11MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsMicrostructure and Phase Transformations in Multicomponent SystemsChapter Outline: Phase Diagrams Definitions and basic concepts Phases and microstructure Binary isomorphous systems (complete solid solubility) Binary eutectic systems (limited solid solubility) Binary systems with intermediate phases/compounds The iron-carbon system (steel and cast iron)2MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsComponent - chemically recognizable species (Fe and C in carbon steel, H2O and Sucrose in sugar solution in water). A binary alloy contains two components, a ternaryalloy – three, etc.Phase – a portion of a system that has uniform physical and chemical characteristics. Two distinct phases in a system have distinct physical and/or chemical characteristics (e.g. water and ice, water and oil) and are separated from each other by definite phase boundaries. A phase may contain one or more components. A single-phase system is called homogeneous, systems with two or more phases are mixtures or heterogeneous systems.Definitions: Components and Phases3MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsSolvent - host or major component in solution, solute -minor component.Solubility Limit of a component in a phase is the maximum amount of the component that can be dissolved in it (e.g. alcohol has unlimited solubility in water, sugar has a limited solubility, oil is insoluble). The same concepts apply to solid phases: Cu and Ni are mutually soluble in any amount (unlimited solid solubility), while C has a limited solubility in Fe. Definitions: Solubility Limit4MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsMicrostructureThe properties of an alloy depend not only on proportions of the phases but also on how they are arranged structurally at the microscopic level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.Microstructure of cast IronPhase diagrams will help us to understand and predict microstructures like the one shown in this pageThe long gray regions are flakes of graphite. The matrix is a fine mixture of BCC Fe and Fe3C compound.http://www2.umist.ac.uk/material/research/intmic/ (link is dead)25MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsA system is at equilibrium if at constant temperature, pressure and composition the system is stable, not changing with time. Equilibrium is the state that is achieved given sufficient time. But the time to achieve equilibrium may be very long (the kinetics can be slow) that a state along the path to the equilibrium may appear to be stable. This is called a metastable state. In thermodynamics the equilibrium is described as a state of a system that corresponds to the minimum of thermodynamic function called the free energy. Thermodynamics tells us that:Equilibrium and Metastable States• Under conditions of a constant temperature and pressure and composition, the direction of any spontaneous change is toward a lower free energy. • The state of stable thermodynamic equilibrium is the one with minimum free energy. • A system at a metastable state is trapped in a local minimum of free energy that is not the global one.metastableequilibriumFree EnergyArrangement of atoms6MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsPhase diagram is a graphical representation of all the equilibrium phases as a function of temperature, pressure, and composition.For one component systems, the equilibrium state of the system is defined by two independent parameters (P and T), (T and V), or (P and V). Phase diagramPressure-temperature phase diagram for H2O:7MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsPVT surface of a pure (1-component) substancehttp://www.eng.usf.edu/~campbell/ThermoI/ThermoI_mod.html8MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsA pure substance is heated at constant pressureTTbV39MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsPressure-temperature phase diagram for carbonWe can see graphite, diamond, liquid carbon on the phase diagram… but where are fullerenes and nanotubes? 10MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsA phase diagrams show what phases exist at equilibrium and what phase transformations we can expect when we change one of the parameters of the system.Real materials are almost always mixtures of different elements rather than pure substances: in addition to T and P, composition is also a variable.We will limit our discussion of phase diagrams of multi-component systems to binary alloys and will assume pressure to be constant at one atmosphere. Phase diagrams for materials with more than two components are complex and difficult to represent. An example of a phase diagram for a ternary alloy is shown for a fixed T and P below.Phase diagrams for binary systemsternary phase diagram of Ni-Cr-Fe11MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsIsomorphous system - complete solid solubility of the two components (both in the liquid and solid phases). Binary Isomorphous Systems (I)Three phase region can be identified on the phase diagram: Liquid (L) , solid + liquid (α +L), solid (α )Liquidus line separates liquid from liquid + solidSolidus line separates solid from liquid + solidα + LαL12MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsBinary Isomorphous Systems (II)Example of isomorphous system: Cu-Ni (the complete solubility occurs because both Cu and Ni have the same crystal structure, FCC, similar radii and electronegativity).413MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsBinary Isomorphous Systems (III)In one-component system melting occurs at a well-defined melting temperature.In multi-component systems melting occurs over the range of temperatures, between the solidus and liquidus lines. Solid and liquid phases are at equilibrium with each other in this temperature range.α + LαLliquid solutionliquid solution +crystallites ofsolid solutionpolycrystalsolid solutionLiquidusSolidusAB20 40 60 80Composition, wt %Temperature14MSE 2090: Introduction to Materials Science Chapter 9, Phase DiagramsInterpretation of a binary phase diagramsFor a given temperature and composition we can use phase diagram to