Sections:9.2, 9.3, 9.4, 9.5

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• Chapter 9
• Sections9.2, 9.3, 9.4, 9.5

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Chapter 9 Phase Diagrams

• Why study?
• One of the reason why a knowledge and
  understanding of phase diagrams is important to
  the engineers related to the design and control
  of heat treating processes.
• Some properties are functions of their
  microstructures, and, consequently, of their
  thermal histories.

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Definitions and Basic Concepts

• Components Pure metals and/or compounds of
  which an alloy is composed
• Example in a copper-zinc brass, the components
  are Cu and Zn.
• System
• First meaning refer to a specific body of
  material under consideration ( e.g., a ladle of
  molten steel)
• Second meaning relate to the series of possible
  alloys consisting of the same components, but
  without regard to alloy composition (e.g., the
  iron-carbon system)
• Solid solution Consists of atoms of at least two
  different types
• Solute ? an element or compound present in a
  minor concentration
• Solvent ? an element or compound in greater
  amount host atoms.
• Solute atoms occupy either substitutional or
  interstitial positions in the solvent lattice
• Crystal structure of the solvent is maintained

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9.2 Solubility Limit

• Solubility Limit The maximum concentration of a
  solute atoms that may dissolve in the solvent to
  form a solid solution at some specific
  temperature.
• The addition in excess results in the formation
  of another solid solution or compound that has a
  distinctly different composition.
• Example Sugar-Water (C12H22O11-H2O) system
• Initially, as sugar added to water, a solution of
  syrup forms.
• As more sugar is added, solution becomes more
  concentrated
• Solution becomes saturated with sugar ?Solubility
  limit is reached
• Not capable to dissolving more ? further addition
  simply settle to the bottom
• System now consists of two separate substances
• A sugar-water syrup liquid solution, and
• Solid crystals of undissolved sugar

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9.3 Phases

• Phase defined as a homogeneous portion of a
  system that has uniform physical and chemical
  characteristics.
• Every pure material is considered to be a phase
• Also every solid, liquid, and gaseous solution
• e.g., syrup solution is one phase, and solid
  sugar is another
• If more than one phase is present, it is not
  necessary that there be difference in both
  physical and chemical properties
• A disparity in one or both is sufficient
• e.g., water and ice in a container ( two phase,
  identical chemically)
• When a substance can exist in two or more
  polymorphic forms (e.g. having both FCC abd BCC)
  ? each structure is a separate phase because of
  difference in physical properties.

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• A single-phase system is termed homogeneous
• Systems composed of two or more phases are termed
  mixture or heterogeneous systems.
• Most metallic alloys, ceramics, polymeric, and
  composite systems are heterogeneous.
• Ordinarily, in multiphase systems
• The phases interact such that the property is
  different and more attractive than individual
  phases.

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9.4 Microstructure

• Physical properties and mechanical behavior
  depend on the microstructure.
• In metal alloys, microstructure is characterized
  by
• Number of phases present
• Their proportions
• The manner they are distributed or arranged
• The microstructure of an alloy depends on such
  variables as
• Alloying elements present
• Their concentrations
• The heat treatment
• Microstructure studies
• surface preparation (Polishing and etching)
• For two phase alloys, one phase may appear light
  and other dark

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9.5 Phase Equilibria

• Free energy is a function of the internal energy
  of a system, and also of the randomness or
  disorder of the atoms or molecules (or entropy).
• A system is at equilibrium if its free energy is
  at a minimum under some specified combination of
  temperature, pressure, and composition.
• In macroscopic sense, this means that the
  characteristics of the system do not change with
  time but persist indefinitely
• ? The system is stable
• A change in temperature, pressure, and/or
  composition in equilibrium ? increase in free
  energy ? another equilibrium state whereby the
  free energy is lowered.

