Thermal Analysis phase diagrams
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1 Thermal Analysis phase diagrams R W McCallum Ames Laboratory And Materials Science and Engineering
2 Why Phase Diagrams Thermal analysis gives us information about phase transitions which are the lines on a phase diagram I never saw one in a physics class
3 Why should I care? If you wish to measure the intrinsic properties of an intermetallic compound you need Single phase Homogenous Often you can't just melt the elements together Why do you need to anneal some samples? At what temperature do you heat treat? How long will it take?
4 Typical ternary phase diagram at constant temperature B Nd 5 Fe 2 B 6 NdFe 4 B 4 FeB Fe 2 B Dy 2 B Dy 12 B Dy 6 B Dy 4 B DyFeB 4 B Nd 2 Fe 14 B Dy 3 Fe 7 B Dy 1.1 Fe 4 B 4 FeB Nd Nd 5 Fe 17 Nd 2 Fe 17 Fe Dy 2 Fe 3 B DyFe 2 B 2 Fe 2 B Dy 2 Fe 14 B Dy DyFe2 Dy 6 Fe 23 DyFe 3 Dy 2 Fe 17 Fe
5 What is a phase In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth). From Wikipedia,
6 What is a phase Phases are sometimes confused with states of matter, but there are significant differences. States of matter refers to the differences between gases, liquids, solids, plasma, etc. If there are two regions in a chemical system that are in different states of matter, then they must be different phases. However, the reverse is not true a system can have multiple phases which are in equilibrium with each other and also in the same state of matter. From Wikipedia,
7 Temperature ( C ) State vs Phase Gas Gas Liquid Liquid Solid Fe Fe 500 Fe 0
8 What distinguishes a phase two different states of a system are in different phases transforming between states results in an abrupt change in physical properties. two states are in the same phase transforming between states results in gradual change in physical properties. exceptions to this definition for example the liquid-gas critical point.
9 Crystal Structure
10 Phase transition From Wikipedia,
11 Free Energy Phase Transition At phase-transition point the two phases have identical free energies equally likely to exist. Below the phasetransition point Low temperature phase is more stable state of the two. Above the phasetransition point High temperature phase is more stable state of the two. Phase Transition Low Temperature Phase Temperature (K) High Temperature Phase
12 Ehrenfest's classification of phase transitions phase transitions labeled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with a thermodynamic variable. solid/liquid/gas transitions are first-order transitions because they involve a discontinuous change in density (which is the first derivative of the free energy with respect to chemcial potential.) Second-order phase transitions continuous in the first derivative exhibit discontinuity in a second derivative of the free energy. example, the ferromagnetic phase transition in materials such as Fe, magnetization ( the first derivative of the free energy with the applied magnetic field strength), increases continuously from zero as the temperature is lowered below Tc magnetic susceptibility (the second derivative of the free energy with the field) changes discontinuously.
13 Types of phase transitions first-order phase transitions involve a latent heat system either absorbs or releases a fixed (and typically large) amount of energy. the temperature of the system will stay constant as heat is added or released. "mixed-phase regimes in which some parts of the system have completed the transition and others have not. a pot of boiling water:» turbulent mixture of water and water vapor bubbles.
14 Single component
15 Gibbs Phase Rule F=C+n- P F Degrees of freedom Temperature Pressure composition C number of components n for the main control parameters Temperature Pressure For high melting materials vapor pressure is negligible n=1 for high vapor pressure materials n=2 P number of phases Binary phase diagram C=2
16 Single component F=C+n- P C=1 N=2 temperature, pressure P=3
17 1 component
18 2 component solid solution (random)
19 2 component ordered
20 2 component ordered
21 Two components
22 Immiscible no compounds FCC Hexagonal Ag Å Co Å
23 Two components
24 Solid Solutions Ag Å Au Å
25 Solid Solution Liquid 1 T/T melting B Liquidus Liquid + Solid Solidus 0.4 Solid % B
26 Solid Solution Liquid 1 T/T melting B Liquidus Liquid + Solid Solidus 0.4 Solid % B
27 Composition in %B Percent Liquid Solid solution Liquid 1 T/T melting B Liquidus Liquid + Solid Solidus Solid Composition of Solid being solidified % B 50 Equilibrium Freezing Composition of Liquid Reduced Temperature T/T melt B 0
28 Composition in %B Percent Liquid Non equilibrium freezing Composition of Solid being solidified Non- Equilibrium Freezing Equilibrium Freezing Composition of Liquid Reduced Temperature T/T melt B 0
29 Composition %B Coring Non-Equilibrium 60 Equilibrium Radius
30 Two components
31 Eutectic Ag + liquid Cu + liquid Ag + Cu Ag Å Cu Å
32 Binary C=2 n=1 P=2 P=3 F=0 P=1, F=2 P=2, F=1 P=2 so F=1
33 Two components
34 Congruently melting intermetalic compound Al + liquid Sb + liquid FCC Al + AlSb AlSb + Sb Rhombohedral
35 Two components
36 Peritectic Fe + Liquid Fe 17 Nd 2 + Liquid Fe + Fe 17 Nd 2 Fe 17 Nd 2 + Nd
37 Two components
38 Invariant Reactions
39 Eutectic Liquid 1 Solid 1 + Solid 2 Ag + liquid Cu + liquid Ag + Cu Ag Å Cu Å
40 Eutectoid solid 1 Solid 2 + Solid 3 S1 S2 S3
41 Peritectic Liquid Solid + Liquid Fe + Liquid Fe 17 Nd 2 + Liquid Fe + Fe 17 Nd 2 Fe 17 Nd 2 + Nd
42 Eutectoid Peritectoid Solid 1 Solid 2 + Solid 3
43 Monotectic Liquid 1 Solid + Liquid 2
44
45
46 Ternary Phase Diagram
47 Ternary Isothermal Cut
48 Typical ternary phase diagram at constant temperature B Nd 5 Fe 2 B 6 NdFe 4 B 4 FeB Fe 2 B Dy 2 B Dy 12 B Dy 6 B Dy 4 B DyFeB 4 B Nd 2 Fe 14 B Dy 3 Fe 7 B Dy 1.1 Fe 4 B 4 FeB Nd Nd 5 Fe 17 Nd 2 Fe 17 Fe Dy 2 Fe 3 B DyFe 2 B 2 Fe 2 B Dy 2 Fe 14 B Dy DyFe2 Dy 6 Fe 23 DyFe 3 Dy 2 Fe 17 Fe
49 ternary liquidus projection
50 Liquidus projection of the Nb-Ti-Si system with isothermal lines
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