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Materials Selection and Testing:

Materials Selection and Testing Phase diagrams


2 Importance In design and control of heat treating procedures (why?) Some properties of materials are functions of their microstructures, and, consequently, of their thermal histories Most phase diagrams represent stable (equilibrium) states and microstructures, They are useful in understanding the development and preservation of nonequilibrium structures and their attendant properties (often the case that these properties are more desirable than those associated with the equilibrium state) Remember: strong correlation between microstructure and mechanical properties!!


3 Definitions Component: pure metals and/or compounds of which an alloy is composed. For example, in a copper–zinc (brass), the components are Cu and Zn. Solute and solvent are also common terms System: series of possible alloys consisting of the same components, but without regard to alloy composition (e.g., the iron–carbon system) Solid solution: consists of atoms of at least two different types; the solute atoms occupy either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained

Solubility limit:

4 Solubility limit At some specific temperature, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution The addition of solute in excess of this solubility limit results in the formation of another solid solution or compound that has a distinctly different composition. Sugar-water system: This also depends on temperature.

Sugar-water system:

5 Sugar-water system


6 Phases Phase: homogeneous portion of a system that has uniform physical and chemical characteristics (pure materials are considered phases) Example: sugar-water syrup is a phase, solid sugar is another If more than one phase is present in a system, each will have distinct properties, and a boundary separating the phases will exist, across which there will be a discontinuous and abrupt change in physical and/or chemical characteristics Single-phase system is termed ‘‘ homogeneous .’’ Systems com- posed of two or more phases are termed ‘‘mixtures’’ or ‘‘ heterogeneous systems.’’


7 Microstruture How do we examine microstructure? In metal alloys, microstructure is characterized by Number of phases present, Proportions of phases present, and Manner in which they are distributed or arranged Microstructure of an alloy depends on the alloying elements present, their concentrations, and the heat treatment of the alloy (i.e., the temperature, the heating time at temperature, and the rate of cooling to room temperature)

Phase Equilibria:

8 Phase Equilibria Equilibrium: described in terms of a thermodynamic quantity called free energy Free Energy: function of the internal energy of a system, and also the randomness or disorder of the atoms or molecules (or entropy). A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition Macroscopically: characteristics of the system do not change with time but persist indefinitely; that is, the system is stable

Phase Equilibrium Example:

9 Phase Equilibrium Example Sugar-water syrup is contained in a closed vessel and the solution is in contact with solid sugar at 20°C. If the system is at equilibrium, the composition of the syrup is 65 wt% C 12 H 22 O 11 –35 wt% H2O and the amounts and compositions of the syrup and solid sugar will remain constant with time. If the temperature of the system is suddenly raised to 100°C equilibrium is temporarily upset and the solubility limit has been increased to 80 wt% C 12 H 22 O 11 . some of the solid sugar will go into solution in the syrup. This will continue until the new equilibrium syrup concentration is established at the higher temperature.

Solid phases:

10 Solid phases In metals, final phases are all solid Free energy considerations and diagrams provide information about equilibrium characteristics of a particular system but do not indicate time period needed to reach new equilibrium state State of equilibrium is never completely achieved: the rate of approach to equilibrium is extremely slow; such a system is said to be in a nonequilibrium or metastable state . A metastable state or microstructure may persist indefinitely, experiencing only extremely slight changes as time passes. Metastable structures are often of more practical significance than equilibrium ones

Equilibrium phase diagrams:

11 Equilibrium phase diagrams Represent the relationships between temperature and the compositions and the quantities of phases at equilibrium Many microstructures develop from phase transformations: the changes that occur between phases when the temperature is altered (ordinarily upon cooling). This can involve the transition from one phase to another, or the appearance or disappearance of a phase. Phase diagrams are helpful in predicting phase transformations and the resulting microstructures, which may have equilibrium or nonequilibrium character

Binary isomorphous systems:

12 Binary isomorphous systems A binary alloy is one that contains two components Easiest one: Copper-Nickel system Three different phase regions appear an alpha (α) field, a liquid (L) field, and two-phase α + L field. Each region is defined by the phase or phases that exist over the range of temperatures and compositions delimited by the phase boundary lines

Slide 13:



14 Notes The liquid L is a homogeneous liquid solution composed of both copper and nickel. The α phase is a substitutional solid solution consisting of both Cu and Ni atoms, and having an FCC crystal structure. At temperatures below 1080°C, copper and nickel are mutually soluble in each other in solid state for all compositions. This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electro-negativities. The Cu–Ni system is termed isomorphous because of this complete liquid and solid solubility of the two components

Comments about symbols:

