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