Introduction to phase diagrams

Transcription

1 ASM Phase Diagram Database Diagram No Department of Physics and Astronomy Introduction to phase diagrams William Meier Physics 590B Fall 2018

2 Outline Part 1 Introduction and basics Part 2 Fundamental concepts Part 3 Using phase diagrams 2

3 A phase diagram is a map Regions on a phase diagram indicate the stable phases for a set of parameters. 3

4 Water phase diagram at 1 atm Phases of H 2 O vs temperature Single phase regions Co-existence T (K) Vapor (steam) Liquid Solid (ice) 4

5 Water p-t phase diagram T (K) Vapor (steam) Liquid Solid (ice) 5

6 ioxide_pressure-temperature_phase_diagram.svg Other p-t phase diagrams Phase fields Boundaries and coexistence Fe CO 2 6

7 T-x phase diagrams Temp v. overall composition Liquid solution Solid solution Boundaries Liquid solution Liquid + Solid (Ag,Au) (Ag,Au) Solid solution 7

8 T-x phase diagrams Limited solid solubility Liquid stable below T melt of elements Eutectic reaction (Ag) + (Cu) Liquid Liquid + Solid (Cu) Liquid + Solid (Ag) Liquid Solid (Ag) + Solid (Cu) 8

9 T-x phase diagrams Compound (KNa 2 ) Line compound Peritectic reaction KNa 2 Liquid + (Na) Liquid Liquid + KNa 2 Liquid + Solid (Na) Solid (K) + Liquid Solid (K) + KNa 2 KNa 2 + Solid (Na) 9

10 T-H phase diagram Magnetic field suppresses the superconducting states 10

11 Application Steel (Fe-C) Carbon modifies phase stability Heat treatments γ + Fe 3 C α + Fe 3 C FCC γ BCC α 11

12 Part 2 Fundamental concepts Definitions Reactions and transitions The lever rule (conservation of matter) 13

13 Definition Phase A region of space occupied by a homogeneous material Mechanically separable? Examples Water vapor Liquid water Ice Diamond Graphite Paramagnet Ferromagnet 14

14 Definition Phase Distinguished by Properties Structure Composition Phase field CO 2 Fe

15 Definition State variables Parameters that determine the configuration of the system Examples Composition Temperature Pressure Electric field Magnetic field 16

16 Definition O Components The chemical constituents needed to describe the compositions of interest Often elements Al Al 2 O 3 SiO 2 Mullite Si Sometimes compounds Mullite Al 2 O 3 SiO 2 17

17 Definition Equilibrium System configuration with minimum free energy Remember Equilibrium is a thermodynamic concept Kinetics plays an important role Unstable (balanced) Meta-stable Stable 18

18 Narayan et al., Journal of Applied Physics 118, (2015) Definition Equilibrium Practical definition: The configuration is independent of time Changes could be slow Is the equilibrium configuration accessible? 19

19 ASM Phase Diagram Database Diagram No Department of Physics and Astronomy Introduction to phase diagrams Day 2 Batman (William Meier) Physics 590B Fall 2018

20 Review Phase diagrams are maps Equilibrium phases as a function of state variables 21

21 Determining the stable phases 1. Find single phase regions 80% Er and 20% 1800 C 22

22 Determining the stable phases 1. Find single phase regions (Er) (Sb) Liquid (L) Phases: Er 0.80 Sb 0.20 Liquid 80% Er and 20% 1800 C Er 5 Sb 3 ErSb rt ErSb ht ErSb 2 hp (room temperature) (high temperature) 23

23 Determining the stable phases 1. Find single phase regions 2. Draw tie line Constant temp. line to single phase regions on left and right 30% Er and 70% 1000 C 24

24 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases ErSb rt 30% Er and 70% 1000 C Liquid Er 0.09 Liquid,Sb

25 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions ErSb rt ErSb rt Liquid Er 0.20,Sb 0.80 Liquid Er 0.09,Sb

26 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions (Er 0.99,Sb 0.01 ) Er 5 Sb 3 ErSb rt + L 27

27 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions (Er) + Er 5 Sb 3 ErSb rt + L 28

28 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions (Er) + Er 5 Sb 3 L + Er 5 Sb 3 ErSb rt + L 29

29 Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions (Er) + Er 5 Sb 3 L + Er 5 Sb 3 L + ErSb rt ErSb rt + L 30

30 Er 5 Sb 3 + ErSb rt Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions (Er) + Er 5 Sb 3 L + Er 5 Sb 3 L + ErSb rt ErSb ht + L ErSb rt + L 31

