Order-Disorder Transformations

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

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

ORIENTATIONAL ORDER Two Possible orientations of NH 4 + in NH 4 Cl Diagrams not to scale

 Usually 2 nd or higher order (including -type)  Many of them display 1 st order characteristics  Examples of 1 st order (order disorder transformations): ( typically based on BCC lattice) CuAu, Cu 3 Au, CoPt, MgCd 3, Mg 3 Cd  Examples of 2 st order (order disorder transformations): ( typically involve a close packed structure) Beta Brass, FeCo, Fe 3 Al, Fe 3 Si  Rotational transformations have some characteristics of displacive transformations Order of order-disorder transformations

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

Electronic or Nuclear Spin states Paramagnetic Anti-ferromagnetic Ferrimagnetic Ferromagnetic Disordered state Ordered state  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

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

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

 Solid solutions which have a negative enthalpy of mixing (  H mix < 0) prefer unlike nearest neighbours → show tendency for ordering ↓ T  Ordered ↑ T  Disordered  r A → probability that A sublattice is occupied with the right atom  X A → mole fraction of A in the alloy  L → Long Range Order

Second Order ~ First Order

Cu 3 Au CuAu

Examples of common ordered structures (superlattices) L1 2 : Cu 3 AuL1 0 : CuAu (I) StructureExamples L2 0 CuZn, FeCo, NiAl, FeAl, AgMg L1 2 Cu 3 Au, Au 3 Cu, Ni 3 Mn, Ni 3 Fe, Ni 3 Al, Pt 3 Fe L1 0 CuAu, CoPt, FePt DO 3 Fe 3 Al, Fe 3 Si, Fe 3 Be, Cu 3 Al DO 19 Mg 3 Cd, Cd 3 Mg, Ti 3 Al, Ni 3 Sn Some of these structures are considered in detail next DO 3 : Fe 3 Al

CuAu Lattice parameter(s)a = 3.96Å, c = 3.67Å Space GroupP4/mmm (123) Strukturbericht notationL1 0 Pearson symboltP4 Other examples with this structureTiAl CuAu (I) Cu Au Cu Au Wyckoff position xyz Au11a000 Au21c0.5 0 Cu2e00.5

CuAu (II) Lattice parameter(s)a = 3.676Å, b = 3.956Å, c = 3.972Å Space GroupImma (74) Strukturbericht notationL1 0 Pearson symboloI40 Other examples with this structure CuAu (II) Cu Au Cu Au Wyckoff position Site Symmetry xyz Occupancy Au14emm Au24emm Au34emm Au44emm Au54emm Cu14emm Cu24emm Cu34emm Cu44emm Cu54emm

Cu 3 Au Lattice parameter(s)a = 3.75 Å Space GroupPm-3m (221) Strukturbericht notationL1 2 Pearson symbolcP4 Other examples with this structureNi 3 Al, TiPt 3 Cu 3 Au Cu Au Cu Au

Fe 3 Al Lattice parameter(s)a = Å Space GroupFm-3m (225) Strukturbericht notationDO 3 Pearson symbolcF16 Other examples with this structureFe 3 Bi Fe 3 Al Al Fe Fe2 (¼,¼,¼) Fe1 (½,½,0) Fe1 (0,0,0) Wyckoff position Fe14a000 Fe28c0.25 Al4b0.500

More views [100] Al Fe Fe 3 Al

More views Fe 3 Al Fe2 (¼,¼,¼) Fe1 (½,½,0) Fe1 and Fe2 have different environments Tetrahedron of Fe Tetrahedron of Al Fe2 (¼,¼,¼) Fe1 (0,0,0) Fe1 (½,½,0) Cube of Fe

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