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• Phase equilibrium ? refers to equilibrium as it
  applied to systems in which more than one phase
  may exist.
• Example
• Sugar-water syrup is contained in a closed vessel
• solution is in contact with solid sugar at 20oC
• If system is in equilibrium,
• Composition of syrup is 65wt C12H22O11-35wt H2O
  (Fig 9.1)
• Amount and composition of syrup and sugar will
  remain constant
• If temperature is raised to 100oC
• Equilibrium is temporarily upset
• Solubility limit of sugar has increased to 80 wt
• Some of the solid sugar will dissolve until new
  equilibrium is reached

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• Metastable state
• Nonequilibrium state
• A state of equilibrium is never completely
  achieved because the rate of approach to
  equilibrium is extremely slow
• Common in many metals or solid solutions
• Persist indefinitely with imperceptible changes
  with time.
• Metastable structure
• More practical than equilibrium
• Some steel and aluminum rely on this for heat
  treatment designing

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• Chapter 9
• Sections 9.6

13
Equilibrium Phase Diagrams

• Equilibrium Phase diagram
• Represents the relationships between temperature
  and the compositions and the quantities of phases
  at equilibrium.
• Also known as phase, equilibrium or
  constitutional diagram
• A binary alloy is one that contains two
  components.
• Temperature and composition are the variable
  parameters for binary alloys.
• Of more than two components, phase diagrams
  become extremely complicated and difficult to
  represents

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9.6 Binary Isomorphous systems

• Phase diagram of the copper-Nickel system is
  shown in Fig 9.2a.
• Ordinate ? Temperature
• Abscissa ? composition
• Composition ranges from 0 wt Ni (100 wt Cu) to
  100 wt Ni (0 wt Cu)
• Three different phase regions, or fields, appear
• An alpha (a) field
• A liquid (L) field
• A two-phase (aL) field

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• Liquid L homogeneous liquid solution composed of
  both copper and nickel
• a phase a substitutional solid solution
  consisting of both Cu and Ni atoms, and having an
  FCC crstal structure.
• Isomorphous complete liquid and solid solubility
  of two components
• Copper-Nickel system is Isomorpous
• At temperatures below about 1080oC, mutually
  soluble in solid state for all compositions
• Complete solubility is due to same crystal
  structure (FCC), nearly identical atomic radii
  and electronegativities, and similar valences

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• Nomenclature
• For metallic alloys, solid solutions are
  designated by a, b, g, etc.
• Liquidus line liquid phase at all temperature
  and composition above this line
• Solidus line solid phase below this line at all
  temperatute and composition
• Liquidus and solidus lines intersect at two
  extreme points
• Correspond to melting temperature of pure
  components
• Copper (1085oC) and Nickel (1453oC)
• Heating of pure copper
• Moving vertically on left-temperature axis
• Remains solid until its melting temperature is
  reached
• No further heating possible, until this
  transformation is complete

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• For any composition other than pure components
• Melting phenomenon occurs over the range of
  temperature between the solidus and liquidus
  lines
• Both solid a and liquid will be in equilibrium
  within this range

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Interpretation of Phase Diagrams

• For binary system of known composition and
  temperature that is in equilibrium, at least
  three kinds of information are available
• The phases that are present
• The composition of these phases
• The or fraction of the phases
• 1.0 Phases present
• Relatively simple
• Example (refer to Fig 9.2a),
• 60 wt Ni-40 wt Cu at 1100oC Point A
  a phase
• 35 wt Ni-65 wt Cu at 1250oC Point B
  a liquid phases

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PHASE DIAGRAMS
Tell us about phases as function of T, Co, P.
For this course --binary systems just
2 components. --independent variables T and
Co (P 1atm is always used).
Phase Diagram for Cu-Ni system
Adapted from Fig. 9.2(a), Callister 6e. (Fig.
9.2(a) is adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash (Ed.), ASM International,
Materials Park, OH (1991).
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PHASE DIAGRAMS and types of phases
Rule 1 If we know T and Co, then we know
--the and types of phases present.
Examples
Cu-Ni phase diagram
Adapted from Fig. 9.2(a), Callister 6e. (Fig.
9.2(a) is adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash (Ed.), ASM International,
Materials Park, OH, 1991).
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PHASE DIAGRAMS composition of phases
Rule 2 If we know T and Co, then we know
--the composition of each phase.
Cu-Ni system
Examples
Adapted from Fig. 9.2(b), Callister 6e. (Fig.
9.2(b) is adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash (Ed.), ASM International,
Materials Park, OH, 1991.)
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PHASE DIAGRAMS weight fractions of phases
Rule 3 If we know T and Co, then we know
--the amount of each phase (given in wt).
Cu-Ni system
Examples
27wt
Adapted from Fig. 9.2(b), Callister 6e. (Fig.
9.2(b) is adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash (Ed.), ASM International,
Materials Park, OH, 1991.)
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THE LEVER RULE A PROOF
Sum of weight fractions
Conservation of mass (Ni)
Combine above equations
A geometric interpretation
9
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• Composition need to be specified in terms of only
  one of the constituents
• For example, composition of Ni is used
• Identical results if composition of Cu is used
• Co 35 wt Ni
• Ca 42.5 wt Ni
• CL 31.5 wt Ni
• WL ( 42.5 35) / (42.5 31.5) 0.68
• Wa (35 31.5) / (42.5 31.5) 0.32
• Volume fraction See equations 9.5 9.7