15 Comments about symbols For metallic alloys, solid solutions are commonly designated by lowercase Greek letters (α, β, γ, etc.). Furthermore, with regard to phase boundaries, the line separating the L and α + L phase fields is termed the liquidus line . ( Liquid phase is present at all temperatures and compositions above this line) The solidus line is located between the α and α + L regions (below that only the solid α phase exists) The solidus and liquidus lines intersect at the two composition extremities (correspond to melting temperatures of pure components)

Latent heat of melting:

16 Latent heat of melting Melting temperatures of pure copper and nickel are 1085°C and 1453°C, respectively. Heating pure copper corresponds to moving vertically up the left-hand temperature axis. Copper remains solid until its melting temperature is reached. The solid-to-liquid transformation takes place at the melting temperature, and no further heating is possible until this transformation has been completed.

For any composition other than pure components:

17 For any composition other than pure components Melting phenomenon occurs over the range of temperatures between the solidus and liquidus lines (up constant composition) both solid α and liquid phases will be in equilibrium within this temperature range


18 Example Upon heating an alloy of composition 50 wt% Ni–50 wt% Cu melting begins at approximately 1280°C; the amount of liquid phase continuously increases with temperature until about 1320°C, at which the alloy is completely liquid

Interpretation of Phase Diagrams:

19 Interpretation of Phase Diagrams Three kinds of information are available: The phases that are present, The compositions of these phases, and The percentages or fractions of the phases. The procedures for making these determinations will be demonstrated using the copper–nickel system

Phases Present:

Phases Present

Phases Present:

21 Simplest task: locate the temperature–composition point on the diagram and notes the phase(s) with which the corresponding phase field is labeled Example: Points A and B in the figure: Phases Present


22 Example Alloy of composition 60 wt% Ni–40 wt% Cu at 1100°C would be located at point A since this is within the α region, only the single α phase will be present. On the other hand, a 35 wt% Ni–65 wt% Cu alloy at 1250°C (point B) will consist of both α and liquid phases at equilibrium (α+L)

Determination of Phases Composition:

Determination of Phases Composition

Determination of Phases Composition:

24 Determination of Phases Composition Find concentration of components Locate the temperature–composition point on the phase diagram Different for single phase and multiphase Trivial (easy) when only one phase present: the composition of this phase is simply the same as the overall composition of the alloy Point A in the figure: At this composition and temperature, only the α phase is present, having a composition of 60 wt% Ni–40 wt% Cu

More than one phase present:

25 More than one phase present In all two-phase regions, construct series of horizontal lines, one at every temperature ( tie line , or isotherm ). Tie lines extend across the two-phase region and terminate at the phase boundary lines on either side. To compute the equilibrium concentrations of the two phases, the following procedure is used: A tie line is constructed across the two-phase region at the temperature of the alloy. The intersections of the tie line and the phase boundaries on either side are noted. Perpendiculars are dropped from these intersections to the horizontal composition axis, from which the composition of each of the respective phases is read.


26 Example Determine the composition (in wt% Ni and Cu) for both the α and liquid phases C L C 0 C α Tie Line


27 Example The tie line constructed across the α+L phase region. The perpendicular from the intersection of the tie line with the liquidus boundary meets the composition axis at 31.5 wt% Ni–68.5 wt% Cu, which is the composition of the liquid phase, C L . Likewise, for the solidus–tie line intersection, we find a composition for the α solid- solution phase, Cα , of 42.5 wt% Ni–57.5 wt% Cu

Determination of Phases Amounts:

Determination of Phases Amounts

Determination of Phases Amounts:

29 Determination of Phases Amounts The relative amounts (as fraction or as percentage) of the phases present at equilibrium may also be computed from phase diagrams Single Phase Multi-Phase Single phase: the alloy is composed entirely of that phase (the phase fraction is 1.0 or the percentage is 100%) From the previous example (60 wt% Ni–40 wt% Cu alloy at 1100°C @ point A), only the α phase is present; hence, the alloy is completely or 100% α)

Two (or more) phase regions:

30 Two (or more) phase regions The tie line must be utilized in conjunction with a procedure that is often called the lever rule Procedure: The tie line is constructed across the two-phase region at the temperature of the alloy. The overall alloy composition is located on the tie line (C 0 ). The fraction of one phase is computed by taking the length of tie line from the overall alloy composition to the phase boundary for the other phase, and dividing by the total tie line length. The fraction of the other phase is determined in the same manner.

Two (or more) phase regions:

31 Two (or more) phase regions If phase percentages are desired: Each phase fraction is multiplied by 100. When the composition axis is scaled in weight percent, the phase fractions computed using the lever rule are mass fractions: Mass (or weight) of a specific phase divided by the total alloy mass (or weight). The mass of each phase is computed from the product of each phase fraction and the total alloy mass.