31 Er 5 Sb 3 + ErSb rt Determining the stable phases 1. Find single phase regions 2. Draw tie line 3. Endpoints identify the composition of stable phases Same phases in whole field Different compositions L + ErSb ht (Er) + Er 5 Sb 3 L + Er 5 Sb 3 L + ErSb rt ErSb ht + L ErSb rt + L 32

32 Stable phases 33

33 Stable phases 34

34 Stable phases 35

35 The lever rule Use the lever rule to find the fractions of stable phases 30% Er 70% Sb ErSb rt + L 36

36 The lever rule T ( C) Phases at% Sb Phase% Overall at% Sb 2000 Liquid Liquid Er 0.30 Sb % Er 70% Sb ErSb rt + L 2000 C Micrograph Liquid Er 0.30 Sb

37 The lever rule T ( C) Phases at% Sb Phase% Overall at% Sb 2000 Liquid ErSb rt Liquid ErSb rt Liquid Er 0.24 Sb 0.76 ErSb rt + L 2000 C Micrograph Liquid Er 0.30 Sb

38 The lever rule T ( C) Phases at% Sb Phase% Overall at% Sb 2000 Liquid ErSb rt Liquid ErSb rt a b Liquid Er 0.24 Sb 0.76 ErSb rt + L Lever Rule f ErSb rt = b a + b composition differences a, b 2000 C 1600 C Micrograph Liquid Er Sb ErSb rt 39

39 The lever rule T ( C) Phases at% Sb Phase% Overall at% Sb 30% Er 70% Sb 2000 Liquid ErSb rt Liquid ErSb rt Liquid Er 0.13 Sb ErSb rt Liquid Liquid Er 0.13 Sb 0.87 a b Lever Rule f ErSb rt = b a + b 1600 C 1200 C Micrograph ErSb rt 40

40 The lever rule T ( C) Phases at% Sb Phase% 2000 Liquid ErSb rt Liquid C Micrograph Liquid Er 0.30 Sb % Er 70% Sb Liquidus 1200 ErSb rt Liquid C Micrograph Liquid Er 0.24 Sb 0.76 Liquid Er 0.13 Sb C Micrograph ErSb rt 41

41 The lever rule 23 at% ErSb 77 at% Liquid Er 0.24 Sb % Er 70% Sb a b Lever Rule f ErSb rt = b a + b composition differences a, b 42

42 Er 5 Sb 3 + ErSb rt Phase transitions Congruent melting Compound melts directly to a liquid of the same composition L + ErSb ht L + ErSb rt L + Er 5 Sb 3 ErSb ht + L (Er) + Er 5 Sb 3 ErSb rt + L 43

43 Er 5 Sb 3 + ErSb rt Phase transitions Congruent melting Solid-solid L + ErSb ht L + ErSb rt L + Er 5 Sb 3 ErSb ht + L (Er) + Er 5 Sb 3 ErSb rt + L 44

44 Er 5 Sb 3 + ErSb rt Invariant reactions Eutectic Consider 13 at% Sb at 1200 C and 1400 C L + Er 5 Sb 3 (Er) + Er 5 Sb 3 ErSb rt + L 45

45 Er 5 Sb 3 + ErSb rt Invariant reactions Eutectic Consider 13 at% Sb at 1200 C and 1400 C Eutectic reaction: (Er 0.97 Sb 0.03 ) sol + Er 5 Sb 3 (Er 0.87 Sb 0.13 ) liq 3 phases only coexist at 1350 C (Er) + Er 5 Sb 3 L + Er 5 Sb 3 ErSb rt + L 46

46 Er 5 Sb 3 + ErSb rt Invariant reactions Peritectic Consider 67 at% Sb at 500 C and 800 C Peritectic reaction: ErSb 2 ErSb rt + (Er 0.03 Sb 0.97 ) liq 3 phases only coexist at 700 C Incongruent melting (Er) + Er 5 Sb 3 L + Er 5 Sb 3 ErSb rt + L 47

47 Invariant reactions Tics Reactions involving liquids Eutectic α + γ L 1 Monotectic γ + L 4 L 3 Peritectic ε L + δ 48

48 Invariant reactions Toids Reaction involving only solids Peritectoid η α + γ Eutectoid η + δ γ 49

49 ASM Phase Diagram Database Diagram No Department of Physics and Astronomy Introduction to phase diagrams Day 3 William Meier Physics 590B Fall 2018

