Terminology

• Alloy- a material made by taking a pure material (usually a metal) and adding another material to it (at the molecular level)
  • Can be single-phase or multi-phase
• Components- the elements that make up an alloy
• Composition- the elemental make up of an alloy; often given by weight %, volume %, or atomic %
  • Both components and composition determine crystalline structures, which determine mechanical properties.
• Phase- any portion of a system that is physically homogeneous and bounded by a surface that separates it from other distinct portions
  • Separate phases do not have to be separate states of matter (solid, liquid, gas)
    • ex: coexisting crystal structures, like FCC and BCC, are separate phases
  • Characteristics of phases:
    1. The same structure or atomic arrangement throughout
    2. Roughly the same composition and properties throughout
    3. A definitive interface between the phase and any surrounding phases
  1. Gibb’s phase rule: $F = C-\pi +2$ (for solid solutions when temperature and composition can vary and pressure is fixed)
     1. $C$- # components
     2. $\pi$- # phases present in system
     3. $F$- # degrees of freedom

        1. of independent intensive properties required to fix the state of the system (ex: temperature, pressure, composition, etc.)

     4. Assumes thermodynamic equilibrium

Solid Solutions

• Solid solution- homogeneous arrangement composed of only one phase; one or more solutes in a solvent
  • Crystal structure of the solvent remains unchanged
  • Solutes and solvent don’t chemically bond; the solution is more like a mixture or compound
  • Most real-life alloys are mixtures of substitutional and interstitial alloys.
  • Can refer to two elements or two compounds
• Unlimited solubility- regardless of the ratio of atoms, only one phase is produced upon combining elements
  • Most metals have unlimited solubility in the liquid phase, but unlimited solubility is harder to achieve in the solid phase.
  • Hume-Rothery Rule- for an alloy system to have an unlimited solid solubility,
    1. Similar size (w/in <15% difference in atomic radius)
    2. Same crystal structure
    3. Same or close valence
    4. Approximately same electronegativity
• Limited solubility- after the solubility limit, additional atoms form a new compound (i.e., phase separation occurs, so two solid phases coexist)
  • Most alloys have limited solubility
• Solid solution strengthening- increased strength in material due to increased resistance to dislocation motion
  • Often occurs when metal solid solutions are formed
  • 2 factors that affect degree of strengthening:
    1. Atomic size: large difference in atomic size —> increased strength
       1. Size difference causes strain field surrounding the solute when there is a dislocation
    2. Amount of alloying element: greater amount —> greater strength
• How solid solution strengthening affects material properties:
  • Strength-based properties (yield strength, ultimate tensile strength, and hardness) of the alloy increase compared to pure metals.
  • Ductility decreases compared to pure metal (because motion of dislocations is limited).
  • Electrical conductivity decreases compared to pure metal (because additional defects are added).
  • Resistance to creep and strength at high temperatures increases compared to pure metal.

Phase Diagrams

• Phase diagram- shows the phases of an alloy and their compositions as a function of temperature and alloy composition; indicates which conditions are thermodynamically stable and steady-state
  • These are plotted at constant pressure, which means that each phase diagram is just a slice of a 3D phase diagram with temperature, pressure, and composition.
• Binary phase diagram- represents a system with only two elements/compounds
  • Pseudo-binary phase diagram- represents equilibria among three or more components using two compounds
• Isomorphous phase diagram- represents system in which only one solid phase forms (complete solid solubility)
  • Features:
    • Liquidus line- line above which there is pure liquid state at any composition
    • Solidus line- line below which there is pure solid state at any composition
    • 2-phase equilibrium- freezing range is between the liquidus and solidus lines
      • For any intermediate alloy, there is a gap between the liquidus and solidus lines; i.e., there is not a single $T_m$, but there’s a range of $T_m$
    • Liquid phase represented by $L$
    • Solid solution phase represented by $\alpha$
    • Tie lines- isotherms within the 2-phase equilibrium region
      • Its intercepts lie on the liquidus and solidus lines. These intercepts give the composition of the last liquid to freeze at a given temperature or the first solid to freeze at a given temperature.
      • Gibb’s phase rule: when temperature is fixed, $F = C - \pi + 1$ —> only one independent intensive property (composition) is needed to fix the state (fully define) the system (alloy)
      • Lever rule- allows the relative amounts of each phase on a tie line to be determined: $phase \ \%=\dfrac{opposite \ arm \ of \ lever}{total \ length \ of \ tie \ line}*100$

Equilibrium and Non-Equilibrium Solidification

• During solidification, both nucleation and growth are required. Solidification starts occurring as temperature decreases when an alloy reaches the liquidus line. The % solid will continue to increase (the tie lines change) until the material reaches the solidus line.
• Equilibrium solidification- solidification at slow cooling rates such that the final structure is in equilibrium; the composition remains fixed, and all that changes is temperature
  • Slow cooling rates allow for the diffusion between phases to produce the compositions given by the phase diagram
  • Doesn’t happen often in real life.
• Non-equilibrium solidification- solidification at rapid cooling rates such that the final structure is not in equilibrium; as temperature decreases, the composition changes because there is not enough time for diffusion to occur
  • Segregation- the nonuniform composition produced by nonequilibrium solidification; the formation of onion-like layers in solidified alloys
    • Effects:
      • Don’t know the composition of an alloy —> don’t know material properties
      • Lowered melting temperature
    • Microsegregation- occurs over short distances, often between dendrite arms
      • Leads to poor casting properties
      • Causes hot shortness, which is the melting of interdendritic lower melting point material below the equilibrium solidus
      • How to fix microsegregation: homogenization- heating the casting to below the nonequilibrium solidus for a few hours eliminates most of the composition differences (like annealing)
        • Diffusion time: $t_d\ \alpha \dfrac{L^2}{D}$ where L is the length and D is diffusivity
          • The larger the length of a material, the more the material would have to be heated to homogenize the material —> homogenization works better on the micro scale than the macro scale
    • Macrosegregation- occurs over a large distance, such as the surface and center of the casting
      • Cannot be eliminated due to large diffusion distanced
      • Can be reduced by hot working