Chapter 7 Phase Equilibria and Phase Diagrams

Transcription

1 Chapter 7 Phase Equilibria and Phase Diagrams The one-component phase diagram Gibbs Phase Rule Phase equilibria in a two-component system The isomorphous diagram The lever rule Equilibrium solidification and microstructure of isomorphous alloys Liquidius and solidus boundaries Deviations from ideal behavior Chapter 7 Phase Equilibria and Phase Diagrams, Continued Phase equilibria in a two-component system The eutectic phase diagram The peritectic phase diagram The monotectic phase diagram Complex diagrams Phase equilibria involving solid-to-solid reactions 1

2 Why important? Some properties that might be difficult to predict using a common sense without the knowledge of the phase diagrams Example: Chip-Solder-Joint-Failure example 1: Melting temperature of a mixture AB (solution) of two components A and B could be either lower or higher than the melting point of each component (!). This could be a failure mechanism in electronic or mechanical components. But could also be used to your advantage. example 2: Upon cooling to a lower temperature a phase transformation of a material could cause expansion, which could cause internal stresses and failure (e.g. tin food cans will crumble at low T) example 3: No abrupt liquid-to-solid transformation when two components are present (solid + liquid in a temperature range) Why important? Some properties that might be difficult to predict using a common sense without the knowledge of the phase diagrams example 4: T melt (Sn) = 232 C, T melt (Pb) = 327 C but T melt (Sn 0.62 Pb 0.38 ) = 183 C, so this is a common soldering alloy example 5: T melt (Au) = 1064 C, T melt (Si) = 2550 C but T melt (Au 0.97 Si 0.03 ) = 363 C, so thin layer of gold is used to attach Si chip to a ceramic substrate (shock protection) example 6: Mechanical properties (hardness and tensile strength) of an alloy could be substantially higher than that of the individual components (e.g. hardness (AgCu) about twice the harness of Ag or Cu) 2

3 One-Component Phase Diagrams # of state variables (e.g. two: P and T) Gibbs Phase rule: F = 2 F = C P + 2 C- Components P- Number of phases F- Degrees of freedom F = 1 F = 0 T F = 1 Two-Component Phase Diagrams Isomorphous system ( complete solubility over the composition range) F = C P + 1 If pressure is fixed (1 atm) F = 2 In a two-phase field need to specify either the temperature or the composition of one of the phases. X s X l Hume-Rothery Rules for substitutional solution: The size < ~15%. The electronegativities and valance similar The crystal structures of the two species must be the same to form a continuous series of solid solutions. 3

4 Two-Component Phase Diagrams f l l s + f = 1 s X = X f + X f f o l l s s = 1 f s ( 1 ) X = X f + X f o l s s s X = X X f + X f o l l s s s ( ) ( Xo Xl) ( Xs Xl) ( X s X o ) ( X X ) X X = f X X f f l o l s s l = = s l Composition, X B The Lever Rule in a Two-Component System 4

5 Two-Component Phase Diagrams Two-Component Phase Diagrams, C Composition, X B Time Time 5

6 Two-Component Phase Diagrams Congruent melting maximum E AB > 0.5 (E AA + E BB ) Deviation from ideal behavior Two-Component Phase Diagrams E AB > 0.5 (E AA + E BB ) Deviation from ideal behavior Congruent melting minimum 6

7 Eutectic Phase Diagrams T A T A X s F = 1 F = 2 X l F = 1 F = 1 F = 2 F = 2 X α F = 0 X β X 1 X E X 2 Composition, X B X l Solvus T Xα X β X s B T B T F = 2, must specify temperature and composition F = 1, must specify temperature or the composition of one of the phases F = 0, temperature and compositions of the phase are fixed. Cooling Curves and Phase Boundaries Alloy 1 Time Composition, X B 7

8 Cooling Curves and Phase Boundaries Alloy 2 Time Composition, X B Cooling Curves and Phase Boundaries Alloy 3 Time Composition, X B 8

9 Various physical properties and their relationship to a eutectic phase diagram Eutectic Phase Diagrams 1. For the alloy composition of 0.27 % B calculate the fraction of solid and the fraction of liquid that forms under equilibrium cooling at the eutectic T Composition, in % B 2. Calculate the amount of β and α that will form from the liquid just below the eutectic isotherm 3. Calculate the amount of α in the alloy at temperature just below the eutectic T 9

