/33) melting point 183C
  • NaCl and water (23/77) melting point -21.1C

Liquid-Solid Phase Diagrams - Reacting Systems
  • Some Binary systems react to produce one (or
    more) compounds
  • Definite composition
  • Unique melting point
  • Congruent melting point, I.e. melts to a liquid
    of identical composition
  • Maximum in phase diagram
  • Phase diagram interpreted as before except now
    there are additional regions

  • High Power Density Nuclear Sources for Space
    Power Propulsion
  • Performance superior to chemical rockets (H2/O2)
  • Enabling technology for Mars mission
  • Multiple coolants possible
  • He for power applications
  • H2, NH3 for propulsion applications
  • High power densities (10s MW/liter)
  • Superior performance to NERVA system (70s era
    nuclear propulsion system)
  • Typical operating temperatures gt2500 K for

PBR - Schematic
Materials Requirements for PBR Hot Components
  • Hot frit, nozzle, etc.
  • Withstand H2 Environment
  • 2800 K
  • 70 atmospheres
  • Large Temperature Gradients
  • 12K to Tmax over a few cm
  • Multiple Thermal Cycles
  • Long Exposure Times
  • 10s minutes
  • Launch Stresses
  • Withstand Radiation Fields
  • Not Affect Reactor Criticality
  • Fuel
  • Same as general components
  • Provide for adequate reactivity
  • Optimize coating thickness and type to maintain
    criticality Maintain (?Keff)?
  • No HfC coatings
  • Maintain coolable geometry
  • No large gaps between layers
  • No particle clumping
  • No reaction with other components, e.g. hot frit
  • Minimum F.P. and U release
  • Criticality and safety criterion

Hot Component Material Selection
  • Reactor Components (Hot Frit)
  • Rhenium (monolithic coatings)
  • Large neutronic penalty for monolithic Re
  • High radiation heating for monolithic Re
  • Extensive alloying of Re with fuel coatings _at_ T gt
    2760 K
  • Pyrolytic BN
  • High cost 11BN required
  • Unacceptable thermal decomposition (3 wt in 10
    min _at_ 2700 K
  • Reaction with baseline ZrC fuel coating
  • Carbide-Coated Carbon (graphite carbon-carbon)
  • Potential for CTE mismatch between coatings and
  • Fuels
  • Baseline fuel HTGR-type with ZrC coating
  • Conclusion Materials development program
    focused on carbide coatings of carbon materials

HTGR Type Fuel
  • Outer carbide shell
  • HTGR - SiC
  • PBR - ZrC
  • Pyrocarbon layer(s)
  • Spongy layer
  • Dense layer
  • Inner kernel
  • HTGR - UO2
  • PBR - UC
  • UC melting point 2525C
  • UC2 2350-2400C

Carbide Phase Diagrams
Liquid-Solid Phase Diagrams - Reacting Systems
(Incongruent Melting)
  • If the compound is not stable as a liquid
    incongruent melting occurs
  • Compound melts into components
  • Called the peritectic melting point
  • One solid phase melts around the other
  • Isopleths
  • a
  • a1-gt a2 liquid phase with A B
  • a2 solid B precipitates
  • a3-gta4 Solid B compound
  • b
  • b2-gt b3 liquid phase with A B
  • b3 B reacts to form compound
  • b3-gtb4 Solidcompound liquid
  • b5 solid A precipitates with compound

Zone Refining
  • Ultra high purity can be obtained by moving a
    small molten zone across a sample.
  • Impurities more soluble in liquid than solid so
    they continually move down the liquid front
  • One end becomes purer while other end is dirtier
  • Multiple passes can be used to achieve high purity

Ternary Phase Diagrams
  • Each composition must be defined by two
    compositions or mole fractions
  • Composition diagrams are therefore two
  • Triangle with each edge one line of binary phase
  • Pressure or temperature add third dimension
  • Usually temperature
  • Phase diagrams are usually given as a succession
    of surfaces at constant temperature
  • To examine temperature variation you hold
    composition constant

Ternary Phase Diagrams