Chapter 10 Phase diagramsAlloys are composed of either pure metals and/or compounds referred to as componentsSolute is the species being dissolved, usually less of itSolvent is the species dissolving the soluteSystem has been used to refer to a specific body or process under inspection, but can also used to describe the general range of compositions and solubilities of mixtures of given species (e.g. the Iron-carbon system)Solid solution

at least two types of atomscrystal structure of solvent maintainedsolute distributed to either substitutional or interstitial positions in solvent lattice

Solubility limit is the maximum concentration/temperature function of when addition of more solute no longer results in the same single solid solution, often creating two solid solutionsE.g.: adding sugar to water slowly with stirring until solubility limit, after which added sugar sinks to bottom as sugar crystals. Phases are described as homogeneous portions of a system that has uniform physical and chemical characteristics. All pure substances and unique solid, liquid, or gaseous solutions are considered phases.Systems with 2+ phases called mixtures or heterogeneous systems. Most metallic alloy, ceramic, polymeric, and composite systems are heterogeneous

MicrostructureMicrostructure is the term that describes the structural characteristics of a system in such a way that is only visible through optical or electron microscopes. In metals, microstructure is variable depending upon the number of phases, the atomic species present, the concentrations of those species, the heat processing, and distribution of unique phasesPhysical properties and specifically the mechanical behavior of a material depends upon the microstructure Recall: to see microstructure, polishing and etching required as pre-treatment.

Phase equilibria-Equilibrium is a function of the Gibbs Free Energy that a substance has, in turn a function of internal energy, U, and the randomness.-Equilibrium is said to be established when the given substance is at a energy minima of the function of G(T,P,%wt)-Equilibrium implies that the characteristics of the material at eq will not change over time with the T,P,%wt held constant, and will persist indefinitely. A change in one of these variables will ultimately change the energy of the system, possibly enough so to create the conditions for spontaneous transition to another phase or state with a lower G.-Phase equilibrium, in turn, is equilibrium as it applies to systems in which more than one phase may exist, and is likewise represented by the variability with time of the phase characteristics of the system.-Not only relative amounts of different phases are crucial in solid systems, but also the arrangement and distribution of those phases.-In many solid systems, equilibrium is approached so slowly that equilibrium can ever really be said to be reached. These are said to be in nonequilibrium or metastable states.-Many systems and structures that are of most use to engineers today are in fact metastable ones.

Phase diagram (AKA equilibrium diagram) is a convenient and concise way to convey much of the relevant phase information of a system, and usually are some comparison of T,P,or%wt-The simplest is the Unary phase diagram, a phase diagram of a pure substance. Think of the Solid/Liquid/Vapor diagrams for water-Often, when pressure is used as the ordinate (vertical axis), it is plotted logarithmically to better show change -When three phases coexist in solution and are in equilibrium with each other, the point on the diagram is referred to as a triple point or invariance point. (Change in P or T would cause one phase to disappear)

Binary Phase diagrams-Often, binary phase diagrams are plotted according to temperature and composition, and pressure is held constant. -Binary phase diagrams represent the various phases and solutions that exist/coexist for a certain system of two components at given Ts and %wts-Many specific microstructures are the results of following certain heating/cooling curves in a phase diagram (also, often the speed the curve is traveled is important)- Phase diagrams would obviously then be useful in predicting phase transitions, which is in turn useful in noting the relation of the phase transitions to the resulting microstructure.-When two components are mutually soluble in each other under a set of conditions and at all compositions, they are said to form an isomorphous systemi.e. Isomorphous systems have components with complete liquid and solid solubility-Phase diagram lines signifying a liquid phase going to a liquid-solid phase are termed liquidus lines. -Liquidus lines may also be thought of as lines one must heat past at a given wt% to have an entirely liquid solution. -The analogous lines representing a change from a liquid+solid phase to an entirely solid phase are called solidus lines. -These may be thought of as the total freezing point for the system at that composition-In binary system diagrams, traveling up a vertical axis may be thought of heating the pure species that axis represents

-Binary phase diagrams yield 3 general types of information:1. Which phases are present2. The composition of those phases (wt%A,wt%B)3. The fractions of the phases (How much of the system is in that phase at t=0)

To find phases, simply find a composition/temperature point on the diagram and determine what phases are present there. -One should be able to identify at least one phase as clearly liquid, and likely others that are unique solid phases, which can in turn allow you to use logic to determine the neighboring phases.

The determination of phase composition is slightly more harrowing an experience:-If the given composition/temperature conditions yield a single phase region, the composition is simply the same as the overall alloy composition-If the comp/T point is in a region where two phases exist, one must go through a algorithm of sorts to actually determine phase compositions.-Drawing a horizontal line representing some given temperature through a two phase region from liquidus to solidus yields a so-called “tie line” (remember it is also an isotherm, something it is reffered to at times)

-Once one has a tie line drawn at the temperature of the comp/T point through the proper region, note the compositions of the points where the tie line intersects the boundaries of the phase region. -These compositions represent the relative compositions of the two phases, the one on the liquidus giving the composition of L, and the one on the solidus giving the composition of the solid phase in wt% of the components.-You should get two compositional values for two-phase composition determination.

The determination of phase amounts is an even more arduous task, but is aided by using the lever rule in conjunction with phase diagrams in analysis. -The lever rule is achieved by a further examination of the tie line

1. Create tie line at the appropriate temperature2. Locate overall alloy composition on tie line (point A)3. Find the length of the tie line in terms of change in composition (wt% or at%), denoted T4. The length of the fraction of the tie line on the liquidus side of A, denoted L, represents the

mass fraction of the solid phase (denoted alpha), so divide L by the total length of the tie line, T. >> W(alpha)=L/T

5. In turn, the inverse of this uses the length of the tie line on the solidus side of A, denoted S, is useful in determining the mass fraction of liquid phase at this comp/T. Again, divide S by T>> W(L)=S/T

-For multiphase alloys, it is more useful to use the relative phase volumes to describe phase fractions. -This requires determining the volume fraction of the phases, denoted V(alpha) and V(beta) in following examples.-A simple examination of V(alpha) shows it is the result of dividing the volume of phase alpha by total volume, or >> v(alpha)/(v(alpha)+v(beta))-Since density relates mass and volume, one can use the densities of the phases to convert weight fractions (W(alpha) and W(beta)) to relative volume fractions of the phases.>> V(alpha)=(W(a)/rho(a))/[(W(a)/rho(a))+(W(b)/rho(b))]-Inversely:>> W(a)=(V(a)*rho(a))/(V(a)*rho(a)+V(b)*rho(b))