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Volume Fractions
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Development of Microstructure in Isomorphous
alloys-- Equilibrium Cooling

• 35 wt Ni-65wt Cu
• as cooled from 1300oC
• Cooling very slowly ? phase equilibrium is
  maintained
• Cooling ? Moving down
• At 1300oC, completely liquid
• At b (1260oC), solidification starts
• At d (1220oC), solidification completes

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Development of Microstructure -- Non-Equilibrium
Cooling

• Extremely slow cooling not valid
• Temperature change ? readjustment in composition
  ? diffusional processes
• Diffusion rates are low for the solid phase and,
  for both phases, decrease with diminishing
  temperature
• Practical solidification processes, cooling rates
  are much too rapid to allow these compositional
  readjustments and maintenance of equilibrium ?
  different microstructure develops

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• At b, a phase begin to form a(46Ni)
• At c,
• liquid composition 29wt Ni-71 wt Cu
• Solid phase 40 wt Ni-60 wt Cu a(40Ni)
• Since diffusion in solid is relatively slow, a
  phase formed at b has not changes composition
  appreciably ? still a(46Ni)
• Composition of a grains continuously changes
  radially from 46 wt Ni at center to 40 wt Ni at
  the outer grains ? average composition (say 42
  wtNi)
• Solidus line has shifted

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• Chapter 9
• Sections 9.7

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9.7 Binary Eutectic Systems

• Binary Eutectic Phase Diagram
• Another type of common and relatively simple
  phase diagram
• Figure 9.6 shows for the copper-silver system
• Features of Binary Eutectic Phase Diagram
• Feature 1 Three single-phase regions ( a, b, and
  liquid )
• The a phase solid solution rich in copper,
  silver as solute, FCC
• The b phase solid solution rich in silver,
  copper as solute, FCC
• Solubility in each of these solids phases is
  limited
• Solubility limit for a phase
• Line ABC ( Increases with temperature, maximum,
  decreases to minimum)
• Solvus line (BC)
• Solidus line (AB)

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• Solubility limit for b phase
• Line FGH ( Increases with temperature, maximum,
  decreases to minimum)
• Solvus line (GH)
• Solidus line (FG)
• Line BEG is also solidus line
• Maximum solubility in both a and b phases occur
  at 779oC
• Feature 2 Three two-phase regions
• a L
• b L
• a b

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• As silver is added to copper,
• The melting temperature of copper is lowered by
  silver additions.
• Line AE the liquidus line
• Same is true as copper is added to silver
• Point E is called the invariant point (CE 71.9
  wt Ag, TE 779oC)
• At E, an important reaction occurs
• Upon cooling, a liquid phase is transformed into
  a and b solid phases
• The opposite reaction occurs upon heating
• This is called eutectic reaction ( Eutectic means
  easily melted)
• CE and TE represents eutectic composition and
  temperature
• Horizontal solidus line at TE is called the
  eutectic isotherm

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• The eutectic reaction, upon cooling, is similar
  to solidification of pure components
• Reaction proceeds to completion at a constant
  temperature
• Isothermal at TE
• Solid products of eutectic solidification is
  always two solid phases
• Another common eutectic system is that for lead
  and tin
• The phase diagram is shown in Figure 9.7
• Example 9.2
• Example 9.3

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Development of Microstructure in Eutectic Alloys

• Depending on composition, several different types
  of microstructures
• These possibilities considered in terms of the
  lead-tin phase diagram
• Figure 9.7

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• First case Composition C1
• Range
• Composition ranging between a pure metal and the
  maximum solid solubility for that component at
  room temperature (20oC)
• Lead-rich alloy (0-2 wt Sn)
• Slowly cooled down

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• Second Case Composition C2
• Range
• Composition ranging between the room temperature
  solubility and the maximum solid solubility at
  the eutectic temperature.
• Corresponds 2 wt Sn to 18.3 wt Sn

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• Third Case Composition C3
• Solidification of the eutectic composition
• Corresponds 61 wt Sn
• The microstructure at i is known as eutectic
  structure.