32 Example Determine the Phase amounts (in wt% Ni and Cu) for both the α and liquid phases (point B) C L C 0 C α S R Tie Line

Mechanical Properties of Isomorphous alloys:

34 Mechanical Properties of Isomorphous alloys For all temperatures and compositions below the melting temperature of the lowest-melting component, only a single solid phase exists. Therefore, each alloy component will experience solid-solution strengthening


35 Important Alloy behavior under non-equilibrium conditions results in different properties because of differing grain microstructure Non-equilibrium conditions are “rapid” change with time (rapid cooling, rapid increase of composition...etc)

Binary Eutectic Systems:

Binary Eutectic Systems

Binary Eutectic systems:

37 Binary Eutectic systems

Binary Eutectic Systems:

38 Binary Eutectic Systems Another type of common and relatively simple phase diagram found for binary alloys shown for the copper–silver system; this is known as a binary eutectic phase diagram. Features: Three single-phase regions are found on the diagram: α, β, and liquid. The α phase is a solid solution rich in copper; it has silver as the solute component and an FCC crystal structure. The β has an FCC structure, but copper is the solute. The α and β phases are considered to include pure copper and pure silver, respectively

Pure phases α and β:

39 Pure phases α and β Solubility in each of the solid phases is limited. At any temperature below line BEG only a limited concentration of silver will dissolve in copper (for the α phase), and similarly for copper in silver (for the β phase). 39

Pure phase α:

40 Pure phase α The solubility limit for the α phase corresponds to the boundary line, labeled CBA, between the α /( α + β ) and α /( α +L) phase regions; it increases with temperature to a maximum [8.0 wt% Ag at 779°C at point B, and decreases back to zero at the melting temperature of pure copper, point A 1085°C] 40

Pure phase β:

41 Pure phase β At temperatures below 779°C , the solid solubility limit line separating the α and α + β phase regions is termed a solvus line ; the boundary AB between the α and α+L fields is the solidus line . For the β phase, both solvus and solidus lines also exist, HG and GF, respectively. The maximum solubility of copper in the β phase, point G (8.8 wt% Cu), also occurs at 779°C. 41

Pure phase β:

42 Pure phase β This horizontal line BEG, which is parallel to the composition axis and extends between these maximum solubility positions, may also be considered to be a solidus line (represents the lowest temperature at which a liquid phase may exist for any copper–silver alloy that is at equilibrium)

Two-phase regions:

43 Two-phase regions There are also three two-phase regions found for the copper–silver system: α + L β + L α + β The α and β phase solid solutions coexist for all compositions and temperatures within the α + β phase field; the α + liquid and β + liquid phases also coexist in their respective phase regions. Compositions and relative amounts for the phases may be determined using tie lines and the lever rule

Eutectic point:

44 Eutectic point As silver is added to copper, the temperature at which the alloys become totally liquid decreases along the liquidus line, line AE; thus, the melting temperature of copper is lowered by silver additions. The same may be said for silver: the introduction of copper reduces the temperature of complete melting along the other liquidus line, FE. These liquidus lines meet at the point E on the phase diagram, through which also passes the horizontal isotherm line BEG. Point E is called an invariant point , which is designated by the composition C E and temperature T E ; for the copper–silver system, the values of C E and T E are 71.9 wt% Ag and 779°C

Eutectic Reaction:

45 Eutectic Reaction An important reaction occurs for an alloy of composition C E as it changes temperature in passing through T E : Upon cooling, a liquid phase is transformed into the two solid α and β phases at the temperature T E ; the opposite reaction occurs upon heating. This is called a eutectic reaction (eutectic means easily melted), and C E and T E represent the eutectic composition and temperature, respectively; C αE and C βE are the respective compositions of the α and β phases at T E

Eutectic reaction for copper-silver system:

46 Eutectic reaction for copper-silver system The Eutectic reaction is: The horizontal solidus line at T E is called the eutectic isotherm

General notes:

47 General notes One or at most two phases may be in equilibrium within a phase field For a eutectic system, three phases (α , β, and L) may be in equilibrium, but only at points along the eutectic isotherm Single-phase regions are always separated from each other by a two-phase region that consists of the two single phases that it separates

Lead-Tin Eutectic system:

48 Lead-Tin Eutectic system


49 Significance On occasion, low-melting-temperature alloys are prepared having near-eutectic compositions. A familiar example is the 60–40 solder, containing 60 wt% Sn and 40 wt% Pb. An alloy of this composition is completely molten at about 185°C, which makes this material especially attractive as a low-temperature solder, since it is easily melted.

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