50 Review Stable phases Lever rule Eutectic Peritectic a Tie line b ASM International Diagram No

51 Conservation of matter T ( C) Phases at% Sb Phase% 2000 Liquid ErSb rt Liquid C Micrograph Liquid Er 0.30 Sb % Er 70% Sb 1200 ErSb rt Liquid C Micrograph Liquid Er 0.24 Sb 0.76 Liquid Er 0.13 Sb C Micrograph ErSb rt 52

52 Conservation of matter T ( C) Phases at% Sb Phase% 30% Er 70% Sb 2000 Liquid Er 70 Sb 53

53 Conservation of matter T ( C) Phases at% Sb Phase% 30% Er 70% Sb 1600 ErSb rt Liquid Er 70 Sb ErSb rt 54

54 Conservation of matter T ( C) Phases at% Sb Phase% 30% Er 70% Sb 1200 ErSb rt Liquid Er 70 Sb ErSb rt 55

55 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) Phases at% Na Phase% Overall at% Na 20 Liquid Liquidus 20 C Micrograph Liquid Cs 0.90 Na 0.10 Cs Na 56

56 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) 0 Phases at% Na Phase% Liquid Cs 0 ~0 Overall at% Na 10 0 C Micrograph Liquid Cs 0.90 Na 0.10 Cs Cs metal Na 57

57 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) -20 Phases at% Na Phase% Liquid Cs 0 41 Overall at% Na 10 Liquid Cs 0.83 Na 0.17 Cs Na -20 C Micrograph Cs metal 58

58 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) -30 Phases at% Na Phase% Liquid Cs 0 50 Overall at% Na 10 Liquid Cs 0.80 Na 0.20 Cs Na -30 C Micrograph Cs metal 59

59 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) Phases at% Na Phase% Overall at% Na Liquid Cs 0 - CsNa Eutectic reaction (Ca 0.80 Na 0.20 ) liq Cs + CsNa 2 Liquid Cs 0.80 Na C Micrograph Cs Cs metal Na 60

60 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.9 Na 0.1 T ( C) Phases at% Na Phase% Overall at% Na -40 Cs 0 85 CsNa Eutectic reaction (Ca 0.80 Na 0.20 ) liq Cs + CsNa 2 Cs + CsNa 2 Eutectic microstructure -40 C Micrograph Cs Cs metal Na 61

61 Eutectic microstructures Liquid rapidly solidifies into thin regions of solid phases on cooling Sn-In Al-Si Sn-Pb Al-Si Al-Cu Mg-Sn 62

62 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) Phases at% Na Phase% Overall at% Na 100 Liquid C Micrograph Liquid Cs 0.50 Na 0.50 Cs Na 63

63 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) Phases at% Na Phase% Overall at% Na 50 Liquid Na 100 ~0 50 Liquidus 50 C Micrograph Liquid Cs 0.50 Na 0.50 Cs Na metal Na 64

64 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) 20 Phases at% Na Phase% Liquid Na Overall at% Na C Micrograph Liquid Cs 0.62 Na 0.38 Cs Na metal Na 65

65 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -5 Phases at% Na Phase% Liquid Na Overall at% Na 50-5 C Micrograph Liquid Cs 0.69 Na 0.31 Cs Na metal Na 66

66 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) Phases at% Na Phase% Overall at% Na Liquid CsNa Na Peritectic reaction (Ca 0.70 Na 0.30 ) liq + Na CsNa 2 CsNa 2-8 C Micrograph Liquid Cs 0.70 Na 0.30 Cs Na metal Na 67

67 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -10 Phases at% Na Phase% Liquid CsNa Overall at% Na 50 CsNa 2 Liquid Cs 0.71 Na C Micrograph Cs Na 68

68 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -30 Phases at% Na Phase% Liquid CsNa Overall at% Na 50 CsNa 2 Liquid Cs 0.78 Na C Micrograph Cs Na 69

69 (Cs) CsNa 2 lt (Na) rt Equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -40 Phases at% Na Phase% Cs 0 25 CsNa Overall at% Na 50 CsNa 2 Cs + CsNa 2 Eutectic microstructure -40 C Micrograph Cs Na 70

70 (Cs) CsNa 2 lt (Na) rt Non-equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -8 Phases at% Na Phase% Liquid 30 - CsNa Na Overall at% Na 50 CsNa 2 Na Na Cs L Rate limited by solid state diffusion -8 C Micrograph Liquid Cs 0.70 Na 0.30 Cs Na metal Na 71

71 (Cs) CsNa 2 lt (Na) rt Non-equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -30 Phases at% Na Phase% Liquid 22 - CsNa Na Overall at% Na 50 CsNa 2 Liquid Cs 0.78 Na 0.22 Cs Na -30 C Micrograph Na metal 72