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• Lamellae
• The microstructure of a solid consisting of
  alternating layers
• Shown in Figure 9.12

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• Fourth Case Composition C4
• All composition other than the eutectic
  composition
• At m, a phase will be present in both
• Eutectic a
• Primary a

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• Microconstituents
• An element of the microstructure having an
  identifiable and characteristic structure.
• At m, two microconstituents ( primary a and the
  eutectic structure )

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• Relative amounts of both eutectic and primary a
  microconstituents
• Eutectic microconstituents forms from liquid
  having eutectic composition (61 wt Sn, Fig
  9.11, point i)
• Apply lever rule using tie line
• Eutectic fraction
• We WL P / (PQ)
• Primary a fraction
• Wprimary a Q / (PQ)
• Total a fraction (primary plus eutectic)
• W a (QR) / (PQR)
• Total b fraction (primary plus eutectic)
• W b P / (PQR)

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• Chapter 9
• Sections 9.8, 9.9, 9.13

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9.8 Equilibrium Diagrams Having Intermediate
Phases or Compounds

• Terminal solid solutions
• Solid phases exist over the composition ranges
  near the concentration extremities of the phase
  diagram
• Examples Copper-Silver system (Figures 9.6)
• Lead Tin system (Figure 9.7)
• Intermediate solid solutions
• Intermediate phases
• Solid phases at other than the two composition
  extremes
• Example Cupper-Zinc system (Figure 9.17)

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• Intermetallic compounds
• Discrete intermediate compounds rather than solid
  solutions
• These compounds have distinc chemical formulas

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9.9 Eutectoid and Peritectic Reactions

• Eutectoid Reaction
• Invariant point E, Figure 9.19
• Upon cooling, a solid phase transforms into two
  other solid phases
• Reverse reaction occurs on heating
• Horizontal line at 560oC eutectoid or eutectoid
  isotherm
• Eutectic ? liquid on cooling transforms into two
  solids
• Importance iron-carbon diagram
• Peritectic Reaction
• Another invariant reaction (Point P, Figure 9.19)
• Upon heating, one solid phase transforms into a
  liquid phase and another solid phase
• (d L) ?on cooling ?e

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THE IRON-CARBON SYSTEM9.13 The iron-iron
carbide (Fe-Fe3C) phase diagram

• Of all binary alloys, the most important is the
  iron-carbon phase diagram.
• A portion is shown in Figure 9.22
• Practically all steels and cast irons have less
  than 6.70 wt C.
• Pure iron
• Upon heating, experiences two changes in crystal
  structure before it melts
• At room temperature, the stable form ( ferrite or
  a iron ) has a BCC.
• At 912oC, Ferrite experiences polymorphic
  transformation FCC austenite, or g iron.
• At 1394oC, reverts back to a BCC phase ( d
  ferrite )
• At 1538oC, d ferrite melts

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• At 6.7 wt C
• Intermediate compound iron carbide, or cementite
  (FE3C), is formed.
• 6.7 wt C corresponds to 100 wt Fe3C
• Carbon is an interstitial impurity in iron
• Forms a solid solution with each of a and d
  ferrites and g austenite
• BCC a ferrite
• Small concentration of carbon are soluble (0.022
  wt at 727oC)
• Even though small concentration, significantly
  influences mechanical properties
• Relatively soft, magnetic at temperature below
  768oC, density of 7.88 g/cm3
• Figure shows photomicrograph

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• Austenite or g phase iron
• Not stable below 727oC
• FCC structure
• Maximum solubility of carbon in austenite 2.14
  wt C at 1147oC.
• Figure 9.23b shows photomicrograph
• BCC d ferrite is virtually same as a ferrite
• Stable only at relatively high temperatures ? no
  technological importance
• Cementite (Fe3C) forms when the solubility limit
  of carbon in a ferrite is exceeded below 727oC
• Coexist with g phase between 727 and 1147oC
• Cementite is very hard and brittle ? strength of
  steel is enhanced by its presence

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• One eutectic reaction for iron-carbon system
• At 4.30 wt C and 1147oC
• L ? on cooling ? g Fe3C
• L ? on heating ? g Fe3C
• Eutectoid invariant point at 0.76 wt C and 727oC
• g (0.76 wt C) ? on cooling ? a (0.022 wt C)
  Fe3C(6.7 wtC)
• g (0.76 wt C) ? on heating ? a (0.022 wt C)
  Fe3C(6.7 wtC)

