PHASE DIAGRAMS Phase –a chemically and structurally homogenous region of a material. Region of uniform physical and chemical characteristics. Phase boundaries separate two distinct phases. A single phase system is called homogeneous. A system with two or more phases is called heterogeneous. Phase Diagram –a graphic representation showing the phase or phases present for a given composition, temperature and pressure. Component –the chemical elements which make up the alloy. Solvent atoms: primary atomic species. Host atoms Solute atoms: the impurities. Normally the minor component Solubility Limit ‐ Maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution. The excess of solute forms another phase of different composition. Example: water‐sugar Phase Diagrams of Pure Substances •Predicts the stable phase as a function of Ptotal and T. Example: water can exist in solid, liquid and vapor phases, depending on the conditions of temperature and pressure. • Characteristic shape punctuated by unique points. –Phase equilibrium lines –Triple Point (three different phases of water in equilibrium) – Critical Point Example: In the pressure‐temperature (PT) phase diagram of water there exists a triple point at low pressure (4.579 torr) and low temperature (0.0098oC) where solid, liquid and vapor phases of water coexists. Vaporization Line –Liquid and vapor coexists Freezing Line – Liquid and solid coexist. Sublimation Line – Solid and vapor coexist Phase ‐ Any portion including the whole of a system, which is physically homogeneous within it and bounded by a surface so that it is mechanically separable from any other portions. Gibbs Phase Rule From thermodynamic considerations, J.W. Gibbs (1839‐1903 American physicist –University of Yale) derived the following equation: P + F = C + 2 Where P = number of phases which coexists in a given system F = degrees of freedom C = number of components in the system 2 = one can vary temperature and pressure F = 0 zero degrees of freedom. Neither P or T can be change (a point – invariant point) F = 1 one degree of freedom. One variable (P or T) can be changed independently (a line) F = 2 two degrees of freedom. Two variables (P or T) can be changed independently (an area). Schematic unary phase diagram for magnesium, showing the melting and boiling temperatures at one atmosphere pressure. C= 1 for pure magnesium Point A: P= 1 for pure liquid phase 2+C=F+P 2+1=F+1 F=2 degrees of freedom – change pressure and temperature in liquid Phase. Point B: P= 2 for liquid and solid 2+C=F+P 2+1=F+2 F=1 degrees of freedom – change pressure or temperature (and the other variable is dependent –to stay on the line). Point X: P= 3 (liquid, solid and vapor coexist) 2+C=F+P 2+1=F+3 F=0 degrees of freedom –pressure and temperature are fixed at the the single point called the triple point. Example ‐ For pure substance where P and T can be changed P + F = C + 2 = 1 + 2 = 3 Pure substance in a triple point, then C = 1 (one component) and P = 3 (number of phases that coexist) The value of F is zero (zero degrees of freedom) the three phases coexist in a point. ‐ For pure substance where P and T can be changed P + F = 1 + 2 = 3 Pure substance in a freezing line, then C = 1 (one component) and P = 2 (number of phases that coexist) The value of F is one (one degree of freedom) the two phases (solid and liquid) coexist in a line. Solubility: The amount of one material that will completely dissolve in a second material without creating a second phase. Unlimited solubility: When the amount of one material that will dissolve in a second material without creating a second phase is unlimited. Limited solubility ‐ When only a maximum amount of a solute material can be dissolved in a solvent material. Solid Solution: Solid‐solution strengthening ‐ Increasing the strength of a metallic material via the formation of a solid solution. Dispersion strengthening ‐ Strengthening, typically used in metallic materials, by the formation of ultra‐fine dispersions of a second phase. The effects of several alloying elements on the yield strength of copper. Resistance to dislocation motion (loss in ductility) Microstructure The structure observed under a microscope Al Brake –more than Iron‐chromium alloy –one phase one phase (solid solution) Phase Equilibria • Free energy: a function of the internal energy of a system • Equilibrium: a system is at equilibrium if its free energy is at a minimum • Phase equilibrium: for a system which has more than one phase • Phase Diagram is a diagram with T and Composition as axes. They define the stability of the