Order-Disorder TransformationsOrder-Disorder Transformations

THE ENTITY IN QUESTION

GEOMETRICAL PHYSICAL

E.g. Atoms, Cluster of AtomsIons, 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 NH4+ in NH4Cl

Diagrams not to scale

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

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

ParamagneticAnti-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

ParaelectricAnti-ferroelectric

Ferrielectric

Ferroelectric Disordered state

Ordered state

Order-disorder transitions in dipoles

Electric dipoles

electronic vibrational rotational configurationalS S S S S

A B

L

L +

1 2

1 + 2

AA and BB bonds stronger than AB bonds

Liquid stabilized → Phase separation in the solid state

Variations to the isomorphous phase diagram

AB bonds stronger than AA and BB 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 (Hmix < 0) prefer unlike nearest neighbours → show tendency for ordering

G H T S

↓ T Ordered

↑ T Disordered

1A A

A

r XL

X

rA → probability that A sublattice is occupied with the right atom

XA → mole fraction of A in the alloy

L → Long Range Order

TC

Long Range Order

1

0

Short Range Order

CuZn Type

T

Second Order

~ First Order

Cu3Au

CuAu

Examples of common ordered structures (superlattices)

L12: Cu3AuL10: CuAu (I)

Structure Examples

L20 CuZn, FeCo, NiAl, FeAl, AgMg

L12 Cu3Au, Au3Cu, Ni3Mn, Ni3Fe, Ni3Al, Pt3Fe

L10 CuAu, CoPt, FePt

DO3 Fe3Al, Fe3Si, Fe3Be, Cu3Al

DO19 Mg3Cd, Cd3Mg, Ti3Al, Ni3SnSome of these structures are considered in detail next

DO3: Fe3Al

CuAuLattice parameter(s) a = 3.96Å, c = 3.67Å

Space Group P4/mmm (123)

Strukturbericht notation L10

Pearson symbol tP4

Other examples with this structure TiAl

CuAu (I)

Cu

Au

Cu

Au

Wyckoff position

x y z

Au1 1a 0 0 0

Au2 1c 0.5 0.5 0

Cu 2e 0 0.5 0.5

CuAu (II)Lattice parameter(s) a = 3.676Å, b = 3.956Å, c = 3.972Å

Space Group Imma (74)

Strukturbericht notation L10

Pearson symbol oI40

Other examples with this structure

CuAu (II)

Cu

Au

Cu

Au

Wyckoff position

SiteSymmetry

x y z Occupancy

Au1 4e mm2 0 0.25 0.0249 1

Au2 4e mm2 0 0.25 0.9252 1

Au3 4e mm2 0 0.25 0.1248 1

Au4 4e mm2 0 0.25 0.8258 1

Au5 4e mm2 0 0.25 0.2238 1

Cu1 4e mm2 0 0.25 0.5258 1

Cu2 4e mm2 0 0.25 0.4243 1

Cu3 4e mm2 0 0.25 0.6258 1

Cu4 4e mm2 0 0.25 0.3230 1

Cu5 4e mm2 0 0.25 0.7269 1

Cu3AuLattice parameter(s) a = 3.75 Å

Space Group Pm-3m (221)

Strukturbericht notation L12

Pearson symbol cP4

Other examples with this structure Ni3Al, TiPt3

Cu3Au

CuAu

Cu

Au

Fe3AlLattice parameter(s) a = 5.792 Å

Space Group Fm-3m (225)

Strukturbericht notation DO3

Pearson symbol cF16

Other examples with this structure Fe3Bi

Fe3Al

Al

Fe

Fe2 (¼,¼,¼)

Fe1 (½,½,0)Fe1 (0,0,0)

Wyckoff position

Fe1 4a 0 0 0

Fe2 8c 0.25 0.25 0.25

Al 4b 0.5 0 0

More views

[100]

Al

Fe

Fe3Al

Fe3AlMore views Fe3Al

Fe2 (¼,¼,¼)

Fe1 (½,½,0)

Fe1 and Fe2 have different environments

Tetrahedron of FeTetrahedron of Al

Fe2 (¼,¼,¼)

Fe1 (0,0,0)

Fe1 (0,0,0)

Fe1 (½,½,0)

Cube of Fe

MechanismNucleation and Growth

Continuous increase in SRO

Occurring homogenously throughout the crystal

Due to an energy barrier to the formation of ordered domains