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Order-Disorder Transformations

Order-Disorder Transformations. THE ENTITY IN QUESTION. GEOMETRICAL. PHYSICAL. E.g. Atoms, Cluster of Atoms Ions, etc. E.g. Electronic Spin, Nuclear spin. ORDER. POSITIONAL. ORIENTATIONAL. Order-disorder of: POSITION, ORIENTATION, ELECTRONIC & NUCLEAR SPIN. ORDER. TRUE. PROBABILISTIC.

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Order-Disorder Transformations

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  1. Order-Disorder Transformations

  2. THE ENTITY IN QUESTION GEOMETRICAL PHYSICAL E.g. Atoms, Cluster of AtomsIons, etc. E.g. Electronic Spin, Nuclear spin ORDER POSITIONAL ORIENTATIONAL Order-disorder of: POSITION, ORIENTATION, ELECTRONIC & NUCLEAR SPIN ORDER TRUE PROBABILISTIC

  3. Perfect Average Average ORIENTATIONAL Perfect POSITIONAL B A Positionally ordered PROBABILISTIC OCCUPATION Probability of occupation: A  50%B  50% Probabilistically ordered

  4. ORIENTATIONAL ORDER Diagrams not to scale Two Possible orientations of NH4+ in NH4Cl

  5. Order of order-disorder transformations • Usually 2nd or higher order (including -type) • Many of them display 1st order characteristics • Examples of 1st order (order disorder transformations): (typically based on BCC lattice)CuAu, Cu3Au, CoPt, MgCd3, Mg3Cd • Examples of 2st order (order disorder transformations): (typically involve a close packed structure)Beta Brass, FeCo, Fe3Al, Fe3Si • Rotational transformations have some characteristics of displacive transformations

  6. Positional Order-disorder Orientational Electronic or Nuclear Spin states • Metal-Insulator transitions may also be included in this class

  7. Electronic or Nuclear Spin states Ordered state Disordered state Ferromagnetic Anti-ferromagnetic Paramagnetic Ferrimagnetic • A state between a paramagnet and a ferromagnet exists in SPIN GLASSES:Random solid solution of moment bearing atoms in a non-magnetic host, which when cooled to low temperatures has frozen solute moments in local molecular fields, these fields have distribution of magnitudes and directions, such that the net magnetization of any region having few tens of solute atoms is zero (Au-Fe, Cu-Mn, Mo-Fe..) • Spin glass → paramagnetic/ferromagnetic state  second order

  8. Order-disorder transitions in dipoles Ordered state Electric dipoles Disordered state Ferroelectric Anti-ferroelectric Paraelectric Ferrielectric

  9. A A B B Variations to the isomorphous phase diagram • AB bonds stronger than AA and BB bonds • Solid stabilized → Ordered solid formation • AA and BB bonds stronger than AB bonds • Liquid stabilized → Phase separation in the solid state L +  L L L +   E.g. Au-Ni  ’ 1 2  + ’ 1 + 2 Ordered solid 1 & 2 are different only in lattice parameter

  10. Solid solutions which have a negative enthalpy of mixing (Hmix < 0) prefer unlike nearest neighbours → show tendency for ordering ↑ T  Disordered ↓ T  Ordered • rA→ probability that A sublattice is occupied with the right atom • XA → mole fraction of A in the alloy • L → Long Range Order

  11. Second Order ~ First Order

  12. Cu3Au CuAu

  13. Examples of common ordered structures (superlattices) DO3: Fe3Al L10: CuAu (I) L12: Cu3Au Some of these structures are considered in detail next

  14. CuAu (I) Cu Au Cu Au

  15. CuAu (II) Cu Au Cu Au

  16. Cu3Au Cu Au Cu Au

  17. Fe3Al Fe Fe2 (¼,¼,¼) Al Fe1 (½,½,0) Fe1 (0,0,0)

  18. Fe3Al More views Fe Al [100]

  19. Fe3Al Fe3Al More views Fe1 and Fe2 have different environments Fe2 (¼,¼,¼) Fe1 (½,½,0) Fe1 (0,0,0) Fe1 (0,0,0) Cube of Fe Tetrahedron of Fe Tetrahedron of Al Fe2 (¼,¼,¼) Fe1 (½,½,0)

  20. Occurring homogenously throughout the crystal Continuous increase in SRO Nucleation and Growth Due to an energy barrier to the formation of ordered domains

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