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1. Diagrama de fases e curvas de energia livre vs composição

1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

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Page 1: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

1. Diagrama de fases e curvas de energia livre vs composição

Page 2: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

1. Diagrama de fases binário: miscibilidade completa

Page 3: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

1. Diagrama de fases binário: miscibilidade completa

Page 4: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

Prerequisites for complete miscibility: 1. Same crystal structure2. rA ≈ rB, r : atomic radius

Not sufficient !

1. Diagrama de fases binário: miscibilidade completa

Page 5: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

2. Diagrama de fases binário: com hiato de miscibilidade

Page 6: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

2. Diagrama de fases binário: com hiato de miscibilidade

The liquid phase is approximately ideal, but for the solid phase AHmix > 0.(the A and B atoms 'dislike' each other).

Therefore at low temperatures (T3) the free energy curve for the solid assumes a negative curvature in the middle and the solid solution is most stable as a mixture of two phases α’ and α’’.At higher temperatures, when -TΔSmix becomes larger, e and f approach each other and eventually disappear.

The α’ and α’’ region is known as a miscibility gap.

Page 7: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

3. Diagrama de fases binário: ligas ordenadas

Page 8: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

4. Diagrama de fases binário: sistemas eutético simples

Page 9: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

4. Diagrama de fases binário: sistemas eutético simples

A similar eutectic phase diagram can result when A and B have different crystal structures

Page 10: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

diagrama de fases correspondente ao diagrama ΔGm versus composição

indicado

Quanto mais negativo for o valor da energia livre de formação da fase

intermediária, mais restritas serão as soluções sólidas terminais α e γ;

ou seja, a fase intermetálica se

forma “às custas” das soluções

sólidas terminais

5. Diagrama de fases binário: contendo fases intermediárias

Page 11: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

atividade dos componentes A e B versus composição

5. Diagrama de fases binário: contendo fases intermediárias

Page 12: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

When stable intermediate phases can form, extra free energy curves appear inthe phase diagram. An example is shown in Fig. 1.34, which also illustrateshow a peritectic transformation is related to the free energy curves

5. Diagrama de fases binário: contendo fases intermediárias

Page 13: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

5. Diagrama de fases binário: contendo fases intermediárias

Page 14: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

5. Diagrama de fases binário: contendo fases intermediárias

Page 15: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

6. Diagrama de fases binário: regra das fases de Gibbs

Page 16: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

6. Diagrama de fases binário: regra das fases de Gibbs

Page 17: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários

Page 18: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários

Page 19: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários

Page 20: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários

Page 21: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários

Page 22: 1. Diagrama de fases e curvas de energia livre vs …§ão/2. Diagramas de Fases.pdf · The liquid phase is approximately ideal, but for the solid phase AH mix > 0. (the A and B atoms

7. Diagrama de fases: sistemas ternários