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• Chapter 9
• Sections 9.14, 9.15

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9.14 Development of Microstructures in
Iron-Carbon Alloys

• Microstructure depends on both the carbon content
  and heat treatment.
• Discussion confined to very slow cooling ?
  equilibrium is continuously maintained.
• Phase change from g austenite region into the a
  Fe3C phase field
• Relatively complex, similar to eutectic system
• Consider cooling of an alloy of eutectoid
  composition
• (Point a at 0.76 wt C and 800oC)
• No changes until the eutectoid temperature
  (727oC)
• At b, pearlite microstructure
• Figure 9.25, photomicrograph of eutectoid steel
  showing the pearlite.

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• The pearlite exists as grains
• Often termed colonies
• Layer orientation is same in each colony
• Thick light layers ? ferrite phase
• Thin lamellae, mostly dark ? cementite
• Ferrite ? soft and ductile
• Cementite ? hard and brittle
• Pearlite ? intermediate between ferrite and
  cementite

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Hypo-Eutectoid Alloys

• Consider a composition Co to the left of
  eutectoid
• Between 0.022 and 0.76 wt C
• Termed a hypoeutectoid (less than eutectoid)
  alloy
• Cooling is shown in Figure 9.27
• At d, about 775oC, a g phase
• Composition of ferrite (a iron) changes along MN
• Slight changes
• Composition of austenite (g iron) changes
  dramatically along MO
• At f, just below the eutectoid
• All g-phase having eutectoid composition
  transforms to pearlite
• No change in a-phase (ferrite )
• Ferrite exist in two phases
• Eutectoid ferrite ? ferrite that is present in
  pearlite
• Proeutectoid ferrite ? pre- or before eutectoid
  formed above Te

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• Figure 9.28 photomicrograph of a 0.38 wt C
  steel
• Large white regions proeutectoid ferrite
• Pearlite
• Dark regions
• Spacing between a and Fe3C layers vary from grain
  to grain

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Hyper-Eutectoid Alloys

• Right side of eutectoid ( between 0.76 and 2.14
  wt C)
• At g, only g phase (austenite ) of composition C1
• Upon cooling at h, g ? g Fe3C phase field
• Proeutectoid cementite ? that forms before the
  eutectoid reaction
• Cementite composition remains constant as the
  temperature changes
• Austenite composition changes along line PO
  towards eutectoid
• Below eutectoid temperature at i,
• All remaining austenite of eutectoid composition
  ? pearlite (aFe3C)
• Microconstituents of resulting microstructure
• ? pearlite and proeutectoid cementite (Fig
  9.30)

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Photomicrograph of hypereutectoid alloys

• Photomicrograph of 1.4 wt C steel is shown in
  Fig. 9.31
• Consists of pearlite and proeutectoid cementite
• Proeutectoid cementite appears light
• Same appearance as proeutectoid ferrite
• ? difficulty in distinguishing between
  hypoeutectoid and hypereutectoid steels on the
  basis of microstructure

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Photomicrograph of hypereutectoid alloys (Contd.)

• Comparison with hypoeutectoid alloys
  photomicrograph

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Relative amounts for hypoeutectoid steel alloys

• Using lever rule
• Tie line extends between 0.022 and 0.76 wt C
• Fraction of pearlite,
• Wp T / (TU) (Co 0.022) / (0.76
  0.022)
• Fraction of proeutectoid a,
• Wa U / (TU) (0.76 - Co) / (0.76
  0.022)

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Relative amounts for hypereutectoid steel alloys

• Using lever rule
• Tie line extends between 0.76 and 6.7 wt C
• Fraction of pearlite,
• Wp X / (VX) (6.70 C1) / (6.70 - 0.76)
• Fraction of proeutectoid cementite (Fe3C)
• WCementite V / (VX) (C1 - 0.76 ) /
  (6.70 - 0.76)

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9.15 The Influence of Other Alloying Elements

• Other alloying elements (Cr, Ni, Ti, etc.) bring
  about dramatic changes
• Changes in the position of phase boundaries and
  shapes
• One important change ? shift in eutectoid
  position w.r.t temperature and composition
• These effects are illustrated in Figures 9.32 and
  9.33

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