10 Eutectic Phase Diagrams This liquid becomes the eutectic mixture of α and β when the temperature drops just below the eutectic temperature which is composed of: fα fβ f 0.68 f 0.32 α Composition, in % B β Just above the eutectic temperature the fraction of liquid and solid are: fl fα f 0.41 fα 0.59 l The first solid that forms is called primary α Just below the eutectic temperature the microstructure is composed of primary α that formed above the eutectic temperature and α from the eutectic mixture f = f + f α α α total primary eutectic f α = (0.41)(0.68) = 0.87 total or f α = f α = Microstructure Above and Below the Eutectic for an Off-Eutectic Alloy Just above T E Just below T E 10

11 Microstructure Above and Below the Eutectic for Off-Eutectic Alloys Just below T E Increasing primary α Decreasing eutectic Decreasing primary α Increasing eutectic Deviation from Hume-Rothery s Rules Increasing deviation leads to decrease in the maximum solid solubility of B in α. A Composition, X B 11

12 Eutectic Phase Diagram, No Solid Solubility Composition, X B Eutectic Phase Diagrams Al-Si System 12

13 Methods for Determining a Phase Diagram Microstructure of an Aluminum-Silicon Alloy Primary α-aluminum α aluminum / silicon eutectic 13

14 Phase Diagrams Containing Two Eutectics Line compound Possible to have several solid solution regions: e.g. 2 eutectic reactions and 3 solid solutions (α, β, and γ) Note that upon cooling from T max at the alloy composition X there is a phase change but no composition change (CONGRUENT melting) Peritectic Phase Diagrams if both the L and S phases have a tendency to cluster, the liquidus temperature increase and the solidus temperature decreases In addition, a miscibility gap (region of non-mixing) appears A progressive increase in the clustering tendency leads to the PERITECTIC phase diagram l + α = β 14

15 The Use of Cooling Curves for Determining a Peritectic Phase Diagram l + α = β T A T L T P X 2 X P X 2 Composition, X B Time Analysis of a Peritectic Phase Diagram Alloy 1 Alloy 2 Alloy 3 Composition Alloy 3 at T2 f f l l = = 0.48 Alloy 3 at T5 f f α α = =

16 Monotectic Phase Diagrams L 1 L 2 A region of immiscibility (nonmixing) develops in the L phase example: oil and water Liquid1 = Liquid2 + α (solid) L 2 L 2 X M Review of Invariant Binary Reactions Eutectic Type Eutectic l α + β α l β Al-Si, Fe-C Eutectoid γ α + β α γ β Fe-C Monotectic α l 1 l 2 Cu-Pb l 1 α + l 2 Monotectoid α 2 α 1 + β α 1 α 2 β Al-Zn, Ti-V On cooling one phase going to two phases 16

17 Review of Invariant Binary Reactions Peritectic Type Peritectic l + β α l α β Fe-C Peritectoid α + β γ α γ β Cu-Al On cooling two phases going to one phase HW Questions 1. When a solid melts congruently, the liquid and solid have different / the same composition(s). 2. At constant temperature the fraction of the phases in a two-phase field changes / remains the same when the overall composition of the alloy is changed, but remains in the two-phase field. 3. Why would alloys close to the eutectic composition be suitable for castings rather than alloy compositions far from the eutectic composition? 4. On cooling when a two-phase liquid plus solid transforms to a solid phase the transformation is eutectic / peritectic in nature. 5. On cooling the peritectoid reaction written symbolically has one phase going to two / two phases going to one. 17

18 HW Questions At what T an alloy containing 88% B will start melting? At what T it will completely transform into liquid? What is the composition of α phase for this T 8? What is the maximum solid solubility of B in a and A in b? Whose rules apply here? For an alloy containing 88% B, calculate the fraction of the liquid and solid phases and their compositions at temperature T3, T4, and T5 At a temperature just below the eutectic temperature, how much β is primary β, what is the total fraction of β, and what is the fraction β in the eutectic. (Alloy composition is 88% B) Labeling Complex Phase Diagrams T B T A 1. Label all phase fields. 2. Identify all invariant reactions. A Composition, X B B 18

19 Labeling Complex Phase Diagrams Peritectic Eutectic Eutectic l = α + β Peritectic l + γ = β Eutectic l = γ + δ Eutectic Labeling Complex Phase Diagrams 19

20 Summary One-component phase diagrams with temperature and pressure as the experimental variables that affect equilibrium. Introduction to the Gibbs Phase Rule and its application to one-component systems. Two-component systems and the rules that govern the composition of the phases, the number of phases and the amount of each phase at equilibrium. The applications of these rules to complex, two-component systems illustrated that regardless of how complex the phase diagram appeared, the rules that were developed could be easily applied. 20