72 (Cs) CsNa 2 lt (Na) rt Non-equilibrium solidification Overall: Cs 0.5 Na 0.5 T ( C) -30 Phases at% Na Phase% Liquid 22 - CsNa Na Overall at% Na 50 CsNa 2 Cs + CsNa 2 Eutectic microstructure -30 C Micrograph Cs Na metal Na 73

73 Campbell, F. C. Phase Diagrams: Understanding the Basics. ASM International, Peritectic microstructure Incomplete peritectic reaction are common Reaction layer Primary phase CsNa 2 Cs + CsNa 2 Eutectic microstructure -30 C Micrograph Na metal Solidified Cu 0.8 Sn 0.2 melt 74

74 Temperature Scanning calorimetry Hypothetical Phase Diagrams liquid 35% 45% 60% 75% 80% d+liquid g+liquid a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Solid δ Figures from Kevin Dennis 75

75 Temperature Scanning calorimetry Hypothetical Phase Diagrams liquid 35% 45% 60% 75% 80% d+liquid g+liquid First heating a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Solid δ C Figures from Kevin Dennis 76

76 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams Peritectic decomposition 1300 δ Liquid + γ liquid 35% 45% 60% 75% 80% d+liquid g+liquid First heating a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Liquid Solid δ Solid γ C Figures from Kevin Dennis 77

77 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams γ dissolves into liquid liquid 35% 45% 60% 75% 80% d+liquid g+liquid First heating a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Liquid Solid γ C Figures from Kevin Dennis 78

78 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams Homogenous liquid liquid 35% 45% 60% 75% 80% d+liquid g+liquid First heating a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Liquid C Figures from Kevin Dennis 79

79 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams γ precipitates from liquid liquid 35% 45% 60% 75% 80% d+liquid g+liquid First cooling a+liquid b+liquid b+d d+g a+b a b 60 d g 75% Liquid Solid γ C Figures from Kevin Dennis 80

80 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams Peritectic reaction 1300 Liquid + γ δ Incomplete liquid 35% 45% 60% 75% 80% d+liquid g+liquid First cooling a+liquid b+liquid b+d d+g a+b a b 60 d g Solid δ 75% Liquid Solid δ Solid γ C Figures from Kevin Dennis 81

81 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams δ crystallizes 1300 Peritectic reaction Liquid + δ β liquid 35% 45% 60% 75% 80% d+liquid g+liquid Incomplete First cooling a+liquid b+liquid b+d d+g a+b a b 60 d g Solid β 75% Liquid Solid δ Solid γ C Figures from Kevin Dennis 82

82 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams β crystallizes 1300 Eutectic reaction Liquid α + β liquid 35% 45% 60% 75% 80% d+liquid g+liquid First cooling a+liquid b+liquid b+d d+g a+b a b 60 d g Solid β 75% Liquid Solid δ Solid γ C Figures from Kevin Dennis 83

83 Temperature Scanning calorimetry 1500 Hypothetical Phase Diagrams β crystallizes 1300 Eutectic reaction Liquid α + β liquid 35% 45% 60% 75% 80% d+liquid g+liquid First cooling a+liquid b+liquid b+d d+g a+b a b 60 d g Solid β 75% α + β eutectic microstructure Solid δ Solid γ C Figures from Kevin Dennis 84

84 CeSb 2 P. C. Canfield et al., Philos. Mag., 96(1), (2016) P.C. Canfield and Z. Fisk, Philos. Mag. B., 65(6), (1992) Crystal growth from solution Batch Melt CeSb 2 Liquidus Crystallize CeSb 2 -Sb Eutectic Decant Ce Target Sb 85

85 From ACerS Phase Equilibria Diagrams Online No Compositions Mole % vs Atom % Spinel (MgAl 2 O 4 ~ MgO Al 2 O 3 ) 50 mol% MgO 50 mol% Al 2 O 3 29 at% Mg 0.5 O at% Al 0.4 O 0.6 Spinel MgAl 2 O 4 MgO mol % Al 2 O 3 86

86 Compositions Atom % vs Weight % W and C have significantly different atomic masses 60 at% ~ 9 wt% carbon 87

87 More reading Introduction to phase equilibria in ceramics (Bergeron) Where to find phase diagrams ASM Alloy Phase Diagram Database (Metals) /journal_content/56/10192/ /data BASE ACerS-NIST Phase Equilibria diagrams (Oxides) Also in book form 88

88 Key concepts Equilibrium phases as a function of state variables Lever rule Invariant reactions (e.g. eutectic and peritectic) Equilibrium vs non-equilibrium processes 89