ch9

• Phase diagram


  A graphical representation of the relationships between the phases of a material as a function of variables such as temperature, pressure, and composition
• The understanding of phase diagrams for alloy systems is extremely important because there is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its phase diagram. In addition, phase diagrams provide valuable information about melting, casting, crystallization, and other phenomena.
• Component


  A pure metal or compound of which an alloy is composed
• Solute


  The minor constituent in a solid solution
• Solvent


  The major constituent in a solid solution
• System


  A specific body of material under consideration or the series of possible alloys consisting of the same components but without regard to alloy composition
• Solid solution


  A solid phase that contains atoms of at least two different types, with the solute atoms occupying either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained
• Solubility limit


  The maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution
• Phase


  A homogeneous portion of a system that has uniform physical and chemical characteristics
• Homogeneous system


  A single-phase system
• Heterogeneous system


  A system composed of two or more phases
• Microstructure


  The number of phases present, their proportions, and the manner in which they are distributed or arranged in a material
• Equilibrium


  A state in which the characteristics of a system do not change with time, but persist indefinitely
• Phase equilibrium


  Equilibrium as it applies to systems in which more than one phase may exist, reflected by a constancy with time in the phase characteristics of a system
• Metastable state


  A state in which a system is not in complete equilibrium, but the rate of approach to equilibrium is extremely slow
• Metastable


  A state or microstructure that may persist indefinitely, experiencing only extremely slight and almost imperceptible changes as time progresses
• Phase diagram


  A diagram that conveniently and concisely displays information about the control of the phase structure of a particular system
• Phase diagram


  • Three externally controllable parameters affect phase structure: temperature, pressure, and composition
  • Phase diagrams are constructed when various combinations of these parameters are plotted against one another
• One-component (or unary) phase diagram

  A phase diagram for a pure substance, where pressure and temperature are the variables
• Most often, the pressure axis in a one-component phase diagram is scaled logarithmically
• One-component phase diagram


  • Phase diagram for H2O
• Triple point


  A point on a P-T phase diagram where all three phases (solid, liquid, vapor) are simultaneously in equilibrium with one another
• Binary phase diagram


  A phase diagram where temperature and composition are variable parameters and pressure is held constant (normally 1 atm)
• Isomorphous system


  A binary system where the two components have complete liquid and solid solubility
• Liquidus line


  The line separating the liquid (L) and liquid + solid (L + α) phase fields
• Solidus line


  The line separating the solid (α) and liquid + solid (L + α) phase fields
• For any composition other than pure components, melting occurs over the range of temperatures between the solidus and liquidus lines
• Both solid α and liquid phases are in equilibrium within the temperature range between the solidus and liquidus lines
• Determining information from a binary phase diagram

  1. Identify phases present

  2. Determine phase compositions

  3. Determine phase amounts
• To determine phase compositions, different methods are used for single-phase and two-phase regions
• Phases


  The phases that are present, the compositions of these phases, and the percentages or fractions of the phases
• Determining phases present


  1. Locate temperature-composition point on diagram

  2. Note phase(s) with which corresponding phase field is labeled
• For a 60 wt% Ni-40 wt% Cu alloy at 1100°C, only the single α phase will be present
• For a 35 wt% Ni-65 wt% Cu alloy at 1250°C, both α and liquid phases are present at equilibrium
• Determining phase compositions


  1. Locate temperature-composition point on phase diagram

  2. Use different methods for single- and two-phase regions

  3. For single phase, composition is same as overall alloy composition

  4. For two-phase, construct tie line and drop perpendiculars to determine compositions
• Determining phase amounts


  1. Use lever rule

  2. Construct tie line at temperature

  3. Locate overall alloy composition on tie line

  4. Compute fraction of each phase from tie line segment lengths
• For 35 wt% Ni-65 wt% Cu alloy at 1250°C, the liquid phase fraction is 0.68 and the α phase fraction is 0.32
• Volume fraction


  Preferred measure of relative phase amount, can be converted from mass fraction using densities
• Equilibrium cooling of isomorphous alloys

  1. Start at fully liquid composition at high temperature

  2. As temperature decreases, first solid α phase forms with different composition than liquid

  3. Compositions of solid and liquid change as cooling continues, maintaining tie line relationship
• For 35 wt% Ni-65 wt% Cu alloy, solid α phase initially forms at ~1260°C with 46 wt% Ni, while liquid is 35 wt% Ni