phases that can occur in an alloy system at constant pressure (P). The plots consist of temperature (vertical) axis and compositional (horizontal) axis. • Constitution: is described by (a) the phases present (b) the composition of each phase (c) the weight fraction of each phase Isomorphous Phase Diagrams Binary phase diagram ‐ A phase diagram for a system with two components (C=2). Ternary phase diagram ‐ A phase diagram for a system with three components (C=3). Isomorphous phase diagram ‐ A phase diagram in which components display unlimited solid solubility. Liquidus temperature ‐ The temperature at which the first solid begins to form during solidification. Solidus temperature ‐ The temperature below which all liquid has completely solidified. Freezing range – between the liquidus and solidus. Binary isomorphous systems • Binary alloy: A mixture of two metals is called a binary alloy and constitute a two‐component system. •Each metallic element in an alloy is called a separate component. [Sometimes a compound is considered a component, (e.g., iron carbide)] • Isomorphous System: In some metallic systems, the two elements are completely soluble in each other in both the liquid and solid states. In these systems only a single type of crystal structure exists for all compositions of the components (alloy) and therefore it is called isomorphous system. Example: Binary Isomorphous System (Cu –Ni) T<1085oC: Cu & Ni are mutually soluble in solid state –complete solubility → •both have the same FCC structures, •atomic radii and electronegativities are nearly identical •similar valences → isomorphous Interpretation of Phase Diagrams Constitution: is described by (a) the phases present (b) the composition of each phase (c) the weight fraction of each phase (a) Phases Present Point A: at T=1100oC 60wt% Ni – 40wt% Cu Only α phase is present Point B: at T= 1250oC 35wt%Ni –65wt% Cu Both α & liquid phases are present at equilibrium (b) Composition of each phase Single phase: Point A: 60wt%Ni –40%Cu alloy at 1100oC Two‐phase region: Tie line: across the two‐ phase region at the temperature of the alloy Point B: T=1250oC Composition of Liquid phase: CL=31.5wt%Ni – 68.5%Cu Composition of α phase: Cα=42.5wt%Ni‐ 57.5wt%Cu (c) Weight fraction of each phase Single phase: 100% Ex: Point A: 100% α phase Two‐phase region: Ex: Point B LEVER RULE (Inverse Lever Rule) S R W = W = L RS+ α RS+ CCα − o CCo− L WL = Wα = CCα − L CCα − L co− c L35− 31. 5 Example: Point B: Wα = = . 0 = or 32 32% cs− 42 c L 5..− 31 5 C0 = 35wt%Ni cs− c o42. 5− 35 Cα = 42.5%, CL = 31.5% WL = = . 0 = or 68 68% cs− 42 c L 5..− 31 5 Volume fraction For an yoall consisting of α and β phases, the volume onfracti of the α phase is defined as vα Vα = , VVα+ β =1 Then, the weight fractions are vα+ v β v ρ vβρ β ν ν W = α α ; W = Where α and β are the α β volumes of α and β αvρ α+ v β ρ β αvρ α+ v β ρ β W β W α ρ α ρ β V α = V β = W W β W W α + α + β ρ α ρ β ρ α ρ β Derivation of the lever rule 1) All material must be in one phase or the other: WWα + L =1 2) Mass of a component that is present in both phases equal to the mass of the component in one phase + mass of the component in the second phase: Wα c α+ L W L= c o c 3) Solution of these equations gives us the Lever rule. c− c c− c W = o L W = α o α c− c L α L cα − cL Equilibrium Cooling ‐ Development of Microstructure in Isomorphous Alloys Example: 35wt%Cu‐65wt%Ni system – Slow cooling from point a to point e a: 1300oC: complete liquid with 35wt%Cu- 65wt%Ni b: ~1260oC: first solid begin to form (α-46wt%Ni) c: ~1250oC: α-43wt%Ni, L- 32wt%Ni d:~1220oC: last liquid to solidify e: 35wt%Cu – 65wt%Ni solid phase Nonequilibrium Cooling ‐ Development of Microstructure in Isomorphous Alloys Fast cooling Compositional changes require diffusion •Diffusion in the solid state is very slow. ⇒ The new layers that solidify on top of the existing grains have the equilibrium composition at that temperature ⇒ Formation of layered (cored) grains. Tie‐line method to determine the composition of the solid phase is invalid. •The tie‐line method works for the liquid phase, where diffusion is fast. •Solidus line is shifted to the right (higher Ni contents), solidification is complete at lower T, the outer part of the grains are richer in the low‐melting component (Cu). •Upon heating grain boundaries will melt first. This can lead to premature mechanical failure. Complete solidification occurs at lower temperature and higher Nickel concentration than equilibrium Solid can’t freeze fast enough: solidus line effectively shifted to higher Ni concentrations.